← #32862635
Subgroups — #32862635
Order 18176.
1908 conjugacy classes of subgroups.
The subgroup lattice has 734 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22601636 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22597496 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #22597485 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #22597470 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22597466 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22597458 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22597449 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #22597270 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #22597065 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #22597051 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #22597008 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×#17986052 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #22596909 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | C2×#423×C71 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C2×#14556136 | C22 | 1 | 4 | yes | — |
| 16 | #17986556 | C4 | 1 | 1 | yes | characteristic |
| 17 | #17986556 | C4 | 1 | 1 | yes | characteristic |
| 18 | #17986556 | C22 | 1 | 1 | yes | characteristic |
| 19 | #17986549 | C4 | 1 | 1 | yes | characteristic |
| 20 | #17986549 | C4 | 1 | 1 | yes | characteristic |
| 21 | #17986549 | C22 | 1 | 1 | yes | characteristic |
| 22 | #17986533 | C4 | 1 | 2 | yes | — |
| 23 | #17986533 | C4 | 1 | 2 | yes | — |
| 24 | #17986533 | C4 | 1 | 2 | yes | — |
| 25 | #17986533 | C4 | 1 | 2 | yes | — |
| 26 | #17986533 | C22 | 1 | 2 | yes | — |
| 27 | #17986533 | C22 | 1 | 2 | yes | — |
| 28 | #17986510 | C4 | 1 | 2 | yes | — |
| 29 | #17986510 | C4 | 1 | 2 | yes | — |
| 30 | #17986510 | C22 | 1 | 2 | yes | — |
| 31 | C4×#11765865 | C22 | 1 | 2 | yes | — |
| 32 | C4×#11765865 | C22 | 1 | 2 | yes | — |
| 33 | C4×#11765865 | C22 | 1 | 2 | yes | — |
| 34 | #17986126 | C22 | 1 | 4 | yes | complemented |
| 35 | #17986126 | C22 | 1 | 4 | yes | complemented |
| 36 | #17986123 | C22 | 1 | 4 | yes | complemented |
| 37 | #17986123 | C22 | 1 | 4 | yes | complemented |
| 38 | #17986076 | C22 | 1 | 4 | yes | complemented |
| 39 | #17986076 | C22 | 1 | 4 | yes | complemented |
| 40 | #17986075 | C22 | 1 | 8 | yes | — |
| 41 | #17986070 | C22 | 1 | 8 | yes | — |
| 42 | #17986068 | C22 | 1 | 8 | yes | — |
| 43 | #17986064 | C22 | 1 | 4 | yes | complemented |
| 44 | #17986064 | C22 | 1 | 4 | yes | complemented |
| 45 | C8×C22⋊D71 | C22 | 1 | 8 | yes | — |
| 46 | #17986059 | C22 | 1 | 8 | yes | complemented |
| 47 | #17986055 | C22 | 1 | 4 | yes | complemented |
| 48 | #17986052 | C22 | 1 | 1 | yes | characteristic |
| 49 | #17986052 | C22 | 1 | 1 | yes | characteristic |
| 50 | #17986052 | C22 | 1 | 1 | yes | characteristic |
| 51 | #17986052 | C22 | 1 | 1 | yes | characteristic |
| 52 | #17986052 | C22 | 1 | 2 | yes | — |
| 53 | #17986052 | C22 | 1 | 2 | yes | — |
| 54 | #17986051 | C22 | 1 | 4 | yes | complemented |
| 55 | #17986027 | C22 | 1 | 4 | yes | — |
| 56 | #17986024 | C22 | 1 | 8 | yes | complemented |
| 57 | #17986021 | C22 | 1 | 4 | yes | complemented |
| 58 | C2×C4⋊(C71⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 59 | C2×C4⋊(C71⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 60 | C4⋊C8×D71 | C22 | 1 | 4 | yes | complemented |
| 61 | #17985967 | C22 | 1 | 4 | yes | — |
| 62 | C2×C22⋊(C71⋊C8) | C22 | 1 | 2 | yes | — |
| 63 | #17985957 | C22 | 1 | 4 | yes | — |
| 64 | C2×C4×C71⋊C8 | C22 | 1 | 2 | yes | — |
| 65 | C22×M16×C71 | C22 | 1 | 2 | yes | — |
| 66 | C22×C42×C71 | C22 | 1 | 1 | yes | characteristic |
| 67 | #423×C71 | C22 | 1 | 2 | yes | — |
| 68 | #423×C71 | C22 | 1 | 2 | yes | — |
| 69 | #423×C71 | C22 | 1 | 2 | yes | — |
| 70 | #423×C71 | C22 | 1 | 2 | yes | — |
| 71 | C2×C4⋊C8×C71 | C22 | 1 | 2 | yes | — |
| 72 | C2×C4⋊C8×C71 | C22 | 1 | 2 | yes | — |
| 73 | C2×#11765865 | C2×C4 | 1 | 2 | yes | — |
| 74 | C2×#11765865 | C2×C4 | 1 | 2 | yes | — |
| 75 | C2×#11765865 | C23 | 1 | 2 | yes | — |
| 76 | #14556136 | — | 4 | 8 | no | — |
| 77 | C2×#11765848 | C23 | 1 | 8 | yes | — |
| 78 | C22×C71⋊C8 | C23 | 1 | 2 | yes | — |
| 79 | C22×C71⋊C8 | C23 | 1 | 2 | yes | — |
| 80 | C2×C8×D71 | C23 | 1 | 8 | yes | — |
