← #31735271
Subgroups — #31735271
Order 17152.
1754 conjugacy classes of subgroups.
The subgroup lattice has 526 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22574076 | C2 | 1 | 2 | yes | maximal |
| 2 | #22572823 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #22572782 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #22572639 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22572601 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22572576 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #22570181 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #22570010 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #22569865 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×C4×Dic268 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #22568922 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #22568806 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | C67×#3160 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C22×Dic268 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#14524049 | C22 | 1 | 2 | yes | — |
| 16 | #16864131 | — | 2 | 2 | no | — |
| 17 | #16864125 | — | 2 | 2 | no | — |
| 18 | #16864120 | C22 | 1 | 4 | yes | — |
| 19 | #16864119 | — | 2 | 4 | no | — |
| 20 | #16864107 | C22 | 1 | 4 | yes | — |
| 21 | #16864084 | C22 | 1 | 8 | yes | — |
| 22 | #16863995 | — | 2 | 4 | no | — |
| 23 | #16863972 | C22 | 1 | 4 | yes | — |
| 24 | #16863946 | C22 | 1 | 1 | yes | characteristic |
| 25 | #16863932 | — | 2 | 4 | no | — |
| 26 | #16863876 | C22 | 1 | 4 | yes | — |
| 27 | C2×C4×Dic134 | C22 | 1 | 2 | yes | — |
| 28 | #16863740 | C22 | 1 | 8 | yes | — |
| 29 | #16863739 | C22 | 1 | 8 | yes | — |
| 30 | #16863733 | C22 | 1 | 8 | yes | — |
| 31 | #16863728 | C22 | 1 | 8 | yes | — |
| 32 | #16863700 | C22 | 1 | 8 | yes | — |
| 33 | #16863688 | C22 | 1 | 4 | yes | — |
| 34 | #16863678 | C22 | 1 | 4 | yes | — |
| 35 | #16863655 | C22 | 1 | 8 | yes | — |
| 36 | #16863638 | C22 | 1 | 4 | yes | — |
| 37 | #16863638 | C22 | 1 | 4 | yes | — |
| 38 | C4×Dic268 | C22 | 1 | 2 | yes | — |
| 39 | C4×Dic268 | C22 | 1 | 2 | yes | — |
| 40 | C4×Dic268 | C22 | 1 | 2 | yes | — |
| 41 | C4×Dic268 | C22 | 1 | 2 | yes | — |
| 42 | #16863475 | C22 | 1 | 2 | yes | — |
| 43 | #16863475 | C22 | 1 | 2 | yes | — |
| 44 | C8×D268 | C22 | 1 | 2 | yes | — |
| 45 | C8×D268 | C22 | 1 | 2 | yes | — |
| 46 | #16863439 | C22 | 1 | 4 | yes | — |
| 47 | #16863435 | C22 | 1 | 8 | yes | — |
| 48 | #16863433 | C22 | 1 | 4 | yes | — |
| 49 | C2×#14523977 | C22 | 1 | 1 | yes | characteristic |
| 50 | #107×D67 | C22 | 1 | 4 | yes | — |
| 51 | #16863420 | C22 | 1 | 1 | yes | characteristic |
| 52 | #16863404 | C22 | 1 | 4 | yes | — |
| 53 | C2×#14523968 | C22 | 1 | 2 | yes | — |
| 54 | #16863362 | C22 | 1 | 2 | yes | — |
| 55 | #533×C67 | C22 | 1 | 2 | yes | — |
| 56 | #500×C67 | C22 | 1 | 1 | yes | characteristic |
| 57 | #500×C67 | C22 | 1 | 1 | yes | characteristic |
