← #31736879
Subgroups — #31736879
Order 17152.
1938 conjugacy classes of subgroups.
The subgroup lattice has 698 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22573806 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22573300 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22573291 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22573281 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #22573267 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22573256 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22573245 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #22573234 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #22570652 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #22569660 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #22569658 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×#16863526 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #22569010 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | C4×#14524065 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C67×#3147 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#14524065 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#14524063 | C22 | 1 | 4 | yes | — |
| 18 | #16864132 | C22 | 1 | 2 | yes | — |
| 19 | #16864128 | C22 | 1 | 4 | yes | — |
| 20 | #16864121 | C22 | 1 | 2 | yes | — |
| 21 | #16864120 | C22 | 1 | 2 | yes | — |
| 22 | #16864115 | C22 | 1 | 4 | yes | — |
| 23 | #16864098 | — | 2 | 2 | no | — |
| 24 | #16864089 | — | 2 | 4 | no | — |
| 25 | #16864066 | C22 | 1 | 2 | yes | — |
| 26 | #16864052 | — | 2 | 2 | no | — |
| 27 | #16863942 | C22 | 1 | 4 | yes | — |
| 28 | #16863928 | — | 2 | 2 | no | — |
| 29 | #16863926 | — | 2 | 4 | no | — |
| 30 | #41×Dic67 | C22 | 1 | 4 | yes | — |
| 31 | C4×#11761628 | C22 | 1 | 2 | yes | — |
| 32 | C4×#11761627 | — | 2 | 2 | no | — |
| 33 | C2×C4×Dic134 | C22 | 1 | 1 | yes | characteristic |
| 34 | #16863789 | C22 | 1 | 4 | yes | — |
| 35 | #16863787 | C22 | 1 | 4 | yes | — |
| 36 | #16863784 | C22 | 1 | 4 | yes | — |
| 37 | #16863782 | C22 | 1 | 4 | yes | — |
| 38 | #16863620 | C22 | 1 | 4 | yes | — |
| 39 | #16863616 | C22 | 1 | 4 | yes | — |
| 40 | #16863615 | C22 | 1 | 4 | yes | — |
| 41 | #16863613 | C22 | 1 | 4 | yes | — |
| 42 | #16863609 | C22 | 1 | 4 | yes | — |
| 43 | #16863608 | C22 | 1 | 4 | yes | — |
| 44 | #16863604 | C22 | 1 | 4 | yes | — |
| 45 | #16863603 | C22 | 1 | 2 | yes | — |
| 46 | #16863599 | C22 | 1 | 4 | yes | — |
| 47 | #16863598 | C22 | 1 | 2 | yes | — |
| 48 | #16863594 | C22 | 1 | 4 | yes | — |
| 49 | #16863593 | C22 | 1 | 2 | yes | — |
| 50 | #16863589 | C22 | 1 | 4 | yes | — |
| 51 | #16863588 | C22 | 1 | 2 | yes | — |
| 52 | #16863526 | C22 | 1 | 2 | yes | — |
| 53 | #16863526 | C22 | 1 | 2 | yes | — |
| 54 | #16863526 | C22 | 1 | 2 | yes | — |
| 55 | #16863526 | C22 | 1 | 2 | yes | — |
| 56 | #16863508 | C22 | 1 | 4 | yes | — |
| 57 | #16863503 | C22 | 1 | 4 | yes | — |
| 58 | #16863497 | C22 | 1 | 4 | yes | — |
| 59 | #16863497 | C22 | 1 | 4 | yes | — |
| 60 | C4×Dic268 | C22 | 1 | 1 | yes | characteristic |
| 61 | C4×Dic268 | C22 | 1 | 1 | yes | characteristic |
| 62 | C4×#11761617 | C22 | 1 | 2 | yes | — |
| 63 | C4×#11761617 | C22 | 1 | 2 | yes | — |
| 64 | C4×D536 | C22 | 1 | 1 | yes | characteristic |
| 65 | C4×D536 | C22 | 1 | 1 | yes | characteristic |
| 66 | #16863434 | C22 | 1 | 1 | yes | characteristic |
| 67 | C2×C4⋊(C67⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 68 | C2×Dic67⋊C8 | C22 | 1 | 2 | yes | — |
| 69 | #16863393 | C22 | 1 | 2 | yes | — |
| 70 | #16863392 | C22 | 1 | 4 | yes | — |
| 71 | C2×#14523953 | C22 | 1 | 2 | yes | — |
| 72 | C2×#135×C67 | C22 | 1 | 2 | yes | — |
| 73 | C2×#135×C67 | C22 | 1 | 2 | yes | — |
| 74 | #532×C67 | C22 | 1 | 2 | yes | — |
