← #31728149
Subgroups — #31728149
Order 17152.
1756 conjugacy classes of subgroups.
The subgroup lattice has 946 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#16863949 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#16863948 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22571420 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #22571414 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22571412 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22571366 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #22571358 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #22571351 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #22570753 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #22570587 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #22570158 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #22570157 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #22570153 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #22570013 | C2 | 1 | 2 | yes | maximal, complemented |
| 15 | #22570011 | C2 | 1 | 2 | yes | maximal, complemented |
| 16 | #22568838 | C2 | 1 | 1 | yes | maximal, characteristic |
| 17 | C67×#3095 | C2 | 1 | 1 | yes | maximal, characteristic |
| 18 | #16863949 | — | 2 | 1 | no | — |
| 19 | #16863949 | — | 2 | 1 | no | — |
| 20 | #16863949 | — | 2 | 1 | no | — |
| 21 | #16863949 | — | 2 | 1 | no | — |
| 22 | #16863949 | C22 | 1 | 2 | yes | — |
| 23 | #16863949 | C22 | 1 | 2 | yes | — |
| 24 | #16863949 | C22 | 1 | 2 | yes | — |
| 25 | #16863949 | C22 | 1 | 2 | yes | — |
| 26 | #16863948 | — | 2 | 1 | no | — |
| 27 | #16863948 | — | 2 | 1 | no | — |
| 28 | #16863948 | — | 2 | 1 | no | — |
| 29 | #16863948 | — | 2 | 1 | no | — |
| 30 | #16863948 | C22 | 1 | 2 | yes | — |
| 31 | #16863948 | C22 | 1 | 2 | yes | — |
| 32 | #16863948 | C22 | 1 | 2 | yes | — |
| 33 | #16863948 | C22 | 1 | 2 | yes | — |
| 34 | C2×#14524042 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×#14524042 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×#14524042 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×#14524041 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×#14524034 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#14524034 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#14524033 | — | 2 | 1 | no | — |
| 41 | C2×#14524022 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×#14524020 | — | 2 | 1 | no | — |
| 43 | C2×#14524020 | — | 2 | 1 | no | — |
| 44 | C2×#14524020 | — | 2 | 1 | no | — |
| 45 | C2×Q8×Dic67 | C22 | 1 | 1 | yes | characteristic |
| 46 | C2×C4×Dic134 | — | 2 | 1 | no | — |
| 47 | C2×C4×Dic134 | — | 2 | 1 | no | — |
| 48 | C2×#14524008 | — | 2 | 1 | no | — |
| 49 | C2×#14524008 | C22 | 1 | 1 | yes | characteristic |
| 50 | C2×#14524002 | C22 | 1 | 1 | yes | characteristic |
| 51 | C2×#14523999 | — | 2 | 1 | no | — |
| 52 | C22×C4×Dic67 | C22 | 1 | 1 | yes | characteristic |
| 53 | #16863804 | C22 | 1 | 4 | yes | complemented |
| 54 | #16863803 | C22 | 1 | 4 | yes | complemented |
| 55 | #16863800 | C22 | 1 | 4 | yes | complemented |
| 56 | #16863793 | C22 | 1 | 4 | yes | complemented |
| 57 | #16863763 | C22 | 1 | 4 | yes | complemented |
| 58 | #16863763 | C22 | 1 | 4 | yes | complemented |
| 59 | #16863745 | C22 | 1 | 4 | yes | complemented |
| 60 | #16863745 | C22 | 1 | 4 | yes | complemented |
| 61 | #16863738 | C22 | 1 | 4 | yes | — |
| 62 | #16863737 | C22 | 1 | 4 | yes | — |
| 63 | #16863734 | C22 | 1 | 4 | yes | — |
| 64 | #16863732 | C22 | 1 | 2 | yes | — |
| 65 | #16863731 | C22 | 1 | 2 | yes | — |
| 66 | #16863729 | C22 | 1 | 2 | yes | — |
| 67 | #16863727 | C22 | 1 | 2 | yes | — |
| 68 | #16863726 | C22 | 1 | 2 | yes | — |
| 69 | #16863724 | C22 | 1 | 2 | yes | — |
| 70 | #16863706 | C22 | 1 | 4 | yes | complemented |
| 71 | #16863705 | C22 | 1 | 4 | yes | complemented |
| 72 | #16863702 | C22 | 1 | 4 | yes | complemented |
| 73 | #16863701 | C22 | 1 | 4 | yes | complemented |
| 74 | #16863690 | C22 | 1 | 4 | yes | complemented |
| 75 | #16863689 | C22 | 1 | 4 | yes | complemented |
| 76 | #16863680 | C22 | 1 | 4 | yes | complemented |
| 77 | #16863679 | C22 | 1 | 4 | yes | complemented |
| 78 | #16863450 | C22 | 1 | 2 | yes | — |
| 79 | #16863450 | C22 | 1 | 2 | yes | — |
| 80 | #16863446 | C22 | 1 | 2 | yes | — |
| 81 | #16863446 | C22 | 1 | 2 | yes | — |
| 82 | #16863439 | C22 | 1 | 2 | yes | — |
| 83 | #16863438 | C22 | 1 | 2 | yes | — |
| 84 | #16863436 | C22 | 1 | 2 | yes | — |
| 85 | #16863419 | C22 | 1 | 2 | yes | — |
| 86 | #16863406 | C22 | 1 | 2 | yes | — |
| 87 | #16863405 | C22 | 1 | 2 | yes | — |
| 88 | #16863404 | C22 | 1 | 2 | yes | — |
| 89 | #16863360 | C22 | 1 | 1 | yes | characteristic |
| 90 | M16×Dic67 | C22 | 1 | 2 | yes | — |
| 91 | C2×C22⋊Q8×C67 | C22 | 1 | 1 | yes | characteristic |
| 92 | C2×#117×C67 | C22 | 1 | 1 | yes | characteristic |
| 93 | #485×C67 | C22 | 1 | 4 | yes | — |
| 94 | #484×C67 | C22 | 1 | 2 | yes | — |
| 95 | #483×C67 | C22 | 1 | 2 | yes | — |
| 96 | #428×C67 | C22 | 1 | 2 | yes | — |
| 97 | #419×C67 | C22 | 1 | 2 | yes | — |
| 98 | #407×C67 | C22 | 1 | 1 | yes | characteristic |
| 99 | C22×Dic134 | — | 2 | 1 | no | — |
| 100 | C22×Dic134 | — | 2 | 1 | no | — |
| 101 | C22×Dic134 | — | 2 | 1 | no | — |
