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Let $G$ be an exceptional simple algebraic group over an algebraically closedfield $k$ and suppose that the characteristic $p$ of $k$ is a good prime for$G$. In this paper we classify the maximal Lie subalgebras $\mathfrak{m}$ ofthe Lie algebra $\mathfrak{g}={\rm Lie}(G)$. Specifically, we show that one ofthe following holds: $\mathfrak{m}={\rm Lie}(M)$ for some maximal connectedsubgroup $M$ of $G$, or $\mathfrak{m}$ is a maximal Witt subalgebra of$\mathfrak{g}$, or $\mathfrak{m}$ is a maximal $\it{\mbox{exotic semidirectproduct}}$. The conjugacy classes of maximal connected subgroups of G are knownthanks to the work of Seitz, Testerman and Liebeck--Seitz. All maximal Wittsubalgebras of $\mathfrak{g}$ are $G$-conjugate and they occur when $G$ is notof type ${\rm E}_6$ and $p-1$ coincides with the Coxeter number of $G$. We showthat there are two conjugacy classes of maximal exotic semidirect products in$\mathfrak{g}$, one in characteristic $5$ and one in characteristic $7$, andboth occur when $G$ is a group of type ${\rm E}_7$.

Classification of the maximal subalgebras of exceptional Lie algebras over fields of good characteristic