Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
426 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C79 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C4×Q8×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #550×C79 | C2 | semidirect |
| 2. D4×Q8×C79 | C2 | semidirect |
| 3. #486×C79 | C2 | semidirect |
| 4. #474×C79 | C2 | semidirect |
| 5. #459×C79 | C2 | semidirect |
| 6. C8×Q8×C79 | C2 | semidirect |
| 7. C4×D8×C79 | C2 | semidirect |
| 47. Q8×C79 | D8 | semidirect |
| 53. D4×C79 | #41 | semidirect |
| 81. #3358 | C79 | direct (N × H) |
| 82. C79 | #3358 | direct (N × H) |
| 83. #550 | C2×C79 | semidirect |
| 84. D4×Q8 | C2×C79 | semidirect |
| 85. #486 | C2×C79 | semidirect |
| 86. #474 | C2×C79 | semidirect |
| 87. #459 | C2×C79 | semidirect |
| 88. C8×Q8 | C2×C79 | semidirect |
| 89. C4×D8 | C2×C79 | semidirect |
| 129. Q8 | D8×C79 | semidirect |
| 135. D4 | #41×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #550×C79 | 2 |
| D4×Q8×C79 | 2 |
| #486×C79 | 2 |
| #474×C79 | 2 |
| #459×C79 | 2 |
| C8×Q8×C79 | 2 |
| C4×D8×C79 | 2 |
| #3358 | 79 |