On maximal parabolic subgroups of GL(V)

My professor today has showed the follwing proposition:

If $V\cong K^n$ where $K$ is a finite field of characteristic $p$, then the maximal parabolic subgroups of $GL(V)$ are exactly the $p$-local maximal subgroups of $GL(V)$.

For me it is clear that every parabolic subgroup is contanied in a $p$-local subgroup, but I don't understand why every $p$-local subgroup is contained in a parabolic subgroup. Can someone help me?

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