Vdovin's depth conjecture for solvable subgroups

Let $G$ be a finite group with trivial solvable radical, and let $d_G(H)$ denote the depth of a subgroup $H\leqslant G$. A subgroup is solvable if it is a solvable group. Vdovin's conjecture. For every solvable subgroup $H$ of $G$, one has

$$d_G(H)\leqslant 9.$$

This is a depth analogue of Vdovin's base-size conjecture for solvable subgroups. The bound is stated to be best possible, and the conclusion is known when $H$ is a solvable maximal subgroup, but the general assertion is disproved: the supplied text says that a Magma computation shows it is false.