Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
910 conjugacy classes of subgroups.
The subgroup lattice has 768 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22603036 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22599360 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22599360 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22599355 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22587640 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22587640 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22587639 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #22587630 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #22586972 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #22586969 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C71×#1535 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #17986753 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | #17986753 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #17986749 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #17986741 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | #17986721 | — | 2 | 1 | no | — |
| 17 | #17986717 | — | 2 | 1 | no | — |
| 18 | #17986716 | — | 2 | 1 | no | — |
| 19 | #17986678 | — | 2 | 1 | no | — |
| 20 | #17986674 | — | 2 | 1 | no | — |
| 21 | #17986673 | — | 2 | 1 | no | — |
| 22 | #17986619 | — | 2 | 1 | no | — |
| 23 | #17986617 | — | 2 | 1 | no | — |
| 24 | #17986614 | — | 2 | 1 | no | — |
| 25 | #17986585 | — | 2 | 1 | no | — |
| 26 | #17986582 | — | 2 | 1 | no | — |
| 27 | #17986581 | — | 2 | 1 | no | — |
| 28 | C2×#14556125 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #17986533 | C22 | 1 | 1 | yes | characteristic |
| 30 | #17986533 | C22 | 1 | 1 | yes | characteristic |
| 31 | #17986389 | C22 | 1 | 2 | yes | — |
| 32 | #17986388 | C22 | 1 | 2 | yes | — |
| 33 | #17986388 | C22 | 1 | 2 | yes | — |
| 34 | #17986365 | C22 | 1 | 2 | yes | complemented |
| 35 | #17986364 | C22 | 1 | 2 | yes | complemented |
| 36 | #17986364 | C22 | 1 | 2 | yes | complemented |
| 37 | #17986200 | — | 2 | 1 | no | — |
| 38 | #17986200 | — | 2 | 1 | no | — |
| 39 | #17986199 | — | 2 | 1 | no | — |
| 40 | #17986195 | — | 2 | 1 | no | — |
| 41 | #17986195 | — | 2 | 1 | no | — |
| 42 | #17986194 | — | 2 | 1 | no | — |
| 43 | #17986152 | — | 2 | 1 | no | — |
| 44 | #17986152 | — | 2 | 1 | no | — |
| 45 | #17986149 | — | 2 | 1 | no | — |
| 46 | #17986135 | — | 2 | 1 | no | — |
| 47 | #17986135 | — | 2 | 1 | no | — |
| 48 | #17986132 | — | 2 | 1 | no | — |
| 49 | #17986056 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #17985740 | C22 | 1 | 2 | yes | complemented |
| 51 | #17985740 | C22 | 1 | 2 | yes | complemented |
| 52 | #17985738 | C22 | 1 | 2 | yes | complemented |
| 53 | #17985738 | C22 | 1 | 2 | yes | complemented |
| 54 | #529×C71 | C22 | 1 | 1 | yes | characteristic |
| 55 | #432×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 56 | #432×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | #330×C71 | C22 | 1 | 2 | yes | complemented |
| 58 | #329×C71 | C22 | 1 | 2 | yes | complemented |
| 59 | C22×D284 | — | 2 | 1 | no | — |
| 60 | C22×D284 | — | 2 | 1 | no | — |
| 61 | C22×D284 | — | 2 | 1 | no | — |
| 62 | C2×#11765854 | — | 2 | 2 | no | — |
| 63 | C2×#11765854 | — | 2 | 2 | no | — |
| 64 | C2×#11765852 | — | 2 | 2 | no | — |
| 65 | C2×D568 | — | 2 | 2 | no | — |
| 66 | C2×D568 | — | 2 | 2 | no | — |
| 67 | C2×#11765850 | — | 2 | 2 | no | — |
| 68 | #14556127 | — | 2 | 1 | no | — |
| 69 | #14556127 | — | 2 | 1 | no | — |
| 70 | #14556126 | — | 2 | 1 | no | — |
| 71 | #14556125 | — | 2 | 1 | no | — |
| 72 | #14556125 | — | 2 | 1 | no | — |
| 73 | #14556125 | — | 2 | 1 | no | — |
| 74 | #14556125 | C23 | 1 | 2 | yes | — |
| 75 | #14556123 | — | 2 | 1 | no | — |
| 76 | #14556123 | — | 2 | 1 | no | — |
| 77 | #14556123 | — | 2 | 1 | no | — |
| 78 | #14556123 | — | 2 | 1 | no | — |
| 79 | #14556123 | — | 2 | 1 | no | — |
| 80 | #14556122 | — | 2 | 1 | no | — |
| 81 | #14556122 | — | 2 | 1 | no | — |
| 82 | #14556122 | — | 2 | 1 | no | — |
| 83 | #14556121 | — | 2 | 1 | no | — |
| 84 | #14556121 | — | 2 | 1 | no | — |
| 85 | #14556121 | — | 2 | 1 | no | — |
| 86 | #14556121 | — | 2 | 1 | no | — |
| 87 | #14556120 | C23 | 1 | 1 | yes | characteristic |
