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

This article gives the statement, and possibly proof, of an embeddability theorem: a result that states that any group of a certain kind can be embedded in a group of a more restricted kind.
View a complete list of embeddability theorems

Statement

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

Facts used

1. Every finite group is a subgroup of a finite symmetric group
2. Symmetric group on a finite set is 2-generated

Proof

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