Subsemigroup of permutable semigroup!

Question

Let $S$ be a semigroup and $n$ integer greater than 1. A sequence $s_{1}, s_{2},...,s_{n}$ of $n$ elements of $S$ is called permutable if the product $s_{1}s_{2}...s_{n}$, remains invariant, under some nontrivial permutation of its factors, that is, there exists a permutation $\sigma\in S_{n}$ different from the identity, such that $s_{1}s_{2}...s_{n}=s_{\sigma(1)}s_{\sigma(2)}...s_{\sigma(n)}$. A semigroup that satisfies this property we call it a permutable semigroup. I am quite sure that every sub-semigroup of this semigroup is also permutable, but I am stuck in showing it?? Can someone help please??