Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
106 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8 | C22⋊D101 |
| commutator | C4×C101 | C22×C4 |
| Frattini | C2×C4 | C22×D101 |
| Fitting | #131×C101 | C2 |
| socle | C2×C101 | C4×D4 |
| hypercenter | #131 | D101 |
| hypocenter | C101 | #443 |
| LCS | G ▷ C4×C101 ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ #131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15692261 | C2 | semidirect |
| 3. #15692190 | C2 | semidirect |
| 4. #15692182 | C2 | semidirect |
| 5. #15692181 | C2 | semidirect |
| 6. C8×Dic101 | C2 | semidirect |
| 7. #131×C101 | C2 | semidirect |
| 9. #13108064 | C4 | semidirect |
| 10. #13108062 | C4 | semidirect |
| 11. #13108061 | C4 | semidirect |
| 12. #13108059 | C4 | semidirect |
| 51. C101 | #443 | semidirect |
| 55. #131 | D101 | semidirect |