← #31737303
Subgroups — #31737303
Order 17152.
1826 conjugacy classes of subgroups.
The subgroup lattice has 406 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22573791 | C2 | 1 | 2 | yes | maximal |
| 2 | Q8×Dic268 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22572883 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22572603 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #22572088 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #22571959 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #22570793 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #22570247 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | C8×#11761629 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C4×Q16×D67 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C67×#3395 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×Q16×D67 | C22 | 1 | 3 | yes | — |
| 13 | Q8×Dic134 | C22 | 1 | 2 | yes | — |
| 14 | #16864122 | — | 2 | 2 | no | — |
| 15 | #16864106 | C22 | 1 | 6 | yes | — |
| 16 | #16864102 | — | 2 | 6 | no | — |
| 17 | #16864061 | C22 | 1 | 6 | yes | — |
| 18 | #16863952 | — | 2 | 6 | no | — |
| 19 | #16863951 | C22 | 1 | 6 | yes | — |
| 20 | C4×#11761629 | — | 2 | 2 | no | — |
| 21 | C4×#11761629 | C22 | 1 | 1 | yes | characteristic |
| 22 | C4×Q8×D67 | C22 | 1 | 6 | yes | — |
| 23 | #16863801 | C22 | 1 | 3 | yes | — |
| 24 | #16863746 | C22 | 1 | 6 | yes | — |
| 25 | #16863730 | C22 | 1 | 12 | yes | — |
| 26 | #16863692 | C22 | 1 | 6 | yes | — |
| 27 | #16863691 | C22 | 1 | 6 | yes | — |
| 28 | #16863634 | C22 | 1 | 6 | yes | — |
| 29 | #16863634 | C22 | 1 | 6 | yes | — |
| 30 | #16863603 | C22 | 1 | 6 | yes | — |
| 31 | #16863550 | C22 | 1 | 12 | yes | — |
| 32 | Q8×C67⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 33 | C4×Dic268 | C22 | 1 | 3 | yes | — |
| 34 | Q16×Dic67 | C22 | 1 | 6 | yes | — |
| 35 | Q16×Dic67 | C22 | 1 | 3 | yes | — |
| 36 | #16863490 | C22 | 1 | 1 | yes | characteristic |
| 37 | C4×#11761618 | C22 | 1 | 6 | yes | — |
| 38 | #16863488 | C22 | 1 | 6 | yes | — |
| 39 | C8×D268 | C22 | 1 | 3 | yes | — |
| 40 | #16863461 | C22 | 1 | 3 | yes | — |
| 41 | #16863448 | C22 | 1 | 3 | yes | — |
| 42 | #107×D67 | C22 | 1 | 3 | yes | — |
| 43 | #103×D67 | C22 | 1 | 6 | yes | — |
| 44 | C4×C8×D67 | C22 | 1 | 3 | yes | — |
| 45 | #557×C67 | C22 | 1 | 2 | yes | — |
| 46 | #494×C67 | C22 | 1 | 3 | yes | — |
| 47 | #462×C67 | C22 | 1 | 6 | yes | — |
| 48 | C8×Q8×C67 | C22 | 1 | 1 | yes | characteristic |