| 75 | #495×C67 | C22 | 1 | 2 | yes | — |
| 76 | #495×C67 | C22 | 1 | 2 | yes | — |
| 77 | #494×C67 | C22 | 1 | 1 | yes | characteristic |
| 78 | #493×C67 | C22 | 1 | 1 | yes | characteristic |
| 79 | #492×C67 | C22 | 1 | 2 | yes | — |
| 80 | C2×C4×C8×C67 | C22 | 1 | 1 | yes | characteristic |
| 81 | C2×#11761628 | C23 | 1 | 2 | yes | — |
| 82 | C2×#11761627 | — | 2 | 2 | no | — |
| 83 | C22×Dic134 | D4 | 1 | 1 | yes | characteristic |
| 84 | #14524065 | — | 2 | 4 | no | — |
| 85 | #14524063 | — | 4 | 8 | no | — |
| 86 | C2×Dic268 | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×#11761618 | C23 | 1 | 4 | yes | — |
| 88 | C2×#11761617 | C23 | 1 | 2 | yes | — |
| 89 | C2×#11761616 | C23 | 1 | 4 | yes | — |
| 90 | C2×#11761615 | C23 | 1 | 4 | yes | — |
| 91 | C2×D536 | C23 | 1 | 1 | yes | characteristic |
| 92 | C2×#11761613 | C23 | 1 | 4 | yes | — |
| 93 | C22×C67⋊C8 | C23 | 1 | 2 | yes | — |
| 94 | #14524041 | C23 | 1 | 4 | yes | — |
| 95 | #14524039 | C23 | 1 | 4 | yes | — |
| 96 | #14524038 | — | 2 | 4 | no | — |
| 97 | #14524036 | — | 2 | 4 | no | — |
| 98 | #14524036 | — | 2 | 4 | no | — |
| 99 | #14524034 | — | 2 | 2 | no | — |
| 100 | #14524033 | — | 2 | 4 | no | — |
| 101 | #14524032 | C23 | 1 | 4 | yes | — |
| 102 | #14524030 | — | 2 | 2 | no | — |
| 103 | #14524030 | C23 | 1 | 4 | yes | — |
| 104 | #14524029 | — | 2 | 4 | no | — |
| 105 | #14524027 | — | 2 | 4 | no | — |
| 106 | #14524025 | — | 2 | 4 | no | — |
| 107 | #14524024 | — | 2 | 4 | no | — |
| 108 | #14524023 | — | 2 | 2 | no | — |
| 109 | #14524020 | — | 2 | 4 | no | — |
| 110 | #14524015 | — | 2 | 4 | no | — |
| 111 | #14524015 | — | 2 | 4 | no | — |
| 112 | #14524015 | — | 2 | 4 | no | — |
| 113 | #14524014 | — | 2 | 2 | no | — |
| 114 | Q8×Dic67 | C23 | 1 | 4 | yes | — |
| 115 | Q8×Dic67 | C23 | 1 | 4 | yes | — |
| 116 | C4×Dic134 | D4 | 1 | 2 | yes | — |
| 117 | C4×Dic134 | D4 | 1 | 2 | yes | — |
| 118 | C4×Dic134 | C23 | 1 | 2 | yes | — |
| 119 | C4×Dic134 | C23 | 1 | 2 | yes | — |
| 120 | C4×Dic134 | C23 | 1 | 2 | yes | — |
| 121 | C4×Dic134 | C23 | 1 | 2 | yes | — |
| 122 | #14524008 | — | 2 | 2 | no | — |
| 123 | C4×D268 | C23 | 1 | 2 | yes | — |
| 124 | C4×D268 | C23 | 1 | 2 | yes | — |
| 125 | D4×Dic67 | — | 2 | 4 | no | — |
| 126 | D4×Dic67 | — | 2 | 4 | no | — |
| 127 | D4×Dic67 | — | 2 | 2 | no | — |
| 128 | D4×Dic67 | C23 | 1 | 4 | yes | — |
| 129 | D4×Dic67 | C23 | 1 | 4 | yes | — |
| 130 | C4×C22⋊D67 | — | 2 | 4 | no | — |
| 131 | C4×C22⋊D67 | — | 2 | 4 | no | — |
| 132 | C4×C22⋊D67 | — | 2 | 2 | no | — |
| 133 | C4×C22⋊D67 | — | 2 | 2 | no | — |
| 134 | (C22⋊D67)⋊C4 | — | 2 | 4 | no | — |
| 135 | #14524002 | — | 2 | 4 | no | — |
| 136 | #14524002 | C23 | 1 | 2 | yes | — |
| 137 | #14524001 | — | 2 | 2 | no | — |
| 138 | #14524000 | — | 2 | 2 | no | — |
| 139 | #14523999 | — | 2 | 4 | no | — |
| 140 | C2×C4⋊Dic67 | D4 | 1 | 1 | yes | characteristic |
| 141 | C2×Dic67⋊C4 | D4 | 1 | 2 | yes | — |
| 142 | C2×C4×Dic67 | — | 2 | 4 | no | — |
| 143 | C2×C4×Dic67 | C23 | 1 | 2 | yes | — |
| 144 | C42×D67 | — | 2 | 2 | no | — |
| 145 | #14523977 | C23 | 1 | 1 | yes | characteristic |
| 146 | #14523977 | C23 | 1 | 1 | yes | characteristic |
| 147 | #14523975 | C23 | 1 | 2 | yes | — |
| 148 | C4⋊(C67⋊C8) | C23 | 1 | 2 | yes | — |
| 149 | C4⋊(C67⋊C8) | C23 | 1 | 2 | yes | — |
| 150 | Dic67⋊C8 | C23 | 1 | 4 | yes | — |
| 151 | Dic67⋊C8 | C23 | 1 | 4 | yes | — |
| 152 | #14523968 | C23 | 1 | 2 | yes | — |
| 153 | #14523968 | C23 | 1 | 2 | yes | — |
| 154 | #14523967 | C23 | 1 | 4 | yes | — |
| 155 | #14523967 | C23 | 1 | 4 | yes | — |
| 156 | #14523965 | C23 | 1 | 2 | yes | — |
| 157 | #14523965 | C23 | 1 | 2 | yes | — |
| 158 | #14523964 | C23 | 1 | 4 | yes | — |
| 159 | #14523964 | C23 | 1 | 4 | yes | — |
