Some verbs take infinitival complements:
We asked to study.
We wanted to study.
We wished to study.
Others take gerund-participial complements:
We suggested studying.
We enjoyed studying.
We avoided studying.
Others can take either:
We liked studying. / We liked to study.
"Suggest" takes a participial clause. (It can also take a "that" clause, or it can govern a direct object.) It cannot normally take an infinitival clause as its complement.
to mention an idea, possible plan, or action for other people to consider:
I suggested an Italian restaurant near the station for the party.
formal Might I suggest a white wine with your salmon, sir?
[ + (that) ] I suggest (that) we wait a while before we make any firm decisions.
Liz suggested (that) I try the shop on Mill Road.
[ + -ing verb ] I suggested putting the matter to the committee.
[ + question word ] Can you suggest where I could buy a dozen roses?
We can use the verb suggest with a noun phrase, a that-clause, the -ing form of a verb or a wh-question word (where, what).
[....] We don’t use suggest + to-infinitive