| 81 | #14556128 | C2×C4 | 1 | 1 | yes | characteristic |
| 82 | #14556128 | C2×C4 | 1 | 1 | yes | characteristic |
| 83 | #14556128 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | #14556125 | C2×C4 | 1 | 1 | yes | characteristic |
| 85 | #14556122 | C2×C4 | 1 | 4 | yes | — |
| 86 | #14556122 | C2×C4 | 1 | 4 | yes | — |
| 87 | #14556120 | C2×C4 | 1 | 2 | yes | — |
| 88 | #14556120 | C2×C4 | 1 | 2 | yes | — |
| 89 | #14556120 | C2×C4 | 1 | 2 | yes | — |
| 90 | #14556116 | C2×C4 | 1 | 2 | yes | — |
| 91 | #14556116 | C2×C4 | 1 | 2 | yes | — |
| 92 | #14556116 | C2×C4 | 1 | 2 | yes | — |
| 93 | #14556111 | C2×C4 | 1 | 4 | yes | — |
| 94 | #14556111 | C2×C4 | 1 | 4 | yes | — |
| 95 | #14556111 | C2×C4 | 1 | 4 | yes | — |
| 96 | #14556107 | C2×C4 | 1 | 2 | yes | — |
| 97 | #14556107 | C2×C4 | 1 | 2 | yes | — |
| 98 | #14556107 | C2×C4 | 1 | 2 | yes | — |
| 99 | #14556107 | C2×C4 | 1 | 2 | yes | — |
| 100 | #14556107 | C2×C4 | 1 | 2 | yes | — |
| 101 | #14556107 | C2×C4 | 1 | 2 | yes | — |
| 102 | #14556102 | C2×C4 | 1 | 2 | yes | — |
| 103 | #14556102 | C2×C4 | 1 | 2 | yes | — |
| 104 | #14556102 | C2×C4 | 1 | 2 | yes | — |
| 105 | #14556102 | C2×C4 | 1 | 2 | yes | — |
| 106 | #14556102 | C2×C4 | 1 | 2 | yes | — |
| 107 | #14556102 | C2×C4 | 1 | 2 | yes | — |
| 108 | #14556097 | C2×C4 | 1 | 4 | yes | — |
| 109 | C4×Dic142 | C2×C4 | 1 | 2 | yes | — |
| 110 | C4×Dic142 | C2×C4 | 1 | 2 | yes | — |
| 111 | C4×Dic142 | C2×C4 | 1 | 2 | yes | — |
| 112 | C4×Dic142 | C2×C4 | 1 | 2 | yes | — |
| 113 | C4×Dic142 | C23 | 1 | 2 | yes | — |
| 114 | C4×Dic142 | C23 | 1 | 2 | yes | — |
| 115 | C4×D284 | C2×C4 | 1 | 2 | yes | — |
| 116 | C4×D284 | C2×C4 | 1 | 2 | yes | — |
| 117 | C4×D284 | C2×C4 | 1 | 2 | yes | — |
| 118 | C4×D284 | C2×C4 | 1 | 2 | yes | — |
| 119 | C4×D284 | C23 | 1 | 2 | yes | — |
| 120 | C4×D284 | C23 | 1 | 2 | yes | — |
| 121 | C4×C22⋊D71 | C2×C4 | 1 | 4 | yes | — |
| 122 | C4×C22⋊D71 | C2×C4 | 1 | 4 | yes | — |
| 123 | C4×C22⋊D71 | C2×C4 | 1 | 4 | yes | — |
| 124 | C4×C22⋊D71 | C2×C4 | 1 | 4 | yes | — |
| 125 | C4×C22⋊D71 | C23 | 1 | 4 | yes | — |
| 126 | C4×C22⋊D71 | C23 | 1 | 4 | yes | — |
| 127 | #14556087 | C2×C4 | 1 | 2 | yes | — |
| 128 | #14556087 | C2×C4 | 1 | 2 | yes | — |
| 129 | #14556087 | C23 | 1 | 2 | yes | — |
| 130 | #14556085 | C2×C4 | 1 | 4 | yes | — |
| 131 | #14556085 | C2×C4 | 1 | 4 | yes | — |
| 132 | #14556085 | C23 | 1 | 4 | yes | — |
| 133 | C42×D71 | C23 | 1 | 4 | yes | — |
| 134 | C4⋊(C71⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 135 | C4⋊(C71⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 136 | C4⋊(C71⋊C8) | C23 | 1 | 2 | yes | — |
| 137 | C4⋊(C71⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 138 | C4⋊(C71⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 139 | C4⋊(C71⋊C8) | C23 | 1 | 2 | yes | — |
| 140 | Dic71⋊C8 | C23 | 1 | 8 | yes | — |
| 141 | Dic71⋊C8 | C23 | 1 | 8 | yes | — |
| 142 | C22⋊(C71⋊C8) | C23 | 1 | 2 | yes | — |
| 143 | C22⋊(C71⋊C8) | C23 | 1 | 2 | yes | — |
| 144 | C22⋊(C71⋊C8) | C23 | 1 | 2 | yes | — |
| 145 | C22⋊(C71⋊C8) | C23 | 1 | 2 | yes | — |
| 146 | (C2×D71)⋊C8 | C23 | 1 | 8 | yes | — |
| 147 | (C2×D71)⋊C8 | C23 | 1 | 8 | yes | — |
| 148 | #14556038 | C23 | 1 | 8 | yes | — |
| 149 | C4×C71⋊C8 | C23 | 1 | 2 | yes | — |
| 150 | C4×C71⋊C8 | C23 | 1 | 2 | yes | — |
| 151 | C4×C71⋊C8 | C23 | 1 | 2 | yes | — |
| 152 | C4×C71⋊C8 | C23 | 1 | 2 | yes | — |
| 153 | C8×Dic71 | C23 | 1 | 8 | yes | — |
| 154 | C23×C4×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 155 | C23×C4×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 156 | C23×C4×C71 | C23 | 1 | 1 | yes | characteristic |
| 157 | C2×M16×C71 | — | 4 | 4 | no | — |
| 158 | C2×M16×C71 | C23 | 1 | 4 | yes | — |
| 159 | C2×M16×C71 | C23 | 1 | 4 | yes | — |
| 160 | C22×C8×C71 | C23 | 1 | 4 | yes | — |
| 161 | C2×C42×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 162 | C2×C42×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 163 | C2×C42×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 164 | C2×C42×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 165 | C2×C42×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 166 | C2×C42×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 167 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 168 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 169 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 170 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 171 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 172 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 173 | C4⋊C8×C71 | C23 | 1 | 4 | yes | — |