| 160 | #14523953 | C23 | 1 | 4 | yes | — |
| 161 | #14523953 | C23 | 1 | 4 | yes | — |
| 162 | C2×#41×C67 | C23 | 1 | 4 | yes | — |
| 163 | #135×C67 | — | 2 | 8 | no | — |
| 164 | #135×C67 | — | 4 | 4 | no | — |
| 165 | C2×Q16×C67 | C23 | 1 | 2 | yes | — |
| 166 | C2×Q16×C67 | C23 | 1 | 2 | yes | — |
| 167 | C2×SD16×C67 | C23 | 1 | 4 | yes | — |
| 168 | C2×SD16×C67 | C23 | 1 | 4 | yes | — |
| 169 | C2×D8×C67 | C23 | 1 | 2 | yes | — |
| 170 | C2×D8×C67 | C23 | 1 | 2 | yes | — |
| 171 | C22×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 172 | C22×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 173 | C4⋊Q8×C67 | C23 | 1 | 2 | yes | — |
| 174 | #127×C67 | C23 | 1 | 2 | yes | — |
| 175 | #124×C67 | C23 | 1 | 4 | yes | — |
| 176 | #121×C67 | — | 2 | 2 | no | — |
| 177 | #121×C67 | — | 2 | 2 | no | — |
| 178 | C4×D4×C67 | — | 2 | 2 | no | — |
| 179 | C4×D4×C67 | — | 2 | 2 | no | — |
| 180 | C2×C42×C67 | C23 | 1 | 1 | yes | characteristic |
| 181 | C4×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 182 | C4×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 183 | C4×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 184 | C4×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 185 | #11761628 | — | 2 | 4 | no | — |
| 186 | #11761628 | — | 2 | 4 | no | — |
| 187 | #11761627 | — | 4 | 8 | no | — |
| 188 | C2×Dic134 | — | 4 | 2 | no | — |
| 189 | C2×Dic134 | C2×D4 | 1 | 2 | yes | — |
| 190 | C2×Dic134 | C2×D4 | 1 | 2 | yes | — |
| 191 | C2×Dic134 | C24 | 1 | 2 | yes | — |
| 192 | C2×D268 | C24 | 1 | 2 | yes | — |
| 193 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 194 | C2×C22⋊D67 | — | 2 | 4 | no | — |
| 195 | C2×C22⋊D67 | — | 2 | 4 | no | — |
| 196 | C22×Dic67 | — | 2 | 4 | no | — |
| 197 | C22×Dic67 | — | 2 | 4 | no | — |
| 198 | C22×Dic67 | C2×D4 | 1 | 2 | yes | — |
| 199 | C22×Dic67 | C2×D4 | 1 | 2 | yes | — |
| 200 | C2×C4×D67 | — | 2 | 2 | no | — |
| 201 | C2×C4×D67 | — | 2 | 2 | no | — |
| 202 | C2×C4×D67 | — | 2 | 2 | no | — |
| 203 | Dic268 | — | 2 | 2 | no | — |
| 204 | #11761618 | — | 4 | 4 | no | — |
| 205 | #11761617 | — | 2 | 4 | no | — |
| 206 | #11761616 | — | 4 | 4 | no | — |
| 207 | #11761615 | — | 4 | 4 | no | — |
| 208 | D536 | — | 2 | 2 | no | — |
| 209 | #11761613 | — | 4 | 4 | no | — |
| 210 | C2×C67⋊C8 | — | 2 | 4 | no | — |
| 211 | C2×C67⋊C8 | C24 | 1 | 4 | yes | — |
| 212 | C4⋊Dic67 | — | 2 | 4 | no | — |
| 213 | C4⋊Dic67 | — | 2 | 4 | no | — |
| 214 | C4⋊Dic67 | C2×D4 | 1 | 2 | yes | — |
| 215 | C4⋊Dic67 | C2×D4 | 1 | 2 | yes | — |
| 216 | C4⋊Dic67 | C24 | 1 | 2 | yes | — |
| 217 | C4⋊Dic67 | C24 | 1 | 2 | yes | — |
| 218 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 219 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 220 | Dic67⋊C4 | — | 2 | 4 | no | — |
| 221 | Dic67⋊C4 | — | 2 | 4 | no | — |
| 222 | Dic67⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 223 | Dic67⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 224 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 225 | C22⋊Dic67 | — | 2 | 4 | no | — |
| 226 | C22⋊Dic67 | — | 2 | 4 | no | — |
| 227 | C22⋊Dic67 | — | 2 | 4 | no | — |
| 228 | C22⋊Dic67 | — | 2 | 4 | no | — |
| 229 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 230 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 231 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 232 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 233 | C4×Dic67 | — | 2 | 2 | no | — |
| 234 | C4×Dic67 | — | 2 | 2 | no | — |
| 235 | C4×Dic67 | — | 2 | 2 | no | — |
| 236 | C4×Dic67 | — | 2 | 4 | no | — |
| 237 | C4×Dic67 | — | 2 | 4 | no | — |
| 238 | C4×Dic67 | C2×D4 | 1 | 4 | yes | — |
| 239 | C4×Dic67 | C24 | 1 | 4 | yes | — |
| 240 | #41×C67 | — | 2 | 8 | no | — |
| 241 | #41×C67 | — | 2 | 8 | no | — |
