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

From Groupprops

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

## Facts used

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

## Proof

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