| 58 | #499×C67 | C22 | 1 | 2 | yes | — |
| 59 | #499×C67 | C22 | 1 | 2 | yes | — |
| 60 | #498×C67 | C22 | 1 | 2 | yes | — |
| 61 | #427×C67 | C22 | 1 | 2 | yes | — |
| 62 | #427×C67 | C22 | 1 | 2 | yes | — |
| 63 | C2×C4×C8×C67 | C22 | 1 | 1 | yes | characteristic |
| 64 | C2×#11761628 | C23 | 1 | 2 | yes | — |
| 65 | C22×Dic134 | C23 | 1 | 2 | yes | — |
| 66 | C2×Dic268 | — | 2 | 4 | no | — |
| 67 | C2×Dic268 | C23 | 1 | 2 | yes | — |
| 68 | C2×Dic268 | C23 | 1 | 2 | yes | — |
| 69 | #14524049 | — | 2 | 8 | no | — |
| 70 | C2×#11761612 | C23 | 1 | 2 | yes | — |
| 71 | C2×#11761611 | C23 | 1 | 4 | yes | — |
| 72 | C2×C8×D67 | C23 | 1 | 4 | yes | — |
| 73 | #14524043 | — | 2 | 4 | no | — |
| 74 | #14524043 | D4 | 1 | 1 | yes | characteristic |
| 75 | #14524040 | D4 | 1 | 1 | yes | characteristic |
| 76 | #14524038 | — | 2 | 8 | no | — |
| 77 | #14524038 | — | 2 | 8 | no | — |
| 78 | #14524034 | — | 2 | 8 | no | — |
| 79 | #14524034 | — | 2 | 4 | no | — |
| 80 | #14524032 | — | 2 | 4 | no | — |
| 81 | #14524031 | — | 2 | 4 | no | — |
| 82 | #14524031 | D4 | 1 | 2 | yes | — |
| 83 | #14524028 | — | 2 | 8 | no | — |
| 84 | #14524027 | — | 2 | 8 | no | — |
| 85 | #14524023 | C23 | 1 | 8 | yes | — |
| 86 | #14524023 | C23 | 1 | 8 | yes | — |
| 87 | #14524019 | — | 2 | 8 | no | — |
| 88 | #14524017 | D4 | 1 | 2 | yes | — |
| 89 | #14524017 | D4 | 1 | 2 | yes | — |
| 90 | Q8×Dic67 | — | 2 | 4 | no | — |
| 91 | C4×Dic134 | — | 2 | 4 | no | — |
| 92 | C4×Dic134 | — | 2 | 2 | no | — |
| 93 | C4×Dic134 | — | 2 | 2 | no | — |
| 94 | C4×Dic134 | C23 | 1 | 4 | yes | — |
| 95 | C4×Dic134 | C23 | 1 | 4 | yes | — |
| 96 | C4×D268 | — | 2 | 4 | no | — |
| 97 | C4×D268 | C23 | 1 | 2 | yes | — |
| 98 | C4×D268 | C23 | 1 | 2 | yes | — |
| 99 | #14524005 | — | 2 | 4 | no | — |
| 100 | (C22⋊D67)⋊C4 | — | 2 | 8 | no | — |
| 101 | #14524001 | — | 2 | 8 | no | — |
| 102 | #14524001 | C23 | 1 | 8 | yes | — |
| 103 | C2×C4⋊Dic67 | C23 | 1 | 2 | yes | — |
| 104 | C2×Dic67⋊C4 | — | 2 | 2 | no | — |
| 105 | C4⋊C4×D67 | C23 | 1 | 8 | yes | — |
| 106 | C2×C4×Dic67 | — | 2 | 2 | no | — |
| 107 | #14523977 | C23 | 1 | 2 | yes | — |
| 108 | #14523977 | C23 | 1 | 2 | yes | — |
| 109 | #14523976 | C23 | 1 | 8 | yes | — |
| 110 | #14523974 | C23 | 1 | 8 | yes | — |
| 111 | C4⋊(C67⋊C8) | C23 | 1 | 2 | yes | — |
| 112 | C4⋊(C67⋊C8) | C23 | 1 | 2 | yes | — |
| 113 | #14523968 | C23 | 1 | 4 | yes | — |
| 114 | #14523968 | C23 | 1 | 4 | yes | — |
| 115 | #14523966 | C23 | 1 | 8 | yes | — |
| 116 | #14523966 | C23 | 1 | 8 | yes | — |
| 117 | (C2×D67)⋊C8 | C23 | 1 | 4 | yes | — |
| 118 | (C2×D67)⋊C8 | C23 | 1 | 4 | yes | — |
| 119 | C22×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 120 | C22×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 121 | C4⋊Q8×C67 | C23 | 1 | 2 | yes | — |
| 122 | C4⋊Q8×C67 | C23 | 1 | 2 | yes | — |
| 123 | #125×C67 | C23 | 1 | 4 | yes | — |