| 242 | C2×Q8×C67 | C24 | 1 | 4 | yes | — |
| 243 | C2×D4×C67 | — | 2 | 4 | no | — |
| 244 | C2×D4×C67 | — | 2 | 2 | no | — |
| 245 | C2×D4×C67 | — | 2 | 2 | no | — |
| 246 | C2×D4×C67 | C24 | 1 | 4 | yes | — |
| 247 | C22×C4×C67 | — | 2 | 4 | no | — |
| 248 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 249 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 250 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 251 | Q16×C67 | — | 2 | 4 | no | — |
| 252 | Q16×C67 | — | 4 | 2 | no | — |
| 253 | SD16×C67 | — | 2 | 8 | no | — |
| 254 | SD16×C67 | — | 4 | 4 | no | — |
| 255 | D8×C67 | — | 2 | 4 | no | — |
| 256 | D8×C67 | — | 4 | 2 | no | — |
| 257 | C2×C8×C67 | — | 2 | 2 | no | — |
| 258 | C2×C8×C67 | #41 | 1 | 4 | yes | complemented |
| 259 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 260 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 261 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 262 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 263 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 264 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 265 | C22⋊C4×C67 | — | 2 | 4 | no | — |
| 266 | C22⋊C4×C67 | — | 2 | 4 | no | — |
| 267 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 268 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 269 | C42×C67 | C24 | 1 | 1 | yes | characteristic |
| 270 | C42×C67 | C24 | 1 | 1 | yes | characteristic |
| 271 | C23×C67 | — | 2 | 4 | no | — |
| 272 | C23×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 273 | C22×D67 | — | 2 | 2 | no | — |
| 274 | Q8×C67 | — | 2 | 4 | no | — |
| 275 | Q8×C67 | — | 2 | 4 | no | — |
| 276 | D4×C67 | — | 2 | 4 | no | — |
| 277 | D4×C67 | — | 2 | 4 | no | — |
| 278 | D4×C67 | — | 4 | 8 | no | — |
| 279 | D4×C67 | — | 4 | 4 | no | — |
| 280 | D4×C67 | — | 8 | 2 | no | — |
| 281 | C2×C4×C67 | — | 2 | 2 | no | — |
| 282 | C2×C4×C67 | — | 2 | 4 | no | — |
| 283 | C2×C4×C67 | — | 4 | 1 | no | — |
| 284 | C2×C4×C67 | — | 4 | 8 | no | — |
| 285 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 286 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 287 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 288 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 289 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 290 | C2×C4×C67 | C2×#41 | 1 | 2 | yes | — |
| 291 | C2×C4×C67 | H(5,𝔽2) | 1 | 2 | yes | — |
| 292 | C2×C4×C67 | C25 | 1 | 1 | yes | characteristic |
| 293 | C22⋊D67 | — | 4 | 8 | no | — |
| 294 | C22⋊D67 | — | 4 | 4 | no | — |
| 295 | C22⋊D67 | — | 8 | 4 | no | — |
| 296 | C2×Dic67 | — | 2 | 2 | no | — |
| 297 | C2×Dic67 | — | 2 | 2 | no | — |
| 298 | C2×Dic67 | — | 2 | 2 | no | — |
| 299 | C2×Dic67 | — | 4 | 2 | no | — |
| 300 | C2×Dic67 | — | 4 | 2 | no | — |
| 301 | C2×Dic67 | — | 4 | 8 | no | — |
| 302 | C2×Dic67 | — | 8 | 4 | no | — |
| 303 | C2×Dic67 | C22×D4 | 1 | 4 | yes | — |
| 304 | C2×Dic67 | C22×D4 | 1 | 4 | yes | — |
| 305 | D268 | — | 2 | 2 | no | — |
| 306 | D268 | — | 2 | 2 | no | — |
| 307 | C4×D67 | — | 4 | 4 | no | — |
| 308 | C4×D67 | — | 4 | 4 | no | — |
| 309 | C4×D67 | — | 8 | 2 | no | — |
| 310 | Dic134 | — | 2 | 4 | no | — |
| 311 | Dic134 | — | 2 | 2 | no | — |
| 312 | Dic134 | — | 2 | 2 | no | — |
| 313 | Dic134 | — | 4 | 2 | no | — |
| 314 | C8×C67 | — | 2 | 1 | no | — |
| 315 | C8×C67 | — | 2 | 1 | no | — |
| 316 | C8×C67 | C2×#41 | 1 | 2 | yes | — |
| 317 | C8×C67 | C2×#41 | 1 | 2 | yes | — |
| 318 | C67⋊C8 | — | 2 | 4 | no | — |
| 319 | C22×C67 | — | 2 | 1 | no | — |
| 320 | C22×C67 | — | 2 | 1 | no | — |
| 321 | C22×C67 | — | 4 | 4 | no | — |
| 322 | C22×C67 | — | 4 | 4 | no | — |
| 323 | C22×C67 | — | 4 | 4 | no | — |
| 324 | C22×C67 | #550 | 1 | 2 | yes | — |
| 325 | C22×C67 | C23×D4 | 1 | 1 | yes | characteristic |
