Who has higher access privilege (local system, domain administrator, local administrator)

Hi, 

I am confused on the user level accesses with some of the types of Windows users. 

MyProblem is, I have windows service running with LogOn as "LocalSystem" which is "NT AUTHORITY\LocalService" and this service holds a mutex, if another service with domain-administrator tries to access the same mutex I get the ERROR_ACCESS_DENIED error.

My analysis is that "LocalSystem" would have more access privileges on the Operating system resources( in my case mutex), hence the domain-administrator will not be able to access it and hence i am seeing this error. 

I see the same issue with the between the "LocalSystem" and "local-administrator" also. 

Can somebody please let me know if my analysis is right? 

Thanks

Santosh