← #30874309
Subgroups — #30874309
Order 17152.
846 conjugacy classes of subgroups.
The subgroup lattice has 446 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#16863513 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22569085 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22568802 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22560994 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22560992 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22560442 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22560440 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #22560372 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #22560266 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #22560089 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C67×#2951 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C2×#14524050 | C22 | 1 | 2 | yes | — |
| 13 | #16863879 | C22 | 1 | 2 | yes | — |
| 14 | #16863513 | C4 | 1 | 8 | yes | complemented |
| 15 | #16863497 | — | 2 | 2 | no | — |
| 16 | Q16×Dic67 | — | 2 | 1 | no | — |
| 17 | D8×Dic67 | — | 2 | 1 | no | — |
| 18 | C2×#14523979 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#14523978 | C22 | 1 | 1 | yes | characteristic |
| 20 | #16863439 | — | 2 | 2 | no | — |
| 21 | #16863439 | C22 | 1 | 2 | yes | — |
| 22 | #16863436 | — | 2 | 2 | no | — |
| 23 | #16863436 | C22 | 1 | 2 | yes | — |
| 24 | #16863432 | — | 2 | 2 | no | — |
| 25 | #16863432 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#14523977 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#14523974 | — | 2 | 2 | no | — |
| 28 | C2×#14523974 | C22 | 1 | 2 | yes | — |
| 29 | C2×#14523970 | C22 | 1 | 2 | yes | — |
| 30 | #16863397 | C22 | 1 | 2 | yes | — |
| 31 | #16863351 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×C8×Dic67 | C22 | 1 | 1 | yes | characteristic |
| 33 | #16863261 | C22 | 1 | 2 | yes | — |
| 34 | #16863165 | C22 | 1 | 2 | yes | — |
| 35 | #16863164 | C22 | 1 | 2 | yes | — |
| 36 | #16863157 | C22 | 1 | 1 | yes | characteristic |
| 37 | #16863155 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×#135×C67 | C22 | 1 | 1 | yes | characteristic |
| 39 | #520×C67 | C22 | 1 | 2 | yes | — |
| 40 | #440×C67 | — | 2 | 2 | no | — |
| 41 | C4×Q16×C67 | — | 2 | 1 | no | — |
| 42 | C4×D8×C67 | — | 2 | 1 | no | — |
| 43 | C2×#107×C67 | C22 | 1 | 1 | yes | characteristic |
| 44 | #417×C67 | C22 | 1 | 2 | yes | — |
| 45 | #405×C67 | C22 | 1 | 1 | yes | characteristic |
| 46 | #14524050 | — | 2 | 4 | no | — |
| 47 | #14524050 | C2×C4 | 1 | 8 | yes | complemented |
| 48 | C2×#11761612 | — | 2 | 2 | no | — |
| 49 | C2×#11761612 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×#11761612 | C23 | 1 | 2 | yes | — |
| 51 | C22×C67⋊C8 | — | 2 | 2 | no | — |
| 52 | C22×C67⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 53 | Q8×Dic67 | — | 2 | 2 | no | — |
