suggest v.

mid-14c., "a prompting to evil," from Anglo-French and Old French suggestioun "hint, temptation," from Latin suggestionem (nominative suggestio) "an addition, intimation, suggestion," noun of action from suggestus, past participle of suggerere "bring up, bring under, lay beneath; furnish, afford, supply; prompt," from sub "under; up from below" (see sub-) + gerere "bring, carry" (see gest). Sense evolution in Latin is from "heap up, build" to "bring forward an idea." Meaning "proposal, statement, declaration" appeared by late 14c., but original English notion of "evil prompting" remains in suggestive. Hypnotism sense is from 1887.

word-forming element meaning "under, beneath; behind; from under; resulting from further division," from Latin preposition sub "under, below, beneath, at the foot of," also "close to, up to, towards;" of time, "within, during;" figuratively "subject to, in the power of;" also "a little, somewhat" (as in sub-horridus "somewhat rough"), from PIE *(s)up- (perhaps representing *ex-upo-), a variant form of the root *upo "under," also "up from under." The Latin word also was used as a prefix and in various combinations.

In Latin assimilated to following -c-, -f-, -g-, -p-, and often -r- and -m-. In Old French the prefix appears in the full Latin form only "in learned adoptions of old Latin compounds" [OED], and in popular use it was represented by sous-, sou-; as in French souvenir from Latin subvenire, souscrire (Old French souzescrire) from subscribere, etc.

The original meaning is now obscured in many words from Latin (suggest, suspect, subject, etc.). The prefix is active in Modern English, sometimes meaning "subordinate" (as in subcontractor); "inferior" (17c., as in subhuman); "smaller" (18c.); "a part or division of" (c. 1800, as in subcontinent).