← #31764389
Subgroups — #31764389
Order 17152.
6930 conjugacy classes of subgroups.
The subgroup lattice has 760 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22574035 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22574033 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #22574030 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #22574024 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #22574022 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22574016 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #22574008 | C2 | 1 | 12 | yes | maximal, complemented |
| 8 | #22573791 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #22573788 | C2 | 1 | 12 | yes | maximal, complemented |
| 10 | #22573613 | C2 | 1 | 6 | yes | maximal, complemented |
| 11 | C2×#16863952 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #533×D67 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #22573409 | C2 | 1 | 2 | yes | maximal |
| 14 | C4×#41×D67 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | C67×#3504 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#41×D67 | C22 | 1 | 1 | yes | characteristic |
| 17 | Q8×Dic134 | C22 | 1 | 4 | yes | complemented |
| 18 | #16864126 | C22 | 1 | 12 | yes | complemented |
| 19 | #16864124 | C22 | 1 | 12 | yes | complemented |
| 20 | #16864123 | C22 | 1 | 12 | yes | complemented |
| 21 | #16864123 | C22 | 1 | 12 | yes | complemented |
| 22 | #16864122 | C22 | 1 | 4 | yes | complemented |
| 23 | #16864122 | C22 | 1 | 4 | yes | complemented |
| 24 | #16864106 | C22 | 1 | 12 | yes | complemented |
| 25 | #16864105 | C22 | 1 | 12 | yes | complemented |
| 26 | #16864105 | C22 | 1 | 12 | yes | complemented |
| 27 | #16864102 | C22 | 1 | 12 | yes | complemented |
| 28 | #16864102 | C22 | 1 | 12 | yes | complemented |
| 29 | #16864101 | C22 | 1 | 24 | yes | complemented |
| 30 | #16864100 | C22 | 1 | 24 | yes | complemented |
| 31 | #16864100 | C22 | 1 | 24 | yes | complemented |
| 32 | D4×Dic134 | C22 | 1 | 12 | yes | complemented |
| 33 | #16864061 | C22 | 1 | 12 | yes | complemented |
| 34 | #16864059 | C22 | 1 | 24 | yes | complemented |
| 35 | #16864027 | C22 | 1 | 6 | yes | complemented |
| 36 | #16864026 | C22 | 1 | 12 | yes | — |
| 37 | #16864026 | C22 | 1 | 12 | yes | complemented |
| 38 | #16864024 | C22 | 1 | 6 | yes | complemented |
| 39 | #16864024 | C22 | 1 | 6 | yes | complemented |
| 40 | #16864023 | C22 | 1 | 12 | yes | — |
| 41 | #16864023 | C22 | 1 | 12 | yes | complemented |
| 42 | #16864021 | C22 | 1 | 24 | yes | — |
| 43 | #16863953 | C22 | 1 | 3 | yes | complemented |
| 44 | #16863952 | C22 | 1 | 6 | yes | — |
| 45 | #16863952 | C22 | 1 | 1 | yes | characteristic |
| 46 | #16863952 | C22 | 1 | 3 | yes | — |
| 47 | #16863952 | C22 | 1 | 12 | yes | — |
| 48 | #16863952 | C22 | 1 | 12 | yes | complemented |
| 49 | #16863952 | C22 | 1 | 6 | yes | complemented |
| 50 | #16863952 | C22 | 1 | 6 | yes | complemented |
| 51 | #16863952 | C22 | 1 | 12 | yes | complemented |
| 52 | #16863951 | C22 | 1 | 6 | yes | — |
| 53 | #16863951 | C22 | 1 | 12 | yes | complemented |
| 54 | #16863950 | C22 | 1 | 12 | yes | — |
| 55 | #16863949 | C22 | 1 | 6 | yes | complemented |
| 56 | #16863948 | C22 | 1 | 24 | yes | complemented |
| 57 | #16863948 | C22 | 1 | 12 | yes | complemented |
| 58 | C2×#14524042 | C22 | 1 | 6 | yes | complemented |
| 59 | C4⋊Q8×D67 | C22 | 1 | 6 | yes | complemented |
| 60 | C2×#14524035 | C22 | 1 | 3 | yes | complemented |
| 61 | #125×D67 | C22 | 1 | 3 | yes | complemented |
| 62 | #125×D67 | C22 | 1 | 3 | yes | complemented |
| 63 | C2×#14524021 | C22 | 1 | 12 | yes | — |
| 64 | C22⋊Q8×D67 | C22 | 1 | 12 | yes | — |
| 65 | #16863879 | C22 | 1 | 2 | yes | — |
| 66 | #16863877 | C22 | 1 | 6 | yes | — |
| 67 | #16863876 | C22 | 1 | 6 | yes | — |
| 68 | #16863872 | C22 | 1 | 4 | yes | — |
| 69 | #16863868 | C22 | 1 | 12 | yes | — |
| 70 | #41×Dic67 | C22 | 1 | 1 | yes | characteristic |
| 71 | C4×#11761629 | C22 | 1 | 2 | yes | — |
| 72 | C4×#11761629 | C22 | 1 | 4 | yes | — |
| 73 | C4×#11761628 | C22 | 1 | 3 | yes | — |
| 74 | #16863864 | C22 | 1 | 3 | yes | — |