| 49 | C4×Q16×C67 | C22 | 1 | 3 | yes | — |
| 50 | C2×#11761629 | D4 | 1 | 1 | yes | characteristic |
| 51 | C2×Q8×D67 | C23 | 1 | 6 | yes | — |
| 52 | C2×Dic268 | C23 | 1 | 1 | yes | characteristic |
| 53 | C2×#11761618 | C23 | 1 | 6 | yes | — |
| 54 | Q16×D67 | — | 2 | 12 | no | — |
| 55 | C2×C8×D67 | C23 | 1 | 3 | yes | — |
| 56 | C2×C8×D67 | C23 | 1 | 3 | yes | — |
| 57 | #14524043 | C23 | 1 | 6 | yes | — |
| 58 | #14524042 | — | 2 | 6 | no | — |
| 59 | #14524042 | — | 2 | 6 | no | — |
| 60 | #14524035 | — | 2 | 6 | no | — |
| 61 | #14524034 | — | 2 | 6 | no | — |
| 62 | #14524023 | — | 2 | 6 | no | — |
| 63 | #14524021 | — | 2 | 12 | no | — |
| 64 | #14524021 | — | 2 | 12 | no | — |
| 65 | #14524019 | C23 | 1 | 12 | yes | — |
| 66 | Q8×Dic67 | — | 2 | 2 | no | — |
| 67 | Q8×Dic67 | D4 | 1 | 1 | yes | characteristic |
| 68 | Q8×Dic67 | C23 | 1 | 6 | yes | — |
| 69 | C4×Dic134 | — | 2 | 6 | no | — |
| 70 | C4×Dic134 | C23 | 1 | 6 | yes | — |
| 71 | #14524008 | — | 2 | 6 | no | — |
| 72 | #14524008 | — | 2 | 6 | no | — |
| 73 | #14524008 | C23 | 1 | 2 | yes | — |
| 74 | C4×D268 | — | 2 | 6 | no | — |
| 75 | C4×D268 | C23 | 1 | 3 | yes | — |
| 76 | #14524005 | — | 2 | 6 | no | — |
| 77 | #14524005 | D4 | 1 | 3 | yes | — |
| 78 | #14524001 | — | 2 | 6 | no | — |
| 79 | #14524001 | D4 | 1 | 3 | yes | — |
| 80 | C4⋊C4×D67 | — | 2 | 6 | no | — |
| 81 | C4⋊C4×D67 | C23 | 1 | 6 | yes | — |
| 82 | C42×D67 | — | 2 | 6 | no | — |
| 83 | C42×D67 | C23 | 1 | 3 | yes | — |
| 84 | #14523977 | C23 | 1 | 3 | yes | — |
| 85 | #14523977 | C23 | 1 | 6 | yes | — |
| 86 | #14523976 | C23 | 1 | 6 | yes | — |
| 87 | C4⋊(C67⋊C8) | C23 | 1 | 3 | yes | — |
| 88 | #14523968 | C23 | 1 | 6 | yes | — |
| 89 | #14523967 | C23 | 1 | 6 | yes | — |
| 90 | #14523967 | C23 | 1 | 12 | yes | — |
| 91 | #14523966 | C23 | 1 | 2 | yes | — |
| 92 | (C2×D67)⋊C8 | C23 | 1 | 6 | yes | — |
| 93 | C4×C67⋊C8 | C23 | 1 | 3 | yes | — |
| 94 | C8×Dic67 | C23 | 1 | 3 | yes | — |
| 95 | C8×Dic67 | C23 | 1 | 1 | yes | characteristic |
| 96 | C2×Q16×C67 | C23 | 1 | 3 | yes | — |
| 97 | C2×Q16×C67 | C23 | 1 | 6 | yes | — |
| 98 | C4⋊Q8×C67 | C23 | 1 | 6 | yes | — |
| 99 | #125×C67 | — | 2 | 6 | no | — |
| 100 | C4×Q8×C67 | — | 2 | 2 | no | — |
| 101 | C4×Q8×C67 | C23 | 1 | 6 | yes | — |
| 102 | C4×Q8×C67 | C23 | 1 | 1 | yes | characteristic |
| 103 | #107×C67 | C23 | 1 | 1 | yes | characteristic |
| 104 | C4⋊C8×C67 | C23 | 1 | 3 | yes | — |
| 105 | #103×C67 | C23 | 1 | 6 | yes | — |
