← #20291285
Subgroups — #20291285
Order 6784.
556 conjugacy classes of subgroups.
The subgroup lattice has 184 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | D53⋊#131 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #41×#6157 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #16811589 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #16811586 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | M16×#6157 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C2×#13133271 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #131×D53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #13133305 | C4 | 1 | 2 | yes | complemented |
| 9 | #13133304 | C4 | 1 | 6 | yes | complemented |
| 10 | D53⋊M16 | C22 | 1 | 3 | yes | — |
| 11 | C2×D53⋊C8 | C22 | 1 | 3 | yes | — |
| 12 | Q8×#6157 | C4 | 1 | 2 | yes | — |
| 13 | D4×#6157 | C4 | 1 | 6 | yes | — |
| 14 | #13133296 | C22 | 1 | 3 | yes | — |
| 15 | C2×C4×#6157 | C22 | 1 | 3 | yes | — |
| 16 | #13133271 | C22 | 1 | 1 | yes | characteristic |
| 17 | #13133271 | C22 | 1 | 3 | yes | — |
| 18 | #13133271 | C22 | 1 | 3 | yes | — |
| 19 | #13133271 | C22 | 1 | 3 | yes | — |
| 20 | C8×#6157 | C22 | 1 | 6 | yes | — |
| 21 | #41×D53 | C22 | 1 | 1 | yes | characteristic |
| 22 | #13133225 | C4 | 1 | 3 | yes | complemented |
| 23 | #13133224 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #13133223 | C4 | 1 | 3 | yes | complemented |
| 25 | M16×D53 | C22 | 1 | 3 | yes | — |
| 26 | C2×C8×D53 | C22 | 1 | 3 | yes | — |
| 27 | #131×C53 | C4 | 1 | 1 | yes | characteristic, complemented |
| 28 | C22×#6157 | C2×C4 | 1 | 6 | yes | — |
| 29 | #41×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | #11719949 | C2×C4 | 1 | 1 | yes | characteristic |
| 31 | Q8×D53 | C2×C4 | 1 | 1 | yes | characteristic |
| 32 | #11719947 | C2×C4 | 1 | 3 | yes | — |
| 33 | D4×D53 | C2×C4 | 1 | 3 | yes | — |
| 34 | #11719945 | C2×C4 | 1 | 3 | yes | — |
| 35 | C2×C4×D53 | C23 | 1 | 3 | yes | — |
| 36 | C22⋊#6157 | C2×C4 | 1 | 6 | yes | — |
| 37 | #11719940 | C2×C4 | 1 | 6 | yes | complemented |
| 38 | C2×#88324 | C2×C4 | 1 | 6 | yes | complemented |
| 39 | C4⋊#6157 | C2×C4 | 1 | 6 | yes | — |
| 40 | C4×#6157 | C2×C4 | 1 | 6 | yes | — |
| 41 | C4×#6157 | C23 | 1 | 3 | yes | — |
| 42 | C4×#6157 | C23 | 1 | 1 | yes | characteristic |
| 43 | #11719936 | C2×C4 | 1 | 6 | yes | complemented |
| 44 | D53⋊C8 | C2×C4 | 1 | 6 | yes | complemented |
| 45 | D53⋊C8 | C23 | 1 | 3 | yes | — |
| 46 | D53⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 47 | M16×C53 | C2×C4 | 1 | 3 | yes | complemented |
| 48 | C2×C8×C53 | C2×C4 | 1 | 3 | yes | complemented |
| 49 | #11719917 | C2×C4 | 1 | 3 | yes | complemented |
| 50 | C2×#88322 | C2×C4 | 1 | 3 | yes | complemented |
