Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 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 | C4 | D4×D101 |
| commutator | C4×C101 | C24 |
| Frattini | C4 | C23×D101 |
| Fitting | #135×C101 | C2 |
| socle | C2×C101 | C22×D4 |
| hypercenter | #135 | D101 |
| hypocenter | C101 | #575 |
| LCS | G ▷ C4×C101 ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #135 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #41×D101 | C2 | semidirect |
| 2. #15692287 | C2 | semidirect |
| 3. #15692284 | C2 | semidirect |
| 4. #15692282 | C2 | semidirect |
| 5. #15692279 | C2 | semidirect |
| 6. #15692277 | C2 | semidirect |
| 7. #15692275 | C2 | semidirect |
| 8. C2×#13108057 | C2 | semidirect |
| 9. #135×C101 | C2 | semidirect |
| 12. #13108074 | C22 | semidirect |
| 15. Q8×D101 | C22 | semidirect |
| 17. D4×D101 | C22 | semidirect |
| 20. Dic404 | C22 | semidirect |
| 21. #13108064 | C22 | semidirect |
| 22. #13108063 | C22 | semidirect |
| 23. #13108062 | C22 | semidirect |
| 24. #13108061 | C22 | semidirect |
| 25. D808 | C22 | semidirect |
| 26. #13108059 | C22 | semidirect |
| 27. #13108057 | C22 | semidirect |
| 28. #13108057 | C22 | semidirect |
| 29. C2×#11717579 | C22 | semidirect |
| 30. #41×C101 | C22 | semidirect |
| 31. Q16×C101 | C22 | semidirect |
| 32. SD16×C101 | C22 | semidirect |
| 33. D8×C101 | C22 | semidirect |
| 34. C2×C8×C101 | C22 | semidirect |
| 75. C101 | #575 | semidirect |
| 84. #135 | D101 | semidirect |
| 91. #41 | C2×D101 | semidirect |
| 99. Q16 | C2×D101 | semidirect |
| 103. SD16 | C2×D101 | semidirect |
| 106. D8 | C2×D101 | semidirect |
| 110. C2×C8 | C2×D101 | semidirect |