| 106 | C4×C8×C67 | C23 | 1 | 3 | yes | — |
| 107 | #11761629 | Q16 | 1 | 8 | yes | complemented |
| 108 | C2×Dic134 | — | 2 | 6 | no | — |
| 109 | C2×Dic134 | — | 2 | 6 | no | — |
| 110 | C2×Dic134 | C24 | 1 | 2 | yes | — |
| 111 | Q8×D67 | — | 2 | 12 | no | — |
| 112 | Q8×D67 | — | 4 | 6 | no | — |
| 113 | C2×D268 | C2×D4 | 1 | 3 | yes | — |
| 114 | C2×C4×D67 | — | 2 | 6 | no | — |
| 115 | C2×C4×D67 | — | 2 | 6 | no | — |
| 116 | C2×C4×D67 | C2×D4 | 1 | 3 | yes | — |
| 117 | C2×C4×D67 | C2×D4 | 1 | 3 | yes | — |
| 118 | C2×C4×D67 | C24 | 1 | 3 | yes | — |
| 119 | Dic268 | #41 | 1 | 4 | yes | complemented |
| 120 | #11761618 | — | 2 | 12 | no | — |
| 121 | C2×C67⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 122 | C2×C67⋊C8 | C24 | 1 | 3 | yes | — |
| 123 | C8×D67 | — | 2 | 6 | no | — |
| 124 | C8×D67 | — | 4 | 3 | no | — |
| 125 | C4⋊Dic67 | — | 2 | 6 | no | — |
| 126 | C4⋊Dic67 | — | 2 | 6 | no | — |
| 127 | C4⋊Dic67 | C2×D4 | 1 | 3 | yes | — |
| 128 | C4⋊Dic67 | C24 | 1 | 6 | yes | — |
| 129 | Dic67⋊C4 | — | 2 | 6 | no | — |
| 130 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 131 | Dic67⋊C4 | — | 2 | 6 | no | — |
| 132 | Dic67⋊C4 | — | 2 | 12 | no | — |
| 133 | (C2×D67)⋊C4 | — | 2 | 12 | no | — |
| 134 | (C2×D67)⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 135 | C4×Dic67 | — | 2 | 6 | no | — |
| 136 | C4×Dic67 | — | 2 | 2 | no | — |
| 137 | C4×Dic67 | — | 2 | 6 | no | — |
| 138 | C4×Dic67 | C2×D4 | 1 | 3 | yes | — |
| 139 | C4×Dic67 | C2×D4 | 1 | 3 | yes | — |
| 140 | C4×Dic67 | C24 | 1 | 1 | yes | characteristic |
| 141 | C2×Q8×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C2×Q8×C67 | C24 | 1 | 6 | yes | — |
| 143 | Q16×C67 | — | 2 | 6 | no | — |
| 144 | Q16×C67 | — | 4 | 6 | no | — |
| 145 | C2×C8×C67 | C24 | 1 | 3 | yes | — |
| 146 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 147 | C4⋊C4×C67 | — | 2 | 6 | no | — |
| 148 | C4⋊C4×C67 | — | 2 | 6 | no | — |
| 149 | C4⋊C4×C67 | — | 2 | 6 | no | — |
| 150 | C4⋊C4×C67 | C2×D4 | 1 | 3 | yes | — |
| 151 | C4⋊C4×C67 | C24 | 1 | 2 | yes | — |
| 152 | C42×C67 | — | 2 | 6 | no | — |
| 153 | C42×C67 | C24 | 1 | 3 | yes | — |
| 154 | C22×D67 | C22×D4 | 1 | 3 | yes | — |
| 155 | Q8×C67 | — | 2 | 6 | no | — |
| 156 | Q8×C67 | — | 2 | 6 | no | — |
| 157 | Q8×C67 | C2×Q16 | 1 | 4 | yes | complemented |
| 158 | C2×C4×C67 | — | 2 | 2 | no | — |
| 159 | C2×C4×C67 | — | 2 | 6 | no | — |
| 160 | C2×C4×C67 | C22×D4 | 1 | 3 | yes | — |
| 161 | C2×C4×C67 | C22×D4 | 1 | 3 | yes | — |
