Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
568 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C43 |
| prime radical | C2×#121×C43 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C43×#2625 | C2 | semidirect |
| 5. C43×#1826 | C2 | semidirect |
| 6. C43×#1508 | C2 | semidirect |
| 7. C43×#1305 | C2 | semidirect |
| 186. #9933 | C43 | direct (N × H) |
| 217. #2625 | C2×C43 | semidirect |
| 219. #1826 | C2×C43 | semidirect |
| 220. #1508 | C2×C43 | semidirect |
| 221. #1305 | C2×C43 | semidirect |
| 255. C43 | #9933 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#3193 | 2 |
| C43×#3094 | 2 |
| C43×#2625 | 2 |
| C43×#1964 | 2 |
| C43×#1826 | 2 |
| C43×#1508 | 2 |
| C43×#1305 | 2 |
| #9933 | 43 |