need to upgrade macOS Sierra on a 2011 iMac

MacOS High Sierra 10.13.6 is as far as any 2011 iMac can go...

macOS High Sierra - Technical Specifications

General Requirements

• OS X 10.8 or later
• 2GB of memory
• 14.3GB of available storage to perform upgrade*
• Some features require an Apple ID; terms apply.
• Some features require a compatible Internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen, choose About This Mac. These Mac models are compatible with macOS High Sierra:

• MacBook (Late 2009 or newer)
• MacBook Pro (Mid 2010 or newer)
• MacBook Air (Late 2010 or newer)
• Mac mini (Mid 2010 or newer)
• iMac (Late 2009 or newer)
• Mac Pro (Mid 2010 or newer)
• Don't use FireFox for these links…

https://support.apple.com/kb/sp765?locale=en_US

https://itunes.apple.com/app/macos-high-sierra/id1246284741?mt=12