← #34058509
Subgroups — #34058509
Order 19072.
1060 conjugacy classes of subgroups.
The subgroup lattice has 246 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | Q8×Dic298 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #23750351 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #23750336 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #23750335 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #23750290 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #23750252 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #23750179 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C4⋊Q8×D149 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #23750107 | C2 | 1 | 2 | yes | maximal |
| 10 | C4×#14558737 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | Q82×C149 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#14558737 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×Q8×D149 | C22 | 1 | 6 | yes | — |
| 14 | #18011911 | C22 | 1 | 3 | yes | — |
| 15 | #18011910 | C22 | 1 | 3 | yes | — |
| 16 | #18011910 | C22 | 1 | 6 | yes | — |
| 17 | #18011910 | C22 | 1 | 6 | yes | — |
| 18 | #18011909 | C22 | 1 | 6 | yes | — |
| 19 | #18011909 | C22 | 1 | 1 | yes | characteristic |
| 20 | #18011903 | C22 | 1 | 6 | yes | — |
| 21 | #18011902 | C22 | 1 | 6 | yes | — |
| 22 | #18011901 | C22 | 1 | 6 | yes | — |
| 23 | #18011891 | C22 | 1 | 3 | yes | — |
| 24 | #18011889 | C22 | 1 | 6 | yes | — |
| 25 | #18011889 | C22 | 1 | 12 | yes | — |
| 26 | #18011887 | C22 | 1 | 3 | yes | — |
| 27 | #18011887 | C22 | 1 | 12 | yes | — |
| 28 | Q8×Dic149 | C22 | 1 | 1 | yes | characteristic |
| 29 | Q8×Dic149 | C22 | 1 | 2 | yes | — |
| 30 | C4×Dic298 | C22 | 1 | 6 | yes | — |
| 31 | C4×Dic298 | C22 | 1 | 3 | yes | — |
| 32 | C4×D596 | C22 | 1 | 6 | yes | — |
| 33 | C4×D596 | C22 | 1 | 3 | yes | — |
| 34 | #18011873 | C22 | 1 | 3 | yes | — |
| 35 | #18011873 | C22 | 1 | 6 | yes | — |
| 36 | #18011869 | C22 | 1 | 3 | yes | — |
| 37 | #18011868 | C22 | 1 | 6 | yes | — |
| 38 | C4⋊C4×D149 | C22 | 1 | 6 | yes | — |
| 39 | C4⋊C4×D149 | C22 | 1 | 6 | yes | — |
| 40 | C42×D149 | C22 | 1 | 3 | yes | — |
| 41 | C4⋊Q8×C149 | C22 | 1 | 3 | yes | — |
| 42 | C4⋊Q8×C149 | C22 | 1 | 6 | yes | — |
| 43 | C4×Q8×C149 | C22 | 1 | 3 | yes | — |
| 44 | C4×Q8×C149 | C22 | 1 | 1 | yes | characteristic |
| 45 | C4×Q8×C149 | C22 | 1 | 2 | yes | — |
| 46 | #14558737 | Q8 | 1 | 8 | yes | complemented |
| 47 | C2×Dic298 | C23 | 1 | 1 | yes | characteristic |
| 48 | C2×Dic298 | C23 | 1 | 6 | yes | — |
| 49 | C2×Dic298 | C23 | 1 | 6 | yes | — |
| 50 | Q8×D149 | — | 4 | 12 | no | — |
| 51 | C2×D596 | C23 | 1 | 3 | yes | — |
| 52 | C2×C4×D149 | C23 | 1 | 3 | yes | — |
| 53 | C2×C4×D149 | C23 | 1 | 3 | yes | — |
