Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
2658 conjugacy classes of subgroups.
The subgroup lattice has 816 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#16864213 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#16864210 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22573978 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22571801 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #22571791 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #22571786 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #22571776 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #22570652 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #22569872 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #22569680 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #22569526 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #22569521 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | C2×#16863502 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #22568925 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C67×#3060 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#14524090 | C22 | 1 | 2 | yes | — |
| 17 | C2×#14524090 | C22 | 1 | 2 | yes | — |
| 18 | #16864213 | — | 2 | 8 | no | — |
| 19 | #16864210 | — | 2 | 8 | no | — |
| 20 | C2×#14524076 | C22 | 1 | 4 | yes | — |
| 21 | C2×#14524076 | C22 | 1 | 2 | yes | — |
| 22 | C2×#14524073 | C22 | 1 | 2 | yes | — |
| 23 | C2×#14524072 | C22 | 1 | 4 | yes | — |
| 24 | C2×#14524065 | C22 | 1 | 2 | yes | — |
| 25 | C2×#14524065 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#14524063 | C22 | 1 | 2 | yes | — |
| 27 | C2×#14524062 | C22 | 1 | 2 | yes | — |
| 28 | C22×Dic268 | C22 | 1 | 2 | yes | — |
| 29 | C22×Dic268 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×Q16×D67 | C22 | 1 | 2 | yes | — |
| 31 | C2×#14524049 | C22 | 1 | 1 | yes | characteristic |
| 32 | #16864064 | — | 2 | 2 | no | — |
| 33 | #16864064 | C22 | 1 | 4 | yes | — |
| 34 | #16864059 | — | 2 | 2 | no | — |
| 35 | #16864059 | C22 | 1 | 4 | yes | — |
| 36 | #16864056 | — | 2 | 2 | no | — |
| 37 | #16864056 | C22 | 1 | 4 | yes | — |
| 38 | #16864052 | — | 2 | 2 | no | — |
| 39 | #16864052 | C22 | 1 | 4 | yes | — |
| 40 | #16863977 | C22 | 1 | 2 | yes | — |
| 41 | #16863973 | — | 2 | 4 | no | — |
| 42 | #16863942 | C22 | 1 | 2 | yes | — |
| 43 | #16863942 | C22 | 1 | 1 | yes | characteristic |
| 44 | #16863941 | — | 2 | 4 | no | — |
| 45 | C2×#14524008 | C22 | 1 | 2 | yes | — |
| 46 | #16863789 | C22 | 1 | 2 | yes | — |
| 47 | #16863787 | C22 | 1 | 2 | yes | — |
| 48 | #16863784 | C22 | 1 | 2 | yes | — |
| 49 | #16863782 | C22 | 1 | 2 | yes | — |
| 50 | #16863655 | C22 | 1 | 2 | yes | — |
| 51 | #16863650 | C22 | 1 | 2 | yes | — |
| 52 | #16863626 | C22 | 1 | 4 | yes | — |
| 53 | #16863621 | C22 | 1 | 4 | yes | — |
| 54 | #16863617 | C22 | 1 | 4 | yes | — |
| 55 | #16863605 | C22 | 1 | 4 | yes | — |
| 56 | #16863595 | C22 | 1 | 4 | yes | — |
| 57 | #16863559 | C22 | 1 | 4 | yes | — |
| 58 | #16863556 | C22 | 1 | 4 | yes | — |
| 59 | #16863553 | C22 | 1 | 4 | yes | — |
| 60 | #16863551 | C22 | 1 | 4 | yes | — |
| 61 | #16863542 | C22 | 1 | 4 | yes | — |
| 62 | #16863539 | C22 | 1 | 4 | yes | — |
| 63 | #16863536 | C22 | 1 | 4 | yes | — |
| 64 | #16863534 | C22 | 1 | 4 | yes | — |
| 65 | #16863502 | C22 | 1 | 4 | yes | — |
| 66 | #16863502 | C22 | 1 | 4 | yes | — |
| 67 | #16863467 | C22 | 1 | 4 | yes | — |
| 68 | #16863465 | C22 | 1 | 4 | yes | — |
| 69 | #16863419 | C22 | 1 | 1 | yes | characteristic |
| 70 | #16863395 | C22 | 1 | 2 | yes | — |
| 71 | C2×#14523966 | C22 | 1 | 2 | yes | — |
| 72 | #16863364 | C22 | 1 | 1 | yes | characteristic |
| 73 | #16863363 | C22 | 1 | 1 | yes | characteristic |
| 74 | C2×#14523953 | C22 | 1 | 1 | yes | characteristic |
| 75 | C2×#135×C67 | C22 | 1 | 1 | yes | characteristic |
| 76 | C2×#131×C67 | C22 | 1 | 1 | yes | characteristic |
| 77 | #537×C67 | C22 | 1 | 2 | yes | — |
| 78 | #470×C67 | C22 | 1 | 2 | yes | — |
| 79 | #469×C67 | C22 | 1 | 2 | yes | — |
| 80 | #465×C67 | C22 | 1 | 4 | yes | — |
| 81 | C2×#106×C67 | C22 | 1 | 1 | yes | characteristic |
| 82 | #417×C67 | C22 | 1 | 2 | yes | — |
| 83 | #14524090 | — | 2 | 8 | no | — |
| 84 | #14524090 | — | 2 | 8 | no | — |
| 85 | #14524090 | — | 4 | 4 | no | — |
| 86 | #14524090 | — | 4 | 4 | no | — |
| 87 | C2×#11761628 | — | 2 | 2 | no | — |
| 88 | C2×#11761628 | C23 | 1 | 2 | yes | — |
