Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
254 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C79 | C2×D8 |
| commutator | C8 | C22×C8×C79 |
| Frattini, cosocle | C4×C8 | C23×C79 |
| socle | C22×C79 | C4×D8 |
| prime radical | C2×D16×C79 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C79 ◁ C4×C8×C79 ◁ C82×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C8×D8×C79 | C2 | semidirect |
| 3. C79×#1372 | C2 | semidirect |
| 4. C79×#1331 | C2 | semidirect |
| 5. C79×#1311 | C2 | semidirect |
| 19. D16×C79 | C8 | semidirect |
| 33. D8×C79 | C2×C8 | semidirect |
| 45. C16×C79 | C2×C8 | semidirect |
| 70. #12045 | C79 | direct (N × H) |
| 76. C8×D8 | C2×C79 | semidirect |
| 77. #1372 | C2×C79 | semidirect |
| 78. #1331 | C2×C79 | semidirect |
| 79. #1311 | C2×C79 | semidirect |
| 80. C79 | #12045 | direct (N × H) |
| 94. D16 | C8×C79 | semidirect |
| 108. D8 | C2×C8×C79 | semidirect |
| 120. C16 | C2×C8×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D16×C79 | 2 |
| C8×D8×C79 | 2 |
| C79×#1372 | 2 |
| C79×#1331 | 2 |
| C79×#1311 | 2 |
| #12045 | 79 |