Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
844 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 844 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, socle | C22×C43 | C2×#99 |
| commutator | C24 | C22×C4×C43 |
| Frattini, cosocle | C22×D4 | C23×C43 |
| prime radical | C43×#2408 | C2 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C22×C4×C43 ◁ C2×C4×D4×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C43×AΣL(1,𝔽16) | C2 | semidirect |
| 3. C43×#1800 | C2 | semidirect |
| 4. C4×#99×C43 | C2 | semidirect |
| 5. C23×D4×C43 | C4 | semidirect |
| 15. C43×#380 | C4 | semidirect |
| 16. C43×#379 | C4 | semidirect |
| 52. #99×C43 | D4 | semidirect |
| 163. #13221 | C43 | direct (N × H) |
| 196. C4×C43 | AΣL(1,𝔽16) | semidirect |
| 198. C2×AΣL(1,𝔽16) | C2×C43 | semidirect |
| 199. #1800 | C2×C43 | semidirect |
| 200. C4×#99 | C2×C43 | semidirect |
| 209. C23×D4 | C4×C43 | semidirect |
| 219. #380 | C4×C43 | semidirect |
| 220. #379 | C4×C43 | semidirect |
| 225. C43 | #13221 | direct (N × H) |
| 257. #99 | D4×C43 | semidirect |
| 400. C4 | C43×AΣL(1,𝔽16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#2408 | 2 |
| C2×C43×AΣL(1,𝔽16) | 2 |
| C43×#1800 | 2 |
| C4×#99×C43 | 2 |
| #13221 | 43 |