Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1078 conjugacy classes of subgroups.
The subgroup lattice has 566 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22602745 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22599337 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22599335 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22598786 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22587648 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #22587630 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #22586974 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #22586950 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C71×#1530 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#14556150 | — | 2 | 2 | no | — |
| 11 | #17986741 | C22 | 1 | 4 | yes | — |
| 12 | #17986715 | — | 2 | 1 | no | — |
| 13 | #17986714 | — | 2 | 1 | no | — |
| 14 | #17986714 | — | 2 | 1 | no | — |
| 15 | D4×D284 | — | 2 | 1 | no | — |
| 16 | D4×D284 | — | 2 | 1 | no | — |
| 17 | #17986634 | — | 2 | 1 | no | — |
| 18 | #17986565 | — | 2 | 2 | no | — |
| 19 | #17986565 | — | 2 | 2 | no | — |
| 20 | #17986563 | — | 2 | 2 | no | — |
| 21 | #17986549 | C22 | 1 | 1 | yes | characteristic |
| 22 | #17986549 | C22 | 1 | 1 | yes | characteristic |
| 23 | #17986549 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #17986393 | — | 2 | 1 | no | — |
| 25 | #17986393 | C22 | 1 | 2 | yes | complemented |
| 26 | #17986389 | C22 | 1 | 2 | yes | complemented |
| 27 | #17986388 | — | 2 | 1 | no | — |
| 28 | #17986388 | C22 | 1 | 2 | yes | complemented |
| 29 | #17986388 | C22 | 1 | 2 | yes | complemented |
| 30 | #17986359 | C22 | 1 | 2 | yes | complemented |
| 31 | #17986358 | C22 | 1 | 2 | yes | complemented |
| 32 | #17986205 | — | 2 | 1 | no | — |
| 33 | #17986201 | — | 2 | 1 | no | — |
| 34 | #17986195 | — | 2 | 1 | no | — |
| 35 | #17986191 | — | 2 | 1 | no | — |
| 36 | #17986146 | — | 2 | 2 | no | — |
| 37 | #17986144 | — | 2 | 2 | no | — |
| 38 | #17986056 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #17985738 | C22 | 1 | 4 | yes | complemented |
| 40 | #17985738 | C22 | 1 | 4 | yes | complemented |
| 41 | #532×C71 | C22 | 1 | 1 | yes | characteristic |
| 42 | #432×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | C2×#97×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | #329×C71 | C22 | 1 | 4 | yes | complemented |
| 45 | C2×#11765865 | — | 2 | 1 | no | — |
| 46 | C2×#11765865 | D4 | 1 | 2 | yes | — |
| 47 | C2×#11765865 | D4 | 1 | 2 | yes | — |
| 48 | C22×D284 | — | 2 | 2 | no | — |
| 49 | C2×D4×D71 | — | 2 | 2 | no | — |
| 50 | C2×D4×D71 | — | 2 | 2 | no | — |
| 51 | #14556150 | — | 4 | 8 | no | — |
| 52 | C2×Dic284 | — | 2 | 2 | no | — |
| 53 | C2×#11765854 | — | 2 | 2 | no | — |
| 54 | C2×#11765854 | — | 2 | 2 | no | — |
| 55 | C2×#11765854 | — | 2 | 2 | no | — |
| 56 | C2×#11765852 | — | 2 | 2 | no | — |
| 57 | C2×D568 | — | 2 | 2 | no | — |
| 58 | C2×D568 | — | 2 | 2 | no | — |
| 59 | C2×#11765850 | — | 2 | 2 | no | — |
| 60 | #14556128 | D4 | 1 | 1 | yes | characteristic |
