  In 2012 the second author obtained a description of the lattice of
subgroupsof a Chevalley group $G(\Phi,A)$, containing the elementary subgroup
$E(\Phi,K)$ over a subring $K\subseteq A$ provided $\Phi=B_n,$ $C_n$ or $F_4$,
$n\ge2$, and $2$ is invertible in $K$. It turns out that this lattice splits
into a disjoint union of "sandwiches", parametrized by intermediate subrings
between $K$ and $A$.
  In the current article a similar result is proved for $\Phi=B_n$ or $C_n$,
$n\ge3$, and $2=0$ in $K$. In this settings one has to introduce more
sandwiches, namely, the sandwiches are parametrized by form rings $(R,\Lambda)$
such that $K\subseteq\Lambda\subseteq R\subseteq A$. In particular, this
result, generalizes a part of Ya.\,N.\,Nuzhin's theorem of 2013 concerning root
systems $\Phi=B_n,$ $C_n$, $n\ge3$, where the same description of the subgroup
lattice is obtained under the condition that $A$ is an algebraic extension
of~$K$.
