  This work is a continuation of Automorphisms of $K$-groups I, P. Flavell,
preprint.
  The main object of study is a finite $K$-group $G$ that admits an elementary
abelian group $A$ acting coprimely. For certain group theoretic properties
$\mathcal P$, we study the $AC_{G}(A)$-invariant $\mathcal P$-subgroups of $G$.
  A number of results of McBride, 'Near solvable signalizer functors on finite
groups' J. Algebra {\bf 78}(1) (1982) 181-214 and 'Nonsolvable signalizer
functors on finite groups', J. Algebra {\bf 78}(1) (1982) 215-238 are extended.
  One purpose of this work is to build a general theory of automorphisms, one
of whose applications will be a new proof of the Nonsolvable Signalizer Functor
Theorem.
  As an illustration, this work concludes with a new proof of a special case of
that theorem due to Gorenstein and Lyons.