| 61 | #14556128 | D4 | 1 | 1 | yes | characteristic |
| 62 | #14556128 | C23 | 1 | 1 | yes | characteristic |
| 63 | #14556125 | D4 | 1 | 1 | yes | characteristic |
| 64 | #14556125 | D4 | 1 | 1 | yes | characteristic |
| 65 | #14556125 | C23 | 1 | 1 | yes | characteristic |
| 66 | #14556124 | — | 2 | 4 | no | — |
| 67 | #14556117 | — | 2 | 4 | no | — |
| 68 | #14556116 | — | 2 | 1 | no | — |
| 69 | #14556116 | C23 | 1 | 2 | yes | — |
| 70 | #14556116 | C23 | 1 | 2 | yes | — |
| 71 | #14556114 | — | 2 | 4 | no | — |
| 72 | #14556114 | — | 2 | 4 | no | — |
| 73 | #14556103 | — | 2 | 2 | no | — |
| 74 | #14556103 | — | 2 | 2 | no | — |
| 75 | #14556102 | — | 2 | 2 | no | — |
| 76 | #14556102 | — | 2 | 2 | no | — |
| 77 | #14556102 | — | 2 | 1 | no | — |
| 78 | #14556102 | — | 2 | 1 | no | — |
| 79 | #14556102 | — | 2 | 1 | no | — |
| 80 | #14556102 | — | 2 | 1 | no | — |
| 81 | #14556102 | — | 2 | 1 | no | — |
| 82 | #14556102 | — | 2 | 1 | no | — |
| 83 | #14556099 | — | 2 | 2 | no | — |
| 84 | #14556099 | — | 2 | 2 | no | — |
| 85 | #14556098 | — | 2 | 4 | no | — |
| 86 | #14556098 | — | 2 | 4 | no | — |
| 87 | #14556096 | — | 2 | 4 | no | — |
| 88 | #14556096 | — | 2 | 4 | no | — |
| 89 | C4×D284 | — | 2 | 1 | no | — |
| 90 | C4×D284 | — | 2 | 1 | no | — |
| 91 | C4×D284 | — | 2 | 1 | no | — |
| 92 | C4×D284 | — | 2 | 1 | no | — |
| 93 | C4×D284 | — | 2 | 1 | no | — |
| 94 | C4×D284 | — | 2 | 1 | no | — |
| 95 | #14556087 | — | 2 | 2 | no | — |
| 96 | #14556086 | — | 2 | 2 | no | — |
| 97 | #14556086 | — | 2 | 2 | no | — |
| 98 | C4⋊(C71⋊C8) | — | 2 | 1 | no | — |
| 99 | #14556053 | — | 2 | 2 | no | — |
| 100 | #14556052 | — | 2 | 2 | no | — |
| 101 | #14556050 | — | 2 | 2 | no | — |
| 102 | #14556049 | — | 2 | 2 | no | — |
| 103 | C22⋊(C71⋊C8) | — | 2 | 1 | no | — |
| 104 | #14556039 | C23 | 1 | 2 | yes | — |
| 105 | C2×#41×C71 | D4 | 1 | 2 | yes | — |
| 106 | C22×C8×C71 | — | 2 | 1 | no | — |
| 107 | C4⋊Q8×C71 | D4 | 1 | 1 | yes | characteristic |
| 108 | #127×C71 | D4 | 1 | 1 | yes | characteristic |
| 109 | #124×C71 | C23 | 1 | 2 | yes | — |
| 110 | #121×C71 | — | 2 | 1 | no | — |
| 111 | #121×C71 | — | 2 | 1 | no | — |
| 112 | C4×D4×C71 | — | 2 | 1 | no | — |
| 113 | C4×D4×C71 | — | 2 | 1 | no | — |
| 114 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 115 | C4⋊C8×C71 | — | 2 | 1 | no | — |
| 116 | C22⋊C8×C71 | — | 2 | 1 | no | — |
| 117 | #97×C71 | — | 2 | 1 | no | — |
| 118 | #97×C71 | C23 | 1 | 2 | yes | — |
| 119 | #97×C71 | C23 | 1 | 2 | yes | — |
| 120 | C23×D71 | — | 2 | 4 | no | — |
| 121 | #11765865 | — | 4 | 4 | no | — |
| 122 | #11765865 | — | 4 | 4 | no | — |
| 123 | #11765865 | — | 8 | 2 | no | — |
| 124 | C2×Dic142 | — | 2 | 1 | no | — |
| 125 | C2×Dic142 | C2×D4 | 1 | 2 | yes | — |
| 126 | C2×Dic142 | C2×D4 | 1 | 2 | yes | — |
| 127 | C2×D284 | — | 2 | 1 | no | — |
| 128 | C2×D284 | — | 2 | 1 | no | — |
| 129 | C2×D284 | — | 2 | 1 | no | — |
| 130 | C2×D284 | — | 2 | 1 | no | — |
| 131 | C2×D284 | — | 2 | 1 | no | — |
| 132 | C2×D284 | — | 2 | 1 | no | — |
| 133 | C2×D284 | — | 2 | 1 | no | — |
| 134 | C2×D284 | — | 2 | 4 | no | — |