| 89 | C2×#11761628 | C23 | 1 | 4 | yes | — |
| 90 | C2×#11761628 | C23 | 1 | 1 | yes | characteristic |
| 91 | C2×#11761627 | — | 2 | 4 | no | — |
| 92 | C2×#11761627 | — | 2 | 2 | no | — |
| 93 | C2×#11761627 | — | 2 | 4 | no | — |
| 94 | C2×#11761627 | C23 | 1 | 4 | yes | — |
| 95 | C22×Dic134 | — | 2 | 2 | no | — |
| 96 | C22×Dic134 | C23 | 1 | 4 | yes | — |
| 97 | C22×Dic134 | C23 | 1 | 2 | yes | — |
| 98 | C2×Q8×D67 | — | 2 | 2 | no | — |
| 99 | C2×Q8×D67 | C23 | 1 | 4 | yes | — |
| 100 | #14524076 | — | 2 | 8 | no | — |
| 101 | #14524076 | — | 2 | 16 | no | — |
| 102 | #14524073 | — | 2 | 8 | no | — |
| 103 | #14524072 | — | 2 | 16 | no | — |
| 104 | #14524065 | — | 2 | 8 | no | — |
| 105 | #14524065 | — | 2 | 4 | no | — |
| 106 | #14524063 | — | 4 | 4 | no | — |
| 107 | #14524062 | — | 2 | 8 | no | — |
| 108 | C2×Dic268 | — | 2 | 8 | no | — |
| 109 | C2×Dic268 | D4 | 1 | 8 | yes | complemented |
| 110 | C2×Dic268 | C23 | 1 | 1 | yes | characteristic |
| 111 | C2×Dic268 | C23 | 1 | 4 | yes | — |
| 112 | C2×Dic268 | C23 | 1 | 2 | yes | — |
| 113 | C2×Dic268 | C23 | 1 | 2 | yes | — |
| 114 | C2×#11761618 | C23 | 1 | 4 | yes | — |
| 115 | C2×#11761618 | C23 | 1 | 2 | yes | — |
| 116 | Q16×D67 | — | 2 | 8 | no | — |
| 117 | C2×#11761617 | C23 | 1 | 2 | yes | — |
| 118 | C2×#11761617 | C23 | 1 | 4 | yes | — |
| 119 | C2×#11761616 | C23 | 1 | 4 | yes | — |
| 120 | C2×#11761616 | C23 | 1 | 2 | yes | — |
| 121 | C2×#11761615 | C23 | 1 | 2 | yes | — |
| 122 | C2×D536 | C23 | 1 | 1 | yes | characteristic |
| 123 | C2×#11761613 | C23 | 1 | 2 | yes | — |
| 124 | #14524049 | — | 2 | 4 | no | — |
| 125 | C2×#11761612 | C23 | 1 | 1 | yes | characteristic |
| 126 | C2×#11761611 | C23 | 1 | 2 | yes | — |
| 127 | C22×C67⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 128 | C2×C8×D67 | C23 | 1 | 2 | yes | — |
| 129 | #14524042 | — | 2 | 4 | no | — |
| 130 | #14524041 | D4 | 1 | 1 | yes | characteristic |
| 131 | #14524041 | C23 | 1 | 2 | yes | — |
| 132 | #14524039 | — | 2 | 4 | no | — |
| 133 | #14524039 | D4 | 1 | 1 | yes | characteristic |
| 134 | #14524039 | C23 | 1 | 2 | yes | — |
| 135 | #14524032 | D4 | 1 | 1 | yes | characteristic |
| 136 | #14524032 | C23 | 1 | 2 | yes | — |
| 137 | #14524030 | D4 | 1 | 1 | yes | characteristic |
| 138 | #14524030 | C23 | 1 | 2 | yes | — |
| 139 | #14524029 | — | 2 | 4 | no | — |
| 140 | #14524029 | — | 2 | 4 | no | — |
| 141 | #14524023 | — | 2 | 2 | no | — |
| 142 | #14524023 | C23 | 1 | 4 | yes | — |
| 143 | #14524021 | — | 2 | 4 | no | — |
| 144 | #14524021 | — | 2 | 4 | no | — |
| 145 | #14524020 | — | 2 | 4 | no | — |
| 146 | #14524020 | — | 2 | 4 | no | — |
| 147 | #14524018 | — | 2 | 2 | no | — |
| 148 | #14524018 | C23 | 1 | 4 | yes | — |
| 149 | #14524017 | — | 2 | 4 | no | — |
| 150 | #14524016 | — | 2 | 4 | no | — |
| 151 | #14524016 | — | 2 | 4 | no | — |
| 152 | #14524015 | — | 2 | 4 | no | — |
| 153 | #14524015 | — | 2 | 2 | no | — |
| 154 | #14524015 | — | 2 | 2 | no | — |
| 155 | #14524015 | — | 2 | 4 | no | — |
| 156 | #14524015 | D4 | 1 | 4 | yes | — |
| 157 | #14524008 | — | 2 | 2 | no | — |
| 158 | #14524008 | — | 2 | 2 | no | — |
| 159 | #14524008 | C23 | 1 | 4 | yes | — |
| 160 | #14524008 | C23 | 1 | 4 | yes | — |
| 161 | D4×Dic67 | — | 2 | 4 | no | — |
| 162 | #14524005 | — | 2 | 4 | no | — |
| 163 | C4×C22⋊D67 | — | 2 | 2 | no | — |
| 164 | C4×C22⋊D67 | — | 2 | 2 | no | — |
| 165 | C4×C22⋊D67 | C23 | 1 | 4 | yes | — |
| 166 | (C22⋊D67)⋊C4 | — | 2 | 4 | no | — |
| 167 | (C22⋊D67)⋊C4 | — | 2 | 4 | no | — |
| 168 | C2×Dic67⋊C4 | — | 2 | 2 | no | — |
| 169 | C2×C4×Dic67 | — | 2 | 2 | no | — |
| 170 | C2×C4×Dic67 | C23 | 1 | 1 | yes | characteristic |
| 171 | Dic67⋊C8 | C23 | 1 | 4 | yes | — |
| 172 | #14523966 | C23 | 1 | 4 | yes | — |
| 173 | #14523966 | C23 | 1 | 4 | yes | — |
| 174 | #14523966 | C23 | 1 | 4 | yes | — |
| 175 | #14523963 | C23 | 1 | 4 | yes | — |
| 176 | C22⋊(C67⋊C8) | C23 | 1 | 4 | yes | — |
| 177 | (C2×D67)⋊C8 | C23 | 1 | 4 | yes | — |
| 178 | #14523953 | C23 | 1 | 2 | yes | — |
| 179 | #14523953 | C23 | 1 | 2 | yes | — |
| 180 | C2×#41×C67 | C23 | 1 | 2 | yes | — |
| 181 | C2×#41×C67 | C23 | 1 | 1 | yes | characteristic |
| 182 | #135×C67 | — | 2 | 4 | no | — |
| 183 | C2×Q16×C67 | C23 | 1 | 1 | yes | characteristic |
| 184 | C2×SD16×C67 | C23 | 1 | 2 | yes | — |
| 185 | C2×D8×C67 | C23 | 1 | 1 | yes | characteristic |
| 186 | #131×C67 | — | 2 | 4 | no | — |
| 187 | C2×M16×C67 | C23 | 1 | 2 | yes | — |
| 188 | C2×M16×C67 | C23 | 1 | 1 | yes | characteristic |
| 189 | C22×C8×C67 | C23 | 1 | 2 | yes | — |
| 190 | C22×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 191 | C22⋊Q8×C67 | — | 2 | 2 | no | — |
| 192 | C22⋊Q8×C67 | C23 | 1 | 4 | yes | — |
| 193 | #121×C67 | — | 2 | 2 | no | — |
| 194 | #121×C67 | — | 2 | 4 | no | — |
| 195 | #121×C67 | C23 | 1 | 4 | yes | — |
| 196 | C2×C4⋊C4×C67 | C23 | 1 | 2 | yes | — |
| 197 | #106×C67 | C23 | 1 | 2 | yes | — |
| 198 | #106×C67 | C23 | 1 | 2 | yes | — |
| 199 | #103×C67 | C23 | 1 | 4 | yes | — |
| 200 | #102×C67 | C23 | 1 | 4 | yes | — |
| 201 | #11761628 | — | 2 | 2 | no | — |
| 202 | #11761628 | — | 2 | 2 | no | — |
| 203 | #11761628 | — | 2 | 4 | no | — |
| 204 | #11761628 | — | 2 | 4 | no | — |
| 205 | #11761628 | — | 2 | 8 | no | — |
| 206 | #11761628 | — | 4 | 4 | no | — |
| 207 | #11761628 | — | 4 | 8 | no | — |
| 208 | #11761627 | — | 2 | 8 | no | — |
| 209 | #11761627 | — | 4 | 4 | no | — |
| 210 | #11761627 | — | 4 | 8 | no | — |
| 211 | #11761627 | — | 4 | 16 | no | — |
| 212 | #11761627 | — | 4 | 16 | no | — |
| 213 | C2×Dic134 | — | 2 | 2 | no | — |
| 214 | C2×Dic134 | — | 2 | 4 | no | — |
| 215 | C2×Dic134 | — | 2 | 8 | no | — |
| 216 | C2×Dic134 | — | 2 | 4 | no | — |
| 217 | C2×Dic134 | — | 2 | 4 | no | — |
| 218 | C2×Dic134 | — | 4 | 4 | no | — |
| 219 | C2×Dic134 | — | 4 | 8 | no | — |
| 220 | C2×Dic134 | C2×D4 | 1 | 1 | yes | characteristic |
| 221 | C2×Dic134 | C2×D4 | 1 | 8 | yes | — |
| 222 | C2×Dic134 | C24 | 1 | 2 | yes | — |
| 223 | C2×Dic134 | C24 | 1 | 4 | yes | — |
| 224 | Q8×D67 | — | 2 | 8 | no | — |
| 225 | Q8×D67 | — | 4 | 4 | no | — |
| 226 | Q8×D67 | — | 4 | 8 | no | — |
| 227 | C2×D268 | — | 2 | 4 | no | — |
| 228 | C2×D268 | C2×D4 | 1 | 1 | yes | characteristic |
| 229 | C2×D268 | C24 | 1 | 2 | yes | — |
| 230 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 231 | C2×C22⋊D67 | — | 2 | 4 | no | — |
| 232 | C2×C22⋊D67 | — | 2 | 4 | no | — |
| 233 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 234 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 235 | C2×C22⋊D67 | C2×D4 | 1 | 2 | yes | — |
| 236 | C2×C22⋊D67 | C2×D4 | 1 | 4 | yes | — |
| 237 | C22×Dic67 | — | 2 | 2 | no | — |
| 238 | C22×Dic67 | — | 2 | 4 | no | — |
| 239 | C22×Dic67 | — | 2 | 4 | no | — |
| 240 | C22×Dic67 | C2×D4 | 1 | 2 | yes | — |
| 241 | C2×C4×D67 | — | 2 | 4 | no | — |
| 242 | C2×C4×D67 | — | 2 | 4 | no | — |
| 243 | C2×C4×D67 | — | 2 | 2 | no | — |
| 244 | C2×C4×D67 | C24 | 1 | 2 | yes | — |
| 245 | Dic268 | — | 2 | 8 | no | — |
| 246 | Dic268 | — | 2 | 2 | no | — |
| 247 | Dic268 | C2×D4 | 1 | 8 | yes | — |
| 248 | Dic268 | C2×D4 | 1 | 8 | yes | — |
| 249 | #11761618 | — | 2 | 8 | no | — |
| 250 | #11761618 | — | 4 | 2 | no | — |
| 251 | #11761617 | — | 2 | 8 | no | — |
| 252 | #11761617 | — | 2 | 4 | no | — |
| 253 | #11761616 | — | 2 | 8 | no | — |
| 254 | #11761616 | — | 4 | 2 | no | — |
| 255 | #11761615 | — | 4 | 2 | no | — |
| 256 | D536 | — | 2 | 2 | no | — |
| 257 | #11761613 | — | 4 | 2 | no | — |
| 258 | #11761612 | — | 2 | 2 | no | — |
| 259 | #11761611 | — | 2 | 4 | no | — |
| 260 | C2×C67⋊C8 | — | 2 | 2 | no | — |
| 261 | C2×C67⋊C8 | C24 | 1 | 2 | yes | — |
| 262 | C2×C67⋊C8 | C24 | 1 | 2 | yes | — |
| 263 | C8×D67 | — | 2 | 4 | no | — |
| 264 | C4⋊Dic67 | — | 2 | 4 | no | — |
| 265 | Dic67⋊C4 | — | 2 | 4 | no | — |
| 266 | Dic67⋊C4 | — | 2 | 4 | no | — |
| 267 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 268 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 269 | Dic67⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 270 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 271 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 272 | C22⋊Dic67 | C2×D4 | 1 | 4 | yes | — |
| 273 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 274 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 275 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 276 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 277 | (C2×D67)⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 278 | C4×Dic67 | — | 2 | 4 | no | — |
| 279 | C4×Dic67 | — | 2 | 4 | no | — |
| 280 | C4×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 281 | C4×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 282 | C4×Dic67 | C24 | 1 | 2 | yes | — |
| 283 | #41×C67 | — | 2 | 2 | no | — |
| 284 | #41×C67 | — | 2 | 2 | no | — |
| 285 | #41×C67 | — | 2 | 4 | no | — |
| 286 | #41×C67 | — | 2 | 4 | no | — |
| 287 | C2×Q8×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 288 | C2×Q8×C67 | C24 | 1 | 2 | yes | — |
| 289 | C2×D4×C67 | — | 2 | 2 | no | — |
| 290 | C2×D4×C67 | — | 2 | 4 | no | — |
| 291 | C2×D4×C67 | C2×D4 | 1 | 2 | yes | — |
| 292 | C2×D4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 293 | C2×D4×C67 | C24 | 1 | 2 | yes | — |
| 294 | C22×C4×C67 | — | 2 | 2 | no | — |
| 295 | C22×C4×C67 | — | 2 | 2 | no | — |
| 296 | C22×C4×C67 | C24 | 1 | 2 | yes | — |
| 297 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 298 | Q16×C67 | — | 2 | 2 | no | — |
| 299 | SD16×C67 | — | 2 | 4 | no | — |
| 300 | D8×C67 | — | 2 | 2 | no | — |
| 301 | M16×C67 | — | 2 | 2 | no | — |
| 302 | M16×C67 | — | 2 | 4 | no | — |
| 303 | C2×C8×C67 | — | 2 | 4 | no | — |
| 304 | C2×C8×C67 | C2×D4 | 1 | 4 | yes | — |
| 305 | C2×C8×C67 | C24 | 1 | 2 | yes | — |
| 306 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 307 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 308 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 309 | C4⋊C4×C67 | — | 2 | 4 | no | — |
| 310 | C4⋊C4×C67 | C24 | 1 | 4 | yes | — |
| 311 | C22⋊C4×C67 | — | 2 | 4 | no | — |
| 312 | C22⋊C4×C67 | — | 2 | 4 | no | — |
| 313 | C23×C67 | — | 2 | 2 | no | — |
| 314 | C23×C67 | C22×D4 | 1 | 2 | yes | — |
| 315 | C23×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 316 | C22×D67 | — | 2 | 2 | no | — |
| 317 | C22×D67 | C22×D4 | 1 | 2 | yes | — |
| 318 | Q8×C67 | — | 2 | 2 | no | — |
| 319 | Q8×C67 | — | 2 | 2 | no | — |
| 320 | Q8×C67 | — | 2 | 2 | no | — |
| 321 | D4×C67 | — | 2 | 4 | no | — |
| 322 | D4×C67 | — | 2 | 2 | no | — |
| 323 | D4×C67 | — | 2 | 2 | no | — |
| 324 | D4×C67 | — | 2 | 2 | no | — |
| 325 | D4×C67 | — | 4 | 4 | no | — |
| 326 | D4×C67 | — | 8 | 4 | no | — |
| 327 | C2×C4×C67 | — | 2 | 2 | no | — |
| 328 | C2×C4×C67 | — | 2 | 2 | no | — |
| 329 | C2×C4×C67 | — | 2 | 4 | no | — |
| 330 | C2×C4×C67 | — | 2 | 2 | no | — |
| 331 | C2×C4×C67 | — | 4 | 4 | no | — |
| 332 | C2×C4×C67 | — | 8 | 2 | no | — |
| 333 | C2×C4×C67 | C22×D4 | 1 | 2 | yes | — |
| 334 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 335 | C2×C4×C67 | C22×D4 | 1 | 2 | yes | — |
| 336 | C2×C4×C67 | H(5,𝔽2) | 1 | 2 | yes | — |
| 337 | C2×C4×C67 | C25 | 1 | 1 | yes | characteristic |
| 338 | C22⋊D67 | — | 2 | 4 | no | — |
| 339 | C22⋊D67 | — | 4 | 4 | no | — |
| 340 | C22⋊D67 | — | 4 | 8 | no | — |
| 341 | C22⋊D67 | — | 4 | 8 | no | — |
| 342 | C22⋊D67 | — | 4 | 4 | no | — |
| 343 | C22⋊D67 | — | 4 | 4 | no | — |
| 344 | C22⋊D67 | — | 8 | 2 | no | — |
| 345 | C2×Dic67 | — | 2 | 8 | no | — |
| 346 | C2×Dic67 | — | 2 | 4 | no | — |
| 347 | C2×Dic67 | — | 2 | 2 | no | — |
| 348 | C2×Dic67 | — | 4 | 2 | no | — |
| 349 | C2×Dic67 | — | 4 | 8 | no | — |
| 350 | C2×Dic67 | — | 4 | 8 | no | — |
| 351 | C2×Dic67 | C22×D4 | 1 | 2 | yes | — |
| 352 | C2×Dic67 | C22×D4 | 1 | 2 | yes | — |
| 353 | C2×Dic67 | C22×D4 | 1 | 2 | yes | — |
| 354 | D268 | — | 2 | 2 | no | — |
| 355 | D268 | — | 2 | 2 | no | — |
| 356 | D268 | — | 2 | 2 | no | — |
| 357 | D268 | — | 8 | 4 | no | — |
| 358 | C4×D67 | — | 2 | 2 | no | — |
| 359 | C4×D67 | — | 2 | 2 | no | — |
| 360 | C4×D67 | — | 4 | 8 | no | — |
| 361 | C4×D67 | — | 4 | 8 | no | — |
| 362 | C4×D67 | — | 4 | 4 | no | — |
| 363 | Dic134 | — | 2 | 8 | no | — |
| 364 | Dic134 | — | 2 | 2 | no | — |
| 365 | Dic134 | — | 2 | 4 | no | — |
| 366 | Dic134 | — | 2 | 2 | no | — |
| 367 | Dic134 | — | 2 | 2 | no | — |
| 368 | Dic134 | — | 4 | 8 | no | — |
| 369 | Dic134 | — | 4 | 8 | no | — |
| 370 | Dic134 | C22×D4 | 1 | 8 | yes | — |
| 371 | C8×C67 | — | 2 | 2 | no | — |
| 372 | C8×C67 | C22×D4 | 1 | 2 | yes | — |
| 373 | C8×C67 | C22×D4 | 1 | 2 | yes | — |
| 374 | C67⋊C8 | — | 2 | 2 | no | — |
| 375 | C67⋊C8 | — | 2 | 2 | no | — |
| 376 | C22×C67 | — | 2 | 2 | no | — |
| 377 | C22×C67 | — | 2 | 4 | no | — |
| 378 | C22×C67 | — | 2 | 2 | no | — |
| 379 | C22×C67 | — | 4 | 2 | no | — |
| 380 | C22×C67 | — | 4 | 2 | no | — |
| 381 | C22×C67 | — | 4 | 2 | no | — |
| 382 | C22×C67 | D42 | 1 | 2 | yes | — |
| 383 | C22×C67 | C23×D4 | 1 | 1 | yes | characteristic |
| 384 | C2×D67 | — | 2 | 4 | no | — |
| 385 | C2×D67 | — | 2 | 2 | no | — |
| 386 | C2×D67 | — | 4 | 2 | no | — |
| 387 | C2×D67 | — | 4 | 2 | no | — |
| 388 | C2×D67 | — | 4 | 2 | no | — |
| 389 | C4×C67 | — | 2 | 2 | no | — |
| 390 | C4×C67 | — | 4 | 4 | no | — |
| 391 | C4×C67 | — | 4 | 2 | no | — |
| 392 | C4×C67 | D42 | 1 | 2 | yes | — |
| 393 | C4×C67 | C23×D4 | 1 | 1 | yes | characteristic |
| 394 | C4×C67 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 395 | Dic67 | — | 2 | 2 | no | — |
| 396 | Dic67 | — | 2 | 2 | no | — |
| 397 | Dic67 | — | 2 | 8 | no | — |
| 398 | Dic67 | — | 2 | 2 | no | — |
| 399 | Dic67 | — | 4 | 2 | no | — |
| 400 | #61081 | — | 67 | 1 | no | maximal, Sylow |
| 401 | C2×C67 | — | 2 | 2 | no | — |
| 402 | C2×C67 | — | 4 | 2 | no | — |
| 403 | C2×C67 | — | 8 | 2 | no | — |
| 404 | C2×C67 | C2×D42 | 1 | 1 | yes | characteristic |
| 405 | C2×C67 | #3586 | 1 | 2 | yes | — |
| 406 | D67 | — | 4 | 2 | no | — |
| 407 | D67 | — | 8 | 2 | no | — |
| 408 | C2×#578 | — | 67 | 1 | no | — |
| 409 | C2×#578 | — | 67 | 1 | no | — |
| 410 | #3497 | — | 67 | 2 | no | — |
| 411 | #3271 | — | 67 | 4 | no | — |
| 412 | #3271 | — | 67 | 4 | no | — |
| 413 | #3270 | — | 67 | 4 | no | — |
| 414 | #3270 | — | 67 | 4 | no | — |
| 415 | #3150 | — | 67 | 1 | no | — |
| 416 | #3060 | — | 67 | 1 | no | — |
| 417 | #3060 | D67 | 1 | 1 | yes | characteristic, complemented |
| 418 | #3037 | — | 67 | 2 | no | — |
| 419 | #3013 | — | 67 | 2 | no | — |
| 420 | #3013 | — | 67 | 2 | no | — |
| 421 | C2×#441 | — | 67 | 1 | no | — |
| 422 | #2932 | — | 67 | 1 | no | — |
| 423 | C67 | #61081 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 424 | C2×2−1+4 | — | 67 | 2 | no | — |
| 425 | C2×2−1+4 | — | 67 | 2 | no | — |
| 426 | #578 | — | 134 | 8 | no | — |
| 427 | #578 | — | 134 | 8 | no | — |
| 428 | C2×#137 | — | 67 | 2 | no | — |
| 429 | C2×#137 | — | 67 | 4 | no | — |
| 430 | C2×#137 | — | 67 | 2 | no | — |
| 431 | C2×#137 | — | 67 | 4 | no | — |
| 432 | C2×#135 | — | 67 | 2 | no | — |
| 433 | C2×#135 | — | 67 | 2 | no | — |
| 434 | C2×#135 | — | 67 | 1 | no | — |
| 435 | C2×#135 | — | 67 | 2 | no | — |
| 436 | C2×#135 | C2×D67 | 1 | 1 | yes | characteristic |
| 437 | C22×Q16 | — | 67 | 2 | no | — |
| 438 | C22×Q16 | — | 67 | 1 | no | — |
| 439 | C22×Q16 | — | 67 | 2 | no | — |
| 440 | C2×#131 | — | 67 | 1 | no | — |
| 441 | C2×#131 | C2×D67 | 1 | 1 | yes | characteristic |
| 442 | #550 | — | 67 | 4 | no | — |
| 443 | #550 | — | 134 | 2 | no | — |
| 444 | D4×Q8 | — | 67 | 4 | no | — |
| 445 | D4×Q8 | — | 134 | 2 | no | — |
| 446 | #548 | — | 67 | 4 | no | — |
| 447 | #548 | — | 67 | 4 | no | — |
| 448 | #548 | — | 134 | 2 | no | — |
| 449 | #548 | — | 134 | 2 | no | — |
| 450 | #537 | — | 67 | 2 | no | — |
| 451 | #537 | — | 134 | 4 | no | — |
| 452 | #537 | C2×D67 | 1 | 2 | yes | — |
| 453 | #532 | — | 67 | 1 | no | — |
| 454 | #532 | — | 67 | 2 | no | — |
| 455 | #532 | — | 134 | 4 | no | — |
| 456 | C2×C4×Q8 | — | 67 | 2 | no | — |
| 457 | #497 | — | 67 | 2 | no | — |
| 458 | #497 | — | 67 | 2 | no | — |
| 459 | #496 | — | 67 | 2 | no | — |
| 460 | #496 | — | 67 | 2 | no | — |
| 461 | #470 | — | 67 | 2 | no | — |
| 462 | #470 | C2×D67 | 1 | 2 | yes | — |
| 463 | #469 | — | 67 | 2 | no | — |
| 464 | #469 | C2×D67 | 1 | 2 | yes | — |
| 465 | #465 | — | 67 | 4 | no | — |
| 466 | #465 | C2×D67 | 1 | 4 | yes | — |
| 467 | #464 | — | 67 | 4 | no | — |
| 468 | #464 | — | 67 | 4 | no | — |
| 469 | #462 | — | 67 | 4 | no | — |
| 470 | #460 | — | 67 | 4 | no | — |
| 471 | #452 | — | 67 | 4 | no | — |
| 472 | #452 | — | 67 | 4 | no | — |
| 473 | #451 | — | 67 | 4 | no | — |
| 474 | #451 | — | 67 | 4 | no | — |
| 475 | #449 | — | 67 | 4 | no | — |
| 476 | #449 | — | 67 | 4 | no | — |
| 477 | #448 | — | 67 | 4 | no | — |
| 478 | #448 | — | 67 | 4 | no | — |
| 479 | #441 | — | 67 | 4 | no | — |
| 480 | #441 | — | 67 | 4 | no | — |
| 481 | #435 | — | 67 | 4 | no | — |
| 482 | #435 | — | 67 | 4 | no | — |
| 483 | C2×#106 | C2×D67 | 1 | 1 | yes | characteristic |
| 484 | #423 | — | 67 | 1 | no | — |
| 485 | #417 | — | 67 | 2 | no | — |
| 486 | #417 | C2×D67 | 1 | 2 | yes | — |
| 487 | C2×#103 | — | 67 | 2 | no | — |
| 488 | #408 | — | 67 | 1 | no | — |
| 489 | #408 | — | 67 | 1 | no | — |
| 490 | C2×#97 | — | 67 | 1 | no | — |
| 491 | 2−1+4 | — | 268 | 4 | no | — |
| 492 | 2−1+4 | — | 268 | 4 | no | — |
| 493 | 2−1+4 | — | 134 | 8 | no | — |
| 494 | 2−1+4 | — | 134 | 8 | no | — |
| 495 | C2×#41 | — | 67 | 1 | no | — |
| 496 | C2×#41 | — | 67 | 4 | no | — |
| 497 | C2×#41 | — | 67 | 4 | no | — |
| 498 | C2×#41 | — | 67 | 2 | no | — |
| 499 | C2×#41 | — | 134 | 2 | no | — |
| 500 | C2×#41 | — | 134 | 4 | no | — |
| 501 | C2×#41 | — | 134 | 4 | no | — |
| 502 | C2×#41 | — | 134 | 2 | no | — |
| 503 | C2×#41 | C22×D67 | 1 | 2 | yes | — |
| 504 | C2×#41 | C22×D67 | 1 | 1 | yes | characteristic |
| 505 | C22×Q8 | — | 67 | 4 | no | — |
| 506 | C22×Q8 | — | 67 | 4 | no | — |
| 507 | C22×Q8 | — | 67 | 2 | no | — |
| 508 | C22×Q8 | — | 134 | 2 | no | — |
| 509 | C22×Q8 | — | 134 | 2 | no | — |
| 510 | #137 | — | 134 | 16 | no | — |
| 511 | #137 | — | 134 | 8 | no | — |
| 512 | #137 | — | 134 | 16 | no | — |
| 513 | #137 | — | 134 | 8 | no | — |
| 514 | #135 | — | 2 | 4 | no | — |
| 515 | #135 | — | 268 | 4 | no | — |
| 516 | #135 | — | 134 | 8 | no | — |
| 517 | #135 | — | 134 | 8 | no | — |
| 518 | #135 | — | 134 | 4 | no | — |
| 519 | C2×Q16 | — | 67 | 2 | no | — |
| 520 | C2×Q16 | — | 67 | 4 | no | — |
| 521 | C2×Q16 | — | 67 | 8 | no | — |
| 522 | C2×Q16 | — | 67 | 2 | no | — |
| 523 | C2×Q16 | — | 67 | 2 | no | — |
| 524 | C2×Q16 | — | 67 | 1 | no | — |
| 525 | C2×Q16 | — | 67 | 4 | no | — |
| 526 | C2×Q16 | — | 134 | 8 | no | — |
| 527 | C2×Q16 | — | 134 | 8 | no | — |
| 528 | C2×Q16 | C22×D67 | 1 | 1 | yes | characteristic |
| 529 | C2×SD16 | — | 67 | 2 | no | — |
| 530 | C2×SD16 | — | 67 | 2 | no | — |
| 531 | C2×SD16 | — | 67 | 4 | no | — |
| 532 | C2×SD16 | — | 67 | 4 | no | — |
| 533 | C2×SD16 | — | 67 | 2 | no | — |
| 534 | C2×SD16 | C22×D67 | 1 | 2 | yes | — |
| 535 | C2×D8 | — | 67 | 2 | no | — |
| 536 | C2×D8 | — | 67 | 1 | no | — |
| 537 | C2×D8 | C22×D67 | 1 | 1 | yes | characteristic |
| 538 | #131 | — | 2 | 4 | no | — |
| 539 | #131 | — | 134 | 4 | no | — |
| 540 | C2×M16 | — | 67 | 1 | no | — |
| 541 | C2×M16 | — | 67 | 2 | no | — |
| 542 | C2×M16 | C22×D67 | 1 | 1 | yes | characteristic |
| 543 | C2×M16 | C22×D67 | 1 | 2 | yes | — |
| 544 | C22×C8 | — | 67 | 1 | no | — |
| 545 | C22×C8 | — | 67 | 2 | no | — |
| 546 | C22×C8 | C22×D67 | 1 | 2 | yes | — |
| 547 | C22×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 548 | C4⋊Q8 | — | 67 | 1 | no | — |
| 549 | C4⋊Q8 | — | 67 | 2 | no | — |
| 550 | C4⋊Q8 | — | 134 | 4 | no | — |
| 551 | #127 | — | 67 | 1 | no | — |
| 552 | #127 | — | 67 | 2 | no | — |
| 553 | #127 | — | 134 | 4 | no | — |
| 554 | #124 | — | 67 | 1 | no | — |
| 555 | #124 | — | 67 | 1 | no | — |
| 556 | #124 | — | 67 | 2 | no | — |
| 557 | #124 | — | 67 | 2 | no | — |
| 558 | #124 | — | 134 | 4 | no | — |
| 559 | #124 | — | 134 | 4 | no | — |
| 560 | C22⋊Q8 | — | 2 | 2 | no | — |
| 561 | C22⋊Q8 | — | 67 | 4 | no | — |
| 562 | C22⋊Q8 | — | 134 | 4 | no | — |
| 563 | C22⋊Q8 | — | 134 | 4 | no | — |
| 564 | C22⋊Q8 | — | 134 | 4 | no | — |
| 565 | C22⋊Q8 | — | 134 | 4 | no | — |
| 566 | C22⋊Q8 | — | 134 | 2 | no | — |
| 567 | C22⋊Q8 | C22×D67 | 1 | 4 | yes | — |
| 568 | #121 | — | 2 | 4 | no | — |
| 569 | #121 | — | 2 | 2 | no | — |
| 570 | #121 | — | 67 | 4 | no | — |
| 571 | #121 | — | 67 | 4 | no | — |
| 572 | #121 | — | 134 | 4 | no | — |
| 573 | #121 | — | 134 | 4 | no | — |
| 574 | #121 | — | 134 | 4 | no | — |
| 575 | #121 | — | 134 | 2 | no | — |
| 576 | #121 | — | 134 | 4 | no | — |
| 577 | #121 | — | 134 | 2 | no | — |
| 578 | #121 | — | 134 | 2 | no | — |
| 579 | #121 | — | 134 | 4 | no | — |
| 580 | #121 | C22×D67 | 1 | 4 | yes | — |
| 581 | C4×Q8 | — | 67 | 4 | no | — |
| 582 | C4×Q8 | — | 67 | 4 | no | — |
| 583 | C4×Q8 | — | 134 | 2 | no | — |
| 584 | C4×Q8 | — | 134 | 2 | no | — |
| 585 | C4×D4 | — | 67 | 4 | no | — |
| 586 | C4×D4 | — | 134 | 2 | no | — |
| 587 | C4×D4 | — | 134 | 2 | no | — |
| 588 | C4×D4 | — | 134 | 4 | no | — |
| 589 | C4×D4 | — | 134 | 4 | no | — |
| 590 | C4×D4 | — | 134 | 4 | no | — |
| 591 | C4×D4 | — | 134 | 4 | no | — |
| 592 | C2×C4⋊C4 | — | 134 | 2 | no | — |
| 593 | C2×C4⋊C4 | C22×D67 | 1 | 2 | yes | — |
| 594 | C2×C42 | — | 67 | 1 | no | — |
| 595 | C2×C42 | — | 134 | 2 | no | — |
| 596 | #106 | C22×D67 | 1 | 2 | yes | — |
| 597 | #106 | C22×D67 | 1 | 2 | yes | — |
| 598 | C4⋊C8 | — | 67 | 4 | no | — |
| 599 | #103 | — | 67 | 4 | no | — |
| 600 | #103 | — | 67 | 4 | no | — |
| 601 | #103 | — | 67 | 4 | no | — |
| 602 | #103 | C22×D67 | 1 | 4 | yes | — |
| 603 | #102 | — | 67 | 4 | no | — |
| 604 | #102 | C22×D67 | 1 | 4 | yes | — |
| 605 | C22⋊C8 | — | 67 | 4 | no | — |
| 606 | C22⋊C8 | — | 67 | 4 | no | — |
| 607 | #97 | — | 67 | 2 | no | — |
| 608 | #97 | — | 67 | 2 | no | — |
| 609 | #41 | — | 2 | 2 | no | — |
| 610 | #41 | — | 2 | 2 | no | — |
| 611 | #41 | — | 2 | 4 | no | — |
| 612 | #41 | — | 2 | 4 | no | — |
