Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1232 conjugacy classes of subgroups.
The subgroup lattice has 1044 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22574435 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22569464 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22569428 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22565932 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22559192 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22559191 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #22559167 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #22559166 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #22559154 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #22559153 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #22559130 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #22558779 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #22558751 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #22558567 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C67×#1596 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C22×#11761627 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#14524072 | — | 2 | 1 | no | — |
| 18 | C2×#14524064 | — | 2 | 1 | no | — |
| 19 | #16864142 | — | 2 | 1 | no | — |
| 20 | #16864142 | — | 2 | 1 | no | — |
| 21 | #16864100 | — | 2 | 1 | no | — |
| 22 | #16864056 | — | 2 | 1 | no | — |
| 23 | #16864048 | — | 2 | 1 | no | — |
| 24 | #16864037 | — | 2 | 1 | no | — |
| 25 | #16864036 | — | 2 | 1 | no | — |
| 26 | #16864036 | — | 2 | 1 | no | — |
| 27 | #16864021 | C22 | 1 | 1 | yes | characteristic |
| 28 | #16864016 | — | 2 | 1 | no | — |
| 29 | #16863992 | — | 2 | 1 | no | — |
| 30 | #16863986 | C22 | 1 | 1 | yes | characteristic |
| 31 | #16863984 | C22 | 1 | 1 | yes | characteristic |
| 32 | #16863976 | — | 2 | 1 | no | — |
| 33 | #16863976 | — | 2 | 1 | no | — |
| 34 | #16863909 | C22 | 1 | 1 | yes | characteristic |
| 35 | C22⋊Q8×D67 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×#14524016 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×#14524015 | — | 2 | 1 | no | — |
| 38 | #16863559 | — | 2 | 1 | no | — |
| 39 | #16863555 | — | 2 | 1 | no | — |
| 40 | #16863555 | — | 2 | 1 | no | — |
| 41 | #16863554 | C22 | 1 | 1 | yes | characteristic |
| 42 | #16863551 | C22 | 1 | 1 | yes | characteristic |
| 43 | #16863551 | C22 | 1 | 1 | yes | characteristic |
| 44 | #16863547 | C22 | 1 | 1 | yes | characteristic |
| 45 | #16863542 | — | 2 | 1 | no | — |
| 46 | #16863537 | C22 | 1 | 1 | yes | characteristic |
| 47 | #16863530 | C22 | 1 | 1 | yes | characteristic |
| 48 | #16863394 | — | 2 | 1 | no | — |
| 49 | #16863389 | — | 2 | 1 | no | — |
| 50 | #16863358 | C22 | 1 | 1 | yes | characteristic |
| 51 | C22⋊C8×D67 | C22 | 1 | 1 | yes | characteristic |
| 52 | #16863309 | C22 | 1 | 1 | yes | characteristic |
| 53 | #16863308 | C22 | 1 | 1 | yes | characteristic |
| 54 | #16863305 | — | 2 | 1 | no | — |
| 55 | #16863304 | — | 2 | 1 | no | — |
| 56 | #16863304 | C22 | 1 | 1 | yes | characteristic |
| 57 | #16863255 | C22 | 1 | 1 | yes | characteristic |
| 58 | #16863254 | — | 2 | 1 | no | — |
| 59 | #16863134 | C22 | 1 | 1 | yes | characteristic |
| 60 | #16863133 | C22 | 1 | 1 | yes | characteristic |
| 61 | #16863133 | C22 | 1 | 1 | yes | characteristic |
| 62 | #16863132 | C22 | 1 | 1 | yes | characteristic |
| 63 | #16863131 | C22 | 1 | 1 | yes | characteristic |
| 64 | #16863129 | C22 | 1 | 1 | yes | characteristic |
| 65 | #16863120 | C22 | 1 | 1 | yes | characteristic |
| 66 | #16863119 | C22 | 1 | 1 | yes | characteristic |
| 67 | #16863119 | C22 | 1 | 1 | yes | characteristic |
| 68 | #543×C67 | C22 | 1 | 1 | yes | characteristic |
| 69 | #450×C67 | C22 | 1 | 1 | yes | characteristic |
| 70 | #450×C67 | C22 | 1 | 1 | yes | characteristic |
| 71 | #392×C67 | C22 | 1 | 1 | yes | characteristic |
| 72 | #328×C67 | C22 | 1 | 1 | yes | characteristic |
| 73 | #328×C67 | C22 | 1 | 1 | yes | characteristic |
| 74 | #323×C67 | C22 | 1 | 1 | yes | characteristic |
| 75 | C2×#11761629 | — | 2 | 1 | no | — |
| 76 | C2×#11761629 | D4 | 1 | 1 | yes | characteristic, complemented |
| 77 | C2×#11761628 | — | 2 | 1 | no | — |
| 78 | C2×#11761628 | — | 2 | 1 | no | — |
| 79 | C2×#11761627 | — | 2 | 1 | no | — |
| 80 | C2×#11761627 | — | 2 | 1 | no | — |
| 81 | C2×#11761627 | — | 2 | 1 | no | — |
| 82 | C2×#11761627 | — | 2 | 1 | no | — |
| 83 | C2×#11761627 | — | 4 | 4 | no | — |
| 84 | C22×Dic134 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×Q8×D67 | D4 | 1 | 1 | yes | characteristic, complemented |
| 86 | C22×D268 | D4 | 1 | 1 | yes | characteristic |
| 87 | C22×C22⋊D67 | — | 2 | 1 | no | — |
| 88 | C22×C22⋊D67 | — | 2 | 1 | no | — |
| 89 | C22×C22⋊D67 | D4 | 1 | 1 | yes | characteristic |
| 90 | C22×C22⋊D67 | D4 | 1 | 1 | yes | characteristic |
| 91 | C23×Dic67 | — | 2 | 1 | no | — |
| 92 | C22×C4×D67 | C23 | 1 | 1 | yes | characteristic |
| 93 | #14524072 | — | 4 | 4 | no | — |
| 94 | #14524064 | — | 4 | 4 | no | — |
| 95 | C2×Dic268 | — | 2 | 1 | no | — |
| 96 | C2×#11761618 | — | 2 | 1 | no | — |
| 97 | C2×#11761618 | — | 2 | 1 | no | — |
| 98 | C2×#11761617 | — | 2 | 1 | no | — |
| 99 | C2×#11761616 | — | 2 | 1 | no | — |
| 100 | C2×#11761613 | — | 2 | 1 | no | — |
| 101 | C2×#11761611 | — | 2 | 1 | no | — |
| 102 | C2×C8×D67 | — | 2 | 1 | no | — |
| 103 | #14524041 | — | 2 | 1 | no | — |
| 104 | #14524038 | — | 2 | 1 | no | — |
| 105 | #14524036 | — | 2 | 1 | no | — |
| 106 | #14524033 | — | 2 | 1 | no | — |
| 107 | #14524033 | — | 2 | 1 | no | — |
| 108 | #14524032 | — | 2 | 1 | no | — |
| 109 | #14524032 | — | 2 | 1 | no | — |
| 110 | #14524029 | — | 2 | 1 | no | — |
| 111 | #14524029 | — | 2 | 1 | no | — |
