I have seen in Which groups are considered critical in the default "Critical Group Membership changes" search (71703) (quest.com) that groups considered critical are:
Server Operators
Print Operators
Network Configuration Operators
Incoming Forest Trust Builders
Backup Operators
Administrators
Account Operators
Cert Publishers
DHCP Administrators
Domain Admins
Domain Controllers
Enterprise Admins
Group Policy Creator Owners
RAS and IAS Servers
Schema Admins
can I add my own groups so I am alerted when there are changes?