← #13506843
Subgroups — #13506843
Order 1792.
658 conjugacy classes of subgroups.
The subgroup lattice has 212 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C7×#2913 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11741230 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×#89912 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11728403 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #11728402 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #11728350 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×#89285 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C2×C7×#131 | C22 | 1 | 1 | yes | characteristic |
| 9 | C7×#520 | — | 2 | 1 | no | — |
| 10 | #90518 | — | 2 | 1 | no | — |
| 11 | C7×#428 | — | 2 | 3 | no | — |
| 12 | C7×#427 | C22 | 1 | 3 | yes | — |
| 13 | C2×C7×#107 | C22 | 1 | 3 | yes | — |
| 14 | #89912 | C4 | 1 | 8 | yes | complemented |
| 15 | #89893 | — | 2 | 3 | no | — |
| 16 | #89878 | C22 | 1 | 3 | yes | — |
| 17 | C2×#6392 | C22 | 1 | 3 | yes | — |
| 18 | C2×#6386 | C22 | 1 | 3 | yes | — |
| 19 | C22×C7⋊C16 | C22 | 1 | 3 | yes | — |
| 20 | #89285 | C22 | 1 | 1 | yes | characteristic |
| 21 | #89285 | C22 | 1 | 3 | yes | — |
| 22 | #89285 | C22 | 1 | 6 | yes | — |
| 23 | #89284 | C22 | 1 | 3 | yes | — |
| 24 | #89284 | C22 | 1 | 3 | yes | — |
| 25 | #33411 | — | 7 | 1 | no | maximal, Sylow |
| 26 | C2×C7×#41 | D4 | 1 | 1 | yes | characteristic |
| 27 | C7×#131 | C2×C4 | 1 | 4 | yes | — |
| 28 | C7×#131 | Q8 | 1 | 4 | yes | — |
| 29 | C2×C7×M16 | D4 | 1 | 3 | yes | — |
| 30 | C22×C7×C8 | C23 | 1 | 3 | yes | — |
| 31 | C4×C7×Q8 | — | 4 | 1 | no | — |
| 32 | C4×C7×D4 | — | 4 | 3 | no | — |
| 33 | C7×#117 | — | 2 | 3 | no | — |
| 34 | C2×C7×C4⋊C4 | — | 2 | 3 | no | — |
| 35 | Q8×Dic7 | — | 4 | 1 | no | — |
| 36 | D4×Dic7 | — | 4 | 3 | no | — |
| 37 | #6489 | — | 2 | 3 | no | — |
| 38 | C2×C4⋊Dic7 | — | 2 | 3 | no | — |
| 39 | C7×#107 | — | 2 | 3 | no | — |
| 40 | C7×#107 | C23 | 1 | 1 | yes | characteristic |
| 41 | C7×#107 | C23 | 1 | 3 | yes | — |
| 42 | C7×#106 | — | 2 | 3 | no | — |
| 43 | #6392 | — | 2 | 3 | no | — |
| 44 | #6392 | C23 | 1 | 3 | yes | — |
| 45 | #6392 | C23 | 1 | 1 | yes | characteristic |
| 46 | #6391 | — | 2 | 3 | no | — |
| 47 | #6386 | C2×C4 | 1 | 12 | yes | complemented |
| 48 | C2×C7⋊C16 | C2×C4 | 1 | 12 | yes | complemented |
| 49 | C2×C7⋊C16 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×C7⋊C16 | C23 | 1 | 3 | yes | — |
| 51 | C2×#504 | — | 7 | 1 | no | — |
| 52 | #2913 | — | 7 | 1 | no | — |
| 53 | #2913 | D7 | 1 | 1 | yes | characteristic |
| 54 | #2159 | — | 7 | 3 | no | — |
| 55 | #2159 | — | 7 | 3 | no | — |
| 56 | #2158 | — | 7 | 3 | no | — |
| 57 | C2×#367 | — | 7 | 3 | no | — |
| 58 | C7×#41 | C4⋊C4 | 1 | 4 | yes | — |
| 59 | C7×#41 | Q16 | 1 | 4 | yes | — |
| 60 | C2×C7×Q8 | D8 | 1 | 1 | yes | characteristic |
| 61 | C2×C7×D4 | D8 | 1 | 3 | yes | — |
| 62 | C22×C4×C7 | — | 4 | 3 | no | — |
| 63 | C22×C4×C7 | C2×D4 | 1 | 3 | yes | — |
| 64 | C22×Dic7 | — | 4 | 3 | no | — |
| 65 | C7×M16 | C4⋊C4 | 1 | 12 | yes | — |
| 66 | C2×C7×C8 | C22×C4 | 1 | 6 | yes | — |
