Site Owner with Full Control but am not able "Add User" to the Site Owners Group

I have full control as a site owner, but when I am trying to add user, I just get the "New Group" option, I don't have permission to add Users.
At the same time I am not a Site member(read,contribute), but I am getting the option of adding user to that group.
How can I enable myself to add users?

thanks,
Harsh