Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
982 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 982 conjugacy classes of subgroups — too many to draw. Only its 230 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 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C43 |
| prime radical | C2×#127×C43 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C43×#3113 | C2 | semidirect |
| 4. C43×#1640 | C2 | semidirect |
| 6. C43×#1491 | C2 | semidirect |
| 19. C43×#475 | C22 | semidirect |
| 20. C43×#462 | C22 | semidirect |
| 27. C43×Q8⋊C8 | C22 | semidirect |
| 130. #18531 | C43 | direct (N × H) |
| 146. #3113 | C2×C43 | semidirect |
| 147. #1640 | C2×C43 | semidirect |
| 149. #1491 | C2×C43 | semidirect |
| 166. #475 | C22×C43 | semidirect |
| 167. #462 | C22×C43 | semidirect |
| 174. Q8⋊C8 | C22×C43 | semidirect |
| 175. C43 | #18531 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C43×#559 | 2 |
| C43×#3138 | 2 |
| C43×#3113 | 2 |
| C43×#1640 | 2 |
| C43×#1555 | 2 |
| C43×#1491 | 2 |
| #18531 | 43 |