| 75 | C4×#11761627 | C22 | 1 | 6 | yes | — |
| 76 | C4×#11761627 | C22 | 1 | 12 | yes | — |
| 77 | C2×#14524008 | C22 | 1 | 12 | yes | complemented |
| 78 | C4×Q8×D67 | C22 | 1 | 2 | yes | — |
| 79 | C4×Q8×D67 | C22 | 1 | 12 | yes | complemented |
| 80 | C4×D4×D67 | C22 | 1 | 6 | yes | — |
| 81 | C2×#14524001 | C22 | 1 | 6 | yes | — |
| 82 | #117×D67 | C22 | 1 | 3 | yes | — |
| 83 | #117×D67 | C22 | 1 | 6 | yes | — |
| 84 | C2×C42×D67 | C22 | 1 | 3 | yes | — |
| 85 | #557×C67 | C22 | 1 | 4 | yes | complemented |
| 86 | #554×C67 | C22 | 1 | 12 | yes | complemented |
| 87 | #544×C67 | C22 | 1 | 6 | yes | complemented |
| 88 | #533×C67 | C22 | 1 | 3 | yes | complemented |
| 89 | C2×#125×C67 | C22 | 1 | 3 | yes | complemented |
| 90 | #520×C67 | C22 | 1 | 2 | yes | — |
| 91 | C4×#41×C67 | C22 | 1 | 1 | yes | characteristic |
| 92 | C2×#11761629 | C23 | 1 | 1 | yes | characteristic |
| 93 | C2×#11761628 | C23 | 1 | 3 | yes | — |
| 94 | C2×#11761627 | C23 | 1 | 3 | yes | — |
| 95 | #41×D67 | Q8 | 1 | 16 | yes | complemented |
| 96 | C22×Dic134 | C23 | 1 | 12 | yes | — |
| 97 | C2×Q8×D67 | C23 | 1 | 12 | yes | — |
| 98 | C2×Q8×D67 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×D4×D67 | C23 | 1 | 3 | yes | — |
| 100 | C22×C4×D67 | C23 | 1 | 6 | yes | — |
| 101 | C22×C4×D67 | C23 | 1 | 3 | yes | — |
| 102 | #14524043 | C23 | 1 | 6 | yes | — |
| 103 | #14524043 | C23 | 1 | 12 | yes | — |
| 104 | #14524042 | C23 | 1 | 12 | yes | — |
| 105 | #14524042 | C23 | 1 | 12 | yes | — |
| 106 | #14524042 | C23 | 1 | 12 | yes | — |
| 107 | #14524042 | C23 | 1 | 24 | yes | — |
| 108 | #14524042 | C23 | 1 | 12 | yes | — |
| 109 | #14524042 | C23 | 1 | 12 | yes | — |
| 110 | #14524042 | C23 | 1 | 12 | yes | — |
| 111 | #14524042 | C23 | 1 | 2 | yes | — |
| 112 | #14524042 | C23 | 1 | 6 | yes | — |
| 113 | #14524041 | C23 | 1 | 24 | yes | — |
| 114 | #14524041 | C23 | 1 | 12 | yes | — |
| 115 | #14524035 | C23 | 1 | 12 | yes | — |
| 116 | #14524035 | C23 | 1 | 6 | yes | — |
| 117 | #14524035 | C23 | 1 | 12 | yes | — |
| 118 | #14524035 | C23 | 1 | 1 | yes | characteristic |
| 119 | #14524035 | C23 | 1 | 3 | yes | — |
| 120 | #14524034 | C23 | 1 | 12 | yes | — |
| 121 | #14524034 | C23 | 1 | 6 | yes | — |
| 122 | #14524034 | C23 | 1 | 12 | yes | — |
| 123 | #14524034 | C23 | 1 | 6 | yes | — |
| 124 | #14524033 | C23 | 1 | 24 | yes | — |
| 125 | #14524033 | C23 | 1 | 24 | yes | — |
| 126 | #14524033 | C23 | 1 | 12 | yes | — |
| 127 | #14524033 | C23 | 1 | 12 | yes | — |
| 128 | #14524023 | C23 | 1 | 12 | yes | — |
| 129 | #14524023 | C23 | 1 | 24 | yes | — |
| 130 | #14524022 | C23 | 1 | 24 | yes | — |
| 131 | #14524022 | C23 | 1 | 12 | yes | — |
| 132 | #14524021 | C23 | 1 | 24 | yes | — |
| 133 | #14524021 | C23 | 1 | 24 | yes | — |
| 134 | #14524021 | C23 | 1 | 24 | yes | — |
| 135 | #14524021 | C23 | 1 | 24 | yes | — |
| 136 | #14524021 | C23 | 1 | 24 | yes | — |
| 137 | #14524021 | C23 | 1 | 4 | yes | — |
| 138 | #14524021 | C23 | 1 | 12 | yes | — |
| 139 | #14524020 | C23 | 1 | 24 | yes | — |
| 140 | #14524020 | C23 | 1 | 24 | yes | — |
| 141 | #14524020 | C23 | 1 | 12 | yes | — |
| 142 | #14524020 | C23 | 1 | 12 | yes | — |
| 143 | #14524019 | C23 | 1 | 12 | yes | — |
| 144 | #14524019 | C23 | 1 | 24 | yes | — |
| 145 | Q8×Dic67 | C23 | 1 | 2 | yes | — |
| 146 | Q8×Dic67 | C23 | 1 | 12 | yes | — |
| 147 | Q8×Dic67 | C23 | 1 | 4 | yes | — |
| 148 | C4×Dic134 | C23 | 1 | 12 | yes | — |
| 149 | C4×Dic134 | C23 | 1 | 12 | yes | — |
| 150 | C4×Dic134 | C23 | 1 | 12 | yes | — |
| 151 | C4×Dic134 | C23 | 1 | 6 | yes | — |
| 152 | C4×Dic134 | C23 | 1 | 12 | yes | — |
| 153 | #14524008 | C23 | 1 | 24 | yes | — |
| 154 | #14524008 | C23 | 1 | 24 | yes | — |
| 155 | #14524008 | C23 | 1 | 6 | yes | — |
| 156 | #14524008 | C23 | 1 | 4 | yes | — |
| 157 | #14524008 | C23 | 1 | 12 | yes | — |
| 158 | #14524008 | C23 | 1 | 12 | yes | — |
| 159 | #14524008 | C23 | 1 | 24 | yes | — |
| 160 | #14524008 | C23 | 1 | 12 | yes | — |
| 161 | C4×D268 | C23 | 1 | 12 | yes | — |
| 162 | C4×D268 | C23 | 1 | 6 | yes | — |
| 163 | D4×Dic67 | C23 | 1 | 6 | yes | — |
| 164 | D4×Dic67 | C23 | 1 | 12 | yes | — |