| 88 | #14556120 | C23 | 1 | 1 | yes | characteristic |
| 89 | #14556117 | — | 2 | 1 | no | — |
| 90 | #14556116 | — | 2 | 1 | no | — |
| 91 | #14556116 | C23 | 1 | 1 | yes | characteristic |
| 92 | #14556116 | C23 | 1 | 1 | yes | characteristic |
| 93 | #14556115 | — | 2 | 1 | no | — |
| 94 | #14556114 | — | 2 | 1 | no | — |
| 95 | #14556114 | — | 2 | 1 | no | — |
| 96 | #14556114 | — | 2 | 1 | no | — |
| 97 | #14556114 | — | 2 | 1 | no | — |
| 98 | #14556114 | — | 2 | 1 | no | — |
| 99 | #14556114 | — | 2 | 1 | no | — |
| 100 | #14556113 | — | 2 | 1 | no | — |
| 101 | #14556113 | — | 2 | 1 | no | — |
| 102 | #14556113 | — | 2 | 1 | no | — |
| 103 | #14556111 | — | 2 | 1 | no | — |
| 104 | #14556111 | — | 2 | 1 | no | — |
| 105 | #14556111 | — | 2 | 1 | no | — |
| 106 | #14556110 | — | 2 | 1 | no | — |
| 107 | #14556109 | — | 2 | 1 | no | — |
| 108 | #14556108 | — | 2 | 1 | no | — |
| 109 | #14556108 | — | 2 | 1 | no | — |
| 110 | #14556107 | — | 2 | 1 | no | — |
| 111 | #14556107 | D4 | 1 | 1 | yes | characteristic |
| 112 | #14556107 | D4 | 1 | 1 | yes | characteristic |
| 113 | #14556106 | — | 2 | 1 | no | — |
| 114 | #14556106 | — | 2 | 1 | no | — |
| 115 | #14556106 | — | 2 | 1 | no | — |
| 116 | #14556106 | — | 2 | 1 | no | — |
| 117 | #14556105 | — | 2 | 1 | no | — |
| 118 | #14556105 | — | 2 | 1 | no | — |
| 119 | #14556102 | D4 | 1 | 1 | yes | characteristic |
| 120 | #14556102 | D4 | 1 | 1 | yes | characteristic |
| 121 | #14556101 | — | 2 | 1 | no | — |
| 122 | #14556100 | — | 2 | 1 | no | — |
| 123 | #14556099 | — | 2 | 1 | no | — |
| 124 | #14556098 | — | 2 | 1 | no | — |
| 125 | #14556098 | — | 2 | 1 | no | — |
| 126 | #14556096 | — | 2 | 1 | no | — |
| 127 | #14556096 | — | 2 | 1 | no | — |
| 128 | C4×Dic142 | — | 2 | 1 | no | — |
| 129 | C4×Dic142 | D4 | 1 | 1 | yes | characteristic |
| 130 | C4×Dic142 | D4 | 1 | 1 | yes | characteristic |
| 131 | #14556093 | — | 2 | 1 | no | — |
| 132 | #14556093 | — | 2 | 1 | no | — |
| 133 | C4×D284 | D4 | 1 | 1 | yes | characteristic |
| 134 | C4×D284 | D4 | 1 | 1 | yes | characteristic |
| 135 | #14556090 | — | 2 | 1 | no | — |
| 136 | C4×C22⋊D71 | — | 2 | 1 | no | — |
| 137 | C4×C22⋊D71 | — | 2 | 1 | no | — |
| 138 | C4×C22⋊D71 | — | 2 | 1 | no | — |
| 139 | (C22⋊D71)⋊C4 | — | 2 | 1 | no | — |
| 140 | #14556086 | — | 2 | 1 | no | — |
| 141 | #14556085 | — | 2 | 1 | no | — |
| 142 | #14556085 | — | 2 | 1 | no | — |
| 143 | #14556085 | — | 2 | 1 | no | — |
| 144 | #14556084 | — | 2 | 1 | no | — |
| 145 | C2×(C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 146 | C22⋊C4×D71 | — | 2 | 1 | no | — |
| 147 | C22⋊C4×D71 | — | 2 | 1 | no | — |
| 148 | C4⋊(C71⋊C8) | — | 2 | 1 | no | — |
| 149 | #14556050 | — | 2 | 2 | no | — |
| 150 | #14556050 | — | 2 | 2 | no | — |
| 151 | #14556050 | — | 2 | 2 | no | — |
| 152 | #14556050 | — | 2 | 2 | no | — |
| 153 | #14556048 | — | 2 | 2 | no | — |
| 154 | #14556048 | — | 2 | 2 | no | — |
| 155 | C22⋊(C71⋊C8) | — | 2 | 1 | no | — |
| 156 | #14556039 | C23 | 1 | 2 | yes | — |
| 157 | #126×C71 | — | 2 | 1 | no | — |
| 158 | #125×C71 | C23 | 1 | 1 | yes | characteristic |
| 159 | #124×C71 | C23 | 1 | 1 | yes | characteristic |
| 160 | #123×C71 | — | 2 | 1 | no | — |
| 161 | C22⋊Q8×C71 | D4 | 1 | 1 | yes | characteristic |
| 162 | #121×C71 | D4 | 1 | 1 | yes | characteristic |
| 163 | C4×Q8×C71 | D4 | 1 | 1 | yes | characteristic |
| 164 | C4×D4×C71 | — | 2 | 1 | no | — |
| 165 | C4×D4×C71 | D4 | 1 | 1 | yes | characteristic |
| 166 | #117×C71 | — | 2 | 1 | no | — |
| 167 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 168 | C4⋊C8×C71 | — | 2 | 1 | no | — |
| 169 | C4⋊C8×C71 | — | 2 | 1 | no | — |
| 170 | C22⋊C8×C71 | — | 2 | 1 | no | — |
| 171 | C22⋊C8×C71 | — | 2 | 1 | no | — |
| 172 | #97×C71 | C23 | 1 | 2 | yes | — |
| 173 | #97×C71 | C23 | 1 | 2 | yes | — |
| 174 | C23×D71 | — | 2 | 1 | no | — |
| 175 | C23×D71 | — | 4 | 1 | no | — |
| 176 | C2×Dic142 | — | 2 | 1 | no | — |
| 177 | C2×Dic142 | — | 2 | 1 | no | — |
| 178 | C2×Dic142 | — | 2 | 1 | no | — |
| 179 | C2×Dic142 | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | C2×Dic142 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C2×D284 | — | 2 | 2 | no | — |
| 182 | C2×D284 | — | 2 | 2 | no | — |
| 183 | C2×D284 | — | 2 | 2 | no | — |
| 184 | C2×D284 | — | 2 | 1 | no | — |
