"Universalist" and "Subjectivist" aren't opposed or conflicting terms. "Subjective" simply says that moral statements are really statements about the attitudes or opinions of people (or something else with a mind). The opposing term is "objective". "Universalist" and "relativist" are on a different dimension from subjective and objective. Universal vs. relative is about how variable or not variable morality is.

If morality varies with individuals, as required by subjectivism, it is not at all universal, so the two are not orthogonal.

You could have a metaethical theory that morality is both objective and relative. For example, you could define morality as what the law says and it will be relative from country to country as laws differ.

If morality is relative to groups rather than individuals, it is still relative, Morality is objective when the truth values of moral statements don't vary with individuals or groups, not when it varies with empirically discoverable facts.

You could also have a subjective and universal meta-ethics. Morality judgments could be statements about the attitudes of people but all people could have the same attitudes.