Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
2738 conjugacy classes of subgroups.
The subgroup lattice has 248 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C43 | C25 |
| commutator | C22 | C24×C4×C43 |
| Frattini, cosocle | C2×C4 | C25×C43 |
| socle | C22×C43 | C24×C4 |
| prime radical | C22×#41×C43 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C43×#2906 | C2 | semidirect |
| 4. C43×#2905 | C2 | semidirect |
| 5. C2×C43×#423 | C2 | semidirect |
| 17. C43×#424 | C22 | semidirect |
| 20. C43×#423 | C22 | semidirect |
| 21. C2×C4⋊C8×C43 | C22 | semidirect |
| 106. #60099 | C43 | direct (N × H) |
| 117. C4×C43 | #568 | semidirect |
| 122. #2906 | C2×C43 | semidirect |
| 123. #2905 | C2×C43 | semidirect |
| 124. C2×#423 | C2×C43 | semidirect |
| 140. #424 | C22×C43 | semidirect |
| 143. #423 | C22×C43 | semidirect |
| 144. C2×C4⋊C8 | C22×C43 | semidirect |
| 145. C43 | #60099 | direct (N × H) |
| 240. C4 | C43×#568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C43×#568 | 2 |
| C2×C4×#41×C43 | 2 |
| C43×#2906 | 2 |
| C43×#2905 | 2 |
| C2×C43×#423 | 2 |
| #60099 | 43 |