← Q8×#14524065 #31736300
Subgroups — Q8×#14524065 #31736300
Order 17152.
1786 conjugacy classes of subgroups.
The subgroup lattice has 416 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | Q8×#11761628 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22573101 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | Q8×Dic268 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22573086 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #22573077 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | Q8×#11761617 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | Q8×D536 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #22570723 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #22569999 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | C4×#14524065 | C2 | 1 | 3 | yes | maximal |
| 11 | C2×C8×Q8×C67 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#14524065 | C22 | 1 | 1 | yes | characteristic |
| 13 | Q8×Dic134 | C22 | 1 | 2 | yes | — |
| 14 | #16864124 | C22 | 1 | 6 | yes | — |
| 15 | #16864106 | C22 | 1 | 6 | yes | — |
| 16 | #16864101 | — | 2 | 6 | no | — |
| 17 | Q8×D268 | C22 | 1 | 2 | yes | — |
| 18 | Q8×C22⋊D67 | — | 2 | 2 | no | — |
| 19 | #16863953 | C22 | 1 | 6 | yes | — |
| 20 | #16863950 | — | 2 | 6 | no | — |
| 21 | C4×#11761628 | C22 | 1 | 6 | yes | — |
| 22 | C4×Q8×D67 | — | 2 | 2 | no | — |
| 23 | #16863801 | C22 | 1 | 3 | yes | — |
| 24 | #16863801 | C22 | 1 | 3 | yes | — |
| 25 | #16863798 | C22 | 1 | 6 | yes | — |
| 26 | #16863798 | C22 | 1 | 6 | yes | — |
| 27 | #16863794 | C22 | 1 | 6 | yes | — |
| 28 | #16863704 | C22 | 1 | 12 | yes | — |
| 29 | #16863697 | C22 | 1 | 12 | yes | — |
| 30 | #16863692 | C22 | 1 | 6 | yes | — |
| 31 | #16863687 | C22 | 1 | 6 | yes | — |
| 32 | #16863682 | C22 | 1 | 6 | yes | — |
| 33 | #16863677 | C22 | 1 | 6 | yes | — |
| 34 | C4×Dic268 | C22 | 1 | 3 | yes | — |
| 35 | C4×Dic268 | C22 | 1 | 3 | yes | — |
| 36 | C4×#11761617 | C22 | 1 | 6 | yes | — |
| 37 | C4×#11761617 | C22 | 1 | 6 | yes | — |
| 38 | C4×D536 | C22 | 1 | 3 | yes | — |
| 39 | C4×D536 | C22 | 1 | 3 | yes | — |
| 40 | #16863434 | C22 | 1 | 6 | yes | — |
| 41 | #16863434 | C22 | 1 | 3 | yes | — |
| 42 | #16863393 | C22 | 1 | 6 | yes | — |
| 43 | C2×C4×Q8×C67 | C22 | 1 | 1 | yes | characteristic |
| 44 | C8×Q8×C67 | C22 | 1 | 1 | yes | characteristic |
| 45 | C8×Q8×C67 | C22 | 1 | 1 | yes | characteristic |
| 46 | C8×Q8×C67 | C22 | 1 | 3 | yes | — |
| 47 | C8×Q8×C67 | C22 | 1 | 3 | yes | — |
| 48 | C2×C4⋊C8×C67 | C22 | 1 | 3 | yes | — |
| 49 | C2×C4×C8×C67 | C22 | 1 | 3 | yes | — |
| 50 | C2×#11761628 | C23 | 1 | 2 | yes | — |
