Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D101 |
| commutator, socle | C22×C101 | C24 |
| Frattini | C22 | C23×D101 |
| Fitting | C4×D4×C101 | C2 |
| hypercenter | C4×D4 | D101 |
| hypocenter | C101 | #525 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13108074 | C2 | semidirect |
| 2. C22×C4×D101 | C2 | semidirect |
| 3. #15692240 | C2 | semidirect |
| 4. #15692237 | C2 | semidirect |
| 5. #15692233 | C2 | semidirect |
| 6. #15692232 | C2 | semidirect |
| 7. #15692228 | C2 | semidirect |
| 8. #15692227 | C2 | semidirect |
| 9. #15692225 | C2 | semidirect |
| 10. #15692223 | C2 | semidirect |
| 11. C4×D404 | C2 | semidirect |
| 12. C4×C22⋊D101 | C2 | semidirect |
| 13. C4×C22⋊D101 | C2 | semidirect |
| 14. #15692212 | C2 | semidirect |
| 15. C4×D4×C101 | C2 | semidirect |
| 18. C2×Dic202 | C22 | semidirect |
| 24. C2×C22⋊D101 | C22 | semidirect |
| 31. C2×C4×D101 | C22 | semidirect |
| 32. C4⋊Dic101 | C22 | semidirect |
| 33. #13108053 | C22 | semidirect |
| 34. #13108053 | C22 | semidirect |
| 35. #13108053 | C22 | semidirect |
| 36. #13108053 | C22 | semidirect |
| 38. C22⋊Dic101 | C22 | semidirect |
| 43. #13108051 | C22 | semidirect |
| 44. #13108051 | C22 | semidirect |
| 45. C4×Dic101 | C22 | semidirect |
| 48. C22×C4×C101 | C22 | semidirect |
| 49. C4⋊C4×C101 | C22 | semidirect |
| 51. C22⋊C4×C101 | C22 | semidirect |
| 52. C42×C101 | C22 | semidirect |
| 85. C4×D101 | D4 | semidirect |
| 92. C22×C101 | #41 | semidirect |
| 103. C2×D101 | #41 | semidirect |
| 122. C101 | #525 | semidirect |
| 137. C4×D4 | D101 | semidirect |
| 157. C22×C4 | C2×D101 | semidirect |
| 163. C4⋊C4 | C2×D101 | semidirect |
| 173. C22⋊C4 | C2×D101 | semidirect |
| 175. C42 | C2×D101 | semidirect |
| 225. C22 | #13108074 | semidirect |