Let $H$ be a normal subgroup of a finite group $G$ and $k$ is a field of characteristic $p$. If $p\nmid|G:H|$ then the induced module $U\uparrow_H^G$ over $k$ of any semisimple $k[H]$-module $U$ is also a semisimple $k[G]$-module. (This can be shown in the way similar to prove Maschke's Theorem.)
I want to find a counterexample when $p||G:H|$.