| 185 | C2×D284 | — | 4 | 1 | no | — |
| 186 | C2×D284 | — | 4 | 1 | no | — |
| 187 | C2×D284 | — | 4 | 1 | no | — |
| 188 | C2×D284 | — | 8 | 2 | no | — |
| 189 | C2×D284 | — | 8 | 2 | no | — |
| 190 | C2×D284 | — | 8 | 2 | no | — |
| 191 | C2×D284 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C2×D284 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C2×C22⋊D71 | — | 2 | 1 | no | — |
| 194 | C2×C22⋊D71 | — | 2 | 1 | no | — |
| 195 | C2×C22⋊D71 | — | 2 | 1 | no | — |
| 196 | C2×C22⋊D71 | — | 2 | 1 | no | — |
| 197 | C22×Dic71 | — | 2 | 1 | no | — |
| 198 | C2×C4×D71 | — | 2 | 1 | no | — |
| 199 | C2×C4×D71 | — | 2 | 1 | no | — |
| 200 | C2×C4×D71 | — | 2 | 1 | no | — |
| 201 | C2×C4×D71 | — | 2 | 1 | no | — |
| 202 | #11765854 | — | 8 | 2 | no | — |
| 203 | #11765854 | — | 8 | 2 | no | — |
| 204 | #11765852 | — | 8 | 2 | no | — |
| 205 | D568 | — | 8 | 2 | no | — |
| 206 | D568 | — | 8 | 2 | no | — |
| 207 | #11765850 | — | 8 | 2 | no | — |
| 208 | C2×C71⋊C8 | — | 2 | 2 | no | — |
| 209 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 210 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 211 | C4⋊Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 212 | C4⋊Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 213 | C4⋊Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 214 | C4⋊Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 215 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 216 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 217 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 218 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 219 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 220 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 221 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 222 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 223 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 224 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 225 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 226 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 227 | C22⋊Dic71 | — | 2 | 1 | no | — |
| 228 | C22⋊Dic71 | — | 2 | 1 | no | — |
| 229 | C22⋊Dic71 | — | 2 | 1 | no | — |
| 230 | C22⋊Dic71 | — | 2 | 1 | no | — |
| 231 | C22⋊Dic71 | — | 2 | 1 | no | — |
| 232 | C22⋊Dic71 | — | 2 | 1 | no | — |
| 233 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 234 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 235 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 236 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 237 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 238 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 239 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 240 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 241 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 242 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 243 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 244 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 245 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 246 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 247 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 248 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 249 | C4×Dic71 | — | 2 | 1 | no | — |
| 250 | C4×Dic71 | — | 2 | 1 | no | — |
| 251 | C4×Dic71 | — | 2 | 1 | no | — |
| 252 | C4×Dic71 | — | 2 | 1 | no | — |
| 253 | C4×Dic71 | — | 2 | 1 | no | — |
| 254 | C4×Dic71 | — | 2 | 1 | no | — |
| 255 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 256 | C2×D4×C71 | — | 2 | 1 | no | — |
| 257 | C2×D4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 258 | C22×C4×C71 | — | 2 | 1 | no | — |
| 259 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 260 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 261 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 262 | C2×C8×C71 | — | 2 | 2 | no | — |
| 263 | C2×C8×C71 | — | 2 | 2 | no | — |
