Let $G$ be a finite group of Lie type and $T$ a maximal torus of $G$. In this paper we complete the study of the question of the existence of a complement for the torus $T$ in its algebraic normalizer $N(G,T)$. It is proved that every maximal torus of the group $G\in\{ G_2(q), { }^2G_2(q), { }^3D_4(q)\}$ has a complement in its algebraic normalizer. The remaining twisted classical groups ${ }^2A_n(q)$ and ${ }^2D_n(q)$ are also considered.
Categories: math.GR