Completeness conjecture for the lattice of coideal subalgebras of odd-dimensional Kac algebras

Let $n$ be odd. The Kac algebra $K\!D(n)$ has lattice of coideal subalgebras $\operatorname{l}(K\!D(n))$, described in Theorem theorem.lattice.nodd, with an exceptional set $\mathcal I$. Completeness conjecture. The description of the lattice $\operatorname{l}(K\!D(n))$ is complete: $\mathcal I$ is empty. The conjecture concerns the computer-explored classification of coideal subalgebras when $n$ is odd and not prime; the theorem cited in the source establishes the listed description except for the possible exceptional set $\mathcal I$, which is known to be empty for $n\leq 51$ but is not resolved in general.