The technical complication with supergroups involves the fact that in going from a group to one of its supergroups, we meet restrictions on unit cell dimensions that we do not have to worry about in going to a subgroup. For example, whereas going from a cubic space group to a tetragonal subgroup, the condition in the cubic group that a = b = c is still compatible with the constraints for a tetragonal group (a = b). However, going the other way, from tetragonal to cubic, we have the problem that one of the unit cell dimensions may have to be adjusted. But these restrictions are only practical limitations of implementing the notation, not a limitation of the notation itself.