| 326 | C2×D67 | — | 4 | 2 | no | — |
| 327 | C2×D67 | — | 4 | 2 | no | — |
| 328 | C2×D67 | — | 4 | 2 | no | — |
| 329 | C4×C67 | — | 2 | 1 | no | — |
| 330 | C4×C67 | — | 2 | 1 | no | — |
| 331 | C4×C67 | — | 2 | 1 | no | — |
| 332 | C4×C67 | — | 4 | 4 | no | — |
| 333 | C4×C67 | #550 | 1 | 2 | yes | — |
| 334 | C4×C67 | #575 | 1 | 2 | yes | — |
| 335 | C4×C67 | C22×#41 | 1 | 1 | yes | characteristic |
| 336 | C4×C67 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 337 | Dic67 | — | 2 | 4 | no | — |
| 338 | Dic67 | — | 2 | 4 | no | — |
| 339 | Dic67 | — | 4 | 2 | no | — |
| 340 | Dic67 | — | 4 | 2 | no | — |
| 341 | Dic67 | — | 4 | 2 | no | — |
| 342 | #61401 | — | 67 | 1 | no | maximal, Sylow |
| 343 | C2×C67 | — | 2 | 2 | no | — |
| 344 | C2×C67 | — | 8 | 4 | no | — |
| 345 | C2×C67 | C2×#550 | 1 | 1 | yes | characteristic |
| 346 | C2×C67 | C2×#575 | 1 | 1 | yes | characteristic |
| 347 | C2×C67 | #3584 | 1 | 1 | yes | characteristic |
| 348 | D67 | — | 8 | 2 | no | — |
| 349 | #3480 | — | 67 | 2 | no | — |
| 350 | #3403 | — | 67 | 2 | no | — |
| 351 | #3402 | — | 67 | 2 | no | — |
| 352 | #3401 | — | 67 | 4 | no | — |
| 353 | #3400 | — | 67 | 2 | no | — |
| 354 | #3399 | — | 67 | 2 | no | — |
| 355 | #3398 | — | 67 | 2 | no | — |
| 356 | #3397 | — | 67 | 2 | no | — |
| 357 | #3150 | — | 67 | 2 | no | — |
| 358 | #3147 | D67 | 1 | 1 | yes | characteristic, complemented |
| 359 | #3035 | — | 67 | 4 | no | — |
| 360 | #3035 | — | 67 | 2 | no | — |
| 361 | C2×#446 | — | 67 | 1 | no | — |
| 362 | #2943 | — | 67 | 2 | no | — |
| 363 | C4×#135 | — | 67 | 1 | no | — |
| 364 | C67 | #61401 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 365 | C2×#135 | — | 67 | 4 | no | — |
| 366 | C2×#135 | — | 67 | 1 | no | — |
| 367 | C2×#135 | C2×D67 | 1 | 2 | yes | — |
| 368 | C2×#135 | C2×D67 | 1 | 2 | yes | — |
| 369 | #559 | — | 67 | 2 | no | — |
| 370 | #559 | — | 67 | 4 | no | — |
| 371 | #557 | — | 67 | 2 | no | — |
| 372 | #556 | — | 67 | 2 | no | — |
| 373 | #556 | — | 67 | 4 | no | — |
| 374 | #553 | — | 134 | 4 | no | — |
| 375 | #553 | — | 134 | 2 | no | — |
| 376 | #550 | — | 67 | 2 | no | — |
| 377 | #548 | — | 134 | 2 | no | — |
| 378 | #532 | — | 67 | 4 | no | — |
| 379 | #532 | C2×D67 | 1 | 2 | yes | — |
| 380 | #529 | — | 134 | 4 | no | — |
| 381 | #529 | — | 134 | 2 | no | — |
| 382 | C4×#41 | — | 67 | 4 | no | — |
| 383 | C4×#41 | — | 67 | 2 | no | — |
| 384 | C4×#41 | — | 134 | 2 | no | — |
| 385 | C2×C4×Q8 | — | 67 | 1 | no | — |
| 386 | #497 | — | 67 | 4 | no | — |
| 387 | #497 | — | 67 | 4 | no | — |
| 388 | #496 | — | 67 | 4 | no | — |
| 389 | #496 | — | 67 | 4 | no | — |
| 390 | #495 | C2×D67 | 1 | 2 | yes | — |
| 391 | #495 | C2×D67 | 1 | 2 | yes | — |
| 392 | #494 | C2×D67 | 1 | 1 | yes | characteristic |
| 393 | #493 | C2×D67 | 1 | 1 | yes | characteristic |
| 394 | #492 | C2×D67 | 1 | 2 | yes | — |
| 395 | #464 | — | 67 | 4 | no | — |
| 396 | #464 | — | 67 | 4 | no | — |
| 397 | #464 | — | 67 | 4 | no | — |
| 398 | #463 | — | 67 | 4 | no | — |
| 399 | #463 | — | 67 | 4 | no | — |
| 400 | #463 | — | 67 | 4 | no | — |
| 401 | #462 | — | 67 | 4 | no | — |
| 402 | #462 | — | 67 | 2 | no | — |
| 403 | #461 | — | 67 | 4 | no | — |
| 404 | #461 | — | 67 | 2 | no | — |
| 405 | #460 | — | 67 | 4 | no | — |
| 406 | #460 | — | 67 | 2 | no | — |
| 407 | #459 | — | 67 | 4 | no | — |
| 408 | #459 | — | 67 | 2 | no | — |
| 409 | #446 | — | 67 | 2 | no | — |
| 410 | #446 | — | 67 | 2 | no | — |
| 411 | #446 | — | 67 | 2 | no | — |
| 412 | #446 | — | 67 | 2 | no | — |
| 413 | #442 | — | 67 | 4 | no | — |
| 414 | #441 | — | 67 | 4 | no | — |
| 415 | #440 | — | 67 | 4 | no | — |
| 416 | #440 | — | 67 | 4 | no | — |
| 417 | C4×Q16 | — | 67 | 1 | no | — |
| 418 | C4×Q16 | — | 67 | 1 | no | — |
