On $p$-complements of finite groups

A subgroup $H$ of a finite group $G$ is called a $p$-complement for a prime $p$, if the order of $H$ is not divided by $p$ and the index $|G:H|$ is a power of $p$. We give examples of a finite group that possesses two nonisomorphic $p$-complements and of a finite group in which all $p$-complements are isomorphic but not conjugate in the automorphism group.