← #31720102
Subgroups — #31720102
Order 17152.
2650 conjugacy classes of subgroups.
The subgroup lattice has 422 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#16864213 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22573420 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22569092 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #22569076 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #22569050 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #22569027 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #22569009 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C2×#16863502 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #22568739 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #22568635 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C67×#2912 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#14524090 | C22 | 1 | 2 | yes | — |
| 13 | #16864213 | C4 | 1 | 16 | yes | complemented |
| 14 | C2×#14524076 | C22 | 1 | 6 | yes | — |
| 15 | C2×#14524065 | C22 | 1 | 3 | yes | — |
| 16 | C22×Dic268 | C22 | 1 | 3 | yes | — |
| 17 | C2×#14524050 | C22 | 1 | 1 | yes | characteristic |
| 18 | #16863877 | C22 | 1 | 6 | yes | — |
| 19 | #16863875 | — | 2 | 6 | no | — |
| 20 | #16863873 | C22 | 1 | 6 | yes | — |
| 21 | #16863872 | — | 2 | 2 | no | — |
| 22 | #41×Dic67 | C22 | 1 | 1 | yes | characteristic |
| 23 | #16863864 | C22 | 1 | 6 | yes | — |
| 24 | C4×#11761627 | — | 2 | 6 | no | — |
| 25 | C2×#14524008 | C22 | 1 | 6 | yes | — |
| 26 | C4×Q8×D67 | — | 2 | 2 | no | — |
| 27 | #16863507 | C22 | 1 | 1 | yes | characteristic |
| 28 | #16863507 | C22 | 1 | 3 | yes | — |
| 29 | #16863502 | C22 | 1 | 3 | yes | — |
| 30 | #16863502 | C22 | 1 | 6 | yes | — |
| 31 | #16863502 | C22 | 1 | 6 | yes | — |
| 32 | #16863502 | C22 | 1 | 6 | yes | — |
| 33 | #16863502 | C22 | 1 | 3 | yes | — |
| 34 | #16863495 | C22 | 1 | 6 | yes | — |
| 35 | #16863495 | C22 | 1 | 6 | yes | — |
| 36 | #16863490 | C22 | 1 | 12 | yes | — |
| 37 | #16863483 | C22 | 1 | 12 | yes | — |
| 38 | #16863404 | C22 | 1 | 6 | yes | — |
| 39 | #16863395 | C22 | 1 | 6 | yes | — |
| 40 | #16863390 | C22 | 1 | 6 | yes | — |
| 41 | C2×#14523966 | C22 | 1 | 6 | yes | — |
| 42 | #16863354 | C22 | 1 | 3 | yes | — |
| 43 | #16863351 | C22 | 1 | 3 | yes | — |
| 44 | M16×Dic67 | C22 | 1 | 3 | yes | — |
| 45 | C2×#14523953 | C22 | 1 | 3 | yes | — |
| 46 | C2×#131×C67 | C22 | 1 | 1 | yes | characteristic |
| 47 | #520×C67 | C22 | 1 | 2 | yes | — |
| 48 | #428×C67 | C22 | 1 | 6 | yes | — |
| 49 | #427×C67 | C22 | 1 | 3 | yes | — |
| 50 | C2×#106×C67 | C22 | 1 | 3 | yes | — |
