  In this paper we prove a sandwich classification theorem for subgroups of the
classical symplectic group over an arbitrary commutative ring $R$ that contain
the elementary block-diagonal (or subsystem) subgroup $\operatorname{Ep}(\nu,
R)$ corresponding to a unitary equivalence realation $\nu$ such that all
self-conjugate equivalence classes of $\nu$ are of size at least 4 and all
not-self-conjugate classes of $\nu$ are of size at least 5. Namely, given a
subgroup $H$ of $\operatorname{Sp}(2n, R)$ such that $\operatorname{Ep}(\nu, R)
\le H$ we show that there exists a unique exact major form net of ideals
$(\sigma, \Gamma)$ over $R$ such that $\operatorname{Ep}(\sigma, \Gamma) \le H
\le N_{\operatorname{Sp}(2n,R)}(\operatorname{Sp}(\sigma, \Gamma))$. Further,
we describe the normalizer
$N_{\operatorname{Sp}(2n,R)}(\operatorname{Sp}(\sigma, \Gamma))$ in terms of
congruences.
