  Let $G_2(q)$ be the Chevalley group of type $G_2$ defined over a finite field
with q=p^n elements, where p is a prime number and $n$ is a positive integer.
In this paper, we determine when the restriction of an absolutely irreducible
representation of $G$ in characteristic other than p to a maximal subgroup of
$G_2(q)$ is still irreducible. Similar results are obtained for $^2B_2(q)$ and
$^2G_2(q)$.
