Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
258 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 101 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 | #137×C101 | C2 |
| socle | C2×C101 | C22×D4 |
| hypercenter | #137 | D101 |
| hypocenter | C101 | C2×#137 |
| LCS | G ▷ C4×C101 ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #137 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×D101 | C2 | semidirect |
| 3. #15692288 | C2 | semidirect |
| 4. #15692287 | C2 | semidirect |
| 5. #15692286 | C2 | semidirect |
| 6. #15692285 | C2 | semidirect |
| 7. #15692284 | C2 | semidirect |
| 8. Q16×D101 | C2 | semidirect |
| 9. SD16×D101 | C2 | semidirect |
| 10. M16×D101 | C2 | semidirect |
| 11. #137×C101 | C2 | semidirect |
| 18. C2×Dic202 | C22 | semidirect |
| 23. Q8×D101 | C22 | semidirect |
| 29. Dic404 | C22 | semidirect |
| 30. #13108064 | C22 | semidirect |
| 31. #13108064 | C22 | semidirect |
| 32. #13108063 | C22 | semidirect |
| 33. #13108062 | C22 | semidirect |
| 34. #13108061 | C22 | semidirect |
| 35. #13108058 | C22 | semidirect |
| 36. #13108057 | C22 | semidirect |
| 39. C2×Q8×C101 | C22 | semidirect |
| 40. Q16×C101 | C22 | semidirect |
| 41. SD16×C101 | C22 | semidirect |
| 42. M16×C101 | C22 | semidirect |
| 98. D101 | #137 | direct (N × H) |
| 99. C101 | C2×#137 | semidirect |
| 108. #137 | D101 | direct (N × H) |
| 125. C2×Q8 | C2×D101 | semidirect |
| 134. Q16 | C2×D101 | semidirect |
| 138. SD16 | C2×D101 | semidirect |
| 141. M16 | C2×D101 | semidirect |