| 264 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 265 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 266 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 267 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 268 | C4⋊C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 269 | C4⋊C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 270 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 271 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 272 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 273 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 274 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 275 | C42×C71 | — | 2 | 1 | no | — |
| 276 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 277 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 278 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 279 | C42×C71 | C24 | 1 | 1 | yes | characteristic |
| 280 | C23×C71 | — | 2 | 1 | no | — |
| 281 | C23×C71 | #120 | 1 | 1 | yes | characteristic |
| 282 | C22×D71 | — | 2 | 1 | no | — |
| 283 | C22×D71 | — | 2 | 1 | no | — |
| 284 | C22×D71 | — | 4 | 2 | no | — |
| 285 | C22×D71 | — | 8 | 1 | no | — |
| 286 | C22×D71 | — | 8 | 1 | no | — |
| 287 | C22×D71 | — | 8 | 1 | no | — |
| 288 | C22×D71 | — | 8 | 2 | no | — |
| 289 | C22×D71 | — | 8 | 2 | no | — |
| 290 | C22×D71 | — | 8 | 2 | no | — |
| 291 | Q8×C71 | — | 4 | 1 | no | — |
| 292 | D4×C71 | — | 4 | 1 | no | — |
| 293 | D4×C71 | — | 8 | 1 | no | — |
| 294 | C2×C4×C71 | — | 2 | 1 | no | — |
| 295 | C2×C4×C71 | — | 2 | 1 | no | — |
| 296 | C2×C4×C71 | — | 2 | 1 | no | — |
| 297 | C2×C4×C71 | — | 4 | 1 | no | — |
| 298 | C2×C4×C71 | — | 4 | 1 | no | — |
| 299 | C2×C4×C71 | — | 4 | 1 | no | — |
| 300 | C2×C4×C71 | — | 8 | 1 | no | — |
| 301 | C2×C4×C71 | #120 | 1 | 1 | yes | characteristic |
| 302 | C2×C4×C71 | #120 | 1 | 1 | yes | characteristic |
| 303 | C2×C4×C71 | #120 | 1 | 1 | yes | characteristic |
| 304 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 305 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 306 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 307 | C22⋊D71 | — | 8 | 1 | no | — |
| 308 | C22⋊D71 | — | 8 | 1 | no | — |
| 309 | C22⋊D71 | — | 8 | 1 | no | — |
| 310 | C22⋊D71 | — | 8 | 1 | no | — |
| 311 | C2×Dic71 | — | 2 | 1 | no | — |
| 312 | C2×Dic71 | — | 2 | 1 | no | — |
| 313 | C2×Dic71 | — | 2 | 1 | no | — |
| 314 | C2×Dic71 | — | 2 | 1 | no | — |
| 315 | C2×Dic71 | — | 2 | 1 | no | — |
| 316 | C2×Dic71 | — | 2 | 1 | no | — |
| 317 | C2×Dic71 | — | 8 | 1 | no | — |
| 318 | D284 | — | 4 | 1 | no | — |
| 319 | D284 | — | 4 | 1 | no | — |
| 320 | D284 | — | 4 | 2 | no | — |
| 321 | D284 | — | 4 | 2 | no | — |
| 322 | D284 | — | 4 | 2 | no | — |
| 323 | D284 | — | 4 | 2 | no | — |
| 324 | D284 | — | 4 | 2 | no | — |
| 325 | D284 | — | 4 | 2 | no | — |
| 326 | D284 | — | 8 | 2 | no | — |
| 327 | D284 | — | 8 | 2 | no | — |
| 328 | D284 | — | 8 | 2 | no | — |
| 329 | D284 | — | 8 | 1 | no | — |
| 330 | C4×D71 | — | 8 | 1 | no | — |
| 331 | C4×D71 | — | 8 | 1 | no | — |
| 332 | C4×D71 | — | 8 | 1 | no | — |
| 333 | C4×D71 | — | 8 | 1 | no | — |
| 334 | Dic142 | — | 4 | 1 | no | — |
| 335 | Dic142 | — | 4 | 1 | no | — |
| 336 | Dic142 | — | 8 | 1 | no | — |
| 337 | Dic142 | — | 8 | 1 | no | — |
| 338 | Dic142 | — | 8 | 1 | no | — |
| 339 | C8×C71 | — | 4 | 2 | no | — |
| 340 | C8×C71 | — | 4 | 2 | no | — |
| 341 | C71⋊C8 | — | 4 | 2 | no | — |
| 342 | C22×C71 | — | 2 | 1 | no | — |
| 343 | C22×C71 | — | 2 | 1 | no | — |
| 344 | C22×C71 | — | 2 | 1 | no | — |
| 345 | C22×C71 | — | 4 | 1 | no | — |
| 346 | C22×C71 | — | 4 | 1 | no | — |
| 347 | C22×C71 | — | 4 | 1 | no | — |
| 348 | C22×C71 | C2×#120 | 1 | 1 | yes | characteristic |
| 349 | C2×D71 | — | 4 | 1 | no | — |
| 350 | C2×D71 | — | 4 | 1 | no | — |
| 351 | C2×D71 | — | 4 | 1 | no | — |
| 352 | C2×D71 | — | 4 | 1 | no | — |
| 353 | C2×D71 | — | 4 | 1 | no | — |
| 354 | C2×D71 | — | 4 | 1 | no | — |
| 355 | C2×D71 | — | 8 | 2 | no | — |
| 356 | C2×D71 | — | 8 | 2 | no | — |
| 357 | C2×D71 | — | 8 | 2 | no | — |
| 358 | C2×D71 | — | 16 | 2 | no | — |
| 359 | C2×D71 | — | 16 | 4 | no | — |
| 360 | C4×C71 | — | 2 | 1 | no | — |
| 361 | C4×C71 | — | 2 | 1 | no | — |
| 362 | C4×C71 | — | 2 | 1 | no | — |
| 363 | C4×C71 | — | 2 | 1 | no | — |
| 364 | C4×C71 | — | 2 | 1 | no | — |
| 365 | C4×C71 | — | 2 | 1 | no | — |
| 366 | C4×C71 | — | 4 | 1 | no | — |
| 367 | C4×C71 | — | 4 | 1 | no | — |
| 368 | C4×C71 | — | 4 | 1 | no | — |
| 369 | Dic71 | — | 4 | 1 | no | — |
| 370 | Dic71 | — | 4 | 1 | no | — |
| 371 | Dic71 | — | 4 | 1 | no | — |