| 54 | D4×Dic67 | — | 2 | 2 | no | — |
| 55 | D4×Dic67 | — | 4 | 2 | no | — |
| 56 | #14524002 | — | 2 | 2 | no | — |
| 57 | #14524002 | C23 | 1 | 1 | yes | characteristic |
| 58 | C2×C4⋊Dic67 | — | 2 | 2 | no | — |
| 59 | C2×C4⋊Dic67 | C23 | 1 | 2 | yes | — |
| 60 | C2×C4×Dic67 | C23 | 1 | 1 | yes | characteristic |
| 61 | #14523979 | C2×C4 | 1 | 4 | yes | complemented |
| 62 | #14523978 | — | 2 | 2 | no | — |
| 63 | #14523977 | — | 2 | 1 | no | — |
| 64 | #14523977 | — | 2 | 1 | no | — |
| 65 | #14523976 | — | 2 | 2 | no | — |
| 66 | #14523976 | — | 2 | 2 | no | — |
| 67 | #14523976 | D4 | 1 | 1 | yes | characteristic |
| 68 | #14523976 | D4 | 1 | 1 | yes | characteristic |
| 69 | #14523974 | — | 2 | 2 | no | — |
| 70 | #14523974 | — | 2 | 2 | no | — |
| 71 | #14523974 | — | 2 | 2 | no | — |
| 72 | #14523974 | — | 2 | 2 | no | — |
| 73 | #14523974 | D4 | 1 | 1 | yes | characteristic |
| 74 | #14523974 | D4 | 1 | 1 | yes | characteristic |
| 75 | #14523970 | C2×C4 | 1 | 8 | yes | complemented |
| 76 | #14523967 | — | 2 | 2 | no | — |
| 77 | #14523964 | — | 2 | 2 | no | — |
| 78 | #14523953 | — | 2 | 1 | no | — |
| 79 | C8×Dic67 | — | 2 | 1 | no | — |
| 80 | C8×Dic67 | C2×C4 | 1 | 4 | yes | complemented |
| 81 | C67⋊#95 | — | 4 | 2 | no | — |
| 82 | C2×#41×C67 | C23 | 1 | 2 | yes | — |
| 83 | #135×C67 | C2×C4 | 1 | 4 | yes | — |
| 84 | #135×C67 | Q8 | 1 | 4 | yes | — |
| 85 | C2×Q16×C67 | D4 | 1 | 1 | yes | characteristic |
| 86 | C2×SD16×C67 | D4 | 1 | 2 | yes | — |
| 87 | C2×D8×C67 | D4 | 1 | 1 | yes | characteristic |
| 88 | C2×M16×C67 | C23 | 1 | 1 | yes | characteristic |
| 89 | C22×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 90 | C4×Q8×C67 | — | 2 | 2 | no | — |
| 91 | C4×D4×C67 | — | 2 | 2 | no | — |
| 92 | C4×D4×C67 | — | 4 | 2 | no | — |
| 93 | #117×C67 | — | 2 | 2 | no | — |
| 94 | #117×C67 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×C4⋊C4×C67 | — | 2 | 2 | no | — |
| 96 | C2×C4⋊C4×C67 | C23 | 1 | 2 | yes | — |
| 97 | #107×C67 | — | 2 | 1 | no | — |
| 98 | #107×C67 | — | 2 | 1 | no | — |
| 99 | #103×C67 | — | 2 | 2 | no | — |
| 100 | #102×C67 | — | 2 | 2 | no | — |
| 101 | #97×C67 | — | 2 | 1 | no | — |
| 102 | C4×C8×C67 | — | 2 | 1 | no | — |
| 103 | C22×Dic67 | — | 2 | 1 | no | — |
| 104 | C22×Dic67 | — | 2 | 2 | no | — |
| 105 | C22×Dic67 | — | 4 | 2 | no | — |
| 106 | #11761612 | — | 2 | 2 | no | — |
| 107 | #11761612 | — | 2 | 8 | no | — |
| 108 | #11761612 | — | 2 | 1 | no | — |
| 109 | #11761612 | — | 2 | 1 | no | — |
| 110 | #11761612 | C22×C4 | 1 | 4 | yes | — |
| 111 | C2×C67⋊C8 | — | 2 | 2 | no | — |
| 112 | C2×C67⋊C8 | — | 2 | 8 | no | — |
| 113 | C2×C67⋊C8 | — | 2 | 1 | no | — |
