On CLT and non-CLT groups

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