| 162 | C2×C4×C67 | C25 | 1 | 1 | yes | characteristic |
| 163 | C2×Dic67 | — | 2 | 2 | no | — |
| 164 | C2×Dic67 | — | 2 | 6 | no | — |
| 165 | C2×Dic67 | C22×D4 | 1 | 1 | yes | characteristic |
| 166 | C2×Dic67 | C22×D4 | 1 | 3 | yes | — |
| 167 | C2×Dic67 | C22×D4 | 1 | 1 | yes | characteristic |
| 168 | D268 | C2×Q16 | 1 | 12 | yes | complemented |
| 169 | C4×D67 | — | 2 | 3 | no | — |
| 170 | C4×D67 | — | 2 | 3 | no | — |
| 171 | C4×D67 | — | 4 | 3 | no | — |
| 172 | C4×D67 | — | 4 | 12 | no | — |
| 173 | C4×D67 | — | 8 | 6 | no | — |
| 174 | C4×D67 | C2×Q16 | 1 | 12 | yes | complemented |
| 175 | Dic134 | — | 2 | 2 | no | — |
| 176 | Dic134 | — | 4 | 12 | no | — |
| 177 | Dic134 | — | 8 | 6 | no | — |
| 178 | Dic134 | C2×#41 | 1 | 4 | yes | — |
| 179 | C8×C67 | — | 2 | 3 | no | — |
| 180 | C8×C67 | C2×#41 | 1 | 2 | yes | — |
| 181 | C67⋊C8 | — | 2 | 3 | no | — |
| 182 | C67⋊C8 | — | 2 | 1 | no | — |
| 183 | C22×C67 | C23×D4 | 1 | 1 | yes | characteristic |
| 184 | C2×D67 | — | 2 | 3 | no | — |
| 185 | C2×D67 | — | 2 | 3 | no | — |
| 186 | C2×D67 | C22×Q16 | 1 | 6 | yes | — |
| 187 | C4×C67 | — | 2 | 3 | no | — |
| 188 | C4×C67 | — | 4 | 2 | no | — |
| 189 | C4×C67 | — | 4 | 6 | no | — |
| 190 | C4×C67 | C22×Q16 | 1 | 6 | yes | — |
| 191 | C4×C67 | C22×#41 | 1 | 1 | yes | characteristic |
| 192 | C4×C67 | #585 | 1 | 1 | yes | characteristic |
| 193 | Dic67 | — | 2 | 1 | no | — |
| 194 | Dic67 | — | 2 | 4 | no | — |
| 195 | Dic67 | — | 2 | 3 | no | — |
| 196 | Dic67 | — | 4 | 6 | no | — |
| 197 | Dic67 | C22×Q16 | 1 | 2 | yes | — |
| 198 | Q16×#41 | — | 67 | 1 | no | maximal, Sylow |
| 199 | C2×C67 | D4×#41 | 1 | 1 | yes | characteristic |
| 200 | C2×C67 | C23×Q16 | 1 | 1 | yes | characteristic |
| 201 | C2×C67 | #3584 | 1 | 1 | yes | characteristic |
| 202 | D67 | — | 2 | 6 | no | — |
| 203 | Q8×#41 | — | 67 | 2 | no | — |
| 204 | #3395 | D67 | 1 | 1 | yes | characteristic, complemented |
| 205 | Q8×Q16 | — | 67 | 1 | no | — |
| 206 | #3363 | — | 67 | 2 | no | — |
| 207 | #3338 | — | 67 | 3 | no | — |
| 208 | #3299 | — | 67 | 6 | no | — |
| 209 | D4×Q16 | — | 67 | 3 | no | — |
| 210 | #3170 | — | 67 | 3 | no | — |
| 211 | #3104 | — | 67 | 6 | no | — |
| 212 | C8×#41 | — | 67 | 1 | no | — |
| 213 | C2×C4×Q16 | — | 67 | 3 | no | — |
| 214 | C67 | Q16×#41 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 215 | C22×Q16 | — | 67 | 3 | no | — |
| 216 | Q82 | — | 67 | 2 | no | — |
| 217 | #557 | — | 134 | 2 | no | — |
