For the full linear group over a matrix-local ring whose quotient by the Jacobson radical is not the field of two elements, we settle the question of the conjugacy of $D$-net subgroups (Ref. Zh. Mat., 1977, 2A280). Two $D$-net subgroups are conjugate if and only if the $D$-nets defining them are similar (i.e., can be transformed into each other by a permutation matrix). An analogous result is obtained for $D$-net subgroups of the symplectic group over a commutative local ring whose residue field contains more than three elements.