Thanks to both of you for your replies. I'm familiar with the book mentioned but neither it nor Kenneth Weant's research covers the Sixth Division First Battalion Company C. Perhaps it's a "lost company." My next thought is to go through all the pages of the register from Springfield in August 1861 and build lists by companies. It would be even greater if someone could build company lists from all the MSG hospital registers. There are probably many many "lost companies."
It's a bigger project than I have the time for now, but might be very valuable.