Template:CreateCat
You can create a new category with this button. Leave the word Category: in place and add the name of your new category after it.
<inputbox> type=create default=Category: buttonlabel=Create Category </inputbox>
You will still need to enter [[Template:CreateCat]] in your new category to have it show up in this list. If you wish to include this template, then add the line {{CreateCat}} also.
In the Subcategories list, clicking on a [caret] will expand the category to show subcategories if any exist.