| 124 | C22⋊Q8×C67 | — | 2 | 2 | no | — |
| 125 | C22⋊Q8×C67 | — | 2 | 2 | no | — |
| 126 | C4×Q8×C67 | — | 2 | 2 | no | — |
| 127 | C4×Q8×C67 | — | 2 | 2 | no | — |
| 128 | #117×C67 | C23 | 1 | 4 | yes | — |
| 129 | C2×C42×C67 | C23 | 1 | 1 | yes | characteristic |
| 130 | #107×C67 | C23 | 1 | 2 | yes | — |
| 131 | #107×C67 | C23 | 1 | 2 | yes | — |
| 132 | #107×C67 | C23 | 1 | 2 | yes | — |
| 133 | #107×C67 | C23 | 1 | 2 | yes | — |
| 134 | #106×C67 | C23 | 1 | 4 | yes | — |
| 135 | #106×C67 | C23 | 1 | 4 | yes | — |
| 136 | C4×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 137 | C4×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 138 | C4×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 139 | C4×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 140 | #11761628 | — | 2 | 4 | no | — |
| 141 | #11761628 | — | 2 | 4 | no | — |
| 142 | C2×Dic134 | — | 2 | 4 | no | — |
| 143 | C2×Dic134 | — | 2 | 4 | no | — |
| 144 | C2×Dic134 | — | 2 | 2 | no | — |
| 145 | C2×Dic134 | C2×D4 | 1 | 2 | yes | — |
| 146 | C2×Dic134 | C24 | 1 | 4 | yes | — |
| 147 | C2×D268 | C2×D4 | 1 | 2 | yes | — |
| 148 | C2×D268 | C2×D4 | 1 | 2 | yes | — |
| 149 | C2×D268 | C2×D4 | 1 | 2 | yes | — |
| 150 | C2×C22⋊D67 | C2×D4 | 1 | 4 | yes | — |
| 151 | C22×Dic67 | — | 2 | 2 | no | — |
| 152 | C22×Dic67 | — | 2 | 2 | no | — |
| 153 | C2×C4×D67 | — | 2 | 8 | no | — |
| 154 | C2×C4×D67 | C24 | 1 | 4 | yes | — |
| 155 | Dic268 | — | 2 | 4 | no | — |
| 156 | Dic268 | — | 2 | 4 | no | — |
| 157 | #11761612 | — | 2 | 4 | no | — |
| 158 | #11761611 | — | 2 | 8 | no | — |
| 159 | C2×C67⋊C8 | C24 | 1 | 4 | yes | — |
| 160 | C8×D67 | — | 2 | 8 | no | — |
| 161 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 162 | C4⋊Dic67 | — | 2 | 8 | no | — |
| 163 | C4⋊Dic67 | — | 2 | 8 | no | — |
| 164 | C4⋊Dic67 | C2×D4 | 1 | 2 | yes | — |
| 165 | C4⋊Dic67 | C2×D4 | 1 | 2 | yes | — |
| 166 | C4⋊Dic67 | C24 | 1 | 4 | yes | — |
| 167 | Dic67⋊C4 | — | 2 | 4 | no | — |
| 168 | Dic67⋊C4 | — | 2 | 4 | no | — |
| 169 | Dic67⋊C4 | — | 2 | 8 | no | — |
| 170 | (C2×D67)⋊C4 | — | 2 | 8 | no | — |
| 171 | (C2×D67)⋊C4 | — | 2 | 8 | no | — |
| 172 | (C2×D67)⋊C4 | — | 2 | 8 | no | — |
| 173 | (C2×D67)⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 174 | (C2×D67)⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 175 | C4×Dic67 | — | 2 | 4 | no | — |
| 176 | C4×Dic67 | — | 2 | 4 | no | — |
| 177 | C4×Dic67 | — | 2 | 8 | no | — |
| 178 | C2×Q8×C67 | — | 2 | 2 | no | — |
| 179 | C2×Q8×C67 | — | 2 | 2 | no | — |
| 180 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 183 | C2×C8×C67 | — | 2 | 2 | no | — |
| 184 | C2×C8×C67 | #41 | 1 | 4 | yes | — |
| 185 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 186 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 187 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 188 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 189 | C4⋊C4×C67 | — | 2 | 4 | no | — |
| 190 | C4⋊C4×C67 | — | 2 | 4 | no | — |
| 191 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 192 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 193 | C4⋊C4×C67 | C24 | 1 | 4 | yes | — |
| 194 | C4⋊C4×C67 | C24 | 1 | 4 | yes | — |
| 195 | C22⋊C4×C67 | — | 2 | 4 | no | — |
| 196 | C42×C67 | — | 2 | 4 | no | — |
| 197 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 198 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 199 | C42×C67 | C24 | 1 | 1 | yes | characteristic |
| 200 | C42×C67 | C24 | 1 | 1 | yes | characteristic |
| 201 | C23×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 202 | C22×D67 | C22×D4 | 1 | 4 | yes | — |
| 203 | Q8×C67 | — | 4 | 4 | no | — |
| 204 | Q8×C67 | — | 8 | 2 | no | — |
| 205 | C2×C4×C67 | — | 2 | 2 | no | — |
| 206 | C2×C4×C67 | — | 2 | 4 | no | — |
| 207 | C2×C4×C67 | — | 2 | 4 | no | — |
| 208 | C2×C4×C67 | — | 4 | 1 | no | — |
| 209 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 210 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 211 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 212 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 213 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 214 | C2×C4×C67 | C2×#41 | 1 | 2 | yes | — |
| 215 | C2×C4×C67 | 2−1+4 | 1 | 2 | yes | — |
| 216 | C2×C4×C67 | C25 | 1 | 1 | yes | characteristic |
| 217 | C22⋊D67 | — | 2 | 8 | no | — |
| 218 | C2×Dic67 | — | 2 | 4 | no | — |
| 219 | C2×Dic67 | — | 2 | 4 | no | — |
| 220 | C2×Dic67 | — | 4 | 4 | no | — |
| 221 | C2×Dic67 | — | 8 | 2 | no | — |
| 222 | C2×Dic67 | C22×D4 | 1 | 4 | yes | — |
| 223 | D268 | — | 2 | 4 | no | — |
| 224 | D268 | — | 2 | 4 | no | — |
| 225 | D268 | — | 4 | 2 | no | — |
| 226 | C4×D67 | — | 2 | 4 | no | — |
| 227 | C4×D67 | — | 2 | 4 | no | — |
| 228 | C4×D67 | — | 8 | 8 | no | — |
| 229 | Dic134 | — | 2 | 4 | no | — |
| 230 | Dic134 | — | 2 | 4 | no | — |
| 231 | Dic134 | — | 2 | 4 | no | — |
| 232 | Dic134 | — | 4 | 4 | no | — |
| 233 | C8×C67 | — | 2 | 1 | no | — |
| 234 | C8×C67 | — | 2 | 1 | no | — |
| 235 | C8×C67 | C2×#41 | 1 | 2 | yes | — |
| 236 | C8×C67 | C2×#41 | 1 | 2 | yes | — |
| 237 | C67⋊C8 | — | 2 | 4 | no | — |
| 238 | C22×C67 | — | 2 | 1 | no | — |
| 239 | C22×C67 | — | 2 | 1 | no | — |
| 240 | C22×C67 | #547 | 1 | 2 | yes | — |
| 241 | C22×C67 | C23×D4 | 1 | 1 | yes | characteristic |
| 242 | C2×D67 | — | 2 | 4 | no | — |
| 243 | C2×D67 | — | 2 | 4 | no | — |
| 244 | C2×D67 | — | 2 | 4 | no | — |
| 245 | C4×C67 | — | 2 | 1 | no | — |
| 246 | C4×C67 | — | 2 | 1 | no | — |
| 247 | C4×C67 | — | 2 | 1 | no | — |
| 248 | C4×C67 | — | 4 | 4 | no | — |
| 249 | C4×C67 | — | 4 | 4 | no | — |
| 250 | C4×C67 | #547 | 1 | 2 | yes | — |
| 251 | C4×C67 | #578 | 1 | 2 | yes | — |
| 252 | C4×C67 | C22×#41 | 1 | 1 | yes | characteristic |
| 253 | C4×C67 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 254 | Dic67 | — | 2 | 4 | no | — |
