Every finite group is a subgroup of a finite perfect group

Statement
For any finite group $$G$$, we can find a finite perfect group $$H$$ such that $$G$$ is a subgroup of $$H$$.

Facts used

 * 1) uses::Every finite group is a subgroup of a finite simple non-abelian group
 * 2) uses::Simple and non-abelian implies perfect

Proof
The proof follows directly by combining Facts (1) and (2).