In my opinion, the best way to think of properties (attributes, characteristics, traits) is to think of them as abstract objects. On this way of thinking of them, anything at all that possesses a property possesses (or, maybe better, instantiates) an abstract object. You possess the property of being human: you instantiate the abstract object humanity. But abstract objects themselves can also possess properties -- most obviously, the property of abstractness. On this view, society (construed as an abstract object) can be (say) immoral provided it makes sense to describe an entire society that way: any obstacle to a society's counting as immoral wouldn't stem from the abstractness of society or the abstractness of immorality.
Much more to be found here.