| 255 | Dic67 | — | 4 | 4 | no | — |
| 256 | Dic67 | — | 4 | 4 | no | — |
| 257 | #61286 | — | 67 | 1 | no | maximal, Sylow |
| 258 | C2×C67 | — | 2 | 2 | no | — |
| 259 | C2×C67 | C2×#547 | 1 | 1 | yes | characteristic |
| 260 | C2×C67 | C2×#578 | 1 | 1 | yes | characteristic |
| 261 | C2×C67 | #3584 | 1 | 1 | yes | characteristic |
| 262 | D67 | — | 4 | 4 | no | — |
| 263 | #3507 | — | 67 | 2 | no | — |
| 264 | #3356 | — | 67 | 4 | no | — |
| 265 | #3352 | — | 67 | 4 | no | — |
| 266 | #3342 | — | 67 | 2 | no | — |
| 267 | #3338 | — | 67 | 2 | no | — |
| 268 | #3336 | — | 67 | 4 | no | — |
| 269 | #3160 | D67 | 1 | 1 | yes | characteristic, complemented |
| 270 | #3097 | — | 67 | 4 | no | — |
| 271 | #3078 | — | 67 | 2 | no | — |
| 272 | #3059 | — | 67 | 2 | no | — |
| 273 | C2×C4×Q16 | — | 67 | 1 | no | — |
| 274 | #2931 | — | 67 | 1 | no | — |
| 275 | #2913 | — | 67 | 2 | no | — |
| 276 | C67 | #61286 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 277 | C22×Q16 | — | 67 | 1 | no | — |
| 278 | C2×#131 | — | 67 | 2 | no | — |
| 279 | #559 | — | 134 | 2 | no | — |
| 280 | #557 | — | 134 | 2 | no | — |
| 281 | #556 | — | 67 | 4 | no | — |
| 282 | #556 | — | 134 | 4 | no | — |
| 283 | #554 | — | 67 | 4 | no | — |
| 284 | #552 | — | 67 | 8 | no | — |
| 285 | #539 | — | 134 | 4 | no | — |
| 286 | #536 | — | 67 | 4 | no | — |
| 287 | #533 | C2×D67 | 1 | 2 | yes | — |
| 288 | #532 | — | 67 | 1 | no | — |
| 289 | #529 | — | 134 | 4 | no | — |
| 290 | #520 | — | 67 | 4 | no | — |
| 291 | C2×C4×Q8 | — | 67 | 2 | no | — |
| 292 | #500 | C2×D67 | 1 | 1 | yes | characteristic |
| 293 | #500 | C2×D67 | 1 | 1 | yes | characteristic |
| 294 | #499 | C2×D67 | 1 | 2 | yes | — |
| 295 | #499 | C2×D67 | 1 | 2 | yes | — |
| 296 | #498 | C2×D67 | 1 | 2 | yes | — |
| 297 | #485 | — | 67 | 8 | no | — |
| 298 | #485 | — | 67 | 8 | no | — |
| 299 | #484 | — | 67 | 8 | no | — |
| 300 | #483 | — | 67 | 8 | no | — |
| 301 | #479 | — | 67 | 8 | no | — |
| 302 | #477 | — | 67 | 4 | no | — |
| 303 | #475 | — | 67 | 4 | no | — |
| 304 | #470 | — | 67 | 8 | no | — |
| 305 | #467 | — | 67 | 4 | no | — |
| 306 | #467 | — | 67 | 4 | no | — |
| 307 | C4×Q16 | — | 67 | 2 | no | — |
| 308 | C4×Q16 | — | 67 | 2 | no | — |
| 309 | C4×Q16 | — | 67 | 2 | no | — |
| 310 | C4×Q16 | — | 67 | 2 | no | — |
| 311 | #436 | — | 67 | 2 | no | — |
| 312 | #436 | — | 67 | 2 | no | — |
| 313 | C8×D4 | — | 67 | 2 | no | — |
| 314 | C8×D4 | — | 67 | 2 | no | — |
| 315 | #428 | — | 67 | 4 | no | — |
| 316 | #428 | — | 67 | 8 | no | — |
| 317 | #427 | — | 67 | 4 | no | — |
| 318 | #427 | C2×D67 | 1 | 2 | yes | — |
| 319 | #427 | C2×D67 | 1 | 2 | yes | — |
| 320 | C2×#107 | — | 67 | 1 | no | — |
| 321 | C2×#107 | — | 67 | 4 | no | — |
| 322 | #423 | — | 67 | 1 | no | — |
| 323 | #419 | — | 67 | 4 | no | — |
| 324 | C2×#103 | — | 67 | 2 | no | — |
| 325 | #408 | — | 67 | 2 | no | — |
| 326 | C2×C4×C8 | C2×D67 | 1 | 1 | yes | characteristic |