| 218 | #557 | C2×D67 | 1 | 2 | yes | — |
| 219 | #554 | — | 67 | 6 | no | — |
| 220 | #554 | — | 134 | 6 | no | — |
| 221 | D4×Q8 | — | 67 | 6 | no | — |
| 222 | #533 | — | 67 | 6 | no | — |
| 223 | #533 | — | 134 | 6 | no | — |
| 224 | C4×#41 | — | 67 | 1 | no | — |
| 225 | C4×#41 | — | 134 | 2 | no | — |
| 226 | C2×C4×Q8 | — | 67 | 6 | no | — |
| 227 | #500 | — | 67 | 3 | no | — |
| 228 | #494 | C2×D67 | 1 | 3 | yes | — |
| 229 | #487 | — | 67 | 6 | no | — |
| 230 | #484 | — | 67 | 12 | no | — |
| 231 | #477 | — | 67 | 6 | no | — |
| 232 | #477 | — | 67 | 6 | no | — |
| 233 | #467 | — | 67 | 6 | no | — |
| 234 | #467 | — | 67 | 6 | no | — |
| 235 | #462 | — | 67 | 6 | no | — |
| 236 | #462 | C2×D67 | 1 | 6 | yes | — |
| 237 | #451 | — | 67 | 12 | no | — |
| 238 | C8×Q8 | — | 67 | 1 | no | — |
| 239 | C8×Q8 | C2×D67 | 1 | 1 | yes | characteristic |
| 240 | C4×Q16 | — | 67 | 6 | no | — |
| 241 | C4×Q16 | — | 67 | 3 | no | — |
| 242 | C4×Q16 | — | 67 | 6 | no | — |
| 243 | C4×Q16 | — | 67 | 1 | no | — |
| 244 | C4×Q16 | — | 67 | 6 | no | — |
| 245 | C4×Q16 | — | 67 | 3 | no | — |
| 246 | C4×Q16 | C2×D67 | 1 | 3 | yes | — |
| 247 | C8×D4 | — | 67 | 3 | no | — |
| 248 | C8×D4 | — | 67 | 3 | no | — |
| 249 | #431 | — | 67 | 3 | no | — |
| 250 | C2×#107 | — | 67 | 3 | no | — |
| 251 | C2×#103 | — | 67 | 6 | no | — |
| 252 | C2×C4×C8 | — | 67 | 3 | no | — |
| 253 | C2×#41 | — | 67 | 1 | no | — |
| 254 | C22×Q8 | — | 67 | 6 | no | — |
| 255 | C2×Q16 | — | 67 | 6 | no | — |
| 256 | C2×Q16 | — | 67 | 1 | no | — |
| 257 | C2×Q16 | — | 134 | 12 | no | — |
| 258 | C2×Q16 | C22×D67 | 1 | 3 | yes | — |
| 259 | C2×Q16 | C22×D67 | 1 | 6 | yes | — |
| 260 | C22×C8 | — | 67 | 3 | no | — |
| 261 | C22×C8 | — | 67 | 3 | no | — |
| 262 | C4⋊Q8 | — | 67 | 6 | no | — |
| 263 | C4⋊Q8 | — | 134 | 6 | no | — |
| 264 | C4⋊Q8 | — | 134 | 6 | no | — |
| 265 | C4⋊Q8 | C22×D67 | 1 | 6 | yes | — |
| 266 | #125 | — | 2 | 6 | no | — |
| 267 | #125 | — | 134 | 6 | no | — |
| 268 | #125 | — | 134 | 6 | no | — |
| 269 | C22⋊Q8 | — | 67 | 12 | no | — |
| 270 | C22⋊Q8 | — | 134 | 12 | no | — |
| 271 | C22⋊Q8 | — | 134 | 12 | no | — |
| 272 | C22⋊Q8 | — | 134 | 6 | no | — |
| 273 | C4×Q8 | — | 2 | 2 | no | — |
| 274 | C4×Q8 | — | 67 | 1 | no | — |
| 275 | C4×Q8 | — | 67 | 6 | no | — |
| 276 | C4×Q8 | — | 67 | 2 | no | — |
| 277 | C4×Q8 | — | 67 | 6 | no | — |
| 278 | C4×Q8 | — | 134 | 6 | no | — |
| 279 | C4×Q8 | — | 134 | 6 | no | — |
| 280 | C4×Q8 | — | 134 | 6 | no | — |
