Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
2018 conjugacy classes of subgroups.
The subgroup lattice has 716 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22602589 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22601987 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22600393 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #22600229 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | D4×Dic284 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #22599915 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #22599425 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #22599235 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #22599123 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #22598641 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #22597637 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×#17986157 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | C71×#2977 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C2×#14556175 | C22 | 1 | 1 | yes | characteristic |
| 15 | C23×Dic142 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#14556161 | C22 | 1 | 2 | yes | complemented |
| 17 | C22×Dic284 | C22 | 1 | 4 | yes | — |
| 18 | C22×Dic284 | C22 | 1 | 2 | yes | complemented |
| 19 | #17986752 | — | 2 | 2 | no | — |
| 20 | #17986689 | C22 | 1 | 4 | yes | — |
| 21 | #17986680 | — | 2 | 2 | no | — |
| 22 | D4×Dic142 | C22 | 1 | 4 | yes | — |
| 23 | D4×Dic142 | C22 | 1 | 4 | yes | — |
| 24 | #17986662 | — | 2 | 2 | no | — |
| 25 | #17986658 | C22 | 1 | 4 | yes | — |
| 26 | #17986655 | — | 2 | 2 | no | — |
| 27 | #17986628 | — | 2 | 2 | no | — |
| 28 | #17986611 | C22 | 1 | 2 | yes | — |
| 29 | #17986594 | — | 2 | 2 | no | — |
| 30 | #17986575 | C22 | 1 | 1 | yes | characteristic |
| 31 | #17986571 | — | 2 | 2 | no | — |
| 32 | #17986570 | C22 | 1 | 1 | yes | characteristic |
| 33 | #17986570 | C22 | 1 | 2 | yes | — |
| 34 | #17986510 | C22 | 1 | 1 | yes | characteristic |
| 35 | #17986505 | — | 2 | 2 | no | — |
| 36 | C2×#14556107 | C22 | 1 | 2 | yes | — |
| 37 | #17986476 | C22 | 1 | 1 | yes | characteristic |
| 38 | #17986393 | C22 | 1 | 2 | yes | complemented |
| 39 | #17986379 | C22 | 1 | 2 | yes | complemented |
| 40 | #17986368 | C22 | 1 | 2 | yes | complemented |
| 41 | #17986354 | C22 | 1 | 2 | yes | complemented |
| 42 | #17986341 | C22 | 1 | 4 | yes | — |
| 43 | #17986341 | C22 | 1 | 4 | yes | complemented |
| 44 | #17986330 | C22 | 1 | 2 | yes | — |
| 45 | #17986313 | C22 | 1 | 2 | yes | — |
| 46 | #17986307 | C22 | 1 | 4 | yes | complemented |
| 47 | #17986257 | C22 | 1 | 4 | yes | complemented |
| 48 | #17986240 | C22 | 1 | 4 | yes | — |
| 49 | #17986240 | C22 | 1 | 4 | yes | complemented |
| 50 | #17986228 | C22 | 1 | 4 | yes | — |
| 51 | #17986222 | C22 | 1 | 4 | yes | complemented |
| 52 | #17986210 | C22 | 1 | 4 | yes | complemented |
| 53 | #17986210 | C22 | 1 | 4 | yes | complemented |
| 54 | #17986163 | C22 | 1 | 4 | yes | — |
| 55 | #17986163 | C22 | 1 | 4 | yes | complemented |
| 56 | #17986157 | C22 | 1 | 4 | yes | — |
| 57 | #17986157 | C22 | 1 | 4 | yes | — |
| 58 | #17986157 | C22 | 1 | 4 | yes | — |
| 59 | #17986157 | C22 | 1 | 2 | yes | — |
| 60 | #17986157 | C22 | 1 | 4 | yes | — |
| 61 | #17986157 | C22 | 1 | 4 | yes | complemented |
| 62 | #17986157 | C22 | 1 | 4 | yes | complemented |
| 63 | #17986140 | C22 | 1 | 2 | yes | — |
| 64 | #17986107 | C22 | 1 | 4 | yes | complemented |
| 65 | C4×Dic284 | C22 | 1 | 4 | yes | complemented |
| 66 | #17986009 | C22 | 1 | 2 | yes | complemented |
| 67 | #17985996 | C22 | 1 | 2 | yes | complemented |
| 68 | C2×#14556053 | C22 | 1 | 4 | yes | — |
| 69 | #525×C71 | C22 | 1 | 1 | yes | characteristic |
| 70 | #435×C71 | C22 | 1 | 4 | yes | — |
| 71 | C8×D4×C71 | C22 | 1 | 4 | yes | — |
| 72 | #433×C71 | C22 | 1 | 2 | yes | — |
| 73 | #408×C71 | C22 | 1 | 2 | yes | — |
| 74 | C2×C22⋊C8×C71 | C22 | 1 | 2 | yes | — |
| 75 | #14556175 | — | 4 | 4 | no | — |