| 102 | C22×Dic134 | C23 | 1 | 1 | yes | characteristic |
| 103 | C23×Dic67 | D4 | 1 | 1 | yes | characteristic |
| 104 | C23×Dic67 | D4 | 1 | 1 | yes | characteristic |
| 105 | C2×#11761612 | C23 | 1 | 2 | yes | — |
| 106 | #14524042 | — | 2 | 1 | no | — |
| 107 | #14524042 | — | 2 | 1 | no | — |
| 108 | #14524042 | — | 2 | 1 | no | — |
| 109 | #14524042 | — | 2 | 1 | no | — |
| 110 | #14524042 | — | 2 | 1 | no | — |
| 111 | #14524042 | — | 2 | 1 | no | — |
| 112 | #14524042 | C23 | 1 | 2 | yes | — |
| 113 | #14524042 | C23 | 1 | 2 | yes | — |
| 114 | #14524042 | C23 | 1 | 2 | yes | — |
| 115 | #14524042 | C23 | 1 | 2 | yes | — |
| 116 | #14524042 | C23 | 1 | 2 | yes | — |
| 117 | #14524042 | C23 | 1 | 2 | yes | — |
| 118 | #14524041 | — | 2 | 1 | no | — |
| 119 | #14524041 | — | 2 | 1 | no | — |
| 120 | #14524041 | C23 | 1 | 2 | yes | — |
| 121 | #14524041 | C23 | 1 | 2 | yes | — |
| 122 | #14524034 | — | 2 | 1 | no | — |
| 123 | #14524034 | — | 2 | 1 | no | — |
| 124 | #14524034 | — | 2 | 1 | no | — |
| 125 | #14524034 | — | 2 | 1 | no | — |
| 126 | #14524034 | C23 | 1 | 2 | yes | — |
| 127 | #14524034 | C23 | 1 | 2 | yes | — |
| 128 | #14524034 | C23 | 1 | 2 | yes | — |
| 129 | #14524034 | C23 | 1 | 2 | yes | — |
| 130 | #14524033 | — | 2 | 2 | no | — |
| 131 | #14524033 | — | 2 | 2 | no | — |
| 132 | #14524033 | — | 2 | 2 | no | — |
| 133 | #14524033 | — | 2 | 2 | no | — |
| 134 | #14524022 | — | 2 | 1 | no | — |
| 135 | #14524022 | — | 2 | 1 | no | — |
| 136 | #14524022 | C23 | 1 | 2 | yes | — |
| 137 | #14524022 | C23 | 1 | 2 | yes | — |
| 138 | #14524020 | — | 2 | 2 | no | — |
| 139 | #14524020 | — | 2 | 2 | no | — |
| 140 | #14524020 | — | 2 | 2 | no | — |
| 141 | #14524020 | — | 2 | 2 | no | — |
| 142 | #14524020 | — | 2 | 2 | no | — |
| 143 | #14524020 | — | 2 | 2 | no | — |
| 144 | #14524020 | — | 2 | 2 | no | — |
| 145 | #14524020 | — | 2 | 2 | no | — |
| 146 | #14524020 | — | 2 | 2 | no | — |
| 147 | #14524020 | — | 2 | 2 | no | — |
| 148 | #14524020 | — | 2 | 2 | no | — |
| 149 | #14524020 | — | 2 | 2 | no | — |
| 150 | Q8×Dic67 | — | 2 | 1 | no | — |
| 151 | Q8×Dic67 | — | 2 | 1 | no | — |
| 152 | Q8×Dic67 | C23 | 1 | 2 | yes | — |
| 153 | Q8×Dic67 | C23 | 1 | 2 | yes | — |
| 154 | C4×Dic134 | — | 2 | 2 | no | — |
| 155 | C4×Dic134 | — | 2 | 2 | no | — |
| 156 | C4×Dic134 | — | 2 | 2 | no | — |
| 157 | C4×Dic134 | — | 2 | 2 | no | — |
| 158 | C4×Dic134 | — | 2 | 2 | no | — |
| 159 | C4×Dic134 | — | 2 | 2 | no | — |
| 160 | C4×Dic134 | — | 2 | 2 | no | — |
| 161 | C4×Dic134 | — | 2 | 2 | no | — |
| 162 | #14524008 | — | 2 | 2 | no | — |
| 163 | #14524008 | — | 2 | 2 | no | — |
| 164 | #14524008 | — | 2 | 2 | no | — |
| 165 | #14524008 | — | 2 | 2 | no | — |
| 166 | #14524008 | — | 2 | 1 | no | — |
| 167 | #14524008 | — | 2 | 1 | no | — |
| 168 | #14524008 | C23 | 1 | 2 | yes | — |
| 169 | #14524008 | C23 | 1 | 2 | yes | — |
| 170 | #14524002 | — | 2 | 1 | no | — |
| 171 | #14524002 | — | 2 | 1 | no | — |
| 172 | #14524002 | C23 | 1 | 2 | yes | — |
| 173 | #14524002 | C23 | 1 | 2 | yes | — |
| 174 | #14523999 | — | 2 | 2 | no | — |
| 175 | #14523999 | — | 2 | 2 | no | — |
| 176 | #14523999 | — | 2 | 2 | no | — |
| 177 | #14523999 | — | 2 | 2 | no | — |
| 178 | C2×C4⋊Dic67 | — | 2 | 1 | no | — |
| 179 | C2×C4⋊Dic67 | — | 2 | 1 | no | — |
| 180 | C2×C4⋊Dic67 | — | 2 | 1 | no | — |
| 181 | C2×C4⋊Dic67 | C23 | 1 | 1 | yes | characteristic |
| 182 | C2×C4⋊Dic67 | C23 | 1 | 1 | yes | characteristic |
| 183 | C2×C4⋊Dic67 | C23 | 1 | 1 | yes | characteristic |
| 184 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 185 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 186 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 187 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 188 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 189 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 190 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 191 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 192 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 193 | C2×C22⋊Dic67 | — | 2 | 1 | no | — |
| 194 | C2×C22⋊Dic67 | — | 2 | 1 | no | — |
| 195 | C2×C4×Dic67 | — | 2 | 1 | no | — |
| 196 | C2×C4×Dic67 | — | 2 | 1 | no | — |
| 197 | C2×C4×Dic67 | — | 2 | 1 | no | — |
| 198 | C2×C4×Dic67 | D4 | 1 | 1 | yes | characteristic |
| 199 | C2×C4×Dic67 | D4 | 1 | 1 | yes | characteristic |
| 200 | C2×C4×Dic67 | D4 | 1 | 1 | yes | characteristic |
| 201 | C2×C4×Dic67 | D4 | 1 | 1 | yes | characteristic |
| 202 | C2×C4×Dic67 | D4 | 1 | 1 | yes | characteristic |
| 203 | C2×C4×Dic67 | D4 | 1 | 1 | yes | characteristic |
| 204 | C2×C4×Dic67 | C23 | 1 | 1 | yes | characteristic |
| 205 | C2×C4×Dic67 | C23 | 1 | 1 | yes | characteristic |
| 206 | C2×C4×Dic67 | C23 | 1 | 1 | yes | characteristic |
| 207 | C2×C4×Dic67 | C23 | 1 | 1 | yes | characteristic |
| 208 | C2×C4×Dic67 | C23 | 1 | 1 | yes | characteristic |
| 209 | C2×C4×Dic67 | C23 | 1 | 1 | yes | characteristic |
| 210 | #14523977 | C23 | 1 | 4 | yes | — |
| 211 | #14523976 | C23 | 1 | 4 | yes | — |
| 212 | #14523976 | C23 | 1 | 4 | yes | — |
| 213 | #14523975 | C23 | 1 | 4 | yes | — |
| 214 | #14523974 | C23 | 1 | 4 | yes | — |
