Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
134 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C43 | D32 |
| commutator, Frattini, cosocle | C32 | C23×C43 |
| prime radical | C2×C43×D32 | C2 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C2×C4×C43 ◁ C2×C8×C43 ◁ C2×C16×C43 ◁ C2×C32×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C43×Q64 | C2 | semidirect |
| 3. C43×SD128 | C2 | direct (N × H) |
| 4. C2×C43×C64 | C2 | semidirect |
| 8. C43×Q64 | C22 | semidirect |
| 12. C43×C64 | C22 | semidirect |
| 40. C2×SD128 | C43 | direct (N × H) |
| 47. C2×Q64 | C2×C43 | semidirect |
| 49. SD128 | C2×C43 | direct (N × H) |
| 50. C2×C64 | C2×C43 | semidirect |
| 52. C2×C43 | SD128 | direct (N × H) |
| 57. Q64 | C22×C43 | semidirect |
| 61. C64 | C22×C43 | semidirect |
| 62. C43 | C2×SD128 | direct (N × H) |
| 97. C2 | C43×SD128 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C43×Q64 | 2 |
| C2×C43×D32 | 2 |
| C43×SD128 | 2 |
| C2×C43×C64 | 2 |
| C2×SD128 | 43 |