Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
250 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 146 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×C479 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C479 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C479 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #126×C479 | C2 | semidirect |
| 2. #124×C479 | C2 | semidirect |
| 3. #123×C479 | C2 | semidirect |
| 4. C22⋊Q8×C479 | C2 | semidirect |
| 5. #121×C479 | C2 | semidirect |
| 6. #121×C479 | C2 | semidirect |
| 7. #120×C479 | C2 | semidirect |
| 8. C4×D4×C479 | C2 | semidirect |
| 9. C2×C22⋊C4×C479 | C2 | semidirect |
| 11. C2×Q8×C479 | C22 | semidirect |
| 15. C2×D4×C479 | C22 | semidirect |
| 18. C22×C4×C479 | C22 | semidirect |
| 19. C4⋊C4×C479 | C22 | semidirect |
| 20. C4⋊C4×C479 | C22 | semidirect |
| 21. C4⋊C4×C479 | C22 | semidirect |
| 22. C4⋊C4×C479 | C22 | semidirect |
| 28. C22⋊C4×C479 | C22 | semidirect |
| 29. C22⋊C4×C479 | C22 | semidirect |
| 30. C42×C479 | C22 | semidirect |
| 74. C479 | #538 | direct (N × H) |
| 75. #538 | C479 | direct (N × H) |
| 76. #126 | C2×C479 | semidirect |
| 77. #124 | C2×C479 | semidirect |
| 78. #123 | C2×C479 | semidirect |
| 79. C22⋊Q8 | C2×C479 | semidirect |
| 80. #121 | C2×C479 | semidirect |
| 81. #121 | C2×C479 | semidirect |
| 82. #120 | C2×C479 | semidirect |
| 83. C4×D4 | C2×C479 | semidirect |
| 84. C2×C22⋊C4 | C2×C479 | semidirect |
| 86. C2×Q8 | C22×C479 | semidirect |
| 90. C2×D4 | C22×C479 | semidirect |
| 93. C22×C4 | C22×C479 | semidirect |
| 94. C4⋊C4 | C22×C479 | semidirect |
| 95. C4⋊C4 | C22×C479 | semidirect |
| 96. C4⋊C4 | C22×C479 | semidirect |
| 97. C4⋊C4 | C22×C479 | semidirect |
| 103. C22⋊C4 | C22×C479 | semidirect |
| 104. C22⋊C4 | C22×C479 | semidirect |
| 105. C42 | C22×C479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #126×C479 | 2 |
| #124×C479 | 2 |
| #123×C479 | 2 |
| C22⋊Q8×C479 | 2 |
| #121×C479 | 2 |
| #120×C479 | 2 |
| C4×D4×C479 | 2 |
| C2×C22⋊C4×C479 | 2 |
| #538 | 479 |