8.6 $M_{11}^{(1)} \vert <a>$

This example has two features: its subgroup is generated by $a$ and only as many cosets are defined as the result has. As for $PSL_2(11) \vert E$ the total number of cosets is interesting.

Here, strategy NONE with the length-lexicographical ordering is optimal because exactly 720 cosets are defined totally. Note, that this ordering performs worst for I-ALL.