| 51 | #14524090 | — | 2 | 8 | no | — |
| 52 | #14524090 | C2×C4 | 1 | 16 | yes | complemented |
| 53 | C2×#11761628 | C23 | 1 | 6 | yes | — |
| 54 | C2×#11761627 | — | 2 | 6 | no | — |
| 55 | C22×Dic134 | C23 | 1 | 6 | yes | — |
| 56 | C2×Q8×D67 | — | 2 | 2 | no | — |
| 57 | #14524076 | C2×C4 | 1 | 48 | yes | complemented |
| 58 | #14524065 | C2×C4 | 1 | 24 | yes | complemented |
| 59 | C2×Dic268 | C2×C4 | 1 | 24 | yes | complemented |
| 60 | C2×Dic268 | C23 | 1 | 6 | yes | — |
| 61 | C2×Dic268 | C23 | 1 | 3 | yes | — |
| 62 | C2×#11761617 | C23 | 1 | 6 | yes | — |
| 63 | C2×D536 | C23 | 1 | 1 | yes | characteristic |
| 64 | #14524050 | — | 2 | 4 | no | — |
| 65 | C2×#11761612 | C23 | 1 | 3 | yes | — |
| 66 | C22×C67⋊C8 | C23 | 1 | 3 | yes | — |
| 67 | Q8×Dic67 | D4 | 1 | 2 | yes | — |
| 68 | C4×Dic134 | — | 2 | 6 | no | — |
| 69 | C4×Dic134 | — | 2 | 6 | no | — |
| 70 | #14524008 | — | 2 | 6 | no | — |
| 71 | #14524008 | — | 2 | 6 | no | — |
| 72 | #14524008 | C23 | 1 | 6 | yes | — |
| 73 | #14524008 | C23 | 1 | 12 | yes | — |
| 74 | #14524008 | C23 | 1 | 6 | yes | — |
| 75 | D4×Dic67 | D4 | 1 | 6 | yes | — |
| 76 | #14524005 | C23 | 1 | 2 | yes | — |
| 77 | #14524005 | C23 | 1 | 6 | yes | — |
| 78 | C4×C22⋊D67 | — | 2 | 12 | no | — |
| 79 | (C22⋊D67)⋊C4 | — | 2 | 6 | no | — |
| 80 | (C22⋊D67)⋊C4 | — | 2 | 6 | no | — |
| 81 | #14524002 | C23 | 1 | 3 | yes | — |
| 82 | #14524001 | — | 2 | 6 | no | — |
| 83 | #14524000 | — | 2 | 6 | no | — |
| 84 | #14523999 | — | 2 | 12 | no | — |
| 85 | C2×Dic67⋊C4 | — | 2 | 6 | no | — |
| 86 | C4⋊C4×D67 | — | 2 | 6 | no | — |
| 87 | C2×C4×Dic67 | — | 2 | 6 | no | — |
| 88 | C2×C4×Dic67 | C23 | 1 | 3 | yes | — |
| 89 | C42×D67 | — | 2 | 6 | no | — |
| 90 | #14523966 | C23 | 1 | 6 | yes | — |
| 91 | #14523966 | C23 | 1 | 12 | yes | — |
| 92 | #14523966 | C23 | 1 | 6 | yes | — |
| 93 | #14523963 | C23 | 1 | 2 | yes | — |
| 94 | #14523963 | C23 | 1 | 6 | yes | — |
| 95 | #14523953 | C23 | 1 | 3 | yes | — |
| 96 | #14523953 | C23 | 1 | 3 | yes | — |
| 97 | #14523953 | C23 | 1 | 1 | yes | characteristic |
| 98 | #14523953 | C23 | 1 | 3 | yes | — |
| 99 | C8×Dic67 | C23 | 1 | 6 | yes | — |
| 100 | C2×#41×C67 | C23 | 1 | 1 | yes | characteristic |
| 101 | #131×C67 | C2×C4 | 1 | 8 | yes | complemented |
| 102 | C2×M16×C67 | C23 | 1 | 3 | yes | — |
| 103 | C22×C8×C67 | C23 | 1 | 3 | yes | — |
| 104 | C4×Q8×C67 | — | 2 | 2 | no | — |
| 105 | C4×D4×C67 | — | 2 | 6 | no | — |
| 106 | #117×C67 | C23 | 1 | 6 | yes | — |
| 107 | C2×C4⋊C4×C67 | C23 | 1 | 6 | yes | — |
| 108 | #107×C67 | C23 | 1 | 6 | yes | — |
