Claim: It is.
Proof: Let us verify the four neccessary conditions to be a subgroup
1. Clearly will inherit 's associativity.
2. You should know that . Thus .
3. Now suppose that , then , so that which of course implies .
4. Suppose then and . Therefore . Therefore
This completes the proof.
Remark: I always find the direct satsifaction of the subgroup axioms to be more instructive. You may (and should) attempt to redo this using the condition that if .