I wrote a config to match common problems with mailman and nginx. If you had and old config and need to rewrite URLs like cgi-bin/mailman/ there is a solution too.

server {
    listen [::]:80 default;
    root /usr/lib/cgi-bin/mailman/;

    if ( $request_filename ~ mailman/.+ ) { 
        rewrite ^/mailman/(.*) /$1 permanent;
    }   

    if ( $request_filename ~ cgi-bin/mailman/.+ ) { 
        rewrite ^/cgi-bin/mailman/(.*) /$1 permanent;
    }   

    location = / { 
        rewrite ^ /listinfo permanent;
    }   

    location / { 
        fastcgi_split_path_info (^/[^/]*)(.*)$;
        fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
        fastcgi_param PATH_INFO $fastcgi_path_info;
        include /etc/nginx/fastcgi_params;
        fastcgi_pass  unix:/var/run/fcgiwrap.socket;
    }   

    location /images/mailman {
        alias /usr/share/images/mailman;
    }   

    location /pipermail {
        alias /var/lib/mailman/archives/public;
        autoindex on; 
    }   
}