Subgroup structure of Mathieu group:M11
This article gives specific information, namely, subgroup structure, about a particular group, namely: Mathieu group:M11.
View subgroup structure of particular groups | View other specific information about Mathieu group:M11
This article describes the subgroup structure of Mathieu group:M11.
Tables for quick information
FACTS TO CHECK AGAINST FOR SUBGROUP STRUCTURE: (finite group)
Lagrange's theorem (order of subgroup times index of subgroup equals order of whole group, so both divide it), |order of quotient group divides order of group (and equals index of corresponding normal subgroup)
Sylow subgroups exist, Sylow implies order-dominating, congruence condition on Sylow numbers|congruence condition on number of subgroups of given prime power order
normal Hall implies permutably complemented, Hall retract implies order-conjugate
Quick summary
| Item | Value |
|---|---|
| number of subgroups | 8651 |
| number of conjugacy classes of subgroups | 39 |
| isomorphism classes of Sylow subgroups and corresponding Sylow numbers | 2-Sylow: semidihedral group:SD16, Sylow number is 495 3-Sylow: elementary abelian group:E9, Sylow number is 55 5-Sylow: cyclic group:Z5, Sylow number is 396 11-Sylow: cyclic group:Z11, Sylow number is 144 |
| Hall subgroups | apart from the whole group, trivial subgroup, and Sylow subgroups, there exist the following Hall subgroups: -Hall (order 144), -Hall (order 55), -Hall (order 720) |
| maximal subgroups | maximal subgroups of order 48, 120, 144, 660, 720 |
| normal subgroups | the group is simple non-abelian, so the only normal subgroups are the whole group and the trivial subgroup |
| subgroups that are simple non-abelian groups (apart from the whole group) | alternating group:A5 (order 60), alternating group:A6 (order 360), projective special linear group:PSL(2,11) (order 660) |