| 215 | #14523974 | C23 | 1 | 4 | yes | — |
| 216 | Dic67⋊C8 | C23 | 1 | 4 | yes | — |
| 217 | Dic67⋊C8 | C23 | 1 | 4 | yes | — |
| 218 | #14523968 | C23 | 1 | 4 | yes | — |
| 219 | #14523968 | C23 | 1 | 4 | yes | — |
| 220 | #14523967 | C23 | 1 | 4 | yes | — |
| 221 | #14523967 | C23 | 1 | 4 | yes | — |
| 222 | #14523966 | C23 | 1 | 4 | yes | — |
| 223 | #14523966 | C23 | 1 | 4 | yes | — |
| 224 | C22⋊(C67⋊C8) | C23 | 1 | 2 | yes | — |
| 225 | C22⋊(C67⋊C8) | C23 | 1 | 2 | yes | — |
| 226 | #14523953 | C23 | 1 | 4 | yes | — |
| 227 | C8×Dic67 | C23 | 1 | 4 | yes | — |
| 228 | C22×Q8×C67 | C23 | 1 | 1 | yes | characteristic |
| 229 | C23×C4×C67 | C23 | 1 | 1 | yes | characteristic |
| 230 | C2×M16×C67 | C23 | 1 | 2 | yes | — |
| 231 | C22⋊Q8×C67 | — | 2 | 1 | no | — |
| 232 | C22⋊Q8×C67 | — | 2 | 1 | no | — |
| 233 | C22⋊Q8×C67 | C23 | 1 | 2 | yes | — |
| 234 | C22⋊Q8×C67 | C23 | 1 | 2 | yes | — |
| 235 | #117×C67 | — | 2 | 1 | no | — |
| 236 | #117×C67 | — | 2 | 1 | no | — |
| 237 | #117×C67 | C23 | 1 | 2 | yes | — |
| 238 | #117×C67 | C23 | 1 | 2 | yes | — |
| 239 | C2×C4⋊C4×C67 | — | 2 | 1 | no | — |
| 240 | C2×C4⋊C4×C67 | C23 | 1 | 1 | yes | characteristic |
| 241 | C2×C4⋊C4×C67 | C23 | 1 | 1 | yes | characteristic |
| 242 | C2×C4⋊C4×C67 | C23 | 1 | 1 | yes | characteristic |
| 243 | C2×C22⋊C4×C67 | — | 2 | 1 | no | — |
| 244 | C2×C22⋊C4×C67 | — | 2 | 1 | no | — |
| 245 | C2×C42×C67 | — | 2 | 1 | no | — |
| 246 | #107×C67 | C23 | 1 | 4 | yes | — |
| 247 | #106×C67 | C23 | 1 | 4 | yes | — |
| 248 | #103×C67 | C23 | 1 | 4 | yes | — |
| 249 | #103×C67 | C23 | 1 | 4 | yes | — |
| 250 | C22⋊C8×C67 | C23 | 1 | 2 | yes | — |
| 251 | C22⋊C8×C67 | C23 | 1 | 2 | yes | — |
| 252 | C2×Dic134 | — | 2 | 4 | no | — |
| 253 | C2×Dic134 | — | 2 | 1 | no | — |
| 254 | C2×Dic134 | — | 2 | 2 | no | — |
| 255 | C2×Dic134 | — | 2 | 2 | no | — |
| 256 | C2×Dic134 | — | 2 | 2 | no | — |
| 257 | C2×Dic134 | — | 2 | 2 | no | — |
| 258 | C2×Dic134 | — | 2 | 2 | no | — |
| 259 | C2×Dic134 | — | 2 | 2 | no | — |
| 260 | C2×Dic134 | — | 4 | 4 | no | — |
| 261 | C2×Dic134 | — | 4 | 4 | no | — |
| 262 | C2×Dic134 | — | 4 | 4 | no | — |
| 263 | C2×Dic134 | C24 | 1 | 2 | yes | — |
| 264 | C22×Dic67 | — | 2 | 4 | no | — |
| 265 | C22×Dic67 | — | 2 | 1 | no | — |
| 266 | C22×Dic67 | — | 2 | 1 | no | — |
| 267 | C22×Dic67 | — | 2 | 1 | no | — |
| 268 | C22×Dic67 | — | 2 | 1 | no | — |
| 269 | C22×Dic67 | — | 4 | 2 | no | — |
| 270 | C22×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 271 | C22×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 272 | C22×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 273 | C22×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 274 | C22×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 275 | C22×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 276 | C22×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 277 | C22×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 278 | C22×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 279 | C22×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 280 | C22×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 281 | C22×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 282 | #11761612 | — | 2 | 4 | no | — |
| 283 | C2×C67⋊C8 | C24 | 1 | 4 | yes | — |
| 284 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 285 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 286 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 287 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 288 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 289 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 290 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 291 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 292 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 293 | C4⋊Dic67 | C24 | 1 | 2 | yes | — |
| 294 | C4⋊Dic67 | C24 | 1 | 2 | yes | — |
| 295 | C4⋊Dic67 | C24 | 1 | 2 | yes | — |
| 296 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 297 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 298 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 299 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 300 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 301 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 302 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 303 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 304 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 305 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 306 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 307 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 308 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 309 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 310 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 311 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 312 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 313 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 314 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 315 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 316 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 317 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 318 | C4×Dic67 | — | 2 | 2 | no | — |