| 174 | C4⋊C8×C71 | C23 | 1 | 4 | yes | — |
| 175 | C4⋊C8×C71 | C23 | 1 | 4 | yes | — |
| 176 | C4⋊C8×C71 | C23 | 1 | 4 | yes | — |
| 177 | #11765865 | — | 2 | 8 | no | — |
| 178 | #11765865 | — | 2 | 4 | no | — |
| 179 | #11765865 | — | 2 | 4 | no | — |
| 180 | #11765865 | — | 4 | 4 | no | — |
| 181 | C2×Dic142 | C22×C4 | 1 | 2 | yes | — |
| 182 | C2×Dic142 | C22×C4 | 1 | 2 | yes | — |
| 183 | C2×Dic142 | C22×C4 | 1 | 2 | yes | — |
| 184 | C2×D284 | C22×C4 | 1 | 2 | yes | — |
| 185 | C2×D284 | C22×C4 | 1 | 2 | yes | — |
| 186 | C2×D284 | C22×C4 | 1 | 2 | yes | — |
| 187 | C2×C22⋊D71 | C22×C4 | 1 | 4 | yes | — |
| 188 | C2×C22⋊D71 | C22×C4 | 1 | 4 | yes | — |
| 189 | C2×C22⋊D71 | C22×C4 | 1 | 4 | yes | — |
| 190 | C2×C4×D71 | C22×C4 | 1 | 4 | yes | — |
| 191 | C2×C4×D71 | C22×C4 | 1 | 4 | yes | — |
| 192 | C2×C4×D71 | C24 | 1 | 4 | yes | — |
| 193 | #11765848 | — | 4 | 8 | no | — |
| 194 | C2×C71⋊C8 | — | 2 | 4 | no | — |
| 195 | C2×C71⋊C8 | — | 2 | 4 | no | — |
| 196 | C2×C71⋊C8 | C24 | 1 | 2 | yes | — |
| 197 | C2×C71⋊C8 | C24 | 1 | 2 | yes | — |
| 198 | C2×C71⋊C8 | C24 | 1 | 2 | yes | — |
| 199 | C2×C71⋊C8 | C24 | 1 | 2 | yes | — |
| 200 | C8×D71 | — | 4 | 8 | no | — |
| 201 | C4⋊Dic71 | C22×C4 | 1 | 2 | yes | — |
| 202 | C4⋊Dic71 | C22×C4 | 1 | 2 | yes | — |
| 203 | C4⋊Dic71 | C22×C4 | 1 | 2 | yes | — |
| 204 | C4⋊Dic71 | C22×C4 | 1 | 2 | yes | — |
| 205 | C4⋊Dic71 | C22×C4 | 1 | 2 | yes | — |
| 206 | C4⋊Dic71 | C22×C4 | 1 | 2 | yes | — |
| 207 | Dic71⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 208 | Dic71⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 209 | Dic71⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 210 | Dic71⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 211 | Dic71⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 212 | Dic71⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 213 | C22⋊Dic71 | C22×C4 | 1 | 4 | yes | — |
| 214 | C22⋊Dic71 | C22×C4 | 1 | 4 | yes | — |
| 215 | C22⋊Dic71 | C22×C4 | 1 | 4 | yes | — |
| 216 | (C2×D71)⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 217 | (C2×D71)⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 218 | (C2×D71)⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 219 | (C2×D71)⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 220 | (C2×D71)⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 221 | (C2×D71)⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 222 | C4×Dic71 | C22×C4 | 1 | 4 | yes | — |
| 223 | C4×Dic71 | C22×C4 | 1 | 4 | yes | — |
| 224 | C4×Dic71 | C24 | 1 | 4 | yes | — |
| 225 | C24×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 226 | C22×C4×C71 | — | 2 | 4 | no | — |
| 227 | C22×C4×C71 | — | 2 | 2 | no | — |
| 228 | C22×C4×C71 | — | 2 | 2 | no | — |
| 229 | C22×C4×C71 | — | 4 | 2 | no | — |
| 230 | C22×C4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 231 | C22×C4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 232 | C22×C4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 233 | C22×C4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 234 | C22×C4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 235 | C22×C4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 236 | C22×C4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 237 | C22×C4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 238 | C22×C4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 239 | C22×C4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 240 | C22×C4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 241 | C22×C4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 242 | C22×C4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 243 | C22×C4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 244 | C22×C4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 245 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 246 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 247 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 248 | M16×C71 | — | 2 | 8 | no | — |
