Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
896 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 | #22574348 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22571427 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22571238 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22570603 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22559545 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22559534 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22559528 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #22559517 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #22558843 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #22558814 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C67×#1529 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #16864150 | C22 | 1 | 1 | yes | characteristic |
| 13 | #16864148 | — | 2 | 1 | no | — |
| 14 | #16864144 | C22 | 1 | 1 | yes | characteristic |
| 15 | #16864143 | — | 2 | 1 | no | — |
| 16 | #16864142 | — | 2 | 1 | no | — |
| 17 | #16864140 | C22 | 1 | 1 | yes | characteristic |
| 18 | #16864138 | C22 | 1 | 1 | yes | characteristic |
| 19 | #16864137 | — | 2 | 1 | no | — |
| 20 | #16864136 | — | 2 | 1 | no | — |
| 21 | #16864134 | — | 2 | 1 | no | — |
| 22 | #16863946 | C22 | 1 | 1 | yes | characteristic |
| 23 | #16863943 | — | 2 | 1 | no | — |
| 24 | C2×#14524043 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #16863933 | — | 2 | 1 | no | — |
| 26 | #16863930 | C22 | 1 | 1 | yes | characteristic |
| 27 | #16863924 | — | 2 | 1 | no | — |
| 28 | #16863908 | — | 2 | 1 | no | — |
| 29 | #16863905 | — | 2 | 1 | no | — |
| 30 | #16863905 | — | 2 | 1 | no | — |
| 31 | #16863806 | C22 | 1 | 2 | yes | complemented |
| 32 | #16863790 | C22 | 1 | 2 | yes | — |
| 33 | #16863765 | C22 | 1 | 2 | yes | complemented |
| 34 | #16863756 | C22 | 1 | 2 | yes | — |
| 35 | #16863756 | C22 | 1 | 2 | yes | complemented |
| 36 | #16863755 | C22 | 1 | 2 | yes | — |
| 37 | #16863747 | — | 2 | 1 | no | — |
| 38 | #16863743 | — | 2 | 1 | no | — |
| 39 | #16863724 | — | 2 | 1 | no | — |
| 40 | #16863707 | — | 2 | 1 | no | — |
| 41 | #16863691 | — | 2 | 1 | no | — |
| 42 | #16863686 | — | 2 | 1 | no | — |
| 43 | #16863607 | — | 2 | 1 | no | — |
| 44 | #16863602 | — | 2 | 1 | no | — |
| 45 | #16863554 | — | 2 | 1 | no | — |
| 46 | #16863537 | — | 2 | 1 | no | — |
| 47 | #16863453 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #16863398 | — | 2 | 1 | no | — |
| 49 | #16863398 | — | 2 | 1 | no | — |
| 50 | #16863137 | C22 | 1 | 2 | yes | complemented |
| 51 | #16863135 | C22 | 1 | 2 | yes | — |
| 52 | #16863135 | C22 | 1 | 2 | yes | — |
| 53 | #16863135 | C22 | 1 | 2 | yes | complemented |
| 54 | #529×C67 | C22 | 1 | 1 | yes | characteristic |
| 55 | #432×C67 | C22 | 1 | 1 | yes | characteristic, complemented |
| 56 | C4×M16×C67 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | #330×C67 | C22 | 1 | 2 | yes | complemented |
| 58 | #329×C67 | C22 | 1 | 2 | yes | — |
| 59 | C2×#11761628 | — | 2 | 1 | no | — |
| 60 | C2×#11761628 | D4 | 1 | 1 | yes | characteristic |
| 61 | C2×#11761628 | D4 | 1 | 1 | yes | characteristic |
| 62 | C22×Dic134 | — | 2 | 1 | no | — |
| 63 | C22×C4×D67 | — | 2 | 1 | no | — |
| 64 | C2×Dic268 | — | 2 | 2 | no | — |
| 65 | C2×#11761617 | — | 2 | 2 | no | — |
| 66 | #14524043 | — | 2 | 1 | no | — |
| 67 | #14524043 | — | 2 | 1 | no | — |
| 68 | #14524043 | — | 2 | 1 | no | — |
| 69 | #14524043 | D4 | 1 | 1 | yes | characteristic |
| 70 | #14524043 | C23 | 1 | 2 | yes | — |
| 71 | #14524042 | — | 2 | 1 | no | — |
| 72 | #14524040 | D4 | 1 | 1 | yes | characteristic |
| 73 | #14524039 | — | 2 | 1 | no | — |
| 74 | #14524038 | — | 2 | 1 | no | — |
| 75 | #14524038 | — | 2 | 1 | no | — |
| 76 | #14524038 | — | 2 | 1 | no | — |
| 77 | #14524037 | — | 2 | 1 | no | — |
| 78 | #14524036 | — | 2 | 1 | no | — |
| 79 | #14524035 | C23 | 1 | 1 | yes | characteristic |
| 80 | #14524034 | — | 2 | 1 | no | — |
| 81 | #14524033 | — | 2 | 1 | no | — |
| 82 | #14524032 | — | 2 | 1 | no | — |
| 83 | #14524031 | C23 | 1 | 1 | yes | characteristic |
| 84 | #14524031 | C23 | 1 | 1 | yes | characteristic |
| 85 | #14524031 | C23 | 1 | 1 | yes | characteristic |
| 86 | #14524029 | — | 2 | 1 | no | — |
| 87 | #14524029 | — | 2 | 1 | no | — |
| 88 | #14524029 | — | 2 | 1 | no | — |
| 89 | #14524028 | — | 2 | 1 | no | — |
| 90 | #14524028 | — | 2 | 1 | no | — |
| 91 | #14524028 | — | 2 | 1 | no | — |
| 92 | #14524028 | — | 2 | 1 | no | — |
| 93 | #14524028 | — | 2 | 1 | no | — |
| 94 | #14524027 | — | 2 | 1 | no | — |
| 95 | #14524027 | — | 2 | 1 | no | — |
| 96 | #14524026 | — | 2 | 1 | no | — |
| 97 | #14524025 | — | 2 | 1 | no | — |
| 98 | #14524025 | — | 2 | 1 | no | — |
| 99 | #14524025 | — | 2 | 1 | no | — |
| 100 | #14524023 | — | 2 | 1 | no | — |
| 101 | #14524023 | — | 2 | 1 | no | — |
| 102 | #14524022 | D4 | 1 | 1 | yes | characteristic |
| 103 | #14524021 | — | 2 | 1 | no | — |
| 104 | #14524021 | — | 2 | 1 | no | — |
| 105 | #14524021 | — | 2 | 1 | no | — |
| 106 | #14524020 | — | 2 | 1 | no | — |
| 107 | #14524020 | — | 2 | 1 | no | — |
| 108 | #14524019 | — | 2 | 1 | no | — |
| 109 | #14524018 | — | 2 | 1 | no | — |
| 110 | #14524018 | — | 2 | 1 | no | — |
| 111 | #14524018 | — | 2 | 1 | no | — |
| 112 | #14524018 | — | 2 | 1 | no | — |
| 113 | #14524017 | — | 2 | 1 | no | — |
| 114 | #14524017 | — | 2 | 1 | no | — |
| 115 | #14524017 | D4 | 1 | 1 | yes | characteristic |
| 116 | #14524016 | — | 2 | 1 | no | — |
| 117 | #14524016 | — | 2 | 1 | no | — |
| 118 | #14524016 | — | 2 | 1 | no | — |
| 119 | #14524016 | — | 2 | 1 | no | — |
| 120 | #14524016 | — | 2 | 1 | no | — |
| 121 | #14524015 | — | 2 | 1 | no | — |
| 122 | #14524015 | — | 2 | 1 | no | — |
| 123 | #14524014 | — | 2 | 1 | no | — |
| 124 | #14524013 | — | 2 | 1 | no | — |
| 125 | #14524013 | — | 2 | 1 | no | — |
| 126 | #14524013 | — | 2 | 1 | no | — |
| 127 | #14524013 | — | 2 | 1 | no | — |
| 128 | #14524011 | — | 2 | 1 | no | — |
| 129 | #14524011 | — | 2 | 1 | no | — |
| 130 | C4×Dic134 | D4 | 1 | 1 | yes | characteristic |
| 131 | C4×D268 | — | 2 | 1 | no | — |
| 132 | C4×D268 | — | 2 | 1 | no | — |
| 133 | C4×D268 | — | 2 | 1 | no | — |
| 134 | C4×D268 | — | 2 | 1 | no | — |
| 135 | C4×D268 | D4 | 1 | 1 | yes | characteristic |
| 136 | C4×C22⋊D67 | — | 2 | 1 | no | — |
| 137 | C4×C22⋊D67 | — | 2 | 1 | no | — |
| 138 | C4×C22⋊D67 | — | 2 | 1 | no | — |
| 139 | #14524000 | — | 2 | 1 | no | — |
| 140 | #14524000 | — | 2 | 1 | no | — |
| 141 | C2×C4⋊Dic67 | — | 2 | 1 | no | — |
| 142 | C2×C4⋊Dic67 | — | 2 | 1 | no | — |
| 143 | C42×D67 | — | 2 | 1 | no | — |
| 144 | #14523976 | — | 2 | 2 | no | — |
| 145 | #14523974 | — | 2 | 2 | no | — |
| 146 | C4⋊(C67⋊C8) | — | 2 | 1 | no | — |
| 147 | #14523968 | — | 2 | 2 | no | — |
| 148 | #14523968 | — | 2 | 2 | no | — |
| 149 | #14523968 | — | 2 | 2 | no | — |
| 150 | #14523968 | — | 2 | 2 | no | — |
| 151 | #14523967 | — | 2 | 2 | no | — |
| 152 | #14523965 | — | 2 | 2 | no | — |
| 153 | #14523965 | — | 2 | 2 | no | — |
| 154 | #14523964 | — | 2 | 2 | no | — |
| 155 | C22⋊(C67⋊C8) | — | 2 | 1 | no | — |
| 156 | #14523954 | C23 | 1 | 2 | yes | — |
| 157 | C2×M16×C67 | — | 2 | 1 | no | — |
| 158 | #126×C67 | — | 2 | 1 | no | — |
| 159 | #125×C67 | C23 | 1 | 1 | yes | characteristic |
| 160 | #124×C67 | C23 | 1 | 1 | yes | characteristic |
| 161 | #123×C67 | — | 2 | 1 | no | — |
| 162 | C22⋊Q8×C67 | D4 | 1 | 1 | yes | characteristic |
| 163 | #121×C67 | D4 | 1 | 1 | yes | characteristic |
| 164 | C4×Q8×C67 | D4 | 1 | 1 | yes | characteristic |
| 165 | C4×D4×C67 | — | 2 | 1 | no | — |
| 166 | C4×D4×C67 | D4 | 1 | 1 | yes | characteristic |
| 167 | #117×C67 | — | 2 | 1 | no | — |
| 168 | C2×C42×C67 | C23 | 1 | 1 | yes | characteristic |
| 169 | C4⋊C8×C67 | — | 2 | 1 | no | — |
| 170 | C22⋊C8×C67 | — | 2 | 1 | no | — |
| 171 | #97×C67 | C23 | 1 | 2 | yes | — |
| 172 | #97×C67 | C23 | 1 | 2 | yes | — |
| 173 | C4×C8×C67 | — | 2 | 1 | no | — |
| 174 | C23×D67 | — | 2 | 1 | no | — |
| 175 | #11761628 | — | 4 | 2 | no | — |
| 176 | #11761628 | — | 4 | 2 | no | — |
| 177 | #11761628 | — | 8 | 2 | no | — |
| 178 | C2×Dic134 | — | 2 | 2 | no | — |
| 179 | C2×Dic134 | — | 2 | 1 | no | — |
| 180 | C2×Dic134 | — | 4 | 1 | no | — |
| 181 | C2×Dic134 | — | 8 | 2 | no | — |
| 182 | C2×Dic134 | C2×D4 | 1 | 1 | yes | characteristic |
| 183 | C2×Dic134 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | C2×Dic134 | C2×D4 | 1 | 1 | yes | characteristic |
| 185 | C2×D268 | — | 2 | 1 | no | — |
| 186 | C2×D268 | — | 2 | 1 | no | — |
| 187 | C2×D268 | — | 2 | 1 | no | — |
| 188 | C2×D268 | — | 2 | 1 | no | — |
| 189 | C2×D268 | — | 2 | 1 | no | — |
| 190 | C2×D268 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C2×D268 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C2×D268 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C2×C22⋊D67 | — | 2 | 1 | no | — |
| 194 | C2×C22⋊D67 | — | 2 | 1 | no | — |
| 195 | C2×C22⋊D67 | — | 2 | 1 | no | — |
| 196 | C2×C22⋊D67 | — | 2 | 1 | no | — |
| 197 | C2×C22⋊D67 | — | 2 | 1 | no | — |
| 198 | C2×C22⋊D67 | — | 2 | 1 | no | — |
| 199 | C2×C22⋊D67 | — | 2 | 1 | no | — |
| 200 | C22×Dic67 | — | 2 | 1 | no | — |
| 201 | C22×Dic67 | — | 4 | 1 | no | — |
| 202 | C2×C4×D67 | — | 2 | 1 | no | — |
| 203 | C2×C4×D67 | — | 2 | 1 | no | — |
| 204 | C2×C4×D67 | — | 2 | 1 | no | — |
| 205 | C2×C4×D67 | — | 2 | 1 | no | — |
| 206 | C2×C4×D67 | — | 2 | 1 | no | — |
| 207 | C2×C4×D67 | — | 2 | 1 | no | — |
| 208 | C2×C4×D67 | — | 2 | 1 | no | — |
| 209 | C2×C4×D67 | — | 8 | 2 | no | — |
| 210 | Dic268 | — | 8 | 2 | no | — |
| 211 | #11761617 | — | 8 | 2 | no | — |
| 212 | C2×C67⋊C8 | — | 2 | 2 | no | — |
| 213 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 214 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 215 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 216 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 217 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 218 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 219 | C4⋊Dic67 | — | 4 | 1 | no | — |
| 220 | C4⋊Dic67 | — | 4 | 1 | no | — |
| 221 | C4⋊Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 222 | C4⋊Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 223 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 224 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 225 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 226 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 227 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 228 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 229 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 230 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 231 | C22⋊Dic67 | — | 2 | 1 | no | — |
| 232 | C22⋊Dic67 | — | 2 | 1 | no | — |
| 233 | C22⋊Dic67 | — | 2 | 1 | no | — |
| 234 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 235 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 236 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 237 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 238 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 239 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 240 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 241 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 242 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 243 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 244 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 245 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 246 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 247 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 248 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 249 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 250 | C4×Dic67 | — | 2 | 1 | no | — |
| 251 | C4×Dic67 | — | 2 | 1 | no | — |
| 252 | C4×Dic67 | — | 2 | 1 | no | — |
| 253 | C2×Q8×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 254 | C2×D4×C67 | — | 2 | 1 | no | — |
| 255 | C2×D4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 256 | C22×C4×C67 | — | 2 | 1 | no | — |
| 257 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 258 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 259 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 260 | M16×C67 | — | 4 | 2 | no | — |
| 261 | C2×C8×C67 | — | 2 | 2 | no | — |
| 262 | C2×C8×C67 | — | 2 | 2 | no | — |
| 263 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 264 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 265 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 266 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 267 | C4⋊C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 268 | C4⋊C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 269 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 270 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 271 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 272 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 273 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 274 | C42×C67 | — | 2 | 1 | no | — |
| 275 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 276 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 277 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 278 | C42×C67 | C24 | 1 | 1 | yes | characteristic |
| 279 | C23×C67 | — | 2 | 1 | no | — |
| 280 | C23×C67 | #120 | 1 | 1 | yes | characteristic |
| 281 | C22×D67 | — | 2 | 1 | no | — |
| 282 | C22×D67 | — | 2 | 1 | no | — |
| 283 | C22×D67 | — | 2 | 1 | no | — |
| 284 | C22×D67 | — | 8 | 1 | no | — |
| 285 | C22×D67 | — | 8 | 1 | no | — |
| 286 | C22×D67 | — | 8 | 1 | no | — |
| 287 | Q8×C67 | — | 4 | 1 | no | — |
| 288 | D4×C67 | — | 4 | 1 | no | — |
| 289 | D4×C67 | — | 8 | 1 | no | — |
| 290 | C2×C4×C67 | — | 2 | 2 | no | — |
| 291 | C2×C4×C67 | — | 2 | 1 | no | — |
| 292 | C2×C4×C67 | — | 2 | 1 | no | — |
| 293 | C2×C4×C67 | — | 2 | 1 | no | — |
| 294 | C2×C4×C67 | — | 4 | 1 | no | — |
| 295 | C2×C4×C67 | — | 4 | 1 | no | — |
| 296 | C2×C4×C67 | — | 4 | 2 | no | — |
| 297 | C2×C4×C67 | #120 | 1 | 1 | yes | characteristic |
| 298 | C2×C4×C67 | #120 | 1 | 1 | yes | characteristic |
| 299 | C2×C4×C67 | #120 | 1 | 1 | yes | characteristic |
| 300 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 301 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 302 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 303 | C22⋊D67 | — | 8 | 1 | no | — |
| 304 | C22⋊D67 | — | 8 | 1 | no | — |
| 305 | C22⋊D67 | — | 8 | 1 | no | — |
| 306 | C22⋊D67 | — | 8 | 1 | no | — |
| 307 | C22⋊D67 | — | 8 | 1 | no | — |
| 308 | C22⋊D67 | — | 8 | 1 | no | — |
| 309 | C22⋊D67 | — | 8 | 1 | no | — |
| 310 | C2×Dic67 | — | 2 | 1 | no | — |
| 311 | C2×Dic67 | — | 2 | 1 | no | — |
| 312 | C2×Dic67 | — | 2 | 1 | no | — |
| 313 | C2×Dic67 | — | 2 | 1 | no | — |
| 314 | C2×Dic67 | — | 2 | 1 | no | — |
| 315 | C2×Dic67 | — | 4 | 2 | no | — |
| 316 | C2×Dic67 | — | 8 | 1 | no | — |
| 317 | C2×Dic67 | — | 8 | 2 | no | — |
| 318 | D268 | — | 4 | 1 | no | — |
| 319 | D268 | — | 4 | 1 | no | — |
| 320 | D268 | — | 4 | 1 | no | — |
| 321 | D268 | — | 8 | 1 | no | — |
| 322 | D268 | — | 8 | 1 | no | — |
| 323 | D268 | — | 8 | 1 | no | — |
| 324 | D268 | — | 8 | 1 | no | — |
| 325 | D268 | — | 8 | 1 | no | — |
| 326 | C4×D67 | — | 4 | 2 | no | — |
| 327 | C4×D67 | — | 4 | 2 | no | — |
| 328 | C4×D67 | — | 4 | 2 | no | — |
| 329 | C4×D67 | — | 8 | 1 | no | — |
| 330 | C4×D67 | — | 8 | 1 | no | — |
| 331 | C4×D67 | — | 8 | 1 | no | — |
| 332 | C4×D67 | — | 8 | 1 | no | — |
| 333 | Dic134 | — | 4 | 1 | no | — |
| 334 | Dic134 | — | 4 | 1 | no | — |
| 335 | Dic134 | — | 4 | 1 | no | — |
| 336 | Dic134 | — | 4 | 2 | no | — |
| 337 | Dic134 | — | 4 | 2 | no | — |
| 338 | Dic134 | — | 8 | 1 | no | — |
| 339 | Dic134 | — | 8 | 2 | no | — |
| 340 | C8×C67 | — | 4 | 2 | no | — |
| 341 | C8×C67 | — | 4 | 2 | no | — |
| 342 | C67⋊C8 | — | 4 | 2 | no | — |
| 343 | C22×C67 | — | 2 | 1 | no | — |
| 344 | C22×C67 | — | 2 | 1 | no | — |
| 345 | C22×C67 | — | 2 | 1 | no | — |
| 346 | C22×C67 | — | 4 | 1 | no | — |
| 347 | C22×C67 | — | 4 | 1 | no | — |
| 348 | C22×C67 | — | 4 | 1 | no | — |
| 349 | C22×C67 | C2×#120 | 1 | 1 | yes | characteristic |
| 350 | C2×D67 | — | 4 | 1 | no | — |
| 351 | C2×D67 | — | 4 | 1 | no | — |
| 352 | C2×D67 | — | 4 | 1 | no | — |
| 353 | C2×D67 | — | 4 | 1 | no | — |
| 354 | C2×D67 | — | 4 | 1 | no | — |
| 355 | C2×D67 | — | 4 | 1 | no | — |
| 356 | C2×D67 | — | 4 | 1 | no | — |
| 357 | C2×D67 | — | 4 | 1 | no | — |
| 358 | C2×D67 | — | 4 | 1 | no | — |
| 359 | C2×D67 | — | 8 | 4 | no | — |
| 360 | C4×C67 | — | 2 | 1 | no | — |
| 361 | C4×C67 | — | 2 | 1 | no | — |
| 362 | C4×C67 | — | 2 | 1 | no | — |
| 363 | C4×C67 | — | 2 | 1 | no | — |
| 364 | C4×C67 | — | 2 | 1 | no | — |
| 365 | C4×C67 | — | 4 | 1 | no | — |
| 366 | C4×C67 | — | 4 | 1 | no | — |
| 367 | C4×C67 | — | 4 | 1 | no | — |
| 368 | C4×C67 | #455 | 1 | 2 | yes | — |
| 369 | Dic67 | — | 4 | 1 | no | — |
| 370 | Dic67 | — | 4 | 1 | no | — |
| 371 | Dic67 | — | 4 | 1 | no | — |
| 372 | Dic67 | — | 4 | 1 | no | — |
| 373 | Dic67 | — | 4 | 1 | no | — |
| 374 | Dic67 | — | 8 | 2 | no | — |
| 375 | #19000 | — | 67 | 1 | no | maximal, Sylow |
| 376 | C2×C67 | — | 4 | 1 | no | — |
| 377 | C2×C67 | — | 8 | 1 | no | — |
| 378 | C2×C67 | C2×#455 | 1 | 1 | yes | characteristic |
| 379 | C2×C67 | #3021 | 1 | 1 | yes | characteristic |
| 380 | C2×C67 | #3022 | 1 | 1 | yes | characteristic |
| 381 | D67 | — | 8 | 1 | no | — |
| 382 | D67 | — | 8 | 1 | no | — |
| 383 | D67 | — | 8 | 1 | no | — |
| 384 | #3529 | — | 67 | 1 | no | — |
| 385 | #3238 | — | 67 | 1 | no | — |
| 386 | #3218 | — | 67 | 1 | no | — |
| 387 | #3141 | — | 67 | 1 | no | — |
| 388 | #1664 | — | 67 | 2 | no | — |
| 389 | #1662 | — | 67 | 2 | no | — |
| 390 | #1661 | — | 67 | 2 | no | — |
| 391 | #1659 | — | 67 | 2 | no | — |
| 392 | #1536 | — | 67 | 1 | no | — |
| 393 | #1529 | — | 67 | 1 | no | — |
| 394 | #1529 | D67 | 1 | 1 | yes | characteristic, complemented |
| 395 | C67 | #19000 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 396 | #563 | — | 67 | 1 | no | — |
| 397 | #563 | — | 134 | 1 | no | — |
| 398 | #562 | — | 67 | 1 | no | — |
| 399 | #562 | — | 67 | 1 | no | — |
| 400 | #562 | — | 134 | 1 | no | — |
| 401 | #562 | — | 134 | 1 | no | — |
| 402 | H(3,𝔽4) | — | 67 | 1 | no | — |
| 403 | #560 | — | 134 | 1 | no | — |
| 404 | #560 | — | 134 | 1 | no | — |
| 405 | #560 | — | 134 | 1 | no | — |
| 406 | #532 | — | 67 | 1 | no | — |
| 407 | #532 | — | 134 | 1 | no | — |
| 408 | C2×C4⋊Q8 | — | 67 | 1 | no | — |
| 409 | #529 | — | 67 | 1 | no | — |
| 410 | #529 | — | 134 | 1 | no | — |
| 411 | #529 | — | 134 | 1 | no | — |
| 412 | #529 | C2×D67 | 1 | 1 | yes | characteristic |
| 413 | #525 | — | 134 | 1 | no | — |
| 414 | #525 | — | 134 | 1 | no | — |
| 415 | #525 | — | 134 | 1 | no | — |
| 416 | #501 | — | 67 | 2 | no | — |
| 417 | #497 | — | 67 | 2 | no | — |
| 418 | #491 | — | 67 | 2 | no | — |
| 419 | #489 | — | 67 | 2 | no | — |
| 420 | #489 | — | 67 | 2 | no | — |
| 421 | #489 | — | 67 | 2 | no | — |
| 422 | #487 | — | 134 | 1 | no | — |
| 423 | #486 | — | 134 | 1 | no | — |
| 424 | #483 | — | 134 | 1 | no | — |
| 425 | #480 | — | 134 | 1 | no | — |
| 426 | #477 | — | 134 | 1 | no | — |
| 427 | #476 | — | 134 | 1 | no | — |
| 428 | #462 | — | 134 | 1 | no | — |
| 429 | #461 | — | 134 | 1 | no | — |
| 430 | #451 | — | 134 | 1 | no | — |
| 431 | #448 | — | 134 | 1 | no | — |
| 432 | #432 | — | 67 | 1 | no | — |
| 433 | #432 | C2×D67 | 1 | 1 | yes | characteristic, complemented |
| 434 | #417 | — | 134 | 1 | no | — |
| 435 | #417 | — | 134 | 1 | no | — |
| 436 | C4×M16 | C2×D67 | 1 | 1 | yes | characteristic, complemented |
| 437 | #330 | — | 67 | 2 | no | — |
| 438 | #330 | C2×D67 | 1 | 2 | yes | complemented |
| 439 | #329 | — | 67 | 2 | no | — |
| 440 | #329 | — | 67 | 2 | no | — |
| 441 | #329 | — | 67 | 2 | no | — |
| 442 | #329 | C2×D67 | 1 | 2 | yes | — |
| 443 | C2×#41 | — | 67 | 1 | no | — |
| 444 | C2×#41 | — | 67 | 1 | no | — |
| 445 | C2×#41 | — | 134 | 1 | no | — |
| 446 | C22×Q8 | — | 134 | 1 | no | — |
| 447 | C23×C4 | — | 134 | 1 | no | — |
| 448 | C2×Q16 | — | 134 | 2 | no | — |
| 449 | C2×SD16 | — | 134 | 2 | no | — |
| 450 | C2×M16 | — | 2 | 1 | no | — |
| 451 | C4⋊Q8 | — | 67 | 1 | no | — |
| 452 | C4⋊Q8 | — | 67 | 2 | no | — |
| 453 | C4⋊Q8 | — | 134 | 1 | no | — |
| 454 | C4⋊Q8 | — | 134 | 1 | no | — |
| 455 | C4⋊Q8 | — | 134 | 1 | no | — |
| 456 | C4⋊Q8 | — | 134 | 1 | no | — |
| 457 | #127 | — | 67 | 1 | no | — |
| 458 | #127 | — | 134 | 1 | no | — |
| 459 | #126 | — | 2 | 1 | no | — |
| 460 | #126 | — | 134 | 1 | no | — |
| 461 | #126 | — | 134 | 1 | no | — |
| 462 | #126 | — | 134 | 1 | no | — |
| 463 | #126 | — | 134 | 1 | no | — |
| 464 | #126 | — | 134 | 1 | no | — |
| 465 | #125 | — | 67 | 1 | no | — |
| 466 | #125 | — | 134 | 1 | no | — |
| 467 | #125 | — | 134 | 1 | no | — |
| 468 | #125 | C22×D67 | 1 | 1 | yes | characteristic |
| 469 | #124 | — | 67 | 1 | no | — |
| 470 | #124 | — | 67 | 1 | no | — |
| 471 | #124 | — | 67 | 1 | no | — |
| 472 | #124 | — | 134 | 1 | no | — |
| 473 | #124 | — | 134 | 1 | no | — |
| 474 | #124 | — | 134 | 1 | no | — |
| 475 | #124 | — | 134 | 1 | no | — |
| 476 | #124 | C22×D67 | 1 | 1 | yes | characteristic |
| 477 | #123 | — | 2 | 1 | no | — |
| 478 | #123 | — | 134 | 1 | no | — |
| 479 | #123 | — | 134 | 1 | no | — |
| 480 | #123 | — | 134 | 1 | no | — |
| 481 | #123 | — | 134 | 1 | no | — |
| 482 | #123 | — | 134 | 1 | no | — |
| 483 | #123 | — | 134 | 1 | no | — |
| 484 | #123 | — | 134 | 1 | no | — |
| 485 | #123 | — | 134 | 1 | no | — |
| 486 | #123 | — | 134 | 1 | no | — |
| 487 | #123 | — | 134 | 1 | no | — |
| 488 | #123 | — | 134 | 1 | no | — |
| 489 | C22⋊Q8 | — | 67 | 1 | no | — |
| 490 | C22⋊Q8 | — | 134 | 1 | no | — |
| 491 | C22⋊Q8 | — | 134 | 1 | no | — |
| 492 | C22⋊Q8 | — | 134 | 1 | no | — |
| 493 | C22⋊Q8 | — | 134 | 1 | no | — |
| 494 | C22⋊Q8 | — | 134 | 1 | no | — |
| 495 | C22⋊Q8 | — | 134 | 1 | no | — |
| 496 | C22⋊Q8 | — | 134 | 1 | no | — |
| 497 | C22⋊Q8 | — | 134 | 1 | no | — |
| 498 | C22⋊Q8 | D268 | 1 | 1 | yes | characteristic |
| 499 | #121 | — | 67 | 1 | no | — |
| 500 | #121 | — | 134 | 1 | no | — |
| 501 | #121 | — | 134 | 1 | no | — |
| 502 | #121 | — | 134 | 1 | no | — |
| 503 | #121 | — | 134 | 1 | no | — |
| 504 | #121 | — | 134 | 1 | no | — |
| 505 | #121 | — | 134 | 1 | no | — |
| 506 | #121 | — | 134 | 1 | no | — |
| 507 | #121 | — | 134 | 1 | no | — |
| 508 | #121 | — | 134 | 1 | no | — |
| 509 | #121 | — | 134 | 1 | no | — |
| 510 | #121 | — | 134 | 1 | no | — |
| 511 | #121 | — | 134 | 1 | no | — |
| 512 | #121 | — | 134 | 1 | no | — |
| 513 | #121 | — | 134 | 1 | no | — |
| 514 | #121 | D268 | 1 | 1 | yes | characteristic |
| 515 | #120 | — | 134 | 1 | no | — |
| 516 | #120 | — | 134 | 1 | no | — |
| 517 | #120 | — | 134 | 1 | no | — |
| 518 | #120 | — | 134 | 1 | no | — |
| 519 | #120 | — | 134 | 1 | no | — |
| 520 | #120 | — | 134 | 1 | no | — |
| 521 | C4×Q8 | — | 67 | 1 | no | — |
| 522 | C4×Q8 | D268 | 1 | 1 | yes | characteristic |
| 523 | C4×D4 | — | 2 | 1 | no | — |
| 524 | C4×D4 | — | 67 | 1 | no | — |
| 525 | C4×D4 | — | 134 | 1 | no | — |
| 526 | C4×D4 | — | 134 | 1 | no | — |
| 527 | C4×D4 | — | 134 | 1 | no | — |
| 528 | C4×D4 | — | 134 | 1 | no | — |
| 529 | C4×D4 | — | 134 | 1 | no | — |
| 530 | C4×D4 | — | 134 | 1 | no | — |
| 531 | C4×D4 | — | 134 | 1 | no | — |
| 532 | C4×D4 | D268 | 1 | 1 | yes | characteristic |
| 533 | #117 | — | 2 | 1 | no | — |
| 534 | #117 | — | 134 | 1 | no | — |
| 535 | #117 | — | 134 | 1 | no | — |
| 536 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 537 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 538 | C2×C42 | — | 134 | 1 | no | — |
| 539 | C2×C42 | C22×D67 | 1 | 1 | yes | characteristic |
| 540 | #107 | — | 134 | 2 | no | — |
| 541 | #106 | — | 134 | 2 | no | — |
| 542 | C4⋊C8 | — | 2 | 1 | no | — |
| 543 | C4⋊C8 | — | 134 | 1 | no | — |
| 544 | #103 | — | 134 | 2 | no | — |
| 545 | #103 | — | 134 | 2 | no | — |
| 546 | #103 | — | 134 | 2 | no | — |
| 547 | #103 | — | 134 | 2 | no | — |
| 548 | #103 | — | 134 | 2 | no | — |
| 549 | #102 | — | 134 | 2 | no | — |
| 550 | #102 | — | 134 | 2 | no | — |
| 551 | #102 | — | 134 | 2 | no | — |
| 552 | C22⋊C8 | — | 2 | 1 | no | — |
| 553 | C22⋊C8 | — | 134 | 1 | no | — |
| 554 | #97 | — | 67 | 2 | no | — |
| 555 | #97 | C22×D67 | 1 | 2 | yes | — |
| 556 | #97 | C22×D67 | 1 | 2 | yes | — |
| 557 | C4×C8 | — | 2 | 1 | no | — |
| 558 | C24 | — | 134 | 1 | no | — |
| 559 | #41 | — | 268 | 2 | no | — |
| 560 | #41 | — | 268 | 2 | no | — |
| 561 | #41 | — | 536 | 2 | no | — |
| 562 | C2×Q8 | — | 268 | 1 | no | — |
| 563 | C2×Q8 | — | 536 | 2 | no | — |
| 564 | C2×Q8 | — | 67 | 1 | no | — |
| 565 | C2×Q8 | — | 67 | 1 | no | — |
| 566 | C2×Q8 | — | 67 | 1 | no | — |
| 567 | C2×Q8 | — | 134 | 1 | no | — |
| 568 | C2×Q8 | — | 134 | 2 | no | — |
| 569 | C2×Q8 | C2×D268 | 1 | 1 | yes | characteristic |
| 570 | C2×D4 | — | 2 | 1 | no | — |
| 571 | C2×D4 | — | 67 | 1 | no | — |
| 572 | C2×D4 | — | 67 | 1 | no | — |
| 573 | C2×D4 | — | 67 | 1 | no | — |
| 574 | C2×D4 | — | 134 | 1 | no | — |
| 575 | C2×D4 | — | 134 | 1 | no | — |
| 576 | C2×D4 | — | 134 | 1 | no | — |
| 577 | C2×D4 | — | 134 | 1 | no | — |
| 578 | C2×D4 | — | 134 | 1 | no | — |
| 579 | C2×D4 | — | 134 | 1 | no | — |
| 580 | C2×D4 | — | 134 | 1 | no | — |
| 581 | C2×D4 | — | 134 | 1 | no | — |
| 582 | C2×D4 | — | 134 | 1 | no | — |
| 583 | C2×D4 | — | 134 | 1 | no | — |
| 584 | C2×D4 | — | 134 | 1 | no | — |
| 585 | C2×D4 | — | 134 | 1 | no | — |
| 586 | C2×D4 | C2×D268 | 1 | 1 | yes | characteristic |
| 587 | C22×C4 | — | 2 | 1 | no | — |
| 588 | C22×C4 | — | 268 | 1 | no | — |
| 589 | C22×C4 | — | 536 | 2 | no | — |
| 590 | C22×C4 | — | 134 | 1 | no | — |
| 591 | C22×C4 | — | 134 | 1 | no | — |
| 592 | C22×C4 | — | 134 | 1 | no | — |
| 593 | C22×C4 | — | 134 | 1 | no | — |
| 594 | C22×C4 | — | 134 | 1 | no | — |
| 595 | C22×C4 | — | 134 | 1 | no | — |
| 596 | C22×C4 | — | 134 | 1 | no | — |
| 597 | C22×C4 | — | 134 | 1 | no | — |
| 598 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 599 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 600 | C22×C4 | C2×D268 | 1 | 1 | yes | characteristic |
| 601 | Q16 | — | 536 | 2 | no | — |
| 602 | SD16 | — | 536 | 2 | no | — |
| 603 | M16 | — | 4 | 2 | no | — |
| 604 | C2×C8 | — | 2 | 2 | no | — |
| 605 | C2×C8 | — | 2 | 2 | no | — |
| 606 | C2×C8 | — | 134 | 2 | no | — |
| 607 | C4⋊C4 | — | 2 | 1 | no | — |
| 608 | C4⋊C4 | — | 2 | 1 | no | — |
| 609 | C4⋊C4 | — | 2 | 1 | no | — |
| 610 | C4⋊C4 | — | 2 | 1 | no | — |
| 611 | C4⋊C4 | — | 268 | 1 | no | — |
| 612 | C4⋊C4 | — | 268 | 1 | no | — |
| 613 | C4⋊C4 | — | 67 | 1 | no | — |
| 614 | C4⋊C4 | — | 67 | 1 | no | — |
| 615 | C4⋊C4 | — | 134 | 1 | no | — |
| 616 | C4⋊C4 | — | 134 | 1 | no | — |
| 617 | C4⋊C4 | — | 134 | 1 | no | — |
| 618 | C4⋊C4 | — | 134 | 1 | no | — |
| 619 | C4⋊C4 | — | 134 | 1 | no | — |
| 620 | C4⋊C4 | — | 134 | 1 | no | — |
| 621 | C4⋊C4 | — | 134 | 2 | no | — |
| 622 | C4⋊C4 | — | 134 | 2 | no | — |
| 623 | C4⋊C4 | — | 134 | 1 | no | — |
| 624 | C4⋊C4 | — | 134 | 1 | no | — |
| 625 | C4⋊C4 | — | 134 | 1 | no | — |
| 626 | C4⋊C4 | — | 134 | 1 | no | — |
| 627 | C4⋊C4 | — | 134 | 1 | no | — |
| 628 | C4⋊C4 | — | 134 | 1 | no | — |
| 629 | C4⋊C4 | C2×D268 | 1 | 1 | yes | characteristic |
| 630 | C4⋊C4 | C2×D268 | 1 | 1 | yes | characteristic |
| 631 | C22⋊C4 | — | 2 | 1 | no | — |
| 632 | C22⋊C4 | — | 2 | 1 | no | — |
| 633 | C22⋊C4 | — | 2 | 1 | no | — |
| 634 | C22⋊C4 | — | 2 | 1 | no | — |
| 635 | C22⋊C4 | — | 2 | 1 | no | — |
| 636 | C22⋊C4 | — | 134 | 1 | no | — |
| 637 | C22⋊C4 | — | 134 | 1 | no | — |
| 638 | C22⋊C4 | — | 134 | 1 | no | — |
| 639 | C22⋊C4 | — | 134 | 1 | no | — |
| 640 | C22⋊C4 | — | 134 | 1 | no | — |
| 641 | C22⋊C4 | — | 134 | 1 | no | — |
| 642 | C22⋊C4 | — | 134 | 1 | no | — |
| 643 | C22⋊C4 | — | 134 | 1 | no | — |
| 644 | C22⋊C4 | — | 134 | 1 | no | — |
| 645 | C22⋊C4 | — | 134 | 1 | no | — |
| 646 | C22⋊C4 | — | 134 | 1 | no | — |
| 647 | C22⋊C4 | — | 134 | 1 | no | — |
| 648 | C22⋊C4 | — | 134 | 1 | no | — |
| 649 | C22⋊C4 | — | 134 | 1 | no | — |
| 650 | C22⋊C4 | — | 134 | 1 | no | — |
| 651 | C22⋊C4 | — | 134 | 1 | no | — |
| 652 | C22⋊C4 | — | 134 | 1 | no | — |
| 653 | C22⋊C4 | — | 134 | 1 | no | — |
| 654 | C22⋊C4 | — | 134 | 1 | no | — |
| 655 | C42 | — | 2 | 1 | no | — |
| 656 | C42 | — | 134 | 1 | no | — |
| 657 | C42 | — | 134 | 1 | no | — |
| 658 | C42 | — | 134 | 1 | no | — |
| 659 | C42 | D4×D67 | 1 | 1 | yes | characteristic |
| 660 | C42 | D4×D67 | 1 | 1 | yes | characteristic |
| 661 | C42 | C2×D268 | 1 | 1 | yes | characteristic |
| 662 | C42 | C23×D67 | 1 | 1 | yes | characteristic |
| 663 | C23 | — | 2 | 1 | no | — |
| 664 | C23 | — | 536 | 1 | no | — |
| 665 | C23 | — | 536 | 1 | no | — |
| 666 | C23 | — | 536 | 1 | no | — |
| 667 | C23 | — | 134 | 1 | no | — |
| 668 | C23 | — | 134 | 1 | no | — |
| 669 | C23 | — | 134 | 1 | no | — |
| 670 | C23 | #14524013 | 1 | 1 | yes | characteristic |
| 671 | Q8 | — | 4 | 1 | no | — |
| 672 | Q8 | — | 268 | 1 | no | — |
| 673 | Q8 | — | 268 | 1 | no | — |
| 674 | Q8 | — | 268 | 1 | no | — |
| 675 | Q8 | — | 268 | 2 | no | — |
| 676 | Q8 | — | 268 | 2 | no | — |
| 677 | Q8 | — | 536 | 2 | no | — |
| 678 | Q8 | — | 536 | 1 | no | — |
| 679 | D4 | — | 4 | 1 | no | — |
| 680 | D4 | — | 8 | 1 | no | — |
| 681 | D4 | — | 268 | 1 | no | — |
| 682 | D4 | — | 268 | 1 | no | — |
| 683 | D4 | — | 268 | 1 | no | — |
| 684 | D4 | — | 536 | 1 | no | — |
