← #510×Dic67 #31009162
Subgroups — #510×Dic67 #31009162
Order 17152.
674 conjugacy classes of subgroups.
The subgroup lattice has 418 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #135×Dic67 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×Q16×Dic67 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22562080 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22562074 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | Q32×Dic67 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | SD32×Dic67 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22561997 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #22561929 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #22561921 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | M32×Dic67 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C2×#510×C67 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #41×Dic67 | — | 2 | 1 | no | — |
| 13 | C2×Q8×Dic67 | — | 2 | 1 | no | — |
| 14 | C2×#14523983 | C22 | 1 | 1 | yes | characteristic |
| 15 | Q16×Dic67 | — | 2 | 1 | no | — |
| 16 | Q16×Dic67 | — | 2 | 1 | no | — |
| 17 | Q16×Dic67 | C22 | 1 | 2 | yes | — |
| 18 | Q16×Dic67 | C22 | 1 | 2 | yes | — |
| 19 | Q16×Dic67 | C22 | 1 | 1 | yes | characteristic |
| 20 | Q16×Dic67 | C22 | 1 | 1 | yes | characteristic |
| 21 | SD16×Dic67 | — | 2 | 1 | no | — |
| 22 | SD16×Dic67 | — | 2 | 1 | no | — |
| 23 | D8×Dic67 | C22 | 1 | 1 | yes | characteristic |
| 24 | D8×Dic67 | C22 | 1 | 1 | yes | characteristic |
| 25 | #16863434 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#14523977 | C22 | 1 | 1 | yes | characteristic |
| 27 | #16863392 | — | 2 | 1 | no | — |
| 28 | C2×#14523967 | — | 2 | 1 | no | — |
| 29 | C2×C8×Dic67 | C22 | 1 | 1 | yes | characteristic |
| 30 | #16863224 | C22 | 1 | 2 | yes | — |
| 31 | #16863222 | C22 | 1 | 2 | yes | — |
| 32 | #16863200 | C22 | 1 | 2 | yes | — |
| 33 | #16863200 | C22 | 1 | 2 | yes | — |
| 34 | #16863200 | C22 | 1 | 2 | yes | — |
| 35 | #16863197 | C22 | 1 | 2 | yes | — |
| 36 | #16863171 | C22 | 1 | 2 | yes | — |
| 37 | C16×Dic67 | C22 | 1 | 2 | yes | — |
| 38 | C2×#135×C67 | C22 | 1 | 1 | yes | characteristic |
| 39 | C22×Q16×C67 | C22 | 1 | 1 | yes | characteristic |
| 40 | #510×C67 | C4 | 1 | 8 | yes | complemented |
| 41 | C2×Q32×C67 | C22 | 1 | 2 | yes | — |
| 42 | C2×SD32×C67 | C22 | 1 | 2 | yes | — |
| 43 | C2×M32×C67 | C22 | 1 | 1 | yes | characteristic |
| 44 | C22×C67⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 45 | Q8×Dic67 | — | 2 | 2 | no | — |
| 46 | Q8×Dic67 | — | 2 | 2 | no | — |
| 47 | Q8×Dic67 | — | 2 | 1 | no | — |
| 48 | Q8×Dic67 | — | 2 | 1 | no | — |
