Your ISP and your DNS provider are able to see that you are connecting to subdomain.domain.com, but neither are able to see the entire URL that you are requesting.
The first thing that happens is that your DNS provider will see that you are requesting the IP address that subdomain.domain.com points to. So, if you are using your ISP's DNS service, your ISP will see that.
Next, your ISP will then see that you are connecting to the web server at the IP address that subdomain.domain.com points to.
Neither your ISP nor your DNS provider will see the entire URL that you are pointing your browser to. The entire URL is sent to the web server only after the SSL/TLS connection to subdomain.domain.com is established.
Note: Even if you use a DNS service other than your ISP's, your ISP is still likely to be able to determine the hostname (but not the entire URL) of the web server that you are connecting to. Many IP addresses used by web servers reverse to the same hostname that forwards to this IP, so your ISP could conceivably do a reverse DNS lookup (for the PTR record) of the IP address that it sees that you are connecting to, and this would reveal the hostname associated with this IP address (subdomain.domain.com). In cases where one web server is hosting many SSL web sites on the same IP, (which can be done if the web server is running SNI), your ISP could still be able to see the hostname that you are connecting to, because this is transmitted from your web browser to the server in clear text before the SSL/TLS handshake.