There is perhaps a definitional question. It seems clear from a whole range of evidence that the brain operates many functions that are not directly part of the consciousness. Whether you want to define a hierarchical layered view, with the conscious brain at the top, or posit a cooperative view with various functions operating and transferring stuff between themselves is more a philosophical question, or indeed, just a matter of perspective. IMHO, I very much doubt there is any physiological evidence for a strict hierarchy. In software engineering we love hierarchical designs, ones with strictly defined interfaces and protocol stacks. There are all sorts of reasons why they are used. Translating ideas derived from technology, and especially computer technology to models of the brain has been around forever. There however not much to suggest it has any value beyond providing existence proofs of possible operational models. That computers work helps us understand that neurons also work. But I would not push it too hard.
If you want stick to hierarchical view, and you place the conscious brain as superior (at the top,) by definition the remainder of the brain is sub-conscious. This is however not really all that helpful, and the existence of a sub-conscious becomes nothing more than a tautology.
The sub-concious came into popular parlance from Freud, and he gave it a very clear set of capabilities that did not, and still do not, have much in the way of evidence to support its existence. His sub-conscious seemed to have all manner of innate emotional and reasoning capabilities that were never externally visible, yet drove conscious behaviour. Even ignoring the silly through to bizarre sexual nature of what he posited, there remains no evidence from structural or neurological work to suggest it is true. As Karl Popper was keen to point out, almost all of Freudian psychology was not science. It simply created new narratives to explain away and and all contradicting evidence. If the question is “is there a Freudian sub-conscious mind?” IMHO the answer is firm “No.”