Can I set a filegroup of database offline,change the location of files and bring it online again?
There is no T-SQL command to take a filegroup offline, though an individual file can be set offline.

From the documentation, ALTER DATABASE File and Filegroup Options (Transact-SQL):




  Use this option only when the file is corrupted and can be restored. A file set to OFFLINE can only be set online by restoring the file from backup. For more information about restoring a single file, see RESTORE (Transact-SQL).


To relocate files, follow the instructions in the documentation, or see the related Q &amp; A:

How do I move SQL Server database files?