| 49 | Q8×Dic67 | — | 4 | 1 | no | — |
| 50 | Q8×Dic67 | — | 4 | 1 | no | — |
| 51 | D4×Dic67 | — | 2 | 1 | no | — |
| 52 | D4×Dic67 | — | 2 | 1 | no | — |
| 53 | D4×Dic67 | — | 4 | 1 | no | — |
| 54 | D4×Dic67 | — | 4 | 1 | no | — |
| 55 | #14524002 | — | 2 | 1 | no | — |
| 56 | #14524002 | — | 4 | 1 | no | — |
| 57 | C2×C4⋊Dic67 | — | 2 | 1 | no | — |
| 58 | C2×C4⋊Dic67 | — | 4 | 1 | no | — |
| 59 | C2×C4×Dic67 | — | 4 | 1 | no | — |
| 60 | C2×C4×Dic67 | — | 4 | 1 | no | — |
| 61 | C2×C4×Dic67 | D4 | 1 | 1 | yes | characteristic |
| 62 | #14523983 | — | 2 | 2 | no | — |
| 63 | C2×C67⋊C16 | C23 | 1 | 2 | yes | — |
| 64 | #14523977 | — | 2 | 1 | no | — |
| 65 | #14523977 | C23 | 1 | 2 | yes | — |
| 66 | #14523977 | C23 | 1 | 1 | yes | characteristic |
| 67 | #14523977 | C23 | 1 | 1 | yes | characteristic |
| 68 | #14523975 | — | 2 | 1 | no | — |
| 69 | #14523967 | — | 2 | 2 | no | — |
| 70 | #14523967 | — | 2 | 2 | no | — |
| 71 | #14523967 | — | 2 | 1 | no | — |
| 72 | #14523967 | — | 2 | 1 | no | — |
| 73 | #14523964 | — | 2 | 1 | no | — |
| 74 | #14523964 | — | 2 | 1 | no | — |
| 75 | C8×Dic67 | D4 | 1 | 1 | yes | characteristic |
| 76 | C8×Dic67 | D4 | 1 | 1 | yes | characteristic |
| 77 | C8×Dic67 | C23 | 1 | 1 | yes | characteristic |
| 78 | C8×Dic67 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×#41×C67 | — | 2 | 1 | no | — |
| 80 | C22×Q8×C67 | — | 2 | 1 | no | — |
| 81 | #135×C67 | — | 2 | 2 | no | — |
| 82 | #135×C67 | C2×C4 | 1 | 4 | yes | — |
| 83 | C2×Q16×C67 | — | 2 | 1 | no | — |
| 84 | C2×Q16×C67 | — | 2 | 2 | no | — |
| 85 | C2×Q16×C67 | C2×C4 | 1 | 4 | yes | complemented |
| 86 | C2×Q16×C67 | C23 | 1 | 2 | yes | — |
| 87 | C2×Q16×C67 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×SD16×C67 | — | 2 | 1 | no | — |
| 89 | C2×D8×C67 | C23 | 1 | 1 | yes | characteristic |
| 90 | C22×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 91 | Q32×C67 | C2×C4 | 1 | 8 | yes | complemented |
| 92 | SD32×C67 | C2×C4 | 1 | 8 | yes | complemented |
| 93 | M32×C67 | C2×C4 | 1 | 4 | yes | complemented |
| 94 | C2×C16×C67 | C23 | 1 | 2 | yes | — |
| 95 | C22×Dic67 | — | 4 | 1 | no | — |
| 96 | C22×Dic67 | — | 4 | 1 | no | — |
| 97 | C22×Dic67 | — | 4 | 1 | no | — |
| 98 | C22×Dic67 | D8 | 1 | 1 | yes | characteristic |
| 99 | C22×Dic67 | D8 | 1 | 1 | yes | characteristic |
| 100 | C2×C67⋊C8 | — | 2 | 2 | no | — |
| 101 | C2×C67⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | C2×C67⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 103 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 104 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 105 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 106 | C4⋊Dic67 | — | 4 | 1 | no | — |
