to quell means:
to stop something that you do not want to happen
to subdue means:
to start to control someone or something, especially by using force
source : cambridge dictionaries
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You don't quell a bank robber, you subdue a bank robber.
When applied to individuals, the word quell is often used with emotions: we quell our fears, we quell our urges, we quell our anger.
When applied to groups, we quell rebellions, insurrections, and revolts. Have a look.
Of course, the two words are roughly synonymous, so there is plenty of room for overlap. We can subdue our anger, for example.