Put a cat and dog in the same household. The cat often becomes the dominant pack member.
Size doesn’t seem to matter.
Photos
More sleeping cats. No pesky dogs.
A cat rules my household. Just ask me. 
They look comfortable.
Jim Davis certainly captured the relationship between cats and dogs in the Garfield strip. Odie loses every time.
I had two queens once who ended up sleeping on either side of my dog. Once the two saw each other they started fighting … and here’s the poor dog waking up to a cat fight on his belly …
I have over-sized pillows for my bed now so it’s safer for me to sleep these days …
Nothing surprising about this.
Dogs are pack animals: they are evolved to live in groups with a pack leader.
Cats are solitary hunters, while they may live in colonies, those don’t have a leader.
So the dog is genetically wired to be part of a 2-animal pack, with a leader in it, and if the dog can’t be the leader, he must be a follower.