| 613 | #41 | — | 268 | 4 | no | — |
| 614 | #41 | — | 268 | 8 | no | — |
| 615 | #41 | — | 268 | 8 | no | — |
| 616 | #41 | — | 268 | 16 | no | — |
| 617 | #41 | — | 268 | 4 | no | — |
| 618 | #41 | — | 268 | 16 | no | — |
| 619 | #41 | — | 134 | 8 | no | — |
| 620 | #41 | — | 134 | 8 | no | — |
| 621 | #41 | — | 134 | 4 | no | — |
| 622 | #41 | — | 134 | 4 | no | — |
| 623 | #41 | — | 134 | 2 | no | — |
| 624 | #41 | — | 134 | 2 | no | — |
| 625 | C2×Q8 | — | 268 | 4 | no | — |
| 626 | C2×Q8 | — | 268 | 8 | no | — |
| 627 | C2×Q8 | — | 268 | 8 | no | — |
| 628 | C2×Q8 | — | 268 | 4 | no | — |
| 629 | C2×Q8 | — | 67 | 1 | no | — |
| 630 | C2×Q8 | — | 67 | 8 | no | — |
| 631 | C2×Q8 | — | 67 | 4 | no | — |
| 632 | C2×Q8 | — | 67 | 2 | no | — |
| 633 | C2×Q8 | — | 134 | 8 | no | — |
| 634 | C2×Q8 | — | 134 | 4 | no | — |
| 635 | C2×Q8 | — | 134 | 8 | no | — |
| 636 | C2×Q8 | — | 134 | 4 | no | — |
| 637 | C2×Q8 | — | 134 | 2 | no | — |
| 638 | C2×Q8 | — | 134 | 4 | no | — |
| 639 | C2×Q8 | D4×D67 | 1 | 1 | yes | characteristic |
| 640 | C2×Q8 | C23×D67 | 1 | 2 | yes | — |
| 641 | C2×D4 | — | 2 | 2 | no | — |
| 642 | C2×D4 | — | 2 | 4 | no | — |
| 643 | C2×D4 | — | 67 | 4 | no | — |
| 644 | C2×D4 | — | 67 | 2 | no | — |
| 645 | C2×D4 | — | 67 | 1 | no | — |
| 646 | C2×D4 | — | 67 | 2 | no | — |
| 647 | C2×D4 | — | 134 | 4 | no | — |
| 648 | C2×D4 | — | 134 | 2 | no | — |
| 649 | C2×D4 | — | 134 | 2 | no | — |
| 650 | C2×D4 | — | 134 | 4 | no | — |
| 651 | C2×D4 | — | 134 | 2 | no | — |
| 652 | C2×D4 | — | 134 | 4 | no | — |
| 653 | C2×D4 | D4×D67 | 1 | 2 | yes | — |
| 654 | C2×D4 | D4×D67 | 1 | 1 | yes | characteristic |
| 655 | C2×D4 | C23×D67 | 1 | 2 | yes | — |
| 656 | C22×C4 | — | 2 | 2 | no | — |
| 657 | C22×C4 | — | 2 | 2 | no | — |
| 658 | C22×C4 | — | 67 | 2 | no | — |
| 659 | C22×C4 | — | 67 | 2 | no | — |
| 660 | C22×C4 | — | 134 | 4 | no | — |
| 661 | C22×C4 | — | 134 | 4 | no | — |
| 662 | C22×C4 | — | 134 | 4 | no | — |
| 663 | C22×C4 | — | 134 | 4 | no | — |
| 664 | C22×C4 | — | 134 | 2 | no | — |
| 665 | C22×C4 | — | 134 | 2 | no | — |
| 666 | C22×C4 | C23×D67 | 1 | 2 | yes | — |
| 667 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 668 | Q16 | — | 2 | 2 | no | — |
| 669 | Q16 | — | 268 | 2 | no | — |
| 670 | Q16 | — | 67 | 8 | no | — |
| 671 | Q16 | — | 67 | 8 | no | — |
| 672 | Q16 | — | 134 | 8 | no | — |
| 673 | Q16 | — | 134 | 8 | no | — |
| 674 | Q16 | — | 134 | 2 | no | — |
| 675 | SD16 | — | 2 | 4 | no | — |
| 676 | SD16 | — | 268 | 2 | no | — |
| 677 | SD16 | — | 268 | 2 | no | — |
| 678 | SD16 | — | 134 | 8 | no | — |
| 679 | SD16 | — | 134 | 8 | no | — |
| 680 | SD16 | — | 134 | 4 | no | — |
| 681 | D8 | — | 2 | 2 | no | — |
| 682 | D8 | — | 268 | 2 | no | — |
| 683 | D8 | — | 134 | 2 | no | — |
| 684 | M16 | — | 2 | 2 | no | — |
| 685 | M16 | — | 2 | 4 | no | — |
| 686 | M16 | — | 134 | 2 | no | — |
| 687 | M16 | — | 134 | 4 | no | — |
| 688 | C2×C8 | — | 2 | 4 | no | — |
| 689 | C2×C8 | — | 67 | 2 | no | — |
| 690 | C2×C8 | — | 67 | 2 | no | — |
| 691 | C2×C8 | — | 134 | 2 | no | — |
| 692 | C2×C8 | — | 134 | 4 | no | — |
| 693 | C2×C8 | D4×D67 | 1 | 4 | yes | — |
| 694 | C2×C8 | C23×D67 | 1 | 2 | yes | — |
| 695 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 696 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 697 | C4⋊C4 | — | 2 | 2 | no | — |
| 698 | C4⋊C4 | — | 2 | 4 | no | — |
| 699 | C4⋊C4 | — | 67 | 4 | no | — |
| 700 | C4⋊C4 | — | 134 | 4 | no | — |
| 701 | C4⋊C4 | — | 134 | 4 | no | — |
| 702 | C4⋊C4 | — | 134 | 2 | no | — |
| 703 | C4⋊C4 | — | 134 | 4 | no | — |
| 704 | C4⋊C4 | — | 134 | 2 | no | — |
| 705 | C4⋊C4 | C23×D67 | 1 | 4 | yes | — |
| 706 | C22⋊C4 | — | 2 | 4 | no | — |
| 707 | C22⋊C4 | — | 2 | 4 | no | — |
| 708 | C22⋊C4 | — | 67 | 4 | no | — |
| 709 | C22⋊C4 | — | 67 | 4 | no | — |
| 710 | C22⋊C4 | — | 134 | 2 | no | — |
| 711 | C22⋊C4 | — | 134 | 4 | no | — |
| 712 | C22⋊C4 | — | 134 | 2 | no | — |
| 713 | C22⋊C4 | — | 134 | 4 | no | — |
| 714 | C22⋊C4 | — | 134 | 2 | no | — |
| 715 | C22⋊C4 | — | 134 | 2 | no | — |
| 716 | C42 | — | 67 | 1 | no | — |
| 717 | C42 | — | 67 | 1 | no | — |
| 718 | C42 | — | 67 | 2 | no | — |
| 719 | C42 | — | 134 | 4 | no | — |
| 720 | C42 | — | 134 | 4 | no | — |
| 721 | C23 | — | 2 | 2 | no | — |
| 722 | C23 | — | 67 | 2 | no | — |
| 723 | C23 | — | 134 | 2 | no | — |
| 724 | C23 | C2×D4×D67 | 1 | 2 | yes | — |
