Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
378 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 58 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 | #2196 |
| commutator, Frattini, cosocle | #124 | C23×C43 |
| prime radical | C43×#3289 | C2 |
| LCS | G ▷ #124 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C43 ◁ C22×C43 ◁ C2×C4×C43 ◁ #124×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C43×#2203 | C2 | semidirect |
| 3. C43×#2201 | C2 | semidirect |
| 4. C43×#1660 | C2 | semidirect |
| 5. C43×#1407 | C2 | semidirect |
| 6. C43×#1404 | C2 | semidirect |
| 7. C43×#1403 | C2 | semidirect |
| 167. #13680 | C43 | direct (N × H) |
| 184. #2203 | C2×C43 | semidirect |
| 185. #2201 | C2×C43 | semidirect |
| 186. #1660 | C2×C43 | semidirect |
| 187. #1407 | C2×C43 | semidirect |
| 188. #1404 | C2×C43 | semidirect |
| 189. #1403 | C2×C43 | semidirect |
| 214. C43 | #13680 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#3289 | 2 |
| C43×#2203 | 2 |
| C43×#2201 | 2 |
| C43×#1660 | 2 |
| C43×#1407 | 2 |
| C43×#1404 | 2 |
| C43×#1403 | 2 |
| #13680 | 43 |