Yes, what you're trying to do is possible in apache (apart from the given data, I'm assuming that the server got a static IP and no other https domains are served via this IP). I'll just brief what you need to do to configure the subdomain with both http and https. There might be many step by step tutorials available on this so feel free to google and find one if you need more detailed information :P
1) Purchase an SSL certificate for the specific domain.
2) Make sure your apache server is compiled with mod_ssl, if not install and enable mod_ssl
3) Copy the certificate and private key to the specific locations (check the virtualhost configuration given below)
4) Create a virtual host entry for your subdomain (this will serve the domain via http)
5) Create one more virtual host entry like this
SSLProtocol all -SSLv2
CustomLog logs/sub.yourdomain.com-ssl_access_log common
6) Check the syntax of the config files and restart the server. Your sub-domain should be accessible at both http and https.
Hope this will help you to get started