Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
420 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C43 | #410 |
| commutator | C22×C4 | C22×C4×C43 |
| Frattini, cosocle | C2×#41 | C23×C43 |
| socle | C2×C43 | #1799 |
| prime radical | C43×#532 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C43 ◁ C2×C8×C43 ◁ C2×#131×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C43×#1812 | C2 | semidirect |
| 4. C43×#1391 | C2 | semidirect |
| 5. C2×#131×C43 | C4 | semidirect |
| 11. C43×#423 | C4 | semidirect |
| 13. C43×#408 | C4 | semidirect |
| 15. C2×#97×C43 | C4 | semidirect |
| 115. #12808 | C43 | direct (N × H) |
| 133. #1812 | C2×C43 | semidirect |
| 134. #1391 | C2×C43 | semidirect |
| 140. C2×#131 | C4×C43 | semidirect |
| 146. #423 | C4×C43 | semidirect |
| 148. #408 | C4×C43 | semidirect |
| 150. C2×#97 | C4×C43 | semidirect |
| 154. C43 | #12808 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#2932 | 2 |
| C43×#2126 | 2 |
| C43×#1812 | 2 |
| C43×#1391 | 2 |
| #12808 | 43 |