| 54 | C2×C4×D149 | C23 | 1 | 12 | yes | — |
| 55 | C2×C4×D149 | C23 | 1 | 3 | yes | — |
| 56 | C4⋊Dic149 | C23 | 1 | 6 | yes | — |
| 57 | C4⋊Dic149 | C23 | 1 | 3 | yes | — |
| 58 | C4⋊Dic149 | C23 | 1 | 3 | yes | — |
| 59 | C4⋊Dic149 | C23 | 1 | 6 | yes | — |
| 60 | #14558715 | C23 | 1 | 6 | yes | — |
| 61 | #14558715 | C23 | 1 | 12 | yes | — |
| 62 | #14558715 | C23 | 1 | 2 | yes | — |
| 63 | #14558715 | C23 | 1 | 2 | yes | — |
| 64 | #14558715 | C23 | 1 | 6 | yes | — |
| 65 | #14558715 | C23 | 1 | 6 | yes | — |
| 66 | #14558713 | C23 | 1 | 6 | yes | — |
| 67 | #14558713 | C23 | 1 | 6 | yes | — |
| 68 | #14558713 | C23 | 1 | 6 | yes | — |
| 69 | C4×Dic149 | C23 | 1 | 3 | yes | — |
| 70 | C4×Dic149 | C23 | 1 | 1 | yes | characteristic |
| 71 | C4×Dic149 | C23 | 1 | 3 | yes | — |
| 72 | C4×Dic149 | C23 | 1 | 6 | yes | — |
| 73 | C2×Q8×C149 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×Q8×C149 | C23 | 1 | 6 | yes | — |
| 75 | C2×Q8×C149 | C23 | 1 | 1 | yes | characteristic |
| 76 | C4⋊C4×C149 | C23 | 1 | 3 | yes | — |
| 77 | C4⋊C4×C149 | C23 | 1 | 3 | yes | — |
| 78 | C4⋊C4×C149 | C23 | 1 | 6 | yes | — |
| 79 | C4⋊C4×C149 | C23 | 1 | 6 | yes | — |
| 80 | C42×C149 | C23 | 1 | 3 | yes | — |
| 81 | C42×C149 | C23 | 1 | 6 | yes | — |
| 82 | C22×D149 | C24 | 1 | 3 | yes | — |
| 83 | Dic298 | — | 2 | 2 | no | — |
| 84 | Dic298 | — | 2 | 12 | no | — |
| 85 | Dic298 | — | 4 | 6 | no | — |
| 86 | D596 | C2×Q8 | 1 | 12 | yes | complemented |
| 87 | C2×Dic149 | C24 | 1 | 6 | yes | — |
| 88 | C2×Dic149 | C24 | 1 | 3 | yes | — |
| 89 | C2×Dic149 | C24 | 1 | 2 | yes | — |
| 90 | C2×Dic149 | C24 | 1 | 1 | yes | characteristic |
| 91 | C2×Dic149 | C24 | 1 | 1 | yes | characteristic |
| 92 | C4×D149 | — | 2 | 6 | no | — |
| 93 | C4×D149 | — | 2 | 6 | no | — |
| 94 | C4×D149 | — | 4 | 12 | no | — |
| 95 | C4×D149 | C2×Q8 | 1 | 12 | yes | complemented |
| 96 | Q8×C149 | — | 2 | 2 | no | — |
| 97 | Q8×C149 | — | 4 | 6 | no | — |
| 98 | Q8×C149 | C2×Q8 | 1 | 4 | yes | complemented |
| 99 | C2×C4×C149 | C24 | 1 | 6 | yes | — |
| 100 | C2×C4×C149 | C24 | 1 | 3 | yes | — |
| 101 | C2×C4×C149 | C24 | 1 | 2 | yes | — |
| 102 | C2×C4×C149 | C24 | 1 | 3 | yes | — |
| 103 | C2×C4×C149 | C24 | 1 | 1 | yes | characteristic |
| 104 | C22×C149 | C25 | 1 | 1 | yes | characteristic |
| 105 | C2×D149 | — | 2 | 3 | no | — |
| 106 | C2×D149 | — | 2 | 3 | no | — |
| 107 | C2×D149 | C22×Q8 | 1 | 6 | yes | — |
| 108 | C4×C149 | — | 2 | 3 | no | — |
| 109 | C4×C149 | — | 2 | 6 | no | — |
| 110 | C4×C149 | — | 2 | 2 | no | — |
| 111 | C4×C149 | C22×Q8 | 1 | 6 | yes | — |
| 112 | C4×C149 | 2−1+4 | 1 | 2 | yes | — |
| 113 | Dic149 | — | 2 | 6 | no | — |
| 114 | Dic149 | — | 2 | 3 | no | — |