| 319 | C4×Dic67 | — | 2 | 2 | no | — |
| 320 | C4×Dic67 | — | 2 | 2 | no | — |
| 321 | C4×Dic67 | — | 2 | 2 | no | — |
| 322 | C4×Dic67 | — | 2 | 2 | no | — |
| 323 | C4×Dic67 | — | 2 | 2 | no | — |
| 324 | C4×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 325 | C4×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 326 | C4×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 327 | C4×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 328 | C4×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 329 | C4×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 330 | C4×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 331 | C4×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 332 | C4×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 333 | C4×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 334 | C4×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 335 | C4×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 336 | C4×Dic67 | C24 | 1 | 1 | yes | characteristic |
| 337 | C4×Dic67 | C24 | 1 | 1 | yes | characteristic |
| 338 | C4×Dic67 | C24 | 1 | 1 | yes | characteristic |
| 339 | C4×Dic67 | C24 | 1 | 1 | yes | characteristic |
| 340 | C24×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 341 | C2×Q8×C67 | — | 2 | 1 | no | — |
| 342 | C2×Q8×C67 | — | 2 | 4 | no | — |
| 343 | C2×Q8×C67 | C24 | 1 | 2 | yes | — |
| 344 | C22×C4×C67 | — | 2 | 4 | no | — |
| 345 | C22×C4×C67 | — | 2 | 1 | no | — |
| 346 | C22×C4×C67 | — | 2 | 1 | no | — |
| 347 | C22×C4×C67 | — | 2 | 1 | no | — |
| 348 | C22×C4×C67 | — | 2 | 1 | no | — |
| 349 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 350 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 351 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 352 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 353 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 354 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 355 | M16×C67 | — | 2 | 4 | no | — |
| 356 | C2×C8×C67 | C24 | 1 | 4 | yes | — |
| 357 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 358 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 359 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 360 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 361 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 362 | C4⋊C4×C67 | C24 | 1 | 2 | yes | — |
| 363 | C4⋊C4×C67 | C24 | 1 | 2 | yes | — |
| 364 | C4⋊C4×C67 | C24 | 1 | 2 | yes | — |
| 365 | C22⋊C4×C67 | — | 2 | 2 | no | — |
| 366 | C22⋊C4×C67 | — | 2 | 2 | no | — |
| 367 | C22⋊C4×C67 | — | 2 | 2 | no | — |
| 368 | C22⋊C4×C67 | — | 2 | 2 | no | — |
| 369 | C42×C67 | — | 2 | 2 | no | — |
| 370 | C42×C67 | — | 2 | 2 | no | — |
| 371 | C23×C67 | — | 2 | 2 | no | — |
| 372 | C23×C67 | — | 2 | 2 | no | — |
| 373 | C23×C67 | — | 4 | 1 | no | — |
| 374 | C23×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 375 | C23×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 376 | C23×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 377 | Q8×C67 | — | 2 | 4 | no | — |
| 378 | Q8×C67 | — | 4 | 2 | no | — |
| 379 | C2×C4×C67 | — | 2 | 2 | no | — |
| 380 | C2×C4×C67 | — | 2 | 2 | no | — |
| 381 | C2×C4×C67 | — | 2 | 2 | no | — |
| 382 | C2×C4×C67 | — | 2 | 2 | no | — |
| 383 | C2×C4×C67 | — | 2 | 2 | no | — |
| 384 | C2×C4×C67 | — | 2 | 2 | no | — |
| 385 | C2×C4×C67 | — | 2 | 2 | no | — |
| 386 | C2×C4×C67 | — | 2 | 2 | no | — |
| 387 | C2×C4×C67 | — | 2 | 2 | no | — |
| 388 | C2×C4×C67 | — | 4 | 2 | no | — |
| 389 | C2×C4×C67 | — | 4 | 2 | no | — |
| 390 | C2×C4×C67 | — | 4 | 2 | no | — |
| 391 | C2×C4×C67 | — | 4 | 2 | no | — |
| 392 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 393 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 394 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 395 | C2×C4×C67 | 2−1+4 | 1 | 4 | yes | — |
| 396 | C2×C4×C67 | C25 | 1 | 1 | yes | characteristic |
| 397 | C2×Dic67 | — | 2 | 2 | no | — |
| 398 | C2×Dic67 | — | 2 | 2 | no | — |
| 399 | C2×Dic67 | — | 2 | 2 | no | — |
| 400 | C2×Dic67 | — | 2 | 2 | no | — |
| 401 | C2×Dic67 | — | 2 | 2 | no | — |
| 402 | C2×Dic67 | — | 2 | 2 | no | — |
| 403 | C2×Dic67 | — | 2 | 2 | no | — |
| 404 | C2×Dic67 | — | 2 | 2 | no | — |
| 405 | C2×Dic67 | — | 2 | 2 | no | — |
| 406 | C2×Dic67 | — | 2 | 2 | no | — |
| 407 | C2×Dic67 | — | 2 | 2 | no | — |
| 408 | C2×Dic67 | — | 2 | 2 | no | — |
| 409 | C2×Dic67 | — | 4 | 1 | no | — |
| 410 | C2×Dic67 | — | 4 | 1 | no | — |
| 411 | C2×Dic67 | — | 4 | 1 | no | — |
| 412 | C2×Dic67 | — | 4 | 2 | no | — |
| 413 | C2×Dic67 | — | 4 | 2 | no | — |
| 414 | C2×Dic67 | — | 4 | 2 | no | — |
| 415 | C2×Dic67 | — | 4 | 2 | no | — |
| 416 | C2×Dic67 | #137 | 1 | 4 | yes | — |
| 417 | C2×Dic67 | C22×D4 | 1 | 1 | yes | characteristic |
| 418 | C2×Dic67 | C22×D4 | 1 | 1 | yes | characteristic |
| 419 | C2×Dic67 | C22×D4 | 1 | 1 | yes | characteristic |
| 420 | C2×Dic67 | C22×D4 | 1 | 1 | yes | characteristic |
| 421 | C2×Dic67 | C22×D4 | 1 | 1 | yes | characteristic |
| 422 | C2×Dic67 | C22×D4 | 1 | 1 | yes | characteristic |
| 423 | C2×Dic67 | C22×D4 | 1 | 1 | yes | characteristic |
| 424 | C2×Dic67 | C22×D4 | 1 | 1 | yes | characteristic |
| 425 | Dic134 | — | 2 | 4 | no | — |
| 426 | Dic134 | — | 4 | 4 | no | — |
