Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
1284 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 1284 conjugacy classes of subgroups — too many to draw. Only its 222 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 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C24×C19 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C19 ◁ C22×Q8×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C19×H(3,𝔽4) | C2 | semidirect |
| 2. C2×C19×#454 | C2 | semidirect |
| 3. C19×#2202 | C2 | direct (N × H) |
| 4. C2×C19×#355 | C2 | semidirect |
| 5. C2×C19×2−1+4 | C22 | semidirect |
| 8. C19×H(3,𝔽4) | C22 | semidirect |
| 13. C19×#454 | C22 | semidirect |
| 15. C2×C19×#101 | C22 | semidirect |
| 16. C19×#355 | C22 | semidirect |
| 20. C19×2−1+4 | C23 | semidirect |
| 45. C19×#101 | C23 | semidirect |
| 87. C2×#2202 | C19 | direct (N × H) |
| 120. C2×H(3,𝔽4) | C2×C19 | semidirect |
| 121. C2×#454 | C2×C19 | semidirect |
| 122. #2202 | C2×C19 | direct (N × H) |
| 123. C2×#355 | C2×C19 | semidirect |
| 139. C2×2−1+4 | C22×C19 | semidirect |
| 142. H(3,𝔽4) | C22×C19 | semidirect |
| 147. #454 | C22×C19 | semidirect |
| 149. C2×#101 | C22×C19 | semidirect |
| 150. #355 | C22×C19 | semidirect |
| 155. C2×C19 | #2202 | direct (N × H) |
| 160. 2−1+4 | C23×C19 | semidirect |
| 185. #101 | C23×C19 | semidirect |
| 186. C19 | C2×#2202 | direct (N × H) |
| 279. C2 | C19×#2202 | 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(3,𝔽4) | 2 |
| C2×C19×#454 | 2 |
| C19×#2202 | 2 |
| C2×C19×#355 | 2 |
| C2×#2202 | 19 |