| 165 | #14524005 | C23 | 1 | 6 | yes | — |
| 166 | #14524005 | C23 | 1 | 12 | yes | — |
| 167 | C4×C22⋊D67 | C23 | 1 | 24 | yes | — |
| 168 | C4×C22⋊D67 | C23 | 1 | 12 | yes | — |
| 169 | (C22⋊D67)⋊C4 | C23 | 1 | 12 | yes | — |
| 170 | (C22⋊D67)⋊C4 | C23 | 1 | 24 | yes | — |
| 171 | #14524002 | C23 | 1 | 3 | yes | — |
| 172 | #14524002 | C23 | 1 | 6 | yes | — |
| 173 | #14524001 | C23 | 1 | 12 | yes | — |
| 174 | #14524001 | C23 | 1 | 12 | yes | — |
| 175 | #14524001 | C23 | 1 | 2 | yes | — |
| 176 | #14524001 | C23 | 1 | 6 | yes | — |
| 177 | #14524001 | C23 | 1 | 6 | yes | — |
| 178 | #14524001 | C23 | 1 | 12 | yes | — |
| 179 | #14524000 | C23 | 1 | 12 | yes | — |
| 180 | #14524000 | C23 | 1 | 6 | yes | — |
| 181 | #14523999 | C23 | 1 | 12 | yes | — |
| 182 | #14523999 | C23 | 1 | 6 | yes | — |
| 183 | C2×C4⋊Dic67 | C23 | 1 | 6 | yes | — |
| 184 | C2×Dic67⋊C4 | C23 | 1 | 12 | yes | — |
| 185 | C2×Dic67⋊C4 | C23 | 1 | 12 | yes | — |
| 186 | C4⋊C4×D67 | C23 | 1 | 6 | yes | — |
| 187 | C4⋊C4×D67 | C23 | 1 | 6 | yes | — |
| 188 | C4⋊C4×D67 | C23 | 1 | 6 | yes | — |
| 189 | C4⋊C4×D67 | C23 | 1 | 12 | yes | — |
| 190 | C4⋊C4×D67 | C23 | 1 | 12 | yes | — |
| 191 | C4⋊C4×D67 | C23 | 1 | 12 | yes | — |
| 192 | C2×(C2×D67)⋊C4 | C23 | 1 | 12 | yes | — |
| 193 | C22⋊C4×D67 | C23 | 1 | 6 | yes | — |
| 194 | C22⋊C4×D67 | C23 | 1 | 12 | yes | — |
| 195 | C2×C4×Dic67 | C23 | 1 | 6 | yes | — |
| 196 | C2×C4×Dic67 | C23 | 1 | 3 | yes | — |
| 197 | C2×C4×Dic67 | C23 | 1 | 12 | yes | — |
| 198 | C42×D67 | C23 | 1 | 1 | yes | characteristic |
| 199 | C42×D67 | C23 | 1 | 3 | yes | — |
| 200 | C42×D67 | C23 | 1 | 6 | yes | — |
| 201 | C42×D67 | C23 | 1 | 6 | yes | — |
| 202 | C42×D67 | C23 | 1 | 3 | yes | — |
| 203 | C42×D67 | C23 | 1 | 3 | yes | — |
| 204 | C42×D67 | C23 | 1 | 12 | yes | — |
| 205 | C2×#41×C67 | C23 | 1 | 1 | yes | characteristic |
| 206 | C4⋊Q8×C67 | C23 | 1 | 12 | yes | — |
| 207 | C4⋊Q8×C67 | C23 | 1 | 6 | yes | — |
| 208 | #125×C67 | C23 | 1 | 12 | yes | — |
| 209 | #125×C67 | C23 | 1 | 6 | yes | — |
| 210 | #125×C67 | C23 | 1 | 3 | yes | — |
| 211 | #125×C67 | C23 | 1 | 12 | yes | — |
| 212 | #125×C67 | C23 | 1 | 1 | yes | characteristic |
| 213 | C22⋊Q8×C67 | C23 | 1 | 24 | yes | — |
| 214 | C22⋊Q8×C67 | C23 | 1 | 12 | yes | — |
| 215 | C4×Q8×C67 | C23 | 1 | 2 | yes | — |
| 216 | C4×Q8×C67 | C23 | 1 | 4 | yes | — |
| 217 | C4×Q8×C67 | C23 | 1 | 12 | yes | — |
| 218 | C4×D4×C67 | C23 | 1 | 12 | yes | — |
| 219 | C4×D4×C67 | C23 | 1 | 6 | yes | — |
| 220 | #117×C67 | C23 | 1 | 3 | yes | — |
| 221 | #117×C67 | C23 | 1 | 6 | yes | — |
| 222 | C2×C4⋊C4×C67 | C23 | 1 | 6 | yes | — |
| 223 | C2×C4⋊C4×C67 | C23 | 1 | 12 | yes | — |
| 224 | C2×C42×C67 | C23 | 1 | 3 | yes | — |
| 225 | C23×D67 | C24 | 1 | 3 | yes | — |
| 226 | #11761629 | C2×Q8 | 1 | 8 | yes | complemented |
| 227 | #11761628 | C2×Q8 | 1 | 24 | yes | complemented |
| 228 | #11761627 | C2×Q8 | 1 | 24 | yes | complemented |
| 229 | C2×Dic134 | — | 4 | 24 | no | — |
| 230 | C2×Dic134 | C24 | 1 | 12 | yes | — |
| 231 | C2×Dic134 | C24 | 1 | 4 | yes | — |
| 232 | C2×Dic134 | C24 | 1 | 24 | yes | — |
| 233 | C2×Dic134 | C24 | 1 | 12 | yes | — |
| 234 | C2×Dic134 | C24 | 1 | 3 | yes | — |
| 235 | Q8×D67 | — | 4 | 24 | no | — |
| 236 | Q8×D67 | C2×Q8 | 1 | 8 | yes | complemented |
| 237 | C2×D268 | C24 | 1 | 3 | yes | — |
| 238 | C2×C22⋊D67 | C24 | 1 | 6 | yes | — |
| 239 | D4×D67 | C2×Q8 | 1 | 24 | yes | complemented |
| 240 | C22×Dic67 | C24 | 1 | 6 | yes | — |
| 241 | C22×Dic67 | C24 | 1 | 12 | yes | — |
| 242 | C22×Dic67 | C24 | 1 | 3 | yes | — |
| 243 | C2×C4×D67 | — | 4 | 12 | no | — |
| 244 | C2×C4×D67 | C2×Q8 | 1 | 24 | yes | complemented |
| 245 | C2×C4×D67 | C24 | 1 | 2 | yes | — |
| 246 | C2×C4×D67 | C24 | 1 | 6 | yes | — |
| 247 | C2×C4×D67 | C24 | 1 | 6 | yes | — |
| 248 | C2×C4×D67 | C24 | 1 | 6 | yes | — |
| 249 | C2×C4×D67 | C24 | 1 | 12 | yes | — |
| 250 | C2×C4×D67 | C24 | 1 | 12 | yes | — |
| 251 | C2×C4×D67 | C24 | 1 | 3 | yes | — |
| 252 | C2×C4×D67 | C24 | 1 | 1 | yes | characteristic |
| 253 | C2×C4×D67 | C24 | 1 | 3 | yes | — |
| 254 | C2×C4×D67 | C24 | 1 | 3 | yes | — |