| 372 | Dic71 | — | 4 | 1 | no | — |
| 373 | Dic71 | — | 4 | 1 | no | — |
| 374 | Dic71 | — | 4 | 1 | no | — |
| 375 | #19094 | — | 71 | 1 | no | maximal, Sylow |
| 376 | C2×C71 | — | 4 | 1 | no | — |
| 377 | C2×C71 | — | 8 | 1 | no | — |
| 378 | C2×C71 | #3021 | 1 | 1 | yes | characteristic |
| 379 | C2×C71 | #3021 | 1 | 1 | yes | characteristic |
| 380 | C2×C71 | #3021 | 1 | 1 | yes | characteristic |
| 381 | D71 | — | 8 | 1 | no | — |
| 382 | D71 | — | 8 | 1 | no | — |
| 383 | D71 | — | 16 | 2 | no | — |
| 384 | #3568 | — | 71 | 1 | no | — |
| 385 | #3217 | — | 71 | 1 | no | — |
| 386 | #3217 | — | 71 | 1 | no | — |
| 387 | #3217 | — | 71 | 1 | no | — |
| 388 | #1657 | — | 71 | 2 | no | — |
| 389 | #1657 | — | 71 | 2 | no | — |
| 390 | #1657 | — | 71 | 2 | no | — |
| 391 | #1655 | — | 71 | 2 | no | — |
| 392 | #1535 | — | 71 | 1 | no | — |
| 393 | #1535 | — | 71 | 1 | no | — |
| 394 | #1535 | D71 | 1 | 1 | yes | characteristic, complemented |
| 395 | C71 | #19094 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 396 | #563 | — | 71 | 1 | no | — |
| 397 | #563 | — | 71 | 1 | no | — |
| 398 | #563 | — | 71 | 1 | no | — |
| 399 | H(3,𝔽4) | — | 71 | 1 | no | — |
| 400 | #556 | — | 142 | 1 | no | — |
| 401 | #556 | — | 142 | 1 | no | — |
| 402 | #556 | — | 142 | 1 | no | — |
| 403 | #551 | — | 142 | 1 | no | — |
| 404 | #551 | — | 142 | 1 | no | — |
| 405 | #551 | — | 142 | 1 | no | — |
| 406 | #542 | — | 142 | 1 | no | — |
| 407 | #542 | — | 142 | 1 | no | — |
| 408 | #542 | — | 142 | 1 | no | — |
| 409 | #538 | — | 142 | 1 | no | — |
| 410 | #538 | — | 142 | 1 | no | — |
| 411 | #538 | — | 142 | 1 | no | — |
| 412 | C2×#127 | — | 71 | 1 | no | — |
| 413 | #529 | — | 71 | 1 | no | — |
| 414 | #529 | — | 71 | 1 | no | — |
| 415 | #529 | C2×D71 | 1 | 1 | yes | characteristic |
| 416 | #496 | — | 71 | 2 | no | — |
| 417 | #496 | — | 71 | 2 | no | — |
| 418 | #496 | — | 71 | 2 | no | — |
| 419 | #490 | — | 71 | 2 | no | — |
| 420 | #490 | — | 71 | 2 | no | — |
| 421 | #490 | — | 71 | 2 | no | — |
| 422 | #460 | — | 142 | 1 | no | — |
| 423 | #460 | — | 142 | 1 | no | — |
| 424 | #460 | — | 142 | 1 | no | — |
| 425 | #459 | — | 142 | 1 | no | — |
| 426 | #459 | — | 142 | 1 | no | — |
| 427 | #459 | — | 142 | 1 | no | — |
| 428 | #450 | — | 142 | 1 | no | — |
| 429 | #450 | — | 142 | 1 | no | — |
| 430 | #450 | — | 142 | 1 | no | — |
| 431 | #447 | — | 142 | 1 | no | — |
| 432 | #447 | — | 142 | 1 | no | — |
| 433 | #447 | — | 142 | 1 | no | — |
| 434 | #432 | — | 71 | 1 | no | — |
| 435 | #432 | C2×D71 | 1 | 1 | yes | characteristic, complemented |
| 436 | #432 | C2×D71 | 1 | 1 | yes | characteristic, complemented |
| 437 | #330 | — | 71 | 2 | no | — |
| 438 | #330 | — | 71 | 2 | no | — |
| 439 | #330 | C2×D71 | 1 | 2 | yes | complemented |
| 440 | #329 | — | 71 | 2 | no | — |
| 441 | #329 | — | 71 | 2 | no | — |
| 442 | #329 | C2×D71 | 1 | 2 | yes | complemented |
| 443 | C22×D4 | — | 142 | 1 | no | — |
| 444 | C22×D4 | — | 142 | 1 | no | — |
| 445 | C22×D4 | — | 142 | 1 | no | — |
| 446 | C2×SD16 | — | 142 | 2 | no | — |
| 447 | C2×SD16 | — | 142 | 2 | no | — |
| 448 | C2×SD16 | — | 142 | 2 | no | — |
| 449 | C2×D8 | — | 142 | 2 | no | — |
| 450 | C2×D8 | — | 142 | 2 | no | — |
| 451 | C2×D8 | — | 142 | 2 | no | — |
| 452 | C4⋊Q8 | — | 142 | 1 | no | — |
| 453 | C4⋊Q8 | — | 142 | 1 | no | — |
| 454 | C4⋊Q8 | — | 142 | 1 | no | — |
| 455 | #127 | — | 71 | 2 | no | — |
| 456 | #127 | — | 142 | 1 | no | — |
| 457 | #127 | — | 142 | 1 | no | — |
| 458 | #127 | — | 142 | 1 | no | — |
| 459 | #126 | — | 2 | 1 | no | — |
| 460 | #126 | — | 142 | 1 | no | — |
| 461 | #126 | — | 142 | 1 | no | — |
| 462 | #126 | — | 142 | 1 | no | — |
| 463 | #126 | — | 142 | 1 | no | — |
| 464 | #126 | — | 142 | 1 | no | — |
| 465 | #126 | — | 142 | 1 | no | — |
| 466 | #126 | — | 142 | 1 | no | — |
| 467 | #126 | — | 142 | 1 | no | — |
| 468 | #126 | — | 142 | 1 | no | — |
| 469 | #126 | — | 142 | 1 | no | — |
| 470 | #126 | — | 142 | 1 | no | — |
| 471 | #126 | — | 142 | 1 | no | — |
| 472 | #125 | — | 71 | 1 | no | — |
| 473 | #125 | — | 71 | 1 | no | — |
| 474 | #125 | C22×D71 | 1 | 1 | yes | characteristic |
| 475 | #124 | — | 71 | 1 | no | — |
| 476 | #124 | — | 71 | 1 | no | — |
| 477 | #124 | — | 142 | 1 | no | — |
| 478 | #124 | — | 142 | 1 | no | — |
