They can as far as I know. I have been tempted to as a practical joke, however I haven't tested it out.
power of group members

I would recommend only giving admin powers to someone you trust.
I don't know if there is any difference in Super-Admin powers and regular admin powers, other than title. I've always wondered this.

That's a really good point. Does this mean each group has an administrator and a super administrator? That doesn't make any sense, since you wouldn't want to start and moderate a group only to have someone come in and take over after you did all the work.

Whoever creates the group is automatically dubbed the "Super-Administrator." This individual may then award administrator abilities to anyone in the group for any reason. Some groups have no administrators other than the Super, and some have a dozen co-administrators.
At times, the Super chooses to step down and hand the reigns to someone else. However, when this happens, and someone clicks on "Contact Group Leader" the message will still be sent to the original Super. (This is a problem that I believe Chess.com is already working on).
My thinking is that there should always be only one Super, but currently there is nothing to stop one from designating everyone in the group a Super (which I've actually seen happen). Technically, any given administrator has the ability to change any given member between the 3 levels (member, admin, Super).
So technically a mutiny can take place in which an admin designates himself as Super, and demotes the original Super to a mere member so he cannot change it back. However, I have not seen this happen, and every co-administrator that I've worked with so far has been very respectful of their boundaries (this is after all the best online community on the internet).
As I said, I'm not aware of any power difference between Super and admin other than title. However, I would like to see it set up somehow that only one person can be designated as the Super. Only that person may change the level of other members/admins. If they choose to hand over Super duties to someone else, they would automatically be reduced to a co-admin in the process. Just a thought.

Well you can always complain to support and if the user totally ruins the group they might have to pay a fine.
I am wondering what power the normal admins of a group have. Can they create team/vote matches. Can super admins make other super admins into normal members. I am a creator of a big group, and am worried that if I make someone a super admin other than myself they will take over, and take away my power in the group decisions.