Semifield planes of order q4 with kernel Fq2 and center Fq

A classification of semifield planes of order $q^4$ with kernel $F_{q^2}$ and center $F_q$ is given. For $q$ odd prime, this proves the conjecture stated in by M.~Cordero and R.~Figueroa. Also, we extend the classification of semifield planes lifted from Desarguesian planes of order $q^2,$ $q$ odd, obtained by Cordero and Figueroa in , to the even characteristic case.