The question is simple one to pose after looking at the symbols to denote the Mathieu groups. Are these five Mathieu groups fit in a chain w.r.t. subgroup relation? (i.e. Is $M_{11}$ subgroup of $M_{12}$? Is $M_{12}$ subgroup of $M_{22}$? so on...)
(Edit with note on wiki:) Consider simple as well as non-simple Mathieu groups $M_8$, $M_9$, $ ...$, $M_{12}$, $M_{20}$, $...$, $M_{24}$. Do they also fit in a chain w.r.t. subgroup relation?)
We have $M_8<M_9<M_{10}<M_{11}<M_{12}$ and $M_{19}<M_{20}<M_{21}<M_{22}<M_{23}<M_{24}$.
$M_8$ is not a subgroup of $M_{19}$.
$M_{8}$ is a subgroup of $M_{20}$, but $M_{9}$ is not.
$M_{9}$ is a subgroup of $M_{21}$, but $M_{10}$ is not.
$M_{10}$ is a subgroup of $M_{22}$, but $M_{11}$ is not.
$M_{11}$ is a subgroup of $M_{23}$, but $M_{24}$ is not.
$M_{12}$ is a subgroup of $M_{24}$.
The ATLAS of Finite Groups is a good source for information like this.