Symmetric Powers

Given a faithful finite-dimensional representation $V$ of a finite group $G$ over any field $\mathbb{F}$, we show that any irreducible $\mathbb{F}G$-module $W$ appears, as a submodule or a quotient, in ${\mathrm{S}\mathrm{y}\mathrm{m}}^m(V)$ for some integer $1\le m\le \mathrm{\mid }G\mathrm{\mid }$ (that may depend on $W$).