| 107 | C4⋊Dic67 | — | 4 | 2 | no | — |
| 108 | C4⋊Dic67 | — | 4 | 2 | no | — |
| 109 | C4⋊Dic67 | — | 4 | 1 | no | — |
| 110 | C4⋊Dic67 | — | 4 | 1 | no | — |
| 111 | C22⋊Dic67 | — | 4 | 1 | no | — |
| 112 | C22⋊Dic67 | — | 4 | 1 | no | — |
| 113 | C22⋊Dic67 | — | 4 | 1 | no | — |
| 114 | C4×Dic67 | — | 4 | 1 | no | — |
| 115 | C4×Dic67 | — | 4 | 1 | no | — |
| 116 | C4×Dic67 | — | 4 | 1 | no | — |
| 117 | C4×Dic67 | — | 4 | 2 | no | — |
| 118 | C4×Dic67 | — | 4 | 2 | no | — |
| 119 | C4×Dic67 | D8 | 1 | 1 | yes | characteristic |
| 120 | C4×Dic67 | D8 | 1 | 1 | yes | characteristic |
| 121 | C4×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | C4×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 123 | C67⋊C16 | — | 2 | 2 | no | — |
| 124 | #41×C67 | — | 2 | 4 | no | — |
| 125 | #41×C67 | — | 4 | 2 | no | — |
| 126 | C2×Q8×C67 | — | 2 | 4 | no | — |
| 127 | C2×Q8×C67 | — | 2 | 1 | no | — |
| 128 | C2×Q8×C67 | — | 2 | 2 | no | — |
| 129 | C2×Q8×C67 | — | 4 | 1 | no | — |
| 130 | C2×Q8×C67 | — | 4 | 2 | no | — |
| 131 | C2×D4×C67 | — | 2 | 1 | no | — |
| 132 | C2×D4×C67 | — | 4 | 1 | no | — |
| 133 | C22×C4×C67 | — | 4 | 1 | no | — |
| 134 | C22×C4×C67 | — | 4 | 1 | no | — |
| 135 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | Q16×C67 | — | 2 | 4 | no | — |
| 137 | Q16×C67 | — | 2 | 2 | no | — |
| 138 | Q16×C67 | — | 2 | 1 | no | — |
| 139 | Q16×C67 | C22×C4 | 1 | 4 | yes | — |
| 140 | Q16×C67 | C22×C4 | 1 | 2 | yes | — |
| 141 | SD16×C67 | — | 2 | 4 | no | — |
| 142 | D8×C67 | — | 2 | 1 | no | — |
| 143 | D8×C67 | C22×C4 | 1 | 2 | yes | — |
| 144 | C2×C8×C67 | C22×C4 | 1 | 2 | yes | — |
| 145 | C2×C8×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 146 | C2×C8×C67 | #41 | 1 | 2 | yes | — |
| 147 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 148 | C16×C67 | C22×C4 | 1 | 4 | yes | — |
| 149 | C23×C67 | — | 4 | 1 | no | — |
| 150 | C23×C67 | C2×D8 | 1 | 1 | yes | characteristic |
| 151 | Q8×C67 | — | 2 | 2 | no | — |
| 152 | Q8×C67 | — | 2 | 4 | no | — |
| 153 | Q8×C67 | — | 4 | 2 | no | — |
| 154 | Q8×C67 | — | 4 | 1 | no | — |
| 155 | Q8×C67 | — | 4 | 4 | no | — |
| 156 | D4×C67 | — | 2 | 2 | no | — |
| 157 | D4×C67 | — | 4 | 4 | no | — |
| 158 | D4×C67 | — | 4 | 1 | no | — |
| 159 | C2×C4×C67 | — | 4 | 1 | no | — |
| 160 | C2×C4×C67 | — | 4 | 2 | no | — |
| 161 | C2×C4×C67 | — | 4 | 4 | no | — |
| 162 | C2×C4×C67 | — | 4 | 4 | no | — |
| 163 | C2×C4×C67 | C4×D4 | 1 | 2 | yes | — |
| 164 | C2×C4×C67 | C2×D8 | 1 | 1 | yes | characteristic |
| 165 | C2×C4×C67 | #135 | 1 | 2 | yes | — |
