We consider a system of differential equations admitting a group of transformations. The Lie algebra of the group generates a hierarchy of submodels. This hierarchy can be chosen so that the solution to each of submodels are solutions to some other submodel in the same hierarchy. For this we must calculate an optimal system of subalgebras and construct a graph of embedded subalgebras and then calculate the differential invariants for each subalgebra. The invariants of a superalgebra are functions of the invariants of the subalgebra. The invariant differentiation operators of a superalgebra are linear combinations of invariant differentiation operators of a subalgebra. The comparison of the representations of group solutions gives a relation between the solutions to the models of the superalgebra and the subalgebra. Some examples are given of embedded submodels for the equations of gas dynamics.