Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
844 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 216 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×C19 | #120 |
| commutator, Frattini, cosocle | C2×C4 | C24×C19 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C19×H(5,𝔽2) | C2 | semidirect |
| 2. C2×C19×AGL(1,ℤ/8) | C2 | semidirect |
| 3. C2×C19×#127 | C2 | semidirect |
| 4. C19×#453 | C2 | direct (N × H) |
| 5. C2×C19×#104 | C2 | semidirect |
| 6. C2×C19×#100 | C2 | semidirect |
| 9. C19×H(5,𝔽2) | C22 | semidirect |
| 16. C22×D4×C19 | C22 | semidirect |
| 18. C19×AGL(1,ℤ/8) | C22 | semidirect |
| 21. C2×M16×C19 | C22 | semidirect |
| 23. C19×#127 | C22 | semidirect |
| 24. C2×C42×C19 | C22 | semidirect |
| 25. C19×#104 | C22 | semidirect |
| 26. C19×#100 | C22 | semidirect |
| 34. #41×C19 | D4 | semidirect |
| 36. C2×Q8×C19 | D4 | semidirect |
| 51. C2×D4×C19 | D4 | semidirect |
| 53. C2×D4×C19 | C23 | semidirect |
| 61. M16×C19 | C23 | semidirect |
| 64. C42×C19 | C23 | semidirect |
| 78. Q8×C19 | C2×D4 | semidirect |
| 88. D4×C19 | C2×D4 | semidirect |
| 100. C2×#453 | C19 | direct (N × H) |
| 120. C2×H(5,𝔽2) | C2×C19 | semidirect |
| 121. C2×AGL(1,ℤ/8) | C2×C19 | semidirect |
| 122. C2×#127 | C2×C19 | semidirect |
| 123. #453 | C2×C19 | direct (N × H) |
| 124. C2×#104 | C2×C19 | semidirect |
| 125. C2×#100 | C2×C19 | semidirect |
| 131. C2×C19 | #453 | direct (N × H) |
| 135. H(5,𝔽2) | C22×C19 | semidirect |
| 142. C22×D4 | C22×C19 | semidirect |
| 144. AGL(1,ℤ/8) | C22×C19 | semidirect |
| 147. C2×M16 | C22×C19 | semidirect |
| 149. #127 | C22×C19 | semidirect |
| 150. C2×C42 | C22×C19 | semidirect |
| 151. #104 | C22×C19 | semidirect |
| 152. #100 | C22×C19 | semidirect |
| 153. C19 | C2×#453 | direct (N × H) |
| 161. #41 | D4×C19 | semidirect |
| 163. C2×Q8 | D4×C19 | semidirect |
| 178. C2×D4 | D4×C19 | semidirect |
| 180. C2×D4 | C23×C19 | semidirect |
| 188. M16 | C23×C19 | semidirect |
| 191. C42 | C23×C19 | semidirect |
| 205. Q8 | C2×D4×C19 | semidirect |
| 215. D4 | C2×D4×C19 | semidirect |
| 251. C2 | C19×#453 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C19×H(5,𝔽2) | 2 |
| C2×C19×AGL(1,ℤ/8) | 2 |
| C2×C19×#127 | 2 |
| C19×#453 | 2 |
| C2×C19×#104 | 2 |
| C2×C19×#100 | 2 |
| C2×#453 | 19 |