It is currently not possible to use the "SearchField" field type in a group template to select an existing user or an existing group and to define this as the manager for this new group (attribute: managedby).
If the "TextField" field type is used, the "managedby" attribute is set successfully.
However, this requires manual maintenance of the available objects in the template, which is very cumbersome in larger environments.
The field type "SearchField" in the template would be much more suitable for this.