| 419 | C4×SD16 | — | 67 | 2 | no | — |
| 420 | C4×SD16 | — | 67 | 2 | no | — |
| 421 | C4×D8 | — | 67 | 1 | no | — |
| 422 | C4×D8 | — | 67 | 1 | no | — |
| 423 | #427 | — | 67 | 1 | no | — |
| 424 | C2×C4⋊C8 | — | 67 | 2 | no | — |
| 425 | C2×C4⋊C8 | — | 67 | 1 | no | — |
| 426 | #416 | — | 67 | 4 | no | — |
| 427 | #416 | — | 67 | 2 | no | — |
| 428 | C2×#97 | — | 67 | 2 | no | — |
| 429 | C2×C4×C8 | C2×D67 | 1 | 1 | yes | characteristic |
| 430 | C2×#41 | — | 67 | 2 | no | — |
| 431 | C2×#41 | — | 134 | 2 | no | — |
| 432 | C2×#41 | C22×D67 | 1 | 4 | yes | — |
| 433 | C22×Q8 | — | 67 | 1 | no | — |
| 434 | #135 | — | 2 | 8 | no | — |
| 435 | #135 | — | 4 | 4 | no | — |
| 436 | #135 | — | 268 | 8 | no | — |
| 437 | #135 | — | 134 | 4 | no | — |
| 438 | C2×Q16 | — | 67 | 4 | no | — |
| 439 | C2×Q16 | — | 67 | 1 | no | — |
| 440 | C2×Q16 | C22×D67 | 1 | 2 | yes | — |
| 441 | C2×Q16 | C22×D67 | 1 | 2 | yes | — |
| 442 | C2×SD16 | — | 67 | 4 | no | — |
| 443 | C2×SD16 | — | 67 | 4 | no | — |
| 444 | C2×SD16 | — | 67 | 2 | no | — |
| 445 | C2×SD16 | C22×D67 | 1 | 4 | yes | — |
| 446 | C2×SD16 | C22×D67 | 1 | 4 | yes | — |
| 447 | C2×D8 | — | 67 | 4 | no | — |
| 448 | C2×D8 | — | 67 | 1 | no | — |
| 449 | C2×D8 | C22×D67 | 1 | 2 | yes | — |
| 450 | C2×D8 | C22×D67 | 1 | 2 | yes | — |
| 451 | C22×C8 | — | 67 | 2 | no | — |
| 452 | C22×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 453 | C22×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 454 | C4⋊Q8 | — | 67 | 4 | no | — |
| 455 | C4⋊Q8 | C22×D67 | 1 | 2 | yes | — |
| 456 | #127 | — | 67 | 4 | no | — |
| 457 | #127 | C22×D67 | 1 | 2 | yes | — |
| 458 | #126 | — | 134 | 4 | no | — |
| 459 | #126 | — | 134 | 4 | no | — |
| 460 | #126 | — | 134 | 4 | no | — |
| 461 | #125 | — | 134 | 4 | no | — |
| 462 | #125 | — | 134 | 2 | no | — |
| 463 | #124 | — | 67 | 4 | no | — |
| 464 | #124 | — | 67 | 4 | no | — |
| 465 | #124 | — | 134 | 4 | no | — |
| 466 | #124 | — | 134 | 2 | no | — |
| 467 | #124 | C22×D67 | 1 | 4 | yes | — |
| 468 | #123 | — | 134 | 4 | no | — |
| 469 | #123 | — | 134 | 4 | no | — |
| 470 | #123 | — | 134 | 4 | no | — |
| 471 | C22⋊Q8 | — | 134 | 4 | no | — |
| 472 | C22⋊Q8 | — | 134 | 2 | no | — |
| 473 | #121 | — | 2 | 2 | no | — |
| 474 | #121 | — | 2 | 2 | no | — |
| 475 | #121 | — | 134 | 2 | no | — |
| 476 | #121 | — | 134 | 4 | no | — |
| 477 | #121 | — | 134 | 4 | no | — |
| 478 | #121 | — | 134 | 4 | no | — |
| 479 | C4×Q8 | — | 67 | 2 | no | — |
| 480 | C4×Q8 | — | 67 | 2 | no | — |
| 481 | C4×Q8 | — | 67 | 2 | no | — |
| 482 | C4×Q8 | — | 67 | 2 | no | — |
| 483 | C4×Q8 | — | 67 | 4 | no | — |
| 484 | C4×Q8 | — | 67 | 4 | no | — |
| 485 | C4×Q8 | — | 67 | 2 | no | — |
| 486 | C4×Q8 | — | 67 | 2 | no | — |
| 487 | C4×Q8 | — | 134 | 2 | no | — |
| 488 | C4×D4 | — | 2 | 2 | no | — |
| 489 | C4×D4 | — | 2 | 2 | no | — |
| 490 | C4×D4 | — | 67 | 4 | no | — |
| 491 | C4×D4 | — | 67 | 4 | no | — |
| 492 | C4×D4 | — | 67 | 2 | no | — |
| 493 | C4×D4 | — | 67 | 2 | no | — |
| 494 | C4×D4 | — | 134 | 4 | no | — |
| 495 | C4×D4 | — | 134 | 4 | no | — |
| 496 | C4×D4 | — | 134 | 4 | no | — |
| 497 | C4×D4 | — | 134 | 2 | no | — |
| 498 | C4×D4 | — | 134 | 4 | no | — |
| 499 | C4×D4 | — | 134 | 4 | no | — |
| 500 | C4×D4 | — | 134 | 2 | no | — |
| 501 | C4×D4 | — | 134 | 2 | no | — |
| 502 | #117 | — | 67 | 2 | no | — |
| 503 | #117 | — | 134 | 4 | no | — |
| 504 | #117 | — | 134 | 4 | no | — |
| 505 | #117 | — | 134 | 2 | no | — |
| 506 | #117 | — | 134 | 2 | no | — |
| 507 | C2×C4⋊C4 | — | 67 | 2 | no | — |
| 508 | C2×C4⋊C4 | — | 67 | 1 | no | — |
| 509 | C2×C42 | — | 67 | 2 | no | — |
| 510 | C2×C42 | — | 134 | 4 | no | — |
| 511 | C2×C42 | — | 134 | 2 | no | — |
| 512 | C2×C42 | C22×D67 | 1 | 1 | yes | characteristic |