| 115 | Dic149 | — | 2 | 2 | no | — |
| 116 | Dic149 | C22×Q8 | 1 | 2 | yes | — |
| 117 | Dic149 | H(5,𝔽2) | 1 | 2 | yes | — |
| 118 | C2×C149 | C23×Q8 | 1 | 1 | yes | characteristic |
| 119 | C2×C149 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 120 | C2×C149 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 121 | D149 | — | 2 | 6 | no | — |
| 122 | C149 | #3503 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 123 | #3503 | — | 149 | 1 | no | maximal, Sylow |
| 124 | Q82 | — | 149 | 1 | no | — |
| 125 | Q82 | D149 | 1 | 1 | yes | characteristic, complemented |
| 126 | #557 | — | 149 | 2 | no | — |
| 127 | #554 | — | 149 | 3 | no | — |
| 128 | #554 | — | 149 | 3 | no | — |
| 129 | D4×Q8 | — | 149 | 6 | no | — |
| 130 | #544 | — | 149 | 6 | no | — |
| 131 | #533 | — | 149 | 3 | no | — |
| 132 | C2×C4⋊Q8 | — | 149 | 3 | no | — |
| 133 | #520 | — | 149 | 2 | no | — |
| 134 | C4×#41 | — | 149 | 1 | no | — |
| 135 | C2×#41 | — | 149 | 1 | no | — |
| 136 | C22×Q8 | — | 149 | 6 | no | — |
| 137 | C4⋊Q8 | — | 149 | 6 | no | — |
| 138 | C4⋊Q8 | — | 149 | 1 | no | — |
| 139 | C4⋊Q8 | — | 149 | 3 | no | — |
| 140 | C4⋊Q8 | — | 149 | 6 | no | — |
| 141 | C4⋊Q8 | — | 149 | 6 | no | — |
| 142 | C4⋊Q8 | — | 149 | 3 | no | — |
| 143 | C4⋊Q8 | C2×D149 | 1 | 3 | yes | — |
| 144 | C4⋊Q8 | C2×D149 | 1 | 6 | yes | — |
| 145 | #125 | — | 149 | 6 | no | — |
| 146 | #125 | — | 149 | 6 | no | — |
| 147 | #125 | — | 149 | 6 | no | — |
| 148 | C22⋊Q8 | — | 149 | 3 | no | — |
| 149 | C22⋊Q8 | — | 149 | 12 | no | — |
| 150 | C22⋊Q8 | — | 149 | 6 | no | — |
| 151 | C22⋊Q8 | — | 149 | 3 | no | — |
| 152 | C22⋊Q8 | — | 149 | 12 | no | — |
| 153 | C4×Q8 | — | 149 | 1 | no | — |
| 154 | C4×Q8 | — | 149 | 2 | no | — |
| 155 | C4×Q8 | — | 149 | 6 | no | — |
| 156 | C4×Q8 | — | 149 | 3 | no | — |
| 157 | C4×Q8 | C2×D149 | 1 | 1 | yes | characteristic |
| 158 | C4×Q8 | C2×D149 | 1 | 2 | yes | — |
| 159 | C4×Q8 | C2×D149 | 1 | 3 | yes | — |
| 160 | C4×D4 | — | 149 | 3 | no | — |
| 161 | C4×D4 | — | 149 | 6 | no | — |
| 162 | C4×D4 | — | 149 | 3 | no | — |
| 163 | C4×D4 | — | 149 | 6 | no | — |
| 164 | #117 | — | 149 | 3 | no | — |
| 165 | #117 | — | 149 | 6 | no | — |
| 166 | C2×C4⋊C4 | — | 149 | 6 | no | — |
| 167 | C2×C4⋊C4 | — | 149 | 6 | no | — |
| 168 | C2×C42 | — | 149 | 3 | no | — |
| 169 | #41 | — | 149 | 8 | no | — |
| 170 | C2×Q8 | — | 596 | 12 | no | — |
| 171 | C2×Q8 | — | 149 | 1 | no | — |
| 172 | C2×Q8 | — | 149 | 6 | no | — |
| 173 | C2×Q8 | — | 149 | 6 | no | — |
| 174 | C2×Q8 | C22×D149 | 1 | 1 | yes | characteristic |
| 175 | C2×Q8 | C22×D149 | 1 | 6 | yes | — |
| 176 | C2×Q8 | C22×D149 | 1 | 1 | yes | characteristic |
| 177 | C2×D4 | — | 149 | 3 | no | — |
| 178 | C22×C4 | — | 149 | 3 | no | — |