| 51 | C2×Q8×D67 | — | 2 | 2 | no | — |
| 52 | #14524065 | Q8 | 1 | 8 | yes | direct product factor |
| 53 | C2×Dic268 | C23 | 1 | 1 | yes | characteristic |
| 54 | C2×#11761617 | C23 | 1 | 2 | yes | — |
| 55 | C2×D536 | C23 | 1 | 1 | yes | characteristic |
| 56 | #14524043 | C23 | 1 | 6 | yes | — |
| 57 | #14524043 | C23 | 1 | 6 | yes | — |
| 58 | #14524042 | — | 2 | 6 | no | — |
| 59 | #14524041 | — | 2 | 6 | no | — |
| 60 | #14524035 | C23 | 1 | 12 | yes | — |
| 61 | #14524033 | — | 2 | 12 | no | — |
| 62 | #14524023 | — | 2 | 6 | no | — |
| 63 | #14524022 | — | 2 | 6 | no | — |
| 64 | #14524022 | — | 2 | 6 | no | — |
| 65 | #14524021 | — | 2 | 12 | no | — |
| 66 | #14524019 | — | 2 | 6 | no | — |
| 67 | Q8×Dic67 | — | 2 | 2 | no | — |
| 68 | C4×Dic134 | — | 2 | 6 | no | — |
| 69 | C4×Dic134 | — | 2 | 6 | no | — |
| 70 | C4×Dic134 | C23 | 1 | 6 | yes | — |
| 71 | C4×Dic134 | C23 | 1 | 6 | yes | — |
| 72 | #14524008 | — | 2 | 6 | no | — |
| 73 | C4×D268 | C23 | 1 | 6 | yes | — |
| 74 | C4×D268 | C23 | 1 | 6 | yes | — |
| 75 | C4×C22⋊D67 | — | 2 | 6 | no | — |
| 76 | C4×C22⋊D67 | — | 2 | 6 | no | — |
| 77 | #14524002 | C23 | 1 | 6 | yes | — |
| 78 | #14524000 | — | 2 | 6 | no | — |
| 79 | C4⋊C4×D67 | — | 2 | 6 | no | — |
| 80 | C42×D67 | — | 2 | 6 | no | — |
| 81 | #14523977 | C23 | 1 | 3 | yes | — |
| 82 | #14523977 | C23 | 1 | 3 | yes | — |
| 83 | #14523977 | C23 | 1 | 6 | yes | — |
| 84 | #14523977 | C23 | 1 | 6 | yes | — |
| 85 | #14523975 | C23 | 1 | 6 | yes | — |
| 86 | #14523975 | C23 | 1 | 12 | yes | — |
| 87 | #14523968 | C23 | 1 | 6 | yes | — |
| 88 | #14523968 | C23 | 1 | 6 | yes | — |
| 89 | #14523965 | C23 | 1 | 6 | yes | — |
| 90 | #14523965 | C23 | 1 | 6 | yes | — |
| 91 | C22×Q8×C67 | D4 | 1 | 1 | yes | characteristic |
| 92 | C22×C8×C67 | C23 | 1 | 3 | yes | — |
| 93 | C22×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 94 | C4×Q8×C67 | D4 | 1 | 1 | yes | characteristic |
| 95 | C4×Q8×C67 | D4 | 1 | 3 | yes | — |
| 96 | C4×Q8×C67 | C23 | 1 | 1 | yes | characteristic |
| 97 | C4×Q8×C67 | C23 | 1 | 3 | yes | — |
| 98 | C2×C4⋊C4×C67 | D4 | 1 | 3 | yes | — |
| 99 | C2×C42×C67 | C23 | 1 | 3 | yes | — |
| 100 | C4⋊C8×C67 | C23 | 1 | 3 | yes | — |
| 101 | C4⋊C8×C67 | C23 | 1 | 3 | yes | — |
| 102 | C4⋊C8×C67 | C23 | 1 | 6 | yes | — |
| 103 | C4×C8×C67 | C23 | 1 | 3 | yes | — |
| 104 | C4×C8×C67 | C23 | 1 | 3 | yes | — |
| 105 | C4×C8×C67 | C23 | 1 | 3 | yes | — |
| 106 | C4×C8×C67 | C23 | 1 | 3 | yes | — |
| 107 | #11761628 | — | 2 | 4 | no | — |
| 108 | #11761628 | C2×Q8 | 1 | 8 | yes | complemented |
