I think nonconscious, unconscious, and subconscious all mean the same thing: mental processes that people are not consciously aware of.
According to Freud's Topology of Mind, there are three levels of mind: The Conscious Mind (reality), The Preconscious Mind (Morality, our beliefs, values, and ideals), and The Subconscious Mind (Pleasure, what people want: food, sex, possessions, power, etc.). The preconscious can be brought to the consious mind easily, but the subconscious cannot. We are completely unaware of the subconsious.
For instance, habits are completely subconsious automatic processes that are guided by beliefs, expectations, and rewards put in place by our society. Nonconscious, unconscious, or subconscious would be correct to use — but personally, I think subconscious is best because it suggests we are still affected at this level of mind, where unconscious or nonconscious suggest we cannot be influenced by our surroundings.