← #31740670
Subgroups — #31740670
Order 17152.
2234 conjugacy classes of subgroups.
The subgroup lattice has 692 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22574012 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#16864042 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22572292 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #22571724 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #22571214 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22571016 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22570984 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #22570309 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #22569471 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×#16863549 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C67×#2973 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C22×#11761628 | C22 | 1 | 1 | yes | characteristic |
| 13 | C23×D268 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#14524076 | C22 | 1 | 4 | yes | complemented |
| 15 | C22×#11761617 | C22 | 1 | 4 | yes | complemented |
| 16 | #16864105 | — | 2 | 4 | no | — |
| 17 | #16864103 | C22 | 1 | 4 | yes | complemented |
| 18 | D4×Dic134 | C22 | 1 | 4 | yes | complemented |
| 19 | #16864042 | — | 2 | 4 | no | — |
| 20 | #16864042 | C22 | 1 | 8 | yes | — |
| 21 | #16864027 | — | 2 | 1 | no | — |
| 22 | #16864022 | — | 2 | 1 | no | — |
| 23 | #16864022 | — | 2 | 1 | no | — |
| 24 | #16863953 | C22 | 1 | 2 | yes | complemented |
| 25 | C2×#14524031 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#14524028 | — | 2 | 1 | no | — |
| 27 | C2×#14524022 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×#14524022 | C22 | 1 | 2 | yes | — |
| 29 | C2×#14524022 | C22 | 1 | 2 | yes | complemented |
| 30 | C2×#14524017 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#14524016 | — | 2 | 1 | no | — |
| 32 | C2×#14524011 | — | 2 | 1 | no | — |
| 33 | #16863871 | — | 2 | 1 | no | — |
| 34 | C2×C4×D268 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×C22⋊C4×D67 | — | 2 | 1 | no | — |
| 36 | #16863790 | C22 | 1 | 4 | yes | complemented |
| 37 | #16863756 | C22 | 1 | 4 | yes | complemented |
| 38 | #16863732 | C22 | 1 | 4 | yes | complemented |
| 39 | #16863732 | C22 | 1 | 4 | yes | complemented |
| 40 | #16863710 | C22 | 1 | 4 | yes | complemented |
| 41 | #16863677 | C22 | 1 | 4 | yes | complemented |
| 42 | #16863642 | C22 | 1 | 8 | yes | complemented |
| 43 | #16863637 | C22 | 1 | 8 | yes | complemented |
| 44 | #16863619 | C22 | 1 | 8 | yes | complemented |
| 45 | #16863602 | C22 | 1 | 4 | yes | complemented |
| 46 | #16863560 | C22 | 1 | 8 | yes | complemented |
| 47 | #16863554 | C22 | 1 | 4 | yes | complemented |
| 48 | #16863554 | C22 | 1 | 4 | yes | complemented |
| 49 | #16863549 | C22 | 1 | 4 | yes | — |
| 50 | #16863549 | C22 | 1 | 4 | yes | — |
| 51 | #16863549 | C22 | 1 | 8 | yes | complemented |
| 52 | #16863537 | C22 | 1 | 4 | yes | complemented |
| 53 | #16863498 | C22 | 1 | 8 | yes | complemented |
| 54 | #16863398 | C22 | 1 | 4 | yes | complemented |
| 55 | C2×#14523965 | C22 | 1 | 4 | yes | complemented |
| 56 | C2×C4×D4×C67 | C22 | 1 | 1 | yes | characteristic |
| 57 | #435×C67 | C22 | 1 | 8 | yes | complemented |
| 58 | #432×C67 | C22 | 1 | 2 | yes | complemented |
| 59 | #407×C67 | C22 | 1 | 2 | yes | complemented |
| 60 | C2×C22⋊C8×C67 | C22 | 1 | 2 | yes | — |
| 61 | C24×D67 | — | 2 | 1 | no | — |
| 62 | C2×#11761628 | — | 2 | 2 | no | — |
| 63 | C2×#11761628 | — | 4 | 4 | no | — |
| 64 | C2×#11761628 | C23 | 1 | 4 | yes | — |
| 65 | C22×Dic134 | C23 | 1 | 2 | yes | — |
| 66 | C22×Dic134 | C23 | 1 | 1 | yes | characteristic |
| 67 | C22×Dic134 | C23 | 1 | 2 | yes | complemented |
| 68 | C22×D268 | — | 2 | 2 | no | — |