| 479 | #124 | — | 142 | 1 | no | — |
| 480 | #124 | — | 142 | 1 | no | — |
| 481 | #124 | — | 142 | 1 | no | — |
| 482 | #124 | — | 142 | 1 | no | — |
| 483 | #124 | — | 142 | 1 | no | — |
| 484 | #124 | — | 142 | 1 | no | — |
| 485 | #124 | — | 142 | 1 | no | — |
| 486 | #124 | C22×D71 | 1 | 1 | yes | characteristic |
| 487 | #123 | — | 2 | 1 | no | — |
| 488 | #123 | — | 142 | 1 | no | — |
| 489 | #123 | — | 142 | 1 | no | — |
| 490 | #123 | — | 142 | 1 | no | — |
| 491 | #123 | — | 142 | 1 | no | — |
| 492 | #123 | — | 142 | 1 | no | — |
| 493 | #123 | — | 142 | 1 | no | — |
| 494 | #123 | — | 142 | 1 | no | — |
| 495 | #123 | — | 142 | 1 | no | — |
| 496 | C22⋊Q8 | — | 71 | 1 | no | — |
| 497 | C22⋊Q8 | — | 71 | 1 | no | — |
| 498 | C22⋊Q8 | — | 142 | 1 | no | — |
| 499 | C22⋊Q8 | — | 142 | 1 | no | — |
| 500 | C22⋊Q8 | — | 142 | 1 | no | — |
| 501 | C22⋊Q8 | — | 142 | 1 | no | — |
| 502 | C22⋊Q8 | — | 142 | 1 | no | — |
| 503 | C22⋊Q8 | — | 142 | 1 | no | — |
| 504 | C22⋊Q8 | — | 142 | 1 | no | — |
| 505 | C22⋊Q8 | — | 142 | 1 | no | — |
| 506 | C22⋊Q8 | — | 142 | 1 | no | — |
| 507 | C22⋊Q8 | D284 | 1 | 1 | yes | characteristic |
| 508 | #121 | — | 71 | 1 | no | — |
| 509 | #121 | — | 71 | 1 | no | — |
| 510 | #121 | — | 142 | 1 | no | — |
| 511 | #121 | — | 142 | 1 | no | — |
| 512 | #121 | — | 142 | 1 | no | — |
| 513 | #121 | D284 | 1 | 1 | yes | characteristic |
| 514 | #120 | — | 142 | 1 | no | — |
| 515 | #120 | — | 142 | 1 | no | — |
| 516 | #120 | — | 142 | 1 | no | — |
| 517 | #120 | — | 142 | 1 | no | — |
| 518 | C4×Q8 | — | 71 | 1 | no | — |
| 519 | C4×Q8 | — | 71 | 1 | no | — |
| 520 | C4×Q8 | — | 142 | 1 | no | — |
| 521 | C4×Q8 | — | 142 | 1 | no | — |
| 522 | C4×Q8 | — | 142 | 1 | no | — |
| 523 | C4×Q8 | D284 | 1 | 1 | yes | characteristic |
| 524 | C4×D4 | — | 2 | 1 | no | — |
| 525 | C4×D4 | — | 71 | 1 | no | — |
| 526 | C4×D4 | — | 71 | 1 | no | — |
| 527 | C4×D4 | — | 142 | 1 | no | — |
| 528 | C4×D4 | — | 142 | 1 | no | — |
| 529 | C4×D4 | — | 142 | 1 | no | — |
| 530 | C4×D4 | — | 142 | 1 | no | — |
| 531 | C4×D4 | — | 142 | 1 | no | — |
| 532 | C4×D4 | D284 | 1 | 1 | yes | characteristic |
| 533 | #117 | — | 2 | 1 | no | — |
| 534 | #117 | — | 142 | 1 | no | — |
| 535 | #117 | — | 142 | 1 | no | — |
| 536 | #117 | — | 142 | 1 | no | — |
| 537 | #117 | — | 142 | 1 | no | — |
| 538 | #117 | — | 142 | 1 | no | — |
| 539 | C2×C22⋊C4 | — | 142 | 1 | no | — |
| 540 | C2×C22⋊C4 | — | 142 | 1 | no | — |
| 541 | C2×C22⋊C4 | — | 142 | 1 | no | — |
| 542 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 543 | C4⋊C8 | — | 2 | 1 | no | — |
| 544 | C4⋊C8 | — | 2 | 1 | no | — |
| 545 | C4⋊C8 | — | 142 | 1 | no | — |
| 546 | #102 | — | 142 | 2 | no | — |
| 547 | #102 | — | 142 | 2 | no | — |
| 548 | #102 | — | 142 | 2 | no | — |
| 549 | #102 | — | 142 | 2 | no | — |
| 550 | #102 | — | 142 | 2 | no | — |
| 551 | #102 | — | 142 | 2 | no | — |
| 552 | C22⋊C8 | — | 2 | 1 | no | — |
| 553 | C22⋊C8 | — | 2 | 1 | no | — |
| 554 | C22⋊C8 | — | 142 | 1 | no | — |
| 555 | #97 | — | 71 | 2 | no | — |
| 556 | #97 | C22×D71 | 1 | 2 | yes | — |
| 557 | #97 | C22×D71 | 1 | 2 | yes | — |
| 558 | C24 | — | 284 | 1 | no | — |
| 559 | C24 | — | 142 | 1 | no | — |
| 560 | C2×Q8 | — | 71 | 1 | no | — |
| 561 | C2×Q8 | — | 71 | 1 | no | — |
| 562 | C2×Q8 | — | 142 | 1 | no | — |
| 563 | C2×Q8 | — | 142 | 1 | no | — |
| 564 | C2×Q8 | — | 142 | 1 | no | — |
| 565 | C2×Q8 | C2×D284 | 1 | 1 | yes | characteristic |
| 566 | C2×D4 | — | 2 | 1 | no | — |
| 567 | C2×D4 | — | 284 | 1 | no | — |
| 568 | C2×D4 | — | 284 | 1 | no | — |
| 569 | C2×D4 | — | 284 | 1 | no | — |
| 570 | C2×D4 | — | 568 | 2 | no | — |
| 571 | C2×D4 | — | 568 | 2 | no | — |
| 572 | C2×D4 | — | 568 | 2 | no | — |
| 573 | C2×D4 | — | 71 | 1 | no | — |
| 574 | C2×D4 | — | 71 | 1 | no | — |
| 575 | C2×D4 | — | 142 | 1 | no | — |
| 576 | C2×D4 | — | 142 | 1 | no | — |
| 577 | C2×D4 | — | 142 | 1 | no | — |
| 578 | C2×D4 | — | 142 | 1 | no | — |
| 579 | C2×D4 | — | 142 | 1 | no | — |
| 580 | C2×D4 | — | 142 | 2 | no | — |
| 581 | C2×D4 | — | 142 | 2 | no | — |
| 582 | C2×D4 | — | 142 | 2 | no | — |
| 583 | C2×D4 | C2×D284 | 1 | 1 | yes | characteristic |
| 584 | C22×C4 | — | 2 | 1 | no | — |
| 585 | C22×C4 | — | 142 | 1 | no | — |
