7.40 (1980)

If the root system has single edges ($A_l$, $D_l$, $E_l$) and the larger ring is not quasi-algebraic over the smaller one, then it is shown that the lattice in question contains the lattice of subgroups of a free product containing one of the factors (A. V. Stepanov, J. Algebra, 324, no. 7 (2010), 1549–1557), which means that a reasonable description is unfeasible. In almost all other cases a good description was obtained in (R. A. Schmidt, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova, 94 (1979), 119–130 (Russian); Ya. N. Nuzhin, Algebra Logic, 22 (1983), 378–389; Ya. N. Nuzhin, A. V. Yakushevich, Algebra Logic, 39 (2000), 199–206; A. Stepanov, J. Algebra, 362 (2012), 12–29; Ya. N. Nuzhin, Siberian Math. J., 54, no. 1 (2013), 119–123; A. Stepanov, A. Bak, St. Petersburg Math. J., 28, no. 4 (2017), 47–61).