| 51 | #11719912 | C2×C4 | 1 | 6 | yes | complemented |
| 52 | C8×D53 | C2×C4 | 1 | 3 | yes | complemented |
| 53 | C8×D53 | C2×C4 | 1 | 3 | yes | complemented |
| 54 | C8×D53 | C23 | 1 | 1 | yes | characteristic |
| 55 | C8×D53 | C23 | 1 | 3 | yes | — |
| 56 | C22×D53 | C22×C4 | 1 | 3 | yes | — |
| 57 | C2×#6157 | — | 4 | 6 | no | — |
| 58 | C2×#6157 | C22×C4 | 1 | 2 | yes | — |
| 59 | C2×#6157 | C22×C4 | 1 | 6 | yes | — |
| 60 | Q8×C53 | C42 | 1 | 1 | yes | characteristic |
| 61 | D4×C53 | C42 | 1 | 3 | yes | — |
| 62 | C2×C4×C53 | C22×C4 | 1 | 3 | yes | — |
| 63 | C22⋊D53 | C42 | 1 | 6 | yes | — |
| 64 | C2×Dic53 | C22×C4 | 1 | 3 | yes | — |
| 65 | D212 | C42 | 1 | 3 | yes | — |
| 66 | C4×D53 | C22×C4 | 1 | 3 | yes | — |
| 67 | C4×D53 | C22×C4 | 1 | 3 | yes | — |
| 68 | C4×D53 | C22×C4 | 1 | 3 | yes | — |
| 69 | C4×D53 | C24 | 1 | 1 | yes | characteristic |
| 70 | Dic106 | C42 | 1 | 3 | yes | — |
| 71 | #88324 | C22×C4 | 1 | 6 | yes | — |
| 72 | #88324 | C22×C4 | 1 | 2 | yes | — |
| 73 | C8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 74 | C8×C53 | C22×C4 | 1 | 3 | yes | — |
| 75 | #88322 | C22×C4 | 1 | 1 | yes | characteristic |
| 76 | #88322 | C22×C4 | 1 | 3 | yes | — |
| 77 | C22×C53 | C2×C42 | 1 | 3 | yes | — |
| 78 | C2×D53 | — | 2 | 6 | no | — |
| 79 | C2×D53 | C2×C42 | 1 | 3 | yes | — |
| 80 | C2×D53 | C23×C4 | 1 | 1 | yes | characteristic |
| 81 | #6157 | — | 2 | 2 | no | — |
| 82 | #6157 | — | 2 | 6 | no | — |
| 83 | C4×C53 | C2×C42 | 1 | 3 | yes | — |
| 84 | C4×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 85 | Dic53 | C2×C42 | 1 | 3 | yes | — |
| 86 | Dic53 | C23×C4 | 1 | 1 | yes | characteristic |
| 87 | #2875 | — | 53 | 1 | no | maximal, Sylow |
| 88 | C2×C53 | — | 2 | 3 | no | — |
| 89 | C2×C53 | C22×C42 | 1 | 1 | yes | characteristic |
| 90 | D53 | — | 2 | 3 | no | — |
| 91 | D53 | #568 | 1 | 2 | yes | — |
| 92 | C2×#131 | — | 53 | 1 | no | — |
| 93 | C2×#131 | — | 53 | 1 | no | — |
| 94 | C4×#41 | — | 53 | 1 | no | — |
| 95 | #405 | — | 53 | 3 | no | — |
| 96 | #405 | — | 53 | 3 | no | — |
| 97 | C4×M16 | — | 53 | 3 | no | — |
| 98 | C2×#97 | — | 53 | 3 | no | — |
| 99 | C53 | #2875 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 100 | C2×#41 | — | 53 | 1 | no | — |
| 101 | #131 | — | 53 | 6 | no | — |
| 102 | #131 | — | 53 | 2 | no | — |
| 103 | #131 | — | 53 | 1 | no | — |
| 104 | #131 | — | 53 | 3 | no | — |
| 105 | #131 | — | 53 | 3 | no | — |
| 106 | #131 | #6157 | 1 | 1 | yes | characteristic, complemented |
| 107 | C2×M16 | — | 53 | 3 | no | — |
| 108 | C2×M16 | — | 53 | 3 | no | — |
| 109 | C22×C8 | — | 53 | 3 | no | — |
| 110 | C22×C8 | — | 53 | 3 | no | — |
| 111 | C4×Q8 | — | 53 | 2 | no | — |
| 112 | C4×D4 | — | 53 | 6 | no | — |
| 113 | #117 | — | 53 | 3 | no | — |
