You can't form a wholly "owned" subsidiary because no one "owns" a nonprofit organization. But you can form a wholly controlled subsidiary that can most likely apply for and obtain recognition of charitable exempt status under Section 501(c)(3) if it will be operated exclusively for charitable purposes. It is not unusual for an organization that is not a charity to control a charity. You will need to be careful to assure that the charity acts as a charity and about transferring funds between the organizations. Charitable money should not be used for trade association purposes.