| 255 | C4⋊Dic67 | C24 | 1 | 2 | yes | — |
| 256 | C4⋊Dic67 | C24 | 1 | 6 | yes | — |
| 257 | C4⋊Dic67 | C24 | 1 | 6 | yes | — |
| 258 | C4⋊Dic67 | C24 | 1 | 12 | yes | — |
| 259 | C4⋊Dic67 | C24 | 1 | 12 | yes | — |
| 260 | C4⋊Dic67 | C24 | 1 | 12 | yes | — |
| 261 | C4⋊Dic67 | C24 | 1 | 12 | yes | — |
| 262 | Dic67⋊C4 | C24 | 1 | 4 | yes | — |
| 263 | Dic67⋊C4 | C24 | 1 | 4 | yes | — |
| 264 | Dic67⋊C4 | C24 | 1 | 12 | yes | — |
| 265 | Dic67⋊C4 | C24 | 1 | 12 | yes | — |
| 266 | Dic67⋊C4 | C24 | 1 | 12 | yes | — |
| 267 | Dic67⋊C4 | C24 | 1 | 12 | yes | — |
| 268 | Dic67⋊C4 | C24 | 1 | 12 | yes | — |
| 269 | Dic67⋊C4 | C24 | 1 | 12 | yes | — |
| 270 | Dic67⋊C4 | C24 | 1 | 12 | yes | — |
| 271 | Dic67⋊C4 | C24 | 1 | 24 | yes | — |
| 272 | Dic67⋊C4 | C24 | 1 | 24 | yes | — |
| 273 | C22⋊Dic67 | C24 | 1 | 12 | yes | — |
| 274 | C22⋊Dic67 | C24 | 1 | 6 | yes | — |
| 275 | (C2×D67)⋊C4 | C24 | 1 | 4 | yes | — |
| 276 | (C2×D67)⋊C4 | C24 | 1 | 12 | yes | — |
| 277 | (C2×D67)⋊C4 | C24 | 1 | 12 | yes | — |
| 278 | (C2×D67)⋊C4 | C24 | 1 | 24 | yes | — |
| 279 | C4×Dic67 | C24 | 1 | 2 | yes | — |
| 280 | C4×Dic67 | C24 | 1 | 1 | yes | characteristic |
| 281 | C4×Dic67 | C24 | 1 | 4 | yes | — |
| 282 | C4×Dic67 | C24 | 1 | 6 | yes | — |
| 283 | C4×Dic67 | C24 | 1 | 3 | yes | — |
| 284 | C4×Dic67 | C24 | 1 | 6 | yes | — |
| 285 | C4×Dic67 | C24 | 1 | 6 | yes | — |
| 286 | C4×Dic67 | C24 | 1 | 6 | yes | — |
| 287 | C4×Dic67 | C24 | 1 | 12 | yes | — |
| 288 | C4×Dic67 | C24 | 1 | 12 | yes | — |
| 289 | C4×Dic67 | C24 | 1 | 24 | yes | — |
| 290 | #41×C67 | C2×Q8 | 1 | 8 | yes | complemented |
| 291 | C2×Q8×C67 | C24 | 1 | 12 | yes | — |
| 292 | C2×Q8×C67 | C24 | 1 | 1 | yes | characteristic |
| 293 | C2×D4×C67 | C24 | 1 | 3 | yes | — |
| 294 | C22×C4×C67 | C24 | 1 | 6 | yes | — |
| 295 | C22×C4×C67 | C24 | 1 | 12 | yes | — |
| 296 | C22×C4×C67 | C24 | 1 | 3 | yes | — |
| 297 | C4⋊C4×C67 | C24 | 1 | 6 | yes | — |
| 298 | C4⋊C4×C67 | C24 | 1 | 12 | yes | — |
| 299 | C4⋊C4×C67 | C24 | 1 | 12 | yes | — |
| 300 | C4⋊C4×C67 | C24 | 1 | 24 | yes | — |
| 301 | C4⋊C4×C67 | C24 | 1 | 2 | yes | — |
| 302 | C4⋊C4×C67 | C24 | 1 | 6 | yes | — |
| 303 | C4⋊C4×C67 | C24 | 1 | 4 | yes | — |
| 304 | C4⋊C4×C67 | C24 | 1 | 12 | yes | — |
| 305 | C22⋊C4×C67 | C24 | 1 | 12 | yes | — |
| 306 | C22⋊C4×C67 | C24 | 1 | 6 | yes | — |
| 307 | C42×C67 | C24 | 1 | 1 | yes | characteristic |
| 308 | C42×C67 | C24 | 1 | 3 | yes | — |
| 309 | C42×C67 | C24 | 1 | 6 | yes | — |
| 310 | C42×C67 | C24 | 1 | 12 | yes | — |
| 311 | C23×C67 | C25 | 1 | 3 | yes | — |
| 312 | C22×D67 | — | 4 | 6 | no | — |
| 313 | C22×D67 | C22×Q8 | 1 | 12 | yes | — |
| 314 | C22×D67 | C25 | 1 | 1 | yes | characteristic |
| 315 | C22×D67 | C25 | 1 | 3 | yes | — |
| 316 | Q8×C67 | — | 4 | 12 | no | — |
| 317 | Q8×C67 | C22×Q8 | 1 | 4 | yes | — |
| 318 | D4×C67 | C22×Q8 | 1 | 12 | yes | — |
| 319 | C2×C4×C67 | — | 4 | 6 | no | — |
| 320 | C2×C4×C67 | — | 4 | 12 | no | — |
| 321 | C2×C4×C67 | C22×Q8 | 1 | 12 | yes | — |
| 322 | C2×C4×C67 | C25 | 1 | 2 | yes | — |
| 323 | C2×C4×C67 | C25 | 1 | 4 | yes | — |
| 324 | C2×C4×C67 | C25 | 1 | 6 | yes | — |
| 325 | C2×C4×C67 | C25 | 1 | 12 | yes | — |
| 326 | C2×C4×C67 | C25 | 1 | 3 | yes | — |
| 327 | C2×C4×C67 | C25 | 1 | 1 | yes | characteristic |
| 328 | C22⋊D67 | C22×Q8 | 1 | 24 | yes | — |
| 329 | C2×Dic67 | — | 2 | 12 | no | — |
| 330 | C2×Dic67 | — | 4 | 12 | no | — |
| 331 | C2×Dic67 | C22×Q8 | 1 | 12 | yes | — |
| 332 | C2×Dic67 | C25 | 1 | 12 | yes | — |
| 333 | C2×Dic67 | C25 | 1 | 6 | yes | — |
| 334 | C2×Dic67 | C25 | 1 | 4 | yes | — |
| 335 | C2×Dic67 | C25 | 1 | 1 | yes | characteristic |
| 336 | C2×Dic67 | C25 | 1 | 3 | yes | — |
| 337 | C2×Dic67 | C25 | 1 | 2 | yes | — |
| 338 | D268 | C22×Q8 | 1 | 12 | yes | — |
| 339 | C4×D67 | — | 2 | 4 | no | — |
| 340 | C4×D67 | — | 2 | 12 | no | — |
| 341 | C4×D67 | — | 4 | 6 | no | — |
| 342 | C4×D67 | — | 4 | 6 | no | — |
| 343 | C4×D67 | — | 4 | 12 | no | — |
| 344 | C4×D67 | — | 4 | 12 | no | — |
| 345 | C4×D67 | C22×Q8 | 1 | 4 | yes | — |
| 346 | C4×D67 | C22×Q8 | 1 | 12 | yes | — |
| 347 | C4×D67 | C22×Q8 | 1 | 12 | yes | — |