| 69 | C22×D268 | — | 2 | 1 | no | — |
| 70 | C22×D268 | — | 4 | 4 | no | — |
| 71 | C22×D268 | C23 | 1 | 1 | yes | characteristic |
| 72 | C22×D268 | C23 | 1 | 4 | yes | — |
| 73 | C22×D268 | C23 | 1 | 1 | yes | characteristic |
| 74 | C22×C22⋊D67 | — | 2 | 1 | no | — |
| 75 | C22×C22⋊D67 | — | 2 | 1 | no | — |
| 76 | C22×C4×D67 | — | 2 | 1 | no | — |
| 77 | C22×C4×D67 | — | 2 | 1 | no | — |
| 78 | #14524076 | — | 4 | 8 | no | — |
| 79 | C2×Dic268 | C23 | 1 | 8 | yes | complemented |
| 80 | C2×#11761617 | — | 4 | 8 | no | — |
| 81 | C2×#11761617 | C23 | 1 | 8 | yes | — |
| 82 | C2×#11761617 | C23 | 1 | 8 | yes | — |
| 83 | #14524043 | C23 | 1 | 2 | yes | complemented |
| 84 | #14524043 | C23 | 1 | 2 | yes | complemented |
| 85 | #14524042 | — | 2 | 4 | no | — |
| 86 | #14524035 | — | 2 | 2 | no | — |
| 87 | #14524034 | — | 2 | 4 | no | — |
| 88 | #14524031 | — | 2 | 2 | no | — |
| 89 | #14524031 | C23 | 1 | 4 | yes | — |
| 90 | #14524028 | — | 2 | 8 | no | — |
| 91 | #14524022 | — | 2 | 2 | no | — |
| 92 | #14524022 | — | 2 | 2 | no | — |
| 93 | #14524022 | — | 2 | 2 | no | — |
| 94 | #14524022 | — | 2 | 2 | no | — |
| 95 | #14524022 | — | 2 | 2 | no | — |
| 96 | #14524022 | — | 2 | 2 | no | — |
| 97 | #14524022 | C23 | 1 | 4 | yes | — |
| 98 | #14524022 | C23 | 1 | 4 | yes | — |
| 99 | #14524022 | C23 | 1 | 4 | yes | — |
| 100 | #14524022 | C23 | 1 | 4 | yes | complemented |
| 101 | #14524020 | — | 2 | 4 | no | — |
| 102 | #14524020 | — | 2 | 4 | no | — |
| 103 | #14524020 | — | 2 | 4 | no | — |
| 104 | #14524020 | — | 2 | 4 | no | — |
| 105 | #14524017 | — | 2 | 2 | no | — |
| 106 | #14524017 | C23 | 1 | 4 | yes | — |
| 107 | #14524016 | — | 2 | 8 | no | — |
| 108 | #14524011 | — | 2 | 8 | no | — |
| 109 | C4×Dic134 | — | 2 | 2 | no | — |
| 110 | C4×Dic134 | C23 | 1 | 4 | yes | complemented |
| 111 | C4×D268 | — | 2 | 2 | no | — |
| 112 | C4×D268 | C23 | 1 | 4 | yes | — |
| 113 | D4×Dic67 | — | 2 | 4 | no | — |
| 114 | D4×Dic67 | — | 2 | 4 | no | — |
| 115 | #14524002 | — | 2 | 2 | no | — |
| 116 | C2×C4⋊Dic67 | C23 | 1 | 2 | yes | — |
| 117 | C2×C4⋊Dic67 | C23 | 1 | 1 | yes | characteristic |
| 118 | C2×C4⋊Dic67 | C23 | 1 | 2 | yes | complemented |
| 119 | C2×Dic67⋊C4 | — | 2 | 2 | no | — |
| 120 | C2×Dic67⋊C4 | — | 2 | 2 | no | — |
| 121 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 122 | C2×C22⋊Dic67 | — | 2 | 2 | no | — |
| 123 | C2×C22⋊Dic67 | — | 2 | 2 | no | — |
| 124 | C2×C22⋊Dic67 | — | 2 | 1 | no | — |
| 125 | C2×(C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 126 | C2×(C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 127 | C2×(C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 128 | C2×(C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 129 | C22⋊C4×D67 | — | 2 | 8 | no | — |
| 130 | #14523977 | C23 | 1 | 8 | yes | complemented |
| 131 | #14523968 | C23 | 1 | 8 | yes | complemented |
| 132 | #14523968 | C23 | 1 | 8 | yes | complemented |
| 133 | #14523965 | C23 | 1 | 8 | yes | — |
| 134 | #14523965 | C23 | 1 | 8 | yes | — |
| 135 | C22×D4×C67 | D4 | 1 | 1 | yes | characteristic |
| 136 | C23×C4×C67 | C23 | 1 | 1 | yes | characteristic |
| 137 | C23×C4×C67 | C23 | 1 | 1 | yes | characteristic |
| 138 | C2×M16×C67 | C23 | 1 | 4 | yes | complemented |
| 139 | C22×C8×C67 | C23 | 1 | 4 | yes | — |
| 140 | C4×D4×C67 | D4 | 1 | 4 | yes | — |
| 141 | C4×D4×C67 | C23 | 1 | 4 | yes | — |
| 142 | C2×C4⋊C4×C67 | D4 | 1 | 1 | yes | characteristic |
| 143 | C2×C22⋊C4×C67 | D4 | 1 | 1 | yes | characteristic |
| 144 | C2×C22⋊C4×C67 | D4 | 1 | 1 | yes | characteristic |
| 145 | C2×C42×C67 | C23 | 1 | 1 | yes | characteristic |
| 146 | C4⋊C8×C67 | C23 | 1 | 4 | yes | complemented |
| 147 | C22⋊C8×C67 | C23 | 1 | 4 | yes | — |
| 148 | C22⋊C8×C67 | C23 | 1 | 4 | yes | — |
