Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
498 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C149 | AΣL(1,𝔽16) |
| commutator | C2×Q8 | C22×C4×C149 |
| Frattini, cosocle | #124 | C23×C149 |
| socle | C2×C149 | C2×AΣL(1,𝔽16) |
| prime radical | #3018×C149 | C2 |
| LCS | G ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C149 ◁ C2×C4×C149 ◁ C22×C4×C149 ◁ #532×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2126×C149 | C2 | semidirect |
| 3. #1525×C149 | C2 | semidirect |
| 4. #1404×C149 | C2 | semidirect |
| 5. #585×C149 | C4 | semidirect |
| 8. #456×C149 | C4 | semidirect |
| 13. #413×C149 | C4 | semidirect |
| 16. #354×C149 | C22 | semidirect |
| 19. #329×C149 | C22 | semidirect |
| 174. #13568 | C149 | direct (N × H) |
| 175. C149 | #13568 | direct (N × H) |
| 177. #2126 | C2×C149 | semidirect |
| 178. #1525 | C2×C149 | semidirect |
| 179. #1404 | C2×C149 | semidirect |
| 180. #585 | C4×C149 | semidirect |
| 183. #456 | C4×C149 | semidirect |
| 188. #413 | C4×C149 | semidirect |
| 191. #354 | C22×C149 | semidirect |
| 194. #329 | C22×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3018×C149 | 2 |
| #2126×C149 | 2 |
| #1525×C149 | 2 |
| #1404×C149 | 2 |
| #13568 | 149 |