10.8 immer, 10.11 mit Einschränkungen

*This system fully supports the last version of OS X 10.8 "Mountain Lion" and OS X 10.9 "Mavericks" except for Power Nap and AirPlay Mirroring functionality (which also requires an Apple TV 2nd Gen or later). It also supports the last viersion of OS X 10.10 "Yosemite" and OS X 10.11 "El Capitan" -- including Mac-to-Mac AirDrop capability -- but no other advanced features are supported, including Metal graphics acceleration. It is not capable of running macOS Sierra (10.12) or subsequent versions of the macOS at all.
https://everymac.com/systems/apple/imac/specs/imac-core-2-duo-2.66-20-inch-aluminum-early-2009-specs.html