| 166 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 167 | C2×Dic67 | — | 2 | 2 | no | — |
| 168 | C2×Dic67 | — | 4 | 1 | no | — |
| 169 | C2×Dic67 | — | 4 | 1 | no | — |
| 170 | C2×Dic67 | — | 4 | 1 | no | — |
| 171 | C2×Dic67 | — | 4 | 2 | no | — |
| 172 | C2×Dic67 | — | 8 | 2 | no | — |
| 173 | C2×Dic67 | — | 8 | 2 | no | — |
| 174 | C2×Dic67 | — | 8 | 2 | no | — |
| 175 | C2×Dic67 | C2×D8 | 1 | 1 | yes | characteristic |
| 176 | C2×Dic67 | C2×D8 | 1 | 1 | yes | characteristic |
| 177 | C2×Dic67 | C2×D8 | 1 | 1 | yes | characteristic |
| 178 | C2×Dic67 | C2×D8 | 1 | 1 | yes | characteristic |
| 179 | C8×C67 | C4×D4 | 1 | 2 | yes | — |
| 180 | C8×C67 | C23×C4 | 1 | 1 | yes | characteristic |
| 181 | C8×C67 | C2×#41 | 1 | 1 | yes | characteristic |
| 182 | C67⋊C8 | — | 2 | 1 | no | — |
| 183 | C67⋊C8 | — | 2 | 1 | no | — |
| 184 | C22×C67 | — | 2 | 1 | no | — |
| 185 | C22×C67 | — | 2 | 1 | no | — |
| 186 | C22×C67 | — | 4 | 2 | no | — |
| 187 | C22×C67 | — | 8 | 1 | no | — |
| 188 | C22×C67 | — | 8 | 1 | no | — |
| 189 | C22×C67 | C4×D8 | 1 | 2 | yes | — |
| 190 | C22×C67 | C22×D8 | 1 | 1 | yes | characteristic |
| 191 | C4×C67 | — | 4 | 2 | no | — |
| 192 | C4×C67 | — | 4 | 4 | no | — |
| 193 | C4×C67 | C4×D8 | 1 | 2 | yes | — |
| 194 | C4×C67 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 195 | C4×C67 | C2×#135 | 1 | 1 | yes | characteristic |
| 196 | Dic67 | — | 2 | 1 | no | — |
| 197 | Dic67 | — | 2 | 1 | no | — |
| 198 | Dic67 | — | 2 | 1 | no | — |
| 199 | Dic67 | — | 8 | 1 | no | — |
| 200 | Dic67 | — | 8 | 1 | no | — |
| 201 | Dic67 | — | 8 | 2 | no | — |
| 202 | Dic67 | #510 | 1 | 2 | yes | direct product factor |
| 203 | C4×#510 | — | 67 | 1 | no | maximal, Sylow |
| 204 | C2×C67 | — | 2 | 2 | no | — |
| 205 | C2×C67 | — | 8 | 2 | no | — |
| 206 | C2×C67 | C2×C4×D8 | 1 | 1 | yes | characteristic |
| 207 | C2×C67 | C2×#510 | 1 | 1 | yes | characteristic |
| 208 | C2×C67 | #3414 | 1 | 1 | yes | characteristic |
| 209 | C2×#510 | D67 | 1 | 1 | yes | characteristic |
| 210 | C4×#135 | — | 67 | 1 | no | — |
| 211 | C2×C4×Q16 | — | 67 | 1 | no | — |
| 212 | #2176 | — | 67 | 2 | no | — |
| 213 | #2175 | — | 67 | 2 | no | — |
| 214 | C4×Q32 | — | 67 | 2 | no | — |
| 215 | C4×SD32 | — | 67 | 2 | no | — |
| 216 | #2159 | — | 67 | 1 | no | — |
| 217 | #2141 | — | 67 | 1 | no | — |
| 218 | #2139 | — | 67 | 1 | no | — |
| 219 | C4×M32 | — | 67 | 1 | no | — |
| 220 | C67 | C4×#510 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 221 | C2×#135 | C2×D67 | 1 | 1 | yes | characteristic |
| 222 | C22×Q16 | C2×D67 | 1 | 1 | yes | characteristic |
