You seem to have posed a very deep question.
Concerning the hierarchy of military units, this may help: an army consists of two or more corps; a corps consists of two or more divisions; a division consists of two or more brigades; a brigade consists of two or more battalions; an infantry battalion consists of a number of companies; a company consists of two or more platoons and a platoon consists of two or more sections.
In the French army from 1806 - 1815 (and in all armies of the Confederation of the Rhine) a battalion had 1 grenadier, 1 voltigeur (or light) company and 4 fusilier (or centre) companies. Such an infantry regiment could have up to 5 battalions.
A French cavalry regiment usually had 4 squadrons, each of two companies.
The artillery equivalent of a company was a battery.
Divisions were either infantry or cavalry and included a battery of artillery.
A corps usually was infantry or cavalry, but both had a light cavalry brigade for reconnaissance purposes and a reserve (heavy) artillery component and an engineer component.
An army would have reserve cavalry, artillery, engineer, transport and other logistical components.
This is all very general, but gives you an idea of the scale of units and formations (a formation is anything larger than a battalion).