Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
536 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 106 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 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C41 |
| prime radical | C2×#127×C41 | C22 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C2×C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#2734 | C2 | semidirect |
| 4. C41×#1272 | C2 | semidirect |
| 5. C41×#1271 | C2 | semidirect |
| 86. C4⋊C4×C41 | SD16 | semidirect |
| 127. #7741 | C41 | direct (N × H) |
| 146. #2734 | C2×C41 | semidirect |
| 149. #1272 | C2×C41 | semidirect |
| 150. #1271 | C2×C41 | semidirect |
| 170. C41 | #7741 | direct (N × H) |
| 238. C4⋊C4 | SD16×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#2734 | 2 |
| C41×#2041 | 2 |
| C41×#2014 | 2 |
| C41×#1272 | 2 |
| C41×#1271 | 2 |
| #7741 | 41 |