| 112 | #14524029 | — | 2 | 1 | no | — |
| 113 | #14524028 | — | 2 | 1 | no | — |
| 114 | #14524028 | — | 2 | 1 | no | — |
| 115 | #14524028 | — | 2 | 1 | no | — |
| 116 | #14524028 | — | 2 | 1 | no | — |
| 117 | #14524026 | — | 2 | 1 | no | — |
| 118 | #14524026 | — | 2 | 1 | no | — |
| 119 | #14524025 | — | 2 | 1 | no | — |
| 120 | #14524025 | — | 2 | 1 | no | — |
| 121 | #14524025 | — | 2 | 1 | no | — |
| 122 | #14524023 | — | 2 | 1 | no | — |
| 123 | #14524023 | D4 | 1 | 1 | yes | characteristic, complemented |
| 124 | #14524022 | C23 | 1 | 1 | yes | characteristic |
| 125 | #14524021 | — | 2 | 1 | no | — |
| 126 | #14524021 | — | 2 | 1 | no | — |
| 127 | #14524021 | — | 2 | 1 | no | — |
| 128 | #14524021 | — | 2 | 1 | no | — |
| 129 | #14524021 | — | 2 | 1 | no | — |
| 130 | #14524020 | — | 2 | 1 | no | — |
| 131 | #14524020 | — | 2 | 1 | no | — |
| 132 | #14524019 | — | 2 | 1 | no | — |
| 133 | #14524019 | — | 2 | 1 | no | — |
| 134 | #14524019 | D4 | 1 | 1 | yes | characteristic, complemented |
| 135 | #14524019 | D4 | 1 | 1 | yes | characteristic, complemented |
| 136 | #14524018 | — | 2 | 1 | no | — |
| 137 | #14524018 | — | 2 | 1 | no | — |
| 138 | #14524018 | — | 2 | 1 | no | — |
| 139 | #14524018 | — | 2 | 1 | no | — |
| 140 | #14524018 | D4 | 1 | 1 | yes | characteristic, complemented |
| 141 | #14524017 | — | 2 | 1 | no | — |
| 142 | #14524017 | — | 2 | 1 | no | — |
| 143 | #14524017 | C23 | 1 | 1 | yes | characteristic |
| 144 | #14524016 | — | 2 | 1 | no | — |
| 145 | #14524016 | — | 2 | 1 | no | — |
| 146 | #14524016 | — | 2 | 1 | no | — |
| 147 | #14524016 | — | 2 | 1 | no | — |
| 148 | #14524016 | — | 2 | 1 | no | — |
| 149 | #14524016 | — | 2 | 1 | no | — |
| 150 | #14524016 | — | 2 | 1 | no | — |
| 151 | #14524016 | — | 2 | 1 | no | — |
| 152 | #14524016 | — | 2 | 1 | no | — |
| 153 | #14524015 | — | 4 | 4 | no | — |
| 154 | #14524013 | — | 2 | 1 | no | — |
| 155 | #14524013 | — | 2 | 1 | no | — |
| 156 | #14524012 | — | 2 | 1 | no | — |
| 157 | #14524008 | — | 2 | 1 | no | — |
| 158 | #14524005 | — | 2 | 1 | no | — |
| 159 | #14524005 | — | 2 | 1 | no | — |
| 160 | C4×C22⋊D67 | — | 2 | 1 | no | — |
| 161 | C4×C22⋊D67 | — | 2 | 1 | no | — |
| 162 | C4×C22⋊D67 | — | 2 | 1 | no | — |
| 163 | (C22⋊D67)⋊C4 | — | 2 | 1 | no | — |
| 164 | (C22⋊D67)⋊C4 | — | 2 | 1 | no | — |
| 165 | #14524001 | D4 | 1 | 1 | yes | characteristic, complemented |
| 166 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 167 | C2×Dic67⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 168 | C4⋊C4×D67 | — | 2 | 1 | no | — |
| 169 | C4⋊C4×D67 | — | 2 | 1 | no | — |
| 170 | C4⋊C4×D67 | D4 | 1 | 1 | yes | characteristic, complemented |
| 171 | C2×C22⋊Dic67 | — | 2 | 1 | no | — |
| 172 | C2×C22⋊Dic67 | — | 2 | 1 | no | — |
| 173 | C2×(C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 174 | C2×(C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 175 | C2×(C2×D67)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 176 | C22⋊C4×D67 | — | 2 | 1 | no | — |
| 177 | C22⋊C4×D67 | — | 2 | 1 | no | — |
| 178 | #14523968 | — | 2 | 1 | no | — |
| 179 | #14523968 | — | 2 | 1 | no | — |
| 180 | #14523966 | — | 2 | 1 | no | — |
| 181 | #14523966 | — | 2 | 1 | no | — |
| 182 | #14523964 | — | 2 | 1 | no | — |
| 183 | #14523964 | — | 2 | 1 | no | — |
| 184 | C22⋊(C67⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 185 | C22⋊(C67⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 186 | (C2×D67)⋊C8 | — | 2 | 1 | no | — |
| 187 | (C2×D67)⋊C8 | — | 2 | 1 | no | — |
| 188 | C67⋊#95 | — | 2 | 1 | no | — |
| 189 | C67⋊#95 | — | 2 | 1 | no | — |
| 190 | C67⋊#95 | C23 | 1 | 1 | yes | characteristic |
| 191 | C22×D4×C67 | — | 2 | 1 | no | — |
| 192 | C22×D4×C67 | C23 | 1 | 1 | yes | characteristic |
| 193 | C2×SD16×C67 | — | 2 | 1 | no | — |
| 194 | C2×SD16×C67 | — | 2 | 1 | no | — |
| 195 | C22⋊Q8×C67 | — | 2 | 1 | no | — |
| 196 | C22⋊Q8×C67 | — | 2 | 1 | no | — |
| 197 | C22⋊Q8×C67 | — | 2 | 1 | no | — |
| 198 | C22⋊Q8×C67 | — | 2 | 1 | no | — |
| 199 | C22⋊Q8×C67 | — | 2 | 1 | no | — |
| 200 | C22⋊Q8×C67 | C23 | 1 | 1 | yes | characteristic |
| 201 | C22⋊Q8×C67 | C23 | 1 | 1 | yes | characteristic |
| 202 | C2×C22⋊C4×C67 | — | 2 | 1 | no | — |
| 203 | C2×C22⋊C4×C67 | — | 2 | 1 | no | — |
| 204 | C2×C22⋊C4×C67 | C23 | 1 | 1 | yes | characteristic |
| 205 | #102×C67 | — | 2 | 1 | no | — |
| 206 | #102×C67 | — | 2 | 1 | no | — |
| 207 | C22⋊C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 208 | C22⋊C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 209 | #95×C67 | C23 | 1 | 1 | yes | characteristic |
| 210 | C23×D67 | C2×D4 | 1 | 1 | yes | characteristic |
| 211 | C23×D67 | C2×D4 | 1 | 1 | yes | characteristic |
| 212 | #11761629 | — | 4 | 2 | no | — |
| 213 | #11761629 | — | 8 | 2 | no | — |
| 214 | #11761628 | — | 8 | 2 | no | — |
| 215 | #11761628 | — | 8 | 2 | no | — |
| 216 | #11761627 | — | 2 | 4 | no | — |
| 217 | #11761627 | — | 2 | 4 | no | — |
| 218 | #11761627 | — | 4 | 2 | no | — |
| 219 | #11761627 | — | 4 | 2 | no | — |
| 220 | #11761627 | — | 4 | 2 | no | — |
| 221 | #11761627 | — | 4 | 2 | no | — |
| 222 | #11761627 | — | 4 | 2 | no | — |
| 223 | #11761627 | — | 4 | 2 | no | — |
| 224 | C2×Dic134 | — | 2 | 1 | no | — |
| 225 | C2×Dic134 | — | 2 | 1 | no | — |
| 226 | C2×Dic134 | — | 2 | 1 | no | — |
| 227 | C2×Dic134 | — | 2 | 1 | no | — |
| 228 | C2×Dic134 | — | 4 | 2 | no | — |
| 229 | C2×Dic134 | C2×D4 | 1 | 1 | yes | characteristic |
| 230 | Q8×D67 | — | 4 | 2 | no | — |
| 231 | C2×D268 | — | 2 | 1 | no | — |
| 232 | C2×D268 | — | 2 | 1 | no | — |
| 233 | C2×D268 | — | 2 | 1 | no | — |
| 234 | C2×D268 | — | 2 | 1 | no | — |
| 235 | C2×D268 | — | 2 | 1 | no | — |
| 236 | C2×D268 | — | 2 | 1 | no | — |