| 76 | C2×#11765865 | C23 | 1 | 2 | yes | — |
| 77 | C2×#11765865 | C23 | 1 | 1 | yes | characteristic |
| 78 | C2×#11765864 | — | 2 | 2 | no | — |
| 79 | C2×#11765864 | — | 2 | 1 | no | — |
| 80 | C22×Dic142 | — | 2 | 1 | no | — |
| 81 | C22×Dic142 | — | 2 | 2 | no | — |
| 82 | C22×Dic142 | — | 4 | 4 | no | — |
| 83 | C22×Dic142 | C23 | 1 | 1 | yes | characteristic |
| 84 | C22×Dic142 | C23 | 1 | 4 | yes | — |
| 85 | C22×Dic142 | C23 | 1 | 2 | yes | — |
| 86 | C22×Dic142 | C23 | 1 | 1 | yes | characteristic |
| 87 | C22×Dic142 | C23 | 1 | 2 | yes | — |
| 88 | C22×Dic142 | C23 | 1 | 2 | yes | — |
| 89 | C2×Q8×D71 | — | 2 | 1 | no | — |
| 90 | C23×Dic71 | — | 2 | 1 | no | — |
| 91 | #14556161 | — | 4 | 4 | no | — |
| 92 | C2×Dic284 | — | 4 | 8 | no | — |
| 93 | C2×Dic284 | — | 4 | 4 | no | — |
| 94 | C2×Dic284 | C23 | 1 | 4 | yes | — |
| 95 | C2×Dic284 | C23 | 1 | 4 | yes | — |
| 96 | C2×Dic284 | C23 | 1 | 4 | yes | — |
| 97 | C2×Dic284 | C23 | 1 | 4 | yes | — |
| 98 | C2×Dic284 | C23 | 1 | 4 | yes | — |
| 99 | C2×#11765854 | C23 | 1 | 4 | yes | — |
| 100 | #14556128 | C23 | 1 | 2 | yes | — |
| 101 | #14556128 | C23 | 1 | 2 | yes | — |
| 102 | #14556127 | — | 2 | 4 | no | — |
| 103 | #14556127 | — | 2 | 4 | no | — |
| 104 | #14556126 | — | 2 | 2 | no | — |
| 105 | #14556126 | — | 2 | 1 | no | — |
| 106 | #14556121 | — | 2 | 4 | no | — |
| 107 | #14556121 | — | 2 | 4 | no | — |
| 108 | #14556120 | C23 | 1 | 2 | yes | — |
| 109 | #14556118 | — | 2 | 4 | no | — |
| 110 | #14556118 | — | 2 | 4 | no | — |
| 111 | #14556116 | C23 | 1 | 2 | yes | — |
| 112 | #14556115 | — | 2 | 1 | no | — |
| 113 | #14556115 | — | 2 | 2 | no | — |
| 114 | #14556114 | — | 2 | 4 | no | — |
| 115 | #14556112 | — | 2 | 2 | no | — |
| 116 | #14556111 | — | 2 | 1 | no | — |
| 117 | #14556109 | — | 2 | 2 | no | — |
| 118 | #14556109 | — | 2 | 2 | no | — |
| 119 | #14556109 | — | 2 | 2 | no | — |
| 120 | #14556109 | — | 2 | 4 | no | — |
| 121 | #14556108 | — | 2 | 2 | no | — |
| 122 | #14556107 | — | 2 | 2 | no | — |
| 123 | #14556107 | — | 2 | 2 | no | — |
| 124 | #14556107 | C23 | 1 | 4 | yes | — |
| 125 | #14556107 | C23 | 1 | 4 | yes | — |
| 126 | #14556107 | C23 | 1 | 4 | yes | — |
| 127 | #14556107 | C23 | 1 | 2 | yes | — |
| 128 | #14556107 | C23 | 1 | 4 | yes | — |
| 129 | #14556106 | — | 2 | 4 | no | — |
| 130 | #14556105 | — | 2 | 4 | no | — |
| 131 | #14556105 | — | 2 | 4 | no | — |
| 132 | #14556105 | — | 2 | 4 | no | — |
| 133 | #14556105 | — | 2 | 4 | no | — |
| 134 | #14556102 | C23 | 1 | 2 | yes | — |
| 135 | #14556100 | — | 2 | 4 | no | — |
| 136 | #14556097 | — | 2 | 1 | no | — |
| 137 | C4×Dic142 | C23 | 1 | 4 | yes | — |
| 138 | C4×Dic142 | C23 | 1 | 4 | yes | — |
| 139 | #14556093 | — | 2 | 2 | no | — |
| 140 | D4×Dic71 | — | 2 | 4 | no | — |
| 141 | D4×Dic71 | — | 2 | 4 | no | — |
| 142 | C4×C22⋊D71 | — | 2 | 2 | no | — |
| 143 | (C22⋊D71)⋊C4 | — | 2 | 4 | no | — |
| 144 | #14556087 | C23 | 1 | 1 | yes | characteristic |
| 145 | #14556087 | C23 | 1 | 2 | yes | — |
| 146 | #14556084 | — | 2 | 2 | no | — |
| 147 | #14556084 | — | 2 | 4 | no | — |
| 148 | C2×C4⋊Dic71 | C23 | 1 | 2 | yes | — |
| 149 | C2×Dic71⋊C4 | — | 2 | 2 | no | — |
| 150 | C2×C22⋊Dic71 | — | 2 | 2 | no | — |
| 151 | #14556062 | C23 | 1 | 4 | yes | — |
| 152 | #14556060 | C23 | 1 | 4 | yes | — |
| 153 | #14556053 | C23 | 1 | 4 | yes | — |
| 154 | #14556053 | C23 | 1 | 4 | yes | — |
| 155 | #14556053 | C23 | 1 | 4 | yes | — |
| 156 | #14556053 | C23 | 1 | 4 | yes | — |
| 157 | #14556053 | C23 | 1 | 4 | yes | — |
| 158 | #14556053 | C23 | 1 | 4 | yes | — |
| 159 | #14556053 | C23 | 1 | 4 | yes | — |
| 160 | #14556050 | C23 | 1 | 4 | yes | — |
| 161 | C2×#41×C71 | C23 | 1 | 1 | yes | characteristic |
| 162 | C23×C4×C71 | C23 | 1 | 1 | yes | characteristic |
| 163 | C2×M16×C71 | C23 | 1 | 2 | yes | — |
| 164 | C22×C8×C71 | C23 | 1 | 4 | yes | — |
| 165 | C22×C8×C71 | C23 | 1 | 2 | yes | — |
| 166 | #123×C71 | D4 | 1 | 2 | yes | — |
| 167 | C22⋊Q8×C71 | D4 | 1 | 2 | yes | — |