| 249 | M16×C71 | — | 4 | 4 | no | — |
| 250 | C2×C8×C71 | — | 4 | 4 | no | — |
| 251 | C2×C8×C71 | C24 | 1 | 8 | yes | — |
| 252 | C42×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 253 | C42×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 254 | C42×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 255 | C42×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 256 | C42×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 257 | C42×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 258 | C42×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 259 | C42×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 260 | C42×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 261 | C42×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 262 | C42×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 263 | C42×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 264 | C42×C71 | C24 | 1 | 1 | yes | characteristic |
| 265 | C42×C71 | C24 | 1 | 1 | yes | characteristic |
| 266 | C42×C71 | C24 | 1 | 1 | yes | characteristic |
| 267 | C42×C71 | C24 | 1 | 1 | yes | characteristic |
| 268 | C23×C71 | — | 2 | 2 | no | — |
| 269 | C23×C71 | — | 2 | 2 | no | — |
| 270 | C23×C71 | — | 4 | 1 | no | — |
| 271 | C23×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 272 | C23×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 273 | C23×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 274 | C22×D71 | C23×C4 | 1 | 4 | yes | — |
| 275 | C2×C4×C71 | — | 2 | 2 | no | — |
| 276 | C2×C4×C71 | — | 2 | 2 | no | — |
| 277 | C2×C4×C71 | — | 2 | 2 | no | — |
| 278 | C2×C4×C71 | — | 2 | 2 | no | — |
| 279 | C2×C4×C71 | — | 2 | 2 | no | — |
| 280 | C2×C4×C71 | — | 2 | 2 | no | — |
| 281 | C2×C4×C71 | — | 2 | 2 | no | — |
| 282 | C2×C4×C71 | — | 2 | 2 | no | — |
| 283 | C2×C4×C71 | — | 2 | 2 | no | — |
| 284 | C2×C4×C71 | — | 2 | 2 | no | — |
| 285 | C2×C4×C71 | — | 2 | 2 | no | — |
| 286 | C2×C4×C71 | — | 2 | 1 | no | — |
| 287 | C2×C4×C71 | — | 2 | 1 | no | — |
| 288 | C2×C4×C71 | — | 2 | 1 | no | — |
| 289 | C2×C4×C71 | — | 2 | 1 | no | — |
| 290 | C2×C4×C71 | — | 4 | 1 | no | — |
| 291 | C2×C4×C71 | — | 4 | 1 | no | — |
| 292 | C2×C4×C71 | — | 4 | 1 | no | — |
| 293 | C2×C4×C71 | #131 | 1 | 4 | yes | complemented |
| 294 | C2×C4×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 295 | C2×C4×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 296 | C2×C4×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 297 | C2×C4×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 298 | C2×C4×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 299 | C2×C4×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 300 | C2×C4×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 301 | C2×C4×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 302 | C2×C4×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 303 | C2×C4×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 304 | C2×C4×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 305 | C2×C4×C71 | H(5,𝔽2) | 1 | 2 | yes | — |
| 306 | C2×C4×C71 | 2−1+4 | 1 | 2 | yes | — |
| 307 | C2×C4×C71 | C25 | 1 | 1 | yes | characteristic |
| 308 | C22⋊D71 | — | 2 | 8 | no | — |
| 309 | C22⋊D71 | — | 2 | 8 | no | — |
| 310 | C22⋊D71 | — | 4 | 4 | no | — |
| 311 | C2×Dic71 | C23×C4 | 1 | 4 | yes | — |
| 312 | C2×Dic71 | C23×C4 | 1 | 4 | yes | — |
| 313 | C2×Dic71 | C23×C4 | 1 | 4 | yes | — |
| 314 | D284 | — | 2 | 4 | no | — |
| 315 | D284 | — | 2 | 4 | no | — |
| 316 | D284 | — | 2 | 4 | no | — |
| 317 | C4×D71 | — | 2 | 8 | no | — |
| 318 | C4×D71 | — | 2 | 4 | no | — |
| 319 | C4×D71 | — | 2 | 4 | no | — |
| 320 | C4×D71 | — | 4 | 4 | no | — |
| 321 | Dic142 | — | 2 | 4 | no | — |
| 322 | Dic142 | — | 2 | 4 | no | — |
| 323 | Dic142 | — | 2 | 4 | no | — |
| 324 | C8×C71 | — | 2 | 8 | no | — |
| 325 | C71⋊C8 | — | 2 | 2 | no | — |
| 326 | C71⋊C8 | — | 2 | 2 | no | — |
| 327 | C71⋊C8 | — | 2 | 2 | no | — |
| 328 | C71⋊C8 | — | 2 | 2 | no | — |
| 329 | C22×C71 | — | 2 | 1 | no | — |
| 330 | C22×C71 | — | 2 | 1 | no | — |
| 331 | C22×C71 | — | 2 | 1 | no | — |
| 332 | C22×C71 | — | 2 | 1 | no | — |
| 333 | C22×C71 | — | 2 | 1 | no | — |
| 334 | C22×C71 | — | 2 | 1 | no | — |
| 335 | C22×C71 | — | 2 | 1 | no | — |