| 109 | C2×Dic134 | — | 2 | 6 | no | — |
| 110 | C2×Dic134 | — | 2 | 6 | no | — |
| 111 | C2×Dic134 | C24 | 1 | 2 | yes | — |
| 112 | Q8×D67 | — | 4 | 8 | no | — |
| 113 | C2×D268 | C24 | 1 | 2 | yes | — |
| 114 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 115 | C2×C4×D67 | — | 2 | 2 | no | — |
| 116 | C2×C4×D67 | — | 2 | 6 | no | — |
| 117 | C2×C4×D67 | — | 2 | 6 | no | — |
| 118 | Dic268 | C2×Q8 | 1 | 4 | yes | complemented |
| 119 | #11761617 | C2×Q8 | 1 | 8 | yes | complemented |
| 120 | D536 | C2×Q8 | 1 | 4 | yes | complemented |
| 121 | C4⋊Dic67 | — | 2 | 6 | no | — |
| 122 | C4⋊Dic67 | — | 2 | 6 | no | — |
| 123 | C4⋊Dic67 | C24 | 1 | 6 | yes | — |
| 124 | C4⋊Dic67 | C24 | 1 | 6 | yes | — |
| 125 | Dic67⋊C4 | — | 2 | 12 | no | — |
| 126 | Dic67⋊C4 | — | 2 | 6 | no | — |
| 127 | Dic67⋊C4 | — | 2 | 6 | no | — |
| 128 | Dic67⋊C4 | — | 2 | 12 | no | — |
| 129 | C22⋊Dic67 | — | 2 | 6 | no | — |
| 130 | (C2×D67)⋊C4 | — | 2 | 6 | no | — |
| 131 | (C2×D67)⋊C4 | — | 2 | 6 | no | — |
| 132 | C4×Dic67 | — | 2 | 6 | no | — |
| 133 | C4×Dic67 | — | 2 | 6 | no | — |
| 134 | C4×Dic67 | — | 2 | 6 | no | — |
| 135 | C2×Q8×C67 | — | 2 | 4 | no | — |
| 136 | C2×Q8×C67 | C2×D4 | 1 | 3 | yes | — |
| 137 | C2×Q8×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | C22×C4×C67 | C2×D4 | 1 | 3 | yes | — |
| 139 | C22×C4×C67 | C2×D4 | 1 | 3 | yes | — |
| 140 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 141 | C2×C8×C67 | — | 2 | 6 | no | — |
| 142 | C2×C8×C67 | C2×Q8 | 1 | 4 | yes | complemented |
| 143 | C2×C8×C67 | C24 | 1 | 3 | yes | — |
| 144 | C2×C8×C67 | C24 | 1 | 3 | yes | — |
| 145 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 146 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 147 | C4⋊C4×C67 | C2×D4 | 1 | 3 | yes | — |
| 148 | C4⋊C4×C67 | C2×D4 | 1 | 6 | yes | — |
| 149 | C4⋊C4×C67 | C2×D4 | 1 | 3 | yes | — |
| 150 | C42×C67 | C2×D4 | 1 | 3 | yes | — |
| 151 | C42×C67 | C2×D4 | 1 | 3 | yes | — |
| 152 | C42×C67 | C24 | 1 | 3 | yes | — |
| 153 | C42×C67 | C24 | 1 | 3 | yes | — |
| 154 | C23×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 155 | C22×D67 | — | 2 | 2 | no | — |
| 156 | Q8×C67 | — | 2 | 6 | no | — |
| 157 | Q8×C67 | #135 | 1 | 4 | yes | complemented |
| 158 | C2×C4×C67 | — | 2 | 6 | no | — |
| 159 | C2×C4×C67 | — | 4 | 3 | no | — |
| 160 | C2×C4×C67 | C22×D4 | 1 | 3 | yes | — |
| 161 | C2×C4×C67 | C22×D4 | 1 | 3 | yes | — |
| 162 | C2×C4×C67 | C22×D4 | 1 | 3 | yes | — |
| 163 | C2×C4×C67 | C22×D4 | 1 | 3 | yes | — |
| 164 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 165 | C2×C4×C67 | C22×Q8 | 1 | 2 | yes | — |