| 427 | Dic134 | — | 4 | 4 | no | — |
| 428 | Dic134 | — | 4 | 2 | no | — |
| 429 | Dic134 | — | 4 | 4 | no | — |
| 430 | Dic134 | — | 4 | 4 | no | — |
| 431 | Dic134 | — | 4 | 4 | no | — |
| 432 | Dic134 | — | 4 | 4 | no | — |
| 433 | C8×C67 | — | 2 | 4 | no | — |
| 434 | C67⋊C8 | — | 2 | 4 | no | — |
| 435 | C22×C67 | — | 2 | 1 | no | — |
| 436 | C22×C67 | — | 2 | 1 | no | — |
| 437 | C22×C67 | — | 2 | 1 | no | — |
| 438 | C22×C67 | — | 2 | 1 | no | — |
| 439 | C22×C67 | — | 2 | 1 | no | — |
| 440 | C22×C67 | — | 2 | 1 | no | — |
| 441 | C22×C67 | — | 2 | 1 | no | — |
| 442 | C22×C67 | — | 4 | 4 | no | — |
| 443 | C22×C67 | #536 | 1 | 2 | yes | — |
| 444 | C22×C67 | C2×#137 | 1 | 2 | yes | — |
| 445 | C22×C67 | C23×D4 | 1 | 1 | yes | characteristic |
| 446 | C4×C67 | — | 2 | 1 | no | — |
| 447 | C4×C67 | — | 2 | 1 | no | — |
| 448 | C4×C67 | — | 4 | 2 | no | — |
| 449 | C4×C67 | — | 4 | 2 | no | — |
| 450 | C4×C67 | — | 4 | 2 | no | — |
| 451 | C4×C67 | — | 4 | 2 | no | — |
| 452 | C4×C67 | #536 | 1 | 2 | yes | — |
| 453 | C4×C67 | C2×2−1+4 | 1 | 2 | yes | — |
| 454 | Dic67 | — | 2 | 1 | no | — |
| 455 | Dic67 | — | 2 | 1 | no | — |
| 456 | Dic67 | — | 2 | 1 | no | — |
| 457 | Dic67 | — | 2 | 1 | no | — |
| 458 | Dic67 | — | 2 | 1 | no | — |
| 459 | Dic67 | — | 4 | 2 | no | — |
| 460 | Dic67 | — | 4 | 2 | no | — |
| 461 | Dic67 | — | 4 | 2 | no | — |
| 462 | Dic67 | — | 4 | 2 | no | — |
| 463 | Dic67 | C2×#137 | 1 | 2 | yes | — |
| 464 | Dic67 | C2×#137 | 1 | 2 | yes | — |
| 465 | Dic67 | #575 | 1 | 2 | yes | — |
| 466 | #60865 | — | 67 | 1 | no | maximal, Sylow |
| 467 | C2×C67 | — | 2 | 2 | no | — |
| 468 | C2×C67 | — | 2 | 2 | no | — |
| 469 | C2×C67 | — | 4 | 1 | no | — |
| 470 | C2×C67 | C2×#536 | 1 | 1 | yes | characteristic |
| 471 | C2×C67 | C22×#137 | 1 | 1 | yes | characteristic |
| 472 | C2×C67 | C2×#575 | 1 | 1 | yes | characteristic |
| 473 | C2×#533 | — | 67 | 1 | no | — |
| 474 | C2×#533 | — | 67 | 1 | no | — |
| 475 | #3237 | — | 67 | 4 | no | — |
| 476 | #3236 | — | 67 | 2 | no | — |
| 477 | #3236 | — | 67 | 2 | no | — |
| 478 | #3231 | — | 67 | 4 | no | — |
| 479 | #3230 | — | 67 | 2 | no | — |
| 480 | #3229 | — | 67 | 2 | no | — |
| 481 | #3165 | — | 67 | 2 | no | — |
| 482 | #3139 | — | 67 | 2 | no | — |
| 483 | #3095 | — | 67 | 1 | no | — |
| 484 | #3095 | — | 67 | 1 | no | — |
| 485 | #3095 | — | 67 | 1 | no | — |
| 486 | #3095 | D67 | 1 | 1 | yes | characteristic |
| 487 | #3078 | — | 67 | 2 | no | — |
| 488 | #3078 | — | 67 | 2 | no | — |
| 489 | #2920 | — | 67 | 1 | no | — |
| 490 | C67 | #60865 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 491 | #533 | — | 67 | 2 | no | — |
| 492 | #533 | — | 67 | 2 | no | — |
| 493 | #533 | — | 67 | 2 | no | — |
| 494 | #533 | — | 67 | 2 | no | — |
| 495 | #533 | — | 67 | 2 | no | — |
| 496 | #533 | — | 67 | 2 | no | — |
| 497 | #533 | — | 67 | 2 | no | — |
| 498 | #533 | — | 67 | 2 | no | — |
| 499 | #533 | — | 134 | 1 | no | — |
| 500 | #533 | — | 134 | 1 | no | — |
| 501 | #533 | — | 134 | 1 | no | — |
| 502 | #533 | — | 134 | 1 | no | — |
| 503 | #533 | — | 134 | 1 | no | — |
| 504 | #533 | — | 134 | 1 | no | — |
| 505 | #533 | — | 134 | 1 | no | — |
| 506 | #533 | — | 134 | 1 | no | — |
| 507 | C2×C4⋊Q8 | — | 67 | 1 | no | — |
| 508 | C2×C4⋊Q8 | — | 67 | 1 | no | — |
| 509 | C2×C4⋊Q8 | — | 67 | 1 | no | — |
| 510 | C2×C4⋊Q8 | — | 67 | 1 | no | — |
| 511 | C2×#125 | — | 67 | 1 | no | — |
| 512 | C2×#125 | — | 67 | 1 | no | — |
| 513 | C2×#125 | — | 134 | 1 | no | — |
| 514 | C2×C22⋊Q8 | — | 67 | 1 | no | — |
| 515 | C2×C22⋊Q8 | — | 134 | 1 | no | — |
| 516 | C2×C22⋊Q8 | — | 134 | 1 | no | — |
| 517 | C2×C22⋊Q8 | — | 134 | 1 | no | — |
| 518 | C2×C22⋊Q8 | C2×D67 | 1 | 1 | yes | characteristic |
| 519 | C2×C4×Q8 | — | 67 | 1 | no | — |
| 520 | C2×C4×Q8 | — | 67 | 1 | no | — |
| 521 | C2×C4×Q8 | — | 134 | 1 | no | — |
| 522 | C2×C4×Q8 | — | 134 | 1 | no | — |
| 523 | C2×C4×Q8 | — | 134 | 1 | no | — |
| 524 | C2×#117 | — | 67 | 1 | no | — |
| 525 | C2×#117 | — | 134 | 1 | no | — |
| 526 | C2×#117 | C2×D67 | 1 | 1 | yes | characteristic |
| 527 | C22×C42 | — | 67 | 1 | no | — |
| 528 | #501 | — | 67 | 4 | no | — |
| 529 | #501 | — | 67 | 4 | no | — |
| 530 | #500 | — | 67 | 4 | no | — |
| 531 | #498 | — | 67 | 4 | no | — |
| 532 | #491 | — | 67 | 4 | no | — |
| 533 | #491 | — | 67 | 4 | no | — |
| 534 | #487 | — | 67 | 4 | no | — |
| 535 | #487 | — | 67 | 4 | no | — |
| 536 | #485 | — | 67 | 4 | no | — |
| 537 | #485 | — | 67 | 4 | no | — |
| 538 | #485 | — | 67 | 4 | no | — |
| 539 | #485 | C2×D67 | 1 | 4 | yes | — |
| 540 | #484 | — | 67 | 2 | no | — |
| 541 | #484 | — | 67 | 2 | no | — |
| 542 | #484 | — | 67 | 2 | no | — |
| 543 | #484 | C2×D67 | 1 | 2 | yes | — |
| 544 | #483 | — | 67 | 2 | no | — |
| 545 | #483 | — | 67 | 2 | no | — |
| 546 | #483 | — | 67 | 2 | no | — |
| 547 | #483 | C2×D67 | 1 | 2 | yes | — |
| 548 | #479 | — | 67 | 4 | no | — |
| 549 | #479 | — | 67 | 4 | no | — |
| 550 | #479 | — | 67 | 4 | no | — |
| 551 | #479 | — | 67 | 4 | no | — |
| 552 | #477 | — | 67 | 4 | no | — |
| 553 | #477 | — | 67 | 4 | no | — |
| 554 | #475 | — | 67 | 4 | no | — |
| 555 | #475 | — | 67 | 4 | no | — |
| 556 | #432 | — | 67 | 2 | no | — |
| 557 | #432 | — | 67 | 2 | no | — |
| 558 | #431 | — | 67 | 2 | no | — |
| 559 | #431 | — | 67 | 2 | no | — |
| 560 | #428 | — | 67 | 2 | no | — |
| 561 | #428 | — | 67 | 2 | no | — |
| 562 | #428 | — | 67 | 2 | no | — |
| 563 | #428 | C2×D67 | 1 | 2 | yes | — |
| 564 | #423 | — | 67 | 2 | no | — |
| 565 | #419 | — | 67 | 2 | no | — |
| 566 | #419 | — | 67 | 2 | no | — |
| 567 | #419 | — | 67 | 2 | no | — |
| 568 | #419 | C2×D67 | 1 | 2 | yes | — |
| 569 | #407 | — | 67 | 1 | no | — |
| 570 | #407 | C2×D67 | 1 | 1 | yes | characteristic |
| 571 | C4×M16 | — | 67 | 2 | no | — |
| 572 | C22×Q8 | — | 67 | 1 | no | — |
| 573 | C22×Q8 | — | 134 | 1 | no | — |
| 574 | C22×Q8 | — | 134 | 1 | no | — |
| 575 | C22×Q8 | — | 134 | 1 | no | — |
| 576 | C22×Q8 | C22×D67 | 1 | 1 | yes | characteristic |
| 577 | C23×C4 | — | 67 | 1 | no | — |
| 578 | C23×C4 | — | 67 | 1 | no | — |
| 579 | C23×C4 | C22×D67 | 1 | 1 | yes | characteristic |
| 580 | C2×M16 | — | 67 | 2 | no | — |
| 581 | C2×M16 | C22×D67 | 1 | 2 | yes | — |
| 582 | C4⋊Q8 | — | 67 | 2 | no | — |
| 583 | C4⋊Q8 | — | 67 | 2 | no | — |
| 584 | C4⋊Q8 | — | 67 | 2 | no | — |
| 585 | C4⋊Q8 | — | 67 | 2 | no | — |
| 586 | C4⋊Q8 | — | 67 | 2 | no | — |
| 587 | C4⋊Q8 | — | 67 | 2 | no | — |
| 588 | C4⋊Q8 | — | 67 | 2 | no | — |
| 589 | C4⋊Q8 | — | 67 | 2 | no | — |
| 590 | C4⋊Q8 | — | 134 | 1 | no | — |
| 591 | C4⋊Q8 | — | 134 | 1 | no | — |
| 592 | C4⋊Q8 | — | 134 | 1 | no | — |
| 593 | C4⋊Q8 | — | 134 | 1 | no | — |
| 594 | C4⋊Q8 | — | 134 | 1 | no | — |
| 595 | C4⋊Q8 | — | 134 | 1 | no | — |
| 596 | C4⋊Q8 | — | 134 | 1 | no | — |
| 597 | C4⋊Q8 | — | 134 | 1 | no | — |
| 598 | #125 | — | 67 | 2 | no | — |
| 599 | #125 | — | 67 | 2 | no | — |
| 600 | #125 | — | 67 | 2 | no | — |
| 601 | #125 | — | 67 | 2 | no | — |
| 602 | #125 | — | 134 | 1 | no | — |
| 603 | #125 | — | 134 | 1 | no | — |
| 604 | #125 | — | 134 | 1 | no | — |
| 605 | #125 | — | 134 | 1 | no | — |
| 606 | #125 | — | 134 | 2 | no | — |
| 607 | #125 | — | 134 | 2 | no | — |
| 608 | #125 | — | 134 | 2 | no | — |
| 609 | #125 | — | 134 | 2 | no | — |
| 610 | C22⋊Q8 | — | 2 | 1 | no | — |
| 611 | C22⋊Q8 | — | 2 | 1 | no | — |
| 612 | C22⋊Q8 | — | 67 | 2 | no | — |
| 613 | C22⋊Q8 | — | 67 | 2 | no | — |
| 614 | C22⋊Q8 | — | 134 | 2 | no | — |
| 615 | C22⋊Q8 | — | 134 | 2 | no | — |
| 616 | C22⋊Q8 | — | 134 | 2 | no | — |
| 617 | C22⋊Q8 | — | 134 | 2 | no | — |
| 618 | C22⋊Q8 | — | 134 | 2 | no | — |
| 619 | C22⋊Q8 | — | 134 | 2 | no | — |
| 620 | C22⋊Q8 | — | 134 | 2 | no | — |
| 621 | C22⋊Q8 | — | 134 | 2 | no | — |
| 622 | C22⋊Q8 | — | 134 | 2 | no | — |
| 623 | C22⋊Q8 | — | 134 | 2 | no | — |
| 624 | C22⋊Q8 | — | 134 | 2 | no | — |
| 625 | C22⋊Q8 | — | 134 | 2 | no | — |
| 626 | C22⋊Q8 | — | 134 | 1 | no | — |
| 627 | C22⋊Q8 | — | 134 | 1 | no | — |
| 628 | C22⋊Q8 | C22×D67 | 1 | 2 | yes | — |
| 629 | C22⋊Q8 | C22×D67 | 1 | 2 | yes | — |
| 630 | C4×Q8 | — | 67 | 2 | no | — |
| 631 | C4×Q8 | — | 67 | 2 | no | — |
| 632 | C4×Q8 | — | 67 | 2 | no | — |
| 633 | C4×Q8 | — | 67 | 2 | no | — |
| 634 | C4×Q8 | — | 134 | 2 | no | — |
| 635 | C4×Q8 | — | 134 | 2 | no | — |
| 636 | C4×Q8 | — | 134 | 2 | no | — |
| 637 | C4×Q8 | — | 134 | 2 | no | — |
| 638 | C4×Q8 | — | 134 | 2 | no | — |
| 639 | C4×Q8 | — | 134 | 2 | no | — |
| 640 | C4×Q8 | — | 134 | 2 | no | — |
| 641 | C4×Q8 | — | 134 | 2 | no | — |
| 642 | C4×Q8 | — | 134 | 1 | no | — |
| 643 | C4×Q8 | — | 134 | 1 | no | — |
| 644 | C4×Q8 | — | 134 | 2 | no | — |
| 645 | C4×Q8 | — | 134 | 2 | no | — |
| 646 | C4×Q8 | — | 134 | 2 | no | — |
| 647 | C4×Q8 | — | 134 | 2 | no | — |
| 648 | C4×Q8 | — | 134 | 1 | no | — |
| 649 | C4×Q8 | — | 134 | 1 | no | — |
| 650 | #117 | — | 2 | 1 | no | — |
| 651 | #117 | — | 2 | 1 | no | — |
| 652 | #117 | — | 67 | 2 | no | — |
| 653 | #117 | — | 67 | 2 | no | — |
| 654 | #117 | — | 134 | 2 | no | — |
| 655 | #117 | — | 134 | 2 | no | — |
| 656 | #117 | — | 134 | 2 | no | — |
| 657 | #117 | — | 134 | 2 | no | — |
| 658 | #117 | — | 134 | 1 | no | — |
| 659 | #117 | — | 134 | 1 | no | — |
| 660 | #117 | C22×D67 | 1 | 2 | yes | — |
| 661 | #117 | C22×D67 | 1 | 2 | yes | — |
| 662 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 663 | C2×C4⋊C4 | — | 67 | 1 | no | — |
| 664 | C2×C4⋊C4 | — | 67 | 1 | no | — |
| 665 | C2×C4⋊C4 | — | 67 | 1 | no | — |
| 666 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 667 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 668 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 669 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 670 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 671 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 672 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 673 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 674 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 675 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 676 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 677 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 678 | C2×C4⋊C4 | C22×D67 | 1 | 1 | yes | characteristic |
| 679 | C2×C4⋊C4 | C22×D67 | 1 | 1 | yes | characteristic |
| 680 | C2×C4⋊C4 | C22×D67 | 1 | 1 | yes | characteristic |
| 681 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 682 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 683 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 684 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 685 | C2×C42 | — | 2 | 1 | no | — |
| 686 | C2×C42 | — | 67 | 1 | no | — |
| 687 | C2×C42 | — | 67 | 1 | no | — |
| 688 | C2×C42 | — | 67 | 1 | no | — |
| 689 | C2×C42 | — | 67 | 1 | no | — |
| 690 | C2×C42 | — | 67 | 1 | no | — |
| 691 | C2×C42 | — | 67 | 1 | no | — |
| 692 | C2×C42 | — | 67 | 1 | no | — |
| 693 | C2×C42 | — | 67 | 1 | no | — |
| 694 | C2×C42 | — | 67 | 1 | no | — |
| 695 | C2×C42 | — | 67 | 1 | no | — |
| 696 | C2×C42 | — | 67 | 1 | no | — |
| 697 | C2×C42 | — | 67 | 1 | no | — |
| 698 | C2×C42 | — | 134 | 1 | no | — |
| 699 | C2×C42 | — | 134 | 1 | no | — |
| 700 | C2×C42 | — | 134 | 1 | no | — |
| 701 | #107 | — | 67 | 4 | no | — |
| 702 | #107 | — | 67 | 4 | no | — |
| 703 | #107 | — | 67 | 4 | no | — |
| 704 | #107 | C22×D67 | 1 | 4 | yes | — |
| 705 | #106 | — | 67 | 4 | no | — |
| 706 | #106 | — | 67 | 4 | no | — |
| 707 | #106 | — | 67 | 4 | no | — |
| 708 | #106 | C22×D67 | 1 | 4 | yes | — |
| 709 | C4⋊C8 | — | 67 | 4 | no | — |
| 710 | C4⋊C8 | — | 67 | 4 | no | — |
| 711 | #103 | — | 67 | 4 | no | — |
| 712 | #103 | — | 67 | 4 | no | — |
| 713 | #103 | — | 67 | 4 | no | — |
| 714 | #103 | — | 67 | 4 | no | — |
| 715 | #103 | — | 67 | 4 | no | — |
| 716 | #103 | — | 67 | 4 | no | — |
| 717 | #103 | C22×D67 | 1 | 4 | yes | — |
| 718 | #103 | C22×D67 | 1 | 4 | yes | — |
| 719 | C22⋊C8 | — | 67 | 2 | no | — |
| 720 | C22⋊C8 | — | 67 | 2 | no | — |
| 721 | C22⋊C8 | C22×D67 | 1 | 2 | yes | — |
| 722 | C22⋊C8 | C22×D67 | 1 | 2 | yes | — |
| 723 | #97 | — | 67 | 4 | no | — |
| 724 | C4×C8 | — | 67 | 4 | no | — |
| 725 | C24 | D4×D67 | 1 | 1 | yes | characteristic |
| 726 | C2×Q8 | — | 2 | 1 | no | — |
| 727 | C2×Q8 | — | 2 | 4 | no | — |
| 728 | C2×Q8 | — | 268 | 4 | no | — |
| 729 | C2×Q8 | — | 268 | 4 | no | — |
| 730 | C2×Q8 | — | 268 | 4 | no | — |
| 731 | C2×Q8 | — | 67 | 2 | no | — |
| 732 | C2×Q8 | — | 134 | 2 | no | — |
| 733 | C2×Q8 | — | 134 | 2 | no | — |
| 734 | C2×Q8 | — | 134 | 2 | no | — |
| 735 | C2×Q8 | — | 134 | 2 | no | — |
| 736 | C2×Q8 | — | 134 | 2 | no | — |
| 737 | C2×Q8 | — | 134 | 2 | no | — |
| 738 | C2×Q8 | — | 134 | 4 | no | — |
| 739 | C2×Q8 | — | 134 | 1 | no | — |
| 740 | C2×Q8 | C23×D67 | 1 | 2 | yes | — |
| 741 | C22×C4 | — | 2 | 4 | no | — |
| 742 | C22×C4 | — | 2 | 1 | no | — |
| 743 | C22×C4 | — | 2 | 1 | no | — |
| 744 | C22×C4 | — | 2 | 1 | no | — |
| 745 | C22×C4 | — | 2 | 1 | no | — |
| 746 | C22×C4 | — | 268 | 2 | no | — |
| 747 | C22×C4 | — | 67 | 1 | no | — |
| 748 | C22×C4 | — | 67 | 1 | no | — |
| 749 | C22×C4 | — | 67 | 1 | no | — |
| 750 | C22×C4 | — | 67 | 1 | no | — |
| 751 | C22×C4 | — | 67 | 1 | no | — |
| 752 | C22×C4 | — | 67 | 1 | no | — |
| 753 | C22×C4 | — | 67 | 1 | no | — |
| 754 | C22×C4 | — | 67 | 1 | no | — |
| 755 | C22×C4 | — | 67 | 1 | no | — |
| 756 | C22×C4 | — | 67 | 1 | no | — |
| 757 | C22×C4 | — | 67 | 1 | no | — |
| 758 | C22×C4 | — | 67 | 1 | no | — |
| 759 | C22×C4 | — | 134 | 1 | no | — |
| 760 | C22×C4 | — | 134 | 1 | no | — |
| 761 | C22×C4 | — | 134 | 1 | no | — |
| 762 | C22×C4 | — | 134 | 1 | no | — |
| 763 | C22×C4 | — | 134 | 4 | no | — |
| 764 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 765 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 766 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 767 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 768 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 769 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 770 | M16 | — | 2 | 4 | no | — |
| 771 | M16 | — | 134 | 4 | no | — |
| 772 | C2×C8 | — | 67 | 4 | no | — |
| 773 | C2×C8 | C23×D67 | 1 | 4 | yes | — |
| 774 | C4⋊C4 | — | 2 | 2 | no | — |
| 775 | C4⋊C4 | — | 2 | 2 | no | — |
| 776 | C4⋊C4 | — | 2 | 1 | no | — |
| 777 | C4⋊C4 | — | 2 | 1 | no | — |
| 778 | C4⋊C4 | — | 2 | 1 | no | — |
| 779 | C4⋊C4 | — | 67 | 2 | no | — |
| 780 | C4⋊C4 | — | 67 | 2 | no | — |
| 781 | C4⋊C4 | — | 67 | 2 | no | — |
| 782 | C4⋊C4 | — | 134 | 2 | no | — |
| 783 | C4⋊C4 | — | 134 | 2 | no | — |
| 784 | C4⋊C4 | — | 134 | 2 | no | — |
| 785 | C4⋊C4 | — | 134 | 2 | no | — |
| 786 | C4⋊C4 | — | 134 | 2 | no | — |
| 787 | C4⋊C4 | — | 134 | 2 | no | — |
| 788 | C4⋊C4 | — | 134 | 2 | no | — |
| 789 | C4⋊C4 | — | 134 | 2 | no | — |
| 790 | C4⋊C4 | — | 134 | 2 | no | — |
| 791 | C4⋊C4 | — | 134 | 2 | no | — |
| 792 | C4⋊C4 | — | 134 | 2 | no | — |
| 793 | C4⋊C4 | — | 134 | 2 | no | — |
| 794 | C4⋊C4 | — | 134 | 2 | no | — |
| 795 | C4⋊C4 | — | 134 | 2 | no | — |
| 796 | C4⋊C4 | — | 134 | 2 | no | — |
| 797 | C4⋊C4 | — | 134 | 2 | no | — |
| 798 | C4⋊C4 | — | 134 | 2 | no | — |
| 799 | C4⋊C4 | — | 134 | 2 | no | — |
| 800 | C4⋊C4 | — | 134 | 2 | no | — |
| 801 | C4⋊C4 | — | 134 | 2 | no | — |
| 802 | C4⋊C4 | — | 134 | 2 | no | — |
| 803 | C4⋊C4 | — | 134 | 2 | no | — |
| 804 | C4⋊C4 | — | 134 | 1 | no | — |
| 805 | C4⋊C4 | — | 134 | 1 | no | — |
| 806 | C4⋊C4 | — | 134 | 1 | no | — |
| 807 | C4⋊C4 | — | 134 | 2 | no | — |
| 808 | C4⋊C4 | — | 134 | 2 | no | — |
| 809 | C4⋊C4 | C23×D67 | 1 | 2 | yes | — |
| 810 | C4⋊C4 | C23×D67 | 1 | 2 | yes | — |