| 513 | #107 | — | 67 | 1 | no | — |
| 514 | #107 | — | 67 | 1 | no | — |
| 515 | #106 | — | 67 | 2 | no | — |
| 516 | C4⋊C8 | — | 67 | 4 | no | — |
| 517 | C4⋊C8 | — | 67 | 4 | no | — |
| 518 | C4⋊C8 | — | 67 | 2 | no | — |
| 519 | C4⋊C8 | — | 67 | 2 | no | — |
| 520 | #103 | — | 67 | 4 | no | — |
| 521 | #103 | — | 67 | 4 | no | — |
| 522 | #103 | — | 67 | 2 | no | — |
| 523 | #103 | — | 67 | 2 | no | — |
| 524 | #102 | — | 67 | 4 | no | — |
| 525 | #102 | — | 67 | 4 | no | — |
| 526 | #102 | — | 67 | 2 | no | — |
| 527 | #102 | — | 67 | 2 | no | — |
| 528 | #97 | — | 67 | 4 | no | — |
| 529 | #97 | — | 67 | 4 | no | — |
| 530 | C4×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 531 | C4×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 532 | C4×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 533 | C4×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 534 | #41 | — | 2 | 8 | no | — |
| 535 | #41 | — | 2 | 8 | no | — |
| 536 | #41 | — | 268 | 8 | no | — |
| 537 | #41 | — | 134 | 4 | no | — |
| 538 | #41 | — | 134 | 4 | no | — |
| 539 | C2×Q8 | — | 268 | 2 | no | — |
| 540 | C2×Q8 | — | 67 | 2 | no | — |
| 541 | C2×Q8 | — | 67 | 2 | no | — |
| 542 | C2×Q8 | — | 67 | 2 | no | — |
| 543 | C2×Q8 | C23×D67 | 1 | 4 | yes | — |
| 544 | C2×D4 | — | 2 | 4 | no | — |
| 545 | C2×D4 | — | 2 | 2 | no | — |
| 546 | C2×D4 | — | 2 | 2 | no | — |
| 547 | C2×D4 | — | 67 | 2 | no | — |
| 548 | C2×D4 | — | 134 | 4 | no | — |
| 549 | C2×D4 | — | 134 | 4 | no | — |
| 550 | C2×D4 | — | 134 | 2 | no | — |
| 551 | C2×D4 | C23×D67 | 1 | 4 | yes | — |
| 552 | C22×C4 | — | 2 | 4 | no | — |
| 553 | C22×C4 | — | 67 | 2 | no | — |
| 554 | C22×C4 | — | 67 | 2 | no | — |
| 555 | C22×C4 | — | 134 | 4 | no | — |
| 556 | C22×C4 | — | 134 | 2 | no | — |
| 557 | C22×C4 | — | 134 | 2 | no | — |
| 558 | C22×C4 | — | 134 | 4 | no | — |
| 559 | C22×C4 | — | 134 | 2 | no | — |
| 560 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 561 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 562 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 563 | Q16 | — | 2 | 4 | no | — |
| 564 | Q16 | — | 4 | 2 | no | — |
| 565 | Q16 | — | 268 | 4 | no | — |
| 566 | Q16 | — | 134 | 2 | no | — |
| 567 | SD16 | — | 2 | 8 | no | — |
| 568 | SD16 | — | 4 | 4 | no | — |
| 569 | SD16 | — | 268 | 4 | no | — |
| 570 | SD16 | — | 268 | 4 | no | — |
| 571 | SD16 | — | 134 | 4 | no | — |
| 572 | D8 | — | 2 | 4 | no | — |
| 573 | D8 | — | 4 | 2 | no | — |
| 574 | D8 | — | 268 | 4 | no | — |
| 575 | D8 | — | 134 | 2 | no | — |
| 576 | C2×C8 | — | 2 | 2 | no | — |
| 577 | C2×C8 | — | 67 | 4 | no | — |
| 578 | C2×C8 | — | 134 | 4 | no | — |
| 579 | C2×C8 | #11761627 | 1 | 4 | yes | complemented |
| 580 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 581 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 582 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 583 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 584 | C4⋊C4 | — | 2 | 2 | no | — |
| 585 | C4⋊C4 | — | 2 | 2 | no | — |
| 586 | C4⋊C4 | — | 67 | 2 | no | — |
| 587 | C4⋊C4 | — | 67 | 4 | no | — |
| 588 | C4⋊C4 | — | 67 | 4 | no | — |
| 589 | C4⋊C4 | — | 67 | 2 | no | — |
| 590 | C4⋊C4 | — | 67 | 2 | no | — |
| 591 | C4⋊C4 | — | 67 | 2 | no | — |
| 592 | C4⋊C4 | — | 134 | 4 | no | — |
| 593 | C4⋊C4 | — | 134 | 4 | no | — |
| 594 | C4⋊C4 | — | 134 | 4 | no | — |
| 595 | C4⋊C4 | — | 134 | 4 | no | — |
| 596 | C4⋊C4 | — | 134 | 2 | no | — |
| 597 | C4⋊C4 | — | 134 | 2 | no | — |
| 598 | C22⋊C4 | — | 2 | 4 | no | — |
| 599 | C22⋊C4 | — | 2 | 4 | no | — |
| 600 | C22⋊C4 | — | 134 | 4 | no | — |
| 601 | C22⋊C4 | — | 134 | 4 | no | — |
| 602 | C22⋊C4 | — | 134 | 4 | no | — |
| 603 | C22⋊C4 | — | 134 | 4 | no | — |
| 604 | C22⋊C4 | — | 134 | 4 | no | — |
| 605 | C22⋊C4 | — | 134 | 4 | no | — |
