Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
476 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 74 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 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×C4⋊C4 | C23×C43 |
| prime radical | C43×#1598 | C2 |
| LCS | G ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C23×C43 ◁ C2×C4⋊C4×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C43×#2728 | C2 | semidirect |
| 2. C43×#2007 | C2 | semidirect |
| 3. C43×#1610 | C2 | semidirect |
| 5. C43×#1346 | C2 | semidirect |
| 6. C43×#1345 | C2 | semidirect |
| 7. C43×#1319 | C2 | semidirect |
| 76. C2×Q8×C43 | D8 | semidirect |
| 171. #12098 | C43 | direct (N × H) |
| 197. #2728 | C2×C43 | semidirect |
| 198. #2007 | C2×C43 | semidirect |
| 199. #1610 | C2×C43 | semidirect |
| 201. #1346 | C2×C43 | semidirect |
| 202. #1345 | C2×C43 | semidirect |
| 203. #1319 | C2×C43 | semidirect |
| 230. C43 | #12098 | direct (N × H) |
| 280. C2×Q8 | D8×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#2728 | 2 |
| C43×#2007 | 2 |
| C43×#1610 | 2 |
| C43×#1598 | 2 |
| C43×#1346 | 2 |
| C43×#1345 | 2 |
| C43×#1319 | 2 |
| #12098 | 43 |