Isaacs–Seitz conjecture on solvable-group derived length

For a finite group $G$, let $\operatorname{Irr}(G)$ be the set of irreducible characters and define the set of irreducible character degrees by

$$\operatorname{cd}(G)=\\{\chi(1)\mid\chi\in\operatorname{Irr}(G)\\}.$$

Let $\operatorname{dl}(G)$ denote the derived length of $G$. Isaacs–Seitz conjecture. If $G$ is solvable, then

$$\operatorname{dl}(G)\le |\operatorname{cd}(G)|.$$

The conjecture has been proved in many cases, but the general problem remains open; the source records Gluck's weaker bound $\operatorname{dl}(G)\le2|\operatorname{cd}(G)|$.