Minimality conjecture for defect subgroups of contragredient quasireductive supergroups

Let $G$ be a quasireductive supergroup whose Lie superalgebra $\operatorname{Lie}G$ is contragredient. A defect subgroup $D$ of $G$ is a subgroup associated with the defect of the contragredient Lie superalgebra, and a splitting subgroup is a quasireductive subgroup satisfying the splitting condition for $G$.

Minimality conjecture. Up to conjugacy, a defect subgroup $D$ of $G$ is the unique minimal splitting subgroup.

The claim identifies the defect subgroup as the smallest splitting subgroup, modulo conjugacy, under the stated contragredient hypothesis. The supplied text gives no evidence that this conjecture has been resolved.