| 348 | C4×D67 | C22×Q8 | 1 | 12 | yes | — |
| 349 | Dic134 | — | 2 | 8 | no | — |
| 350 | Dic134 | — | 2 | 24 | no | — |
| 351 | Dic134 | — | 4 | 12 | no | — |
| 352 | Dic134 | — | 4 | 24 | no | — |
| 353 | Dic134 | C22×Q8 | 1 | 12 | yes | — |
| 354 | C22×C67 | — | 2 | 6 | no | — |
| 355 | C22×C67 | C23×Q8 | 1 | 6 | yes | — |
| 356 | C22×C67 | C26 | 1 | 1 | yes | characteristic |
| 357 | C2×D67 | — | 2 | 6 | no | — |
| 358 | C2×D67 | — | 2 | 2 | no | — |
| 359 | C2×D67 | — | 4 | 12 | no | — |
| 360 | C2×D67 | C23×Q8 | 1 | 2 | yes | — |
| 361 | C2×D67 | C23×Q8 | 1 | 6 | yes | — |
| 362 | C4×C67 | — | 2 | 12 | no | — |
| 363 | C4×C67 | — | 2 | 4 | no | — |
| 364 | C4×C67 | — | 2 | 6 | no | — |
| 365 | C4×C67 | — | 2 | 2 | no | — |
| 366 | C4×C67 | C23×Q8 | 1 | 6 | yes | — |
| 367 | C4×C67 | C23×Q8 | 1 | 2 | yes | — |
| 368 | Dic67 | — | 2 | 4 | no | — |
| 369 | Dic67 | — | 2 | 12 | no | — |
| 370 | Dic67 | — | 2 | 6 | no | — |
| 371 | Dic67 | C23×Q8 | 1 | 6 | yes | — |
| 372 | Dic67 | C23×Q8 | 1 | 2 | yes | — |
| 373 | Dic67 | #585 | 1 | 4 | yes | — |
| 374 | #62813 | — | 67 | 1 | no | maximal, Sylow |
| 375 | C2×C67 | — | 2 | 6 | no | — |
| 376 | C2×C67 | C24×Q8 | 1 | 1 | yes | characteristic |
| 377 | C2×C67 | C2×#585 | 1 | 2 | yes | — |
| 378 | D67 | — | 2 | 2 | no | — |
| 379 | D67 | — | 2 | 6 | no | — |
| 380 | #3504 | — | 67 | 3 | no | — |
| 381 | #3504 | — | 67 | 3 | no | — |
| 382 | #3504 | — | 67 | 1 | no | — |
| 383 | #3504 | D67 | 1 | 1 | yes | characteristic, complemented |
| 384 | #3503 | — | 67 | 6 | no | — |
| 385 | #3503 | — | 67 | 2 | no | — |
| 386 | #3502 | — | 67 | 4 | no | — |
| 387 | #3501 | — | 67 | 12 | no | — |
| 388 | Q8×#41 | — | 67 | 4 | no | — |
| 389 | Q8×#41 | — | 67 | 12 | no | — |
| 390 | #3458 | — | 67 | 6 | no | — |
| 391 | C2×#533 | — | 67 | 3 | no | — |
| 392 | C2×#533 | — | 67 | 3 | no | — |
| 393 | #3428 | — | 67 | 2 | no | — |
| 394 | C2×C4×#41 | — | 67 | 1 | no | — |
| 395 | C67 | #62813 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 396 | C22×#41 | — | 67 | 1 | no | — |
| 397 | Q82 | — | 67 | 12 | no | — |
| 398 | Q82 | — | 67 | 4 | no | — |
| 399 | #557 | — | 67 | 12 | no | — |
| 400 | #557 | — | 67 | 12 | no | — |
| 401 | #557 | — | 67 | 4 | no | — |
| 402 | #557 | — | 67 | 4 | no | — |
| 403 | #557 | — | 67 | 12 | no | — |
| 404 | #557 | C2×D67 | 1 | 4 | yes | complemented |
| 405 | #554 | — | 67 | 12 | no | — |
| 406 | #554 | — | 67 | 12 | no | — |
| 407 | #554 | — | 67 | 24 | no | — |
| 408 | #554 | — | 67 | 24 | no | — |
| 409 | #554 | — | 67 | 12 | no | — |
| 410 | #554 | — | 67 | 12 | no | — |
| 411 | #554 | — | 67 | 12 | no | — |
| 412 | #554 | — | 67 | 24 | no | — |
| 413 | #554 | C2×D67 | 1 | 12 | yes | complemented |
| 414 | D4×Q8 | — | 67 | 12 | no | — |
| 415 | D4×Q8 | — | 67 | 24 | no | — |
| 416 | D4×Q8 | — | 67 | 12 | no | — |
| 417 | #544 | — | 67 | 12 | no | — |
| 418 | #544 | — | 67 | 12 | no | — |
| 419 | #544 | — | 67 | 12 | no | — |
| 420 | #544 | — | 67 | 12 | no | — |
| 421 | #544 | — | 67 | 6 | no | — |
| 422 | #544 | — | 67 | 6 | no | — |
| 423 | #544 | — | 67 | 6 | no | — |
| 424 | #544 | C2×D67 | 1 | 6 | yes | complemented |
| 425 | #543 | — | 67 | 24 | no | — |
| 426 | #533 | — | 67 | 6 | no | — |
| 427 | #533 | — | 67 | 12 | no | — |
| 428 | #533 | — | 67 | 1 | no | — |
| 429 | #533 | — | 67 | 3 | no | — |
| 430 | #533 | — | 67 | 6 | no | — |
| 431 | #533 | — | 67 | 12 | no | — |
| 432 | #533 | — | 67 | 12 | no | — |
| 433 | #533 | — | 67 | 6 | no | — |
| 434 | #533 | — | 67 | 6 | no | — |
| 435 | #533 | — | 67 | 12 | no | — |
| 436 | #533 | — | 67 | 12 | no | — |
| 437 | #533 | — | 67 | 24 | no | — |
| 438 | #533 | — | 67 | 12 | no | — |
| 439 | #533 | — | 67 | 6 | no | — |
| 440 | #533 | — | 67 | 3 | no | — |
| 441 | #533 | C2×D67 | 1 | 3 | yes | complemented |
| 442 | C2×C4⋊Q8 | — | 67 | 6 | no | — |
| 443 | C2×C4⋊Q8 | — | 67 | 6 | no | — |
| 444 | C2×#125 | — | 67 | 3 | no | — |
| 445 | C2×#125 | — | 67 | 3 | no | — |
| 446 | C2×#125 | — | 67 | 3 | no | — |
| 447 | C2×#125 | C2×D67 | 1 | 3 | yes | complemented |
| 448 | C2×C22⋊Q8 | — | 67 | 12 | no | — |
| 449 | C2×C22⋊Q8 | — | 67 | 12 | no | — |
