Which process must the cell undergo to have genetically different cells at the end of the subdivision

That process is known as "Meiosis" when cell goes through "Crossing Over"

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Mitosis. Mitosis is cell division that takes place during the growth of cells. It is such that the genetic material in the parent cell is duplicated by DNA replication and the resultant daughter cells are about exactly thesame. Meiosis on the other hand is cell division that occurs during gamete formation or sexual reproduction. The resultant cells which will be reproductive cells are not identical as much as we find in mitotic division. This is because of the phenomenon of crossing over which allows for the independent assortment of genetic materials in the cell. Crossing over occurs in the diplotene stage of prophase 1 in meiotic division.