I have done my own custom permissions system. Everything else works properly except this.
They can't change the group icons for any members. The server admin group can.
I have had a look in the advanced permission with the filter on icon and the server admin and admin have exactly the same permissions but the admin can't do it.
When you try to change the group icon, it comes up with this: "insufficient permission modify power".
I'm not sure why but any help would be appreciated.

Here are some screenshots which may help you figure out why this isn't working:
Server Admin: http://gyazo.com/25fb3f11dfe9a41340f9e1f751ebca4a
Admin: http://gyazo.com/f6127b7e242062b086f2a4f6f492e4e5
Server Admin: http://gyazo.com/344ddcb66966e5cad90c809b7a02f14d
Admin: http://gyazo.com/bf08b1a112d10393a58c225b1486c357

Thanks, Conor.