| 135 | C2×D284 | — | 8 | 4 | no | — |
| 136 | C2×D284 | C2×D4 | 1 | 2 | yes | — |
| 137 | C2×D284 | C2×D4 | 1 | 2 | yes | — |
| 138 | C2×C22⋊D71 | — | 2 | 4 | no | — |
| 139 | C2×C22⋊D71 | — | 2 | 4 | no | — |
| 140 | C2×C22⋊D71 | — | 2 | 2 | no | — |
| 141 | C2×C22⋊D71 | — | 2 | 2 | no | — |
| 142 | C2×C22⋊D71 | — | 4 | 1 | no | — |
| 143 | D4×D71 | — | 8 | 4 | no | — |
| 144 | D4×D71 | — | 8 | 4 | no | — |
| 145 | C2×C4×D71 | — | 2 | 2 | no | — |
| 146 | C2×C4×D71 | — | 2 | 2 | no | — |
| 147 | C2×C4×D71 | — | 4 | 1 | no | — |
| 148 | Dic284 | — | 4 | 4 | no | — |
| 149 | #11765854 | — | 4 | 4 | no | — |
| 150 | #11765854 | — | 4 | 4 | no | — |
| 151 | #11765854 | — | 8 | 2 | no | — |
| 152 | #11765852 | — | 8 | 2 | no | — |
| 153 | D568 | — | 4 | 4 | no | — |
| 154 | D568 | — | 8 | 2 | no | — |
| 155 | #11765850 | — | 8 | 2 | no | — |
| 156 | C2×C71⋊C8 | — | 2 | 2 | no | — |
| 157 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 158 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 159 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 160 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 161 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 162 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 163 | C22⋊Dic71 | — | 2 | 4 | no | — |
| 164 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 165 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 166 | (C2×D71)⋊C4 | — | 2 | 2 | no | — |
| 167 | (C2×D71)⋊C4 | — | 2 | 2 | no | — |
| 168 | (C2×D71)⋊C4 | — | 2 | 2 | no | — |
| 169 | (C2×D71)⋊C4 | — | 2 | 2 | no | — |
| 170 | (C2×D71)⋊C4 | — | 4 | 1 | no | — |
| 171 | (C2×D71)⋊C4 | — | 4 | 1 | no | — |
| 172 | C4×Dic71 | — | 2 | 4 | no | — |
| 173 | #41×C71 | — | 8 | 2 | no | — |
| 174 | C2×Q8×C71 | C2×D4 | 1 | 2 | yes | — |
| 175 | C2×D4×C71 | — | 2 | 2 | no | — |
| 176 | C2×D4×C71 | — | 2 | 1 | no | — |
| 177 | C2×D4×C71 | — | 2 | 1 | no | — |
| 178 | C2×D4×C71 | C2×D4 | 1 | 2 | yes | — |
| 179 | C22×C4×C71 | — | 2 | 2 | no | — |
| 180 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 183 | C2×C8×C71 | — | 2 | 4 | no | — |
| 184 | C2×C8×C71 | — | 2 | 2 | no | — |
| 185 | C2×C8×C71 | — | 2 | 2 | no | — |
| 186 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 187 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 188 | C22⋊C4×C71 | — | 2 | 2 | no | — |
| 189 | C22⋊C4×C71 | — | 2 | 2 | no | — |
| 190 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C42×C71 | C24 | 1 | 1 | yes | characteristic |
| 194 | C23×C71 | — | 2 | 2 | no | — |
| 195 | C23×C71 | #120 | 1 | 1 | yes | characteristic |
| 196 | C22×D71 | — | 2 | 2 | no | — |
| 197 | C22×D71 | — | 2 | 2 | no | — |
| 198 | C22×D71 | — | 4 | 1 | no | — |
| 199 | C22×D71 | — | 8 | 4 | no | — |
| 200 | C22×D71 | — | 8 | 4 | no | — |
| 201 | C22×D71 | — | 8 | 4 | no | — |
| 202 | Q8×C71 | — | 4 | 2 | no | — |
| 203 | D4×C71 | — | 4 | 2 | no | — |
| 204 | D4×C71 | — | 4 | 2 | no | — |
| 205 | D4×C71 | — | 4 | 2 | no | — |
| 206 | D4×C71 | — | 8 | 2 | no | — |
| 207 | C2×C4×C71 | — | 2 | 2 | no | — |
| 208 | C2×C4×C71 | — | 2 | 2 | no | — |