| 811 | C4⋊C4 | C23×D67 | 1 | 2 | yes | — |
| 812 | C22⋊C4 | — | 2 | 2 | no | — |
| 813 | C22⋊C4 | — | 2 | 2 | no | — |
| 814 | C22⋊C4 | — | 2 | 2 | no | — |
| 815 | C22⋊C4 | — | 2 | 2 | no | — |
| 816 | C22⋊C4 | — | 134 | 2 | no | — |
| 817 | C22⋊C4 | — | 134 | 2 | no | — |
| 818 | C22⋊C4 | — | 134 | 2 | no | — |
| 819 | C22⋊C4 | — | 134 | 2 | no | — |
| 820 | C42 | — | 2 | 2 | no | — |
| 821 | C42 | — | 2 | 2 | no | — |
| 822 | C42 | — | 67 | 1 | no | — |
| 823 | C42 | — | 67 | 1 | no | — |
| 824 | C42 | — | 67 | 1 | no | — |
| 825 | C42 | — | 67 | 1 | no | — |
| 826 | C42 | — | 67 | 1 | no | — |
| 827 | C42 | — | 67 | 1 | no | — |
| 828 | C42 | — | 67 | 1 | no | — |
| 829 | C42 | — | 67 | 1 | no | — |
| 830 | C42 | — | 67 | 1 | no | — |
| 831 | C42 | — | 67 | 1 | no | — |
| 832 | C42 | — | 67 | 1 | no | — |
| 833 | C42 | — | 67 | 1 | no | — |
| 834 | C42 | — | 67 | 1 | no | — |
| 835 | C42 | — | 67 | 1 | no | — |
| 836 | C42 | — | 67 | 1 | no | — |
| 837 | C42 | — | 67 | 1 | no | — |
| 838 | C42 | — | 134 | 2 | no | — |
| 839 | C42 | — | 134 | 2 | no | — |
| 840 | C42 | — | 134 | 2 | no | — |
| 841 | C42 | — | 134 | 2 | no | — |
| 842 | C42 | — | 134 | 2 | no | — |
| 843 | C42 | — | 134 | 2 | no | — |
| 844 | C23 | — | 2 | 2 | no | — |
| 845 | C23 | — | 2 | 2 | no | — |
| 846 | C23 | — | 4 | 1 | no | — |
| 847 | C23 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 848 | C23 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 849 | C23 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 850 | Q8 | — | 2 | 4 | no | — |
| 851 | Q8 | — | 4 | 2 | no | — |
| 852 | Q8 | — | 268 | 4 | no | — |
| 853 | Q8 | — | 268 | 4 | no | — |
| 854 | Q8 | — | 268 | 4 | no | — |
| 855 | Q8 | — | 268 | 4 | no | — |
| 856 | Q8 | — | 268 | 4 | no | — |
| 857 | Q8 | — | 268 | 4 | no | — |
| 858 | Q8 | — | 268 | 2 | no | — |
| 859 | Q8 | — | 134 | 4 | no | — |
| 860 | C2×C4 | — | 2 | 2 | no | — |
| 861 | C2×C4 | — | 2 | 2 | no | — |
| 862 | C2×C4 | — | 2 | 2 | no | — |
| 863 | C2×C4 | — | 2 | 2 | no | — |
| 864 | C2×C4 | — | 2 | 2 | no | — |
| 865 | C2×C4 | — | 2 | 2 | no | — |
| 866 | C2×C4 | — | 2 | 2 | no | — |
| 867 | C2×C4 | — | 2 | 2 | no | — |
| 868 | C2×C4 | — | 2 | 2 | no | — |
| 869 | C2×C4 | — | 4 | 2 | no | — |
| 870 | C2×C4 | — | 4 | 2 | no | — |
| 871 | C2×C4 | — | 4 | 2 | no | — |
| 872 | C2×C4 | — | 4 | 2 | no | — |
| 873 | C2×C4 | — | 268 | 2 | no | — |
| 874 | C2×C4 | — | 268 | 2 | no | — |
| 875 | C2×C4 | — | 268 | 2 | no | — |
| 876 | C2×C4 | — | 268 | 2 | no | — |
| 877 | C2×C4 | — | 268 | 1 | no | — |
| 878 | C2×C4 | — | 268 | 1 | no | — |
| 879 | C2×C4 | — | 268 | 1 | no | — |
| 880 | C2×C4 | — | 67 | 4 | no | — |
| 881 | C2×C4 | — | 67 | 1 | no | — |
| 882 | C2×C4 | — | 67 | 1 | no | — |
| 883 | C2×C4 | — | 67 | 1 | no | — |
| 884 | C2×C4 | — | 67 | 1 | no | — |
| 885 | C2×C4 | — | 67 | 1 | no | — |
| 886 | C2×C4 | — | 67 | 1 | no | — |
| 887 | C2×C4 | — | 67 | 1 | no | — |
| 888 | C2×C4 | — | 67 | 1 | no | — |
| 889 | C2×C4 | — | 134 | 2 | no | — |
| 890 | C2×C4 | — | 134 | 2 | no | — |
| 891 | C2×C4 | — | 134 | 2 | no | — |
| 892 | C2×C4 | — | 134 | 2 | no | — |
| 893 | C2×C4 | — | 134 | 2 | no | — |
| 894 | C2×C4 | — | 134 | 2 | no | — |
| 895 | C2×C4 | — | 134 | 2 | no | — |
| 896 | C2×C4 | — | 134 | 2 | no | — |
| 897 | C2×C4 | — | 134 | 2 | no | — |
| 898 | C2×C4 | — | 134 | 2 | no | — |
| 899 | C2×C4 | — | 134 | 2 | no | — |
| 900 | C2×C4 | — | 134 | 2 | no | — |
| 901 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 902 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 903 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 904 | C2×C4 | #14524090 | 1 | 4 | yes | — |
| 905 | C2×C4 | C24×D67 | 1 | 1 | yes | characteristic |
| 906 | C8 | — | 2 | 4 | no | — |
| 907 | C8 | — | 134 | 4 | no | — |
| 908 | C22 | — | 2 | 1 | no | — |
| 909 | C22 | — | 2 | 1 | no | — |
| 910 | C22 | — | 2 | 1 | no | — |
| 911 | C22 | — | 2 | 1 | no | — |
| 912 | C22 | — | 2 | 1 | no | — |
| 913 | C22 | — | 2 | 1 | no | — |
| 914 | C22 | — | 2 | 1 | no | — |
| 915 | C22 | — | 4 | 4 | no | — |
| 916 | C22 | #16863968 | 1 | 2 | yes | — |
| 917 | C22 | #137×D67 | 1 | 2 | yes | — |
| 918 | C22 | C22×D4×D67 | 1 | 1 | yes | characteristic |
| 919 | C4 | — | 2 | 1 | no | — |
| 920 | C4 | — | 2 | 1 | no | — |
| 921 | C4 | — | 4 | 2 | no | — |
| 922 | C4 | — | 4 | 2 | no | — |
| 923 | C4 | — | 4 | 2 | no | — |
| 924 | C4 | — | 4 | 2 | no | — |
| 925 | C4 | — | 268 | 2 | no | — |
| 926 | C4 | — | 268 | 2 | no | — |
| 927 | C4 | — | 268 | 2 | no | — |
| 928 | C4 | — | 268 | 2 | no | — |
| 929 | C4 | — | 67 | 2 | no | — |
| 930 | C4 | — | 67 | 2 | no | — |
| 931 | C4 | — | 67 | 2 | no | — |
| 932 | C4 | — | 134 | 1 | no | — |
| 933 | C4 | — | 134 | 1 | no | — |
| 934 | C4 | — | 134 | 1 | no | — |
| 935 | C4 | — | 134 | 1 | no | — |
| 936 | C4 | — | 134 | 1 | no | — |
| 937 | C4 | #16863968 | 1 | 2 | yes | — |
| 938 | C4 | C2×#14524090 | 1 | 2 | yes | — |
| 939 | C2 | — | 2 | 2 | no | — |
| 940 | C2 | — | 2 | 2 | no | — |
| 941 | C2 | — | 4 | 1 | no | — |
| 942 | C2 | C2×#16863968 | 1 | 1 | yes | characteristic |
| 943 | C2 | C2×#137×D67 | 1 | 1 | yes | characteristic |
| 944 | C2 | #575×D67 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta