If you don’t pay really close attention to every step during the creation of a group in SharePoint, you’ll probably fall prey to one of the unintentional pitfalls that can happen.
By default, the person who creates the group becomes the group owner. If you leave it there and you stay working in your current position forever, that’s fine.
However, if you leave that job or position, then other people moved into your position might have a hard time administering that group. The best bet is to assign the owner to the Administrators group. That way, anyone in the Administrator group can administer the group you created at any time.
All Things DotNet Discussed – Winforms/ASP.Net/SharePoint/WPF