| 209 | C2×C4×C71 | — | 4 | 1 | no | — |
| 210 | C2×C4×C71 | — | 4 | 1 | no | — |
| 211 | C2×C4×C71 | — | 4 | 4 | no | — |
| 212 | C2×C4×C71 | #120 | 1 | 1 | yes | characteristic |
| 213 | C2×C4×C71 | #120 | 1 | 1 | yes | characteristic |
| 214 | C2×C4×C71 | #120 | 1 | 1 | yes | characteristic |
| 215 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 216 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 217 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 218 | C22⋊D71 | — | 8 | 2 | no | — |
| 219 | C22⋊D71 | — | 8 | 2 | no | — |
| 220 | C22⋊D71 | — | 8 | 4 | no | — |
| 221 | C22⋊D71 | — | 8 | 4 | no | — |
| 222 | C22⋊D71 | — | 8 | 2 | no | — |
| 223 | C2×Dic71 | — | 2 | 2 | no | — |
| 224 | C2×Dic71 | — | 2 | 2 | no | — |
| 225 | C2×Dic71 | — | 4 | 1 | no | — |
| 226 | D284 | — | 4 | 2 | no | — |
| 227 | D284 | — | 4 | 2 | no | — |
| 228 | D284 | — | 4 | 2 | no | — |
| 229 | D284 | — | 4 | 2 | no | — |
| 230 | D284 | — | 4 | 2 | no | — |
| 231 | D284 | — | 4 | 1 | no | — |
| 232 | D284 | — | 4 | 2 | no | — |
| 233 | D284 | — | 4 | 1 | no | — |
| 234 | D284 | — | 4 | 1 | no | — |
| 235 | D284 | — | 4 | 1 | no | — |
| 236 | D284 | — | 4 | 2 | no | — |
| 237 | D284 | — | 8 | 4 | no | — |
| 238 | C4×D71 | — | 4 | 4 | no | — |
| 239 | C4×D71 | — | 4 | 4 | no | — |
| 240 | C4×D71 | — | 8 | 2 | no | — |
| 241 | Dic142 | — | 4 | 2 | no | — |
| 242 | Dic142 | — | 4 | 2 | no | — |
| 243 | Dic142 | — | 4 | 2 | no | — |
| 244 | C8×C71 | — | 2 | 4 | no | — |
| 245 | C8×C71 | — | 4 | 2 | no | — |
| 246 | C71⋊C8 | — | 4 | 2 | no | — |
| 247 | C22×C71 | — | 2 | 1 | no | — |
| 248 | C22×C71 | — | 2 | 1 | no | — |
| 249 | C22×C71 | — | 2 | 1 | no | — |
| 250 | C22×C71 | — | 4 | 2 | no | — |
| 251 | C22×C71 | — | 4 | 2 | no | — |
| 252 | C22×C71 | — | 4 | 2 | no | — |
| 253 | C22×C71 | C2×#120 | 1 | 1 | yes | characteristic |
| 254 | C2×D71 | — | 4 | 2 | no | — |
| 255 | C2×D71 | — | 4 | 2 | no | — |
| 256 | C2×D71 | — | 4 | 2 | no | — |
| 257 | C2×D71 | — | 4 | 2 | no | — |
| 258 | C2×D71 | — | 4 | 2 | no | — |
| 259 | C2×D71 | — | 4 | 2 | no | — |
| 260 | C2×D71 | — | 8 | 1 | no | — |
| 261 | C2×D71 | — | 8 | 1 | no | — |
| 262 | C2×D71 | — | 8 | 1 | no | — |
| 263 | C2×D71 | — | 16 | 8 | no | — |
| 264 | C4×C71 | — | 2 | 1 | no | — |
| 265 | C4×C71 | — | 2 | 1 | no | — |
| 266 | C4×C71 | — | 2 | 1 | no | — |
| 267 | C4×C71 | — | 2 | 1 | no | — |
| 268 | C4×C71 | — | 2 | 1 | no | — |
| 269 | C4×C71 | — | 4 | 2 | no | — |
| 270 | C4×C71 | #453 | 1 | 2 | yes | — |
| 271 | Dic71 | — | 4 | 2 | no | — |
| 272 | Dic71 | — | 4 | 2 | no | — |
| 273 | Dic71 | — | 8 | 1 | no | — |
| 274 | #19052 | — | 71 | 1 | no | maximal, Sylow |
| 275 | C2×C71 | — | 4 | 1 | no | — |
| 276 | C2×C71 | — | 8 | 2 | no | — |
| 277 | C2×C71 | C2×#453 | 1 | 1 | yes | characteristic |
| 278 | C2×C71 | #3019 | 1 | 1 | yes | characteristic |
| 279 | C2×C71 | #3019 | 1 | 1 | yes | characteristic |
| 280 | D71 | — | 8 | 2 | no | — |
| 281 | D71 | — | 8 | 2 | no | — |
| 282 | D71 | — | 16 | 1 | no | — |
| 283 | #3549 | — | 71 | 1 | no | — |
