The article is part of a project aimed at describing the subgroup lattice of a Chevalley group over a ring. Namely, we consider the subgroups of a Chevalley group G(Φ,A), containing the elementary subgroup E(Φ,R) over a subring R of A. Conjecturally, if Φ is a simply laced root system, then the lattice is standard if and only if the ring extension R⊆A is quasi-algebraic. Roughly speaking, a ring extension R⊆A is quasi-algebraic if it cannot be reduced to the extension F⊆F[t], where F is a field and t is an independent variable, by taking subrings of A and quotients. To prove the conjecture we plan to use a localization method. The first step is to consider the case when R is semilocal. We show that in this case all finitely generated R-subalgebras of A are semilocal as well. In fact, the latter condition is even equivalent, thus, we obtain a new characterization of quasi-algebraic extensions.