Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
486 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 486 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 | C4⋊Q8 | C23×C43 |
| prime radical | C43×#3018 | C2 |
| LCS | G ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C43 ◁ C2×C4×C43 ◁ C22×C4×C43 ◁ C43×#532 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C43×#2132 | C2 | semidirect |
| 3. C43×#1560 | C2 | semidirect |
| 4. C43×#1405 | C2 | semidirect |
| 16. C43×#356 | C22 | semidirect |
| 18. C43×#333 | C22 | semidirect |
| 151. #13574 | C43 | direct (N × H) |
| 172. #2132 | C2×C43 | semidirect |
| 173. #1560 | C2×C43 | semidirect |
| 174. #1405 | C2×C43 | semidirect |
| 192. #356 | C22×C43 | semidirect |
| 194. #333 | C22×C43 | semidirect |
| 196. C43 | #13574 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#3018 | 2 |
| C43×#2132 | 2 |
| C43×#1560 | 2 |
| C43×#1405 | 2 |
| #13574 | 43 |