| 149 | C22⋊C8×C67 | C23 | 1 | 4 | yes | complemented |
| 150 | #97×C67 | C23 | 1 | 4 | yes | complemented |
| 151 | C23×D67 | — | 2 | 1 | no | — |
| 152 | C23×D67 | — | 2 | 1 | no | — |
| 153 | C23×D67 | — | 2 | 4 | no | — |
| 154 | C23×D67 | — | 4 | 4 | no | — |
| 155 | C23×D67 | — | 4 | 4 | no | — |
| 156 | C23×D67 | — | 8 | 2 | no | — |
| 157 | #11761628 | — | 2 | 8 | no | — |
| 158 | #11761628 | — | 4 | 4 | no | — |
| 159 | #11761628 | — | 4 | 8 | no | — |
| 160 | C2×Dic134 | — | 2 | 1 | no | — |
| 161 | C2×Dic134 | — | 2 | 2 | no | — |
| 162 | C2×Dic134 | — | 2 | 2 | no | — |
| 163 | C2×Dic134 | — | 2 | 2 | no | — |
| 164 | C2×Dic134 | — | 4 | 2 | no | — |
| 165 | C2×Dic134 | — | 4 | 4 | no | — |
| 166 | C2×Dic134 | — | 4 | 4 | no | — |
| 167 | C2×Dic134 | C24 | 1 | 2 | yes | — |
| 168 | C2×Dic134 | C24 | 1 | 4 | yes | — |
| 169 | C2×D268 | — | 2 | 1 | no | — |
| 170 | C2×D268 | — | 2 | 4 | no | — |
| 171 | C2×D268 | — | 2 | 8 | no | — |
| 172 | C2×D268 | — | 2 | 4 | no | — |
| 173 | C2×D268 | — | 2 | 1 | no | — |
| 174 | C2×D268 | — | 4 | 4 | no | — |
| 175 | C2×D268 | — | 4 | 2 | no | — |
| 176 | C2×D268 | — | 4 | 8 | no | — |
| 177 | C2×D268 | — | 4 | 4 | no | — |
| 178 | C2×D268 | C24 | 1 | 2 | yes | — |
| 179 | C2×D268 | C24 | 1 | 2 | yes | — |
| 180 | C2×C22⋊D67 | — | 2 | 4 | no | — |
| 181 | C2×C22⋊D67 | — | 2 | 4 | no | — |
| 182 | C2×C22⋊D67 | — | 4 | 4 | no | — |
| 183 | C2×C22⋊D67 | — | 8 | 2 | no | — |
| 184 | C22×Dic67 | — | 2 | 1 | no | — |
| 185 | C22×Dic67 | — | 2 | 1 | no | — |
| 186 | C22×Dic67 | — | 2 | 2 | no | — |
| 187 | C22×Dic67 | — | 2 | 2 | no | — |
| 188 | C22×Dic67 | — | 2 | 2 | no | — |
| 189 | C22×Dic67 | — | 2 | 2 | no | — |
| 190 | C2×C4×D67 | — | 2 | 4 | no | — |
| 191 | C2×C4×D67 | — | 2 | 4 | no | — |
| 192 | C2×C4×D67 | — | 4 | 4 | no | — |
| 193 | C2×C4×D67 | — | 8 | 2 | no | — |
| 194 | Dic268 | — | 4 | 8 | no | — |
| 195 | #11761617 | — | 2 | 16 | no | — |
| 196 | #11761617 | — | 4 | 8 | no | — |
| 197 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 198 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 199 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 200 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 201 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 202 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 203 | C4⋊Dic67 | C24 | 1 | 4 | yes | — |
| 204 | C4⋊Dic67 | C24 | 1 | 2 | yes | — |
| 205 | Dic67⋊C4 | — | 2 | 4 | no | — |
| 206 | Dic67⋊C4 | — | 2 | 4 | no | — |
| 207 | Dic67⋊C4 | — | 2 | 4 | no | — |
| 208 | Dic67⋊C4 | — | 2 | 4 | no | — |
| 209 | Dic67⋊C4 | — | 2 | 4 | no | — |
| 210 | C22⋊Dic67 | — | 2 | 4 | no | — |
| 211 | C22⋊Dic67 | — | 2 | 4 | no | — |
| 212 | C22⋊Dic67 | — | 2 | 4 | no | — |
| 213 | C22⋊Dic67 | — | 2 | 4 | no | — |
| 214 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 215 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 216 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 217 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 218 | C4×Dic67 | — | 2 | 4 | no | — |
| 219 | C24×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 220 | C24×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 221 | C2×D4×C67 | — | 2 | 4 | no | — |
| 222 | C2×D4×C67 | C2×D4 | 1 | 4 | yes | — |
| 223 | C22×C4×C67 | — | 4 | 2 | no | — |
| 224 | C22×C4×C67 | — | 4 | 2 | no | — |
| 225 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 226 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 227 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 228 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 229 | C22×C4×C67 | C2×D4 | 1 | 2 | yes | — |
| 230 | C22×C4×C67 | C2×D4 | 1 | 2 | yes | — |
| 231 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 232 | C22×C4×C67 | C24 | 1 | 2 | yes | — |
