You want to create in SharePoint a SearchCenter as a subsite of the main site collection, but when you Access to site contents and add subsite, you realice that is not even posible to select the template of Advanced Search Center and only is possible to select the Basic Search Center.
So what we can do?
To get the Enterprise search center template, you need to activate the site collection feature:
SharePoint Server Standard Site Collection features
Once that’s activated, then you can create an enterprise search center as a subsite.
Hope it helps!