| 114 | C2×C67⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 115 | C2×C67⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C2×C67⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 117 | C2×C67⋊C8 | #41 | 1 | 2 | yes | — |
| 118 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 119 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 120 | C4⋊Dic67 | — | 4 | 2 | no | — |
| 121 | C4⋊Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | C4⋊Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 123 | C22⋊Dic67 | — | 2 | 1 | no | — |
| 124 | C22⋊Dic67 | — | 4 | 2 | no | — |
| 125 | C4×Dic67 | — | 2 | 1 | no | — |
| 126 | C4×Dic67 | — | 2 | 1 | no | — |
| 127 | C4×Dic67 | — | 4 | 2 | no | — |
| 128 | C4×Dic67 | C22×C4 | 1 | 2 | yes | — |
| 129 | #41×C67 | — | 2 | 2 | no | — |
| 130 | #41×C67 | — | 2 | 2 | no | — |
| 131 | #41×C67 | C22×C4 | 1 | 4 | yes | — |
| 132 | #41×C67 | C2×Q8 | 1 | 4 | yes | — |
| 133 | C2×Q8×C67 | C2×D4 | 1 | 2 | yes | — |
| 134 | C2×D4×C67 | — | 2 | 2 | no | — |
| 135 | C2×D4×C67 | C2×D4 | 1 | 2 | yes | — |
| 136 | C22×C4×C67 | — | 2 | 2 | no | — |
| 137 | C22×C4×C67 | — | 2 | 2 | no | — |
| 138 | C22×C4×C67 | — | 4 | 2 | no | — |
| 139 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 140 | Q16×C67 | C4⋊C4 | 1 | 4 | yes | — |
| 141 | SD16×C67 | C4⋊C4 | 1 | 8 | yes | — |
| 142 | D8×C67 | C4⋊C4 | 1 | 4 | yes | — |
| 143 | M16×C67 | — | 2 | 1 | no | — |
| 144 | M16×C67 | — | 2 | 1 | no | — |
| 145 | C2×C8×C67 | — | 2 | 1 | no | — |
| 146 | C2×C8×C67 | C22×C4 | 1 | 2 | yes | — |
| 147 | C2×C8×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C2×C8×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | C2×C8×C67 | C2×Q8 | 1 | 2 | yes | — |
| 150 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 151 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 152 | C4⋊C4×C67 | — | 4 | 2 | no | — |
| 153 | C4⋊C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C4⋊C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 156 | C22⋊C4×C67 | — | 4 | 2 | no | — |
| 157 | C42×C67 | — | 2 | 1 | no | — |
| 158 | C42×C67 | — | 4 | 2 | no | — |
| 159 | C23×C67 | — | 2 | 2 | no | — |
| 160 | C23×C67 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 161 | Q8×C67 | — | 2 | 2 | no | — |
| 162 | Q8×C67 | C2×C4⋊C4 | 1 | 4 | yes | — |
| 163 | D4×C67 | — | 2 | 4 | no | — |
| 164 | D4×C67 | — | 2 | 4 | no | — |
| 165 | D4×C67 | — | 2 | 2 | no | — |
| 166 | D4×C67 | C2×C4⋊C4 | 1 | 4 | yes | — |
| 167 | C2×C4×C67 | — | 2 | 2 | no | — |
| 168 | C2×C4×C67 | — | 2 | 4 | no | — |
| 169 | C2×C4×C67 | — | 2 | 4 | no | — |
| 170 | C2×C4×C67 | — | 2 | 1 | no | — |
| 171 | C2×C4×C67 | — | 2 | 1 | no | — |
| 172 | C2×C4×C67 | — | 4 | 2 | no | — |
| 173 | C2×C4×C67 | — | 8 | 2 | no | — |
| 174 | C2×C4×C67 | — | 16 | 2 | no | — |
| 175 | C2×C4×C67 | C23×C4 | 1 | 1 | yes | characteristic |