| 336 | C22×C71 | — | 4 | 4 | no | — |
| 337 | C22×C71 | #520 | 1 | 2 | yes | — |
| 338 | C22×C71 | C2×#131 | 1 | 2 | yes | — |
| 339 | C22×C71 | C24×C4 | 1 | 1 | yes | characteristic |
| 340 | C2×D71 | — | 2 | 4 | no | — |
| 341 | C2×D71 | — | 2 | 4 | no | — |
| 342 | C2×D71 | — | 2 | 4 | no | — |
| 343 | C4×C71 | — | 2 | 1 | no | — |
| 344 | C4×C71 | — | 2 | 1 | no | — |
| 345 | C4×C71 | — | 2 | 1 | no | — |
| 346 | C4×C71 | — | 2 | 1 | no | — |
| 347 | C4×C71 | — | 2 | 1 | no | — |
| 348 | C4×C71 | — | 2 | 1 | no | — |
| 349 | C4×C71 | — | 2 | 1 | no | — |
| 350 | C4×C71 | #520 | 1 | 2 | yes | — |
| 351 | C4×C71 | C2×#131 | 1 | 2 | yes | — |
| 352 | C4×C71 | C2×#131 | 1 | 2 | yes | — |
| 353 | C4×C71 | #568 | 1 | 2 | yes | — |
| 354 | C4×C71 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 355 | C4×C71 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 356 | Dic71 | — | 2 | 4 | no | — |
| 357 | Dic71 | — | 2 | 4 | no | — |
| 358 | Dic71 | — | 2 | 4 | no | — |
| 359 | #60268 | — | 71 | 1 | no | maximal, Sylow |
| 360 | C2×C71 | — | 2 | 2 | no | — |
| 361 | C2×C71 | — | 2 | 2 | no | — |
| 362 | C2×C71 | — | 4 | 1 | no | — |
| 363 | C2×C71 | C2×#520 | 1 | 1 | yes | characteristic |
| 364 | C2×C71 | C22×#131 | 1 | 1 | yes | characteristic |
| 365 | C2×C71 | C2×#568 | 1 | 1 | yes | characteristic |
| 366 | D71 | — | 4 | 4 | no | — |
| 367 | #3444 | — | 71 | 1 | no | — |
| 368 | #2994 | — | 71 | 4 | no | — |
| 369 | #2993 | — | 71 | 4 | no | — |
| 370 | #2991 | — | 71 | 2 | no | — |
| 371 | #2990 | — | 71 | 2 | no | — |
| 372 | #2989 | — | 71 | 2 | no | — |
| 373 | #2988 | — | 71 | 2 | no | — |
| 374 | #2960 | — | 71 | 2 | no | — |
| 375 | #2933 | — | 71 | 4 | no | — |
| 376 | #2931 | — | 71 | 2 | no | — |
| 377 | #2925 | — | 71 | 2 | no | — |
| 378 | C2×#431 | — | 71 | 1 | no | — |
| 379 | #2906 | — | 71 | 2 | no | — |
| 380 | C2×#423 | D71 | 1 | 1 | yes | characteristic, complemented |
| 381 | C71 | #60268 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 382 | C2×#131 | — | 71 | 4 | no | — |
| 383 | C22×M16 | C2×D71 | 1 | 2 | yes | — |
| 384 | #533 | — | 71 | 1 | no | — |
| 385 | #533 | — | 71 | 1 | no | — |
| 386 | #533 | — | 71 | 1 | no | — |
| 387 | #532 | — | 71 | 1 | no | — |
| 388 | #532 | — | 71 | 1 | no | — |
| 389 | #532 | — | 71 | 1 | no | — |
| 390 | #529 | — | 71 | 2 | no | — |
| 391 | #529 | — | 71 | 2 | no | — |
| 392 | #529 | — | 71 | 2 | no | — |
| 393 | #529 | — | 71 | 2 | no | — |
| 394 | #529 | — | 71 | 2 | no | — |
| 395 | #529 | — | 71 | 2 | no | — |
| 396 | #525 | — | 71 | 2 | no | — |
| 397 | #525 | — | 71 | 2 | no | — |
| 398 | #525 | — | 71 | 2 | no | — |
| 399 | C4×#41 | — | 71 | 2 | no | — |
| 400 | C4×#41 | — | 71 | 2 | no | — |
| 401 | C4×#41 | — | 71 | 2 | no | — |
| 402 | C22×C42 | C2×D71 | 1 | 1 | yes | characteristic |
| 403 | #446 | — | 71 | 4 | no | — |
| 404 | #446 | — | 71 | 4 | no | — |
| 405 | C8×Q8 | — | 71 | 4 | no | — |
| 406 | C8×Q8 | — | 71 | 4 | no | — |
| 407 | #436 | — | 71 | 8 | no | — |
| 408 | #436 | — | 71 | 4 | no | — |
| 409 | #436 | — | 71 | 4 | no | — |
| 410 | #435 | — | 71 | 8 | no | — |
| 411 | #435 | — | 71 | 8 | no | — |
| 412 | C8×D4 | — | 71 | 8 | no | — |
| 413 | C8×D4 | — | 71 | 4 | no | — |
| 414 | C8×D4 | — | 71 | 4 | no | — |
| 415 | #433 | — | 71 | 8 | no | — |
| 416 | #432 | — | 71 | 4 | no | — |
| 417 | #431 | — | 71 | 1 | no | — |
| 418 | #431 | — | 71 | 1 | no | — |
| 419 | #431 | — | 71 | 1 | no | — |
| 420 | #431 | — | 71 | 1 | no | — |
| 421 | #431 | — | 71 | 2 | no | — |
| 422 | #431 | — | 71 | 2 | no | — |
| 423 | #431 | — | 71 | 4 | no | — |
| 424 | #424 | — | 71 | 4 | no | — |
| 425 | #424 | — | 71 | 8 | no | — |
| 426 | #423 | — | 71 | 4 | no | — |
| 427 | #423 | C2×D71 | 1 | 2 | yes | — |
| 428 | #423 | C2×D71 | 1 | 2 | yes | — |
| 429 | #423 | C2×D71 | 1 | 2 | yes | — |
| 430 | #423 | C2×D71 | 1 | 2 | yes | — |
| 431 | C2×C4⋊C8 | — | 71 | 1 | no | — |
| 432 | C2×C4⋊C8 | — | 71 | 1 | no | — |
| 433 | C2×C4⋊C8 | — | 71 | 4 | no | — |
| 434 | C2×C4⋊C8 | C2×D71 | 1 | 2 | yes | — |
| 435 | C2×C4⋊C8 | C2×D71 | 1 | 2 | yes | — |
| 436 | #408 | — | 71 | 4 | no | — |
| 437 | C2×C22⋊C8 | — | 71 | 2 | no | — |
| 438 | #405 | — | 71 | 4 | no | — |
| 439 | C2×C4×C8 | — | 71 | 2 | no | — |
| 440 | C2×#41 | — | 71 | 2 | no | — |
