Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
438 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 88 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×C23 | #99 |
| commutator | C23 | C22×C4×C23 |
| Frattini, cosocle | C2×D4 | C23×C23 |
| prime radical | C2×C23×#120 | C2 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C23×C23 ◁ C22×D4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C23×#100 | C2 | semidirect |
| 3. C2×C23×#99 | C2 | semidirect |
| 4. C23×AΣL(1,𝔽16) | C2 | direct (N × H) |
| 5. C25×C23 | C4 | semidirect |
| 11. C23×#120 | C4 | semidirect |
| 15. C2×C22⋊C4×C23 | C4 | semidirect |
| 17. C23×#100 | C22 | semidirect |
| 19. C23×#99 | C22 | semidirect |
| 26. C24×C23 | C2×C4 | semidirect |
| 48. C22⋊C4×C23 | C2×C4 | semidirect |
| 87. C2×AΣL(1,𝔽16) | C23 | direct (N × H) |
| 117. C2×#100 | C2×C23 | semidirect |
| 118. C2×#99 | C2×C23 | semidirect |
| 119. AΣL(1,𝔽16) | C2×C23 | direct (N × H) |
| 127. C2×C23 | AΣL(1,𝔽16) | direct (N × H) |
| 129. C25 | C4×C23 | semidirect |
| 135. #120 | C4×C23 | semidirect |
| 139. C2×C22⋊C4 | C4×C23 | semidirect |
| 141. #100 | C22×C23 | semidirect |
| 143. #99 | C22×C23 | semidirect |
| 144. C23 | C2×AΣL(1,𝔽16) | direct (N × H) |
| 151. C24 | C2×C4×C23 | semidirect |
| 173. C22⋊C4 | C2×C4×C23 | semidirect |
| 247. C2 | C23×AΣL(1,𝔽16) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C23×#120 | 2 |
| C2×C23×#100 | 2 |
| C2×C23×#99 | 2 |
| C23×AΣL(1,𝔽16) | 2 |
| C2×AΣL(1,𝔽16) | 23 |