| 168 | #121×C71 | D4 | 1 | 2 | yes | — |
| 169 | #120×C71 | D4 | 1 | 2 | yes | — |
| 170 | C4×D4×C71 | C23 | 1 | 4 | yes | — |
| 171 | #117×C71 | C23 | 1 | 1 | yes | characteristic |
| 172 | C4⋊C8×C71 | C23 | 1 | 4 | yes | — |
| 173 | C22⋊C8×C71 | C23 | 1 | 4 | yes | — |
| 174 | C22⋊C8×C71 | C23 | 1 | 2 | yes | — |
| 175 | C22⋊C8×C71 | C23 | 1 | 2 | yes | — |
| 176 | C22⋊C8×C71 | C23 | 1 | 4 | yes | — |
| 177 | #97×C71 | C23 | 1 | 2 | yes | — |
| 178 | C4×C8×C71 | C23 | 1 | 2 | yes | — |
| 179 | #11765865 | — | 2 | 4 | no | — |
| 180 | #11765865 | — | 4 | 2 | no | — |
| 181 | #11765865 | — | 4 | 2 | no | — |
| 182 | #11765864 | — | 4 | 4 | no | — |
| 183 | #11765864 | — | 4 | 8 | no | — |
| 184 | C2×Dic142 | — | 2 | 1 | no | — |
| 185 | C2×Dic142 | — | 2 | 4 | no | — |
| 186 | C2×Dic142 | — | 2 | 8 | no | — |
| 187 | C2×Dic142 | — | 2 | 4 | no | — |
| 188 | C2×Dic142 | — | 2 | 2 | no | — |
| 189 | C2×Dic142 | — | 2 | 4 | no | — |
| 190 | C2×Dic142 | — | 2 | 1 | no | — |
| 191 | C2×Dic142 | — | 2 | 2 | no | — |
| 192 | C2×Dic142 | — | 2 | 2 | no | — |
| 193 | C2×Dic142 | — | 4 | 4 | no | — |
| 194 | C2×Dic142 | — | 4 | 2 | no | — |
| 195 | C2×Dic142 | — | 4 | 2 | no | — |
| 196 | C2×Dic142 | — | 4 | 2 | no | — |
| 197 | C2×Dic142 | — | 4 | 4 | no | — |
| 198 | C2×Dic142 | — | 4 | 2 | no | — |
| 199 | C2×Dic142 | — | 4 | 8 | no | — |
| 200 | C2×Dic142 | — | 4 | 4 | no | — |
| 201 | C2×Dic142 | C24 | 1 | 2 | yes | — |
| 202 | C2×Dic142 | C24 | 1 | 1 | yes | characteristic |
| 203 | C2×Dic142 | C24 | 1 | 4 | yes | — |
| 204 | C2×Dic142 | C24 | 1 | 2 | yes | — |
| 205 | Q8×D71 | — | 4 | 4 | no | — |
| 206 | C2×D284 | C24 | 1 | 1 | yes | characteristic |
| 207 | C2×C22⋊D71 | — | 2 | 1 | no | — |
| 208 | C2×C22⋊D71 | — | 2 | 2 | no | — |
| 209 | C2×C22⋊D71 | — | 2 | 2 | no | — |
| 210 | C22×Dic71 | — | 2 | 1 | no | — |
| 211 | C22×Dic71 | — | 2 | 4 | no | — |
| 212 | C22×Dic71 | — | 2 | 1 | no | — |
| 213 | C22×Dic71 | — | 2 | 2 | no | — |
| 214 | C22×Dic71 | — | 2 | 2 | no | — |
| 215 | C22×Dic71 | — | 2 | 2 | no | — |
| 216 | C22×Dic71 | — | 2 | 2 | no | — |
| 217 | C22×Dic71 | — | 4 | 4 | no | — |
| 218 | C2×C4×D71 | — | 2 | 2 | no | — |
| 219 | C2×C4×D71 | — | 2 | 1 | no | — |
| 220 | Dic284 | — | 2 | 8 | no | — |
| 221 | Dic284 | — | 2 | 8 | no | — |
| 222 | Dic284 | — | 4 | 4 | no | — |
| 223 | Dic284 | — | 4 | 4 | no | — |
| 224 | Dic284 | — | 4 | 4 | no | — |
| 225 | #11765854 | — | 4 | 4 | no | — |
| 226 | C4⋊Dic71 | — | 2 | 2 | no | — |
| 227 | C4⋊Dic71 | — | 2 | 4 | no | — |
| 228 | C4⋊Dic71 | — | 2 | 4 | no | — |
| 229 | C4⋊Dic71 | C24 | 1 | 4 | yes | — |
| 230 | C4⋊Dic71 | C24 | 1 | 2 | yes | — |
| 231 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 232 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 233 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 234 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 235 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 236 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 237 | Dic71⋊C4 | — | 2 | 2 | no | — |
| 238 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 239 | C22⋊Dic71 | — | 2 | 4 | no | — |
| 240 | C22⋊Dic71 | — | 2 | 4 | no | — |
| 241 | C22⋊Dic71 | — | 2 | 1 | no | — |
| 242 | C22⋊Dic71 | — | 2 | 2 | no | — |
| 243 | C22⋊Dic71 | — | 2 | 2 | no | — |
| 244 | C22⋊Dic71 | — | 2 | 4 | no | — |
| 245 | C22⋊Dic71 | — | 2 | 4 | no | — |
| 246 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 247 | (C2×D71)⋊C4 | — | 2 | 2 | no | — |
| 248 | C4×Dic71 | — | 2 | 2 | no | — |
| 249 | C4×Dic71 | — | 2 | 4 | no | — |
| 250 | C4×Dic71 | — | 2 | 4 | no | — |
| 251 | C4×Dic71 | — | 2 | 1 | no | — |
| 252 | C24×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 253 | #41×C71 | — | 4 | 2 | no | — |
| 254 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 255 | C2×D4×C71 | C2×D4 | 1 | 4 | yes | — |
| 256 | C2×D4×C71 | C2×D4 | 1 | 2 | yes | — |
| 257 | C2×D4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 258 | C22×C4×C71 | — | 4 | 2 | no | — |
