  Let $G$ be a finite group and $\chi\in \irr(G)$. The codegree of $\chi$ is
defined as $\cod(\chi)=\frac{|G:\ker(\chi)|}{\chi(1)}$ and
$\cod(G)=\{\cod(\chi) \ |\ \chi\in \irr(G)\}$ is called the set of codegrees of
$G$. In this paper, we show that the set of codegrees of $\Sy_4(4), \U_4(2)$,
$\Sy_4(q)\ (q \geq 4)$, $\U_4(3)$, ${}^2\F_4(2)'$, $\J_3$, $\G_2(3)$, $\A_9$,
$\J_2$, $\PSL(4,3)$, $\McL$, $\Sy_4(5)$, $\G_2(4)$, $\HS$, $\ON$ and $\M_{24}$
determines the group up to isomorphism.
