Finite Group DatabasebetaFinite Group DatabasebetaOrder 4544.
218 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D71 |
| commutator, socle, cosocle | C22×C71 | C24 |
| Fitting | C22⋊Q8×C71 | C2 |
| prime radical | #14556101 | C2 |
| hypercenter | C22⋊Q8 | D71 |
| hypocenter | C71 | #539 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14556123 | C2 | semidirect |
| 2. #14556121 | C2 | semidirect |
| 3. #14556118 | C2 | semidirect |
| 4. #14556118 | C2 | semidirect |
| 5. #14556113 | C2 | semidirect |
| 6. #14556111 | C2 | semidirect |
| 7. #14556110 | C2 | semidirect |
| 8. #14556110 | C2 | semidirect |
| 9. #14556104 | C2 | semidirect |
| 10. #14556104 | C2 | semidirect |
| 12. #14556090 | C2 | semidirect |
| 13. C4×C22⋊D71 | C2 | semidirect |
| 14. C4⋊C4×D71 | C2 | semidirect |
| 15. C22⋊Q8×C71 | C2 | semidirect |
| 103. C71 | #539 | semidirect |
| 115. C22⋊Q8 | D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14556123 | 2 |
| #14556121 | 2 |
| #14556118 | 2 |
| #14556113 | 2 |
| #14556111 | 2 |
| #14556110 | 2 |
| #14556104 | 2 |
| #14556101 | 2 |
| #14556090 | 2 |
| C4×C22⋊D71 | 2 |
| C4⋊C4×D71 | 2 |
| C22⋊Q8×C71 | 2 |
| #539 | 71 |