Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1810 conjugacy classes of subgroups.
The subgroup lattice has 170 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C43 | C24 |
| commutator | C22 | C24×C4×C43 |
| Frattini, cosocle | C2×C4 | C25×C43 |
| socle | C22×C43 | C24×C4 |
| prime radical | C24×C43 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C43×#2961 | C2 | semidirect |
| 3. C43×#2960 | C2 | semidirect |
| 12. C43×#446 | C22 | semidirect |
| 13. C8×Q8×C43 | C22 | semidirect |
| 23. C22×C8×C43 | Q8 | semidirect |
| 73. #60191 | C43 | direct (N × H) |
| 83. #2961 | C2×C43 | semidirect |
| 84. #2960 | C2×C43 | semidirect |
| 96. #446 | C22×C43 | semidirect |
| 97. C8×Q8 | C22×C43 | semidirect |
| 104. C43 | #60191 | direct (N × H) |
| 108. C22×C8 | Q8×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#3458 | 2 |
| C43×#2961 | 2 |
| C43×#2960 | 2 |
| C43×#2905 | 2 |
| C2×C43×#405 | 2 |
| #60191 | 43 |