| 114 | C2×C42 | — | 53 | 3 | no | — |
| 115 | #97 | — | 53 | 1 | no | — |
| 116 | #97 | — | 53 | 3 | no | — |
| 117 | #97 | — | 53 | 3 | no | — |
| 118 | #97 | — | 53 | 3 | no | — |
| 119 | C4×C8 | — | 53 | 6 | no | — |
| 120 | #41 | — | 53 | 1 | no | — |
| 121 | #41 | — | 53 | 3 | no | — |
| 122 | #41 | — | 53 | 3 | no | — |
| 123 | #41 | C2×#6157 | 1 | 1 | yes | characteristic |
| 124 | C2×Q8 | — | 53 | 1 | no | — |
| 125 | C2×D4 | — | 53 | 3 | no | — |
| 126 | C22×C4 | — | 53 | 3 | no | — |
| 127 | C22×C4 | — | 53 | 6 | no | — |
| 128 | M16 | — | 53 | 6 | no | — |
| 129 | M16 | — | 53 | 6 | no | — |
| 130 | M16 | — | 53 | 3 | no | — |
| 131 | M16 | — | 53 | 6 | no | — |
| 132 | M16 | C2×#6157 | 1 | 3 | yes | complemented |
| 133 | C2×C8 | — | 53 | 6 | no | — |
| 134 | C2×C8 | — | 53 | 3 | no | — |
| 135 | C2×C8 | — | 53 | 1 | no | — |
| 136 | C2×C8 | — | 53 | 6 | no | — |
| 137 | C2×C8 | — | 53 | 3 | no | — |
| 138 | C2×C8 | — | 53 | 3 | no | — |
| 139 | C2×C8 | — | 53 | 1 | no | — |
| 140 | C2×C8 | — | 53 | 3 | no | — |
| 141 | C2×C8 | — | 53 | 3 | no | — |
| 142 | C2×C8 | C2×#6157 | 1 | 3 | yes | complemented |
| 143 | C4⋊C4 | — | 53 | 6 | no | — |
| 144 | C22⋊C4 | — | 53 | 6 | no | — |
| 145 | C42 | — | 53 | 6 | no | — |
| 146 | C42 | — | 53 | 3 | no | — |
| 147 | C42 | — | 53 | 1 | no | — |
| 148 | C23 | — | 53 | 3 | no | — |
| 149 | Q8 | — | 53 | 3 | no | — |
| 150 | Q8 | C4×#6157 | 1 | 1 | yes | characteristic |
| 151 | D4 | — | 53 | 6 | no | — |
| 152 | D4 | — | 53 | 3 | no | — |
| 153 | D4 | C4×#6157 | 1 | 3 | yes | — |
| 154 | C2×C4 | — | 53 | 3 | no | — |
| 155 | C2×C4 | — | 53 | 3 | no | — |
| 156 | C2×C4 | — | 53 | 3 | no | — |
| 157 | C2×C4 | — | 53 | 3 | no | — |
| 158 | C2×C4 | — | 53 | 1 | no | — |
| 159 | C2×C4 | — | 53 | 2 | no | — |
| 160 | C2×C4 | — | 53 | 6 | no | — |
| 161 | C2×C4 | — | 212 | 6 | no | — |
| 162 | C2×C4 | C22×#6157 | 1 | 3 | yes | — |
| 163 | C8 | — | 53 | 2 | no | — |
| 164 | C8 | — | 53 | 6 | no | — |
| 165 | C8 | — | 53 | 1 | no | — |
| 166 | C8 | — | 53 | 3 | no | — |
| 167 | C8 | C22×#6157 | 1 | 1 | yes | characteristic |
| 168 | C8 | C22×#6157 | 1 | 3 | yes | — |
| 169 | C22 | — | 53 | 1 | no | — |
| 170 | C22 | — | 53 | 3 | no | — |
| 171 | C22 | — | 106 | 6 | no | — |
| 172 | C22 | C2×C4×#6157 | 1 | 3 | yes | — |
| 173 | C4 | — | 53 | 1 | no | — |
| 174 | C4 | — | 53 | 3 | no | — |
| 175 | C4 | — | 106 | 2 | no | — |
| 176 | C4 | — | 106 | 6 | no | — |
| 177 | C4 | C2×C4×#6157 | 1 | 3 | yes | — |
| 178 | C4 | C23×#6157 | 1 | 1 | yes | characteristic |
| 179 | C2 | — | 2 | 3 | no | — |
| 180 | C2 | — | 53 | 2 | no | — |
| 181 | C2 | — | 106 | 3 | no | — |
| 182 | C2 | C22×C4×#6157 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Finite Group Databasebeta