| 233 | C22×C4×C67 | C24 | 1 | 2 | yes | — |
| 234 | M16×C67 | — | 4 | 4 | no | — |
| 235 | C2×C8×C67 | — | 4 | 4 | no | — |
| 236 | C2×C8×C67 | C24 | 1 | 8 | yes | — |
| 237 | C4⋊C4×C67 | C2×D4 | 1 | 4 | yes | — |
| 238 | C22⋊C4×C67 | C2×D4 | 1 | 4 | yes | — |
| 239 | C22⋊C4×C67 | C2×D4 | 1 | 4 | yes | — |
| 240 | C42×C67 | C2×D4 | 1 | 2 | yes | — |
| 241 | C42×C67 | C24 | 1 | 2 | yes | — |
| 242 | C23×C67 | — | 2 | 2 | no | — |
| 243 | C23×C67 | — | 4 | 1 | no | — |
| 244 | C23×C67 | — | 4 | 1 | no | — |
| 245 | C23×C67 | — | 4 | 1 | no | — |
| 246 | C23×C67 | — | 4 | 1 | no | — |
| 247 | C23×C67 | #137 | 1 | 4 | yes | complemented |
| 248 | C23×C67 | C22×D4 | 1 | 2 | yes | — |
| 249 | C23×C67 | C22×D4 | 1 | 2 | yes | — |
| 250 | C23×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 251 | C22×D67 | — | 2 | 4 | no | — |
| 252 | C22×D67 | — | 2 | 2 | no | — |
| 253 | C22×D67 | — | 2 | 2 | no | — |
| 254 | C22×D67 | — | 4 | 8 | no | — |
| 255 | C22×D67 | — | 4 | 2 | no | — |
| 256 | C22×D67 | — | 4 | 2 | no | — |
| 257 | C22×D67 | — | 4 | 2 | no | — |
| 258 | C22×D67 | — | 4 | 2 | no | — |
| 259 | C22×D67 | — | 4 | 8 | no | — |
| 260 | C22×D67 | — | 4 | 2 | no | — |
| 261 | C22×D67 | — | 8 | 4 | no | — |
| 262 | C22×D67 | — | 8 | 16 | no | — |
| 263 | D4×C67 | — | 2 | 8 | no | — |
| 264 | C2×C4×C67 | — | 2 | 2 | no | — |
| 265 | C2×C4×C67 | — | 2 | 4 | no | — |
| 266 | C2×C4×C67 | — | 2 | 4 | no | — |
| 267 | C2×C4×C67 | — | 2 | 2 | no | — |
| 268 | C2×C4×C67 | — | 4 | 1 | no | — |
| 269 | C2×C4×C67 | — | 4 | 2 | no | — |
| 270 | C2×C4×C67 | — | 4 | 1 | no | — |
| 271 | C2×C4×C67 | — | 4 | 2 | no | — |
| 272 | C2×C4×C67 | — | 4 | 1 | no | — |
| 273 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 274 | C2×C4×C67 | C22×D4 | 1 | 2 | yes | — |
| 275 | C2×C4×C67 | C22×D4 | 1 | 2 | yes | — |
| 276 | C2×C4×C67 | C22×D4 | 1 | 2 | yes | — |
| 277 | C2×C4×C67 | C22×D4 | 1 | 2 | yes | — |
| 278 | C2×C4×C67 | C25 | 1 | 1 | yes | characteristic |
| 279 | C22⋊D67 | — | 4 | 8 | no | — |
| 280 | C22⋊D67 | — | 8 | 4 | no | — |
| 281 | C2×Dic67 | — | 2 | 4 | no | — |
| 282 | C2×Dic67 | — | 2 | 4 | no | — |
| 283 | C2×Dic67 | — | 2 | 2 | no | — |
| 284 | C2×Dic67 | — | 2 | 2 | no | — |
| 285 | C2×Dic67 | — | 4 | 2 | no | — |
| 286 | C2×Dic67 | — | 4 | 2 | no | — |
| 287 | C2×Dic67 | — | 8 | 2 | no | — |
| 288 | C2×Dic67 | — | 8 | 2 | no | — |
| 289 | C2×Dic67 | — | 8 | 2 | no | — |
| 290 | C2×Dic67 | — | 8 | 2 | no | — |
| 291 | D268 | — | 2 | 4 | no | — |
| 292 | D268 | — | 2 | 2 | no | — |
| 293 | D268 | — | 2 | 4 | no | — |
| 294 | D268 | — | 4 | 8 | no | — |
| 295 | D268 | — | 4 | 2 | no | — |
| 296 | D268 | H(5,𝔽2) | 1 | 4 | yes | — |
| 297 | C4×D67 | — | 4 | 8 | no | — |
| 298 | C4×D67 | — | 8 | 4 | no | — |
| 299 | Dic134 | — | 2 | 8 | no | — |
| 300 | Dic134 | — | 2 | 4 | no | — |
| 301 | Dic134 | — | 4 | 2 | no | — |
| 302 | Dic134 | — | 8 | 2 | no | — |
| 303 | Dic134 | — | 8 | 2 | no | — |
| 304 | Dic134 | — | 8 | 2 | no | — |
| 305 | C8×C67 | — | 2 | 8 | no | — |
| 306 | C22×C67 | — | 2 | 1 | no | — |
| 307 | C22×C67 | — | 2 | 2 | no | — |
| 308 | C22×C67 | — | 2 | 1 | no | — |
| 309 | C22×C67 | — | 2 | 2 | no | — |
| 310 | C22×C67 | — | 2 | 2 | no | — |
| 311 | C22×C67 | — | 2 | 2 | no | — |
| 312 | C22×C67 | — | 2 | 2 | no | — |
| 313 | C22×C67 | — | 4 | 4 | no | — |
| 314 | C22×C67 | — | 8 | 2 | no | — |
| 315 | C22×C67 | C2×#137 | 1 | 2 | yes | — |
| 316 | C22×C67 | C2×#137 | 1 | 4 | yes | — |
| 317 | C22×C67 | C23×D4 | 1 | 1 | yes | characteristic |
| 318 | C2×D67 | — | 2 | 4 | no | — |
| 319 | C2×D67 | — | 4 | 8 | no | — |
| 320 | C2×D67 | — | 4 | 2 | no | — |
| 321 | C2×D67 | — | 4 | 2 | no | — |
| 322 | C2×D67 | — | 4 | 2 | no | — |