| 441 | C2×#41 | — | 71 | 2 | no | — |
| 442 | C2×#41 | — | 71 | 2 | no | — |
| 443 | C23×C4 | C4×D71 | 1 | 1 | yes | characteristic |
| 444 | C23×C4 | C4×D71 | 1 | 1 | yes | characteristic |
| 445 | C23×C4 | C22×D71 | 1 | 1 | yes | characteristic |
| 446 | #131 | — | 284 | 8 | no | — |
| 447 | C2×M16 | — | 4 | 4 | no | — |
| 448 | C2×M16 | — | 71 | 8 | no | — |
| 449 | C2×M16 | C22×D71 | 1 | 4 | yes | — |
| 450 | C2×M16 | C22×D71 | 1 | 4 | yes | — |
| 451 | C22×C8 | — | 71 | 8 | no | — |
| 452 | C22×C8 | — | 71 | 2 | no | — |
| 453 | C22×C8 | — | 71 | 2 | no | — |
| 454 | C22×C8 | C22×D71 | 1 | 4 | yes | — |
| 455 | C4⋊Q8 | — | 71 | 1 | no | — |
| 456 | C4⋊Q8 | — | 71 | 1 | no | — |
| 457 | C4⋊Q8 | — | 71 | 1 | no | — |
| 458 | #127 | — | 71 | 1 | no | — |
| 459 | #126 | — | 71 | 4 | no | — |
| 460 | #126 | — | 71 | 4 | no | — |
| 461 | #125 | — | 71 | 2 | no | — |
| 462 | #125 | — | 71 | 2 | no | — |
| 463 | #125 | — | 71 | 2 | no | — |
| 464 | #124 | — | 71 | 2 | no | — |
| 465 | #124 | — | 71 | 2 | no | — |
| 466 | #124 | — | 71 | 2 | no | — |
| 467 | #123 | — | 71 | 4 | no | — |
| 468 | #123 | — | 71 | 4 | no | — |
| 469 | #123 | — | 71 | 4 | no | — |
| 470 | C22⋊Q8 | — | 71 | 2 | no | — |
| 471 | C22⋊Q8 | — | 71 | 2 | no | — |
| 472 | C22⋊Q8 | — | 71 | 2 | no | — |
| 473 | C22⋊Q8 | — | 71 | 2 | no | — |
| 474 | C22⋊Q8 | — | 71 | 2 | no | — |
| 475 | C22⋊Q8 | — | 71 | 2 | no | — |
| 476 | #121 | — | 71 | 2 | no | — |
| 477 | #121 | — | 71 | 2 | no | — |
| 478 | #121 | — | 71 | 2 | no | — |
| 479 | #121 | — | 71 | 2 | no | — |
| 480 | #121 | — | 71 | 2 | no | — |
| 481 | #121 | — | 71 | 2 | no | — |
| 482 | #120 | — | 71 | 4 | no | — |
| 483 | C4×Q8 | — | 71 | 2 | no | — |
| 484 | C4×Q8 | — | 71 | 2 | no | — |
| 485 | C4×Q8 | — | 71 | 2 | no | — |
| 486 | C4×Q8 | — | 71 | 2 | no | — |
| 487 | C4×Q8 | — | 71 | 2 | no | — |
| 488 | C4×Q8 | — | 71 | 2 | no | — |
| 489 | C4×D4 | — | 71 | 4 | no | — |
| 490 | C4×D4 | — | 71 | 4 | no | — |
| 491 | C4×D4 | — | 71 | 4 | no | — |
| 492 | C4×D4 | — | 71 | 4 | no | — |
| 493 | C4×D4 | — | 71 | 4 | no | — |
| 494 | C4×D4 | — | 71 | 4 | no | — |
| 495 | C4×D4 | — | 71 | 2 | no | — |
| 496 | C4×D4 | — | 71 | 2 | no | — |
| 497 | C4×D4 | — | 71 | 2 | no | — |
| 498 | C4×D4 | — | 71 | 2 | no | — |
| 499 | C4×D4 | — | 71 | 2 | no | — |
| 500 | C4×D4 | — | 71 | 2 | no | — |
| 501 | #117 | — | 71 | 2 | no | — |
| 502 | #117 | — | 71 | 2 | no | — |
| 503 | #117 | — | 71 | 2 | no | — |
| 504 | #117 | — | 71 | 4 | no | — |
| 505 | #117 | — | 71 | 4 | no | — |
| 506 | #117 | — | 71 | 4 | no | — |
| 507 | C2×C42 | — | 71 | 4 | no | — |
| 508 | C2×C42 | C4×D71 | 1 | 1 | yes | characteristic |
| 509 | C2×C42 | C4×D71 | 1 | 1 | yes | characteristic |
| 510 | C2×C42 | C4×D71 | 1 | 1 | yes | characteristic |
| 511 | C2×C42 | C4×D71 | 1 | 1 | yes | characteristic |
| 512 | C2×C42 | C4×D71 | 1 | 1 | yes | characteristic |
| 513 | C2×C42 | C4×D71 | 1 | 1 | yes | characteristic |
| 514 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 515 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 516 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 517 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 518 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 519 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 520 | C4⋊C8 | — | 71 | 8 | no | — |
| 521 | C4⋊C8 | — | 71 | 8 | no | — |
| 522 | C4⋊C8 | — | 71 | 1 | no | — |
| 523 | C4⋊C8 | — | 71 | 1 | no | — |
| 524 | C4⋊C8 | — | 71 | 2 | no | — |
| 525 | C4⋊C8 | — | 71 | 1 | no | — |
| 526 | C4⋊C8 | — | 71 | 1 | no | — |
| 527 | C4⋊C8 | — | 71 | 2 | no | — |
| 528 | C4⋊C8 | C22×D71 | 1 | 4 | yes | — |
| 529 | C4⋊C8 | C22×D71 | 1 | 4 | yes | — |
| 530 | C4⋊C8 | C22×D71 | 1 | 4 | yes | — |
| 531 | C4⋊C8 | C22×D71 | 1 | 4 | yes | — |
| 532 | C22⋊C8 | — | 71 | 2 | no | — |
| 533 | C22⋊C8 | — | 71 | 2 | no | — |
| 534 | C22⋊C8 | — | 71 | 2 | no | — |
| 535 | C22⋊C8 | — | 71 | 2 | no | — |
| 536 | C22⋊C8 | — | 71 | 8 | no | — |
| 537 | C22⋊C8 | — | 71 | 8 | no | — |
| 538 | #97 | — | 71 | 8 | no | — |
| 539 | C4×C8 | — | 71 | 8 | no | — |
| 540 | C4×C8 | — | 71 | 2 | no | — |
| 541 | C4×C8 | — | 71 | 2 | no | — |
| 542 | C4×C8 | — | 71 | 2 | no | — |
| 543 | C4×C8 | — | 71 | 2 | no | — |
