Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
1556 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 1556 conjugacy classes of subgroups — too many to draw. Only its 142 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×C41 | B(4,𝔽2) |
| commutator | C2×D4 | C22×C4×C41 |
| Frattini, cosocle | C22×D4 | C23×C41 |
| prime radical | C2×D42×C41 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C23×C41 ◁ C22×D4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C41×#353 | C2 | semidirect |
| 3. C2×C41×AΣL(1,𝔽16) | C2 | semidirect |
| 4. C41×#1889 | C2 | semidirect |
| 5. C41×#1887 | C2 | semidirect |
| 9. D42×C41 | C4 | semidirect |
| 14. C41×#518 | C22 | semidirect |
| 17. C2×#100×C41 | C22 | semidirect |
| 18. C2×#99×C41 | C22 | semidirect |
| 74. C24×C41 | C22⋊C4 | semidirect |
| 93. C2×D4×C41 | C22⋊C4 | semidirect |
| 118. C22⋊C4×C41 | C22⋊C4 | semidirect |
| 121. C42×C41 | C22⋊C4 | semidirect |
| 173. #12759 | C41 | direct (N × H) |
| 204. C2×#353 | C2×C41 | semidirect |
| 205. C2×AΣL(1,𝔽16) | C2×C41 | semidirect |
| 206. #1889 | C2×C41 | semidirect |
| 207. #1887 | C2×C41 | semidirect |
| 219. D42 | C4×C41 | semidirect |
| 224. #518 | C22×C41 | semidirect |
| 227. C2×#100 | C22×C41 | semidirect |
| 228. C2×#99 | C22×C41 | semidirect |
| 234. C41 | #12759 | direct (N × H) |
| 285. C24 | C22⋊C4×C41 | semidirect |
| 304. C2×D4 | C22⋊C4×C41 | semidirect |
| 329. C22⋊C4 | C22⋊C4×C41 | semidirect |
| 332. C42 | C22⋊C4×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D42×C41 | 2 |
| C2×C41×#353 | 2 |
| C2×C41×AΣL(1,𝔽16) | 2 |
| C41×#1889 | 2 |
| C41×#1887 | 2 |
| #12759 | 41 |