Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
850 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 850 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 |
| 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×#3192 | C2 | semidirect |
| 2. C43×#3006 | C2 | semidirect |
| 3. C43×#2615 | C2 | semidirect |
| 4. C43×#1964 | C2 | semidirect |
| 5. C43×#1789 | C2 | semidirect |
| 6. C43×#1507 | C2 | semidirect |
| 7. C43×#1305 | C2 | semidirect |
| 45. C22×D4×C43 | D4 | semidirect |
| 53. C2×M16×C43 | D4 | semidirect |
| 65. C2×C4⋊C4×C43 | D4 | semidirect |
| 83. C22⋊C8×C43 | D4 | semidirect |
| 233. #9930 | C43 | direct (N × H) |
| 272. #3192 | C2×C43 | semidirect |
| 273. #3006 | C2×C43 | semidirect |
| 274. #2615 | C2×C43 | semidirect |
| 275. #1964 | C2×C43 | semidirect |
| 276. #1789 | C2×C43 | semidirect |
| 277. #1507 | C2×C43 | semidirect |
| 278. #1305 | C2×C43 | semidirect |
| 314. C43 | #9930 | direct (N × H) |
| 327. C22×D4 | D4×C43 | semidirect |
| 335. C2×M16 | D4×C43 | semidirect |
| 347. C2×C4⋊C4 | D4×C43 | semidirect |
| 365. 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×#3192 | 2 |
| C43×#3006 | 2 |
| C43×#2615 | 2 |
| C43×#1964 | 2 |
| C43×#1789 | 2 |
| C43×#1507 | 2 |
| C43×#1305 | 2 |
| #9930 | 43 |