Is the subconscious mind a lesser side of God?
No. The subconscious mind is the memory repository for the conscious mind. Being automatic, it reproduces good and bad memories equally. Hence the subconscious mind must be trained through the conscious mind.
The subconscious mind is just like a psychological parrot. You can train it to utter the name of God or to swear. Just as a parrot, once taught to swear, will keep on swearing anytime, anywhere, so the subconscious mind, once accustomed to bad habits, begins to manifest those bad habits anytime, anywhere.
All care should be taken that only good thoughts and good habits percolate from the conscious mind into the subconscious mind.