| 450 | #520 | — | 67 | 2 | no | — |
| 451 | #520 | — | 67 | 6 | no | — |
| 452 | #520 | — | 67 | 6 | no | — |
| 453 | #520 | C2×D67 | 1 | 2 | yes | — |
| 454 | #519 | — | 67 | 4 | no | — |
| 455 | #518 | — | 67 | 12 | no | — |
| 456 | C4×#41 | — | 67 | 1 | no | — |
| 457 | C4×#41 | — | 67 | 2 | no | — |
| 458 | C4×#41 | — | 67 | 4 | no | — |
| 459 | C4×#41 | — | 67 | 6 | no | — |
| 460 | C4×#41 | — | 67 | 12 | no | — |
| 461 | C4×#41 | — | 67 | 3 | no | — |
| 462 | C4×#41 | — | 67 | 3 | no | — |
| 463 | C4×#41 | C2×D67 | 1 | 1 | yes | characteristic |
| 464 | C2×C4×Q8 | — | 67 | 2 | no | — |
| 465 | C2×C4×Q8 | — | 67 | 12 | no | — |
| 466 | C2×C4×Q8 | — | 67 | 12 | no | — |
| 467 | C2×C4×D4 | — | 67 | 6 | no | — |
| 468 | C2×#117 | — | 67 | 3 | no | — |
| 469 | C2×#117 | — | 67 | 6 | no | — |
| 470 | C2×#117 | — | 67 | 6 | no | — |
| 471 | C22×C42 | — | 67 | 3 | no | — |
| 472 | C2×#41 | — | 67 | 16 | no | — |
| 473 | C2×#41 | — | 67 | 1 | no | — |
| 474 | C2×#41 | — | 67 | 3 | no | — |
| 475 | C2×#41 | — | 67 | 3 | no | — |
| 476 | C2×#41 | C22×D67 | 1 | 1 | yes | characteristic |
| 477 | C22×Q8 | — | 67 | 12 | no | — |
| 478 | C22×Q8 | — | 67 | 1 | no | — |
| 479 | C22×Q8 | — | 67 | 12 | no | — |
| 480 | C22×D4 | — | 67 | 3 | no | — |
| 481 | C23×C4 | — | 67 | 6 | no | — |
| 482 | C23×C4 | — | 67 | 3 | no | — |
| 483 | C4⋊Q8 | — | 67 | 12 | no | — |
| 484 | C4⋊Q8 | — | 67 | 24 | no | — |
| 485 | C4⋊Q8 | — | 67 | 2 | no | — |
| 486 | C4⋊Q8 | — | 67 | 6 | no | — |
| 487 | C4⋊Q8 | — | 67 | 12 | no | — |
| 488 | C4⋊Q8 | — | 67 | 12 | no | — |
| 489 | C4⋊Q8 | — | 67 | 12 | no | — |
| 490 | C4⋊Q8 | — | 67 | 12 | no | — |
| 491 | C4⋊Q8 | — | 67 | 24 | no | — |
| 492 | C4⋊Q8 | — | 67 | 12 | no | — |
| 493 | C4⋊Q8 | — | 67 | 12 | no | — |
| 494 | C4⋊Q8 | — | 67 | 6 | no | — |
| 495 | C4⋊Q8 | — | 67 | 12 | no | — |
| 496 | C4⋊Q8 | C22×D67 | 1 | 6 | yes | — |
| 497 | C4⋊Q8 | C22×D67 | 1 | 12 | yes | — |
| 498 | #125 | — | 67 | 6 | no | — |
| 499 | #125 | — | 67 | 6 | no | — |
| 500 | #125 | — | 67 | 12 | no | — |
| 501 | #125 | — | 67 | 12 | no | — |
| 502 | #125 | — | 67 | 24 | no | — |
| 503 | #125 | — | 67 | 24 | no | — |
| 504 | #125 | — | 67 | 12 | no | — |
| 505 | #125 | — | 67 | 12 | no | — |
| 506 | #125 | — | 67 | 1 | no | — |
| 507 | #125 | — | 67 | 3 | no | — |
| 508 | #125 | — | 67 | 6 | no | — |
| 509 | #125 | — | 67 | 12 | no | — |
| 510 | #125 | — | 67 | 12 | no | — |
| 511 | #125 | C22×D67 | 1 | 1 | yes | characteristic |
| 512 | #125 | C22×D67 | 1 | 3 | yes | — |
| 513 | #125 | C22×D67 | 1 | 6 | yes | — |
| 514 | #125 | C22×D67 | 1 | 12 | yes | — |
| 515 | #125 | C22×D67 | 1 | 12 | yes | — |
| 516 | C22⋊Q8 | — | 67 | 12 | no | — |
| 517 | C22⋊Q8 | — | 67 | 24 | no | — |
| 518 | C22⋊Q8 | — | 67 | 12 | no | — |
| 519 | C22⋊Q8 | — | 67 | 24 | no | — |
| 520 | C22⋊Q8 | — | 67 | 4 | no | — |
| 521 | C22⋊Q8 | — | 67 | 12 | no | — |
| 522 | C22⋊Q8 | — | 67 | 24 | no | — |
| 523 | C22⋊Q8 | — | 67 | 12 | no | — |
| 524 | C22⋊Q8 | — | 67 | 24 | no | — |
| 525 | C22⋊Q8 | — | 67 | 24 | no | — |
| 526 | C22⋊Q8 | — | 67 | 24 | no | — |
| 527 | C22⋊Q8 | — | 67 | 24 | no | — |
| 528 | C22⋊Q8 | — | 67 | 24 | no | — |
| 529 | C22⋊Q8 | — | 67 | 12 | no | — |
| 530 | C22⋊Q8 | — | 67 | 12 | no | — |
| 531 | C22⋊Q8 | — | 67 | 24 | no | — |
| 532 | C22⋊Q8 | — | 67 | 24 | no | — |
| 533 | C22⋊Q8 | C22×D67 | 1 | 12 | yes | — |
| 534 | C22⋊Q8 | C22×D67 | 1 | 24 | yes | — |
| 535 | C4×Q8 | — | 67 | 2 | no | — |
| 536 | C4×Q8 | — | 67 | 12 | no | — |
| 537 | C4×Q8 | — | 67 | 4 | no | — |
| 538 | C4×Q8 | — | 67 | 4 | no | — |
| 539 | C4×Q8 | — | 67 | 12 | no | — |
| 540 | C4×Q8 | — | 67 | 6 | no | — |
| 541 | C4×Q8 | — | 67 | 12 | no | — |
| 542 | C4×Q8 | — | 67 | 24 | no | — |
| 543 | C4×Q8 | — | 67 | 24 | no | — |
| 544 | C4×Q8 | — | 67 | 24 | no | — |
| 545 | C4×Q8 | — | 67 | 12 | no | — |
| 546 | C4×Q8 | — | 67 | 6 | no | — |
| 547 | C4×Q8 | — | 67 | 12 | no | — |
| 548 | C4×Q8 | — | 67 | 12 | no | — |
| 549 | C4×Q8 | — | 67 | 12 | no | — |
| 550 | C4×Q8 | — | 67 | 12 | no | — |
| 551 | C4×Q8 | C22×D67 | 1 | 2 | yes | — |
| 552 | C4×Q8 | C22×D67 | 1 | 12 | yes | — |