| 281 | C4×Q8 | — | 134 | 2 | no | — |
| 282 | C4×Q8 | C22×D67 | 1 | 6 | yes | — |
| 283 | C4×Q8 | C22×D67 | 1 | 1 | yes | characteristic |
| 284 | C4×D4 | — | 67 | 3 | no | — |
| 285 | C4×D4 | — | 67 | 3 | no | — |
| 286 | C4×D4 | — | 134 | 6 | no | — |
| 287 | C4×D4 | — | 134 | 6 | no | — |
| 288 | #117 | — | 67 | 3 | no | — |
| 289 | #117 | — | 134 | 6 | no | — |
| 290 | C2×C4⋊C4 | — | 67 | 6 | no | — |
| 291 | C2×C4⋊C4 | — | 134 | 6 | no | — |
| 292 | C2×C42 | — | 67 | 3 | no | — |
| 293 | C2×C42 | — | 134 | 6 | no | — |
| 294 | #107 | — | 67 | 3 | no | — |
| 295 | #107 | — | 67 | 6 | no | — |
| 296 | #107 | — | 67 | 6 | no | — |
| 297 | #107 | C22×D67 | 1 | 1 | yes | characteristic |
| 298 | C4⋊C8 | — | 67 | 3 | no | — |
| 299 | C4⋊C8 | C22×D67 | 1 | 3 | yes | — |
| 300 | #103 | — | 67 | 6 | no | — |
| 301 | #103 | — | 67 | 12 | no | — |
| 302 | #103 | — | 67 | 6 | no | — |
| 303 | #103 | — | 67 | 2 | no | — |
| 304 | #103 | C22×D67 | 1 | 6 | yes | — |
| 305 | C22⋊C8 | — | 67 | 6 | no | — |
| 306 | C4×C8 | — | 67 | 1 | no | — |
| 307 | C4×C8 | — | 67 | 3 | no | — |
| 308 | C4×C8 | — | 67 | 3 | no | — |
| 309 | C4×C8 | C22×D67 | 1 | 3 | yes | — |
| 310 | #41 | — | 67 | 8 | no | — |
| 311 | C2×Q8 | — | 268 | 6 | no | — |
| 312 | C2×Q8 | — | 67 | 2 | no | — |
| 313 | C2×Q8 | — | 134 | 6 | no | — |
| 314 | C2×Q8 | — | 134 | 12 | no | — |
| 315 | C2×Q8 | — | 134 | 6 | no | — |
| 316 | C2×Q8 | D4×D67 | 1 | 1 | yes | characteristic |
| 317 | C2×Q8 | C23×D67 | 1 | 6 | yes | — |
| 318 | C2×D4 | — | 67 | 3 | no | — |
| 319 | C22×C4 | — | 67 | 3 | no | — |
| 320 | C22×C4 | — | 67 | 3 | no | — |
| 321 | C22×C4 | — | 67 | 3 | no | — |
| 322 | C22×C4 | — | 134 | 6 | no | — |
| 323 | C22×C4 | — | 134 | 6 | no | — |
| 324 | Q16 | — | 2 | 6 | no | — |
| 325 | Q16 | — | 4 | 6 | no | — |
| 326 | Q16 | — | 67 | 4 | no | — |
| 327 | Q16 | — | 134 | 12 | no | — |
| 328 | C2×C8 | — | 268 | 3 | no | — |
| 329 | C2×C8 | — | 67 | 1 | no | — |
| 330 | C2×C8 | — | 67 | 3 | no | — |
| 331 | C2×C8 | — | 134 | 6 | no | — |
| 332 | C2×C8 | C23×D67 | 1 | 3 | yes | — |
| 333 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 334 | C4⋊C4 | — | 2 | 6 | no | — |
| 335 | C4⋊C4 | — | 2 | 6 | no | — |
| 336 | C4⋊C4 | — | 2 | 6 | no | — |
| 337 | C4⋊C4 | — | 67 | 3 | no | — |
| 338 | C4⋊C4 | — | 67 | 6 | no | — |
| 339 | C4⋊C4 | — | 134 | 6 | no | — |
| 340 | C4⋊C4 | — | 134 | 2 | no | — |
| 341 | C4⋊C4 | — | 134 | 6 | no | — |
| 342 | C4⋊C4 | — | 134 | 12 | no | — |
| 343 | C4⋊C4 | — | 134 | 6 | no | — |