| 284 | #3214 | — | 71 | 1 | no | — |
| 285 | #3214 | — | 71 | 1 | no | — |
| 286 | #3150 | — | 71 | 1 | no | — |
| 287 | #1659 | — | 71 | 4 | no | — |
| 288 | #1655 | — | 71 | 4 | no | — |
| 289 | #1536 | — | 71 | 1 | no | — |
| 290 | #1530 | — | 71 | 1 | no | — |
| 291 | #1530 | D71 | 1 | 1 | yes | characteristic, complemented |
| 292 | C71 | #19052 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 293 | C2×#135 | — | 142 | 2 | no | — |
| 294 | H(3,𝔽4) | — | 71 | 4 | no | — |
| 295 | #555 | — | 142 | 1 | no | — |
| 296 | #555 | — | 142 | 1 | no | — |
| 297 | #555 | — | 142 | 1 | no | — |
| 298 | D42 | — | 142 | 1 | no | — |
| 299 | D42 | — | 142 | 1 | no | — |
| 300 | D42 | — | 142 | 1 | no | — |
| 301 | #535 | — | 142 | 2 | no | — |
| 302 | #535 | — | 142 | 2 | no | — |
| 303 | #535 | — | 142 | 2 | no | — |
| 304 | #532 | — | 71 | 1 | no | — |
| 305 | #532 | — | 71 | 1 | no | — |
| 306 | #532 | — | 71 | 1 | no | — |
| 307 | #532 | C2×D71 | 1 | 1 | yes | characteristic |
| 308 | #497 | — | 71 | 2 | no | — |
| 309 | #497 | — | 142 | 1 | no | — |
| 310 | #496 | — | 71 | 2 | no | — |
| 311 | #496 | — | 71 | 2 | no | — |
| 312 | #496 | — | 71 | 2 | no | — |
| 313 | #496 | — | 142 | 1 | no | — |
| 314 | #489 | — | 71 | 2 | no | — |
| 315 | #489 | — | 71 | 2 | no | — |
| 316 | #461 | — | 142 | 1 | no | — |
| 317 | #461 | — | 142 | 1 | no | — |
| 318 | #459 | — | 142 | 1 | no | — |
| 319 | #459 | — | 142 | 1 | no | — |
| 320 | #449 | — | 142 | 2 | no | — |
| 321 | #449 | — | 142 | 2 | no | — |
| 322 | #432 | — | 71 | 1 | no | — |
| 323 | #432 | C2×D71 | 1 | 1 | yes | characteristic, complemented |
| 324 | C2×#97 | C2×D71 | 1 | 1 | yes | characteristic, complemented |
| 325 | #329 | — | 71 | 4 | no | — |
| 326 | #329 | — | 71 | 4 | no | — |
| 327 | #329 | C2×D71 | 1 | 4 | yes | complemented |
| 328 | C2×#41 | — | 71 | 2 | no | — |
| 329 | C2×#41 | — | 71 | 2 | no | — |
| 330 | C2×#41 | — | 142 | 1 | no | — |
| 331 | C2×#41 | D284 | 1 | 2 | yes | — |
| 332 | C22×D4 | — | 142 | 2 | no | — |
| 333 | C22×D4 | — | 142 | 2 | no | — |
| 334 | C22×D4 | — | 142 | 2 | no | — |
| 335 | #135 | — | 284 | 8 | no | — |
| 336 | C2×Q16 | — | 142 | 2 | no | — |
| 337 | C2×SD16 | — | 142 | 2 | no | — |
| 338 | C2×SD16 | — | 142 | 2 | no | — |
| 339 | C2×SD16 | — | 142 | 2 | no | — |
| 340 | C2×SD16 | — | 142 | 2 | no | — |
| 341 | C2×D8 | — | 142 | 2 | no | — |
| 342 | C2×D8 | — | 142 | 2 | no | — |
| 343 | C2×D8 | — | 142 | 2 | no | — |
| 344 | C22×C8 | — | 2 | 1 | no | — |
| 345 | C4⋊Q8 | — | 71 | 1 | no | — |
| 346 | C4⋊Q8 | — | 71 | 1 | no | — |
| 347 | C4⋊Q8 | — | 71 | 1 | no | — |
| 348 | C4⋊Q8 | D284 | 1 | 1 | yes | characteristic |
| 349 | #127 | — | 71 | 1 | no | — |
| 350 | #127 | — | 71 | 1 | no | — |
| 351 | #127 | — | 71 | 1 | no | — |
| 352 | #127 | — | 142 | 4 | no | — |
| 353 | #127 | D284 | 1 | 1 | yes | characteristic |
| 354 | #124 | — | 71 | 2 | no | — |
| 355 | #124 | — | 71 | 2 | no | — |
| 356 | #124 | — | 142 | 4 | no | — |
| 357 | #124 | — | 142 | 4 | no | — |
| 358 | #124 | — | 142 | 4 | no | — |
| 359 | #124 | — | 142 | 1 | no | — |