| 223 | C4×#41 | — | 134 | 1 | no | — |
| 224 | C2×C4×Q8 | — | 134 | 1 | no | — |
| 225 | #510 | Dic67 | 1 | 8 | yes | direct product factor |
| 226 | C2×Q32 | C2×D67 | 1 | 2 | yes | — |
| 227 | C2×SD32 | C2×D67 | 1 | 2 | yes | — |
| 228 | C2×M32 | — | 67 | 1 | no | — |
| 229 | C2×M32 | C2×D67 | 1 | 1 | yes | characteristic |
| 230 | C4×Q16 | — | 67 | 2 | no | — |
| 231 | C4×Q16 | — | 67 | 2 | no | — |
| 232 | C4×Q16 | — | 67 | 1 | no | — |
| 233 | C4×Q16 | — | 67 | 1 | no | — |
| 234 | C4×Q16 | — | 134 | 1 | no | — |
| 235 | C4×Q16 | — | 134 | 1 | no | — |
| 236 | C4×SD16 | — | 134 | 1 | no | — |
| 237 | C4×SD16 | — | 134 | 1 | no | — |
| 238 | C4×D8 | — | 67 | 1 | no | — |
| 239 | C4×D8 | — | 67 | 1 | no | — |
| 240 | #427 | — | 67 | 1 | no | — |
| 241 | C2×#107 | — | 67 | 1 | no | — |
| 242 | #416 | — | 134 | 1 | no | — |
| 243 | C2×#103 | — | 134 | 1 | no | — |
| 244 | C2×C4×C8 | — | 67 | 1 | no | — |
| 245 | #367 | — | 67 | 2 | no | — |
| 246 | #366 | — | 67 | 2 | no | — |
| 247 | #358 | — | 67 | 2 | no | — |
| 248 | #358 | — | 67 | 2 | no | — |
| 249 | #358 | — | 67 | 2 | no | — |
| 250 | #357 | — | 67 | 2 | no | — |
| 251 | #346 | — | 67 | 2 | no | — |
| 252 | C4×C16 | — | 67 | 2 | no | — |
| 253 | C2×#41 | — | 2 | 1 | no | — |
| 254 | C22×Q8 | — | 2 | 1 | no | — |
| 255 | #135 | — | 2 | 2 | no | — |
| 256 | #135 | C2×Dic67 | 1 | 4 | yes | — |
| 257 | C2×Q16 | — | 2 | 1 | no | — |
| 258 | C2×Q16 | — | 2 | 2 | no | — |
| 259 | C2×Q16 | C2×Dic67 | 1 | 4 | yes | complemented |
| 260 | C2×Q16 | C22×D67 | 1 | 2 | yes | — |
| 261 | C2×Q16 | C22×D67 | 1 | 1 | yes | characteristic |
| 262 | C2×SD16 | — | 2 | 1 | no | — |
| 263 | C2×D8 | C22×D67 | 1 | 1 | yes | characteristic |
| 264 | C22×C8 | — | 67 | 1 | no | — |
| 265 | C22×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 266 | C4×Q8 | — | 268 | 1 | no | — |
| 267 | C4×Q8 | — | 268 | 1 | no | — |
| 268 | C4×Q8 | — | 134 | 2 | no | — |
| 269 | C4×Q8 | — | 134 | 2 | no | — |
| 270 | C4×Q8 | — | 134 | 1 | no | — |
| 271 | C4×Q8 | — | 134 | 1 | no | — |
| 272 | C4×D4 | — | 268 | 1 | no | — |
| 273 | C4×D4 | — | 268 | 1 | no | — |
| 274 | C4×D4 | — | 134 | 1 | no | — |
| 275 | C4×D4 | — | 134 | 1 | no | — |
| 276 | #117 | — | 268 | 1 | no | — |
| 277 | #117 | — | 134 | 1 | no | — |
| 278 | C2×C4⋊C4 | — | 268 | 1 | no | — |
| 279 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 280 | C2×C42 | — | 268 | 1 | no | — |
| 281 | C2×C42 | — | 268 | 1 | no | — |
| 282 | C2×C42 | — | 67 | 1 | no | — |
| 283 | Q32 | C2×Dic67 | 1 | 8 | yes | complemented |
| 284 | SD32 | C2×Dic67 | 1 | 8 | yes | complemented |
| 285 | M32 | — | 134 | 2 | no | — |
