word-forming element usually meaning "with, together," from Latin com, archaic form of classical Latin cum "together, together with, in combination," from PIE *kom- "beside, near, by, with" (compare Old English ge-, German ge-). The prefix in Latin sometimes was used as an intensive.
Before vowels and aspirates, it is reduced to co-; before -g-, it is assimilated to cog- or con-; before -l-, assimilated to col-; before -r-, assimilated to cor-; before -c-, -d-, -j-, -n-, -q-, -s-, -t-, and -v-, it is assimilated to con-, which was so frequent that it often was used as the normal form.
also noncom, by 1817, short for non-commissioned(officer).
The "non-coms" — non-commissioned, meaning, not non compos; though evil-minded high privates declare it might well mean that — have assigned to them an upper cabin, with staterooms, over the quarters of the officers, in the after-part of the ship. [James K. Hosmer, "The Color-Guard," Boston, 1864]
before vowels coen-, word-forming element meaning "common," from Latinized form of Greek koinos "common, public, shared, general, ordinary," from PIE *kom "beside, near, by, with" (see com-).