No. BMW is a self owned brand. Though BMW own Rolls Royce car division, and is the successor of the original Mini, it does defiantly not own VW.
Audi, Seat, Skoda, Bugatti, Lamborghini, and Bentley. It has more then 50% of the shares in Porsche, and is in partnership with Mercedes Benz.
Which is why the Volkswagen group is currently the 3rd largest car industry in the world.