Full access permission required
How to Create a subsite in SharePoint Online
1. Go to your SharePoint online site
2. Click on Site Contents in the settings menu
3. At the Site Contents page, click +New and select Subsite.
4. Fill up the information based on your requirements.
Note: There are many templates to choose from under Templates Selection, if this is for document collaboration and sharing, you may use the default template - Team site.
Note: If you are planning to create new set of permissions to this subsite, select "User unique Permission". Otherwise, the default is Use same permission as parent site.
5. Click Create.