  Let $R$ be a finite unitary ring such that $R=R_0[R^*]$ where $R_0$ is the
prime ring and $R^*$ is not a nilpotent group. We show that if all proper
subgroups of $R^*$ are nilpotent groups, then the cardinal of $R$ is a power of
prime number 2. In addition, if $(R/Jac(R))^*$ is not a $p-$group, then either
$R\cong M_2(GF(2))$ or $R\cong M_2(GF(2))\oplus A$ where $M_2(GF(2))$ is the
ring of $2\times 2$ matrices over the finite field $GF(2)$ and $A$ is a direct
sum of finite field $GF(2)$.
