  Let $G$ be a simple algebraic group of exceptional type over an algebraically
closed field of characteristic $p > 0$. This paper continues a long-standing
effort to classify the connected reductive subgroups of $G$. Having previously
completed the classification when $p$ is sufficiently large, we focus here on
the case that $p$ is bad for $G$. We classify the connected reductive subgroups
of $G$ which are not $G$-completely reducible, whose simple components have
rank at least $3$. For each such subgroup $X$, we determine the action of $X$
on the adjoint module $L(G)$ and on a minimal non-trivial $G$-module, and the
connected centraliser of $X$ in $G$. As corollaries we obtain information on:
subgroups which are maximal among connected reductive subgroups; products of
commuting $G$-completely reducible subgroups; subgroups with trivial connected
centraliser; and subgroups which act indecomposably on an adjoint or minimal
module for $G$.
