Absolutely, Mozilla is another relevant example where the Mozilla Foundation is a non-profit that owns the Mozilla Corporation, which is for-profit. Furthermore many non-profits also buy shares of for-profit corporations, for example the Gates Foundation owns a large chunk of Microsoft.

You can imagine a non-profit buying enough shares of a for-profit company that it can appoint the for-profit company's board of directors, at which point it's a subsidiary.

Heck a non-profit is even allowed and encouraged to make a profit. There are certainly rules about what non-profits can and can't do, but the big rule is that a non-profit can't distribute its profits, ie. pay out a dividend. It must demonstrate that their expenditures support their tax exempt status, but the for-profit subsidiary is more than welcome to pay out dividends or engage in activities that serve private interests.