Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
510 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 94 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×C149 | AΣL(1,𝔽16) |
| commutator | C2×Q8 | C22×C4×C149 |
| Frattini, cosocle | #124 | C23×C149 |
| prime radical | C2×#454×C149 | C2 |
| LCS | G ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C23×C149 ◁ C22×C4×C149 ◁ C2×#124×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#354×C149 | C2 | semidirect |
| 3. C2×#329×C149 | C2 | semidirect |
| 4. #1404×C149 | C2 | direct (N × H) |
| 5. C2×2−1+4×C149 | C4 | semidirect |
| 10. #454×C149 | C4 | semidirect |
| 13. C2×#101×C149 | C4 | semidirect |
| 17. #354×C149 | C22 | semidirect |
| 19. #329×C149 | C22 | semidirect |
| 23. 2−1+4×C149 | C2×C4 | semidirect |
| 48. #101×C149 | C2×C4 | semidirect |
| 175. C2×C149 | #1404 | direct (N × H) |
| 177. C2×#1404 | C149 | direct (N × H) |
| 178. C149 | C2×#1404 | direct (N × H) |
| 180. C2×#354 | C2×C149 | semidirect |
| 181. C2×#329 | C2×C149 | semidirect |
| 182. #1404 | C2×C149 | direct (N × H) |
| 183. C2×2−1+4 | C4×C149 | semidirect |
| 188. #454 | C4×C149 | semidirect |
| 191. C2×#101 | C4×C149 | semidirect |
| 195. #354 | C22×C149 | semidirect |
| 197. #329 | C22×C149 | semidirect |
| 201. 2−1+4 | C2×C4×C149 | semidirect |
| 226. #101 | C2×C4×C149 | semidirect |
| 353. C2 | #1404×C149 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#454×C149 | 2 |
| C2×#354×C149 | 2 |
| C2×#329×C149 | 2 |
| #1404×C149 | 2 |
| C2×#1404 | 149 |