| 166 | C2×C4×C67 | 2−1+4 | 1 | 2 | yes | — |
| 167 | C2×C4×C67 | C25 | 1 | 1 | yes | characteristic |
| 168 | C22⋊D67 | — | 2 | 8 | no | — |
| 169 | C2×Dic67 | — | 2 | 2 | no | — |
| 170 | C2×Dic67 | — | 2 | 6 | no | — |
| 171 | C2×Dic67 | — | 2 | 6 | no | — |
| 172 | D268 | — | 2 | 2 | no | — |
| 173 | D268 | C22×Q8 | 1 | 4 | yes | — |
| 174 | C4×D67 | — | 2 | 8 | no | — |
| 175 | C4×D67 | — | 4 | 12 | no | — |
| 176 | C4×D67 | — | 8 | 6 | no | — |
| 177 | Dic134 | — | 2 | 2 | no | — |
| 178 | Dic134 | — | 4 | 12 | no | — |
| 179 | Dic134 | — | 8 | 6 | no | — |
| 180 | Dic134 | C22×Q8 | 1 | 4 | yes | — |
| 181 | C8×C67 | — | 2 | 3 | no | — |
| 182 | C8×C67 | — | 2 | 3 | no | — |
| 183 | C8×C67 | C22×Q8 | 1 | 2 | yes | — |
| 184 | C8×C67 | C22×Q8 | 1 | 2 | yes | — |
| 185 | C22×C67 | — | 2 | 1 | no | — |
| 186 | C22×C67 | — | 2 | 1 | no | — |
| 187 | C22×C67 | D4×Q8 | 1 | 2 | yes | — |
| 188 | C22×C67 | C23×D4 | 1 | 1 | yes | characteristic |
| 189 | C2×D67 | — | 2 | 4 | no | — |
| 190 | C2×D67 | — | 4 | 2 | no | — |
| 191 | C2×D67 | — | 4 | 2 | no | — |
| 192 | C4×C67 | — | 2 | 3 | no | — |
| 193 | C4×C67 | — | 2 | 3 | no | — |
| 194 | C4×C67 | — | 2 | 3 | no | — |
| 195 | C4×C67 | D4×Q8 | 1 | 2 | yes | — |
| 196 | C4×C67 | C2×#135 | 1 | 6 | yes | — |
| 197 | C4×C67 | C23×Q8 | 1 | 1 | yes | characteristic |
| 198 | C4×C67 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 199 | Dic67 | — | 2 | 4 | no | — |
| 200 | Dic67 | — | 4 | 6 | no | — |
| 201 | Dic67 | — | 4 | 6 | no | — |
| 202 | Q8×#135 | — | 67 | 1 | no | maximal, Sylow |
| 203 | C2×C67 | — | 2 | 2 | no | — |
| 204 | C2×C67 | C2×D4×Q8 | 1 | 1 | yes | characteristic |
| 205 | C2×C67 | C22×#135 | 1 | 1 | yes | characteristic |
| 206 | C2×C67 | #3584 | 1 | 1 | yes | characteristic |
| 207 | D67 | — | 4 | 4 | no | — |
| 208 | Q8×#41 | — | 67 | 2 | no | — |
| 209 | #3383 | — | 67 | 3 | no | — |
| 210 | Q8×Q16 | — | 67 | 1 | no | — |
| 211 | #3381 | — | 67 | 6 | no | — |
| 212 | #3380 | — | 67 | 3 | no | — |
| 213 | Q8×SD16 | — | 67 | 2 | no | — |
| 214 | Q8×D8 | — | 67 | 1 | no | — |
| 215 | #3160 | — | 67 | 3 | no | — |
| 216 | #3076 | — | 67 | 6 | no | — |
| 217 | C2×C8×Q8 | D67 | 1 | 1 | yes | characteristic, complemented |
| 218 | C4×#135 | — | 67 | 3 | no | — |
| 219 | C67 | Q8×#135 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 220 | C2×#135 | — | 67 | 1 | no | — |
| 221 | Q82 | — | 67 | 2 | no | — |
| 222 | #557 | — | 67 | 6 | no | — |
| 223 | #554 | — | 67 | 6 | no | — |
| 224 | #554 | — | 134 | 6 | no | — |
| 225 | D4×Q8 | — | 67 | 2 | no | — |
| 226 | D4×Q8 | — | 134 | 2 | no | — |