| 67 | C2×C7×C8 | C2×D4 | 1 | 3 | yes | — |
| 68 | C2×C7×C8 | C2×Q8 | 1 | 6 | yes | — |
| 69 | C2×C7×C8 | C24 | 1 | 1 | yes | characteristic |
| 70 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 71 | C7×C4⋊C4 | — | 2 | 3 | no | — |
| 72 | C7×C4⋊C4 | — | 4 | 3 | no | — |
| 73 | C7×C22⋊C4 | — | 4 | 3 | no | — |
| 74 | C42×C7 | — | 4 | 3 | no | — |
| 75 | C22⋊Dic7 | — | 4 | 3 | no | — |
| 76 | C4⋊Dic7 | — | 2 | 3 | no | — |
| 77 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 78 | C4⋊Dic7 | — | 4 | 3 | no | — |
| 79 | C4×Dic7 | — | 4 | 3 | no | — |
| 80 | C7⋊C16 | C22×C4 | 1 | 2 | yes | — |
| 81 | C7⋊C16 | C22×C4 | 1 | 6 | yes | — |
| 82 | C2×#131 | C2×D7 | 1 | 1 | yes | characteristic |
| 83 | #520 | — | 2 | 1 | no | — |
| 84 | #520 | — | 14 | 1 | no | — |
| 85 | #504 | — | 7 | 8 | no | — |
| 86 | C2×M32 | — | 7 | 3 | no | — |
| 87 | C22×C16 | — | 7 | 3 | no | — |
| 88 | #428 | — | 2 | 3 | no | — |
| 89 | #428 | — | 14 | 3 | no | — |
| 90 | #427 | — | 7 | 3 | no | — |
| 91 | #427 | C2×D7 | 1 | 3 | yes | — |
| 92 | C2×#107 | — | 7 | 3 | no | — |
| 93 | C2×#107 | C2×D7 | 1 | 3 | yes | — |
| 94 | #367 | — | 7 | 3 | no | — |
| 95 | #367 | — | 7 | 6 | no | — |
| 96 | #367 | — | 7 | 1 | no | — |
| 97 | #366 | — | 7 | 3 | no | — |
| 98 | #366 | — | 7 | 3 | no | — |
| 99 | C23×C7 | C2×D8 | 1 | 3 | yes | — |
| 100 | C7×Q8 | #107 | 1 | 4 | yes | — |
| 101 | C7×D4 | #107 | 1 | 12 | yes | — |
| 102 | C2×C4×C7 | — | 4 | 1 | no | — |
| 103 | C2×C4×C7 | — | 4 | 3 | no | — |
| 104 | C2×C4×C7 | — | 16 | 3 | no | — |
| 105 | C2×C4×C7 | C2×C4⋊C4 | 1 | 6 | yes | — |
| 106 | C2×C4×C7 | C2×D8 | 1 | 3 | yes | — |
| 107 | C2×C4×C7 | C2×Q16 | 1 | 6 | yes | — |
| 108 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 109 | C2×Dic7 | — | 4 | 1 | no | — |
| 110 | C2×Dic7 | — | 4 | 3 | no | — |
| 111 | C2×Dic7 | — | 16 | 3 | no | — |
| 112 | C7×C8 | C2×C4⋊C4 | 1 | 6 | yes | — |
| 113 | C7×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 114 | C7×C8 | C22×Q8 | 1 | 1 | yes | characteristic |
| 115 | C2×#41 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 116 | #131 | Dic14 | 1 | 4 | yes | — |
| 117 | #131 | C4×D7 | 1 | 4 | yes | — |
| 118 | C2×M16 | C22⋊D7 | 1 | 3 | yes | — |
| 119 | C22×C8 | C22×D7 | 1 | 3 | yes | — |
| 120 | C4×Q8 | — | 4 | 1 | no | — |
| 121 | C4×Q8 | — | 28 | 1 | no | — |
| 122 | C4×D4 | — | 4 | 3 | no | — |
| 123 | C4×D4 | — | 28 | 3 | no | — |
| 124 | #117 | — | 2 | 3 | no | — |
| 125 | #117 | — | 14 | 3 | no | — |
| 126 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 127 | C2×C4⋊C4 | — | 14 | 3 | no | — |
| 128 | M32 | — | 7 | 12 | no | — |
| 129 | C2×C16 | — | 7 | 12 | no | — |
| 130 | C2×C16 | — | 7 | 3 | no | — |
| 131 | C2×C16 | — | 7 | 1 | no | — |
| 132 | #107 | — | 2 | 3 | no | — |
| 133 | #107 | — | 7 | 1 | no | — |
| 134 | #107 | — | 7 | 3 | no | — |
| 135 | #107 | — | 14 | 3 | no | — |
| 136 | #107 | C22×D7 | 1 | 1 | yes | characteristic |
| 137 | #107 | C22×D7 | 1 | 3 | yes | — |
| 138 | #106 | — | 2 | 3 | no | — |
| 139 | #106 | — | 14 | 3 | no | — |
| 140 | C22×C7 | — | 2 | 3 | no | — |