| 259 | C22×C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 260 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 261 | C22×C4×C71 | C24 | 1 | 2 | yes | — |
| 262 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 263 | C22×C4×C71 | C24 | 1 | 2 | yes | — |
| 264 | M16×C71 | — | 4 | 2 | no | — |
| 265 | C2×C8×C71 | — | 4 | 2 | no | — |
| 266 | C2×C8×C71 | — | 4 | 4 | no | — |
| 267 | C2×C8×C71 | C24 | 1 | 4 | yes | — |
| 268 | C2×C8×C71 | C24 | 1 | 4 | yes | — |
| 269 | C4⋊C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 270 | C4⋊C4×C71 | C2×D4 | 1 | 4 | yes | — |
| 271 | C22⋊C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 272 | C22⋊C4×C71 | C2×D4 | 1 | 4 | yes | — |
| 273 | C22⋊C4×C71 | C2×D4 | 1 | 4 | yes | — |
| 274 | C42×C71 | C24 | 1 | 2 | yes | — |
| 275 | C23×C71 | — | 2 | 4 | no | — |
| 276 | C23×C71 | — | 4 | 1 | no | — |
| 277 | C23×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 278 | C23×C71 | C22×D4 | 1 | 2 | yes | — |
| 279 | C23×C71 | C22×D4 | 1 | 2 | yes | — |
| 280 | C22×D71 | — | 2 | 1 | no | — |
| 281 | Q8×C71 | — | 4 | 1 | no | — |
| 282 | D4×C71 | — | 2 | 8 | no | — |
| 283 | D4×C71 | — | 4 | 1 | no | — |
| 284 | D4×C71 | — | 4 | 2 | no | — |
| 285 | C2×C4×C71 | — | 2 | 4 | no | — |
| 286 | C2×C4×C71 | — | 2 | 2 | no | — |
| 287 | C2×C4×C71 | — | 2 | 2 | no | — |
| 288 | C2×C4×C71 | — | 2 | 2 | no | — |
| 289 | C2×C4×C71 | — | 4 | 2 | no | — |
| 290 | C2×C4×C71 | — | 4 | 1 | no | — |
| 291 | C2×C4×C71 | C22×D4 | 1 | 4 | yes | — |
| 292 | C2×C4×C71 | C22×D4 | 1 | 2 | yes | — |
| 293 | C2×C4×C71 | C22×D4 | 1 | 2 | yes | — |
| 294 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 295 | C2×C4×C71 | C25 | 1 | 1 | yes | characteristic |
| 296 | C22⋊D71 | — | 4 | 4 | no | — |
| 297 | C22⋊D71 | — | 4 | 2 | no | — |
| 298 | C22⋊D71 | — | 4 | 4 | no | — |
| 299 | C2×Dic71 | — | 2 | 4 | no | — |
| 300 | C2×Dic71 | — | 2 | 2 | no | — |
| 301 | C2×Dic71 | — | 2 | 2 | no | — |
| 302 | C2×Dic71 | — | 2 | 4 | no | — |
| 303 | C2×Dic71 | — | 2 | 4 | no | — |
| 304 | C2×Dic71 | — | 2 | 2 | no | — |
| 305 | C2×Dic71 | — | 2 | 1 | no | — |
| 306 | C2×Dic71 | — | 4 | 8 | no | — |
| 307 | C2×Dic71 | — | 4 | 4 | no | — |
| 308 | C2×Dic71 | — | 4 | 2 | no | — |
| 309 | C2×Dic71 | — | 4 | 4 | no | — |
| 310 | C2×Dic71 | — | 8 | 2 | no | — |
| 311 | C2×Dic71 | — | 8 | 2 | no | — |
| 312 | D284 | — | 2 | 2 | no | — |
| 313 | C4×D71 | — | 4 | 4 | no | — |
| 314 | C4×D71 | — | 4 | 2 | no | — |
| 315 | Dic142 | — | 2 | 4 | no | — |
| 316 | Dic142 | — | 2 | 2 | no | — |
| 317 | Dic142 | — | 2 | 4 | no | — |
| 318 | Dic142 | — | 2 | 4 | no | — |
| 319 | Dic142 | — | 2 | 4 | no | — |
| 320 | Dic142 | — | 2 | 2 | no | — |
| 321 | Dic142 | — | 4 | 4 | no | — |
| 322 | Dic142 | — | 4 | 8 | no | — |
| 323 | Dic142 | — | 4 | 2 | no | — |
| 324 | Dic142 | — | 8 | 2 | no | — |
| 325 | Dic142 | — | 8 | 2 | no | — |
| 326 | Dic142 | H(5,𝔽2) | 1 | 4 | yes | — |
| 327 | C8×C71 | — | 2 | 4 | no | — |
| 328 | C8×C71 | — | 2 | 4 | no | — |
| 329 | C22×C71 | — | 2 | 2 | no | — |
| 330 | C22×C71 | — | 2 | 2 | no | — |
| 331 | C22×C71 | — | 2 | 1 | no | — |
| 332 | C22×C71 | — | 2 | 2 | no | — |
| 333 | C22×C71 | — | 2 | 4 | no | — |
| 334 | C22×C71 | — | 2 | 2 | no | — |
| 335 | C22×C71 | — | 4 | 4 | no | — |
| 336 | C22×C71 | #578 | 1 | 4 | yes | — |
| 337 | C22×C71 | C23×D4 | 1 | 1 | yes | characteristic |
| 338 | C2×D71 | — | 4 | 1 | no | — |
| 339 | C2×D71 | — | 4 | 2 | no | — |
| 340 | C4×C71 | — | 2 | 1 | no | — |
| 341 | C4×C71 | — | 2 | 2 | no | — |
| 342 | C4×C71 | — | 2 | 2 | no | — |
| 343 | C4×C71 | — | 2 | 4 | no | — |
| 344 | C4×C71 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 345 | Dic71 | — | 2 | 4 | no | — |
| 346 | Dic71 | — | 4 | 2 | no | — |
| 347 | Dic71 | — | 4 | 1 | no | — |
| 348 | Dic71 | — | 4 | 4 | no | — |
| 349 | Dic71 | — | 4 | 4 | no | — |
| 350 | Dic71 | — | 4 | 2 | no | — |
| 351 | #61634 | — | 71 | 1 | no | maximal, Sylow |
| 352 | C2×C71 | — | 2 | 4 | no | — |
| 353 | C2×C71 | — | 4 | 2 | no | — |
| 354 | C2×C71 | — | 4 | 1 | no | — |
| 355 | C2×C71 | #3484 | 1 | 1 | yes | characteristic |
| 356 | C2×C71 | C2×#578 | 1 | 2 | yes | — |
| 357 | D71 | — | 8 | 1 | no | — |
| 358 | #3538 | — | 71 | 1 | no | — |
| 359 | #3486 | — | 71 | 1 | no | — |
| 360 | #3312 | — | 71 | 4 | no | — |
| 361 | #3300 | — | 71 | 4 | no | — |
| 362 | D4×Q16 | — | 71 | 4 | no | — |
| 363 | #3270 | — | 71 | 4 | no | — |
| 364 | #3223 | — | 71 | 2 | no | — |
| 365 | #3202 | — | 71 | 2 | no | — |
| 366 | #3190 | — | 71 | 2 | no | — |
| 367 | #3127 | — | 71 | 2 | no | — |
| 368 | #3011 | — | 71 | 2 | no | — |
| 369 | C2×#451 | — | 71 | 2 | no | — |
| 370 | #2977 | D71 | 1 | 1 | yes | characteristic, complemented |
| 371 | C71 | #61634 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 372 | C2×2−1+4 | — | 71 | 1 | no | — |
| 373 | C23×Q8 | — | 71 | 1 | no | — |
| 374 | C2×#137 | — | 71 | 2 | no | — |
| 375 | C22×Q16 | — | 71 | 4 | no | — |
| 376 | C22×Q16 | — | 71 | 2 | no | — |
| 377 | #563 | — | 142 | 2 | no | — |
| 378 | #552 | — | 71 | 4 | no | — |
| 379 | #551 | — | 142 | 2 | no | — |
| 380 | D4×Q8 | — | 71 | 4 | no | — |
| 381 | D4×Q8 | — | 71 | 4 | no | — |
| 382 | D4×Q8 | — | 142 | 2 | no | — |
| 383 | #548 | — | 71 | 4 | no | — |
| 384 | #548 | — | 142 | 2 | no | — |
| 385 | #544 | — | 142 | 2 | no | — |
| 386 | #541 | — | 71 | 2 | no | — |
| 387 | #539 | — | 142 | 2 | no | — |
| 388 | #536 | — | 71 | 1 | no | — |
| 389 | #536 | — | 71 | 2 | no | — |
| 390 | #536 | — | 71 | 1 | no | — |
| 391 | #536 | — | 142 | 2 | no | — |
| 392 | #525 | — | 71 | 1 | no | — |
| 393 | #525 | — | 142 | 2 | no | — |
| 394 | #525 | C2×D71 | 1 | 1 | yes | characteristic |
| 395 | C2×C22⋊Q8 | — | 71 | 2 | no | — |
| 396 | #519 | — | 71 | 1 | no | — |
| 397 | #497 | — | 71 | 2 | no | — |
| 398 | #494 | — | 71 | 2 | no | — |
| 399 | #491 | — | 71 | 2 | no | — |
| 400 | #488 | — | 71 | 2 | no | — |
| 401 | #485 | — | 71 | 4 | no | — |
| 402 | #485 | — | 71 | 4 | no | — |
| 403 | #483 | — | 71 | 2 | no | — |
| 404 | #480 | — | 71 | 2 | no | — |
| 405 | #479 | — | 71 | 4 | no | — |
| 406 | #470 | — | 71 | 4 | no | — |
| 407 | #467 | — | 71 | 4 | no | — |
| 408 | #467 | — | 71 | 4 | no | — |
| 409 | #465 | — | 71 | 4 | no | — |
| 410 | #464 | — | 71 | 4 | no | — |
| 411 | #462 | — | 71 | 4 | no | — |
| 412 | #462 | — | 71 | 4 | no | — |
| 413 | #452 | — | 71 | 4 | no | — |
| 414 | #452 | — | 71 | 4 | no | — |
| 415 | #451 | — | 71 | 4 | no | — |
| 416 | #451 | — | 71 | 2 | no | — |
| 417 | #451 | — | 71 | 4 | no | — |
| 418 | #451 | — | 71 | 4 | no | — |
| 419 | #451 | — | 71 | 4 | no | — |
| 420 | #451 | — | 71 | 4 | no | — |
| 421 | #451 | — | 71 | 4 | no | — |
| 422 | #448 | — | 71 | 2 | no | — |
| 423 | #441 | — | 71 | 4 | no | — |
| 424 | C4×Q16 | — | 71 | 4 | no | — |
| 425 | #435 | C2×D71 | 1 | 4 | yes | — |
| 426 | C8×D4 | C2×D71 | 1 | 4 | yes | — |
| 427 | #433 | C2×D71 | 1 | 2 | yes | — |
| 428 | #419 | — | 71 | 2 | no | — |
| 429 | #416 | — | 71 | 2 | no | — |
| 430 | C2×#103 | — | 71 | 4 | no | — |
| 431 | #408 | C2×D71 | 1 | 2 | yes | — |
| 432 | C2×C22⋊C8 | C2×D71 | 1 | 2 | yes | — |
| 433 | 2−1+4 | — | 284 | 4 | no | — |
| 434 | C2×#41 | — | 71 | 1 | no | — |
| 435 | C2×#41 | — | 71 | 2 | no | — |
| 436 | C2×#41 | — | 142 | 2 | no | — |
| 437 | C2×#41 | — | 142 | 1 | no | — |
| 438 | C2×#41 | C22×D71 | 1 | 1 | yes | characteristic |
| 439 | C22×Q8 | — | 284 | 4 | no | — |
| 440 | C22×Q8 | — | 71 | 2 | no | — |
| 441 | C22×Q8 | — | 71 | 1 | no | — |
| 442 | C22×Q8 | — | 71 | 2 | no | — |
| 443 | C22×Q8 | — | 71 | 4 | no | — |
| 444 | C22×Q8 | — | 71 | 2 | no | — |
| 445 | C22×Q8 | — | 71 | 1 | no | — |
| 446 | C22×Q8 | — | 142 | 1 | no | — |
| 447 | C22×Q8 | — | 142 | 1 | no | — |
| 448 | C22×Q8 | — | 142 | 2 | no | — |
| 449 | C23×C4 | — | 142 | 1 | no | — |
| 450 | C23×C4 | C22×D71 | 1 | 1 | yes | characteristic |
| 451 | #137 | — | 284 | 4 | no | — |
| 452 | C2×Q16 | — | 284 | 4 | no | — |
| 453 | C2×Q16 | — | 284 | 8 | no | — |
| 454 | C2×Q16 | — | 71 | 4 | no | — |
| 455 | C2×Q16 | — | 71 | 4 | no | — |
| 456 | C2×Q16 | — | 71 | 4 | no | — |
| 457 | C2×Q16 | — | 71 | 4 | no | — |
| 458 | C2×Q16 | — | 71 | 4 | no | — |
| 459 | C2×SD16 | — | 71 | 4 | no | — |
| 460 | C2×M16 | C22×D71 | 1 | 2 | yes | — |
| 461 | C22×C8 | C22×D71 | 1 | 4 | yes | — |
| 462 | C22×C8 | C22×D71 | 1 | 2 | yes | — |
| 463 | C4⋊Q8 | — | 71 | 2 | no | — |
| 464 | C4⋊Q8 | — | 71 | 2 | no | — |
| 465 | C4⋊Q8 | — | 142 | 2 | no | — |
| 466 | C4⋊Q8 | — | 142 | 1 | no | — |
| 467 | C4⋊Q8 | — | 142 | 4 | no | — |
| 468 | C4⋊Q8 | — | 142 | 4 | no | — |
| 469 | #126 | — | 142 | 4 | no | — |
| 470 | #126 | — | 142 | 4 | no | — |
| 471 | #125 | — | 71 | 2 | no | — |
| 472 | #125 | — | 142 | 4 | no | — |
| 473 | #125 | — | 142 | 4 | no | — |
| 474 | #124 | — | 71 | 2 | no | — |
| 475 | #124 | — | 142 | 1 | no | — |
| 476 | #124 | — | 142 | 2 | no | — |
| 477 | #124 | — | 142 | 4 | no | — |
| 478 | #123 | — | 142 | 2 | no | — |
| 479 | #123 | — | 142 | 2 | no | — |
| 480 | #123 | — | 142 | 2 | no | — |
| 481 | #123 | — | 142 | 4 | no | — |
| 482 | #123 | — | 142 | 1 | no | — |
| 483 | #123 | — | 142 | 2 | no | — |
| 484 | #123 | D284 | 1 | 2 | yes | — |
| 485 | C22⋊Q8 | — | 71 | 4 | no | — |
| 486 | C22⋊Q8 | — | 71 | 4 | no | — |
| 487 | C22⋊Q8 | — | 71 | 2 | no | — |
| 488 | C22⋊Q8 | — | 71 | 4 | no | — |
| 489 | C22⋊Q8 | — | 71 | 4 | no | — |
| 490 | C22⋊Q8 | — | 142 | 2 | no | — |
| 491 | C22⋊Q8 | — | 142 | 2 | no | — |
| 492 | C22⋊Q8 | — | 142 | 2 | no | — |
| 493 | C22⋊Q8 | — | 142 | 4 | no | — |
| 494 | C22⋊Q8 | — | 142 | 4 | no | — |
| 495 | C22⋊Q8 | — | 142 | 4 | no | — |
| 496 | C22⋊Q8 | — | 142 | 4 | no | — |
| 497 | C22⋊Q8 | — | 142 | 4 | no | — |
| 498 | C22⋊Q8 | D284 | 1 | 2 | yes | — |
| 499 | #121 | — | 71 | 2 | no | — |
| 500 | #121 | — | 142 | 4 | no | — |
| 501 | #121 | D284 | 1 | 2 | yes | — |
| 502 | #120 | — | 142 | 1 | no | — |
| 503 | #120 | D284 | 1 | 2 | yes | — |
| 504 | C4×Q8 | — | 71 | 4 | no | — |
| 505 | C4×Q8 | — | 71 | 4 | no | — |
| 506 | C4×Q8 | — | 142 | 2 | no | — |
| 507 | C4×D4 | — | 142 | 4 | no | — |
| 508 | C4×D4 | — | 142 | 4 | no | — |
| 509 | C4×D4 | — | 142 | 2 | no | — |
| 510 | C4×D4 | — | 142 | 4 | no | — |
| 511 | C4×D4 | C22×D71 | 1 | 4 | yes | — |
| 512 | #117 | — | 71 | 1 | no | — |
| 513 | #117 | — | 71 | 2 | no | — |
| 514 | #117 | — | 142 | 2 | no | — |
| 515 | #117 | — | 142 | 4 | no | — |
| 516 | #117 | C22×D71 | 1 | 1 | yes | characteristic |
| 517 | C2×C4⋊C4 | — | 71 | 2 | no | — |
| 518 | C2×C4⋊C4 | — | 142 | 2 | no | — |
| 519 | C2×C22⋊C4 | — | 142 | 2 | no | — |
| 520 | #107 | — | 71 | 4 | no | — |
| 521 | #106 | — | 71 | 4 | no | — |
| 522 | C4⋊C8 | C22×D71 | 1 | 4 | yes | — |
| 523 | #103 | — | 71 | 4 | no | — |
| 524 | #103 | — | 71 | 4 | no | — |
| 525 | #103 | — | 71 | 4 | no | — |
| 526 | #103 | — | 71 | 4 | no | — |
| 527 | #103 | — | 71 | 4 | no | — |
| 528 | #103 | — | 71 | 4 | no | — |
| 529 | #103 | — | 71 | 4 | no | — |
| 530 | #102 | — | 71 | 4 | no | — |
| 531 | C22⋊C8 | C22×D71 | 1 | 4 | yes | — |
| 532 | C22⋊C8 | C22×D71 | 1 | 2 | yes | — |
| 533 | C22⋊C8 | C22×D71 | 1 | 2 | yes | — |
| 534 | C22⋊C8 | C22×D71 | 1 | 4 | yes | — |
| 535 | #97 | C22×D71 | 1 | 2 | yes | — |
| 536 | C4×C8 | C22×D71 | 1 | 2 | yes | — |
| 537 | C24 | C2×D284 | 1 | 1 | yes | characteristic |
| 538 | #41 | — | 4 | 2 | no | — |
| 539 | #41 | — | 284 | 2 | no | — |
| 540 | #41 | — | 284 | 2 | no | — |
| 541 | #41 | — | 284 | 4 | no | — |
| 542 | #41 | — | 284 | 8 | no | — |
| 543 | #41 | — | 142 | 4 | no | — |
| 544 | C2×Q8 | — | 284 | 4 | no | — |
| 545 | C2×Q8 | — | 284 | 2 | no | — |
| 546 | C2×Q8 | — | 284 | 2 | no | — |
| 547 | C2×Q8 | — | 284 | 4 | no | — |
| 548 | C2×Q8 | — | 284 | 2 | no | — |
| 549 | C2×Q8 | — | 284 | 2 | no | — |
| 550 | C2×Q8 | — | 284 | 8 | no | — |
| 551 | C2×Q8 | — | 284 | 4 | no | — |
| 552 | C2×Q8 | — | 284 | 4 | no | — |
| 553 | C2×Q8 | — | 71 | 2 | no | — |
| 554 | C2×Q8 | — | 71 | 2 | no | — |
| 555 | C2×Q8 | — | 71 | 1 | no | — |
| 556 | C2×Q8 | — | 71 | 4 | no | — |
| 557 | C2×Q8 | — | 142 | 8 | no | — |
| 558 | C2×Q8 | — | 142 | 4 | no | — |
| 559 | C2×Q8 | — | 142 | 4 | no | — |
| 560 | C2×Q8 | — | 142 | 1 | no | — |
| 561 | C2×Q8 | — | 142 | 4 | no | — |
| 562 | C2×Q8 | — | 142 | 2 | no | — |
| 563 | C2×Q8 | — | 142 | 2 | no | — |
| 564 | C2×Q8 | — | 142 | 2 | no | — |
| 565 | C2×Q8 | — | 142 | 1 | no | — |
| 566 | C2×Q8 | C2×D284 | 1 | 1 | yes | characteristic |
| 567 | C2×D4 | — | 71 | 1 | no | — |
| 568 | C2×D4 | — | 142 | 2 | no | — |
| 569 | C2×D4 | — | 142 | 1 | no | — |
| 570 | C2×D4 | — | 142 | 2 | no | — |
| 571 | C2×D4 | C2×D284 | 1 | 4 | yes | — |
| 572 | C2×D4 | C2×D284 | 1 | 2 | yes | — |
| 573 | C2×D4 | C2×D284 | 1 | 1 | yes | characteristic |
| 574 | C22×C4 | — | 4 | 2 | no | — |
| 575 | C22×C4 | — | 284 | 4 | no | — |
| 576 | C22×C4 | — | 142 | 2 | no | — |
| 577 | C22×C4 | — | 142 | 4 | no | — |
| 578 | C22×C4 | — | 142 | 2 | no | — |
| 579 | C22×C4 | — | 142 | 1 | no | — |
| 580 | C22×C4 | — | 142 | 1 | no | — |
| 581 | C22×C4 | — | 142 | 2 | no | — |
| 582 | C22×C4 | — | 142 | 2 | no | — |
| 583 | C22×C4 | — | 142 | 2 | no | — |
| 584 | C22×C4 | — | 142 | 1 | no | — |
| 585 | C22×C4 | C2×D284 | 1 | 2 | yes | — |
| 586 | C22×C4 | C2×D284 | 1 | 1 | yes | characteristic |
| 587 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 588 | C22×C4 | C23×D71 | 1 | 2 | yes | — |
| 589 | C22×C4 | C23×D71 | 1 | 2 | yes | — |
| 590 | Q16 | — | 284 | 4 | no | — |
| 591 | Q16 | — | 284 | 4 | no | — |
| 592 | Q16 | — | 284 | 4 | no | — |
| 593 | Q16 | — | 142 | 8 | no | — |
| 594 | Q16 | — | 142 | 8 | no | — |
| 595 | SD16 | — | 284 | 4 | no | — |
| 596 | M16 | — | 4 | 2 | no | — |
| 597 | C2×C8 | — | 4 | 2 | no | — |
| 598 | C2×C8 | — | 4 | 4 | no | — |
| 599 | C2×C8 | C23×D71 | 1 | 4 | yes | — |
| 600 | C2×C8 | C23×D71 | 1 | 4 | yes | — |
| 601 | C4⋊C4 | — | 71 | 4 | no | — |
| 602 | C4⋊C4 | — | 71 | 2 | no | — |
| 603 | C4⋊C4 | — | 142 | 4 | no | — |
| 604 | C4⋊C4 | — | 142 | 4 | no | — |
| 605 | C4⋊C4 | — | 142 | 4 | no | — |
| 606 | C4⋊C4 | — | 142 | 4 | no | — |
| 607 | C4⋊C4 | — | 142 | 4 | no | — |
| 608 | C4⋊C4 | — | 142 | 4 | no | — |
| 609 | C4⋊C4 | — | 142 | 2 | no | — |
| 610 | C4⋊C4 | — | 142 | 4 | no | — |
| 611 | C4⋊C4 | — | 142 | 2 | no | — |
| 612 | C4⋊C4 | — | 142 | 4 | no | — |
| 613 | C4⋊C4 | — | 142 | 4 | no | — |
| 614 | C4⋊C4 | C2×D284 | 1 | 2 | yes | — |
| 615 | C4⋊C4 | C2×D284 | 1 | 4 | yes | — |
| 616 | C22⋊C4 | — | 142 | 4 | no | — |
| 617 | C22⋊C4 | — | 142 | 4 | no | — |
| 618 | C22⋊C4 | — | 142 | 1 | no | — |
| 619 | C22⋊C4 | — | 142 | 2 | no | — |
| 620 | C22⋊C4 | — | 142 | 2 | no | — |
| 621 | C22⋊C4 | — | 142 | 4 | no | — |
| 622 | C22⋊C4 | — | 142 | 4 | no | — |
| 623 | C22⋊C4 | — | 142 | 2 | no | — |
| 624 | C22⋊C4 | — | 142 | 4 | no | — |
| 625 | C22⋊C4 | C2×D284 | 1 | 2 | yes | — |
| 626 | C22⋊C4 | C2×D284 | 1 | 4 | yes | — |
| 627 | C22⋊C4 | C2×D284 | 1 | 4 | yes | — |
| 628 | C42 | — | 142 | 2 | no | — |
| 629 | C42 | — | 142 | 1 | no | — |
| 630 | C42 | — | 142 | 4 | no | — |
| 631 | C42 | — | 142 | 4 | no | — |
| 632 | C42 | C23×D71 | 1 | 2 | yes | — |
| 633 | C23 | — | 2 | 4 | no | — |
| 634 | C23 | — | 4 | 1 | no | — |
| 635 | C23 | — | 142 | 1 | no | — |
| 636 | C23 | C22×D284 | 1 | 1 | yes | characteristic |
| 637 | C23 | C22×D284 | 1 | 2 | yes | — |
| 638 | C23 | C22×D284 | 1 | 2 | yes | — |
| 639 | Q8 | — | 4 | 1 | no | — |
| 640 | Q8 | — | 284 | 2 | no | — |
| 641 | Q8 | — | 284 | 8 | no | — |
| 642 | Q8 | — | 284 | 4 | no | — |
| 643 | Q8 | — | 568 | 2 | no | — |
| 644 | Q8 | — | 568 | 2 | no | — |
| 645 | Q8 | — | 71 | 4 | no | — |
| 646 | Q8 | — | 142 | 4 | no | — |
| 647 | Q8 | — | 142 | 4 | no | — |
| 648 | Q8 | — | 142 | 4 | no | — |
| 649 | Q8 | — | 142 | 4 | no | — |
| 650 | Q8 | — | 142 | 2 | no | — |
| 651 | Q8 | — | 142 | 2 | no | — |
