Another solution would be to use https://github.com/jwilder/nginx-proxy.
This tool automatically forwards requests to the appropriate container (based on subdomain via the VIRTUAL_HOST container environment variable).
For instance, if you want to redirect box1.domain.com to a container, simply set the VIRTUAL_HOST container environment variable to “box1.domain.com“.
Here is a detailed tutorial I wrote about it: http://blog.florianlopes.io/host-multiple-websites-on-single-host-docker.