Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
288 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 288 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 | C2×C43 | #2184 |
| commutator, Frattini, cosocle | C2×C16 | C23×C43 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C43 ◁ C2×C4×C43 ◁ #131×C43 ◁ C43×#504 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C43×#3415 | C2 | semidirect |
| 2. C43×#2263 | C2 | semidirect |
| 3. C2×C43×D32 | C2 | semidirect |
| 4. C43×#2221 | C2 | semidirect |
| 5. C43×#1419 | C2 | semidirect |
| 6. C43×#1417 | C2 | semidirect |
| 7. C43×#1401 | C2 | semidirect |
| 15. C2×D16×C43 | C22 | semidirect |
| 21. C43×M64 | C22 | semidirect |
| 22. C2×C32×C43 | C22 | semidirect |
| 23. C43×#368 | C22 | semidirect |
| 103. #13669 | C43 | direct (N × H) |
| 116. #3415 | C2×C43 | semidirect |
| 117. #2263 | C2×C43 | semidirect |
| 118. C2×D32 | C2×C43 | semidirect |
| 119. #2221 | C2×C43 | semidirect |
| 120. #1419 | C2×C43 | semidirect |
| 121. #1417 | C2×C43 | semidirect |
| 122. #1401 | C2×C43 | semidirect |
| 136. C2×D16 | C22×C43 | semidirect |
| 142. M64 | C22×C43 | semidirect |
| 143. C2×C32 | C22×C43 | semidirect |
| 144. #368 | C22×C43 | semidirect |
| 146. C43 | #13669 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#3415 | 2 |
| C43×#2263 | 2 |
| C2×C43×D32 | 2 |
| C43×#2221 | 2 |
| C43×#1419 | 2 |
| C43×#1417 | 2 |
| C43×#1401 | 2 |
| #13669 | 43 |