| 586 | C22×C4 | — | 142 | 1 | no | — |
| 587 | C22×C4 | — | 142 | 1 | no | — |
| 588 | C22×C4 | — | 142 | 1 | no | — |
| 589 | C22×C4 | — | 142 | 1 | no | — |
| 590 | C22×C4 | D4×D71 | 1 | 1 | yes | characteristic |
| 591 | C22×C4 | D4×D71 | 1 | 1 | yes | characteristic |
| 592 | C22×C4 | C2×D284 | 1 | 1 | yes | characteristic |
| 593 | SD16 | — | 568 | 2 | no | — |
| 594 | SD16 | — | 568 | 2 | no | — |
| 595 | SD16 | — | 568 | 2 | no | — |
| 596 | D8 | — | 568 | 2 | no | — |
| 597 | D8 | — | 568 | 2 | no | — |
| 598 | D8 | — | 568 | 2 | no | — |
| 599 | C2×C8 | — | 2 | 2 | no | — |
| 600 | C2×C8 | — | 2 | 2 | no | — |
| 601 | C2×C8 | — | 142 | 2 | no | — |
| 602 | C4⋊C4 | — | 2 | 1 | no | — |
| 603 | C4⋊C4 | — | 2 | 1 | no | — |
| 604 | C4⋊C4 | — | 2 | 1 | no | — |
| 605 | C4⋊C4 | — | 2 | 1 | no | — |
| 606 | C4⋊C4 | — | 71 | 1 | no | — |
| 607 | C4⋊C4 | — | 71 | 1 | no | — |
| 608 | C4⋊C4 | — | 71 | 1 | no | — |
| 609 | C4⋊C4 | — | 71 | 1 | no | — |
| 610 | C4⋊C4 | — | 142 | 1 | no | — |
| 611 | C4⋊C4 | — | 142 | 1 | no | — |
| 612 | C4⋊C4 | — | 142 | 1 | no | — |
| 613 | C4⋊C4 | — | 142 | 1 | no | — |
| 614 | C4⋊C4 | — | 142 | 1 | no | — |
| 615 | C4⋊C4 | — | 142 | 1 | no | — |
| 616 | C4⋊C4 | — | 142 | 1 | no | — |
| 617 | C4⋊C4 | — | 142 | 1 | no | — |
| 618 | C4⋊C4 | — | 142 | 1 | no | — |
| 619 | C4⋊C4 | — | 142 | 1 | no | — |
| 620 | C4⋊C4 | — | 142 | 1 | no | — |
| 621 | C4⋊C4 | — | 142 | 1 | no | — |
| 622 | C4⋊C4 | — | 142 | 1 | no | — |
| 623 | C4⋊C4 | — | 142 | 1 | no | — |
| 624 | C4⋊C4 | C2×D284 | 1 | 1 | yes | characteristic |
| 625 | C4⋊C4 | C2×D284 | 1 | 1 | yes | characteristic |
| 626 | C22⋊C4 | — | 2 | 1 | no | — |
| 627 | C22⋊C4 | — | 2 | 1 | no | — |
| 628 | C22⋊C4 | — | 2 | 1 | no | — |
| 629 | C22⋊C4 | — | 2 | 1 | no | — |
| 630 | C22⋊C4 | — | 2 | 1 | no | — |
| 631 | C22⋊C4 | — | 142 | 1 | no | — |
| 632 | C22⋊C4 | — | 142 | 1 | no | — |
| 633 | C22⋊C4 | — | 142 | 1 | no | — |
| 634 | C22⋊C4 | — | 142 | 1 | no | — |
| 635 | C22⋊C4 | — | 142 | 1 | no | — |
| 636 | C22⋊C4 | — | 142 | 1 | no | — |
| 637 | C22⋊C4 | — | 142 | 1 | no | — |
| 638 | C22⋊C4 | — | 142 | 1 | no | — |
| 639 | C22⋊C4 | — | 142 | 1 | no | — |
| 640 | C22⋊C4 | — | 142 | 1 | no | — |
| 641 | C22⋊C4 | — | 142 | 1 | no | — |
| 642 | C22⋊C4 | — | 142 | 1 | no | — |
| 643 | C22⋊C4 | — | 142 | 1 | no | — |
| 644 | C22⋊C4 | — | 142 | 1 | no | — |
| 645 | C22⋊C4 | — | 142 | 1 | no | — |
| 646 | C22⋊C4 | — | 142 | 1 | no | — |
| 647 | C22⋊C4 | — | 142 | 1 | no | — |
| 648 | C22⋊C4 | — | 142 | 1 | no | — |
| 649 | C22⋊C4 | — | 142 | 1 | no | — |
| 650 | C22⋊C4 | — | 142 | 1 | no | — |
| 651 | C22⋊C4 | — | 142 | 1 | no | — |
| 652 | C22⋊C4 | — | 142 | 1 | no | — |
| 653 | C42 | — | 2 | 1 | no | — |
| 654 | C42 | — | 142 | 1 | no | — |
| 655 | C42 | — | 142 | 1 | no | — |
| 656 | C42 | — | 142 | 1 | no | — |
| 657 | C42 | — | 142 | 1 | no | — |
| 658 | C42 | — | 142 | 1 | no | — |
| 659 | C42 | — | 142 | 1 | no | — |
| 660 | C42 | D4×D71 | 1 | 1 | yes | characteristic |
| 661 | C42 | D4×D71 | 1 | 1 | yes | characteristic |
| 662 | C42 | C2×D284 | 1 | 1 | yes | characteristic |
| 663 | C42 | C23×D71 | 1 | 1 | yes | characteristic |
| 664 | C23 | — | 2 | 1 | no | — |
| 665 | C23 | — | 284 | 2 | no | — |
| 666 | C23 | — | 568 | 2 | no | — |
| 667 | C23 | — | 568 | 2 | no | — |
| 668 | C23 | — | 568 | 2 | no | — |
| 669 | C23 | — | 568 | 1 | no | — |
| 670 | C23 | — | 568 | 1 | no | — |
| 671 | C23 | — | 568 | 1 | no | — |
| 672 | C23 | — | 142 | 1 | no | — |
| 673 | C23 | — | 142 | 1 | no | — |
| 674 | C23 | #14556098 | 1 | 1 | yes | characteristic |
| 675 | Q8 | — | 4 | 1 | no | — |
| 676 | Q8 | — | 284 | 1 | no | — |
| 677 | Q8 | — | 284 | 1 | no | — |
| 678 | Q8 | — | 568 | 1 | no | — |
| 679 | Q8 | — | 568 | 1 | no | — |
| 680 | Q8 | — | 568 | 1 | no | — |
| 681 | D4 | — | 4 | 1 | no | — |
| 682 | D4 | — | 8 | 1 | no | — |
| 683 | D4 | — | 284 | 1 | no | — |
| 684 | D4 | — | 284 | 1 | no | — |
| 685 | D4 | — | 284 | 2 | no | — |
| 686 | D4 | — | 284 | 2 | no | — |
| 687 | D4 | — | 284 | 2 | no | — |
| 688 | D4 | — | 284 | 2 | no | — |
| 689 | D4 | — | 284 | 2 | no | — |
| 690 | D4 | — | 284 | 2 | no | — |
| 691 | D4 | — | 568 | 2 | no | — |
| 692 | D4 | — | 568 | 2 | no | — |
| 693 | D4 | — | 568 | 2 | no | — |
| 694 | D4 | — | 568 | 1 | no | — |