| 323 | C2×D67 | — | 4 | 2 | no | — |
| 324 | C2×D67 | — | 4 | 2 | no | — |
| 325 | C2×D67 | — | 8 | 16 | no | — |
| 326 | C2×D67 | — | 8 | 4 | no | — |
| 327 | C4×C67 | — | 2 | 2 | no | — |
| 328 | C4×C67 | — | 2 | 1 | no | — |
| 329 | C4×C67 | — | 2 | 2 | no | — |
| 330 | C4×C67 | — | 2 | 2 | no | — |
| 331 | C4×C67 | — | 2 | 2 | no | — |
| 332 | C4×C67 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 333 | Dic67 | — | 4 | 4 | no | — |
| 334 | Dic67 | — | 4 | 2 | no | — |
| 335 | Dic67 | — | 4 | 2 | no | — |
| 336 | Dic67 | — | 4 | 4 | no | — |
| 337 | #61570 | — | 67 | 1 | no | maximal, Sylow |
| 338 | C2×C67 | — | 2 | 2 | no | — |
| 339 | C2×C67 | — | 2 | 4 | no | — |
| 340 | C2×C67 | — | 4 | 2 | no | — |
| 341 | C2×C67 | #3484 | 1 | 1 | yes | characteristic |
| 342 | C2×C67 | C22×#137 | 1 | 1 | yes | characteristic |
| 343 | C2×C67 | #3585 | 1 | 1 | yes | characteristic |
| 344 | D67 | — | 4 | 4 | no | — |
| 345 | D67 | — | 8 | 2 | no | — |
| 346 | #3501 | — | 67 | 1 | no | — |
| 347 | C2×#546 | — | 67 | 1 | no | — |
| 348 | #3314 | — | 67 | 8 | no | — |
| 349 | #3266 | — | 67 | 8 | no | — |
| 350 | #3215 | — | 67 | 2 | no | — |
| 351 | #3193 | — | 67 | 2 | no | — |
| 352 | #3189 | — | 67 | 2 | no | — |
| 353 | #3110 | — | 67 | 2 | no | — |
| 354 | #3007 | — | 67 | 2 | no | — |
| 355 | C2×#450 | — | 67 | 2 | no | — |
| 356 | #2973 | D67 | 1 | 1 | yes | characteristic, complemented |
| 357 | C67 | #61570 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 358 | C22×#41 | — | 67 | 1 | no | — |
| 359 | C23×D4 | — | 67 | 1 | no | — |
| 360 | C2×#137 | — | 67 | 4 | no | — |
| 361 | C22×SD16 | — | 67 | 4 | no | — |
| 362 | #554 | — | 67 | 4 | no | — |
| 363 | #554 | — | 134 | 4 | no | — |
| 364 | D4×Q8 | — | 67 | 4 | no | — |
| 365 | #546 | — | 67 | 8 | no | — |
| 366 | #546 | — | 134 | 4 | no | — |
| 367 | #544 | — | 134 | 1 | no | — |
| 368 | #543 | — | 134 | 1 | no | — |
| 369 | #543 | — | 134 | 1 | no | — |
| 370 | #533 | — | 67 | 2 | no | — |
| 371 | C2×#124 | — | 67 | 1 | no | — |
| 372 | C2×#123 | — | 134 | 1 | no | — |
| 373 | C2×C22⋊Q8 | — | 67 | 1 | no | — |
| 374 | C2×C22⋊Q8 | — | 67 | 2 | no | — |
| 375 | C2×C22⋊Q8 | — | 67 | 2 | no | — |
| 376 | C2×#121 | — | 67 | 1 | no | — |
| 377 | C2×#121 | — | 134 | 1 | no | — |
| 378 | C2×#120 | — | 134 | 1 | no | — |
| 379 | #518 | — | 134 | 1 | no | — |
| 380 | C2×C4×D4 | — | 67 | 1 | no | — |
| 381 | C2×C4×D4 | C2×D67 | 1 | 1 | yes | characteristic |
| 382 | C22×C22⋊C4 | — | 134 | 1 | no | — |
| 383 | #497 | — | 67 | 4 | no | — |
| 384 | #489 | — | 67 | 4 | no | — |
| 385 | #484 | — | 67 | 4 | no | — |
| 386 | #484 | — | 67 | 4 | no | — |
| 387 | #480 | — | 67 | 4 | no | — |
| 388 | #474 | — | 67 | 4 | no | — |
| 389 | #468 | — | 67 | 8 | no | — |
| 390 | #467 | — | 67 | 8 | no | — |
| 391 | #464 | — | 67 | 8 | no | — |
| 392 | #461 | — | 67 | 4 | no | — |
| 393 | #452 | — | 67 | 8 | no | — |
| 394 | #451 | — | 67 | 4 | no | — |
| 395 | #451 | — | 67 | 4 | no | — |
| 396 | #450 | — | 67 | 4 | no | — |
| 397 | #450 | — | 67 | 4 | no | — |
| 398 | #450 | — | 67 | 8 | no | — |
| 399 | #448 | — | 67 | 4 | no | — |
| 400 | #440 | — | 67 | 8 | no | — |
| 401 | #435 | C2×D67 | 1 | 8 | yes | complemented |
| 402 | #432 | C2×D67 | 1 | 2 | yes | complemented |
| 403 | #417 | — | 67 | 4 | no | — |
| 404 | C2×#102 | — | 67 | 4 | no | — |
| 405 | #407 | C2×D67 | 1 | 2 | yes | complemented |
| 406 | C2×C22⋊C8 | C2×D67 | 1 | 2 | yes | — |
| 407 | C25 | — | 134 | 1 | no | — |
| 408 | C2×#41 | — | 268 | 4 | no | — |
| 409 | C2×#41 | — | 67 | 4 | no | — |
| 410 | C2×#41 | — | 134 | 2 | no | — |
| 411 | C22×Q8 | — | 67 | 1 | no | — |
| 412 | C22×Q8 | — | 67 | 2 | no | — |
| 413 | C22×Q8 | — | 67 | 2 | no | — |
| 414 | C22×D4 | — | 268 | 4 | no | — |
