You can create numerous administrator roles within your group settings. You can also name the roles; ie. Coach or Supporter.
The group admin will have all permissions available by default.
If an admin has permission to do something - ie. Create events - they will be able to do this in all sub groups within that group.
All admins will be able to see the members' contact information.
To add new admin roles, go to the group, press the three dots in the menu and Settings > Roles and permissions > Add administrator roles.
To edit all members permissions go into each of the member or admin roles and set the permissions
Here is an example from the desktop interface: