My guess would be that the "set" is only a container for a set of attributes, you cannot group this as it has no real transform data. The set is used for you to easily access and set keys to relevant attributes that animates your character. What you probably want to do instead is try to group the "master" nodes, ie. the…
If you choose the Animation menu set (not the shelf), there should be a menu labeled Constrain. Some of the constraints you can set are Aim (the object constrained will rotate about its pivot point to aim at the object it is constrained to), Point (the object constrained will move to follow the object it is constrained…