| 109 | #106×C67 | C23 | 1 | 3 | yes | — |
| 110 | #106×C67 | C23 | 1 | 1 | yes | characteristic |
| 111 | #106×C67 | C23 | 1 | 6 | yes | — |
| 112 | #11761628 | — | 2 | 12 | no | — |
| 113 | #11761628 | C22×C4 | 1 | 24 | yes | — |
| 114 | #11761627 | — | 2 | 48 | no | — |
| 115 | C2×Dic134 | — | 2 | 6 | no | — |
| 116 | C2×Dic134 | — | 2 | 12 | no | — |
| 117 | C2×Dic134 | C22×C4 | 1 | 24 | yes | — |
| 118 | C2×Dic134 | C24 | 1 | 6 | yes | — |
| 119 | Q8×D67 | — | 2 | 16 | no | — |
| 120 | C2×D268 | C24 | 1 | 2 | yes | — |
| 121 | C2×C22⋊D67 | — | 2 | 6 | no | — |
| 122 | C22×Dic67 | — | 2 | 6 | no | — |
| 123 | C22×Dic67 | C2×D4 | 1 | 6 | yes | — |
| 124 | C2×C4×D67 | — | 2 | 6 | no | — |
| 125 | C2×C4×D67 | — | 2 | 2 | no | — |
| 126 | C2×C4×D67 | — | 2 | 6 | no | — |
| 127 | Dic268 | C22×C4 | 1 | 12 | yes | — |
| 128 | Dic268 | C22×C4 | 1 | 24 | yes | — |
| 129 | #11761617 | C22×C4 | 1 | 24 | yes | — |
| 130 | D536 | C22×C4 | 1 | 4 | yes | — |
| 131 | #11761612 | — | 2 | 6 | no | — |
| 132 | C2×C67⋊C8 | — | 2 | 6 | no | — |
| 133 | C2×C67⋊C8 | C24 | 1 | 3 | yes | — |
| 134 | C2×C67⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 135 | C4⋊Dic67 | C2×D4 | 1 | 6 | yes | — |
| 136 | Dic67⋊C4 | — | 2 | 12 | no | — |
| 137 | Dic67⋊C4 | — | 2 | 6 | no | — |
| 138 | Dic67⋊C4 | — | 2 | 6 | no | — |
| 139 | C22⋊Dic67 | C2×D4 | 1 | 6 | yes | — |
| 140 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 141 | (C2×D67)⋊C4 | — | 2 | 6 | no | — |
| 142 | C4×Dic67 | — | 2 | 6 | no | — |
| 143 | C4×Dic67 | — | 2 | 6 | no | — |
| 144 | C4×Dic67 | — | 2 | 12 | no | — |
| 145 | C4×Dic67 | C2×D4 | 1 | 6 | yes | — |
| 146 | C4×Dic67 | C24 | 1 | 3 | yes | — |
| 147 | C4×Dic67 | C24 | 1 | 1 | yes | characteristic |
| 148 | #41×C67 | C22×C4 | 1 | 4 | yes | — |
| 149 | #41×C67 | #41 | 1 | 4 | yes | — |
| 150 | C2×Q8×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 151 | C2×D4×C67 | C2×D4 | 1 | 3 | yes | — |
| 152 | C22×C4×C67 | — | 2 | 6 | no | — |
| 153 | C22×C4×C67 | C24 | 1 | 3 | yes | — |
| 154 | M16×C67 | C22×C4 | 1 | 12 | yes | — |
| 155 | C2×C8×C67 | C22×C4 | 1 | 12 | yes | — |
| 156 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 157 | C2×C8×C67 | C24 | 1 | 3 | yes | — |
| 158 | C4⋊C4×C67 | — | 2 | 6 | no | — |
| 159 | C4⋊C4×C67 | C24 | 1 | 6 | yes | — |
| 160 | C4⋊C4×C67 | C24 | 1 | 2 | yes | — |
| 161 | C22⋊C4×C67 | — | 2 | 6 | no | — |
| 162 | C42×C67 | — | 2 | 6 | no | — |
| 163 | C23×C67 | C22×D4 | 1 | 3 | yes | — |
| 164 | C22×D67 | — | 2 | 2 | no | — |
| 165 | Q8×C67 | C4×D4 | 1 | 4 | yes | — |
| 166 | D4×C67 | C4×D4 | 1 | 12 | yes | — |
