Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D4×D101 |
| commutator | C4×C101 | C24 |
| Frattini | C4 | C23×D101 |
| Fitting | C2×D8×C101 | C2 |
| socle | C2×C101 | C22×D4 |
| hypercenter | C2×D8 | D101 |
| hypocenter | C101 | #576 |
| LCS | G ▷ C4×C101 ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15692300 | C2 | semidirect |
| 2. #15692281 | C2 | semidirect |
| 3. #15692279 | C2 | semidirect |
| 4. #15692277 | C2 | semidirect |
| 5. #15692274 | C2 | semidirect |
| 6. D8×D101 | C2 | semidirect |
| 7. #15692261 | C2 | semidirect |
| 8. C2×D8×C101 | C2 | semidirect |
| 10. #13108074 | C22 | semidirect |
| 12. #13108073 | C22 | semidirect |
| 15. D4×D101 | C22 | semidirect |
| 16. Dic404 | C22 | semidirect |
| 17. #13108063 | C22 | semidirect |
| 18. #13108062 | C22 | semidirect |
| 19. D808 | C22 | semidirect |
| 20. #13108059 | C22 | semidirect |
| 21. #13108058 | C22 | semidirect |
| 22. #13108057 | C22 | semidirect |
| 23. C8×D101 | C22 | semidirect |
| 24. C2×D4×C101 | C22 | semidirect |
| 25. D8×C101 | C22 | semidirect |
| 26. D8×C101 | C22 | semidirect |
| 27. C2×C8×C101 | C22 | semidirect |
| 62. C101 | #576 | semidirect |
| 70. C2×D8 | D101 | semidirect |
| 79. C2×D4 | C2×D101 | semidirect |
| 85. D8 | C2×D101 | semidirect |
| 86. D8 | C2×D101 | semidirect |
| 90. C2×C8 | C2×D101 | semidirect |