Let $F=\mathrm{GF}\left(p^k\right)$ be any finite field. Let $G$ be the group of all affine permutations on $F$ (i.e. permutations of form $x\mapsto ax+b$). Then the set of all functions from $F$ to $\bar{F}$ is a linear representation of $G$, where $g(f)(x)=f(gx)$.

What are all sub-representations of this representation? Is it possible to characterize them?

Note: that in this case $\mathrm{gcd}\left(\left|G\right|,F\right)$ not equal to $1$.