In the present paper, we study the subgroup lattice of a
Chevalley group G(Φ, R) over a commutative ring R, containing the
subgroup D(R), where D is a subfunctor of G(Φ, ). Assuming that
over any field F the normalizer of the group D(F) is “closed to be
maximal”, we formulate some technical conditions, which imply that
the lattice is standard. We also study the conditions concerning the
normalizer of D(R) in the case, where D(R) is the elementary subgroup of another Chevalley group G(Ψ, R) embedded into G(Φ, R)