A system of government in which power is divided between the national government and the states, and one in which the federal government is supreme over state governments in × of conflict, is known as a

A confederal system features a loose alliance of independent states that delegate limited powers to a central authority. In this arrangement, the national government typically lacks supremacy over the states, which retain most of their sovereign powers. Therefore, it does not meet the criteria of the question regarding federal supremacy during conflicts.

A unitary system centralizes power within a single national government that can create or abolish regional authorities at will. In this structure, states or regions derive their authority from the central government and do not possess independent power. This contradicts the notion of a divided government system where federal supremacy exists over state governments.

A socialist system primarily focuses on the collective or governmental ownership of the means of production and the redistribution of wealth, rather than the distribution of governmental powers between national and state levels. It does not specifically address the hierarchy of power between different government tiers, making it an inappropriate choice for the question.

A corporatist system emphasizes the role of organized groups in shaping government policy and often involves the collaboration between the state and various sectors of society (e.g., business and labor). However, this system does not define a power structure in which federal supremacy exists over states, thus failing to align with the question's premise.