You can install this hanger on metallic surfaces (like locker doors, fridges, racks, etc.) by using a couple of 7x3mm neodymium magnets (such as https://www.amazon.de/-/en/10-Mini-Neodymium-Magnets-Ultra-Strong-Original/dp/B01JCRGOX8/ )

The magnets should fit very snugly (you may have to remove a bit of material out of the holes) and can be glued with superglue for extra support. 

No supports are needed (just print it with the holes facing down). If you scale it up (or down), just be aware the holes will change as well (so magnets will not fit perfectly, or at all).