You can search for administrators in child groups by email in the search section at the bottom of the "Network" tab on group manage page of any group in the network.
Enter an email address to search child groups. Each group where this person is an administrator will be listed in the search results, with manage buttons allowing you to jump to that group.
You can also download a CSV list of administrators in child groups in your network in that tab.
The administrators report will contain a list of all administrators and organizers for that group and its children, including the administrator's first and last name, email address, and list of groups they are an administrator or organizer on.