| 176 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 177 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 178 | C2×C4×C67 | C22×Q8 | 1 | 1 | yes | characteristic |
| 179 | C2×C4×C67 | C2×#41 | 1 | 1 | yes | characteristic |
| 180 | C2×C4×C67 | 2−1+4 | 1 | 1 | yes | characteristic |
| 181 | C2×Dic67 | — | 2 | 2 | no | — |
| 182 | C2×Dic67 | — | 2 | 1 | no | — |
| 183 | C2×Dic67 | — | 2 | 1 | no | — |
| 184 | C2×Dic67 | — | 4 | 1 | no | — |
| 185 | C2×Dic67 | — | 4 | 1 | no | — |
| 186 | C2×Dic67 | — | 4 | 2 | no | — |
| 187 | C2×Dic67 | — | 8 | 2 | no | — |
| 188 | C2×Dic67 | — | 16 | 2 | no | — |
| 189 | C8×C67 | — | 4 | 1 | no | — |
| 190 | C8×C67 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 191 | C8×C67 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 192 | C67⋊C8 | — | 2 | 4 | no | — |
| 193 | C67⋊C8 | — | 4 | 1 | no | — |
| 194 | C67⋊C8 | C4×D4 | 1 | 2 | yes | — |
| 195 | C67⋊C8 | C4×D4 | 1 | 2 | yes | — |
| 196 | C22×C67 | — | 2 | 1 | no | — |
| 197 | C22×C67 | — | 2 | 1 | no | — |
| 198 | C22×C67 | — | 2 | 4 | no | — |
| 199 | C22×C67 | — | 4 | 2 | no | — |
| 200 | C22×C67 | — | 4 | 2 | no | — |
| 201 | C22×C67 | #520 | 1 | 1 | yes | characteristic |
| 202 | C22×C67 | D42 | 1 | 1 | yes | characteristic |
| 203 | C22×C67 | #554 | 1 | 1 | yes | characteristic |
| 204 | C4×C67 | — | 2 | 4 | no | — |
| 205 | C4×C67 | — | 4 | 1 | no | — |
| 206 | C4×C67 | — | 4 | 1 | no | — |
| 207 | C4×C67 | — | 8 | 2 | no | — |
| 208 | C4×C67 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 209 | C4×C67 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 210 | C4×C67 | #547 | 1 | 1 | yes | characteristic |
| 211 | C4×C67 | D4×Q8 | 1 | 1 | yes | characteristic |
| 212 | Dic67 | — | 4 | 2 | no | — |
| 213 | Dic67 | — | 4 | 1 | no | — |
| 214 | Dic67 | — | 4 | 1 | no | — |
| 215 | Dic67 | — | 8 | 2 | no | — |
| 216 | #22690 | — | 67 | 1 | no | maximal, Sylow |
| 217 | C2×C67 | — | 2 | 1 | no | — |
| 218 | C2×C67 | — | 2 | 1 | no | — |
| 219 | C2×C67 | — | 4 | 4 | no | — |
| 220 | C2×C67 | D4×C4⋊C4 | 1 | 1 | yes | characteristic |
| 221 | C2×C67 | #3290 | 1 | 1 | yes | characteristic |
| 222 | C2×C67 | #3290 | 1 | 1 | yes | characteristic |
| 223 | C2×#443 | — | 67 | 1 | no | — |
| 224 | #2951 | — | 67 | 1 | no | — |
| 225 | #2951 | D67 | 1 | 1 | yes | characteristic |
| 226 | #2912 | — | 67 | 2 | no | — |
| 227 | #1952 | — | 67 | 1 | no | — |
| 228 | #1952 | — | 67 | 1 | no | — |
| 229 | #1860 | — | 67 | 2 | no | — |
| 230 | #1860 | — | 67 | 2 | no | — |
| 231 | #1846 | — | 67 | 1 | no | — |
| 232 | #1815 | — | 67 | 2 | no | — |
| 233 | #1772 | — | 67 | 1 | no | — |
| 234 | C67 | #22690 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 235 | C2×#135 | C2×D67 | 1 | 1 | yes | characteristic |
| 236 | C2×#131 | — | 67 | 2 | no | — |
| 237 | #520 | — | 67 | 2 | no | — |
| 238 | #520 | C2×D67 | 1 | 2 | yes | — |