| 685 | D4 | — | 536 | 1 | no | — |
| 686 | D4 | — | 536 | 1 | no | — |
| 687 | D4 | — | 536 | 1 | no | — |
| 688 | D4 | — | 536 | 1 | no | — |
| 689 | D4 | — | 536 | 1 | no | — |
| 690 | D4 | — | 536 | 1 | no | — |
| 691 | D4 | — | 536 | 1 | no | — |
| 692 | D4 | — | 536 | 1 | no | — |
| 693 | D4 | — | 536 | 1 | no | — |
| 694 | D4 | — | 536 | 1 | no | — |
| 695 | D4 | — | 536 | 1 | no | — |
| 696 | C2×C4 | — | 2 | 2 | no | — |
| 697 | C2×C4 | — | 2 | 1 | no | — |
| 698 | C2×C4 | — | 2 | 1 | no | — |
| 699 | C2×C4 | — | 2 | 1 | no | — |
| 700 | C2×C4 | — | 4 | 1 | no | — |
| 701 | C2×C4 | — | 4 | 1 | no | — |
| 702 | C2×C4 | — | 4 | 2 | no | — |
| 703 | C2×C4 | — | 268 | 2 | no | — |
| 704 | C2×C4 | — | 268 | 2 | no | — |
| 705 | C2×C4 | — | 268 | 2 | no | — |
| 706 | C2×C4 | — | 268 | 2 | no | — |
| 707 | C2×C4 | — | 536 | 1 | no | — |
| 708 | C2×C4 | — | 536 | 1 | no | — |
| 709 | C2×C4 | — | 536 | 1 | no | — |
| 710 | C2×C4 | — | 536 | 1 | no | — |
| 711 | C2×C4 | — | 536 | 1 | no | — |
| 712 | C2×C4 | — | 536 | 2 | no | — |
| 713 | C2×C4 | — | 134 | 1 | no | — |
| 714 | C2×C4 | — | 134 | 1 | no | — |
| 715 | C2×C4 | — | 134 | 1 | no | — |
| 716 | C2×C4 | — | 134 | 1 | no | — |
| 717 | C2×C4 | — | 134 | 1 | no | — |
| 718 | C2×C4 | #14524013 | 1 | 1 | yes | characteristic |
| 719 | C2×C4 | #14524013 | 1 | 1 | yes | characteristic |
| 720 | C2×C4 | #14524013 | 1 | 1 | yes | characteristic |
| 721 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 722 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 723 | C2×C4 | C22×D268 | 1 | 1 | yes | characteristic |
| 724 | C8 | — | 4 | 2 | no | — |
| 725 | C8 | — | 4 | 2 | no | — |
| 726 | C8 | — | 268 | 2 | no | — |
| 727 | C22 | — | 2 | 1 | no | — |
| 728 | C22 | — | 2 | 1 | no | — |
| 729 | C22 | — | 2 | 1 | no | — |
| 730 | C22 | — | 4 | 1 | no | — |
| 731 | C22 | — | 4 | 1 | no | — |
| 732 | C22 | — | 4 | 1 | no | — |
| 733 | C22 | — | 268 | 1 | no | — |
| 734 | C22 | — | 268 | 1 | no | — |
| 735 | C22 | — | 268 | 1 | no | — |
| 736 | C22 | — | 268 | 1 | no | — |
| 737 | C22 | — | 268 | 1 | no | — |
| 738 | C22 | — | 268 | 1 | no | — |
| 739 | C22 | — | 268 | 1 | no | — |
| 740 | C22 | — | 268 | 1 | no | — |
| 741 | C22 | — | 268 | 1 | no | — |
| 742 | C22 | — | 536 | 4 | no | — |
| 743 | C22 | C2×#14524013 | 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 | — | 4 | 1 | no | — |
| 750 | C4 | — | 4 | 1 | no | — |
| 751 | C4 | — | 4 | 1 | no | — |
| 752 | C4 | — | 268 | 1 | no | — |
| 753 | C4 | — | 268 | 1 | no | — |
| 754 | C4 | — | 268 | 1 | no | — |
| 755 | C4 | — | 268 | 1 | no | — |
| 756 | C4 | — | 268 | 1 | no | — |
| 757 | C4 | — | 536 | 2 | no | — |
| 758 | C4 | #16863575 | 1 | 2 | yes | — |
| 759 | C2 | — | 4 | 1 | no | — |
| 760 | C2 | — | 8 | 1 | no | — |
| 761 | C2 | — | 536 | 1 | no | — |
| 762 | C2 | — | 536 | 1 | no | — |
| 763 | C2 | — | 536 | 1 | no | — |
| 764 | C2 | C2×#16863575 | 1 | 1 | yes | characteristic |
| 765 | C2 | #22569582 | 1 | 1 | yes | characteristic |
| 766 | C2 | #22569590 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22571427 | C2 | semidirect |
| 3. #22571238 | C2 | semidirect |
| 4. #22570603 | C2 | semidirect |
| 5. #22559545 | C2 | semidirect |
| 6. #22559534 | C2 | semidirect |
| 7. #22559528 | C2 | semidirect |
| 8. #22559517 | C2 | semidirect |
| 9. #22558843 | C2 | semidirect |
| 10. #22558814 | C2 | semidirect |
| 11. C67×#1529 | C2 | semidirect |
| 24. C2×#14524043 | C22 | semidirect |
| 31. #16863806 | C22 | semidirect |
| 33. #16863765 | C22 | semidirect |
| 35. #16863756 | C22 | semidirect |
| 47. #16863453 | C22 | semidirect |
| 50. #16863137 | C22 | semidirect |
| 53. #16863135 | C22 | semidirect |
| 55. #432×C67 | C22 | semidirect |
| 56. C4×M16×C67 | C22 | semidirect |
| 57. #330×C67 | C22 | semidirect |
| 394. #1529 | D67 | semidirect |
| 395. C67 | #19000 | semidirect |
| 433. #432 | C2×D67 | semidirect |
| 436. C4×M16 | C2×D67 | semidirect |
| 438. #330 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574348 | 2 |
| #22571427 | 2 |
| #22571238 | 2 |
| #22570603 | 2 |
| #22559545 | 2 |
| #22559534 | 2 |
| #22559528 | 2 |
| #22559517 | 2 |
| #22558843 | 2 |
| #22558814 | 2 |
| C67×#1529 | 2 |
| #19000 | 67 |