| 327 | C2×#41 | — | 67 | 2 | no | — |
| 328 | C22×Q8 | — | 67 | 2 | no | — |
| 329 | C2×Q16 | — | 67 | 2 | no | — |
| 330 | C2×Q16 | — | 67 | 2 | no | — |
| 331 | C2×Q16 | — | 134 | 4 | no | — |
| 332 | #131 | — | 134 | 8 | no | — |
| 333 | C2×M16 | — | 67 | 2 | no | — |
| 334 | C2×M16 | — | 67 | 4 | no | — |
| 335 | C22×C8 | — | 67 | 4 | no | — |
| 336 | C22×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 337 | C22×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 338 | C4⋊Q8 | — | 67 | 1 | no | — |
| 339 | C4⋊Q8 | — | 134 | 4 | no | — |
| 340 | C4⋊Q8 | C22×D67 | 1 | 2 | yes | — |
| 341 | C4⋊Q8 | C22×D67 | 1 | 2 | yes | — |
| 342 | #127 | — | 67 | 1 | no | — |
| 343 | #126 | — | 134 | 8 | no | — |
| 344 | #126 | — | 134 | 8 | no | — |
| 345 | #125 | — | 134 | 4 | no | — |
| 346 | #125 | — | 134 | 8 | no | — |
| 347 | #125 | C22×D67 | 1 | 4 | yes | — |
| 348 | #124 | — | 67 | 2 | no | — |
| 349 | #124 | — | 134 | 4 | no | — |
| 350 | #124 | — | 134 | 4 | no | — |
| 351 | #123 | — | 134 | 8 | no | — |
| 352 | #123 | — | 134 | 8 | no | — |
| 353 | C22⋊Q8 | — | 2 | 2 | no | — |
| 354 | C22⋊Q8 | — | 2 | 2 | no | — |
| 355 | C22⋊Q8 | — | 67 | 8 | no | — |
| 356 | C22⋊Q8 | — | 67 | 8 | no | — |
| 357 | C22⋊Q8 | — | 134 | 8 | no | — |
| 358 | #121 | — | 67 | 2 | no | — |
| 359 | #121 | — | 67 | 2 | no | — |
| 360 | C4×Q8 | — | 2 | 2 | no | — |
| 361 | C4×Q8 | — | 2 | 2 | no | — |
| 362 | C4×Q8 | — | 67 | 4 | no | — |
| 363 | C4×Q8 | — | 67 | 4 | no | — |
| 364 | C4×Q8 | — | 134 | 4 | no | — |
| 365 | C4×Q8 | — | 134 | 4 | no | — |
| 366 | C4×Q8 | — | 134 | 2 | no | — |
| 367 | C4×Q8 | — | 134 | 2 | no | — |
| 368 | C4×D4 | — | 67 | 2 | no | — |
| 369 | C4×D4 | — | 67 | 2 | no | — |
| 370 | C4×D4 | — | 134 | 4 | no | — |
| 371 | C4×D4 | — | 134 | 8 | no | — |
| 372 | C4×D4 | — | 134 | 4 | no | — |
| 373 | #117 | — | 67 | 8 | no | — |
| 374 | #117 | — | 134 | 8 | no | — |
| 375 | #117 | C22×D67 | 1 | 4 | yes | — |
| 376 | C2×C4⋊C4 | — | 67 | 2 | no | — |
| 377 | C2×C4⋊C4 | — | 67 | 8 | no | — |
| 378 | C2×C4⋊C4 | — | 134 | 2 | no | — |
| 379 | C2×C42 | — | 134 | 2 | no | — |
| 380 | C2×C42 | C22×D67 | 1 | 1 | yes | characteristic |
| 381 | #107 | — | 67 | 2 | no | — |
| 382 | #107 | — | 67 | 2 | no | — |
| 383 | #107 | — | 67 | 8 | no | — |
| 384 | #107 | C22×D67 | 1 | 2 | yes | — |
| 385 | #107 | C22×D67 | 1 | 2 | yes | — |
| 386 | #107 | C22×D67 | 1 | 2 | yes | — |
| 387 | #107 | C22×D67 | 1 | 2 | yes | — |
| 388 | #106 | — | 67 | 8 | no | — |
| 389 | #106 | C22×D67 | 1 | 4 | yes | — |
| 390 | #106 | C22×D67 | 1 | 4 | yes | — |
| 391 | C4⋊C8 | — | 67 | 2 | no | — |
| 392 | C4⋊C8 | — | 67 | 2 | no | — |
| 393 | #103 | — | 67 | 4 | no | — |
| 394 | #103 | — | 67 | 4 | no | — |
| 395 | #103 | — | 67 | 8 | no | — |
| 396 | #103 | — | 67 | 8 | no | — |
| 397 | C22⋊C8 | — | 67 | 4 | no | — |
| 398 | C22⋊C8 | — | 67 | 4 | no | — |
