Catch 404 errors in nested installations

I have a site at the root of my /http/ folder (I’m using Apache).

In a subfolder, I have another WP site. When a 404 is encountered within the subsite, like this:

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www.mysite.com/subsite/thisDoesntExist/

the 404 page for www.mysite.com comes up – instead of the 404 for www.mysite.com/subsite/

Can I make the subsite catch these 404 errors?

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