Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
234 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#87938 |
| commutator, socle | C22×C101 | C22×C4 |
| Fitting | C22⋊C4×C101 | C4 |
| hypercenter | C22⋊C4 | #87938 |
| hypocenter | C101 | #385 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4⋊#87938 | C2 | semidirect |
| 4. (C2×#87938)⋊C4 | C2 | semidirect |
| 15. C22⋊Dic101 | C4 | semidirect |
| 16. #13108051 | C4 | semidirect |
| 17. C22⋊C4×C101 | C4 | semidirect |
| 33. C2×C4×C101 | C2×C4 | semidirect |
| 34. C2×Dic101 | C2×C4 | semidirect |
| 38. C22×C101 | C4⋊C4 | semidirect |
| 44. C2×D101 | C4⋊C4 | semidirect |
| 61. C101 | #385 | semidirect |
| 79. C22⋊C4 | #87938 | semidirect |
| 98. C2×C4 | C2×#87938 | semidirect |
| 109. C22 | C4⋊#87938 | semidirect |