| 695 | D4 | — | 568 | 1 | no | — |
| 696 | D4 | — | 568 | 1 | no | — |
| 697 | D4 | — | 568 | 1 | no | — |
| 698 | D4 | — | 568 | 1 | no | — |
| 699 | C2×C4 | — | 2 | 1 | no | — |
| 700 | C2×C4 | — | 2 | 1 | no | — |
| 701 | C2×C4 | — | 2 | 1 | no | — |
| 702 | C2×C4 | — | 4 | 1 | no | — |
| 703 | C2×C4 | — | 4 | 1 | no | — |
| 704 | C2×C4 | — | 4 | 1 | no | — |
| 705 | C2×C4 | — | 8 | 1 | no | — |
| 706 | C2×C4 | — | 568 | 1 | no | — |
| 707 | C2×C4 | — | 568 | 1 | no | — |
| 708 | C2×C4 | — | 568 | 1 | no | — |
| 709 | C2×C4 | — | 568 | 1 | no | — |
| 710 | C2×C4 | — | 568 | 1 | no | — |
| 711 | C2×C4 | — | 142 | 1 | no | — |
| 712 | C2×C4 | — | 142 | 1 | no | — |
| 713 | C2×C4 | — | 142 | 1 | no | — |
| 714 | C2×C4 | — | 142 | 1 | no | — |
| 715 | C2×C4 | — | 142 | 1 | no | — |
| 716 | C2×C4 | — | 142 | 1 | no | — |
| 717 | C2×C4 | #14556098 | 1 | 1 | yes | characteristic |
| 718 | C2×C4 | #14556098 | 1 | 1 | yes | characteristic |
| 719 | C2×C4 | #14556098 | 1 | 1 | yes | characteristic |
| 720 | C2×C4 | C2×D4×D71 | 1 | 1 | yes | characteristic |
| 721 | C2×C4 | C2×D4×D71 | 1 | 1 | yes | characteristic |
| 722 | C2×C4 | C22×D284 | 1 | 1 | yes | characteristic |
| 723 | C8 | — | 4 | 2 | no | — |
| 724 | C8 | — | 4 | 2 | no | — |
| 725 | C8 | — | 284 | 2 | no | — |
| 726 | C22 | — | 2 | 1 | no | — |
| 727 | C22 | — | 2 | 1 | no | — |
| 728 | C22 | — | 2 | 1 | no | — |
| 729 | C22 | — | 4 | 1 | no | — |
| 730 | C22 | — | 4 | 1 | no | — |
| 731 | C22 | — | 4 | 1 | no | — |
| 732 | C22 | — | 284 | 1 | no | — |
| 733 | C22 | — | 284 | 1 | no | — |
| 734 | C22 | — | 284 | 1 | no | — |
| 735 | C22 | — | 284 | 1 | no | — |
| 736 | C22 | — | 284 | 1 | no | — |
| 737 | C22 | — | 284 | 1 | no | — |
| 738 | C22 | — | 568 | 2 | no | — |
| 739 | C22 | — | 568 | 2 | no | — |
| 740 | C22 | — | 568 | 2 | no | — |
| 741 | C22 | — | 1136 | 4 | no | — |
| 742 | C22 | — | 1136 | 2 | no | — |
| 743 | C22 | C2×#14556098 | 1 | 1 | yes | characteristic |
| 744 | C4 | — | 2 | 1 | no | — |
| 745 | C4 | — | 2 | 1 | no | — |
| 746 | C4 | — | 2 | 1 | no | — |
| 747 | C4 | — | 2 | 1 | no | — |
| 748 | C4 | — | 2 | 1 | no | — |
| 749 | C4 | — | 2 | 1 | no | — |
| 750 | C4 | — | 4 | 1 | no | — |
| 751 | C4 | — | 4 | 1 | no | — |
| 752 | C4 | — | 4 | 1 | no | — |
| 753 | C4 | — | 284 | 1 | no | — |
| 754 | C4 | — | 284 | 1 | no | — |
| 755 | C4 | — | 284 | 1 | no | — |
| 756 | C4 | — | 284 | 1 | no | — |
| 757 | C4 | — | 284 | 1 | no | — |
| 758 | C4 | — | 284 | 1 | no | — |
| 759 | C2 | — | 4 | 1 | no | — |
| 760 | C2 | — | 8 | 1 | no | — |
| 761 | C2 | — | 568 | 1 | no | — |
| 762 | C2 | — | 568 | 1 | no | — |
| 763 | C2 | — | 1136 | 2 | no | — |
| 764 | C2 | #22597713 | 1 | 1 | yes | characteristic |
| 765 | C2 | #22597713 | 1 | 1 | yes | characteristic |
| 766 | C2 | #22597714 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22603036 | C2 | semidirect |
| 2. #22599360 | C2 | semidirect |
| 3. #22599360 | C2 | semidirect |
| 4. #22599355 | C2 | semidirect |
| 5. #22587640 | C2 | semidirect |
| 6. #22587640 | C2 | semidirect |
| 7. #22587639 | C2 | semidirect |
| 8. #22587630 | C2 | semidirect |
| 9. #22586972 | C2 | semidirect |
| 10. #22586969 | C2 | semidirect |
| 11. C71×#1535 | C2 | semidirect |
| 12. #17986753 | C22 | semidirect |
| 13. #17986753 | C22 | semidirect |
| 14. #17986749 | C22 | semidirect |
| 15. #17986741 | C22 | semidirect |
| 28. C2×#14556125 | C22 | semidirect |
| 34. #17986365 | C22 | semidirect |
| 35. #17986364 | C22 | semidirect |
| 36. #17986364 | C22 | semidirect |
| 49. #17986056 | C22 | semidirect |
| 50. #17985740 | C22 | semidirect |
| 51. #17985740 | C22 | semidirect |
| 52. #17985738 | C22 | semidirect |
| 53. #17985738 | C22 | semidirect |
| 55. #432×C71 | C22 | semidirect |
| 56. #432×C71 | C22 | semidirect |
| 57. #330×C71 | C22 | semidirect |
| 58. #329×C71 | C22 | semidirect |
| 394. #1535 | D71 | semidirect |
| 395. C71 | #19094 | semidirect |
| 435. #432 | C2×D71 | semidirect |
| 436. #432 | C2×D71 | semidirect |
| 439. #330 | C2×D71 | semidirect |
| 442. #329 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22603036 | 2 |
| #22599360 | 2 |
| #22599355 | 2 |
| #22587640 | 2 |
| #22587639 | 2 |
| #22587630 | 2 |
| #22586972 | 2 |
| #22586969 | 2 |
| C71×#1535 | 2 |
| #19094 | 71 |