Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
8094 conjugacy classes of subgroups; only the 5547 normal subgroups are shown.
This group has 8094 conjugacy classes of subgroups — too many to draw. Only its 5547 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C42 | D43 |
| commutator, hypocenter | C43 | C22×C43 |
| Frattini | C23 | C24×D43 |
| Fitting | C23×C42×C43 | C2 |
| socle, prime radical | C25×C43 | C23 |
| cosocle | C23×C43 | C25 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C23×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C42×Dic43 | C2 | direct (N × H) |
| 5. C22×C4×Dic43 | C4 | direct (N × H) |
| 7. C42×Dic43 | C22 | direct (N × H) |
| 9. C22×C42×C43 | C4 | semidirect |
| 13. C2×C4×Dic43 | C2×C4 | direct (N × H) |
| 19. C2×C42×C43 | C2×C4 | semidirect |
| 24. C22×C4×C43 | C42 | semidirect |
| 28. C22×Dic43 | C42 | direct (N × H) |
| 31. C42×C43 | C22×C4 | semidirect |
| 32. C4×Dic43 | C22×C4 | direct (N × H) |
| 38. C2×C4×C43 | C2×C42 | semidirect |
| 41. C2×Dic43 | C2×C42 | direct (N × H) |
| 44. C22×C43 | C43 | semidirect |
| 49. C4×C43 | C22×C42 | semidirect |
| 50. Dic43 | C22×C42 | direct (N × H) |
| 54. C2×C43 | C2×C43 | semidirect |
| 61. C22×C42 | Dic43 | direct (N × H) |
| 64. C43 | C22×C43 | semidirect |
| 73. C2×C42 | C2×Dic43 | direct (N × H) |
| 81. C22×C4 | C4×Dic43 | direct (N × H) |
| 86. C42 | C22×Dic43 | direct (N × H) |
| 94. C2×C4 | C2×C4×Dic43 | direct (N × H) |
| 97. C22 | C42×Dic43 | direct (N × H) |
| 103. C4 | C22×C4×Dic43 | direct (N × H) |
| 104. C2 | C2×C42×Dic43 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×Dic43 | 2 |
| C2×C42×Dic43 | 2 |
| C23×C42×C43 | 2 |
| C22×C43 | 43 |