Finite Group DatabasebetaFinite Group DatabasebetaOrder 11456.
248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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×D179 |
| commutator, socle, cosocle | C22×C179 | C24 |
| Fitting | #117×C179 | C2 |
| prime radical | #19153083 | C2 |
| hypercenter | #117 | D179 |
| hypocenter | C179 | #551 |
| LCS | G ▷ C22×C179 ▷ C179 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19153108 | C2 | semidirect |
| 2. #19153107 | C2 | semidirect |
| 3. #19153101 | C2 | semidirect |
| 4. #19153098 | C2 | semidirect |
| 5. #19153098 | C2 | semidirect |
| 6. #19153096 | C2 | semidirect |
| 7. #19153091 | C2 | semidirect |
| 8. #19153090 | C2 | semidirect |
| 10. C4×D716 | C2 | semidirect |
| 11. (C22⋊D179)⋊C4 | C2 | semidirect |
| 12. #19153070 | C2 | semidirect |
| 13. C2×(C2×D179)⋊C4 | C2 | semidirect |
| 14. C22⋊C4×D179 | C2 | semidirect |
| 15. #117×C179 | C2 | semidirect |
| 17. C2×Dic358 | C22 | semidirect |
| 24. C2×C4×D179 | C22 | semidirect |
| 25. C4⋊Dic179 | C22 | semidirect |
| 26. Dic179⋊C4 | C22 | semidirect |
| 27. Dic179⋊C4 | C22 | semidirect |
| 28. Dic179⋊C4 | C22 | semidirect |
| 29. Dic179⋊C4 | C22 | semidirect |
| 30. Dic179⋊C4 | C22 | semidirect |
| 40. (C2×D179)⋊C4 | C22 | semidirect |
| 41. (C2×D179)⋊C4 | C22 | semidirect |
| 42. (C2×D179)⋊C4 | C22 | semidirect |
| 43. C4×Dic179 | C22 | semidirect |
| 45. C4⋊C4×C179 | C22 | semidirect |
| 46. C4⋊C4×C179 | C22 | semidirect |
| 49. C42×C179 | C22 | semidirect |
| 50. C42×C179 | C22 | semidirect |
| 110. C179 | #551 | semidirect |
| 124. #117 | D179 | semidirect |
| 143. C4⋊C4 | C2×D179 | semidirect |
| 144. C4⋊C4 | C2×D179 | semidirect |
| 160. C42 | C2×D179 | semidirect |
| 161. C42 | C2×D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19153108 | 2 |
| #19153107 | 2 |
| #19153101 | 2 |
| #19153098 | 2 |
| #19153096 | 2 |
| #19153091 | 2 |
| #19153090 | 2 |
| #19153083 | 2 |
| C4×D716 | 2 |
| (C22⋊D179)⋊C4 | 2 |
| #19153070 | 2 |
| C2×(C2×D179)⋊C4 | 2 |
| C22⋊C4×D179 | 2 |
| #117×C179 | 2 |
| #551 | 179 |