| 239 | #443 | — | 67 | 8 | no | — |
| 240 | #440 | — | 2 | 2 | no | — |
| 241 | #440 | — | 134 | 2 | no | — |
| 242 | C4×Q16 | — | 2 | 1 | no | — |
| 243 | C4×Q16 | — | 134 | 1 | no | — |
| 244 | C4×D8 | — | 2 | 1 | no | — |
| 245 | C4×D8 | — | 134 | 1 | no | — |
| 246 | C2×#108 | — | 67 | 1 | no | — |
| 247 | C2×#108 | — | 67 | 1 | no | — |
| 248 | #428 | — | 67 | 2 | no | — |
| 249 | #428 | — | 67 | 2 | no | — |
| 250 | #428 | — | 134 | 2 | no | — |
| 251 | #428 | — | 134 | 2 | no | — |
| 252 | #427 | — | 67 | 1 | no | — |
| 253 | #427 | — | 134 | 2 | no | — |
| 254 | C2×#107 | — | 67 | 1 | no | — |
| 255 | C2×#107 | C2×D67 | 1 | 1 | yes | characteristic |
| 256 | C2×#106 | — | 67 | 2 | no | — |
| 257 | C2×#106 | — | 134 | 2 | no | — |
| 258 | C2×#104 | — | 67 | 2 | no | — |
| 259 | #417 | — | 67 | 2 | no | — |
| 260 | #417 | C2×D67 | 1 | 2 | yes | — |
| 261 | #405 | — | 67 | 1 | no | — |
| 262 | #405 | C2×D67 | 1 | 1 | yes | characteristic |
| 263 | C2×C4×C8 | — | 67 | 1 | no | — |
| 264 | #382 | — | 67 | 2 | no | — |
| 265 | #343 | — | 67 | 2 | no | — |
| 266 | #343 | — | 67 | 2 | no | — |
| 267 | #339 | — | 67 | 1 | no | — |
| 268 | #339 | — | 67 | 1 | no | — |
| 269 | C2×#41 | C22×D67 | 1 | 2 | yes | — |
| 270 | #135 | Dic134 | 1 | 4 | yes | — |
| 271 | #135 | C4×D67 | 1 | 4 | yes | — |
| 272 | C2×Q16 | C22⋊D67 | 1 | 1 | yes | characteristic |
| 273 | C2×SD16 | C22⋊D67 | 1 | 2 | yes | — |
| 274 | C2×D8 | C22⋊D67 | 1 | 1 | yes | characteristic |
| 275 | #131 | — | 67 | 8 | no | — |
| 276 | #131 | — | 134 | 4 | no | — |
| 277 | C2×M16 | — | 67 | 2 | no | — |
| 278 | C2×M16 | — | 67 | 1 | no | — |
| 279 | C2×M16 | — | 134 | 2 | no | — |
| 280 | C2×M16 | C22×D67 | 1 | 1 | yes | characteristic |
| 281 | C22×C8 | — | 67 | 1 | no | — |
| 282 | C22×C8 | — | 134 | 2 | no | — |
| 283 | C22×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 284 | C4×Q8 | — | 2 | 2 | no | — |
| 285 | C4×Q8 | — | 134 | 2 | no | — |
| 286 | C4×D4 | — | 2 | 2 | no | — |
| 287 | C4×D4 | — | 4 | 2 | no | — |
| 288 | C4×D4 | — | 268 | 2 | no | — |
| 289 | C4×D4 | — | 134 | 2 | no | — |
| 290 | #117 | — | 2 | 2 | no | — |
| 291 | #117 | — | 67 | 1 | no | — |
| 292 | #117 | — | 134 | 2 | no | — |
| 293 | #117 | C22×D67 | 1 | 1 | yes | characteristic |
| 294 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 295 | C2×C4⋊C4 | — | 67 | 2 | no | — |
| 296 | C2×C4⋊C4 | — | 134 | 2 | no | — |
| 297 | C2×C4⋊C4 | C22×D67 | 1 | 2 | yes | — |
| 298 | C2×C42 | — | 67 | 1 | no | — |
| 299 | #108 | — | 67 | 4 | no | — |
| 300 | #108 | — | 134 | 2 | no | — |
| 301 | #107 | — | 2 | 1 | no | — |
| 302 | #107 | — | 2 | 1 | no | — |
| 303 | #107 | — | 67 | 1 | no | — |
| 304 | #107 | — | 67 | 1 | no | — |
| 305 | #107 | — | 134 | 2 | no | — |
| 306 | #107 | — | 134 | 1 | no | — |
| 307 | #107 | — | 134 | 1 | no | — |
