Organizations included
Cavalry: 13 regiments, 5 battalions, 10 companies
Heavy Artillery: 2 regiments
Light Artillery: 42 batteries
Infantry: 227 regiments, 1 battalion, 5 companies
Source: Dyer, Frederick, Compendium of the War of the Rebellion
13th Light Artillery Bty failed to organize & 23rd L A Bty was organized from a Kentucky regiment and eventually designated Simmonds Ky L A Battery
Based on numerical designation Ohio provided 197 infantry regiments. The 1st through 22nd were organized for three months then for three years and I suspect there was enough overlap in the regimental rosters that they should be counted once each.
The 44th Infantry became the 8th Cavalry and the 117th became the 1st Heavy Artillery Rgt.
The 109th, 112th, 119th, 158th and 190th Infantry failed to complete their organization.
All of this said I think the actual number of infantry regiments is 190