Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
1386 conjugacy classes of subgroups; only the 366 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 366 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C41 |
| prime radical | C41×#2867 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C43×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C41×#460 | C2 | semidirect |
| 3. C42×Q8×C41 | C2 | semidirect |
| 4. C41×#1982 | C2 | semidirect |
| 5. C41×#1842 | C2 | semidirect |
| 29. C4×Q8×C41 | D4 | semidirect |
| 63. C42×C41 | SD16 | semidirect |
| 71. Q8×C41 | #127 | semidirect |
| 87. #33161 | C41 | direct (N × H) |
| 97. C4×C41 | #460 | semidirect |
| 100. C2×#460 | C2×C41 | semidirect |
| 102. C42×Q8 | C2×C41 | semidirect |
| 103. #1982 | C2×C41 | semidirect |
| 104. #1842 | C2×C41 | semidirect |
| 121. C41 | #33161 | direct (N × H) |
| 133. C4×Q8 | D4×C41 | semidirect |
| 167. C42 | SD16×C41 | semidirect |
| 175. Q8 | #127×C41 | semidirect |
| 200. C4 | C41×#460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C41×#460 | 2 |
| C41×#2867 | 2 |
| C42×Q8×C41 | 2 |
| C41×#1982 | 2 |
| C41×#1842 | 2 |
| #33161 | 41 |