Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
808 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 808 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 | C43×#2615 | C2 |
| 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 |
|---|---|---|
| 1. C43×#3193 | C2 | semidirect |
| 2. C43×#3007 | C2 | semidirect |
| 4. C43×#1996 | C2 | semidirect |
| 5. C43×#1789 | C2 | semidirect |
| 6. C43×#1507 | C2 | semidirect |
| 7. C43×#1305 | C2 | semidirect |
| 39. C22×Q8×C43 | D4 | semidirect |
| 52. C2×M16×C43 | D4 | semidirect |
| 65. C2×C4⋊C4×C43 | D4 | semidirect |
| 82. C22⋊C8×C43 | D4 | semidirect |
| 225. #9934 | C43 | direct (N × H) |
| 261. #3193 | C2×C43 | semidirect |
| 262. #3007 | C2×C43 | semidirect |
| 264. #1996 | C2×C43 | semidirect |
| 265. #1789 | C2×C43 | semidirect |
| 266. #1507 | C2×C43 | semidirect |
| 267. #1305 | C2×C43 | semidirect |
| 302. C43 | #9934 | direct (N × H) |
| 309. C22×Q8 | D4×C43 | semidirect |
| 322. C2×M16 | D4×C43 | semidirect |
| 335. C2×C4⋊C4 | D4×C43 | semidirect |
| 352. C22⋊C8 | D4×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#3193 | 2 |
| C43×#3007 | 2 |
| C43×#2615 | 2 |
| C43×#1996 | 2 |
| C43×#1789 | 2 |
| C43×#1507 | 2 |
| C43×#1305 | 2 |
| #9934 | 43 |