| 360 | #124 | C22×D71 | 1 | 2 | yes | — |
| 361 | #121 | — | 2 | 1 | no | — |
| 362 | #121 | — | 2 | 1 | no | — |
| 363 | #121 | — | 142 | 1 | no | — |
| 364 | #121 | — | 142 | 1 | no | — |
| 365 | #121 | — | 142 | 2 | no | — |
| 366 | #121 | — | 142 | 2 | no | — |
| 367 | #121 | — | 142 | 2 | no | — |
| 368 | #121 | — | 142 | 2 | no | — |
| 369 | #121 | — | 142 | 2 | no | — |
| 370 | #121 | — | 142 | 2 | no | — |
| 371 | #121 | — | 142 | 1 | no | — |
| 372 | #121 | — | 142 | 1 | no | — |
| 373 | #121 | — | 142 | 1 | no | — |
| 374 | #121 | — | 142 | 1 | no | — |
| 375 | #120 | — | 142 | 4 | no | — |
| 376 | #120 | — | 142 | 4 | no | — |
| 377 | #120 | — | 142 | 4 | no | — |
| 378 | #120 | — | 142 | 4 | no | — |
| 379 | C4×D4 | — | 2 | 1 | no | — |
| 380 | C4×D4 | — | 2 | 1 | no | — |
| 381 | C4×D4 | — | 142 | 1 | no | — |
| 382 | C4×D4 | — | 142 | 1 | no | — |
| 383 | C4×D4 | — | 142 | 1 | no | — |
| 384 | C4×D4 | — | 142 | 1 | no | — |
| 385 | C4×D4 | — | 142 | 1 | no | — |
| 386 | C4×D4 | — | 142 | 1 | no | — |
| 387 | #117 | — | 142 | 2 | no | — |
| 388 | #117 | — | 142 | 2 | no | — |
| 389 | #117 | — | 142 | 2 | no | — |
| 390 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 391 | C4⋊C8 | — | 2 | 1 | no | — |
| 392 | C4⋊C8 | — | 142 | 1 | no | — |
| 393 | #103 | — | 142 | 2 | no | — |
| 394 | #103 | — | 142 | 2 | no | — |
| 395 | #102 | — | 142 | 2 | no | — |
| 396 | #102 | — | 142 | 2 | no | — |
| 397 | C22⋊C8 | — | 2 | 1 | no | — |
| 398 | C22⋊C8 | — | 142 | 1 | no | — |
| 399 | #97 | — | 2 | 1 | no | — |
| 400 | #97 | — | 71 | 2 | no | — |
| 401 | #97 | C22×D71 | 1 | 2 | yes | — |
| 402 | #97 | C22×D71 | 1 | 2 | yes | — |
| 403 | C24 | — | 142 | 4 | no | — |
| 404 | #41 | — | 8 | 2 | no | — |
| 405 | #41 | — | 284 | 4 | no | — |
| 406 | #41 | — | 284 | 4 | no | — |
| 407 | #41 | — | 568 | 2 | no | — |
| 408 | C2×Q8 | — | 71 | 2 | no | — |
| 409 | C2×Q8 | — | 71 | 2 | no | — |
| 410 | C2×Q8 | — | 142 | 1 | no | — |
| 411 | C2×Q8 | C2×D284 | 1 | 2 | yes | — |
| 412 | C2×D4 | — | 2 | 2 | no | — |
| 413 | C2×D4 | — | 2 | 1 | no | — |
| 414 | C2×D4 | — | 2 | 1 | no | — |
| 415 | C2×D4 | — | 284 | 1 | no | — |
| 416 | C2×D4 | — | 568 | 4 | no | — |
| 417 | C2×D4 | — | 568 | 4 | no | — |
| 418 | C2×D4 | — | 568 | 4 | no | — |
| 419 | C2×D4 | — | 71 | 2 | no | — |
| 420 | C2×D4 | — | 71 | 2 | no | — |
| 421 | C2×D4 | — | 142 | 4 | no | — |
| 422 | C2×D4 | — | 142 | 4 | no | — |
| 423 | C2×D4 | — | 142 | 4 | no | — |
| 424 | C2×D4 | — | 142 | 2 | no | — |
| 425 | C2×D4 | — | 142 | 2 | no | — |
| 426 | C2×D4 | — | 142 | 1 | no | — |
| 427 | C2×D4 | — | 142 | 1 | no | — |
| 428 | C2×D4 | — | 142 | 1 | no | — |
| 429 | C2×D4 | — | 142 | 1 | no | — |
| 430 | C2×D4 | — | 142 | 1 | no | — |
| 431 | C2×D4 | — | 142 | 1 | no | — |
| 432 | C2×D4 | — | 142 | 1 | no | — |
| 433 | C2×D4 | C2×D284 | 1 | 2 | yes | — |
| 434 | C22×C4 | — | 2 | 2 | no | — |
| 435 | C22×C4 | — | 284 | 1 | no | — |
| 436 | C22×C4 | — | 142 | 2 | no | — |
| 437 | C22×C4 | — | 142 | 2 | no | — |
| 438 | C22×C4 | D4×D71 | 1 | 1 | yes | characteristic |
