Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
840 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D79 |
| commutator, socle, cosocle | C23×C79 | C24 |
| Fitting | #380×C79 | C2 |
| prime radical | C22×C22⋊D79 | C22 |
| hypercenter | #380 | D79 |
| hypocenter | C79 | #2409 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×Dic158 | C2 | semidirect |
| 2. C2×#14579141 | C2 | semidirect |
| 4. #19098484 | C2 | semidirect |
| 5. #19098476 | C2 | semidirect |
| 6. #19098468 | C2 | semidirect |
| 8. #19098438 | C2 | semidirect |
| 9. #380×C79 | C2 | semidirect |
| 37. C2×Dic158 | D4 | semidirect |
| 40. C2×C22⋊D79 | Q8 | semidirect |
| 73. C22×D79 | C2×Q8 | semidirect |
| 93. C2×Dic79 | C2×Q8 | semidirect |
| 101. C22×C79 | C22⋊Q8 | semidirect |
| 127. C79 | #2409 | semidirect |
| 136. #380 | D79 | semidirect |
| 233. C22 | #14579141 | semidirect |