In Microsoft Office 365 dedicated, you have Full Control or Design permissions to a Microsoft SharePoint site. However, you cannot change the site theme of a subsite. Additionally, you receive one of the following error messages:
You need access to http://<SiteName> before you can change the look of this site.
This issue occurs because the subsite does not inherit permissions from the root site collection on which it resides.
Verify whether the subsite in question does not inherit permissions. Only site collection administrators can change the site theme regardless of the permission model that is used on the subsites when they don't inherit permissions. If you have the Full Control permissions on the root, but the subsites do not inherit permissions, you will not have access to change the subsite theme.