Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1386 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 382 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C43 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C43 |
| prime radical | C22×D8×C43 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C43 ◁ C43×#376 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C43×#497 | C2 | semidirect |
| 3. C2×C43×#494 | C2 | semidirect |
| 4. C43×#2658 | C2 | semidirect |
| 5. C43×#1726 | C2 | semidirect |
| 77. #33309 | C43 | direct (N × H) |
| 86. C2×#497 | C2×C43 | semidirect |
| 88. C2×#494 | C2×C43 | semidirect |
| 89. #2658 | C2×C43 | semidirect |
| 90. #1726 | C2×C43 | semidirect |
| 107. C43 | #33309 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C43×#497 | 2 |
| C2×C43×#495 | 2 |
| C2×C43×#494 | 2 |
| C43×#2658 | 2 |
| C43×#1726 | 2 |
| #33309 | 43 |