Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
994 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 254 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×#3184 | C2 | semidirect |
| 2. C43×#3151 | C2 | semidirect |
| 3. C43×#1721 | C2 | semidirect |
| 4. C43×#1715 | C2 | semidirect |
| 5. C43×#1712 | C2 | semidirect |
| 6. C43×#1705 | C2 | semidirect |
| 7. C43×#1455 | C2 | semidirect |
| 11. C43×#498 | C22 | semidirect |
| 15. C43×#493 | C22 | semidirect |
| 18. C43×#486 | C22 | semidirect |
| 22. C43×#322 | C22 | semidirect |
| 23. C82×C43 | C22 | semidirect |
| 89. C8×C43 | AGL(1,ℤ/8) | semidirect |
| 90. #19745 | C43 | direct (N × H) |
| 101. #3184 | C2×C43 | semidirect |
| 102. #3151 | C2×C43 | semidirect |
| 103. #1721 | C2×C43 | semidirect |
| 104. #1715 | C2×C43 | semidirect |
| 105. #1712 | C2×C43 | semidirect |
| 106. #1705 | C2×C43 | semidirect |
| 107. #1455 | C2×C43 | semidirect |
| 116. #498 | C22×C43 | semidirect |
| 120. #493 | C22×C43 | semidirect |
| 123. #486 | C22×C43 | semidirect |
| 127. #322 | C22×C43 | semidirect |
| 128. C82 | C22×C43 | semidirect |
| 129. C43 | #19745 | direct (N × H) |
| 195. C8 | AGL(1,ℤ/8)×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#3184 | 2 |
| C43×#3151 | 2 |
| C43×#1721 | 2 |
| C43×#1715 | 2 |
| C43×#1712 | 2 |
| C43×#1705 | 2 |
| C43×#1455 | 2 |
| #19745 | 43 |