Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
506 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D101 |
| commutator | C22×C101 | C22×C4 |
| Fitting | C2×C22⋊C4×C101 | C2 |
| socle | C23×C101 | C23 |
| hypercenter | C2×C22⋊C4 | D101 |
| hypocenter | C101 | #379 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊Dic101 | C2 | semidirect |
| 3. C2×#13108051 | C2 | semidirect |
| 4. C2×C22⋊C4×C101 | C2 | semidirect |
| 8. C23×D101 | C4 | semidirect |
| 10. C22×Dic101 | C22 | semidirect |
| 14. C22×C4×C101 | C22 | semidirect |
| 37. C22×C101 | C22⋊C4 | semidirect |
| 47. C2×D101 | C22⋊C4 | semidirect |
| 56. C101 | #379 | semidirect |
| 61. C2×C22⋊C4 | D101 | semidirect |
| 69. C22×C4 | C2×D101 | semidirect |
| 100. C22 | #13108051 | semidirect |