Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1568 conjugacy classes of subgroups; only the 621 normal subgroups are shown.
This group has 1568 conjugacy classes of subgroups — too many to draw. Only its 621 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D43 |
| commutator | C22×C43 | C25 |
| Frattini | C22 | C24×D43 |
| Fitting | C2×C4×Q8×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C2×C4×Q8 | D43 |
| hypocenter | C43 | C2×D4×Q8 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q8×D43 | C2 | semidirect |
| 2. Q8×D172 | C2 | direct (N × H) |
| 3. C2×#13063325 | C2 | semidirect |
| 4. C2×#13063305 | C2 | semidirect |
| 6. C2×C4×Q8×C43 | C2 | semidirect |
| 9. C2×Q8×D43 | C22 | semidirect |
| 12. #13063325 | C22 | semidirect |
| 13. #13063305 | C22 | semidirect |
| 19. C4×Q8×C43 | C22 | semidirect |
| 23. C2×Q8×C43 | D4 | semidirect |
| 30. C2×D172 | Q8 | direct (N × H) |
| 44. C22×D43 | C2×Q8 | semidirect |
| 46. Q8×C43 | C2×D4 | semidirect |
| 49. C2×C4×C43 | C2×Q8 | semidirect |
| 55. D172 | C2×Q8 | direct (N × H) |
| 65. C2×D43 | C22×Q8 | semidirect |
| 68. C4×C43 | C22×Q8 | semidirect |
| 71. C2×C43 | D4×Q8 | semidirect |
| 80. C2×C4×Q8 | D43 | semidirect |
| 82. C43 | C2×D4×Q8 | semidirect |
| 91. C4×Q8 | C2×D43 | semidirect |
| 102. C2×Q8 | D172 | direct (N × H) |
| 123. Q8 | C2×D172 | direct (N × H) |
| 130. C2×C4 | Q8×D43 | semidirect |
| 145. C4 | C2×Q8×D43 | semidirect |
| 147. C2 | Q8×D172 | direct (N × H) |