| 415 | C22×D4 | — | 67 | 1 | no | — |
| 416 | C22×D4 | — | 67 | 4 | no | — |
| 417 | C22×D4 | — | 67 | 1 | no | — |
| 418 | C22×D4 | — | 134 | 1 | no | — |
| 419 | C22×D4 | — | 134 | 1 | no | — |
| 420 | C22×D4 | — | 134 | 1 | no | — |
| 421 | C22×D4 | — | 134 | 2 | no | — |
| 422 | C22×D4 | D268 | 1 | 1 | yes | characteristic |
| 423 | C23×C4 | — | 134 | 1 | no | — |
| 424 | C23×C4 | — | 134 | 1 | no | — |
| 425 | C23×C4 | C22×D67 | 1 | 1 | yes | characteristic |
| 426 | C23×C4 | C22×D67 | 1 | 1 | yes | characteristic |
| 427 | #137 | — | 268 | 8 | no | — |
| 428 | C2×Q16 | — | 67 | 8 | no | — |
| 429 | C2×SD16 | — | 268 | 8 | no | — |
| 430 | C2×SD16 | — | 67 | 8 | no | — |
| 431 | C2×SD16 | — | 67 | 8 | no | — |
| 432 | C2×M16 | C22×D67 | 1 | 4 | yes | complemented |
| 433 | C22×C8 | C22×D67 | 1 | 4 | yes | — |
| 434 | C4⋊Q8 | — | 67 | 2 | no | — |
| 435 | C4⋊Q8 | — | 67 | 2 | no | — |
| 436 | C4⋊Q8 | — | 134 | 4 | no | — |
| 437 | #125 | — | 134 | 4 | no | — |
| 438 | #125 | — | 134 | 2 | no | — |
| 439 | #124 | — | 67 | 4 | no | — |
| 440 | #124 | — | 134 | 2 | no | — |
| 441 | #123 | — | 134 | 8 | no | — |
| 442 | C22⋊Q8 | — | 67 | 4 | no | — |
| 443 | C22⋊Q8 | — | 67 | 4 | no | — |
| 444 | C22⋊Q8 | — | 67 | 4 | no | — |
| 445 | C22⋊Q8 | — | 67 | 4 | no | — |
| 446 | C22⋊Q8 | — | 134 | 2 | no | — |
| 447 | C22⋊Q8 | — | 134 | 2 | no | — |
| 448 | C22⋊Q8 | — | 134 | 2 | no | — |
| 449 | C22⋊Q8 | — | 134 | 2 | no | — |
| 450 | C22⋊Q8 | — | 134 | 2 | no | — |
| 451 | C22⋊Q8 | — | 134 | 2 | no | — |
| 452 | C22⋊Q8 | — | 134 | 4 | no | — |
| 453 | C22⋊Q8 | — | 134 | 4 | no | — |
| 454 | C22⋊Q8 | — | 134 | 4 | no | — |
| 455 | C22⋊Q8 | — | 134 | 4 | no | — |
| 456 | #121 | — | 67 | 4 | no | — |
| 457 | #121 | — | 134 | 2 | no | — |
| 458 | #121 | — | 134 | 8 | no | — |
| 459 | #120 | — | 134 | 8 | no | — |
| 460 | C4×Q8 | — | 67 | 4 | no | — |
| 461 | C4×Q8 | — | 134 | 2 | no | — |
| 462 | C4×D4 | — | 67 | 4 | no | — |
| 463 | C4×D4 | — | 134 | 4 | no | — |
| 464 | C4×D4 | — | 134 | 4 | no | — |
| 465 | C4×D4 | — | 134 | 2 | no | — |
| 466 | C4×D4 | D268 | 1 | 4 | yes | — |
| 467 | C4×D4 | C22×D67 | 1 | 4 | yes | — |
| 468 | #117 | — | 134 | 2 | no | — |
| 469 | C2×C4⋊C4 | — | 67 | 1 | no | — |
| 470 | C2×C4⋊C4 | — | 67 | 2 | no | — |
| 471 | C2×C4⋊C4 | — | 67 | 2 | no | — |
| 472 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 473 | C2×C4⋊C4 | — | 134 | 2 | no | — |
| 474 | C2×C4⋊C4 | — | 134 | 2 | no | — |
| 475 | C2×C4⋊C4 | D268 | 1 | 1 | yes | characteristic |
| 476 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 477 | C2×C22⋊C4 | — | 134 | 2 | no | — |
| 478 | C2×C22⋊C4 | — | 134 | 2 | no | — |
| 479 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 480 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 481 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 482 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 483 | C2×C22⋊C4 | — | 134 | 8 | no | — |
| 484 | C2×C22⋊C4 | D268 | 1 | 1 | yes | characteristic |
| 485 | C2×C22⋊C4 | D268 | 1 | 1 | yes | characteristic |
| 486 | C2×C42 | C22×D67 | 1 | 1 | yes | characteristic |
| 487 | #107 | — | 67 | 8 | no | — |
| 488 | C4⋊C8 | C22×D67 | 1 | 4 | yes | complemented |
| 489 | #103 | — | 67 | 8 | no | — |
| 490 | #103 | — | 67 | 8 | no | — |
| 491 | #102 | — | 67 | 8 | no | — |
| 492 | #102 | — | 67 | 8 | no | — |
| 493 | C22⋊C8 | C22×D67 | 1 | 4 | yes | — |
| 494 | C22⋊C8 | C22×D67 | 1 | 4 | yes | — |
| 495 | C22⋊C8 | C22×D67 | 1 | 4 | yes | complemented |
| 496 | #97 | C22×D67 | 1 | 4 | yes | complemented |
| 497 | C24 | — | 268 | 4 | no | — |
| 498 | C24 | — | 268 | 4 | no | — |
| 499 | C24 | — | 536 | 2 | no | — |
| 500 | C24 | — | 134 | 1 | no | — |
| 501 | C24 | — | 134 | 4 | no | — |
| 502 | C24 | — | 134 | 1 | no | — |
