# Finite-extensible implies subgroup-conjugating

Suppose $G$ is a finite group and $\sigma$ is a finite-extensible automorphism of $G$. In other words, for any finite group $H$ containing $G$, there is an automorphism $\sigma'$ of $H$ whose restriction to $G$ equals $\sigma$.
Then, $\sigma$ is a subgroup-conjugating automorphism of $G$: it sends every subgroup of $G$ to a conjugate subgroup.