| 227 | #533 | — | 67 | 6 | no | — |
| 228 | #533 | — | 134 | 6 | no | — |
| 229 | C4×#41 | — | 67 | 6 | no | — |
| 230 | C2×C4×Q8 | — | 134 | 2 | no | — |
| 231 | C2×C4×Q8 | C2×D67 | 1 | 1 | yes | characteristic |
| 232 | #500 | — | 67 | 3 | no | — |
| 233 | #500 | — | 67 | 3 | no | — |
| 234 | #499 | — | 67 | 6 | no | — |
| 235 | #499 | — | 67 | 6 | no | — |
| 236 | #498 | — | 67 | 6 | no | — |
| 237 | #479 | — | 67 | 12 | no | — |
| 238 | #478 | — | 67 | 12 | no | — |
| 239 | #477 | — | 67 | 6 | no | — |
| 240 | #476 | — | 67 | 6 | no | — |
| 241 | #475 | — | 67 | 6 | no | — |
| 242 | #474 | — | 67 | 6 | no | — |
| 243 | C8×Q8 | C2×D67 | 1 | 1 | yes | characteristic |
| 244 | C8×Q8 | C2×D67 | 1 | 1 | yes | characteristic |
| 245 | C8×Q8 | C2×D67 | 1 | 3 | yes | — |
| 246 | C8×Q8 | C2×D67 | 1 | 3 | yes | — |
| 247 | C4×Q16 | — | 67 | 3 | no | — |
| 248 | C4×Q16 | — | 67 | 3 | no | — |
| 249 | C4×SD16 | — | 67 | 6 | no | — |
| 250 | C4×SD16 | — | 67 | 6 | no | — |
| 251 | C4×D8 | — | 67 | 3 | no | — |
| 252 | C4×D8 | — | 67 | 3 | no | — |
| 253 | #427 | — | 67 | 6 | no | — |
| 254 | #427 | — | 67 | 3 | no | — |
| 255 | C2×C4⋊C8 | C2×D67 | 1 | 3 | yes | — |
| 256 | #416 | — | 67 | 6 | no | — |
| 257 | C2×C4×C8 | C2×D67 | 1 | 3 | yes | — |
| 258 | C2×#41 | — | 67 | 2 | no | — |
| 259 | C22×Q8 | — | 134 | 2 | no | — |
| 260 | C22×Q8 | D268 | 1 | 1 | yes | characteristic |
| 261 | #135 | — | 67 | 8 | no | — |
| 262 | C2×Q16 | — | 67 | 1 | no | — |
| 263 | C2×SD16 | — | 67 | 2 | no | — |
| 264 | C2×D8 | — | 67 | 1 | no | — |
| 265 | C22×C8 | C22×D67 | 1 | 3 | yes | — |
| 266 | C22×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 267 | C4⋊Q8 | — | 67 | 6 | no | — |
| 268 | C4⋊Q8 | — | 67 | 6 | no | — |
| 269 | C4⋊Q8 | — | 134 | 6 | no | — |
| 270 | C4⋊Q8 | — | 134 | 6 | no | — |
| 271 | #125 | — | 67 | 12 | no | — |
| 272 | #125 | — | 134 | 12 | no | — |
| 273 | C22⋊Q8 | — | 134 | 6 | no | — |
| 274 | C22⋊Q8 | — | 134 | 6 | no | — |
| 275 | C22⋊Q8 | — | 134 | 6 | no | — |
| 276 | C22⋊Q8 | — | 134 | 6 | no | — |
| 277 | C22⋊Q8 | — | 134 | 12 | no | — |
| 278 | C4×Q8 | — | 67 | 6 | no | — |
| 279 | C4×Q8 | — | 67 | 6 | no | — |
| 280 | C4×Q8 | — | 134 | 2 | no | — |
| 281 | C4×Q8 | — | 134 | 6 | no | — |
| 282 | C4×Q8 | — | 134 | 6 | no | — |
| 283 | C4×Q8 | — | 134 | 6 | no | — |
| 284 | C4×Q8 | D268 | 1 | 1 | yes | characteristic |
| 285 | C4×Q8 | D268 | 1 | 3 | yes | — |
| 286 | C4×Q8 | C22×D67 | 1 | 1 | yes | characteristic |
| 287 | C4×Q8 | C22×D67 | 1 | 3 | yes | — |
| 288 | C4×D4 | — | 67 | 6 | no | — |
| 289 | C4×D4 | — | 67 | 6 | no | — |
