Armies HQ are formed around a general. The better he is, the more powerful the bonuses given to attached corps will be.
Corps are attached to specific armies (Army of Northern Virginia, army of the Ohio, etc.). Each one is commanded by a corp commander, and receives bonuses from the parent Army.
Divisions and brigades are the fighting bricks of the corps.
Regiments, artillery batteries and cavalry squadrons are the smallest element of AACW. They are integrated into divisions and brigades, and can't be detached from them. You can still manipulate them indirectly by forming or splitting divisions into brigades.
Samples of the Union Corps available:
