Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
814 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 814 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×#127 |
| commutator, Frattini, cosocle | C42 | C24×C43 |
| 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 |
|---|---|---|
| 1. C43×#3207 | C2 | semidirect |
| 2. C43×#3205 | C2 | semidirect |
| 3. C43×#1721 | C2 | semidirect |
| 4. C43×#1717 | C2 | semidirect |
| 5. C43×#1712 | C2 | semidirect |
| 6. C43×#1711 | C2 | semidirect |
| 7. C43×#1454 | C2 | semidirect |
| 12. C43×#493 | C22 | semidirect |
| 13. C43×#492 | C22 | semidirect |
| 14. C43×#487 | C22 | semidirect |
| 17. C43×#486 | C22 | semidirect |
| 23. C43×#322 | C22 | semidirect |
| 24. C82×C43 | C22 | semidirect |
| 95. #19743 | C43 | direct (N × H) |
| 107. #3207 | C2×C43 | semidirect |
| 108. #3205 | C2×C43 | semidirect |
| 109. #1721 | C2×C43 | semidirect |
| 110. #1717 | C2×C43 | semidirect |
| 111. #1712 | C2×C43 | semidirect |
| 112. #1711 | C2×C43 | semidirect |
| 113. #1454 | C2×C43 | semidirect |
| 123. #493 | C22×C43 | semidirect |
| 124. #492 | C22×C43 | semidirect |
| 125. #487 | C22×C43 | semidirect |
| 128. #486 | C22×C43 | semidirect |
| 134. #322 | C22×C43 | semidirect |
| 135. C82 | C22×C43 | semidirect |
| 136. C43 | #19743 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#3207 | 2 |
| C43×#3205 | 2 |
| C43×#1721 | 2 |
| C43×#1717 | 2 |
| C43×#1712 | 2 |
| C43×#1711 | 2 |
| C43×#1454 | 2 |
| #19743 | 43 |