| 167 | C2×C4×C67 | — | 2 | 2 | no | — |
| 168 | C2×C4×C67 | — | 2 | 6 | no | — |
| 169 | C2×C4×C67 | — | 8 | 6 | no | — |
| 170 | C2×C4×C67 | C23×C4 | 1 | 6 | yes | — |
| 171 | C2×C4×C67 | C22×D4 | 1 | 3 | yes | — |
| 172 | C2×C4×C67 | C2×#41 | 1 | 6 | yes | — |
| 173 | C2×C4×C67 | C25 | 1 | 1 | yes | characteristic |
| 174 | C22⋊D67 | — | 2 | 24 | no | — |
| 175 | C2×Dic67 | — | 2 | 24 | no | — |
| 176 | C2×Dic67 | — | 2 | 6 | no | — |
| 177 | C2×Dic67 | — | 4 | 6 | no | — |
| 178 | C2×Dic67 | C22×D4 | 1 | 2 | yes | — |
| 179 | C2×Dic67 | C22×D4 | 1 | 6 | yes | — |
| 180 | D268 | — | 2 | 2 | no | — |
| 181 | D268 | C23×C4 | 1 | 4 | yes | — |
| 182 | C4×D67 | — | 2 | 24 | no | — |
| 183 | C4×D67 | — | 4 | 4 | no | — |
| 184 | C4×D67 | — | 8 | 6 | no | — |
| 185 | Dic134 | — | 2 | 24 | no | — |
| 186 | Dic134 | — | 2 | 6 | no | — |
| 187 | Dic134 | C23×C4 | 1 | 12 | yes | — |
| 188 | C8×C67 | C23×C4 | 1 | 2 | yes | — |
| 189 | C8×C67 | C23×C4 | 1 | 6 | yes | — |
| 190 | C67⋊C8 | — | 2 | 1 | no | — |
| 191 | C67⋊C8 | — | 2 | 3 | no | — |
| 192 | C22×C67 | — | 2 | 6 | no | — |
| 193 | C22×C67 | C2×C4×D4 | 1 | 6 | yes | — |
| 194 | C22×C67 | C23×D4 | 1 | 1 | yes | characteristic |
| 195 | C2×D67 | — | 2 | 4 | no | — |
| 196 | C2×D67 | — | 4 | 2 | no | — |
| 197 | C2×D67 | — | 4 | 2 | no | — |
| 198 | C4×C67 | — | 4 | 2 | no | — |
| 199 | C4×C67 | — | 4 | 6 | no | — |
| 200 | C4×C67 | C2×C4×D4 | 1 | 6 | yes | — |
| 201 | C4×C67 | C24×C4 | 1 | 1 | yes | characteristic |
| 202 | C4×C67 | C22×#41 | 1 | 1 | yes | characteristic |
| 203 | Dic67 | — | 2 | 2 | no | — |
| 204 | Dic67 | — | 2 | 6 | no | — |
| 205 | Dic67 | — | 2 | 12 | no | — |
| 206 | #60175 | — | 67 | 1 | no | maximal, Sylow |
| 207 | C2×C67 | — | 2 | 6 | no | — |
| 208 | C2×C67 | C22×C4×D4 | 1 | 1 | yes | characteristic |
| 209 | C2×C67 | #3586 | 1 | 2 | yes | — |
| 210 | D67 | — | 4 | 4 | no | — |
| 211 | C2×#578 | — | 67 | 1 | no | — |
| 212 | C4×2−1+4 | — | 67 | 2 | no | — |
| 213 | #2952 | — | 67 | 3 | no | — |
| 214 | #2950 | — | 67 | 3 | no | — |
| 215 | #2947 | — | 67 | 6 | no | — |
| 216 | C4×#137 | — | 67 | 6 | no | — |
| 217 | #2943 | — | 67 | 3 | no | — |
| 218 | C2×#441 | — | 67 | 3 | no | — |
| 219 | #2912 | D67 | 1 | 1 | yes | characteristic, complemented |
| 220 | #2898 | — | 67 | 2 | no | — |
| 221 | #2875 | — | 67 | 1 | no | — |
| 222 | C67 | #60175 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 223 | C2×2−1+4 | — | 67 | 2 | no | — |
| 224 | #578 | — | 67 | 16 | no | — |
| 225 | C2×#137 | — | 67 | 6 | no | — |
| 226 | C2×#135 | — | 67 | 3 | no | — |
| 227 | C22×Q16 | — | 67 | 3 | no | — |