| 290 | C4×D4 | — | 134 | 6 | no | — |
| 291 | C4×D4 | — | 134 | 6 | no | — |
| 292 | #117 | — | 67 | 6 | no | — |
| 293 | #117 | — | 134 | 6 | no | — |
| 294 | C2×C4⋊C4 | — | 134 | 6 | no | — |
| 295 | C2×C4⋊C4 | D268 | 1 | 3 | yes | — |
| 296 | C2×C42 | — | 134 | 6 | no | — |
| 297 | C2×C42 | C22×D67 | 1 | 3 | yes | — |
| 298 | #107 | — | 67 | 3 | no | — |
| 299 | #107 | — | 67 | 3 | no | — |
| 300 | #107 | — | 67 | 6 | no | — |
| 301 | #107 | — | 67 | 6 | no | — |
| 302 | #106 | — | 67 | 6 | no | — |
| 303 | #106 | — | 67 | 12 | no | — |
| 304 | C4⋊C8 | C22×D67 | 1 | 3 | yes | — |
| 305 | C4⋊C8 | C22×D67 | 1 | 3 | yes | — |
| 306 | C4⋊C8 | C22×D67 | 1 | 6 | yes | — |
| 307 | #103 | — | 67 | 6 | no | — |
| 308 | #103 | — | 67 | 6 | no | — |
| 309 | #102 | — | 67 | 6 | no | — |
| 310 | #102 | — | 67 | 6 | no | — |
| 311 | C4×C8 | C22×D67 | 1 | 3 | yes | — |
| 312 | C4×C8 | C22×D67 | 1 | 3 | yes | — |
| 313 | C4×C8 | C22×D67 | 1 | 3 | yes | — |
| 314 | C4×C8 | C22×D67 | 1 | 3 | yes | — |
| 315 | #41 | — | 67 | 8 | no | — |
| 316 | #41 | — | 134 | 4 | no | — |
| 317 | C2×Q8 | — | 2 | 4 | no | — |
| 318 | C2×Q8 | — | 268 | 8 | no | — |
| 319 | C2×Q8 | — | 67 | 2 | no | — |
| 320 | C2×Q8 | — | 134 | 6 | no | — |
| 321 | C2×Q8 | — | 134 | 6 | no | — |
| 322 | C2×Q8 | C2×D268 | 1 | 3 | yes | — |
| 323 | C2×Q8 | C2×D268 | 1 | 1 | yes | characteristic |
| 324 | C2×D4 | — | 67 | 2 | no | — |
| 325 | C2×D4 | — | 134 | 2 | no | — |
| 326 | C22×C4 | — | 134 | 6 | no | — |
| 327 | C22×C4 | — | 134 | 6 | no | — |
| 328 | C22×C4 | — | 134 | 2 | no | — |
| 329 | C22×C4 | C2×D268 | 1 | 3 | yes | — |
| 330 | C22×C4 | C2×D268 | 1 | 3 | yes | — |
| 331 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 332 | Q16 | — | 67 | 4 | no | — |
| 333 | SD16 | — | 67 | 8 | no | — |
| 334 | D8 | — | 67 | 4 | no | — |
| 335 | C2×C8 | — | 2 | 6 | no | — |
| 336 | C2×C8 | Q8×D67 | 1 | 4 | yes | complemented |
| 337 | C2×C8 | C23×D67 | 1 | 3 | yes | — |
| 338 | C2×C8 | C23×D67 | 1 | 3 | yes | — |
| 339 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 340 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 341 | C4⋊C4 | — | 67 | 6 | no | — |
| 342 | C4⋊C4 | — | 67 | 6 | no | — |
| 343 | C4⋊C4 | — | 134 | 12 | no | — |
| 344 | C4⋊C4 | — | 134 | 6 | no | — |
| 345 | C4⋊C4 | — | 134 | 6 | no | — |
| 346 | C4⋊C4 | — | 134 | 6 | no | — |
| 347 | C4⋊C4 | — | 134 | 12 | no | — |
| 348 | C4⋊C4 | — | 134 | 6 | no | — |
| 349 | C4⋊C4 | C2×D268 | 1 | 3 | yes | — |
| 350 | C4⋊C4 | C2×D268 | 1 | 6 | yes | — |
| 351 | C4⋊C4 | C2×D268 | 1 | 3 | yes | — |
| 352 | C22⋊C4 | — | 134 | 6 | no | — |