| 439 | C22×C4 | D4×D71 | 1 | 1 | yes | characteristic |
| 440 | C22×C4 | C2×D284 | 1 | 1 | yes | characteristic |
| 441 | Q16 | — | 284 | 4 | no | — |
| 442 | SD16 | — | 284 | 4 | no | — |
| 443 | SD16 | — | 284 | 4 | no | — |
| 444 | SD16 | — | 568 | 2 | no | — |
| 445 | SD16 | — | 568 | 2 | no | — |
| 446 | D8 | — | 284 | 4 | no | — |
| 447 | D8 | — | 568 | 2 | no | — |
| 448 | D8 | — | 568 | 2 | no | — |
| 449 | C2×C8 | — | 2 | 4 | no | — |
| 450 | C2×C8 | — | 2 | 2 | no | — |
| 451 | C2×C8 | — | 2 | 2 | no | — |
| 452 | C2×C8 | — | 142 | 2 | no | — |
| 453 | C4⋊C4 | — | 2 | 1 | no | — |
| 454 | C4⋊C4 | — | 2 | 1 | no | — |
| 455 | C4⋊C4 | — | 142 | 1 | no | — |
| 456 | C4⋊C4 | — | 142 | 1 | no | — |
| 457 | C4⋊C4 | — | 142 | 1 | no | — |
| 458 | C4⋊C4 | — | 142 | 1 | no | — |
| 459 | C4⋊C4 | — | 142 | 1 | no | — |
| 460 | C4⋊C4 | — | 142 | 1 | no | — |
| 461 | C22⋊C4 | — | 2 | 2 | no | — |
| 462 | C22⋊C4 | — | 2 | 2 | no | — |
| 463 | C22⋊C4 | — | 284 | 1 | no | — |
| 464 | C22⋊C4 | — | 284 | 1 | no | — |
| 465 | C22⋊C4 | — | 142 | 4 | no | — |
| 466 | C22⋊C4 | — | 142 | 4 | no | — |
| 467 | C22⋊C4 | — | 142 | 4 | no | — |
| 468 | C22⋊C4 | — | 142 | 2 | no | — |
| 469 | C22⋊C4 | — | 142 | 2 | no | — |
| 470 | C22⋊C4 | — | 142 | 2 | no | — |
| 471 | C22⋊C4 | — | 142 | 2 | no | — |
| 472 | C42 | — | 142 | 4 | no | — |
| 473 | C42 | D4×D71 | 1 | 1 | yes | characteristic |
| 474 | C42 | D4×D71 | 1 | 1 | yes | characteristic |
| 475 | C42 | C2×D284 | 1 | 1 | yes | characteristic |
| 476 | C42 | C23×D71 | 1 | 1 | yes | characteristic |
| 477 | C23 | — | 2 | 2 | no | — |
| 478 | C23 | — | 284 | 1 | no | — |
| 479 | C23 | — | 568 | 4 | no | — |
| 480 | C23 | — | 568 | 4 | no | — |
| 481 | C23 | — | 568 | 4 | no | — |
| 482 | C23 | — | 142 | 2 | no | — |
| 483 | C23 | — | 142 | 2 | no | — |
| 484 | C23 | #14556098 | 1 | 1 | yes | characteristic |
| 485 | Q8 | — | 4 | 2 | no | — |
| 486 | Q8 | — | 284 | 2 | no | — |
| 487 | Q8 | — | 284 | 2 | no | — |
| 488 | Q8 | — | 284 | 2 | no | — |
| 489 | D4 | — | 4 | 2 | no | — |
| 490 | D4 | — | 4 | 2 | no | — |
| 491 | D4 | — | 4 | 2 | no | — |
| 492 | D4 | — | 8 | 2 | no | — |
| 493 | D4 | — | 284 | 2 | no | — |
| 494 | D4 | — | 284 | 2 | no | — |
| 495 | D4 | — | 284 | 2 | no | — |
| 496 | D4 | — | 284 | 2 | no | — |
| 497 | D4 | — | 284 | 2 | no | — |
| 498 | D4 | — | 284 | 2 | no | — |
| 499 | D4 | — | 284 | 1 | no | — |
| 500 | D4 | — | 284 | 1 | no | — |
| 501 | D4 | — | 284 | 1 | no | — |
| 502 | D4 | — | 284 | 1 | no | — |
| 503 | D4 | — | 284 | 2 | no | — |
| 504 | D4 | — | 568 | 4 | no | — |
| 505 | D4 | — | 568 | 2 | no | — |
| 506 | D4 | — | 568 | 2 | no | — |
| 507 | D4 | — | 568 | 4 | no | — |
| 508 | D4 | — | 568 | 4 | no | — |
| 509 | D4 | — | 568 | 2 | no | — |
| 510 | C2×C4 | — | 2 | 2 | no | — |
| 511 | C2×C4 | — | 2 | 2 | no | — |
| 512 | C2×C4 | — | 4 | 1 | no | — |
| 513 | C2×C4 | — | 4 | 1 | no | — |
| 514 | C2×C4 | — | 4 | 4 | no | — |
| 515 | C2×C4 | — | 284 | 4 | no | — |
| 516 | C2×C4 | — | 284 | 4 | no | — |
| 517 | C2×C4 | — | 284 | 1 | no | — |
| 518 | C2×C4 | — | 568 | 2 | no | — |