| 228 | C2×#131 | — | 67 | 1 | no | — |
| 229 | C2×#131 | C2×D67 | 1 | 1 | yes | characteristic |
| 230 | #520 | — | 67 | 6 | no | — |
| 231 | #520 | — | 134 | 6 | no | — |
| 232 | #520 | C2×D67 | 1 | 2 | yes | — |
| 233 | #519 | — | 67 | 6 | no | — |
| 234 | #519 | — | 134 | 2 | no | — |
| 235 | C4×#41 | — | 67 | 1 | no | — |
| 236 | C4×#41 | — | 67 | 6 | no | — |
| 237 | C4×#41 | — | 134 | 6 | no | — |
| 238 | C2×C4×Q8 | — | 67 | 6 | no | — |
| 239 | C2×C4×Q8 | — | 134 | 2 | no | — |
| 240 | #442 | — | 67 | 1 | no | — |
| 241 | #442 | — | 67 | 3 | no | — |
| 242 | #441 | — | 67 | 3 | no | — |
| 243 | #441 | — | 67 | 6 | no | — |
| 244 | #441 | — | 67 | 6 | no | — |
| 245 | #441 | — | 67 | 6 | no | — |
| 246 | #441 | — | 67 | 3 | no | — |
| 247 | #440 | — | 67 | 6 | no | — |
| 248 | #440 | — | 67 | 6 | no | — |
| 249 | C4×Q16 | — | 67 | 12 | no | — |
| 250 | C4×SD16 | — | 67 | 12 | no | — |
| 251 | #428 | C2×D67 | 1 | 6 | yes | — |
| 252 | #427 | C2×D67 | 1 | 3 | yes | — |
| 253 | C2×#106 | C2×D67 | 1 | 3 | yes | — |
| 254 | #419 | — | 67 | 6 | no | — |
| 255 | #417 | — | 67 | 6 | no | — |
| 256 | #416 | — | 67 | 6 | no | — |
| 257 | C2×#103 | — | 67 | 6 | no | — |
| 258 | #405 | — | 67 | 3 | no | — |
| 259 | #405 | — | 67 | 3 | no | — |
| 260 | C4×M16 | — | 67 | 3 | no | — |
| 261 | C2×#97 | — | 67 | 3 | no | — |
| 262 | 2−1+4 | — | 67 | 16 | no | — |
| 263 | 2−1+4 | — | 134 | 8 | no | — |
| 264 | C2×#41 | — | 67 | 6 | no | — |
| 265 | C2×#41 | — | 134 | 6 | no | — |
| 266 | C2×#41 | C22×D67 | 1 | 1 | yes | characteristic |
| 267 | C22×Q8 | — | 67 | 6 | no | — |
| 268 | C22×Q8 | — | 134 | 2 | no | — |
| 269 | #137 | — | 67 | 48 | no | — |
| 270 | #135 | — | 67 | 24 | no | — |
| 271 | C2×Q16 | — | 67 | 24 | no | — |
| 272 | C2×Q16 | — | 67 | 3 | no | — |
| 273 | C2×Q16 | — | 67 | 6 | no | — |
| 274 | C2×SD16 | — | 67 | 6 | no | — |
| 275 | C2×D8 | — | 67 | 1 | no | — |
| 276 | #131 | — | 134 | 4 | no | — |
| 277 | #131 | C4×D67 | 1 | 8 | yes | complemented |
| 278 | C2×M16 | — | 67 | 3 | no | — |
| 279 | C2×M16 | C22×D67 | 1 | 3 | yes | — |
| 280 | C22×C8 | — | 67 | 3 | no | — |
| 281 | C22×C8 | C22×D67 | 1 | 3 | yes | — |
| 282 | C4×Q8 | — | 2 | 2 | no | — |
| 283 | C4×Q8 | — | 67 | 2 | no | — |
| 284 | C4×Q8 | — | 67 | 6 | no | — |
| 285 | C4×Q8 | — | 67 | 12 | no | — |
| 286 | C4×Q8 | — | 67 | 6 | no | — |
| 287 | C4×Q8 | — | 134 | 6 | no | — |
| 288 | C4×Q8 | — | 134 | 6 | no | — |
| 289 | C4×Q8 | — | 134 | 6 | no | — |
| 290 | C4×Q8 | — | 134 | 6 | no | — |
| 291 | C4×D4 | — | 2 | 6 | no | — |
| 292 | C4×D4 | — | 67 | 6 | no | — |
