Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
2528 conjugacy classes of subgroups; only the 685 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 685 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D43 |
| commutator | C22×C43 | C25 |
| Frattini | C22 | C24×D43 |
| Fitting | C22×C4⋊C4×C43 | C2 |
| socle | C24×C43 | C23 |
| hypercenter | C22×C4⋊C4 | D43 |
| hypocenter | C43 | C22×#121 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D172 | C2 | semidirect |
| 2. C23×D172 | C2 | semidirect |
| 3. C23×C4×D43 | C2 | semidirect |
| 4. C2×#13063300 | C2 | direct (N × H) |
| 5. C22×(C2×D43)⋊C4 | C2 | semidirect |
| 6. C22×C4⋊C4×C43 | C2 | semidirect |
| 11. C22×D172 | C22 | semidirect |
| 12. C22×D172 | C22 | semidirect |
| 15. C22×C4×D43 | C22 | semidirect |
| 16. #13063300 | C22 | direct (N × H) |
| 17. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 20. C2×C4⋊C4×C43 | C22 | semidirect |
| 27. C23×D43 | D4 | semidirect |
| 31. C22×C4×C43 | D4 | semidirect |
| 38. C2×D172 | C23 | semidirect |
| 39. C2×D172 | C23 | semidirect |
| 41. C2×C4×D43 | C23 | semidirect |
| 42. C4⋊C4×C43 | C23 | semidirect |
| 43. (C2×D43)⋊C4 | C23 | semidirect |
| 55. C22×D43 | C2×D4 | semidirect |
| 59. C2×C4×C43 | C2×D4 | semidirect |
| 67. C22×C43 | #121 | semidirect |
| 79. C2×D43 | C22×D4 | semidirect |
| 81. C4×C43 | C22×D4 | semidirect |
| 84. C2×C43 | C2×#121 | semidirect |
| 94. C22×C4⋊C4 | D43 | semidirect |
| 96. C43 | C22×#121 | semidirect |
| 109. C2×C4⋊C4 | C2×D43 | semidirect |
| 129. C22×C4 | D172 | semidirect |
| 132. C4⋊C4 | C22×D43 | semidirect |
| 154. C2×C4 | C2×D172 | semidirect |
| 165. C22 | #13063300 | direct (N × H) |
| 172. C4 | C22×D172 | semidirect |
| 175. C2 | C2×#13063300 | direct (N × H) |