# Subring of a commutative Noetherian ring

We know that it's possible subring of a commutative Noetherian ring is not Noetherian (for example: Subring of a finitely generated Noetherian ring need not be Noetherian?).

But if $S$ be a subring of commutative Noetherian ring $R$, and $R$ is finitely generated as a $S$-module, is it true that we conclude $S$ is a Noetherian ring?