| 293 | C4×D4 | — | 67 | 2 | no | — |
| 294 | C4×D4 | — | 67 | 6 | no | — |
| 295 | C4×D4 | — | 134 | 6 | no | — |
| 296 | C4×D4 | — | 134 | 6 | no | — |
| 297 | C4×D4 | — | 134 | 12 | no | — |
| 298 | #117 | — | 67 | 3 | no | — |
| 299 | #117 | — | 134 | 6 | no | — |
| 300 | #117 | — | 134 | 12 | no | — |
| 301 | #117 | — | 134 | 6 | no | — |
| 302 | #117 | C22×D67 | 1 | 6 | yes | — |
| 303 | C2×C4⋊C4 | — | 134 | 6 | no | — |
| 304 | C2×C4⋊C4 | — | 134 | 6 | no | — |
| 305 | C2×C4⋊C4 | C22×D67 | 1 | 6 | yes | — |
| 306 | C2×C42 | — | 67 | 3 | no | — |
| 307 | C2×C42 | — | 134 | 6 | no | — |
| 308 | C2×C42 | — | 134 | 6 | no | — |
| 309 | #107 | C22×D67 | 1 | 6 | yes | — |
| 310 | #106 | C22×D67 | 1 | 3 | yes | — |
| 311 | #106 | C22×D67 | 1 | 6 | yes | — |
| 312 | #106 | C22×D67 | 1 | 1 | yes | characteristic |
| 313 | #103 | — | 67 | 6 | no | — |
| 314 | #103 | — | 67 | 12 | no | — |
| 315 | #103 | — | 67 | 6 | no | — |
| 316 | #102 | — | 67 | 2 | no | — |
| 317 | #102 | — | 67 | 6 | no | — |
| 318 | #97 | — | 67 | 1 | no | — |
| 319 | #97 | — | 67 | 3 | no | — |
| 320 | #97 | — | 67 | 3 | no | — |
| 321 | #97 | — | 67 | 3 | no | — |
| 322 | C4×C8 | — | 67 | 6 | no | — |
| 323 | #41 | — | 67 | 24 | no | — |
| 324 | #41 | — | 134 | 48 | no | — |
| 325 | #41 | — | 134 | 12 | no | — |
| 326 | #41 | C2×C4×D67 | 1 | 4 | yes | — |
| 327 | #41 | #11761629 | 1 | 4 | yes | — |
| 328 | C2×Q8 | — | 67 | 24 | no | — |
| 329 | C2×Q8 | — | 67 | 6 | no | — |
| 330 | C2×Q8 | — | 134 | 16 | no | — |
| 331 | C2×Q8 | — | 134 | 6 | no | — |
| 332 | C2×Q8 | — | 134 | 12 | no | — |
| 333 | C2×Q8 | D4×D67 | 1 | 1 | yes | characteristic |
| 334 | C2×D4 | — | 67 | 2 | no | — |
| 335 | C2×D4 | — | 134 | 6 | no | — |
| 336 | C2×D4 | D4×D67 | 1 | 3 | yes | — |
| 337 | C22×C4 | — | 2 | 6 | no | — |
| 338 | C22×C4 | — | 67 | 6 | no | — |
| 339 | C22×C4 | — | 134 | 2 | no | — |
| 340 | C22×C4 | — | 134 | 6 | no | — |
| 341 | C22×C4 | — | 134 | 6 | no | — |
| 342 | C22×C4 | — | 134 | 6 | no | — |
| 343 | C22×C4 | C23×D67 | 1 | 3 | yes | — |
| 344 | Q16 | — | 67 | 12 | no | — |
| 345 | Q16 | — | 67 | 24 | no | — |
| 346 | SD16 | — | 67 | 24 | no | — |
| 347 | D8 | — | 67 | 4 | no | — |
| 348 | M16 | — | 134 | 6 | no | — |
| 349 | M16 | C2×C4×D67 | 1 | 12 | yes | — |
| 350 | C2×C8 | — | 67 | 3 | no | — |
| 351 | C2×C8 | — | 67 | 1 | no | — |
| 352 | C2×C8 | — | 134 | 6 | no | — |
| 353 | C2×C8 | C2×C4×D67 | 1 | 12 | yes | — |
| 354 | C2×C8 | C23×D67 | 1 | 3 | yes | — |
| 355 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 356 | C4⋊C4 | — | 2 | 6 | no | — |
| 357 | C4⋊C4 | — | 67 | 6 | no | — |
