Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
238 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C79 | C2×#99 |
| commutator | C2×C4 | C22×C4×C79 |
| Frattini, cosocle | C2×D4 | C23×C79 |
| prime radical | C2×#41×C79 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C2×C4×C79 ◁ C2×#41×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #354×C79 | C2 | semidirect |
| 5. C22×Q8×C79 | C4 | semidirect |
| 6. C4⋊Q8×C79 | C4 | semidirect |
| 11. #117×C79 | C4 | semidirect |
| 64. #2129 | C79 | direct (N × H) |
| 65. C79 | #2129 | direct (N × H) |
| 68. #354 | C2×C79 | semidirect |
| 70. C22×Q8 | C4×C79 | semidirect |
| 71. C4⋊Q8 | C4×C79 | semidirect |
| 76. #117 | C4×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #536×C79 | 2 |
| #410×C79 | 2 |
| #354×C79 | 2 |
| #2129 | 79 |