| 286 | M32 | C2×Dic67 | 1 | 4 | yes | complemented |
| 287 | C2×C16 | — | 67 | 2 | no | — |
| 288 | C2×C16 | C22×D67 | 1 | 2 | yes | — |
| 289 | #107 | — | 67 | 2 | no | — |
| 290 | #107 | — | 67 | 1 | no | — |
| 291 | #107 | — | 67 | 1 | no | — |
| 292 | #107 | — | 134 | 1 | no | — |
| 293 | #106 | — | 134 | 1 | no | — |
| 294 | #103 | — | 134 | 2 | no | — |
| 295 | #103 | — | 134 | 2 | no | — |
| 296 | #103 | — | 134 | 1 | no | — |
| 297 | #103 | — | 134 | 1 | no | — |
| 298 | #102 | — | 134 | 1 | no | — |
| 299 | #102 | — | 134 | 1 | no | — |
| 300 | C4×C8 | — | 67 | 1 | no | — |
| 301 | C4×C8 | — | 67 | 1 | no | — |
| 302 | C4×C8 | — | 67 | 1 | no | — |
| 303 | C4×C8 | — | 67 | 1 | no | — |
| 304 | #41 | — | 2 | 4 | no | — |
| 305 | #41 | — | 4 | 2 | no | — |
| 306 | C2×Q8 | — | 2 | 4 | no | — |
| 307 | C2×Q8 | — | 2 | 1 | no | — |
| 308 | C2×Q8 | — | 2 | 2 | no | — |
| 309 | C2×Q8 | — | 4 | 1 | no | — |
| 310 | C2×Q8 | — | 4 | 2 | no | — |
| 311 | C2×D4 | — | 2 | 1 | no | — |
| 312 | C2×D4 | — | 4 | 1 | no | — |
| 313 | C22×C4 | — | 4 | 1 | no | — |
| 314 | C22×C4 | — | 4 | 1 | no | — |
| 315 | C22×C4 | — | 268 | 1 | no | — |
| 316 | C22×C4 | — | 268 | 1 | no | — |
| 317 | C22×C4 | — | 268 | 1 | no | — |
| 318 | C22×C4 | — | 67 | 1 | no | — |
| 319 | C22×C4 | — | 67 | 1 | no | — |
| 320 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 321 | Q16 | — | 2 | 4 | no | — |
| 322 | Q16 | — | 2 | 2 | no | — |
| 323 | Q16 | — | 2 | 1 | no | — |
| 324 | Q16 | C22×Dic67 | 1 | 4 | yes | — |
| 325 | Q16 | C22×Dic67 | 1 | 2 | yes | — |
| 326 | SD16 | — | 2 | 4 | no | — |
| 327 | D8 | — | 2 | 1 | no | — |
| 328 | D8 | C22×Dic67 | 1 | 2 | yes | — |
| 329 | C2×C8 | — | 67 | 1 | no | — |
| 330 | C2×C8 | — | 67 | 1 | no | — |
| 331 | C2×C8 | — | 134 | 2 | no | — |
| 332 | C2×C8 | C22×Dic67 | 1 | 2 | yes | — |
| 333 | C2×C8 | D4×D67 | 1 | 1 | yes | characteristic |
| 334 | C2×C8 | #11761627 | 1 | 2 | yes | — |
| 335 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 336 | C4⋊C4 | — | 268 | 2 | no | — |
| 337 | C4⋊C4 | — | 268 | 2 | no | — |
| 338 | C4⋊C4 | — | 268 | 1 | no | — |
| 339 | C4⋊C4 | — | 268 | 1 | no | — |
| 340 | C4⋊C4 | — | 268 | 1 | no | — |
| 341 | C4⋊C4 | — | 134 | 1 | no | — |
| 342 | C4⋊C4 | — | 134 | 1 | no | — |
| 343 | C4⋊C4 | — | 134 | 2 | no | — |
| 344 | C22⋊C4 | — | 268 | 1 | no | — |
| 345 | C22⋊C4 | — | 268 | 1 | no | — |
| 346 | C22⋊C4 | — | 268 | 1 | no | — |
| 347 | C42 | — | 268 | 1 | no | — |
| 348 | C42 | — | 268 | 1 | no | — |
| 349 | C42 | — | 268 | 2 | no | — |
| 350 | C42 | — | 268 | 2 | no | — |
| 351 | C42 | — | 268 | 1 | no | — |