| 308 | #107 | — | 134 | 2 | no | — |
| 309 | #106 | — | 67 | 1 | no | — |
| 310 | #106 | — | 67 | 1 | no | — |
| 311 | #106 | — | 134 | 2 | no | — |
| 312 | #106 | — | 134 | 2 | no | — |
| 313 | #106 | — | 134 | 2 | no | — |
| 314 | #106 | — | 134 | 2 | no | — |
| 315 | #104 | — | 67 | 8 | no | — |
| 316 | #103 | — | 2 | 2 | no | — |
| 317 | #103 | — | 134 | 2 | no | — |
| 318 | #102 | — | 2 | 2 | no | — |
| 319 | #102 | — | 134 | 2 | no | — |
| 320 | #97 | — | 2 | 1 | no | — |
| 321 | #97 | — | 134 | 1 | no | — |
| 322 | C4×C8 | — | 2 | 1 | no | — |
| 323 | C4×C8 | — | 67 | 4 | no | — |
| 324 | C4×C8 | — | 134 | 1 | no | — |
| 325 | #95 | — | 268 | 2 | no | — |
| 326 | #41 | — | 2 | 2 | no | — |
| 327 | #41 | — | 2 | 2 | no | — |
| 328 | #41 | C2×C4×D67 | 1 | 4 | yes | — |
| 329 | #41 | C2×Dic134 | 1 | 4 | yes | — |
| 330 | C2×Q8 | C2×C22⋊D67 | 1 | 2 | yes | — |
| 331 | C2×D4 | — | 2 | 2 | no | — |
| 332 | C2×D4 | C2×C22⋊D67 | 1 | 2 | yes | — |
| 333 | C22×C4 | — | 2 | 2 | no | — |
| 334 | C22×C4 | — | 2 | 2 | no | — |
| 335 | C22×C4 | — | 4 | 2 | no | — |
| 336 | C22×C4 | — | 268 | 2 | no | — |
| 337 | C22×C4 | — | 134 | 1 | no | — |
| 338 | C22×C4 | — | 134 | 2 | no | — |
| 339 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 340 | Q16 | Dic67⋊C4 | 1 | 4 | yes | — |
| 341 | SD16 | Dic67⋊C4 | 1 | 8 | yes | — |
| 342 | D8 | Dic67⋊C4 | 1 | 4 | yes | — |
| 343 | M16 | — | 2 | 1 | no | — |
| 344 | M16 | — | 2 | 1 | no | — |
| 345 | M16 | — | 67 | 4 | no | — |
| 346 | M16 | — | 134 | 1 | no | — |
| 347 | M16 | — | 134 | 1 | no | — |
| 348 | M16 | — | 134 | 8 | no | — |
| 349 | M16 | — | 134 | 2 | no | — |
| 350 | C2×C8 | — | 2 | 1 | no | — |
| 351 | C2×C8 | — | 67 | 2 | no | — |
| 352 | C2×C8 | — | 67 | 1 | no | — |
| 353 | C2×C8 | — | 67 | 1 | no | — |
| 354 | C2×C8 | — | 67 | 2 | no | — |
| 355 | C2×C8 | — | 134 | 1 | no | — |
| 356 | C2×C8 | — | 134 | 8 | no | — |
| 357 | C2×C8 | — | 134 | 2 | no | — |
| 358 | C2×C8 | C2×C4×D67 | 1 | 2 | yes | — |
| 359 | C2×C8 | C2×C22⋊D67 | 1 | 1 | yes | characteristic |
| 360 | C2×C8 | C2×C22⋊D67 | 1 | 1 | yes | characteristic |
| 361 | C2×C8 | C2×Dic134 | 1 | 2 | yes | — |
| 362 | C4⋊C4 | — | 2 | 2 | no | — |
| 363 | C4⋊C4 | — | 2 | 2 | no | — |
| 364 | C4⋊C4 | — | 4 | 2 | no | — |
| 365 | C4⋊C4 | — | 268 | 2 | no | — |
| 366 | C4⋊C4 | — | 67 | 1 | no | — |
| 367 | C4⋊C4 | — | 67 | 1 | no | — |
| 368 | C4⋊C4 | — | 134 | 2 | no | — |
| 369 | C4⋊C4 | — | 134 | 2 | no | — |
| 370 | C4⋊C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 371 | C4⋊C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 372 | C22⋊C4 | — | 2 | 1 | no | — |
| 373 | C22⋊C4 | — | 4 | 2 | no | — |
| 374 | C22⋊C4 | — | 268 | 2 | no | — |
| 375 | C22⋊C4 | — | 134 | 1 | no | — |
| 376 | C42 | — | 2 | 1 | no | — |
| 377 | C42 | — | 4 | 2 | no | — |
| 378 | C42 | — | 268 | 2 | no | — |