| 544 | C24 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 545 | #41 | — | 284 | 4 | no | — |
| 546 | #41 | — | 142 | 4 | no | — |
| 547 | #41 | — | 142 | 4 | no | — |
| 548 | #41 | — | 142 | 8 | no | — |
| 549 | C2×Q8 | — | 71 | 2 | no | — |
| 550 | C2×Q8 | — | 71 | 2 | no | — |
| 551 | C2×Q8 | — | 71 | 2 | no | — |
| 552 | C2×D4 | — | 71 | 4 | no | — |
| 553 | C2×D4 | — | 71 | 4 | no | — |
| 554 | C2×D4 | — | 71 | 4 | no | — |
| 555 | C2×D4 | — | 71 | 2 | no | — |
| 556 | C2×D4 | — | 71 | 2 | no | — |
| 557 | C2×D4 | — | 71 | 2 | no | — |
| 558 | C22×C4 | — | 2 | 2 | no | — |
| 559 | C22×C4 | — | 2 | 2 | no | — |
| 560 | C22×C4 | — | 2 | 4 | no | — |
| 561 | C22×C4 | — | 4 | 2 | no | — |
| 562 | C22×C4 | — | 71 | 4 | no | — |
| 563 | C22×C4 | — | 71 | 4 | no | — |
| 564 | C22×C4 | — | 71 | 4 | no | — |
| 565 | C22×C4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 566 | C22×C4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 567 | C22×C4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 568 | C22×C4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 569 | C22×C4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 570 | C22×C4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 571 | C22×C4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 572 | C22×C4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 573 | C22×C4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 574 | C22×C4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 575 | C22×C4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 576 | C22×C4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 577 | C22×C4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 578 | C22×C4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 579 | C22×C4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 580 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 581 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 582 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 583 | M16 | — | 2 | 8 | no | — |
| 584 | M16 | — | 4 | 4 | no | — |
| 585 | M16 | — | 284 | 8 | no | — |
| 586 | C2×C8 | — | 4 | 4 | no | — |
| 587 | C2×C8 | — | 284 | 8 | no | — |
| 588 | C2×C8 | — | 71 | 2 | no | — |
| 589 | C2×C8 | — | 71 | 2 | no | — |
| 590 | C2×C8 | — | 71 | 2 | no | — |
| 591 | C2×C8 | — | 71 | 2 | no | — |
| 592 | C2×C8 | — | 142 | 4 | no | — |
| 593 | C2×C8 | — | 142 | 4 | no | — |
| 594 | C2×C8 | C23×D71 | 1 | 8 | yes | — |
| 595 | C4⋊C4 | — | 71 | 4 | no | — |
| 596 | C4⋊C4 | — | 71 | 4 | no | — |
| 597 | C4⋊C4 | — | 71 | 4 | no | — |
| 598 | C4⋊C4 | — | 71 | 4 | no | — |
| 599 | C4⋊C4 | — | 71 | 4 | no | — |
| 600 | C4⋊C4 | — | 71 | 4 | no | — |
| 601 | C4⋊C4 | — | 71 | 2 | no | — |
| 602 | C4⋊C4 | — | 71 | 2 | no | — |
| 603 | C4⋊C4 | — | 71 | 2 | no | — |
| 604 | C4⋊C4 | — | 71 | 2 | no | — |
| 605 | C4⋊C4 | — | 71 | 2 | no | — |
| 606 | C4⋊C4 | — | 71 | 2 | no | — |
| 607 | C22⋊C4 | — | 71 | 4 | no | — |
| 608 | C22⋊C4 | — | 71 | 4 | no | — |
| 609 | C22⋊C4 | — | 71 | 4 | no | — |
| 610 | C22⋊C4 | — | 71 | 4 | no | — |
| 611 | C22⋊C4 | — | 71 | 4 | no | — |
| 612 | C22⋊C4 | — | 71 | 4 | no | — |
| 613 | C22⋊C4 | — | 71 | 4 | no | — |
| 614 | C22⋊C4 | — | 71 | 4 | no | — |
| 615 | C22⋊C4 | — | 71 | 4 | no | — |
| 616 | C42 | — | 71 | 4 | no | — |
| 617 | C42 | — | 71 | 4 | no | — |
| 618 | C42 | — | 71 | 4 | no | — |
| 619 | C42 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 620 | C42 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 621 | C42 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 622 | C42 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 623 | C42 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 624 | C42 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 625 | C42 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 626 | C42 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 627 | C42 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 628 | C42 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 629 | C42 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 630 | C42 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 631 | C42 | C23×D71 | 1 | 1 | yes | characteristic |
| 632 | C42 | C23×D71 | 1 | 1 | yes | characteristic |
| 633 | C42 | C23×D71 | 1 | 1 | yes | characteristic |
