To set the Managed By on a Group, and allow them to add and remove members to the group:
Right-click on the group and select Properties.
Select the Managed By tab.
Click the Change button.
In the Select User, Contact, or Group window that appears, enter the group (or less preferable the user) that you want to be able to add and remove members to the selected group.
Click Check Names to verify the group or user that you entered.
If multiple names are found, select the one you want and click OK.
If no names are found, you may have not entered the group or user name correctly.
Click OK.Check the box labelled Manager can update membership list.
The members of Managed By can add and remove members to the group using the following methods:
Active Directory Users and Computers console
PowerShell