Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
290 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 74 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 | #342 |
| commutator | C22×C4 | C42×C43 |
| Frattini, cosocle | C2×#117 | C22×C43 |
| prime radical | C24×C43 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C22×C4×C43 ◁ C2×#117×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C2×#97×C43 | C4 | semidirect |
| 8. C2×C4×C8×C43 | C4 | semidirect |
| 13. C43×#324 | C4 | semidirect |
| 93. #7214 | C43 | direct (N × H) |
| 124. C2×#97 | C4×C43 | semidirect |
| 125. C2×C4×C8 | C4×C43 | semidirect |
| 130. #324 | C4×C43 | semidirect |
| 132. C43 | #7214 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#1820 | 2 |
| C43×#1750 | 2 |
| C43×#1464 | 2 |
| #7214 | 43 |