Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
874 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 874 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C43 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C43 |
| Frattini, cosocle | C2×C42 | C23×C43 |
| prime radical | C23×D4×C43 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C43 ◁ C22×C42×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C43×#1749 | C2 | semidirect |
| 3. C43×#1270 | C2 | semidirect |
| 13. C43×#336 | C22 | semidirect |
| 111. #7626 | C43 | direct (N × H) |
| 134. #1749 | C2×C43 | semidirect |
| 135. #1270 | C2×C43 | semidirect |
| 152. #336 | C22×C43 | semidirect |
| 153. C43 | #7626 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C43×#390 | 2 |
| C43×#1749 | 2 |
| C43×#1270 | 2 |
| #7626 | 43 |