I think CTRL+[group key] is meant to be the key combination but rebinding the key combination in-game doesn't work at all. It used to work fine. You sometimes had to unbind what was on that key, but not even that works (not even 'unbind [key]' in console).

My key combination is CTRL+F1 for hero, CTRL+F2... for the rest of the groups.

Usually I have F1-F2 set to 'missing top/mid/bottom' etc. I used to be able to just go into options and bind control groups to replace those binds.

Suffered the indignity of randoming Visage and not being able to bind control groups. Not that fun.