Updating iMac 2011 operating system MacOS HIgh Sierra version 10.13.6

10.13 High Sierra is the highest macOS version that a Mid 2011 27" iMac can run.

see > Identify your iMac model - Apple Support

iMac (27-inch, Mid 2011)

Model Identifier: iMac12,2

Part Number: MC813xx/A, MC814xx/A

Newest compatible operating system: macOS High Sierra

Tech Specs: iMac (27-inch, Mid 2011)

User Guide: iMac (27-inch, Mid 2011)

If you are on an earlier OS X or macOS version and need to get 10.13 High Sierra?

Open Safari and go to > How to download and install macOS - Apple Support

Are you having trouble updating to High Sierra, or from High Sierra to something else?

10.13.6 is as far as that machine can go.