| 379 | C42 | — | 67 | 2 | no | — |
| 380 | C42 | — | 134 | 1 | no | — |
| 381 | C42 | — | 134 | 1 | no | — |
| 382 | C23 | — | 2 | 2 | no | — |
| 383 | C23 | #14524088 | 1 | 1 | yes | characteristic |
| 384 | Q8 | — | 2 | 2 | no | — |
| 385 | Q8 | C2×Dic67⋊C4 | 1 | 4 | yes | — |
| 386 | D4 | — | 2 | 4 | no | — |
| 387 | D4 | — | 2 | 4 | no | — |
| 388 | D4 | — | 2 | 2 | no | — |
| 389 | D4 | C2×Dic67⋊C4 | 1 | 4 | yes | — |
| 390 | C2×C4 | — | 2 | 2 | no | — |
| 391 | C2×C4 | — | 2 | 4 | no | — |
| 392 | C2×C4 | — | 2 | 4 | no | — |
| 393 | C2×C4 | — | 2 | 1 | no | — |
| 394 | C2×C4 | — | 2 | 1 | no | — |
| 395 | C2×C4 | — | 4 | 2 | no | — |
| 396 | C2×C4 | — | 8 | 2 | no | — |
| 397 | C2×C4 | — | 268 | 1 | no | — |
| 398 | C2×C4 | — | 268 | 1 | no | — |
| 399 | C2×C4 | — | 268 | 2 | no | — |
| 400 | C2×C4 | — | 16 | 2 | no | — |
| 401 | C2×C4 | — | 536 | 2 | no | — |
| 402 | C2×C4 | — | 1072 | 2 | no | — |
| 403 | C2×C4 | — | 134 | 1 | no | — |
| 404 | C2×C4 | — | 134 | 1 | no | — |
| 405 | C2×C4 | — | 134 | 2 | no | — |
| 406 | C2×C4 | C22×C4×D67 | 1 | 1 | yes | characteristic |
| 407 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 408 | C2×C4 | C22×C22⋊D67 | 1 | 1 | yes | characteristic |
| 409 | C2×C4 | C22×Dic134 | 1 | 1 | yes | characteristic |
| 410 | C2×C4 | #41×D67 | 1 | 1 | yes | characteristic |
| 411 | C2×C4 | #14524090 | 1 | 1 | yes | characteristic |
| 412 | C8 | — | 4 | 1 | no | — |
| 413 | C8 | — | 268 | 1 | no | — |
| 414 | C8 | — | 67 | 2 | no | — |
| 415 | C8 | — | 67 | 2 | no | — |
| 416 | C8 | — | 134 | 4 | no | — |
| 417 | C8 | C2×Dic67⋊C4 | 1 | 2 | yes | — |
| 418 | C8 | C2×Dic67⋊C4 | 1 | 2 | yes | — |
| 419 | C22 | — | 2 | 1 | no | — |
| 420 | C22 | — | 2 | 1 | no | — |
| 421 | C22 | — | 2 | 4 | no | — |
| 422 | C22 | — | 4 | 2 | no | — |
| 423 | C22 | — | 4 | 2 | no | — |
| 424 | C22 | #16863875 | 1 | 1 | yes | characteristic |
| 425 | C22 | D4×C22⋊D67 | 1 | 1 | yes | characteristic |
| 426 | C22 | #16864105 | 1 | 1 | yes | characteristic |
| 427 | C4 | — | 2 | 4 | no | — |
| 428 | C4 | — | 4 | 1 | no | — |
| 429 | C4 | — | 4 | 1 | no | — |
| 430 | C4 | — | 8 | 2 | no | — |
| 431 | C4 | — | 268 | 2 | no | — |
| 432 | C4 | — | 268 | 1 | no | — |
| 433 | C4 | — | 268 | 1 | no | — |
| 434 | C4 | — | 536 | 2 | no | — |
| 435 | C4 | C22×Dic67⋊C4 | 1 | 1 | yes | characteristic |
| 436 | C4 | C4×D4×D67 | 1 | 1 | yes | characteristic |
| 437 | C4 | #16864045 | 1 | 1 | yes | characteristic |
| 438 | C4 | D4×Dic134 | 1 | 1 | yes | characteristic |
| 439 | C2 | — | 2 | 1 | no | — |
| 440 | C2 | — | 2 | 1 | no | — |
| 441 | C2 | — | 4 | 4 | no | — |
| 442 | C2 | D4×Dic67⋊C4 | 1 | 1 | yes | characteristic |
| 443 | C2 | #22571991 | 1 | 1 | yes | characteristic |
| 444 | C2 | #22571995 | 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