| 503 | C24 | C2×D268 | 1 | 1 | yes | characteristic |
| 504 | C24 | C2×D268 | 1 | 1 | yes | characteristic |
| 505 | #41 | — | 268 | 4 | no | — |
| 506 | #41 | — | 268 | 8 | no | — |
| 507 | #41 | — | 134 | 8 | no | — |
| 508 | C2×Q8 | — | 268 | 2 | no | — |
| 509 | C2×Q8 | — | 268 | 4 | no | — |
| 510 | C2×Q8 | — | 268 | 4 | no | — |
| 511 | C2×Q8 | — | 67 | 2 | no | — |
| 512 | C2×Q8 | — | 67 | 4 | no | — |
| 513 | C2×Q8 | — | 134 | 1 | no | — |
| 514 | C2×Q8 | — | 134 | 2 | no | — |
| 515 | C2×Q8 | — | 134 | 2 | no | — |
| 516 | C2×Q8 | — | 134 | 2 | no | — |
| 517 | C2×D4 | — | 2 | 4 | no | — |
| 518 | C2×D4 | — | 268 | 4 | no | — |
| 519 | C2×D4 | — | 268 | 2 | no | — |
| 520 | C2×D4 | — | 268 | 4 | no | — |
| 521 | C2×D4 | — | 268 | 8 | no | — |
| 522 | C2×D4 | — | 268 | 4 | no | — |
| 523 | C2×D4 | — | 536 | 2 | no | — |
| 524 | C2×D4 | — | 67 | 2 | no | — |
| 525 | C2×D4 | — | 67 | 2 | no | — |
| 526 | C2×D4 | — | 134 | 8 | no | — |
| 527 | C2×D4 | — | 134 | 4 | no | — |
| 528 | C2×D4 | — | 134 | 4 | no | — |
| 529 | C2×D4 | — | 134 | 4 | no | — |
| 530 | C2×D4 | — | 134 | 4 | no | — |
| 531 | C2×D4 | — | 134 | 1 | no | — |
| 532 | C2×D4 | — | 134 | 1 | no | — |
| 533 | C2×D4 | C2×D268 | 1 | 4 | yes | — |
| 534 | C22×C4 | — | 4 | 2 | no | — |
| 535 | C22×C4 | — | 4 | 2 | no | — |
| 536 | C22×C4 | — | 268 | 4 | no | — |
| 537 | C22×C4 | — | 536 | 2 | no | — |
| 538 | C22×C4 | — | 134 | 1 | no | — |
| 539 | C22×C4 | — | 134 | 1 | no | — |
| 540 | C22×C4 | — | 134 | 4 | no | — |
| 541 | C22×C4 | — | 134 | 2 | no | — |
| 542 | C22×C4 | — | 134 | 2 | no | — |
| 543 | C22×C4 | — | 134 | 2 | no | — |
| 544 | C22×C4 | — | 134 | 2 | no | — |
| 545 | C22×C4 | — | 134 | 4 | no | — |
| 546 | C22×C4 | C2×D268 | 1 | 1 | yes | characteristic |
| 547 | C22×C4 | C2×D268 | 1 | 1 | yes | characteristic |
| 548 | C22×C4 | C2×D268 | 1 | 1 | yes | characteristic |
| 549 | C22×C4 | C2×D268 | 1 | 1 | yes | characteristic |
| 550 | C22×C4 | C2×D268 | 1 | 2 | yes | — |
| 551 | C22×C4 | C2×D268 | 1 | 2 | yes | — |
| 552 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 553 | C22×C4 | C23×D67 | 1 | 2 | yes | — |
| 554 | C22×C4 | C23×D67 | 1 | 2 | yes | — |
| 555 | Q16 | — | 268 | 8 | no | — |
| 556 | SD16 | — | 268 | 8 | no | — |
| 557 | SD16 | — | 134 | 16 | no | — |
| 558 | M16 | — | 4 | 4 | no | — |
| 559 | C2×C8 | — | 4 | 4 | no | — |
| 560 | C2×C8 | C23×D67 | 1 | 8 | yes | — |
| 561 | C4⋊C4 | — | 67 | 4 | no | — |
| 562 | C4⋊C4 | — | 67 | 2 | no | — |
| 563 | C4⋊C4 | — | 134 | 1 | no | — |
| 564 | C4⋊C4 | — | 134 | 2 | no | — |
| 565 | C4⋊C4 | — | 134 | 2 | no | — |
| 566 | C4⋊C4 | — | 134 | 4 | no | — |
| 567 | C4⋊C4 | — | 134 | 4 | no | — |
| 568 | C4⋊C4 | — | 134 | 4 | no | — |
| 569 | C4⋊C4 | — | 134 | 4 | no | — |
| 570 | C4⋊C4 | — | 134 | 2 | no | — |
| 571 | C4⋊C4 | — | 134 | 2 | no | — |
| 572 | C4⋊C4 | — | 134 | 4 | no | — |
| 573 | C4⋊C4 | — | 134 | 2 | no | — |
| 574 | C4⋊C4 | C2×D268 | 1 | 4 | yes | — |
| 575 | C22⋊C4 | — | 134 | 4 | no | — |
| 576 | C22⋊C4 | — | 134 | 4 | no | — |
| 577 | C22⋊C4 | — | 134 | 4 | no | — |
| 578 | C22⋊C4 | — | 134 | 4 | no | — |
| 579 | C22⋊C4 | — | 134 | 4 | no | — |
| 580 | C22⋊C4 | — | 134 | 4 | no | — |
| 581 | C22⋊C4 | — | 134 | 4 | no | — |
| 582 | C22⋊C4 | — | 134 | 4 | no | — |
| 583 | C22⋊C4 | C2×D268 | 1 | 4 | yes | — |
| 584 | C22⋊C4 | C2×D268 | 1 | 4 | yes | — |
| 585 | C42 | — | 134 | 4 | no | — |
| 586 | C42 | C2×D268 | 1 | 2 | yes | — |
| 587 | C42 | C23×D67 | 1 | 2 | yes | — |
| 588 | C23 | — | 2 | 2 | no | — |
| 589 | C23 | — | 4 | 1 | no | — |
| 590 | C23 | — | 4 | 1 | no | — |
| 591 | C23 | — | 4 | 1 | no | — |
| 592 | C23 | — | 4 | 1 | no | — |
| 593 | C23 | — | 268 | 2 | no | — |
| 594 | C23 | — | 268 | 2 | no | — |
