A for-profit company cannot technically have non-profit subsidiaries, but it can do so effectively by design of non-profit by-laws.
According to IAS 27, a subsidiary is an entity that is controlled by a parent. Control is defined accordingly:
- over more than one half of the voting rights by virtue of an agreement with other investors, or
- to govern the financial and operating policies of the entity under a statute or an agreement; or
- to appoint or remove the majority of the members of the board of directors; or
- to cast the majority of votes at a meeting of the board of directors.
Unlike a for-profit business, non-profits do not have any shareholders. They are not owned by anyone in particular, although governance responsibilities are vested in the board of directors, who are in turn accountable to state and federal authorities.
Technical control (ie. points 3 and 4) is exercised through share ownership. Majority shareholders naturally have the right to appoint/remove a majority of directors, and by definition cast the majority of votes at a meeting of the directors. Since non-profits do not have any shareholders, for-profits (or any other kind of organization) cannot exercise technical control over non-profits.
However, effective control (ie. points 1 and 2) can be exercised by for-profits over non-profits. For example, a for-profit could design its non-profit subsidiary's by-laws to ensure that a majority of board seats are appointed by the for-profit.
The best example of non-profits being effectively owned by for-profits are corporate foundations like the Walmart Foundation.