Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
492 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C43 | C2×AΣL(1,𝔽16) |
| commutator | C2×Q8 | C22×C4×C43 |
| Frattini, cosocle | #124 | C23×C43 |
| prime radical | C2×C43×#454 | C2 |
| LCS | G ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C43 ◁ C23×C43 ◁ C22×C4×C43 ◁ C2×#124×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C43×#354 | C2 | semidirect |
| 3. C43×#1533 | C2 | semidirect |
| 4. C43×#1404 | C2 | semidirect |
| 5. C2×2−1+4×C43 | C4 | semidirect |
| 10. C43×#454 | C4 | semidirect |
| 14. C2×#101×C43 | C4 | semidirect |
| 17. C43×#354 | C22 | semidirect |
| 19. C43×#329 | C22 | semidirect |
| 23. 2−1+4×C43 | C2×C4 | semidirect |
| 48. #101×C43 | C2×C4 | semidirect |
| 149. #13569 | C43 | direct (N × H) |
| 171. C2×#354 | C2×C43 | semidirect |
| 172. #1533 | C2×C43 | semidirect |
| 173. #1404 | C2×C43 | semidirect |
| 181. C2×2−1+4 | C4×C43 | semidirect |
| 186. #454 | C4×C43 | semidirect |
| 190. C2×#101 | C4×C43 | semidirect |
| 193. #354 | C22×C43 | semidirect |
| 195. #329 | C22×C43 | semidirect |
| 196. C43 | #13569 | direct (N × H) |
| 200. 2−1+4 | C2×C4×C43 | semidirect |
| 225. #101 | C2×C4×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C43×#454 | 2 |
| C2×C43×#354 | 2 |
| C43×#1533 | 2 |
| C43×#1404 | 2 |
| #13569 | 43 |