Every finite group is a subgroup of a finite 2-generated group

Statement
For any finite group $$G$$, there exists a finite group $$K$$ containing $$G$$ such that $$K$$ is a fact about::2-generated group, i.e., the minimum size of generating set of $$K$$ is at most two.

Facts used

 * 1) uses::Every finite group is a subgroup of a finite symmetric group
 * 2) uses::Symmetric group on a finite set is 2-generated

Proof
The proof follows by piecing together facts (1) and (2).