| 595 | C23 | — | 268 | 2 | no | — |
| 596 | C23 | — | 268 | 8 | no | — |
| 597 | C23 | — | 268 | 2 | no | — |
| 598 | C23 | — | 268 | 8 | no | — |
| 599 | C23 | — | 268 | 2 | no | — |
| 600 | C23 | — | 536 | 4 | no | — |
| 601 | C23 | — | 536 | 16 | no | — |
| 602 | C23 | — | 134 | 4 | no | — |
| 603 | C23 | — | 134 | 2 | no | — |
| 604 | C23 | — | 134 | 2 | no | — |
| 605 | C23 | #14524076 | 1 | 4 | yes | complemented |
| 606 | C23 | C22×D268 | 1 | 2 | yes | — |
| 607 | C23 | C22×D268 | 1 | 2 | yes | — |
| 608 | C23 | C22×D268 | 1 | 1 | yes | characteristic |
| 609 | Q8 | — | 268 | 2 | no | — |
| 610 | Q8 | — | 536 | 2 | no | — |
| 611 | Q8 | — | 536 | 2 | no | — |
| 612 | Q8 | — | 536 | 2 | no | — |
| 613 | Q8 | — | 134 | 8 | no | — |
| 614 | Q8 | — | 134 | 4 | no | — |
| 615 | D4 | — | 2 | 8 | no | — |
| 616 | D4 | — | 268 | 2 | no | — |
| 617 | D4 | — | 268 | 8 | no | — |
| 618 | D4 | — | 268 | 8 | no | — |
| 619 | D4 | — | 536 | 4 | no | — |
| 620 | D4 | — | 67 | 4 | no | — |
| 621 | D4 | — | 134 | 4 | no | — |
| 622 | D4 | — | 134 | 4 | no | — |
| 623 | D4 | — | 134 | 2 | no | — |
| 624 | C2×C4 | — | 2 | 2 | no | — |
| 625 | C2×C4 | — | 2 | 4 | no | — |
| 626 | C2×C4 | — | 2 | 4 | no | — |
| 627 | C2×C4 | — | 2 | 2 | no | — |
| 628 | C2×C4 | — | 4 | 1 | no | — |
| 629 | C2×C4 | — | 4 | 2 | no | — |
| 630 | C2×C4 | — | 4 | 1 | no | — |
| 631 | C2×C4 | — | 4 | 2 | no | — |
| 632 | C2×C4 | — | 4 | 1 | no | — |
| 633 | C2×C4 | — | 268 | 8 | no | — |
| 634 | C2×C4 | — | 268 | 2 | no | — |
| 635 | C2×C4 | — | 268 | 2 | no | — |
| 636 | C2×C4 | — | 536 | 4 | no | — |
| 637 | C2×C4 | — | 536 | 2 | no | — |
| 638 | C2×C4 | — | 536 | 2 | no | — |
| 639 | C2×C4 | — | 536 | 2 | no | — |
| 640 | C2×C4 | — | 536 | 2 | no | — |
| 641 | C2×C4 | — | 134 | 4 | no | — |
| 642 | C2×C4 | — | 134 | 4 | no | — |
| 643 | C2×C4 | — | 134 | 2 | no | — |
| 644 | C2×C4 | — | 134 | 2 | no | — |
| 645 | C2×C4 | C22×D268 | 1 | 2 | yes | — |
| 646 | C2×C4 | C22×D268 | 1 | 1 | yes | characteristic |
| 647 | C2×C4 | C22×D268 | 1 | 2 | yes | — |
| 648 | C2×C4 | C22×D268 | 1 | 2 | yes | — |
| 649 | C2×C4 | C22×D268 | 1 | 2 | yes | — |
| 650 | C2×C4 | C24×D67 | 1 | 1 | yes | characteristic |
| 651 | C8 | — | 2 | 8 | no | — |
| 652 | C22 | — | 2 | 1 | no | — |
| 653 | C22 | — | 2 | 2 | no | — |
| 654 | C22 | — | 2 | 1 | no | — |
| 655 | C22 | — | 2 | 2 | no | — |
| 656 | C22 | — | 2 | 2 | no | — |
| 657 | C22 | — | 2 | 2 | no | — |
| 658 | C22 | — | 2 | 2 | no | — |
| 659 | C22 | — | 4 | 4 | no | — |
| 660 | C22 | — | 8 | 2 | no | — |
| 661 | C22 | — | 268 | 8 | no | — |
| 662 | C22 | — | 268 | 2 | no | — |
| 663 | C22 | — | 268 | 2 | no | — |
| 664 | C22 | — | 268 | 2 | no | — |
| 665 | C22 | — | 268 | 2 | no | — |
| 666 | C22 | — | 268 | 2 | no | — |
| 667 | C22 | — | 536 | 16 | no | — |
| 668 | C22 | — | 536 | 4 | no | — |
| 669 | C22 | — | 134 | 4 | no | — |
| 670 | C22 | C2×#14524076 | 1 | 2 | yes | — |
| 671 | C22 | C2×#14524076 | 1 | 4 | yes | — |
| 672 | C22 | C23×D268 | 1 | 1 | yes | characteristic |
| 673 | C4 | — | 2 | 1 | no | — |
| 674 | C4 | — | 2 | 2 | no | — |
| 675 | C4 | — | 2 | 2 | no | — |
| 676 | C4 | — | 2 | 2 | no | — |
| 677 | C4 | — | 2 | 2 | no | — |
| 678 | C4 | — | 268 | 2 | no | — |
| 679 | C4 | — | 268 | 4 | no | — |
| 680 | C4 | — | 268 | 2 | no | — |
| 681 | C4 | — | 268 | 4 | no | — |
| 682 | C4 | H(5,𝔽2)×D67 | 1 | 2 | yes | — |
| 683 | C2 | — | 2 | 2 | no | — |
| 684 | C2 | — | 2 | 4 | no | — |
| 685 | C2 | — | 4 | 2 | no | — |
| 686 | C2 | — | 268 | 4 | no | — |
| 687 | C2 | — | 536 | 2 | no | — |
| 688 | C2 | #22573845 | 1 | 1 | yes | characteristic |
| 689 | C2 | C22×#14524076 | 1 | 1 | yes | characteristic |
| 690 | C2 | #22574990 | 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