| 179 | C22×C4 | — | 149 | 3 | no | — |
| 180 | C22×C4 | — | 149 | 12 | no | — |
| 181 | C22×C4 | — | 149 | 3 | no | — |
| 182 | C4⋊C4 | — | 149 | 6 | no | — |
| 183 | C4⋊C4 | — | 149 | 3 | no | — |
| 184 | C4⋊C4 | — | 149 | 6 | no | — |
| 185 | C4⋊C4 | — | 149 | 12 | no | — |
| 186 | C4⋊C4 | — | 149 | 2 | no | — |
| 187 | C4⋊C4 | — | 149 | 3 | no | — |
| 188 | C4⋊C4 | — | 149 | 2 | no | — |
| 189 | C4⋊C4 | — | 149 | 6 | no | — |
| 190 | C4⋊C4 | — | 149 | 6 | no | — |
| 191 | C4⋊C4 | — | 149 | 6 | no | — |
| 192 | C4⋊C4 | C22×D149 | 1 | 3 | yes | — |
| 193 | C4⋊C4 | C22×D149 | 1 | 6 | yes | — |
| 194 | C4⋊C4 | C22×D149 | 1 | 3 | yes | — |
| 195 | C4⋊C4 | C22×D149 | 1 | 6 | yes | — |
| 196 | C22⋊C4 | — | 149 | 6 | no | — |
| 197 | C22⋊C4 | — | 149 | 6 | no | — |
| 198 | C22⋊C4 | — | 149 | 6 | no | — |
| 199 | C42 | — | 149 | 1 | no | — |
| 200 | C42 | — | 149 | 3 | no | — |
| 201 | C42 | — | 149 | 3 | no | — |
| 202 | C42 | — | 149 | 6 | no | — |
| 203 | C42 | C22×D149 | 1 | 3 | yes | — |
| 204 | C42 | C22×D149 | 1 | 6 | yes | — |
| 205 | C23 | — | 149 | 3 | no | — |
| 206 | Q8 | — | 2 | 2 | no | — |
| 207 | Q8 | — | 4 | 6 | no | — |
| 208 | Q8 | — | 298 | 12 | no | — |
| 209 | Q8 | — | 298 | 2 | no | — |
| 210 | Q8 | — | 596 | 6 | no | — |
| 211 | Q8 | Q8×D149 | 1 | 4 | yes | complemented |
| 212 | D4 | — | 149 | 12 | no | — |
| 213 | C2×C4 | — | 298 | 6 | no | — |
| 214 | C2×C4 | — | 298 | 6 | no | — |
| 215 | C2×C4 | — | 596 | 12 | no | — |
| 216 | C2×C4 | — | 149 | 2 | no | — |
| 217 | C2×C4 | — | 149 | 3 | no | — |
| 218 | C2×C4 | — | 149 | 6 | no | — |
| 219 | C2×C4 | — | 149 | 1 | no | — |
| 220 | C2×C4 | — | 149 | 1 | no | — |
| 221 | C2×C4 | — | 149 | 12 | no | — |
| 222 | C2×C4 | C23×D149 | 1 | 3 | yes | — |
| 223 | C2×C4 | C23×D149 | 1 | 2 | yes | — |
| 224 | C2×C4 | C23×D149 | 1 | 6 | yes | — |
| 225 | C2×C4 | C23×D149 | 1 | 3 | yes | — |
| 226 | C2×C4 | C23×D149 | 1 | 1 | yes | characteristic |
| 227 | C22 | — | 298 | 3 | no | — |
| 228 | C22 | — | 298 | 3 | no | — |
| 229 | C22 | — | 149 | 6 | no | — |
| 230 | C22 | C24×D149 | 1 | 1 | yes | characteristic |
| 231 | C4 | — | 2 | 3 | no | — |
| 232 | C4 | — | 2 | 6 | no | — |
| 233 | C4 | — | 2 | 2 | no | — |
| 234 | C4 | — | 298 | 6 | no | — |
| 235 | C4 | — | 298 | 3 | no | — |
| 236 | C4 | — | 298 | 2 | no | — |
| 237 | C4 | — | 149 | 2 | no | — |
| 238 | C4 | — | 149 | 2 | no | — |
| 239 | C4 | C2×Q8×D149 | 1 | 6 | yes | — |
| 240 | C4 | #18011959 | 1 | 2 | yes | — |
| 241 | C2 | — | 298 | 6 | no | — |
| 242 | C2 | C22×Q8×D149 | 1 | 1 | yes | characteristic |
| 243 | C2 | H(5,𝔽2)×D149 | 1 | 1 | yes | characteristic |
| 244 | C2 | C2×#18011959 | 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