On CLT and non-CLT groups

In this note, we prove that for every integer $d\ge 2$ which is not a prime power, there exists a finite solvable group $G$ such that $d\mid \mathrm{\mid }G\mathrm{\mid }$, $\pi (G)=\pi (d)$ and $G$ has no subgroup of order $d$. We also introduce the CLT-degree of a finite group and answer two questions about it.