| 606 | C22⋊C4 | — | 134 | 2 | no | — |
| 607 | C22⋊C4 | — | 134 | 2 | no | — |
| 608 | C22⋊C4 | — | 134 | 2 | no | — |
| 609 | C42 | — | 67 | 4 | no | — |
| 610 | C42 | — | 67 | 4 | no | — |
| 611 | C42 | — | 134 | 4 | no | — |
| 612 | C42 | — | 134 | 4 | no | — |
| 613 | C42 | — | 134 | 2 | no | — |
| 614 | C42 | — | 134 | 2 | no | — |
| 615 | C42 | — | 134 | 2 | no | — |
| 616 | C42 | D4×D67 | 1 | 1 | yes | characteristic |
| 617 | C42 | D4×D67 | 1 | 1 | yes | characteristic |
| 618 | C42 | C23×D67 | 1 | 1 | yes | characteristic |
| 619 | C42 | C23×D67 | 1 | 1 | yes | characteristic |
| 620 | C23 | — | 2 | 4 | no | — |
| 621 | C23 | — | 134 | 2 | no | — |
| 622 | C23 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 623 | Q8 | — | 2 | 4 | no | — |
| 624 | Q8 | — | 2 | 4 | no | — |
| 625 | Q8 | — | 268 | 2 | no | — |
| 626 | Q8 | — | 134 | 2 | no | — |
| 627 | Q8 | — | 134 | 2 | no | — |
| 628 | Q8 | — | 134 | 4 | no | — |
| 629 | D4 | — | 2 | 4 | no | — |
| 630 | D4 | — | 2 | 4 | no | — |
| 631 | D4 | — | 4 | 8 | no | — |
| 632 | D4 | — | 4 | 4 | no | — |
| 633 | D4 | — | 8 | 2 | no | — |
| 634 | D4 | — | 268 | 4 | no | — |
| 635 | D4 | — | 268 | 8 | no | — |
| 636 | D4 | — | 536 | 4 | no | — |
| 637 | D4 | — | 134 | 2 | no | — |
| 638 | D4 | — | 134 | 2 | no | — |
| 639 | C2×C4 | — | 2 | 2 | no | — |
| 640 | C2×C4 | — | 2 | 4 | no | — |
| 641 | C2×C4 | — | 4 | 1 | no | — |
| 642 | C2×C4 | — | 4 | 8 | no | — |
| 643 | C2×C4 | — | 268 | 8 | no | — |
| 644 | C2×C4 | — | 268 | 4 | no | — |
| 645 | C2×C4 | — | 268 | 4 | no | — |
| 646 | C2×C4 | — | 268 | 2 | no | — |
| 647 | C2×C4 | — | 268 | 2 | no | — |
| 648 | C2×C4 | — | 536 | 2 | no | — |
| 649 | C2×C4 | — | 536 | 4 | no | — |
| 650 | C2×C4 | — | 67 | 4 | no | — |
| 651 | C2×C4 | — | 67 | 4 | no | — |
| 652 | C2×C4 | — | 134 | 2 | no | — |
| 653 | C2×C4 | — | 134 | 2 | no | — |
| 654 | C2×C4 | — | 134 | 2 | no | — |
| 655 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 656 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 657 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 658 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 659 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 660 | C2×C4 | C2×#11761627 | 1 | 2 | yes | — |
| 661 | C2×C4 | #14524088 | 1 | 2 | yes | — |
| 662 | C2×C4 | C24×D67 | 1 | 1 | yes | characteristic |
| 663 | C8 | — | 2 | 1 | no | — |
| 664 | C8 | — | 2 | 1 | no | — |
| 665 | C8 | — | 134 | 4 | no | — |
| 666 | C8 | C2×#11761627 | 1 | 2 | yes | — |
| 667 | C8 | C2×#11761627 | 1 | 2 | yes | — |
| 668 | C22 | — | 2 | 1 | no | — |
| 669 | C22 | — | 2 | 1 | no | — |
| 670 | C22 | — | 4 | 4 | no | — |
| 671 | C22 | — | 4 | 4 | no | — |
| 672 | C22 | — | 4 | 4 | no | — |
| 673 | C22 | — | 268 | 2 | no | — |
| 674 | C22 | — | 268 | 2 | no | — |
| 675 | C22 | — | 268 | 2 | no | — |
| 676 | C22 | #16864066 | 1 | 2 | yes | — |
| 677 | C22 | C22×D4×D67 | 1 | 1 | yes | characteristic |
| 678 | C4 | — | 2 | 1 | no | — |
| 679 | C4 | — | 2 | 1 | no | — |
| 680 | C4 | — | 2 | 1 | no | — |
| 681 | C4 | — | 4 | 4 | no | — |
| 682 | C4 | — | 268 | 2 | no | — |
| 683 | C4 | — | 268 | 2 | no | — |
| 684 | C4 | — | 268 | 2 | no | — |
| 685 | C4 | — | 134 | 4 | no | — |
| 686 | C4 | — | 134 | 4 | no | — |
| 687 | C4 | #16864066 | 1 | 2 | yes | — |
| 688 | C4 | #16864193 | 1 | 2 | yes | — |
| 689 | C4 | C22×#11761627 | 1 | 1 | yes | characteristic |
| 690 | C4 | C2×#14524088 | 1 | 1 | yes | characteristic |
| 691 | C2 | — | 2 | 2 | no | — |
| 692 | C2 | — | 8 | 4 | no | — |
| 693 | C2 | — | 536 | 2 | no | — |
| 694 | C2 | C2×#16864066 | 1 | 1 | yes | characteristic |
| 695 | C2 | C2×#16864193 | 1 | 1 | yes | characteristic |
| 696 | C2 | #22574978 | 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