Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D101 |
| commutator | C2×C101 | C2×C42 |
| Frattini | C23 | C22×D101 |
| Fitting | C2×C42×C101 | C2 |
| socle | C23×C101 | C23 |
| hypercenter | C2×C42 | D101 |
| hypocenter | C101 | C4×C22⋊C4 |
| LCS | G ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C4×Dic101 | C2 | semidirect |
| 4. #15692162 | C2 | semidirect |
| 5. C2×C42×C101 | C2 | semidirect |
| 11. C2×C4×D101 | C4 | semidirect |
| 12. #13108051 | C4 | direct (N × H) |
| 26. C2×C4×C101 | C2×C4 | semidirect |
| 34. C2×Dic101 | C2×C4 | semidirect |
| 45. C2×D101 | C42 | semidirect |
| 47. C4×C101 | C22⋊C4 | semidirect |
| 56. C101 | C4×C22⋊C4 | semidirect |
| 61. C2×C42 | D101 | semidirect |
| 90. C2×C4 | C4×D101 | semidirect |
| 106. C4 | #13108051 | direct (N × H) |