| 652 | D4 | — | 2 | 8 | no | — |
| 653 | D4 | — | 4 | 1 | no | — |
| 654 | D4 | — | 4 | 2 | no | — |
| 655 | D4 | — | 284 | 2 | no | — |
| 656 | D4 | — | 284 | 4 | no | — |
| 657 | D4 | — | 284 | 4 | no | — |
| 658 | D4 | — | 142 | 2 | no | — |
| 659 | C2×C4 | — | 2 | 4 | no | — |
| 660 | C2×C4 | — | 2 | 2 | no | — |
| 661 | C2×C4 | — | 2 | 2 | no | — |
| 662 | C2×C4 | — | 2 | 2 | no | — |
| 663 | C2×C4 | — | 4 | 2 | no | — |
| 664 | C2×C4 | — | 4 | 1 | no | — |
| 665 | C2×C4 | — | 284 | 2 | no | — |
| 666 | C2×C4 | — | 284 | 4 | no | — |
| 667 | C2×C4 | — | 284 | 2 | no | — |
| 668 | C2×C4 | — | 284 | 4 | no | — |
| 669 | C2×C4 | — | 284 | 8 | no | — |
| 670 | C2×C4 | — | 284 | 4 | no | — |
| 671 | C2×C4 | — | 568 | 2 | no | — |
| 672 | C2×C4 | — | 568 | 2 | no | — |
| 673 | C2×C4 | — | 142 | 2 | no | — |
| 674 | C2×C4 | — | 142 | 4 | no | — |
| 675 | C2×C4 | — | 142 | 4 | no | — |
| 676 | C2×C4 | — | 142 | 2 | no | — |
| 677 | C2×C4 | — | 142 | 1 | no | — |
| 678 | C2×C4 | — | 142 | 4 | no | — |
| 679 | C2×C4 | — | 142 | 2 | no | — |
| 680 | C2×C4 | C22×D284 | 1 | 4 | yes | — |
| 681 | C2×C4 | C22×D284 | 1 | 2 | yes | — |
| 682 | C2×C4 | C22×D284 | 1 | 1 | yes | characteristic |
| 683 | C2×C4 | C22×D284 | 1 | 2 | yes | — |
| 684 | C2×C4 | C24×D71 | 1 | 1 | yes | characteristic |
| 685 | C8 | — | 2 | 4 | no | — |
| 686 | C8 | — | 2 | 4 | no | — |
| 687 | C22 | — | 2 | 2 | no | — |
| 688 | C22 | — | 2 | 2 | no | — |
| 689 | C22 | — | 2 | 4 | no | — |
| 690 | C22 | — | 2 | 2 | no | — |
| 691 | C22 | — | 2 | 1 | no | — |
| 692 | C22 | — | 2 | 2 | no | — |
| 693 | C22 | — | 4 | 4 | no | — |
| 694 | C22 | — | 284 | 2 | no | — |
| 695 | C22 | — | 284 | 1 | no | — |
| 696 | C22 | #17986816 | 1 | 4 | yes | — |
| 697 | C22 | C23×D284 | 1 | 1 | yes | characteristic |
| 698 | C4 | — | 2 | 4 | no | — |
| 699 | C4 | — | 2 | 1 | no | — |
| 700 | C4 | — | 2 | 2 | no | — |
| 701 | C4 | — | 2 | 2 | no | — |
| 702 | C4 | — | 284 | 4 | no | — |
| 703 | C4 | — | 284 | 2 | no | — |
| 704 | C4 | — | 284 | 1 | no | — |
| 705 | C4 | — | 284 | 2 | no | — |
| 706 | C4 | — | 284 | 4 | no | — |
| 707 | C4 | — | 142 | 4 | no | — |
| 708 | C4 | H(5,𝔽2)×D71 | 1 | 2 | yes | — |
| 709 | C2 | — | 2 | 4 | no | — |
| 710 | C2 | — | 4 | 1 | no | — |
| 711 | C2 | — | 4 | 2 | no | — |
| 712 | C2 | — | 568 | 1 | no | — |
| 713 | C2 | #22601976 | 1 | 1 | yes | characteristic |
| 714 | C2 | C2×#17986816 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22602589 | C2 | semidirect |
| 3. #22600393 | C2 | semidirect |
| 4. #22600229 | C2 | semidirect |
| 5. D4×Dic284 | C2 | semidirect |
| 6. #22599915 | C2 | semidirect |
| 7. #22599425 | C2 | semidirect |
| 8. #22599235 | C2 | semidirect |
| 9. #22599123 | C2 | semidirect |
| 10. #22598641 | C2 | semidirect |
| 11. #22597637 | C2 | semidirect |
| 12. C2×#17986157 | C2 | semidirect |
| 13. C71×#2977 | C2 | semidirect |
| 16. C2×#14556161 | C22 | semidirect |
| 18. C22×Dic284 | C22 | semidirect |
| 38. #17986393 | C22 | semidirect |
| 39. #17986379 | C22 | semidirect |
| 40. #17986368 | C22 | semidirect |
| 41. #17986354 | C22 | semidirect |
| 43. #17986341 | C22 | semidirect |
| 46. #17986307 | C22 | semidirect |
| 47. #17986257 | C22 | semidirect |
| 49. #17986240 | C22 | semidirect |
| 51. #17986222 | C22 | semidirect |
| 52. #17986210 | C22 | semidirect |
| 53. #17986210 | C22 | semidirect |
| 55. #17986163 | C22 | semidirect |
| 61. #17986157 | C22 | semidirect |
| 62. #17986157 | C22 | semidirect |
| 64. #17986107 | C22 | semidirect |
| 65. C4×Dic284 | C22 | semidirect |
| 66. #17986009 | C22 | semidirect |
| 67. #17985996 | C22 | semidirect |
| 370. #2977 | D71 | semidirect |
| 371. C71 | #61634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602589 | 2 |
| #22601987 | 2 |
| #22600393 | 2 |
| #22600229 | 2 |
| D4×Dic284 | 2 |
| #22599915 | 2 |
| #22599425 | 2 |
| #22599235 | 2 |
| #22599123 | 2 |
| #22598641 | 2 |
| #22597637 | 2 |
| C2×#17986157 | 2 |
| C71×#2977 | 2 |
| #61634 | 71 |