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Let $G_2(q)$ be the Chevalley group of type $G_2$ defined over a finite fieldwith 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 irreduciblerepresentation 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$^2G_2(q)$.

Irreducible restrictions of Brauer characters of the Chevalley group G_2(q) to its proper subgroups