| 344 | C4⋊C4 | — | 134 | 6 | no | — |
| 345 | C4⋊C4 | D4×D67 | 1 | 3 | yes | — |
| 346 | C4⋊C4 | C23×D67 | 1 | 2 | yes | — |
| 347 | C22⋊C4 | — | 67 | 6 | no | — |
| 348 | C22⋊C4 | — | 134 | 12 | no | — |
| 349 | C42 | — | 2 | 6 | no | — |
| 350 | C42 | — | 67 | 3 | no | — |
| 351 | C42 | — | 67 | 3 | no | — |
| 352 | C42 | — | 67 | 1 | no | — |
| 353 | C42 | — | 134 | 2 | no | — |
| 354 | C42 | — | 134 | 6 | no | — |
| 355 | C42 | — | 134 | 6 | no | — |
| 356 | C42 | C23×D67 | 1 | 3 | yes | — |
| 357 | C23 | — | 67 | 3 | no | — |
| 358 | Q8 | — | 2 | 6 | no | — |
| 359 | Q8 | — | 2 | 6 | no | — |
| 360 | Q8 | — | 268 | 12 | no | — |
| 361 | Q8 | — | 536 | 6 | no | — |
| 362 | Q8 | — | 67 | 4 | no | — |
| 363 | Q8 | — | 134 | 2 | no | — |
| 364 | Q8 | Q16×D67 | 1 | 4 | yes | complemented |
| 365 | D4 | — | 67 | 12 | no | — |
| 366 | C2×C4 | — | 2 | 2 | no | — |
| 367 | C2×C4 | — | 2 | 6 | no | — |
| 368 | C2×C4 | — | 268 | 3 | no | — |
| 369 | C2×C4 | — | 268 | 12 | no | — |
| 370 | C2×C4 | — | 536 | 6 | no | — |
| 371 | C2×C4 | — | 67 | 1 | no | — |
| 372 | C2×C4 | — | 67 | 12 | no | — |
| 373 | C2×C4 | — | 67 | 1 | no | — |
| 374 | C2×C4 | — | 67 | 3 | no | — |
| 375 | C2×C4 | — | 134 | 6 | no | — |
| 376 | C2×C4 | — | 134 | 2 | no | — |
| 377 | C2×C4 | — | 134 | 3 | no | — |
| 378 | C2×C4 | — | 134 | 3 | no | — |
| 379 | C2×C4 | C2×D4×D67 | 1 | 3 | yes | — |
| 380 | C2×C4 | C2×D4×D67 | 1 | 3 | yes | — |
| 381 | C2×C4 | C24×D67 | 1 | 1 | yes | characteristic |
| 382 | C8 | — | 2 | 3 | no | — |
| 383 | C8 | — | 134 | 3 | no | — |
| 384 | C8 | — | 134 | 1 | no | — |
| 385 | C8 | #41×D67 | 1 | 2 | yes | — |
| 386 | C22 | — | 67 | 6 | no | — |
| 387 | C22 | — | 134 | 3 | no | — |
| 388 | C22 | — | 134 | 3 | no | — |
| 389 | C22 | C22×D4×D67 | 1 | 1 | yes | characteristic |
| 390 | C4 | — | 2 | 3 | no | — |
| 391 | C4 | — | 4 | 6 | no | — |
| 392 | C4 | — | 4 | 2 | no | — |
| 393 | C4 | — | 268 | 6 | no | — |
| 394 | C4 | — | 67 | 2 | no | — |
| 395 | C4 | — | 134 | 4 | no | — |
| 396 | C4 | — | 134 | 3 | no | — |
| 397 | C4 | — | 134 | 1 | no | — |
| 398 | C4 | C2×Q16×D67 | 1 | 6 | yes | — |
| 399 | C4 | C2×#41×D67 | 1 | 1 | yes | characteristic |
| 400 | C4 | #16864231 | 1 | 1 | yes | characteristic |
| 401 | C2 | — | 134 | 6 | no | — |
| 402 | C2 | #22573699 | 1 | 1 | yes | characteristic |
| 403 | C2 | C22×Q16×D67 | 1 | 1 | yes | characteristic |
| 404 | C2 | #22574979 | 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