wp-admin with subdomain

I have wordpress in a subdomain via a subdir (subdir.domain.com = https://www.domain.com/subdir). I have the correct urls in WordPress url and site url. When I try to go to wp-admin, I get the password box. When I give correct un and pw, the password box appears again.

The site url in the redirect-to param always gets the sub directory (i.e. subdir.domain.com/subdir/wp-admin…) so I think this is partly the problem. what can I do to make this work?