| 353 | C22⋊C4 | — | 134 | 6 | no | — |
| 354 | C22⋊C4 | — | 134 | 6 | no | — |
| 355 | C42 | — | 134 | 6 | no | — |
| 356 | C42 | — | 134 | 6 | no | — |
| 357 | C42 | — | 134 | 6 | no | — |
| 358 | C42 | C2×D268 | 1 | 3 | yes | — |
| 359 | C42 | C2×D268 | 1 | 3 | yes | — |
| 360 | C42 | C23×D67 | 1 | 3 | yes | — |
| 361 | C42 | C23×D67 | 1 | 3 | yes | — |
| 362 | C23 | — | 134 | 2 | no | — |
| 363 | C23 | C22×D268 | 1 | 1 | yes | characteristic |
| 364 | Q8 | — | 2 | 6 | no | — |
| 365 | Q8 | — | 268 | 12 | no | — |
| 366 | Q8 | — | 536 | 6 | no | — |
| 367 | Q8 | — | 67 | 4 | no | — |
| 368 | Q8 | — | 134 | 2 | no | — |
| 369 | Q8 | #14524065 | 1 | 4 | yes | direct product factor |
| 370 | D4 | — | 67 | 4 | no | — |
| 371 | D4 | — | 134 | 8 | no | — |
| 372 | D4 | — | 134 | 2 | no | — |
| 373 | C2×C4 | — | 2 | 6 | no | — |
| 374 | C2×C4 | — | 4 | 3 | no | — |
| 375 | C2×C4 | — | 268 | 12 | no | — |
| 376 | C2×C4 | — | 536 | 6 | no | — |
| 377 | C2×C4 | — | 134 | 6 | no | — |
| 378 | C2×C4 | — | 134 | 6 | no | — |
| 379 | C2×C4 | — | 134 | 2 | no | — |
| 380 | C2×C4 | — | 134 | 8 | no | — |
| 381 | C2×C4 | C22×D268 | 1 | 3 | yes | — |
| 382 | C2×C4 | C22×D268 | 1 | 3 | yes | — |
| 383 | C2×C4 | C22×D268 | 1 | 3 | yes | — |
| 384 | C2×C4 | C22×D268 | 1 | 3 | yes | — |
| 385 | C2×C4 | C22×D268 | 1 | 1 | yes | characteristic |
| 386 | C2×C4 | C2×Q8×D67 | 1 | 2 | yes | — |
| 387 | C2×C4 | #14524090 | 1 | 2 | yes | — |
| 388 | C2×C4 | C24×D67 | 1 | 1 | yes | characteristic |
| 389 | C8 | — | 2 | 3 | no | — |
| 390 | C8 | — | 2 | 3 | no | — |
| 391 | C8 | C2×Q8×D67 | 1 | 2 | yes | — |
| 392 | C8 | C2×Q8×D67 | 1 | 2 | yes | — |
| 393 | C22 | — | 2 | 1 | no | — |
| 394 | C22 | — | 2 | 1 | no | — |
| 395 | C22 | — | 268 | 2 | no | — |
| 396 | C22 | — | 268 | 2 | no | — |
| 397 | C22 | — | 134 | 4 | no | — |
| 398 | C22 | Q8×D268 | 1 | 2 | yes | — |
| 399 | C22 | C23×D268 | 1 | 1 | yes | characteristic |
| 400 | C4 | — | 2 | 3 | no | — |
| 401 | C4 | — | 2 | 3 | no | — |
| 402 | C4 | — | 2 | 3 | no | — |
| 403 | C4 | — | 268 | 6 | no | — |
| 404 | C4 | — | 268 | 6 | no | — |
| 405 | C4 | — | 134 | 4 | no | — |
| 406 | C4 | Q8×D268 | 1 | 2 | yes | — |
| 407 | C4 | C2×#14524065 | 1 | 6 | yes | — |
| 408 | C4 | C22×Q8×D67 | 1 | 1 | yes | characteristic |
| 409 | C4 | C2×#14524090 | 1 | 1 | yes | characteristic |
| 410 | C2 | — | 2 | 2 | no | — |
| 411 | C2 | — | 268 | 4 | no | — |
| 412 | C2 | C2×Q8×D268 | 1 | 1 | yes | characteristic |
| 413 | C2 | C22×#14524065 | 1 | 1 | yes | characteristic |
| 414 | C2 | #22574983 | 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