Will Illustrator CS 11 run on Windows 11?

Best Advice, don't upgrade.  Keep your old computer as is for as long as you need to support legacy Creative Suite.  I think you have until mid-October before Win10 reaches End of Life.

Start budgeting for new software that's compatible with Win11.  

MODERN OPTIONS

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FREE Acrobat Reader -- view, comment, print & sign PDF.
https://www.adobe.com/acrobat/pdf-reader.html

Paid Acrobat Pro -- the complete solution for creating and saving PDF.
https://www.adobe.com/acrobat/acrobat-pro.html

PS or PR Elements 2025 (3 year license).
https://www.adobe.com/products/photoshop-elements.html

Creative Cloud Photography Plan (12 month plan).
https://www.adobe.com/creativecloud/photography.html

Creative Cloud Bundles & Single App Plans for mobile, web & desktops
https://www.adobe.com/creativecloud/plans.html

Hi @Bob72,

Welcome to the community!
Are you using any Creative Suite version of Adobe Illustrator? I checked your account details and found that you have purchased Adobe Premiere Elements, however there is no other subscription or perpetual product associated with your email address.

Could you check if your product is associated with a different email address. Also, please confirm the application version. I'll be able to provide you better help.

Looking forward to your response.

you can't activate illustrator v 11.  and that's not cs 11.

but you might be able to install using compatibility mode.