The structure of quasifields of small even orders

We study the structure of a finite quasifield: maximal subfields, the orders of nonzero elements of its multiplicative loop, and the conjecture that the multiplicative loop of any finite semifield is one-generated. We consider the structure of all semifields of order 16; the Knuth-Rua semifield of order 32, which disproves Wene's conjecture; and representatives of isotope classes of quasifields of orders 16 and 32.