| 358 | C4⋊C4 | — | 134 | 6 | no | — |
| 359 | C4⋊C4 | — | 134 | 12 | no | — |
| 360 | C4⋊C4 | — | 134 | 6 | no | — |
| 361 | C4⋊C4 | C23×D67 | 1 | 6 | yes | — |
| 362 | C4⋊C4 | C23×D67 | 1 | 2 | yes | — |
| 363 | C22⋊C4 | — | 2 | 6 | no | — |
| 364 | C22⋊C4 | — | 67 | 6 | no | — |
| 365 | C22⋊C4 | — | 134 | 2 | no | — |
| 366 | C22⋊C4 | — | 134 | 6 | no | — |
| 367 | C42 | — | 2 | 6 | no | — |
| 368 | C42 | — | 67 | 6 | no | — |
| 369 | C42 | — | 67 | 3 | no | — |
| 370 | C42 | — | 67 | 1 | no | — |
| 371 | C42 | — | 134 | 6 | no | — |
| 372 | C42 | — | 134 | 6 | no | — |
| 373 | C42 | — | 134 | 12 | no | — |
| 374 | C23 | — | 134 | 2 | no | — |
| 375 | C23 | C2×D4×D67 | 1 | 3 | yes | — |
| 376 | Q8 | — | 67 | 12 | no | — |
| 377 | Q8 | — | 134 | 24 | no | — |
| 378 | Q8 | — | 134 | 6 | no | — |
| 379 | Q8 | #14524005 | 1 | 4 | yes | — |
| 380 | D4 | — | 67 | 4 | no | — |
| 381 | D4 | — | 134 | 24 | no | — |
| 382 | D4 | — | 134 | 2 | no | — |
| 383 | D4 | #14524005 | 1 | 12 | yes | — |
| 384 | C2×C4 | — | 2 | 2 | no | — |
| 385 | C2×C4 | — | 2 | 6 | no | — |
| 386 | C2×C4 | — | 8 | 6 | no | — |
| 387 | C2×C4 | — | 268 | 4 | no | — |
| 388 | C2×C4 | — | 268 | 6 | no | — |
| 389 | C2×C4 | — | 536 | 6 | no | — |
| 390 | C2×C4 | — | 67 | 2 | no | — |
| 391 | C2×C4 | — | 67 | 6 | no | — |
| 392 | C2×C4 | — | 134 | 24 | no | — |
| 393 | C2×C4 | — | 134 | 6 | no | — |
| 394 | C2×C4 | — | 134 | 24 | no | — |
| 395 | C2×C4 | C22×C4×D67 | 1 | 6 | yes | — |
| 396 | C2×C4 | C2×D4×D67 | 1 | 3 | yes | — |
| 397 | C2×C4 | C2×#11761629 | 1 | 6 | yes | — |
| 398 | C2×C4 | C24×D67 | 1 | 1 | yes | characteristic |
| 399 | C8 | — | 134 | 1 | no | — |
| 400 | C8 | — | 134 | 3 | no | — |
| 401 | C8 | C22×C4×D67 | 1 | 2 | yes | — |
| 402 | C8 | C22×C4×D67 | 1 | 6 | yes | — |
| 403 | C22 | — | 2 | 6 | no | — |
| 404 | C22 | — | 268 | 2 | no | — |
| 405 | C22 | — | 268 | 2 | no | — |
| 406 | C22 | — | 134 | 4 | no | — |
| 407 | C22 | C2×#14524005 | 1 | 6 | yes | — |
| 408 | C22 | C22×D4×D67 | 1 | 1 | yes | characteristic |
| 409 | C4 | — | 4 | 6 | no | — |
| 410 | C4 | — | 4 | 2 | no | — |
| 411 | C4 | — | 134 | 12 | no | — |
| 412 | C4 | — | 134 | 2 | no | — |
| 413 | C4 | — | 134 | 6 | no | — |
| 414 | C4 | C2×#14524005 | 1 | 6 | yes | — |
| 415 | C4 | C23×C4×D67 | 1 | 1 | yes | characteristic |
| 416 | C4 | C22×#11761629 | 1 | 1 | yes | characteristic |
| 417 | C2 | — | 2 | 6 | no | — |
| 418 | C2 | — | 268 | 4 | no | — |
| 419 | C2 | C22×#14524005 | 1 | 1 | yes | characteristic |
| 420 | C2 | #22574991 | 1 | 2 | yes | — |
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