There was also an I. B. (or J. B.?):
http://www.sos.mo.gov/TIF2PDFConsumer/DispPDF.aspx?fTiff=/archives/AdjutantGeneral/Civil_War/ServiceCards/s889/1300.tif&Fln=S73561.pdf
They would not have been authorized pensions as they only served 57 days, and 90 days were required.
The unit may also not have been federally recognized.