High sierra 10.13.6 no longer supported

The model year of an iMac is available at Apple menu > About This Mac.

A late 2009 through mid 2011 iMac can be upgraded to High Sierra 10.13.6 but no later version.

A late 2012 through late 2013 iMac can be upgraded to Catalina 10.15.7 but no later. See: How to download and install macOS - Apple Support

A mid 2014 and late 2014 iMac can be upgraded to the latest version of Big Sur macOS 11 but no later. See: How to download and install macOS - Apple Support

A late 2015 iMac can be upgraded to the latest version of Monterey macOS 12 but no later. See: How to download and install macOS - Apple Support

A 2017 iMac can be upgraded to the latest version of Ventura macOS 13 but no later. See: How to download and install macOS - Apple Support  

A 2019 or later iMac can be upgraded to the current version of Sonoma macOS 14. See:How to upgrade to macOS Sonoma - Apple Support

Sorry, you cannot upgrade it beyond macOS 10.13.6. A mid 2011 iMac can be upgraded to High Sierra 10.13.6 but no later version.

Also note iOS is the operating system for iPhones, macOS is for Macs.

Also see the following from 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

iMac (21.5-inch, Mid 2011)

Model Identifier: iMac12,1

Part Number: MC309xx/A, MC812xx/A

Newest compatible operating system: macOS High Sierra

You may want to install Firefox 115 ESR.

https://support.mozilla.org/en-US/kb/firefox-users-macos-1012-1013-1014-moving-to-extended-support

The High Sierra version of Firefox is not getting new features any more, but it is newer than the version of Safari in High Sierra. Mozilla says they will be providing "critical security updates" for Firefox 115 ESR through September 2024. So Firefox might be useful for browsing some Web sites that don't work quite right with High Sierra's Safari, or that are complaining that High Sierra's Safari is too old and insecure.