  In this paper we initiate the study of the maximal subalgebras of exceptional
simple classical Lie algebras \g over algebraically closed fields k of positive
characteristic p, such that the prime characteristic is good for \g. In this
paper we deal with what is surely the most unnatural case; that is, where the
maximal subalgebra in question is a simple subalgebra of non-classical type. We
show that only the first Witt algebra can occur as a subalgebra of \g and give
explicit details on when it may be maximal in \g.