| 634 | C42 | C23×D71 | 1 | 1 | yes | characteristic |
| 635 | C23 | — | 2 | 2 | no | — |
| 636 | C23 | — | 2 | 2 | no | — |
| 637 | C23 | — | 4 | 1 | no | — |
| 638 | C23 | — | 71 | 4 | no | — |
| 639 | C23 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 640 | C23 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 641 | C23 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 642 | Q8 | — | 142 | 4 | no | — |
| 643 | Q8 | — | 142 | 4 | no | — |
| 644 | Q8 | — | 142 | 4 | no | — |
| 645 | D4 | — | 284 | 4 | no | — |
| 646 | D4 | — | 142 | 8 | no | — |
| 647 | D4 | — | 142 | 8 | no | — |
| 648 | D4 | — | 142 | 4 | no | — |
| 649 | D4 | — | 142 | 4 | no | — |
| 650 | D4 | — | 142 | 4 | no | — |
| 651 | C2×C4 | — | 2 | 2 | no | — |
| 652 | C2×C4 | — | 2 | 2 | no | — |
| 653 | C2×C4 | — | 2 | 1 | no | — |
| 654 | C2×C4 | — | 2 | 1 | no | — |
| 655 | C2×C4 | — | 2 | 1 | no | — |
| 656 | C2×C4 | — | 2 | 1 | no | — |
| 657 | C2×C4 | — | 2 | 2 | no | — |
| 658 | C2×C4 | — | 2 | 2 | no | — |
| 659 | C2×C4 | — | 2 | 2 | no | — |
| 660 | C2×C4 | — | 2 | 2 | no | — |
| 661 | C2×C4 | — | 2 | 2 | no | — |
| 662 | C2×C4 | — | 2 | 2 | no | — |
| 663 | C2×C4 | — | 2 | 2 | no | — |
| 664 | C2×C4 | — | 2 | 2 | no | — |
| 665 | C2×C4 | — | 2 | 2 | no | — |
| 666 | C2×C4 | — | 4 | 1 | no | — |
| 667 | C2×C4 | — | 4 | 1 | no | — |
| 668 | C2×C4 | — | 4 | 1 | no | — |
| 669 | C2×C4 | — | 284 | 4 | no | — |
| 670 | C2×C4 | — | 71 | 4 | no | — |
| 671 | C2×C4 | — | 71 | 4 | no | — |
| 672 | C2×C4 | — | 71 | 4 | no | — |
| 673 | C2×C4 | — | 142 | 4 | no | — |
| 674 | C2×C4 | — | 142 | 4 | no | — |
| 675 | C2×C4 | — | 142 | 8 | no | — |
| 676 | C2×C4 | #14556136 | 1 | 4 | yes | complemented |
| 677 | C2×C4 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 678 | C2×C4 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 679 | C2×C4 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 680 | C2×C4 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 681 | C2×C4 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 682 | C2×C4 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 683 | C2×C4 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 684 | C2×C4 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 685 | C2×C4 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 686 | C2×C4 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 687 | C2×C4 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 688 | C2×C4 | #14556173 | 1 | 2 | yes | — |
| 689 | C2×C4 | #14556176 | 1 | 2 | yes | — |
| 690 | C2×C4 | C24×D71 | 1 | 1 | yes | characteristic |
| 691 | C8 | — | 2 | 8 | no | — |
| 692 | C8 | — | 142 | 2 | no | — |
| 693 | C8 | — | 142 | 2 | no | — |
| 694 | C8 | — | 142 | 2 | no | — |
| 695 | C8 | — | 142 | 2 | no | — |
| 696 | C22 | — | 2 | 1 | no | — |
| 697 | C22 | — | 2 | 1 | no | — |
| 698 | C22 | — | 2 | 1 | no | — |
| 699 | C22 | — | 2 | 1 | no | — |
| 700 | C22 | — | 2 | 1 | no | — |
| 701 | C22 | — | 2 | 1 | no | — |
| 702 | C22 | — | 2 | 1 | no | — |
| 703 | C22 | — | 4 | 4 | no | — |
| 704 | C22 | — | 142 | 4 | no | — |
| 705 | C22 | — | 142 | 4 | no | — |
| 706 | C22 | — | 142 | 4 | no | — |
| 707 | C22 | #17986480 | 1 | 2 | yes | — |
| 708 | C22 | C2×#14556136 | 1 | 2 | yes | — |
| 709 | C22 | C23×C4×D71 | 1 | 1 | yes | characteristic |
| 710 | C4 | — | 2 | 1 | no | — |
| 711 | C4 | — | 2 | 1 | no | — |
| 712 | C4 | — | 2 | 1 | no | — |
| 713 | C4 | — | 2 | 1 | no | — |
| 714 | C4 | — | 2 | 1 | no | — |
| 715 | C4 | — | 2 | 1 | no | — |
| 716 | C4 | — | 2 | 1 | no | — |
| 717 | C4 | — | 142 | 4 | no | — |
| 718 | C4 | — | 142 | 4 | no | — |
| 719 | C4 | — | 142 | 4 | no | — |
| 720 | C4 | #17986480 | 1 | 2 | yes | — |
| 721 | C4 | C2×#14556136 | 1 | 2 | yes | — |
| 722 | C4 | C2×#14556136 | 1 | 2 | yes | — |
| 723 | C4 | #17986765 | 1 | 2 | yes | — |
| 724 | C4 | C2×#14556173 | 1 | 1 | yes | characteristic |
| 725 | C4 | C2×#14556176 | 1 | 1 | yes | characteristic |
| 726 | C2 | — | 2 | 2 | no | — |
| 727 | C2 | — | 2 | 2 | no | — |
| 728 | C2 | — | 4 | 1 | no | — |
| 729 | C2 | — | 284 | 4 | no | — |
| 730 | C2 | C2×#17986480 | 1 | 1 | yes | characteristic |
| 731 | C2 | C22×#14556136 | 1 | 1 | yes | characteristic |
| 732 | C2 | C2×#17986765 | 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