I was recently asked to do SEO for a subdomain, which is something I have never worked on subdomains before, but common sense dictates it should be the same. Doing SEO for a normal domain is no different from doing it for a subdomain, right?
If the subdomain is published from a CMS+database on a root host (such as the WordPress multisite subdomains are), then some of the things you do to the root domain may affect the subdomain(s) as well.
That said, either way you cut it, the subdomain may appear in the sitelinks for the root domain and the root domain’s pages/folders may appear in the sitelinks for the subdomain. That’s normal and to be expected on a large site with a lot of subdomains. It may not happen if you only have 1 subdomain.
And though you can differentiate a subdomain from a root host by design and logically preventing them from linking to each other, sometimes the search engine is smart enough to see that similar content is published on both hosts and it treats them as kind of one big complicated site.
Whatever you do, do NOT use “rel=’nofollow'” on any links between the hosts. If you link from subdomain to root domain or from root domain to subdomain, link naturally.