ARMY STRUCTURE
Unit.......................Unit Multiples...........# of soldiers
Company........................................................100
Regiment..............10 Companies..............1,000
Brigade..................4 Regiments.................4,000
Division..................3 Brigades.................... 12,000
Corps.....................3 Divisions.................... 36,000
Army.......................Any # of Corps................. ??
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Commanding Officer of:
Regiment..............Colonel, Lt. Colonel, or Major
Brigade..................Brigadier General
Division..................Brigadier General or Major General
Corps.....................Major General or Lt. General
Army...................... (Union) Major General

DEPARTMENTS:
??

ARMIES:
Armies were the largest of the "operational organizations." In the case of the Federal forces, these generally took their name from their department. "The Federals followed a general policy of naming their armies for the rivers near which they operated; the Confederates named theirs from the states or regions in which they were active. Thus, the Federals had an Army of the Tennessee -not to be confused with the Confederate Army of Tennessee." The Union armies took their names from the departments in which they operated (or were originally formed), and these departments took their names from rivers in the case of the Federals and from states or regions in the case of the Confederates.
List Of the Union Armies:
Army of the Cumberland
Army of the Frontier
Army of Georgia
Army of the Gulf
Army of the James
Army of Kansas
Army of the Mississippi (there were several)
Army of the Mountain Department
Army of the Ohio
Army of the Potomac
Army of the Shenandoah
Army of the Southwest
Army of the Tennessee
Army of Virginia
Army of West Tennessee
Army of West Virginia

CORPS:
The term corps comes from the French corps d'armee.  Although corps d'armee existed in the French army before Napoleon, he revamped them and popularized the phrase.   A typical Union corps was composed of 2 or more divisions and, except for Cavalry corps, included all arms of service.

Corps were established in the Union army in March 1862 by Maj. Gen. George B. McClellan.  A major general commanded each of the 43 corps that were established in the Union army before the end of the war.  Each corps was designated by a number, I to XXV.  Corps badges such as triangles, crescents, arrows, and acorns were adopted by most corps and worn by officers and enlisted men.  Of the Union corps 2 were noted for their failures:  the XI Corps, which took flight after a surprise attack by Lt. Gen. Thomas J. "Stonewall" Jackson's men at Chancellorsville and the IX Corps, which bungled the opportunity of the Crater at Petersburg.  More successful corps included the I and II/ Army of the Potomac, known for their bravery; the XXV, composed entirely of black troops and the XXII corps, which garrisoned the fortifications around Washington, D.C. during most of the war and guarded the Union capital.

Corps were organized in the Confederate army November, 1862 and were designated by numbers duplicated in the East and West but were often referred to by the name of their commander.  Thus, the II Corps in the East was called Jackson's Corps, even after he was killed.  This corps endured some of the hardest marching and heaviest fighting of the war.
DIVISIONS:
In field armies on both sides in the Civil War, the division was the second largest unit.  In ascending order of size, units were: company, regiment brigade, division, corps.   Theoretically, company strength was 100; regiment, 1,000; brigade, 4,000; and division, 12,000.  Occasionally, more often in the Confederate army battalions of 2 to 10 companies were accepted into the ranks.  In the Union army, the actual numbers, by the attrition of war, were only 40-50% of those figures by 1863; the percentage was higher in the Confederate army, thanks to its system of assigning recruits to existing regiments instead of creating new regiments.

In the Union armies the number of division in a corps varied from 2 to 4, though usually there were 3.  In spring 1863, Maj. Gen. Joseph "Fighting Joe" Hooker ordered the army of the Potomac to wear Corps Badges, which led to designating divisions by badges and by flags in red, white, and blue, for 1st, 2nd, and 3rd, divisions, respectively;  the few 4th divisions had green badges and flags; 5th divisions, orange.  Without uniform badges and flags, the Confederates used a less complicated system.  Though they began by numbering their divisions, in a short time divisions, as well as other army units, come to be known by their commanders' name.

Union division were commanded by brigadier or major generals, and the frontage of an average 1863 Union division, drawn up in double-rank line of battle with no skirmishers deployed, would have been just short of a mile.  The Confederates were more logical:  with rare exceptions, brigadiers commanded brigades and major generals led division, and these units were usually numerically superior to their Union counterparts. 
INFANTRY REGIMENT:
Infantry Regiment were composed of 10 companies, except in the case of the 12-company heavy artillery regiments that had been retrained as infantry. Cavalry regiments also had 12 companies. These companies were lettered in alphabetical order, with the letter "J" omitted. There has been much erroneous theorizing as to why the US Army has never had a J Company.   Battalions did not exist in the infantry regiments, but the "heavies" were composed of three four company battalions, each commanded by a major.

Confederate regiments were organized in generally the same manner as the Federal, although some had battalions.

In the Union Army an infantry company had a maximum authorized strength of 101 officers and men, and a minimum strength of 83. The company was allowed to recruit a minimum of 64 or a maximum of 82 privates. Other company positions were fixed as follows: 1 captain, one 1st lieutenant, one 2nd lieutenant, one 1st sergeant, 4 sergeants, 8 corporals, 2 musicians, and 1 wagoner. Company officers were elected in most volunteer units.

As Schiebert, the Prussian observer, points out, this was the only possible way of getting rapidly the large number of troop leaders needed. By the second year of the war a system of examinations was instituted by both armies, and incompetent officers could be eliminated.

Regimental headquarters consisted of a colonel, lieutenant colonel, major, adjutant, quartermaster, surgeon (major), 2 assistant surgeons, and a chaplain. Regimental headquarters noncommissioned officers were the sergeant major, quartermaster sergeant, commissary sergeant, hospital steward, and 2 principal musicians. Authorized strength of an infantry regiment was a maximum of 1,025 and a minimum of 845. Since it was the Civil War practice to organize recruits into new regiments rather than to send them to replace losses in veteran units, regimental strengths steadily declined. .

The North raised the equivalent of 2,047 regiments during the war of which 1,696 were infantry, 272 were cavalry, and 78 were artillery. Allowing for the fact that nine infantry regiments of the Regular Army had 24 instead of the normal 10 companies, the total number of regiments would come to about 2,050, not including the Veteran Reserve Corps. The South raised the equivalent of 764 regiments that served all or most of the war. Using later data, and including militia and other irregular organizations, Col. Henry Stone estimated an equivalent of 1,009 ½ Confederate regiments.

TYPICAL REGIMENT:
Field and Staff..........................Company
1 Colonel.............................1 Captain
1 Lt. Colonel........................1 1st Lt
1 Major..................................1 2nd Lt.
1 Adjutant.............................1 First Sergeant
1 Quartermaster.................4 Sergeants
1 Surgeon............................8 Corporals
2 Asst. Surgeons................2 Musicians
1 Chaplain............................1 Wagoneer
1 Sergeant Major.................82 Privates
1 Quartermaster Sergeant
1 Commisary Sergeant
1 Hospital Steward
2 Principal Musicians

10 Companies........845 to 1,010 Officers and men
Field and Staff.........15 Officers and Noncommisioned Officers

Heavy Artillery Regiment (U.S.)...12 Companies- 1,800 officers and men

Number of men in the war.......2.5 to 2.7 million
Percentage of poulation..........9.1%

On the eve of the Civil War, the Regular Army had a total enlisted strength of 16,000 men. After the loss at Fort Sumter, President Lincoln called for the recruitment of an additional 22,700 Regular Army troops. At no time during the war did the Regular Army reach its modest goal of 42,000 troops.