| 237 | C2×D268 | — | 8 | 1 | no | — |
| 238 | C2×D268 | C2×D4 | 1 | 1 | yes | characteristic |
| 239 | C2×C22⋊D67 | — | 2 | 1 | no | — |
| 240 | C2×C22⋊D67 | — | 2 | 1 | no | — |
| 241 | C2×C22⋊D67 | — | 2 | 1 | no | — |
| 242 | C2×C22⋊D67 | — | 2 | 1 | no | — |
| 243 | C2×C22⋊D67 | — | 2 | 1 | no | — |
| 244 | C2×C22⋊D67 | — | 2 | 1 | no | — |
| 245 | C2×C22⋊D67 | — | 2 | 1 | no | — |
| 246 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 247 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 248 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 249 | C2×C22⋊D67 | — | 4 | 1 | no | — |
| 250 | C2×C22⋊D67 | — | 4 | 1 | no | — |
| 251 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 252 | C2×C22⋊D67 | — | 8 | 1 | no | — |
| 253 | C2×C22⋊D67 | — | 8 | 1 | no | — |
| 254 | C2×C22⋊D67 | — | 8 | 1 | no | — |
| 255 | C22×Dic67 | — | 2 | 4 | no | — |
| 256 | C22×Dic67 | — | 2 | 1 | no | — |
| 257 | C22×Dic67 | — | 2 | 1 | no | — |
| 258 | C22×Dic67 | — | 4 | 2 | no | — |
| 259 | C22×Dic67 | — | 4 | 1 | no | — |
| 260 | C22×Dic67 | — | 4 | 1 | no | — |
| 261 | C22×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 262 | C22×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 263 | C2×C4×D67 | — | 2 | 1 | no | — |
| 264 | C2×C4×D67 | — | 2 | 1 | no | — |
| 265 | C2×C4×D67 | — | 2 | 1 | no | — |
| 266 | C2×C4×D67 | — | 2 | 1 | no | — |
| 267 | C2×C4×D67 | — | 2 | 1 | no | — |
| 268 | C2×C4×D67 | — | 2 | 1 | no | — |
| 269 | C2×C4×D67 | — | 2 | 1 | no | — |
| 270 | C2×C4×D67 | — | 4 | 2 | no | — |
| 271 | C2×C4×D67 | C2×D4 | 1 | 1 | yes | characteristic |
| 272 | C2×C4×D67 | C2×D4 | 1 | 1 | yes | characteristic |
| 273 | C2×C4×D67 | C2×D4 | 1 | 1 | yes | characteristic |
| 274 | C2×C4×D67 | C2×D4 | 1 | 1 | yes | characteristic |
| 275 | Dic268 | — | 4 | 2 | no | — |
| 276 | #11761618 | — | 4 | 2 | no | — |
| 277 | #11761618 | — | 4 | 2 | no | — |
| 278 | #11761617 | — | 4 | 2 | no | — |
| 279 | #11761616 | — | 4 | 2 | no | — |
| 280 | #11761613 | — | 4 | 2 | no | — |
| 281 | #11761611 | — | 4 | 2 | no | — |
| 282 | C2×C67⋊C8 | — | 2 | 1 | no | — |
| 283 | C2×C67⋊C8 | — | 2 | 1 | no | — |
| 284 | C8×D67 | — | 4 | 2 | no | — |
| 285 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 286 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 287 | C4⋊Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 288 | C4⋊Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 289 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 290 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 291 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 292 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 293 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 294 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 295 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 296 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 297 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 298 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 299 | Dic67⋊C4 | — | 4 | 2 | no | — |
| 300 | C22⋊Dic67 | — | 2 | 1 | no | — |
| 301 | C22⋊Dic67 | — | 2 | 1 | no | — |
| 302 | C22⋊Dic67 | — | 2 | 1 | no | — |
| 303 | C22⋊Dic67 | — | 4 | 2 | no | — |
| 304 | C22⋊Dic67 | — | 8 | 1 | no | — |
| 305 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 306 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 307 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 308 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 309 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 310 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 311 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 312 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 313 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 314 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 315 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 316 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 317 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 318 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 319 | (C2×D67)⋊C4 | — | 4 | 2 | no | — |
| 320 | (C2×D67)⋊C4 | — | 8 | 1 | no | — |
| 321 | C4×Dic67 | — | 2 | 1 | no | — |
| 322 | C4×Dic67 | — | 2 | 1 | no | — |
| 323 | C4×Dic67 | — | 2 | 1 | no | — |
| 324 | C24×C67 | — | 2 | 1 | no | — |
| 325 | C24×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 326 | C2×Q8×C67 | — | 2 | 1 | no | — |
| 327 | C2×Q8×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 328 | C2×Q8×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 329 | C2×D4×C67 | — | 2 | 1 | no | — |
| 330 | C2×D4×C67 | — | 2 | 1 | no | — |
| 331 | C2×D4×C67 | — | 4 | 2 | no | — |
| 332 | C2×D4×C67 | — | 4 | 2 | no | — |
| 333 | C2×D4×C67 | — | 8 | 1 | no | — |
| 334 | C2×D4×C67 | — | 8 | 1 | no | — |
| 335 | C22×C4×C67 | — | 2 | 1 | no | — |
| 336 | C22×C4×C67 | — | 2 | 1 | no | — |
| 337 | C22×C4×C67 | — | 2 | 1 | no | — |
| 338 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 339 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 340 | SD16×C67 | — | 4 | 2 | no | — |
| 341 | SD16×C67 | — | 4 | 2 | no | — |
| 342 | C2×C8×C67 | — | 2 | 1 | no | — |
| 343 | C2×C8×C67 | — | 2 | 1 | no | — |
| 344 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 345 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 346 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 347 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 348 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 349 | C4⋊C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 350 | C4⋊C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 351 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 352 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 353 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 354 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 355 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 356 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 357 | C22⋊C4×C67 | — | 8 | 1 | no | — |
| 358 | C23×C67 | — | 2 | 2 | no | — |
| 359 | C23×C67 | — | 2 | 1 | no | — |
| 360 | C23×C67 | — | 2 | 1 | no | — |
| 361 | C23×C67 | — | 2 | 1 | no | — |
| 362 | C23×C67 | — | 4 | 1 | no | — |
| 363 | C23×C67 | — | 4 | 1 | no | — |
| 364 | C23×C67 | — | 4 | 1 | no | — |
| 365 | C23×C67 | — | 4 | 1 | no | — |
| 366 | C23×C67 | — | 4 | 1 | no | — |
| 367 | C23×C67 | — | 4 | 1 | no | — |
| 368 | C23×C67 | — | 4 | 1 | no | — |
| 369 | C23×C67 | — | 4 | 1 | no | — |
| 370 | C23×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 371 | C22×D67 | — | 2 | 1 | no | — |
| 372 | C22×D67 | — | 2 | 1 | no | — |
| 373 | C22×D67 | — | 2 | 1 | no | — |
| 374 | C22×D67 | — | 2 | 1 | no | — |
| 375 | C22×D67 | — | 2 | 1 | no | — |
| 376 | C22×D67 | — | 2 | 1 | no | — |
| 377 | C22×D67 | — | 4 | 1 | no | — |
| 378 | C22×D67 | — | 4 | 1 | no | — |
| 379 | C22×D67 | — | 4 | 1 | no | — |
| 380 | C22×D67 | — | 4 | 1 | no | — |
| 381 | C22×D67 | #120 | 1 | 1 | yes | characteristic |
| 382 | C22×D67 | #120 | 1 | 1 | yes | characteristic |
| 383 | Q8×C67 | — | 4 | 1 | no | — |
| 384 | Q8×C67 | — | 4 | 1 | no | — |
| 385 | Q8×C67 | — | 8 | 1 | no | — |
| 386 | D4×C67 | — | 2 | 2 | no | — |
| 387 | D4×C67 | — | 2 | 2 | no | — |
| 388 | D4×C67 | — | 4 | 1 | no | — |
| 389 | D4×C67 | — | 4 | 1 | no | — |
| 390 | D4×C67 | — | 8 | 4 | no | — |
| 391 | C2×C4×C67 | — | 2 | 1 | no | — |
| 392 | C2×C4×C67 | — | 2 | 1 | no | — |
| 393 | C2×C4×C67 | — | 2 | 1 | no | — |
| 394 | C2×C4×C67 | — | 2 | 1 | no | — |
| 395 | C2×C4×C67 | — | 2 | 1 | no | — |
| 396 | C2×C4×C67 | — | 4 | 1 | no | — |
| 397 | C2×C4×C67 | — | 4 | 1 | no | — |
| 398 | C2×C4×C67 | — | 4 | 1 | no | — |
| 399 | C2×C4×C67 | — | 4 | 1 | no | — |
| 400 | C2×C4×C67 | — | 4 | 1 | no | — |
| 401 | C2×C4×C67 | — | 8 | 1 | no | — |
| 402 | C2×C4×C67 | — | 8 | 1 | no | — |
| 403 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 404 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 405 | C22⋊D67 | — | 4 | 2 | no | — |
| 406 | C22⋊D67 | — | 4 | 4 | no | — |
| 407 | C22⋊D67 | — | 4 | 4 | no | — |
| 408 | C22⋊D67 | — | 4 | 1 | no | — |
| 409 | C22⋊D67 | — | 4 | 1 | no | — |
| 410 | C22⋊D67 | — | 4 | 2 | no | — |
| 411 | C22⋊D67 | — | 8 | 1 | no | — |
| 412 | C22⋊D67 | — | 8 | 1 | no | — |
| 413 | C22⋊D67 | — | 8 | 1 | no | — |
| 414 | C22⋊D67 | — | 8 | 1 | no | — |
| 415 | C22⋊D67 | — | 8 | 4 | no | — |
| 416 | C2×Dic67 | — | 2 | 2 | no | — |
| 417 | C2×Dic67 | — | 2 | 2 | no | — |
| 418 | C2×Dic67 | — | 2 | 1 | no | — |
| 419 | C2×Dic67 | — | 2 | 1 | no | — |
| 420 | C2×Dic67 | — | 2 | 1 | no | — |
| 421 | C2×Dic67 | — | 2 | 1 | no | — |
| 422 | C2×Dic67 | — | 4 | 4 | no | — |
| 423 | C2×Dic67 | — | 4 | 1 | no | — |
| 424 | C2×Dic67 | — | 4 | 1 | no | — |
| 425 | C2×Dic67 | — | 4 | 4 | no | — |
| 426 | C2×Dic67 | — | 4 | 1 | no | — |
| 427 | C2×Dic67 | — | 4 | 1 | no | — |
| 428 | C2×Dic67 | — | 4 | 1 | no | — |
| 429 | C2×Dic67 | — | 4 | 1 | no | — |
| 430 | C2×Dic67 | #120 | 1 | 1 | yes | characteristic |
| 431 | C2×Dic67 | #120 | 1 | 1 | yes | characteristic |
| 432 | D268 | — | 4 | 1 | no | — |
| 433 | D268 | — | 4 | 2 | no | — |
| 434 | D268 | — | 4 | 2 | no | — |
| 435 | D268 | — | 8 | 1 | no | — |
| 436 | D268 | — | 8 | 1 | no | — |
| 437 | D268 | — | 8 | 1 | no | — |
| 438 | D268 | — | 8 | 1 | no | — |
| 439 | C4×D67 | — | 2 | 2 | no | — |
| 440 | C4×D67 | — | 2 | 2 | no | — |
| 441 | C4×D67 | — | 4 | 1 | no | — |
| 442 | C4×D67 | — | 4 | 1 | no | — |
| 443 | C4×D67 | — | 4 | 2 | no | — |
| 444 | C4×D67 | — | 4 | 2 | no | — |
| 445 | C4×D67 | — | 8 | 1 | no | — |
| 446 | C4×D67 | — | 8 | 1 | no | — |
| 447 | C4×D67 | — | 8 | 1 | no | — |
| 448 | C4×D67 | — | 8 | 1 | no | — |
| 449 | C4×D67 | — | 8 | 1 | no | — |
| 450 | Dic134 | — | 2 | 2 | no | — |
| 451 | Dic134 | — | 2 | 2 | no | — |
| 452 | Dic134 | — | 4 | 1 | no | — |
| 453 | Dic134 | — | 4 | 1 | no | — |
| 454 | Dic134 | — | 4 | 2 | no | — |
| 455 | Dic134 | — | 4 | 1 | no | — |
| 456 | Dic134 | — | 8 | 1 | no | — |
| 457 | C8×C67 | — | 4 | 1 | no | — |
| 458 | C8×C67 | — | 4 | 1 | no | — |
| 459 | C67⋊C8 | — | 4 | 1 | no | — |
| 460 | C67⋊C8 | — | 4 | 1 | no | — |
| 461 | C22×C67 | — | 2 | 1 | no | — |
| 462 | C22×C67 | — | 2 | 1 | no | — |
| 463 | C22×C67 | — | 4 | 2 | no | — |
| 464 | C22×C67 | — | 4 | 2 | no | — |
| 465 | C22×C67 | — | 4 | 1 | no | — |
| 466 | C22×C67 | — | 4 | 1 | no | — |
| 467 | C22×C67 | — | 4 | 2 | no | — |
| 468 | C22×C67 | — | 4 | 1 | no | — |
| 469 | C22×C67 | — | 8 | 1 | no | — |
| 470 | C22×C67 | — | 8 | 1 | no | — |
| 471 | C22×C67 | — | 8 | 1 | no | — |
| 472 | C22×C67 | — | 8 | 1 | no | — |
| 473 | C22×C67 | — | 8 | 1 | no | — |
| 474 | C22×C67 | — | 8 | 1 | no | — |
| 475 | C22×C67 | C2×#120 | 1 | 1 | yes | characteristic |
| 476 | C22×C67 | #577 | 1 | 1 | yes | characteristic |
| 477 | C22×C67 | #578 | 1 | 1 | yes | characteristic |
| 478 | C2×D67 | — | 2 | 1 | no | — |
| 479 | C2×D67 | — | 2 | 1 | no | — |
| 480 | C2×D67 | — | 2 | 1 | no | — |
| 481 | C2×D67 | — | 2 | 1 | no | — |
| 482 | C2×D67 | — | 2 | 1 | no | — |
| 483 | C2×D67 | — | 2 | 1 | no | — |
| 484 | C2×D67 | — | 4 | 1 | no | — |
| 485 | C2×D67 | — | 4 | 1 | no | — |
| 486 | C2×D67 | — | 4 | 1 | no | — |
| 487 | C2×D67 | — | 4 | 1 | no | — |
| 488 | C2×D67 | — | 4 | 1 | no | — |
| 489 | C2×D67 | — | 4 | 1 | no | — |
| 490 | C2×D67 | — | 8 | 1 | no | — |
| 491 | C2×D67 | — | 8 | 1 | no | — |
| 492 | C2×D67 | — | 8 | 1 | no | — |
| 493 | C2×D67 | — | 8 | 1 | no | — |
| 494 | C4×C67 | — | 2 | 1 | no | — |
| 495 | C4×C67 | — | 2 | 1 | no | — |
| 496 | C4×C67 | — | 4 | 1 | no | — |
| 497 | C4×C67 | — | 4 | 1 | no | — |
| 498 | C4×C67 | — | 4 | 1 | no | — |
| 499 | C4×C67 | — | 4 | 1 | no | — |
| 500 | C4×C67 | — | 4 | 1 | no | — |
| 501 | C4×C67 | — | 8 | 1 | no | — |
| 502 | Dic67 | — | 2 | 1 | no | — |
| 503 | Dic67 | — | 4 | 1 | no | — |
| 504 | Dic67 | — | 4 | 1 | no | — |
| 505 | Dic67 | — | 4 | 1 | no | — |
| 506 | Dic67 | — | 4 | 2 | no | — |
| 507 | Dic67 | — | 4 | 1 | no | — |
| 508 | Dic67 | — | 8 | 1 | no | — |
| 509 | Dic67 | B(4,𝔽2) | 1 | 2 | yes | — |
| 510 | #18229 | — | 67 | 1 | no | maximal, Sylow |
| 511 | C2×C67 | — | 2 | 1 | no | — |
| 512 | C2×C67 | — | 2 | 1 | no | — |
| 513 | C2×C67 | — | 8 | 1 | no | — |
| 514 | C2×C67 | — | 8 | 2 | no | — |
| 515 | C2×C67 | #3013 | 1 | 1 | yes | characteristic |
| 516 | C2×C67 | #3019 | 1 | 1 | yes | characteristic |
| 517 | C2×C67 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 518 | D67 | — | 4 | 1 | no | — |
| 519 | D67 | — | 4 | 1 | no | — |
| 520 | D67 | — | 8 | 1 | no | — |
| 521 | D67 | — | 8 | 1 | no | — |
| 522 | #3536 | — | 67 | 1 | no | — |
| 523 | #3007 | — | 67 | 1 | no | — |
| 524 | #3002 | — | 67 | 1 | no | — |
| 525 | #2615 | — | 67 | 1 | no | — |
| 526 | #1606 | — | 67 | 1 | no | — |
| 527 | #1606 | — | 67 | 1 | no | — |
| 528 | #1602 | — | 67 | 1 | no | — |
| 529 | #1602 | — | 67 | 1 | no | — |
| 530 | #1600 | — | 67 | 1 | no | — |
| 531 | #1600 | — | 67 | 1 | no | — |
| 532 | #1596 | — | 67 | 1 | no | — |
| 533 | #1596 | D67 | 1 | 1 | yes | characteristic, complemented |
| 534 | #1520 | — | 67 | 1 | no | — |
| 535 | #1513 | — | 67 | 1 | no | — |
| 536 | #1471 | — | 67 | 1 | no | — |
| 537 | C67 | #18229 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 538 | C22×#41 | — | 67 | 1 | no | — |
| 539 | C2×#137 | — | 134 | 1 | no | — |
| 540 | C2×#135 | — | 134 | 1 | no | — |
| 541 | #562 | — | 134 | 1 | no | — |
| 542 | #562 | — | 134 | 1 | no | — |
| 543 | #554 | — | 134 | 1 | no | — |
| 544 | #548 | — | 134 | 1 | no | — |
| 545 | #547 | — | 134 | 1 | no | — |
| 546 | #546 | — | 134 | 1 | no | — |
| 547 | #546 | — | 134 | 1 | no | — |
| 548 | #546 | — | 134 | 1 | no | — |
| 549 | #543 | — | 67 | 1 | no | — |
| 550 | #543 | C2×D67 | 1 | 1 | yes | characteristic |
| 551 | #542 | — | 134 | 1 | no | — |
| 552 | #539 | — | 134 | 1 | no | — |
| 553 | #538 | — | 67 | 1 | no | — |
| 554 | #538 | — | 67 | 1 | no | — |
| 555 | #537 | — | 134 | 1 | no | — |
| 556 | #537 | — | 134 | 1 | no | — |
| 557 | #525 | — | 67 | 1 | no | — |
| 558 | C2×C22⋊Q8 | — | 67 | 1 | no | — |
| 559 | C2×#121 | — | 67 | 1 | no | — |
| 560 | C2×#121 | — | 134 | 1 | no | — |
| 561 | #452 | — | 134 | 1 | no | — |
| 562 | #452 | — | 134 | 1 | no | — |
| 563 | #452 | — | 134 | 1 | no | — |
| 564 | #451 | — | 67 | 1 | no | — |
| 565 | #451 | — | 67 | 1 | no | — |
| 566 | #451 | — | 67 | 1 | no | — |
| 567 | #450 | — | 67 | 1 | no | — |
| 568 | #450 | C2×D67 | 1 | 1 | yes | characteristic |
| 569 | #450 | C2×D67 | 1 | 1 | yes | characteristic |
| 570 | #449 | — | 134 | 1 | no | — |
| 571 | #448 | — | 67 | 1 | no | — |
| 572 | #447 | — | 67 | 1 | no | — |
| 573 | #417 | — | 134 | 1 | no | — |
| 574 | #416 | — | 134 | 1 | no | — |
| 575 | #407 | — | 67 | 1 | no | — |
| 576 | C2×C22⋊C8 | — | 67 | 1 | no | — |
| 577 | #393 | — | 67 | 1 | no | — |
| 578 | #393 | — | 67 | 1 | no | — |
| 579 | #392 | — | 67 | 1 | no | — |
| 580 | #392 | — | 134 | 1 | no | — |
| 581 | #392 | — | 134 | 1 | no | — |
| 582 | #392 | C2×D67 | 1 | 1 | yes | characteristic |
| 583 | #380 | — | 67 | 1 | no | — |
| 584 | #380 | — | 134 | 1 | no | — |
| 585 | #328 | — | 67 | 1 | no | — |
| 586 | #328 | — | 67 | 1 | no | — |
| 587 | #328 | — | 67 | 1 | no | — |
| 588 | #328 | — | 67 | 1 | no | — |
| 589 | #328 | C2×D67 | 1 | 1 | yes | characteristic |
| 590 | #328 | C2×D67 | 1 | 1 | yes | characteristic |
| 591 | #327 | — | 67 | 1 | no | — |
| 592 | #327 | — | 67 | 1 | no | — |
| 593 | #323 | — | 67 | 1 | no | — |
| 594 | #323 | — | 67 | 1 | no | — |
| 595 | #323 | — | 67 | 1 | no | — |
| 596 | #323 | C2×D67 | 1 | 1 | yes | characteristic |
| 597 | C2×#41 | — | 268 | 4 | no | — |
| 598 | C2×#41 | — | 67 | 1 | no | — |
| 599 | C2×#41 | — | 134 | 1 | no | — |
| 600 | C2×#41 | — | 134 | 1 | no | — |
| 601 | C2×#41 | — | 134 | 1 | no | — |
| 602 | C2×#41 | — | 134 | 1 | no | — |
| 603 | C2×#41 | — | 134 | 1 | no | — |
| 604 | C2×#41 | — | 134 | 1 | no | — |
| 605 | C2×#41 | — | 134 | 1 | no | — |
| 606 | C22×Q8 | — | 67 | 1 | no | — |
| 607 | C22×Q8 | — | 67 | 1 | no | — |
| 608 | C22×D4 | — | 2 | 1 | no | — |
| 609 | C22×D4 | — | 67 | 1 | no | — |
| 610 | C22×D4 | — | 67 | 1 | no | — |
| 611 | C22×D4 | — | 67 | 1 | no | — |
| 612 | C22×D4 | — | 134 | 1 | no | — |
| 613 | C22×D4 | — | 134 | 1 | no | — |
| 614 | C22×D4 | C22×D67 | 1 | 1 | yes | characteristic |
| 615 | C23×C4 | — | 67 | 1 | no | — |
| 616 | C23×C4 | — | 134 | 1 | no | — |
| 617 | #137 | — | 268 | 4 | no | — |
| 618 | #135 | — | 268 | 4 | no | — |
| 619 | C2×Q16 | — | 134 | 1 | no | — |
| 620 | C2×Q16 | — | 134 | 1 | no | — |
| 621 | C2×Q16 | — | 134 | 1 | no | — |
| 622 | C2×SD16 | — | 2 | 1 | no | — |
| 623 | C2×SD16 | — | 2 | 1 | no | — |
| 624 | C2×SD16 | — | 134 | 1 | no | — |
| 625 | C2×SD16 | — | 134 | 1 | no | — |
| 626 | C2×D8 | — | 134 | 1 | no | — |
| 627 | C2×M16 | — | 134 | 1 | no | — |
| 628 | C22×C8 | — | 134 | 1 | no | — |
| 629 | C4⋊Q8 | — | 134 | 1 | no | — |
| 630 | #126 | — | 134 | 1 | no | — |
| 631 | #126 | — | 134 | 1 | no | — |
| 632 | #125 | — | 134 | 1 | no | — |
| 633 | #125 | — | 134 | 1 | no | — |
| 634 | #124 | — | 134 | 1 | no | — |
| 635 | #124 | — | 134 | 1 | no | — |
| 636 | #124 | — | 134 | 1 | no | — |
| 637 | #124 | — | 134 | 1 | no | — |
| 638 | #124 | — | 134 | 1 | no | — |
| 639 | #123 | — | 134 | 1 | no | — |
| 640 | #123 | — | 134 | 1 | no | — |
| 641 | #123 | — | 134 | 1 | no | — |
| 642 | #123 | — | 134 | 1 | no | — |
| 643 | #123 | — | 134 | 1 | no | — |
| 644 | #123 | — | 134 | 1 | no | — |
| 645 | #123 | — | 134 | 1 | no | — |
| 646 | #123 | — | 134 | 1 | no | — |
| 647 | #123 | — | 134 | 1 | no | — |
| 648 | C22⋊Q8 | — | 2 | 1 | no | — |
| 649 | C22⋊Q8 | — | 2 | 1 | no | — |
| 650 | C22⋊Q8 | — | 2 | 1 | no | — |
| 651 | C22⋊Q8 | — | 2 | 1 | no | — |
| 652 | C22⋊Q8 | — | 2 | 1 | no | — |
| 653 | C22⋊Q8 | — | 67 | 1 | no | — |
| 654 | C22⋊Q8 | — | 67 | 1 | no | — |
| 655 | C22⋊Q8 | — | 67 | 1 | no | — |
| 656 | C22⋊Q8 | — | 67 | 1 | no | — |
| 657 | C22⋊Q8 | — | 134 | 1 | no | — |
| 658 | C22⋊Q8 | — | 134 | 1 | no | — |
| 659 | C22⋊Q8 | — | 134 | 1 | no | — |
| 660 | C22⋊Q8 | — | 134 | 1 | no | — |
| 661 | C22⋊Q8 | — | 134 | 1 | no | — |
| 662 | C22⋊Q8 | — | 134 | 1 | no | — |
| 663 | C22⋊Q8 | — | 134 | 1 | no | — |
| 664 | C22⋊Q8 | — | 134 | 1 | no | — |
| 665 | C22⋊Q8 | — | 134 | 1 | no | — |
| 666 | C22⋊Q8 | — | 134 | 1 | no | — |
| 667 | C22⋊Q8 | C22×D67 | 1 | 1 | yes | characteristic |
| 668 | C22⋊Q8 | C22×D67 | 1 | 1 | yes | characteristic |
| 669 | #121 | — | 268 | 4 | no | — |
| 670 | #121 | — | 67 | 1 | no | — |
| 671 | #121 | — | 67 | 1 | no | — |
| 672 | #121 | — | 134 | 1 | no | — |
| 673 | #121 | — | 134 | 1 | no | — |
| 674 | #121 | — | 134 | 1 | no | — |
| 675 | #121 | — | 134 | 1 | no | — |
| 676 | #121 | — | 134 | 1 | no | — |
| 677 | #121 | — | 134 | 1 | no | — |
| 678 | #121 | — | 134 | 1 | no | — |
| 679 | #121 | — | 134 | 1 | no | — |
| 680 | #121 | — | 134 | 1 | no | — |
| 681 | #121 | — | 134 | 1 | no | — |
| 682 | #121 | — | 134 | 1 | no | — |
| 683 | #121 | — | 134 | 1 | no | — |
| 684 | #121 | — | 134 | 1 | no | — |
| 685 | #121 | — | 134 | 1 | no | — |
| 686 | #121 | — | 134 | 1 | no | — |
| 687 | #120 | — | 134 | 1 | no | — |
| 688 | #120 | — | 134 | 1 | no | — |
| 689 | #120 | — | 134 | 1 | no | — |
| 690 | C4×Q8 | — | 134 | 1 | no | — |
| 691 | C4×D4 | — | 134 | 1 | no | — |
| 692 | C4×D4 | — | 134 | 1 | no | — |
| 693 | C4×D4 | — | 134 | 1 | no | — |
| 694 | C4×D4 | — | 134 | 1 | no | — |
| 695 | C4×D4 | — | 134 | 1 | no | — |
| 696 | C4×D4 | — | 134 | 1 | no | — |
| 697 | C4×D4 | — | 134 | 1 | no | — |
| 698 | #117 | — | 67 | 1 | no | — |
| 699 | C2×C4⋊C4 | — | 67 | 1 | no | — |
| 700 | C2×C4⋊C4 | — | 67 | 1 | no | — |
| 701 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 702 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 703 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 704 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 705 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 706 | C2×C22⋊C4 | — | 67 | 1 | no | — |
| 707 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 708 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 709 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 710 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 711 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 712 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 713 | C2×C22⋊C4 | C22×D67 | 1 | 1 | yes | characteristic |
| 714 | #103 | — | 134 | 1 | no | — |
| 715 | #103 | — | 134 | 1 | no | — |
| 716 | #103 | — | 134 | 1 | no | — |
| 717 | #103 | — | 134 | 1 | no | — |
| 718 | #102 | — | 2 | 1 | no | — |
| 719 | #102 | — | 2 | 1 | no | — |
| 720 | #102 | — | 134 | 1 | no | — |
| 721 | #102 | — | 134 | 1 | no | — |
| 722 | C22⋊C8 | — | 67 | 1 | no | — |
| 723 | C22⋊C8 | — | 67 | 1 | no | — |
| 724 | C22⋊C8 | — | 134 | 1 | no | — |
| 725 | C22⋊C8 | — | 134 | 1 | no | — |
| 726 | C22⋊C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 727 | C22⋊C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 728 | #95 | — | 67 | 1 | no | — |
| 729 | #95 | — | 134 | 1 | no | — |
| 730 | #95 | — | 134 | 1 | no | — |
| 731 | #95 | C22×D67 | 1 | 1 | yes | characteristic |
| 732 | C24 | — | 2 | 1 | no | — |
| 733 | C24 | — | 67 | 1 | no | — |
| 734 | C24 | — | 67 | 1 | no | — |
| 735 | C24 | D4×D67 | 1 | 1 | yes | characteristic |
| 736 | #41 | — | 268 | 2 | no | — |
| 737 | #41 | — | 268 | 2 | no | — |
| 738 | #41 | — | 268 | 2 | no | — |
| 739 | #41 | — | 268 | 2 | no | — |
| 740 | #41 | — | 268 | 2 | no | — |
| 741 | #41 | — | 268 | 2 | no | — |
| 742 | #41 | — | 268 | 2 | no | — |
| 743 | #41 | — | 536 | 2 | no | — |
| 744 | #41 | — | 536 | 2 | no | — |
| 745 | #41 | — | 536 | 2 | no | — |
| 746 | #41 | — | 134 | 4 | no | — |
| 747 | #41 | — | 134 | 4 | no | — |
| 748 | C2×Q8 | — | 2 | 1 | no | — |
| 749 | C2×Q8 | — | 268 | 2 | no | — |
| 750 | C2×Q8 | — | 268 | 2 | no | — |
| 751 | C2×Q8 | — | 67 | 1 | no | — |
| 752 | C2×Q8 | — | 134 | 1 | no | — |
| 753 | C2×Q8 | — | 134 | 1 | no | — |
| 754 | C2×Q8 | — | 134 | 1 | no | — |
| 755 | C2×Q8 | — | 134 | 1 | no | — |
| 756 | C2×Q8 | D4×D67 | 1 | 1 | yes | characteristic |
| 757 | C2×Q8 | D4×D67 | 1 | 1 | yes | characteristic |
| 758 | C2×D4 | — | 2 | 1 | no | — |
| 759 | C2×D4 | — | 2 | 1 | no | — |
| 760 | C2×D4 | — | 4 | 2 | no | — |
| 761 | C2×D4 | — | 4 | 2 | no | — |
| 762 | C2×D4 | — | 8 | 1 | no | — |
| 763 | C2×D4 | — | 8 | 1 | no | — |
| 764 | C2×D4 | — | 268 | 2 | no | — |
| 765 | C2×D4 | — | 268 | 1 | no | — |
| 766 | C2×D4 | — | 268 | 1 | no | — |
| 767 | C2×D4 | — | 268 | 2 | no | — |
| 768 | C2×D4 | — | 268 | 2 | no | — |
| 769 | C2×D4 | — | 268 | 2 | no | — |
| 770 | C2×D4 | — | 536 | 1 | no | — |
| 771 | C2×D4 | — | 536 | 1 | no | — |
| 772 | C2×D4 | — | 536 | 1 | no | — |
| 773 | C2×D4 | — | 536 | 1 | no | — |
| 774 | C2×D4 | — | 67 | 1 | no | — |
| 775 | C2×D4 | — | 134 | 1 | no | — |
| 776 | C2×D4 | — | 134 | 1 | no | — |
| 777 | C2×D4 | — | 134 | 1 | no | — |
| 778 | C2×D4 | — | 134 | 1 | no | — |
| 779 | C2×D4 | — | 134 | 1 | no | — |
| 780 | C2×D4 | — | 134 | 1 | no | — |
| 781 | C2×D4 | — | 134 | 1 | no | — |
| 782 | C2×D4 | — | 134 | 1 | no | — |
| 783 | C2×D4 | — | 134 | 1 | no | — |
| 784 | C2×D4 | — | 134 | 1 | no | — |
| 785 | C2×D4 | — | 134 | 1 | no | — |
| 786 | C2×D4 | — | 134 | 1 | no | — |
| 787 | C2×D4 | — | 134 | 1 | no | — |
| 788 | C22×C4 | — | 2 | 1 | no | — |
| 789 | C22×C4 | — | 2 | 1 | no | — |
| 790 | C22×C4 | — | 2 | 1 | no | — |
| 791 | C22×C4 | — | 268 | 2 | no | — |
| 792 | C22×C4 | — | 268 | 1 | no | — |
| 793 | C22×C4 | — | 268 | 1 | no | — |
| 794 | C22×C4 | — | 268 | 2 | no | — |
| 795 | C22×C4 | — | 67 | 1 | no | — |
| 796 | C22×C4 | — | 67 | 1 | no | — |
| 797 | C22×C4 | — | 67 | 1 | no | — |
| 798 | C22×C4 | — | 67 | 1 | no | — |
| 799 | C22×C4 | — | 67 | 1 | no | — |
| 800 | C22×C4 | — | 67 | 1 | no | — |
| 801 | C22×C4 | — | 134 | 1 | no | — |
| 802 | C22×C4 | — | 134 | 1 | no | — |
| 803 | C22×C4 | — | 134 | 1 | no | — |
| 804 | C22×C4 | — | 134 | 1 | no | — |
| 805 | C22×C4 | — | 134 | 1 | no | — |
| 806 | C22×C4 | — | 134 | 1 | no | — |
| 807 | C22×C4 | — | 134 | 1 | no | — |
| 808 | C22×C4 | — | 134 | 1 | no | — |
| 809 | C22×C4 | — | 134 | 4 | no | — |
| 810 | C22×C4 | — | 134 | 1 | no | — |
| 811 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 812 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 813 | Q16 | — | 268 | 2 | no | — |
| 814 | Q16 | — | 268 | 2 | no | — |
| 815 | Q16 | — | 268 | 2 | no | — |
| 816 | SD16 | — | 4 | 2 | no | — |
| 817 | SD16 | — | 4 | 2 | no | — |
| 818 | SD16 | — | 268 | 2 | no | — |
| 819 | SD16 | — | 268 | 2 | no | — |
| 820 | D8 | — | 268 | 2 | no | — |
| 821 | M16 | — | 268 | 2 | no | — |
| 822 | C2×C8 | — | 2 | 1 | no | — |
| 823 | C2×C8 | — | 2 | 1 | no | — |
| 824 | C2×C8 | — | 268 | 2 | no | — |
| 825 | C2×C8 | — | 134 | 1 | no | — |
| 826 | C2×C8 | — | 134 | 1 | no | — |
| 827 | C4⋊C4 | — | 2 | 1 | no | — |
| 828 | C4⋊C4 | — | 2 | 1 | no | — |
| 829 | C4⋊C4 | — | 2 | 1 | no | — |
| 830 | C4⋊C4 | — | 2 | 1 | no | — |
| 831 | C4⋊C4 | — | 2 | 1 | no | — |
| 832 | C4⋊C4 | — | 268 | 2 | no | — |
| 833 | C4⋊C4 | — | 67 | 1 | no | — |
| 834 | C4⋊C4 | — | 67 | 1 | no | — |
| 835 | C4⋊C4 | — | 134 | 1 | no | — |
| 836 | C4⋊C4 | — | 134 | 1 | no | — |
| 837 | C4⋊C4 | — | 134 | 1 | no | — |
| 838 | C4⋊C4 | — | 134 | 1 | no | — |
| 839 | C4⋊C4 | — | 134 | 1 | no | — |
| 840 | C4⋊C4 | — | 134 | 1 | no | — |
| 841 | C4⋊C4 | — | 134 | 1 | no | — |
| 842 | C4⋊C4 | — | 134 | 1 | no | — |
| 843 | C4⋊C4 | — | 134 | 1 | no | — |
| 844 | C4⋊C4 | — | 134 | 1 | no | — |
| 845 | C4⋊C4 | — | 134 | 1 | no | — |
| 846 | C4⋊C4 | — | 134 | 1 | no | — |
| 847 | C4⋊C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 848 | C4⋊C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 849 | C22⋊C4 | — | 2 | 1 | no | — |
| 850 | C22⋊C4 | — | 2 | 1 | no | — |
| 851 | C22⋊C4 | — | 2 | 1 | no | — |
| 852 | C22⋊C4 | — | 2 | 1 | no | — |
| 853 | C22⋊C4 | — | 2 | 1 | no | — |
| 854 | C22⋊C4 | — | 2 | 1 | no | — |
| 855 | C22⋊C4 | — | 8 | 1 | no | — |
| 856 | C22⋊C4 | — | 268 | 2 | no | — |
| 857 | C22⋊C4 | — | 268 | 2 | no | — |
| 858 | C22⋊C4 | — | 536 | 1 | no | — |
| 859 | C22⋊C4 | — | 536 | 1 | no | — |
| 860 | C22⋊C4 | — | 134 | 1 | no | — |
| 861 | C22⋊C4 | — | 134 | 1 | no | — |
| 862 | C22⋊C4 | — | 134 | 1 | no | — |
| 863 | C22⋊C4 | — | 134 | 1 | no | — |
| 864 | C22⋊C4 | — | 134 | 1 | no | — |
| 865 | C22⋊C4 | — | 134 | 1 | no | — |
| 866 | C22⋊C4 | — | 134 | 1 | no | — |
| 867 | C22⋊C4 | — | 134 | 1 | no | — |
| 868 | C22⋊C4 | — | 134 | 1 | no | — |
| 869 | C22⋊C4 | — | 134 | 1 | no | — |
| 870 | C22⋊C4 | — | 134 | 1 | no | — |
| 871 | C22⋊C4 | — | 134 | 1 | no | — |
| 872 | C22⋊C4 | — | 134 | 1 | no | — |
| 873 | C22⋊C4 | — | 134 | 1 | no | — |
| 874 | C22⋊C4 | — | 134 | 1 | no | — |
| 875 | C22⋊C4 | — | 134 | 1 | no | — |
| 876 | C22⋊C4 | — | 134 | 1 | no | — |
| 877 | C42 | — | 134 | 1 | no | — |
| 878 | C42 | — | 134 | 1 | no | — |
| 879 | C42 | — | 134 | 1 | no | — |
| 880 | C23 | — | 2 | 2 | no | — |
| 881 | C23 | — | 2 | 1 | no | — |
| 882 | C23 | — | 2 | 1 | no | — |
| 883 | C23 | — | 2 | 1 | no | — |
| 884 | C23 | — | 4 | 1 | no | — |
| 885 | C23 | — | 4 | 1 | no | — |
| 886 | C23 | — | 4 | 1 | no | — |
| 887 | C23 | — | 4 | 1 | no | — |
| 888 | C23 | — | 4 | 1 | no | — |
| 889 | C23 | — | 4 | 1 | no | — |
| 890 | C23 | — | 4 | 1 | no | — |
| 891 | C23 | — | 4 | 1 | no | — |
| 892 | C23 | — | 268 | 1 | no | — |
| 893 | C23 | — | 268 | 1 | no | — |
| 894 | C23 | — | 268 | 1 | no | — |
| 895 | C23 | — | 268 | 1 | no | — |
| 896 | C23 | — | 67 | 1 | no | — |
| 897 | C23 | — | 67 | 1 | no | — |
| 898 | C23 | — | 134 | 1 | no | — |
| 899 | C23 | — | 134 | 1 | no | — |
| 900 | C23 | — | 134 | 1 | no | — |
| 901 | C23 | — | 134 | 1 | no | — |
| 902 | C23 | — | 134 | 1 | no | — |
| 903 | C23 | — | 134 | 1 | no | — |
| 904 | C23 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 905 | Q8 | — | 4 | 1 | no | — |
| 906 | Q8 | — | 4 | 1 | no | — |
| 907 | Q8 | — | 8 | 1 | no | — |
| 908 | Q8 | — | 268 | 1 | no | — |
| 909 | Q8 | — | 268 | 1 | no | — |
| 910 | Q8 | — | 268 | 1 | no | — |
| 911 | Q8 | — | 268 | 2 | no | — |
| 912 | Q8 | — | 536 | 1 | no | — |
| 913 | Q8 | — | 134 | 2 | no | — |
| 914 | Q8 | — | 134 | 2 | no | — |
| 915 | D4 | — | 2 | 2 | no | — |
| 916 | D4 | — | 2 | 2 | no | — |
| 917 | D4 | — | 4 | 1 | no | — |
| 918 | D4 | — | 4 | 1 | no | — |
| 919 | D4 | — | 8 | 4 | no | — |
| 920 | D4 | — | 268 | 1 | no | — |
| 921 | D4 | — | 268 | 2 | no | — |
| 922 | D4 | — | 268 | 2 | no | — |
| 923 | D4 | — | 268 | 4 | no | — |
| 924 | D4 | — | 268 | 4 | no | — |