| 553 | C4×Q8 | C22×D67 | 1 | 4 | yes | — |
| 554 | C4×D4 | — | 67 | 6 | no | — |
| 555 | C4×D4 | — | 67 | 12 | no | — |
| 556 | C4×D4 | — | 67 | 12 | no | — |
| 557 | C4×D4 | — | 67 | 24 | no | — |
| 558 | C4×D4 | — | 67 | 6 | no | — |
| 559 | C4×D4 | — | 67 | 12 | no | — |
| 560 | C4×D4 | — | 67 | 12 | no | — |
| 561 | C4×D4 | — | 67 | 24 | no | — |
| 562 | C4×D4 | — | 67 | 6 | no | — |
| 563 | C4×D4 | — | 67 | 12 | no | — |
| 564 | C4×D4 | C22×D67 | 1 | 6 | yes | — |
| 565 | C4×D4 | C22×D67 | 1 | 12 | yes | — |
| 566 | #117 | — | 67 | 3 | no | — |
| 567 | #117 | — | 67 | 6 | no | — |
| 568 | #117 | — | 67 | 2 | no | — |
| 569 | #117 | — | 67 | 6 | no | — |
| 570 | #117 | — | 67 | 6 | no | — |
| 571 | #117 | — | 67 | 12 | no | — |
| 572 | #117 | — | 67 | 12 | no | — |
| 573 | #117 | — | 67 | 12 | no | — |
| 574 | #117 | — | 67 | 6 | no | — |
| 575 | #117 | — | 67 | 12 | no | — |
| 576 | #117 | — | 67 | 6 | no | — |
| 577 | #117 | — | 67 | 12 | no | — |
| 578 | #117 | C22×D67 | 1 | 3 | yes | — |
| 579 | #117 | C22×D67 | 1 | 6 | yes | — |
| 580 | C2×C4⋊C4 | — | 67 | 6 | no | — |
| 581 | C2×C4⋊C4 | — | 67 | 12 | no | — |
| 582 | C2×C4⋊C4 | — | 67 | 12 | no | — |
| 583 | C2×C4⋊C4 | — | 67 | 6 | no | — |
| 584 | C2×C4⋊C4 | — | 67 | 6 | no | — |
| 585 | C2×C4⋊C4 | — | 67 | 6 | no | — |
| 586 | C2×C4⋊C4 | — | 67 | 12 | no | — |
| 587 | C2×C4⋊C4 | — | 67 | 12 | no | — |
| 588 | C2×C4⋊C4 | — | 67 | 12 | no | — |
| 589 | C2×C4⋊C4 | C22×D67 | 1 | 6 | yes | — |
| 590 | C2×C4⋊C4 | C22×D67 | 1 | 12 | yes | — |
| 591 | C2×C22⋊C4 | — | 67 | 12 | no | — |
| 592 | C2×C22⋊C4 | — | 67 | 6 | no | — |
| 593 | C2×C22⋊C4 | — | 67 | 12 | no | — |
| 594 | C2×C42 | — | 67 | 12 | no | — |
| 595 | C2×C42 | — | 67 | 6 | no | — |
| 596 | C2×C42 | — | 67 | 3 | no | — |
| 597 | C2×C42 | — | 67 | 3 | no | — |
| 598 | C2×C42 | — | 67 | 12 | no | — |
| 599 | C2×C42 | — | 67 | 6 | no | — |
| 600 | C2×C42 | — | 67 | 6 | no | — |
| 601 | C2×C42 | — | 67 | 3 | no | — |
| 602 | C2×C42 | — | 67 | 3 | no | — |
| 603 | C2×C42 | — | 67 | 1 | no | — |
| 604 | C2×C42 | C22×D67 | 1 | 3 | yes | — |
| 605 | C24 | — | 67 | 3 | no | — |
| 606 | #41 | — | 67 | 8 | no | — |
| 607 | #41 | — | 67 | 24 | no | — |
| 608 | #41 | — | 67 | 24 | no | — |
| 609 | #41 | Q8×D67 | 1 | 8 | yes | complemented |
| 610 | C2×Q8 | — | 268 | 24 | no | — |
| 611 | C2×Q8 | — | 268 | 24 | no | — |
| 612 | C2×Q8 | — | 67 | 8 | no | — |
| 613 | C2×Q8 | — | 67 | 24 | no | — |
| 614 | C2×Q8 | — | 67 | 12 | no | — |
| 615 | C2×Q8 | — | 67 | 3 | no | — |
| 616 | C2×Q8 | — | 67 | 12 | no | — |
| 617 | C2×Q8 | — | 67 | 4 | no | — |
| 618 | C2×Q8 | C23×D67 | 1 | 12 | yes | — |
| 619 | C2×Q8 | C23×D67 | 1 | 1 | yes | characteristic |
| 620 | C2×D4 | — | 67 | 6 | no | — |
| 621 | C2×D4 | — | 67 | 24 | no | — |
| 622 | C2×D4 | — | 67 | 3 | no | — |
| 623 | C2×D4 | C23×D67 | 1 | 3 | yes | — |
| 624 | C22×C4 | — | 268 | 12 | no | — |
| 625 | C22×C4 | — | 67 | 12 | no | — |
| 626 | C22×C4 | — | 67 | 6 | no | — |
| 627 | C22×C4 | — | 67 | 6 | no | — |
| 628 | C22×C4 | — | 67 | 12 | no | — |
| 629 | C22×C4 | — | 67 | 12 | no | — |
| 630 | C22×C4 | — | 67 | 3 | no | — |
| 631 | C22×C4 | — | 67 | 24 | no | — |
| 632 | C22×C4 | — | 67 | 3 | no | — |
| 633 | C22×C4 | — | 67 | 1 | no | — |
| 634 | C22×C4 | — | 67 | 3 | no | — |
| 635 | C22×C4 | — | 67 | 3 | no | — |
| 636 | C22×C4 | — | 67 | 6 | no | — |
| 637 | C22×C4 | — | 67 | 2 | no | — |
| 638 | C22×C4 | — | 67 | 6 | no | — |
| 639 | C22×C4 | C23×D67 | 1 | 6 | yes | — |
| 640 | C22×C4 | C23×D67 | 1 | 12 | yes | — |
| 641 | C22×C4 | C23×D67 | 1 | 3 | yes | — |
| 642 | C4⋊C4 | — | 67 | 6 | no | — |
| 643 | C4⋊C4 | — | 67 | 2 | no | — |
| 644 | C4⋊C4 | — | 67 | 12 | no | — |
| 645 | C4⋊C4 | — | 67 | 4 | no | — |
| 646 | C4⋊C4 | — | 67 | 12 | no | — |
| 647 | C4⋊C4 | — | 67 | 4 | no | — |
| 648 | C4⋊C4 | — | 67 | 12 | no | — |
| 649 | C4⋊C4 | — | 67 | 12 | no | — |
| 650 | C4⋊C4 | — | 67 | 12 | no | — |
| 651 | C4⋊C4 | — | 67 | 12 | no | — |
| 652 | C4⋊C4 | — | 67 | 6 | no | — |
| 653 | C4⋊C4 | — | 67 | 24 | no | — |
| 654 | C4⋊C4 | — | 67 | 12 | no | — |
| 655 | C4⋊C4 | — | 67 | 24 | no | — |