| 519 | C2×C4 | — | 142 | 2 | no | — |
| 520 | C2×C4 | — | 142 | 2 | no | — |
| 521 | C2×C4 | #14556098 | 1 | 1 | yes | characteristic |
| 522 | C2×C4 | #14556098 | 1 | 1 | yes | characteristic |
| 523 | C2×C4 | #14556098 | 1 | 1 | yes | characteristic |
| 524 | C2×C4 | C2×D4×D71 | 1 | 1 | yes | characteristic |
| 525 | C2×C4 | C2×D4×D71 | 1 | 1 | yes | characteristic |
| 526 | C2×C4 | C22×D284 | 1 | 1 | yes | characteristic |
| 527 | C8 | — | 2 | 4 | no | — |
| 528 | C8 | — | 4 | 2 | no | — |
| 529 | C8 | — | 284 | 2 | no | — |
| 530 | C22 | — | 2 | 1 | no | — |
| 531 | C22 | — | 2 | 1 | no | — |
| 532 | C22 | — | 2 | 1 | no | — |
| 533 | C22 | — | 4 | 2 | no | — |
| 534 | C22 | — | 4 | 2 | no | — |
| 535 | C22 | — | 4 | 2 | no | — |
| 536 | C22 | — | 284 | 2 | no | — |
| 537 | C22 | — | 284 | 2 | no | — |
| 538 | C22 | — | 284 | 2 | no | — |
| 539 | C22 | — | 284 | 2 | no | — |
| 540 | C22 | — | 284 | 2 | no | — |
| 541 | C22 | — | 284 | 2 | no | — |
| 542 | C22 | — | 568 | 1 | no | — |
| 543 | C22 | — | 568 | 1 | no | — |
| 544 | C22 | — | 568 | 1 | no | — |
| 545 | C22 | — | 1136 | 8 | no | — |
| 546 | C22 | C2×#14556098 | 1 | 1 | yes | characteristic |
| 547 | C4 | — | 2 | 1 | no | — |
| 548 | C4 | — | 2 | 1 | no | — |
| 549 | C4 | — | 2 | 1 | no | — |
| 550 | C4 | — | 2 | 1 | no | — |
| 551 | C4 | — | 2 | 1 | no | — |
| 552 | C4 | — | 4 | 2 | no | — |
| 553 | C4 | — | 284 | 2 | no | — |
| 554 | C4 | — | 284 | 2 | no | — |
| 555 | C4 | — | 568 | 1 | no | — |
| 556 | C4 | #17986168 | 1 | 2 | yes | — |
| 557 | C2 | — | 4 | 1 | no | — |
| 558 | C2 | — | 8 | 2 | no | — |
| 559 | C2 | — | 568 | 2 | no | — |
| 560 | C2 | — | 568 | 2 | no | — |
| 561 | C2 | — | 1136 | 1 | no | — |
| 562 | C2 | C2×#17986168 | 1 | 1 | yes | characteristic |
| 563 | C2 | #22597699 | 1 | 1 | yes | characteristic |
| 564 | C2 | #22597700 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22602745 | C2 | semidirect |
| 2. #22599337 | C2 | semidirect |
| 3. #22599335 | C2 | semidirect |
| 4. #22598786 | C2 | semidirect |
| 5. #22587648 | C2 | semidirect |
| 6. #22587630 | C2 | semidirect |
| 7. #22586974 | C2 | semidirect |
| 8. #22586950 | C2 | semidirect |
| 9. C71×#1530 | C2 | semidirect |
| 23. #17986549 | C22 | semidirect |
| 25. #17986393 | C22 | semidirect |
| 26. #17986389 | C22 | semidirect |
| 28. #17986388 | C22 | semidirect |
| 29. #17986388 | C22 | semidirect |
| 30. #17986359 | C22 | semidirect |
| 31. #17986358 | C22 | semidirect |
| 38. #17986056 | C22 | semidirect |
| 39. #17985738 | C22 | semidirect |
| 40. #17985738 | C22 | semidirect |
| 42. #432×C71 | C22 | semidirect |
| 43. C2×#97×C71 | C22 | semidirect |
| 44. #329×C71 | C22 | semidirect |
| 291. #1530 | D71 | semidirect |
| 292. C71 | #19052 | semidirect |
| 323. #432 | C2×D71 | semidirect |
| 324. C2×#97 | C2×D71 | semidirect |
| 327. #329 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602745 | 2 |
| #22599337 | 2 |
| #22599335 | 2 |
| #22598786 | 2 |
| #22587648 | 2 |
| #22587630 | 2 |
| #22586974 | 2 |
| #22586950 | 2 |
| C71×#1530 | 2 |
| #19052 | 71 |