| 925 | D4 | — | 268 | 2 | no | — |
| 926 | D4 | — | 268 | 1 | no | — |
| 927 | D4 | — | 268 | 1 | no | — |
| 928 | D4 | — | 268 | 2 | no | — |
| 929 | D4 | — | 536 | 1 | no | — |
| 930 | D4 | — | 536 | 1 | no | — |
| 931 | D4 | — | 536 | 1 | no | — |
| 932 | D4 | — | 536 | 1 | no | — |
| 933 | D4 | — | 536 | 1 | no | — |
| 934 | D4 | — | 536 | 1 | no | — |
| 935 | D4 | — | 536 | 1 | no | — |
| 936 | D4 | — | 536 | 4 | no | — |
| 937 | D4 | — | 536 | 1 | no | — |
| 938 | C2×C4 | — | 2 | 1 | no | — |
| 939 | C2×C4 | — | 2 | 1 | no | — |
| 940 | C2×C4 | — | 2 | 1 | no | — |
| 941 | C2×C4 | — | 2 | 1 | no | — |
| 942 | C2×C4 | — | 2 | 1 | no | — |
| 943 | C2×C4 | — | 4 | 1 | no | — |
| 944 | C2×C4 | — | 4 | 1 | no | — |
| 945 | C2×C4 | — | 4 | 1 | no | — |
| 946 | C2×C4 | — | 4 | 1 | no | — |
| 947 | C2×C4 | — | 4 | 1 | no | — |
| 948 | C2×C4 | — | 8 | 1 | no | — |
| 949 | C2×C4 | — | 8 | 1 | no | — |
| 950 | C2×C4 | — | 268 | 1 | no | — |
| 951 | C2×C4 | — | 268 | 1 | no | — |
| 952 | C2×C4 | — | 268 | 2 | no | — |
| 953 | C2×C4 | — | 268 | 2 | no | — |
| 954 | C2×C4 | — | 268 | 1 | no | — |
| 955 | C2×C4 | — | 268 | 1 | no | — |
| 956 | C2×C4 | — | 268 | 4 | no | — |
| 957 | C2×C4 | — | 268 | 4 | no | — |
| 958 | C2×C4 | — | 268 | 1 | no | — |
| 959 | C2×C4 | — | 268 | 1 | no | — |
| 960 | C2×C4 | — | 268 | 1 | no | — |
| 961 | C2×C4 | — | 268 | 1 | no | — |
| 962 | C2×C4 | — | 536 | 1 | no | — |
| 963 | C2×C4 | — | 536 | 1 | no | — |
| 964 | C2×C4 | — | 536 | 1 | no | — |
| 965 | C2×C4 | — | 536 | 1 | no | — |
| 966 | C2×C4 | — | 536 | 1 | no | — |
| 967 | C2×C4 | — | 67 | 1 | no | — |
| 968 | C2×C4 | — | 67 | 1 | no | — |
| 969 | C2×C4 | — | 134 | 2 | no | — |
| 970 | C2×C4 | — | 134 | 2 | no | — |
| 971 | C2×C4 | — | 134 | 2 | no | — |
| 972 | C2×C4 | — | 134 | 1 | no | — |
| 973 | C2×C4 | — | 134 | 1 | no | — |
| 974 | C2×C4 | — | 134 | 1 | no | — |
| 975 | C2×C4 | — | 134 | 1 | no | — |
| 976 | C2×C4 | — | 134 | 2 | no | — |
| 977 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 978 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 979 | C8 | — | 4 | 1 | no | — |
| 980 | C8 | — | 4 | 1 | no | — |
| 981 | C8 | — | 268 | 1 | no | — |
| 982 | C8 | — | 268 | 1 | no | — |
| 983 | C22 | — | 2 | 1 | no | — |
| 984 | C22 | — | 2 | 1 | no | — |
| 985 | C22 | — | 4 | 2 | no | — |
| 986 | C22 | — | 4 | 2 | no | — |
| 987 | C22 | — | 4 | 1 | no | — |
| 988 | C22 | — | 4 | 1 | no | — |
| 989 | C22 | — | 4 | 1 | no | — |
| 990 | C22 | — | 4 | 2 | no | — |
| 991 | C22 | — | 8 | 1 | no | — |
| 992 | C22 | — | 8 | 1 | no | — |
| 993 | C22 | — | 8 | 1 | no | — |
| 994 | C22 | — | 8 | 1 | no | — |
| 995 | C22 | — | 8 | 1 | no | — |
| 996 | C22 | — | 8 | 1 | no | — |
| 997 | C22 | — | 268 | 1 | no | — |
| 998 | C22 | — | 268 | 1 | no | — |
| 999 | C22 | — | 268 | 1 | no | — |
| 1000 | C22 | — | 268 | 1 | no | — |
| 1001 | C22 | — | 268 | 1 | no | — |
| 1002 | C22 | — | 268 | 1 | no | — |
| 1003 | C22 | — | 536 | 1 | no | — |
| 1004 | C22 | — | 536 | 1 | no | — |
| 1005 | C22 | — | 536 | 1 | no | — |
| 1006 | C22 | — | 536 | 1 | no | — |
| 1007 | C22 | — | 134 | 1 | no | — |
| 1008 | C22 | — | 134 | 1 | no | — |
| 1009 | C22 | — | 134 | 1 | no | — |
| 1010 | C22 | — | 134 | 1 | no | — |
| 1011 | C22 | — | 134 | 1 | no | — |
| 1012 | C22 | — | 134 | 1 | no | — |
| 1013 | C22 | #120×D67 | 1 | 1 | yes | characteristic |
| 1014 | C22 | #16864202 | 1 | 1 | yes | characteristic |
| 1015 | C22 | #16864212 | 1 | 1 | yes | characteristic |
| 1016 | C4 | — | 2 | 1 | no | — |
| 1017 | C4 | — | 2 | 1 | no | — |
| 1018 | C4 | — | 4 | 1 | no | — |
| 1019 | C4 | — | 4 | 1 | no | — |
| 1020 | C4 | — | 4 | 1 | no | — |
| 1021 | C4 | — | 4 | 1 | no | — |
| 1022 | C4 | — | 4 | 1 | no | — |
| 1023 | C4 | — | 8 | 1 | no | — |
| 1024 | C4 | — | 268 | 1 | no | — |
| 1025 | C4 | — | 268 | 1 | no | — |
| 1026 | C4 | — | 268 | 1 | no | — |
| 1027 | C4 | — | 268 | 2 | no | — |
| 1028 | C4 | — | 268 | 1 | no | — |
| 1029 | C4 | — | 536 | 1 | no | — |
| 1030 | C4 | — | 67 | 2 | no | — |
| 1031 | C4 | — | 134 | 1 | no | — |
| 1032 | C2 | — | 2 | 1 | no | — |
| 1033 | C2 | — | 2 | 1 | no | — |
| 1034 | C2 | — | 8 | 2 | no | — |
| 1035 | C2 | — | 8 | 1 | no | — |
| 1036 | C2 | — | 268 | 1 | no | — |
| 1037 | C2 | — | 268 | 1 | no | — |
| 1038 | C2 | — | 536 | 1 | no | — |
| 1039 | C2 | — | 536 | 1 | no | — |
| 1040 | C2 | #22569519 | 1 | 1 | yes | characteristic |
| 1041 | C2 | #22569563 | 1 | 1 | yes | characteristic |
| 1042 | C2 | B(4,𝔽2)×D67 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22574435 | C2 | semidirect |
| 2. #22569464 | C2 | semidirect |
| 3. #22569428 | C2 | semidirect |
| 4. #22565932 | C2 | semidirect |
| 5. #22559192 | C2 | semidirect |
| 6. #22559191 | C2 | semidirect |
| 7. #22559167 | C2 | semidirect |
| 8. #22559166 | C2 | semidirect |
| 9. #22559154 | C2 | semidirect |
| 10. #22559153 | C2 | semidirect |
| 11. #22559130 | C2 | semidirect |
| 12. #22558779 | C2 | semidirect |
| 13. #22558751 | C2 | semidirect |
| 14. #22558567 | C2 | semidirect |
| 15. C67×#1596 | C2 | semidirect |
| 76. C2×#11761629 | D4 | semidirect |
| 85. C2×Q8×D67 | D4 | semidirect |
| 123. #14524023 | D4 | semidirect |
| 134. #14524019 | D4 | semidirect |
| 135. #14524019 | D4 | semidirect |
| 140. #14524018 | D4 | semidirect |
| 165. #14524001 | D4 | semidirect |
| 170. C4⋊C4×D67 | D4 | semidirect |
| 533. #1596 | D67 | semidirect |
| 537. C67 | #18229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574435 | 2 |
| #22569464 | 2 |
| #22569428 | 2 |
| #22565932 | 2 |
| #22559192 | 2 |
| #22559191 | 2 |
| #22559167 | 2 |
| #22559166 | 2 |
| #22559154 | 2 |
| #22559153 | 2 |
| #22559130 | 2 |
| #22558779 | 2 |
| #22558751 | 2 |
| #22558567 | 2 |
| C67×#1596 | 2 |
| #18229 | 67 |