| 141 | C22×C7 | — | 2 | 3 | no | — |
| 142 | C22×C7 | C2×#107 | 1 | 6 | yes | — |
| 143 | C22×C7 | C22×D8 | 1 | 1 | yes | characteristic |
| 144 | C4×C7 | — | 8 | 1 | no | — |
| 145 | C4×C7 | — | 8 | 3 | no | — |
| 146 | C4×C7 | C2×#107 | 1 | 6 | yes | — |
| 147 | C4×C7 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 148 | C4×C7 | C22×Q16 | 1 | 1 | yes | characteristic |
| 149 | Dic7 | — | 8 | 1 | no | — |
| 150 | Dic7 | — | 8 | 3 | no | — |
| 151 | #41 | Dic7⋊C4 | 1 | 4 | yes | — |
| 152 | #41 | #1144 | 1 | 4 | yes | — |
| 153 | C2×Q8 | #1141 | 1 | 1 | yes | characteristic |
| 154 | C2×D4 | #1141 | 1 | 3 | yes | — |
| 155 | C22×C4 | — | 4 | 3 | no | — |
| 156 | C22×C4 | — | 28 | 3 | no | — |
| 157 | C22×C4 | C2×C22⋊D7 | 1 | 3 | yes | — |
| 158 | M16 | Dic7⋊C4 | 1 | 12 | yes | — |
| 159 | C2×C8 | C2×Dic14 | 1 | 6 | yes | — |
| 160 | C2×C8 | C2×C4×D7 | 1 | 6 | yes | — |
| 161 | C2×C8 | C2×C22⋊D7 | 1 | 3 | yes | — |
| 162 | C2×C8 | C23×D7 | 1 | 1 | yes | characteristic |
| 163 | C4⋊C4 | — | 2 | 1 | no | — |
| 164 | C4⋊C4 | — | 2 | 3 | no | — |
| 165 | C4⋊C4 | — | 4 | 3 | no | — |
| 166 | C4⋊C4 | — | 14 | 1 | no | — |
| 167 | C4⋊C4 | — | 14 | 3 | no | — |
| 168 | C4⋊C4 | — | 28 | 3 | no | — |
| 169 | C22⋊C4 | — | 4 | 3 | no | — |
| 170 | C22⋊C4 | — | 28 | 3 | no | — |
| 171 | C42 | — | 4 | 3 | no | — |
| 172 | C42 | — | 28 | 3 | no | — |
| 173 | C16 | — | 7 | 2 | no | — |
| 174 | C16 | — | 7 | 6 | no | — |
| 175 | C2×C7 | — | 2 | 6 | no | — |
| 176 | C2×C7 | C22×#107 | 1 | 1 | yes | characteristic |
| 177 | C2×C7 | #3416 | 1 | 1 | yes | characteristic |
| 178 | C2×C7 | #3416 | 1 | 1 | yes | characteristic |
| 179 | C23 | C2×#1141 | 1 | 3 | yes | — |
| 180 | Q8 | #6381 | 1 | 4 | yes | — |
| 181 | D4 | #6381 | 1 | 12 | yes | — |
| 182 | C2×C4 | — | 4 | 1 | no | — |
| 183 | C2×C4 | — | 4 | 3 | no | — |
| 184 | C2×C4 | — | 16 | 3 | no | — |
| 185 | C2×C4 | — | 28 | 1 | no | — |
| 186 | C2×C4 | — | 28 | 3 | no | — |
| 187 | C2×C4 | — | 112 | 3 | no | — |
| 188 | C2×C4 | C2×Dic7⋊C4 | 1 | 6 | yes | — |
| 189 | C2×C4 | C2×#1141 | 1 | 3 | yes | — |
| 190 | C2×C4 | C2×#1144 | 1 | 6 | yes | — |
| 191 | C2×C4 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 192 | C8 | C2×Dic7⋊C4 | 1 | 6 | yes | — |
| 193 | C8 | C22×Dic14 | 1 | 1 | yes | characteristic |
| 194 | C8 | C22×C4×D7 | 1 | 1 | yes | characteristic |
| 195 | C7 | #33411 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 196 | C22 | — | 2 | 3 | no | — |
| 197 | C22 | — | 2 | 3 | no | — |
| 198 | C22 | C2×#6381 | 1 | 6 | yes | — |
| 199 | C22 | C22×#1141 | 1 | 1 | yes | characteristic |
| 200 | C4 | — | 8 | 3 | no | — |
| 201 | C4 | — | 8 | 1 | no | — |
| 202 | C4 | — | 56 | 1 | no | — |
| 203 | C4 | — | 56 | 3 | no | — |
| 204 | C4 | C2×#6381 | 1 | 6 | yes | — |
| 205 | C4 | C22×Dic7⋊C4 | 1 | 1 | yes | characteristic |
| 206 | C4 | C22×#1144 | 1 | 1 | yes | characteristic |
| 207 | C2 | — | 2 | 6 | no | — |
| 208 | C2 | C22×#6381 | 1 | 1 | yes | characteristic |
| 209 | C2 | #11741453 | 1 | 1 | yes | characteristic |
| 210 | C2 | #11741461 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta