However, despite their reputation in cartoons for chasing yowling moggies up trees, fewer than one in five owners have seen their dog threaten their cat.
The findings come from a study of almost 750 pet owners who overwhelmingly believe cat is king.
The knowledge could help Britain's pet owners, as almost a quarter of us own a dog and 17 per cent have cats, with an estimated seven per cent keeping both types of animal.
Dr Sophie Hall, co-author of the paper from the School of Life Sciences at the University of Lincoln, said: "On the face of it, these results suggest that the cat is the kingpin in a household with dogs. They are the princess and the dog is lower down in the hierarchy.
"It may be that cats" threatening acts are more obvious to owners, as they hiss or strike out with their paws at a dog.
"But it may also be the case that cats are less domesticated in their behaviours than dogs, so are less used to getting along with other four and two-legged members of the family and have had less training to do so."
Despite their diminutive size, the latest research shows cats often injure dogs, with almost one in ten owners reporting this.
Fewer than one per cent said their dog had injured the cat.
A questionnaire on their pets, found dogs and cats can live together amicably but their owners rarely describe it as a "close relationship".
Whether they get on is mainly up to the cat, with cats which were frequently uncomfortable with dogs less likely to have an amicable relationship.
In total, 56.5 per cent of owners said their cat had ever threatened their dog, compared to 18 per cent whose dog had threatened the cat.
Dr Hall said: "It is important to note that these findings are the owners perceptions of their pets' relationships, but it seems that the cat has to be happy and content, rather than the dog, for them to live happily together."
The study, published in the Journal of Veterinary Behaviour, said that cats and dogs may get along better if the feline is younger when they begin living together.
John Fishwick, president of the British Veterinary Association, said: "The basic explanation of these findings is that while dogs are pack animals, cats tend to be solitary creatures.
"For a harmonious household, the important thing is to give both animals their space, perhaps with a child gate separating them or a cat flap so the cat can escape the house when necessary.
"They should eat in separate areas to avoid conflict, so both can do so undisturbed."