| 656 | C4⋊C4 | — | 67 | 12 | no | — |
| 657 | C4⋊C4 | — | 67 | 12 | no | — |
| 658 | C4⋊C4 | — | 67 | 12 | no | — |
| 659 | C4⋊C4 | — | 67 | 12 | no | — |
| 660 | C4⋊C4 | C23×D67 | 1 | 2 | yes | — |
| 661 | C4⋊C4 | C23×D67 | 1 | 4 | yes | — |
| 662 | C4⋊C4 | C23×D67 | 1 | 6 | yes | — |
| 663 | C4⋊C4 | C23×D67 | 1 | 12 | yes | — |
| 664 | C4⋊C4 | C23×D67 | 1 | 6 | yes | — |
| 665 | C4⋊C4 | C23×D67 | 1 | 12 | yes | — |
| 666 | C4⋊C4 | C23×D67 | 1 | 12 | yes | — |
| 667 | C4⋊C4 | C23×D67 | 1 | 24 | yes | — |
| 668 | C22⋊C4 | — | 67 | 6 | no | — |
| 669 | C22⋊C4 | — | 67 | 12 | no | — |
| 670 | C22⋊C4 | — | 67 | 12 | no | — |
| 671 | C22⋊C4 | — | 67 | 4 | no | — |
| 672 | C22⋊C4 | — | 67 | 24 | no | — |
| 673 | C22⋊C4 | — | 67 | 12 | no | — |
| 674 | C22⋊C4 | C23×D67 | 1 | 12 | yes | — |
| 675 | C22⋊C4 | C23×D67 | 1 | 6 | yes | — |
| 676 | C42 | — | 67 | 2 | no | — |
| 677 | C42 | — | 67 | 1 | no | — |
| 678 | C42 | — | 67 | 12 | no | — |
| 679 | C42 | — | 67 | 6 | no | — |
| 680 | C42 | — | 67 | 4 | no | — |
| 681 | C42 | — | 67 | 3 | no | — |
| 682 | C42 | — | 67 | 6 | no | — |
| 683 | C42 | — | 67 | 6 | no | — |
| 684 | C42 | — | 67 | 6 | no | — |
| 685 | C42 | — | 67 | 24 | no | — |
| 686 | C42 | — | 67 | 12 | no | — |
| 687 | C42 | C23×D67 | 1 | 1 | yes | characteristic |
| 688 | C42 | C23×D67 | 1 | 3 | yes | — |
| 689 | C42 | C23×D67 | 1 | 6 | yes | — |
| 690 | C42 | C23×D67 | 1 | 12 | yes | — |
| 691 | C23 | — | 268 | 6 | no | — |
| 692 | C23 | — | 67 | 12 | no | — |
| 693 | C23 | — | 67 | 1 | no | — |
| 694 | C23 | — | 67 | 3 | no | — |
| 695 | C23 | C24×D67 | 1 | 3 | yes | — |
| 696 | Q8 | — | 4 | 12 | no | — |
| 697 | Q8 | — | 268 | 24 | no | — |
| 698 | Q8 | — | 268 | 12 | no | — |
| 699 | Q8 | — | 67 | 12 | no | — |
| 700 | Q8 | — | 134 | 24 | no | — |
| 701 | Q8 | — | 134 | 8 | no | — |
| 702 | Q8 | C2×Q8×D67 | 1 | 4 | yes | — |
| 703 | D4 | — | 67 | 24 | no | — |
| 704 | D4 | — | 67 | 12 | no | — |
| 705 | D4 | C2×Q8×D67 | 1 | 12 | yes | — |
| 706 | C2×C4 | — | 4 | 6 | no | — |
| 707 | C2×C4 | — | 4 | 12 | no | — |
| 708 | C2×C4 | — | 268 | 6 | no | — |
| 709 | C2×C4 | — | 268 | 6 | no | — |
| 710 | C2×C4 | — | 268 | 12 | no | — |
| 711 | C2×C4 | — | 268 | 12 | no | — |
| 712 | C2×C4 | — | 268 | 12 | no | — |
| 713 | C2×C4 | — | 67 | 12 | no | — |
| 714 | C2×C4 | — | 67 | 1 | no | — |
| 715 | C2×C4 | — | 67 | 3 | no | — |
| 716 | C2×C4 | — | 67 | 2 | no | — |
| 717 | C2×C4 | — | 67 | 4 | no | — |
| 718 | C2×C4 | — | 67 | 12 | no | — |
| 719 | C2×C4 | — | 67 | 12 | no | — |
| 720 | C2×C4 | — | 67 | 12 | no | — |
| 721 | C2×C4 | — | 67 | 4 | no | — |
| 722 | C2×C4 | — | 67 | 12 | no | — |
| 723 | C2×C4 | — | 67 | 6 | no | — |
| 724 | C2×C4 | — | 134 | 4 | no | — |
| 725 | C2×C4 | — | 134 | 12 | no | — |
| 726 | C2×C4 | — | 134 | 12 | no | — |
| 727 | C2×C4 | C2×Q8×D67 | 1 | 12 | yes | — |
| 728 | C2×C4 | C24×D67 | 1 | 2 | yes | — |
| 729 | C2×C4 | C24×D67 | 1 | 12 | yes | — |
| 730 | C2×C4 | C24×D67 | 1 | 6 | yes | — |
| 731 | C2×C4 | C24×D67 | 1 | 4 | yes | — |
| 732 | C2×C4 | C24×D67 | 1 | 3 | yes | — |
| 733 | C2×C4 | C24×D67 | 1 | 1 | yes | characteristic |
| 734 | C22 | — | 2 | 6 | no | — |
| 735 | C22 | — | 268 | 12 | no | — |
| 736 | C22 | — | 67 | 2 | no | — |
| 737 | C22 | — | 67 | 6 | no | — |
| 738 | C22 | — | 134 | 6 | no | — |
| 739 | C22 | — | 134 | 2 | no | — |
| 740 | C22 | C22×Q8×D67 | 1 | 6 | yes | — |
| 741 | C22 | C25×D67 | 1 | 1 | yes | characteristic |
| 742 | C4 | — | 2 | 2 | no | — |
| 743 | C4 | — | 2 | 12 | no | — |
| 744 | C4 | — | 2 | 6 | no | — |
| 745 | C4 | — | 2 | 4 | no | — |
| 746 | C4 | — | 67 | 2 | no | — |
| 747 | C4 | — | 67 | 6 | no | — |
| 748 | C4 | — | 67 | 4 | no | — |
| 749 | C4 | — | 134 | 4 | no | — |
| 750 | C4 | — | 134 | 12 | no | — |
| 751 | C4 | — | 134 | 6 | no | — |
| 752 | C4 | C22×Q8×D67 | 1 | 2 | yes | — |
| 753 | C4 | C22×Q8×D67 | 1 | 6 | yes | — |
| 754 | C2 | — | 2 | 6 | no | — |
| 755 | C2 | — | 134 | 2 | no | — |
| 756 | C2 | — | 134 | 6 | no | — |
| 757 | C2 | C23×Q8×D67 | 1 | 1 | yes | characteristic |
| 758 | C2 | #585×D67 | 1 | 2 | yes | — |
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