← #22618869
Subgroups — #22618869
Order 9344.
348 conjugacy classes of subgroups.
The subgroup lattice has 168 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #17989140 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #17988717 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #17988715 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #17988615 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #17988614 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #17988610 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #17988542 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×#14556501 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #405×C73 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C2×#11924012 | C22 | 1 | 1 | yes | characteristic |
| 11 | C22×#10596831 | C22 | 1 | 1 | yes | characteristic |
| 12 | #14556590 | C4 | 1 | 2 | yes | — |
| 13 | #14556582 | C4 | 1 | 2 | yes | — |
| 14 | #14556568 | C4 | 1 | 4 | yes | — |
| 15 | C4×Dic146 | C22 | 1 | 4 | yes | — |
| 16 | #14556550 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C4×Dic73 | C22 | 1 | 1 | yes | characteristic |
| 18 | C4⋊#10596831 | C22 | 1 | 4 | yes | — |
| 19 | #14556520 | C22 | 1 | 4 | yes | — |
| 20 | #14556520 | C22 | 1 | 4 | yes | — |
| 21 | #14556501 | C22 | 1 | 2 | yes | — |
| 22 | #14556501 | C22 | 1 | 2 | yes | — |
| 23 | #14556501 | C22 | 1 | 2 | yes | — |
| 24 | C8×Dic73 | C22 | 1 | 2 | yes | — |
| 25 | C2×M16×C73 | C22 | 1 | 1 | yes | characteristic |
| 26 | C22×C8×C73 | C22 | 1 | 1 | yes | characteristic |
| 27 | #117×C73 | C22 | 1 | 1 | yes | characteristic |
| 28 | #97×C73 | C22 | 1 | 2 | yes | — |
| 29 | C4×C8×C73 | C22 | 1 | 2 | yes | — |
| 30 | C2×Dic146 | C2×C4 | 1 | 4 | yes | — |
| 31 | C22×Dic73 | C2×C4 | 1 | 2 | yes | — |
| 32 | #11924012 | — | 2 | 2 | no | — |
| 33 | C2×#10596831 | — | 2 | 2 | no | — |
| 34 | C2×#10596831 | C23 | 1 | 2 | yes | — |
| 35 | C2×#10596831 | C23 | 1 | 2 | yes | — |
| 36 | C4⋊Dic73 | C2×C4 | 1 | 2 | yes | — |
| 37 | C4⋊Dic73 | C2×C4 | 1 | 4 | yes | — |
| 38 | #11924007 | C2×C4 | 1 | 4 | yes | — |
| 39 | #11924007 | C2×C4 | 1 | 4 | yes | — |
| 40 | C22⋊Dic73 | C2×C4 | 1 | 2 | yes | — |
| 41 | C4×Dic73 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | C4×Dic73 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | C4×Dic73 | C23 | 1 | 2 | yes | — |
| 44 | C4×Dic73 | C23 | 1 | 2 | yes | — |
| 45 | C22×C4×C73 | C23 | 1 | 1 | yes | characteristic |
| 46 | M16×C73 | — | 2 | 2 | no | — |
| 47 | C2×C8×C73 | Q8 | 1 | 4 | yes | complemented |
| 48 | C2×C8×C73 | C23 | 1 | 2 | yes | — |
| 49 | C2×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 51 | C4⋊C4×C73 | C2×C4 | 1 | 2 | yes | — |
| 52 | C22⋊C4×C73 | C2×C4 | 1 | 2 | yes | — |
| 53 | C42×C73 | C23 | 1 | 2 | yes | — |
| 54 | C23×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 55 | C2×C4×C73 | C22×C4 | 1 | 4 | yes | — |
| 56 | C2×C4×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 57 | C2×C4×C73 | C2×Q8 | 1 | 2 | yes | — |
| 58 | C2×C4×C73 | #41 | 1 | 2 | yes | — |
| 59 | C2×C4×C73 | C24 | 1 | 1 | yes | characteristic |
| 60 | C2×Dic73 | — | 4 | 2 | no | — |
| 61 | C2×Dic73 | C22×C4 | 1 | 2 | yes | — |
| 62 | C2×Dic73 | C22×C4 | 1 | 2 | yes | — |
| 63 | C2×Dic73 | C22×C4 | 1 | 4 | yes | — |
| 64 | Dic146 | — | 4 | 4 | no | — |
| 65 | C8×C73 | — | 2 | 2 | no | — |
| 66 | C8×C73 | C2×Q8 | 1 | 2 | yes | — |
| 67 | C8×C73 | C2×Q8 | 1 | 2 | yes | — |
| 68 | #10596831 | — | 2 | 2 | no | — |
| 69 | #10596831 | — | 2 | 2 | no | — |
| 70 | C22×C73 | — | 2 | 2 | no | — |
| 71 | C22×C73 | C4×Q8 | 1 | 2 | yes | — |
| 72 | C22×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 73 | C4×C73 | — | 2 | 4 | no | — |
| 74 | C4×C73 | C4×Q8 | 1 | 2 | yes | — |
| 75 | C4×C73 | C22×Q8 | 1 | 1 | yes | characteristic |
| 76 | C4×C73 | C2×#41 | 1 | 1 | yes | characteristic |
| 77 | Dic73 | — | 2 | 2 | no | — |
| 78 | Dic73 | — | 2 | 4 | no | — |
| 79 | Dic73 | — | 2 | 2 | no | — |
| 80 | C2×C73 | — | 2 | 2 | no | — |
| 81 | C2×C73 | C2×C4×Q8 | 1 | 1 | yes | characteristic |
| 82 | C2×C73 | #568 | 1 | 2 | yes | — |
| 83 | #2961 | — | 73 | 1 | no | maximal, Sylow |
| 84 | C73 | #2961 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 85 | #533 | — | 73 | 1 | no | — |
| 86 | #446 | — | 73 | 4 | no | — |
| 87 | #446 | — | 73 | 4 | no | — |
| 88 | #424 | — | 73 | 1 | no | — |
| 89 | #424 | — | 73 | 1 | no | — |
| 90 | #423 | — | 73 | 1 | no | — |
| 91 | #405 | — | 73 | 1 | no | — |
| 92 | #405 | D73 | 1 | 1 | yes | characteristic |
| 93 | C2×#97 | — | 73 | 1 | no | — |
| 94 | C2×M16 | — | 73 | 1 | no | — |
| 95 | C2×M16 | C2×D73 | 1 | 1 | yes | characteristic |
| 96 | C22×C8 | — | 73 | 1 | no | — |
| 97 | C22×C8 | C2×D73 | 1 | 1 | yes | characteristic |
| 98 | C4⋊Q8 | — | 73 | 2 | no | — |
| 99 | #125 | — | 73 | 2 | no | — |
| 100 | C22⋊Q8 | — | 73 | 4 | no | — |
| 101 | C4×Q8 | — | 73 | 4 | no | — |
| 102 | #117 | — | 73 | 1 | no | — |
| 103 | #117 | C2×D73 | 1 | 1 | yes | characteristic |
| 104 | C2×C42 | — | 73 | 1 | no | — |
| 105 | C4⋊C8 | — | 73 | 4 | no | — |
| 106 | C4⋊C8 | — | 73 | 4 | no | — |
| 107 | C4⋊C8 | — | 73 | 4 | no | — |
| 108 | #97 | — | 73 | 2 | no | — |
| 109 | #97 | — | 73 | 2 | no | — |
| 110 | #97 | — | 73 | 2 | no | — |
| 111 | #97 | C2×D73 | 1 | 2 | yes | — |
| 112 | C4×C8 | — | 73 | 2 | no | — |
| 113 | C4×C8 | C2×D73 | 1 | 2 | yes | — |
| 114 | C2×Q8 | — | 73 | 4 | no | — |
| 115 | C22×C4 | — | 73 | 2 | no | — |
| 116 | C22×C4 | C22×D73 | 1 | 1 | yes | characteristic |
| 117 | M16 | — | 2 | 2 | no | — |
| 118 | M16 | — | 146 | 2 | no | — |
| 119 | C2×C8 | — | 73 | 2 | no | — |
| 120 | C2×C8 | — | 73 | 2 | no | — |
| 121 | C2×C8 | — | 146 | 2 | no | — |
| 122 | C2×C8 | Dic146 | 1 | 4 | yes | complemented |
| 123 | C2×C8 | C22×D73 | 1 | 2 | yes | — |
| 124 | C2×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 125 | C2×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 126 | C4⋊C4 | — | 73 | 4 | no | — |
| 127 | C4⋊C4 | — | 73 | 4 | no | — |
| 128 | C4⋊C4 | — | 73 | 2 | no | — |
| 129 | C4⋊C4 | — | 73 | 4 | no | — |
| 130 | C4⋊C4 | C4×D73 | 1 | 2 | yes | — |
| 131 | C22⋊C4 | — | 73 | 2 | no | — |
| 132 | C22⋊C4 | C4×D73 | 1 | 2 | yes | — |
| 133 | C42 | — | 73 | 1 | no | — |
| 134 | C42 | — | 73 | 1 | no | — |
| 135 | C42 | — | 73 | 2 | no | — |
| 136 | C42 | — | 73 | 2 | no | — |
| 137 | C42 | C22×D73 | 1 | 2 | yes | — |
| 138 | C23 | C2×C4×D73 | 1 | 1 | yes | characteristic |
| 139 | Q8 | — | 292 | 4 | no | — |
| 140 | C2×C4 | — | 292 | 2 | no | — |
| 141 | C2×C4 | — | 73 | 2 | no | — |
| 142 | C2×C4 | — | 73 | 2 | no | — |
| 143 | C2×C4 | — | 73 | 4 | no | — |
| 144 | C2×C4 | C2×C4×D73 | 1 | 4 | yes | — |
| 145 | C2×C4 | C2×C4×D73 | 1 | 1 | yes | characteristic |
| 146 | C2×C4 | C2×Dic146 | 1 | 2 | yes | — |
| 147 | C2×C4 | #11924028 | 1 | 2 | yes | — |
| 148 | C2×C4 | C23×D73 | 1 | 1 | yes | characteristic |
| 149 | C8 | — | 2 | 2 | no | — |
| 150 | C8 | — | 146 | 2 | no | — |
| 151 | C8 | — | 146 | 2 | no | — |
| 152 | C8 | C2×Dic146 | 1 | 2 | yes | — |
| 153 | C8 | C2×Dic146 | 1 | 2 | yes | — |
| 154 | C22 | — | 2 | 2 | no | — |
| 155 | C22 | C4×Dic146 | 1 | 2 | yes | — |
| 156 | C22 | C22×C4×D73 | 1 | 1 | yes | characteristic |
| 157 | C4 | — | 2 | 4 | no | — |
| 158 | C4 | — | 146 | 2 | no | — |
| 159 | C4 | — | 146 | 2 | no | — |
| 160 | C4 | — | 146 | 4 | no | — |
| 161 | C4 | C4×Dic146 | 1 | 2 | yes | — |
| 162 | C4 | C22×Dic146 | 1 | 1 | yes | characteristic |
| 163 | C4 | C2×#11924028 | 1 | 1 | yes | characteristic |
| 164 | C2 | — | 2 | 2 | no | — |
| 165 | C2 | C2×C4×Dic146 | 1 | 1 | yes | characteristic |
| 166 | C2 | #17989352 | 1 | 2 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Finite Group Databasebeta