| 352 | C42 | — | 67 | 1 | no | — |
| 353 | C42 | — | 67 | 1 | no | — |
| 354 | C42 | — | 67 | 1 | no | — |
| 355 | C42 | — | 67 | 1 | no | — |
| 356 | C16 | — | 134 | 2 | no | — |
| 357 | C16 | C22×Dic67 | 1 | 4 | yes | — |
| 358 | C23 | — | 4 | 1 | no | — |
| 359 | C23 | D8×D67 | 1 | 1 | yes | characteristic |
| 360 | Q8 | — | 2 | 2 | no | — |
| 361 | Q8 | — | 2 | 4 | no | — |
| 362 | Q8 | — | 4 | 2 | no | — |
| 363 | Q8 | — | 4 | 1 | no | — |
| 364 | Q8 | — | 4 | 4 | no | — |
| 365 | D4 | — | 2 | 2 | no | — |
| 366 | D4 | — | 4 | 4 | no | — |
| 367 | D4 | — | 4 | 1 | no | — |
| 368 | C2×C4 | — | 4 | 1 | no | — |
| 369 | C2×C4 | — | 4 | 2 | no | — |
| 370 | C2×C4 | — | 4 | 4 | no | — |
| 371 | C2×C4 | — | 4 | 4 | no | — |
| 372 | C2×C4 | — | 268 | 1 | no | — |
| 373 | C2×C4 | — | 268 | 1 | no | — |
| 374 | C2×C4 | — | 268 | 2 | no | — |
| 375 | C2×C4 | — | 268 | 1 | no | — |
| 376 | C2×C4 | — | 536 | 2 | no | — |
| 377 | C2×C4 | — | 536 | 2 | no | — |
| 378 | C2×C4 | — | 536 | 2 | no | — |
| 379 | C2×C4 | — | 67 | 1 | no | — |
| 380 | C2×C4 | — | 67 | 1 | no | — |
| 381 | C2×C4 | — | 67 | 1 | no | — |
| 382 | C2×C4 | — | 67 | 1 | no | — |
| 383 | C2×C4 | — | 134 | 2 | no | — |
| 384 | C2×C4 | D4×Dic67 | 1 | 2 | yes | — |
| 385 | C2×C4 | D8×D67 | 1 | 1 | yes | characteristic |
| 386 | C2×C4 | #14524062 | 1 | 2 | yes | — |
| 387 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 388 | C8 | — | 134 | 1 | no | — |
| 389 | C8 | — | 134 | 1 | no | — |
| 390 | C8 | D4×Dic67 | 1 | 2 | yes | — |
| 391 | C8 | C23×Dic67 | 1 | 1 | yes | characteristic |
| 392 | C8 | C2×#11761627 | 1 | 1 | yes | characteristic |
| 393 | C22 | — | 2 | 1 | no | — |
| 394 | C22 | — | 2 | 1 | no | — |
| 395 | C22 | — | 4 | 2 | no | — |
| 396 | C22 | — | 8 | 1 | no | — |
| 397 | C22 | — | 8 | 1 | no | — |
| 398 | C22 | D8×Dic67 | 1 | 2 | yes | — |
| 399 | C22 | C2×D8×D67 | 1 | 1 | yes | characteristic |
| 400 | C4 | — | 4 | 2 | no | — |
| 401 | C4 | — | 4 | 4 | no | — |
| 402 | C4 | — | 536 | 1 | no | — |
| 403 | C4 | — | 536 | 1 | no | — |
| 404 | C4 | — | 536 | 2 | no | — |
| 405 | C4 | — | 67 | 2 | no | — |
| 406 | C4 | — | 134 | 1 | no | — |
| 407 | C4 | — | 134 | 1 | no | — |
| 408 | C4 | — | 134 | 1 | no | — |
| 409 | C4 | D8×Dic67 | 1 | 2 | yes | — |
| 410 | C4 | C2×D4×Dic67 | 1 | 1 | yes | characteristic |
| 411 | C4 | C2×#14524062 | 1 | 1 | yes | characteristic |
| 412 | C2 | — | 2 | 2 | no | — |
| 413 | C2 | — | 8 | 2 | no | — |
| 414 | C2 | C2×D8×Dic67 | 1 | 1 | yes | characteristic |
| 415 | C2 | #510×D67 | 1 | 1 | yes | characteristic |
| 416 | C2 | #22573344 | 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