| 725 | C23 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 726 | Q8 | — | 2 | 2 | no | — |
| 727 | Q8 | — | 2 | 2 | no | — |
| 728 | Q8 | — | 2 | 2 | no | — |
| 729 | Q8 | — | 268 | 8 | no | — |
| 730 | Q8 | — | 268 | 8 | no | — |
| 731 | Q8 | — | 67 | 8 | no | — |
| 732 | Q8 | — | 134 | 2 | no | — |
| 733 | Q8 | — | 134 | 2 | no | — |
| 734 | Q8 | — | 134 | 2 | no | — |
| 735 | Q8 | — | 134 | 8 | no | — |
| 736 | Q8 | — | 134 | 4 | no | — |
| 737 | D4 | — | 2 | 4 | no | — |
| 738 | D4 | — | 2 | 2 | no | — |
| 739 | D4 | — | 2 | 2 | no | — |
| 740 | D4 | — | 2 | 2 | no | — |
| 741 | D4 | — | 4 | 4 | no | — |
| 742 | D4 | — | 8 | 4 | no | — |
| 743 | D4 | — | 268 | 4 | no | — |
| 744 | D4 | — | 268 | 8 | no | — |
| 745 | D4 | — | 268 | 4 | no | — |
| 746 | D4 | — | 268 | 4 | no | — |
| 747 | D4 | — | 268 | 8 | no | — |
| 748 | D4 | — | 536 | 4 | no | — |
| 749 | D4 | — | 536 | 2 | no | — |
| 750 | D4 | — | 134 | 4 | no | — |
| 751 | D4 | — | 134 | 2 | no | — |
| 752 | D4 | — | 134 | 2 | no | — |
| 753 | D4 | — | 134 | 2 | no | — |
| 754 | C2×C4 | — | 2 | 2 | no | — |
| 755 | C2×C4 | — | 2 | 2 | no | — |
| 756 | C2×C4 | — | 2 | 4 | no | — |
| 757 | C2×C4 | — | 2 | 2 | no | — |
| 758 | C2×C4 | — | 4 | 4 | no | — |
| 759 | C2×C4 | — | 8 | 2 | no | — |
| 760 | C2×C4 | — | 268 | 8 | no | — |
| 761 | C2×C4 | — | 268 | 8 | no | — |
| 762 | C2×C4 | — | 268 | 8 | no | — |
| 763 | C2×C4 | — | 268 | 4 | no | — |
| 764 | C2×C4 | — | 268 | 2 | no | — |
| 765 | C2×C4 | — | 268 | 8 | no | — |
| 766 | C2×C4 | — | 67 | 2 | no | — |
| 767 | C2×C4 | — | 67 | 2 | no | — |
| 768 | C2×C4 | — | 67 | 2 | no | — |
| 769 | C2×C4 | — | 134 | 2 | no | — |
| 770 | C2×C4 | — | 134 | 8 | no | — |
| 771 | C2×C4 | — | 134 | 4 | no | — |
| 772 | C2×C4 | — | 134 | 2 | no | — |
| 773 | C2×C4 | — | 134 | 2 | no | — |
| 774 | C2×C4 | C2×D4×D67 | 1 | 2 | yes | — |
| 775 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 776 | C2×C4 | C2×D4×D67 | 1 | 2 | yes | — |
| 777 | C2×C4 | #14524089 | 1 | 2 | yes | — |
| 778 | C2×C4 | C24×D67 | 1 | 1 | yes | characteristic |
| 779 | C8 | — | 2 | 2 | no | — |
| 780 | C8 | — | 134 | 2 | no | — |
| 781 | C8 | — | 134 | 2 | no | — |
| 782 | C8 | C2×D4×D67 | 1 | 2 | yes | — |
| 783 | C8 | C2×D4×D67 | 1 | 2 | yes | — |
| 784 | C22 | — | 2 | 2 | no | — |
| 785 | C22 | — | 2 | 2 | no | — |
| 786 | C22 | — | 2 | 4 | no | — |
| 787 | C22 | — | 4 | 2 | no | — |
| 788 | C22 | — | 4 | 2 | no | — |
| 789 | C22 | — | 4 | 2 | no | — |
| 790 | C22 | — | 268 | 2 | no | — |
| 791 | C22 | — | 268 | 2 | no | — |
| 792 | C22 | — | 268 | 2 | no | — |
| 793 | C22 | — | 134 | 2 | no | — |
| 794 | C22 | — | 134 | 4 | no | — |
| 795 | C22 | #16864030 | 1 | 2 | yes | — |
| 796 | C22 | C22×D4×D67 | 1 | 1 | yes | characteristic |
| 797 | C4 | — | 2 | 2 | no | — |
| 798 | C4 | — | 4 | 2 | no | — |
| 799 | C4 | — | 4 | 4 | no | — |
| 800 | C4 | — | 268 | 2 | no | — |
| 801 | C4 | — | 134 | 2 | no | — |
| 802 | C4 | — | 134 | 8 | no | — |
| 803 | C4 | — | 134 | 2 | no | — |
| 804 | C4 | — | 134 | 2 | no | — |
| 805 | C4 | #16864030 | 1 | 2 | yes | — |
| 806 | C4 | C22×D4×D67 | 1 | 1 | yes | characteristic |
| 807 | C4 | C2×#14524089 | 1 | 1 | yes | characteristic |
| 808 | C2 | — | 2 | 2 | no | — |
| 809 | C2 | — | 4 | 2 | no | — |
| 810 | C2 | — | 8 | 2 | no | — |
| 811 | C2 | — | 268 | 2 | no | — |
| 812 | C2 | — | 536 | 2 | no | — |
| 813 | C2 | C2×#16864030 | 1 | 1 | yes | characteristic |
| 814 | C2 | #22574991 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16864213 | C2 | semidirect |
| 2. C2×#16864210 | C2 | semidirect |
| 3. #22573978 | C2 | semidirect |
| 4. #22571801 | C2 | semidirect |
| 5. #22571791 | C2 | semidirect |
| 6. #22571786 | C2 | semidirect |
| 7. #22571776 | C2 | semidirect |
| 8. #22570652 | C2 | semidirect |
| 9. #22569872 | C2 | semidirect |
| 10. #22569680 | C2 | semidirect |
| 11. #22569526 | C2 | semidirect |
| 12. #22569521 | C2 | semidirect |
| 13. C2×#16863502 | C2 | semidirect |
| 14. #22568925 | C2 | semidirect |
| 15. C67×#3060 | C2 | semidirect |
| 109. C2×Dic268 | D4 | semidirect |
| 417. #3060 | D67 | semidirect |
| 423. C67 | #61081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864213 | 2 |
| C2×#16864210 | 2 |
| #22573978 | 2 |
| #22571801 | 2 |
| #22571791 | 2 |
| #22571786 | 2 |
| #22571776 | 2 |
| #22570652 | 2 |
| #22569872 | 2 |
| #22569680 | 2 |
| #22569526 | 2 |
| #22569521 | 2 |
| C2×#16863502 | 2 |
| #22568925 | 2 |
| C67×#3060 | 2 |
| #61081 | 67 |