| 399 | C4×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 400 | C4×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 401 | C4×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 402 | C4×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 403 | #41 | — | 134 | 4 | no | — |
| 404 | #41 | — | 134 | 4 | no | — |
| 405 | C2×Q8 | — | 2 | 2 | no | — |
| 406 | C2×Q8 | — | 2 | 2 | no | — |
| 407 | C2×Q8 | — | 67 | 2 | no | — |
| 408 | C2×Q8 | — | 67 | 4 | no | — |
| 409 | C2×Q8 | — | 134 | 4 | no | — |
| 410 | C2×Q8 | — | 134 | 4 | no | — |
| 411 | C2×Q8 | — | 134 | 2 | no | — |
| 412 | C2×D4 | — | 67 | 4 | no | — |
| 413 | C2×D4 | — | 67 | 2 | no | — |
| 414 | C2×D4 | — | 67 | 2 | no | — |
| 415 | C2×D4 | — | 67 | 2 | no | — |
| 416 | C22×C4 | — | 67 | 4 | no | — |
| 417 | C22×C4 | — | 134 | 8 | no | — |
| 418 | C22×C4 | — | 134 | 2 | no | — |
| 419 | C22×C4 | — | 134 | 2 | no | — |
| 420 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 421 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 422 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 423 | Q16 | — | 134 | 4 | no | — |
| 424 | Q16 | — | 134 | 4 | no | — |
| 425 | M16 | — | 134 | 4 | no | — |
| 426 | M16 | — | 134 | 8 | no | — |
| 427 | C2×C8 | — | 2 | 2 | no | — |
| 428 | C2×C8 | — | 67 | 4 | no | — |
| 429 | C2×C8 | — | 134 | 8 | no | — |
| 430 | C2×C8 | #11761629 | 1 | 4 | yes | — |
| 431 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 432 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 433 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 434 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 435 | C4⋊C4 | — | 2 | 4 | no | — |
| 436 | C4⋊C4 | — | 2 | 2 | no | — |
| 437 | C4⋊C4 | — | 2 | 4 | no | — |
| 438 | C4⋊C4 | — | 2 | 2 | no | — |
| 439 | C4⋊C4 | — | 67 | 2 | no | — |
| 440 | C4⋊C4 | — | 67 | 2 | no | — |
| 441 | C4⋊C4 | — | 67 | 4 | no | — |
| 442 | C4⋊C4 | — | 134 | 8 | no | — |
| 443 | C4⋊C4 | — | 134 | 8 | no | — |
| 444 | C4⋊C4 | — | 134 | 8 | no | — |
| 445 | C4⋊C4 | — | 134 | 2 | no | — |
| 446 | C4⋊C4 | — | 134 | 4 | no | — |
| 447 | C4⋊C4 | — | 134 | 4 | no | — |
| 448 | C4⋊C4 | C23×D67 | 1 | 4 | yes | — |
| 449 | C4⋊C4 | C23×D67 | 1 | 4 | yes | — |
| 450 | C22⋊C4 | — | 2 | 4 | no | — |
| 451 | C22⋊C4 | — | 67 | 4 | no | — |
| 452 | C22⋊C4 | — | 67 | 4 | no | — |
| 453 | C22⋊C4 | — | 134 | 8 | no | — |
| 454 | C22⋊C4 | — | 134 | 8 | no | — |
| 455 | C22⋊C4 | — | 134 | 8 | no | — |
| 456 | C42 | — | 2 | 4 | no | — |
| 457 | C42 | — | 134 | 8 | no | — |
| 458 | C42 | — | 134 | 4 | no | — |
| 459 | C42 | — | 134 | 4 | no | — |
| 460 | C42 | D4×D67 | 1 | 1 | yes | characteristic |
| 461 | C42 | D4×D67 | 1 | 1 | yes | characteristic |
| 462 | C42 | C23×D67 | 1 | 1 | yes | characteristic |
| 463 | C42 | C23×D67 | 1 | 1 | yes | characteristic |
| 464 | C23 | — | 67 | 4 | no | — |
| 465 | C23 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 466 | Q8 | — | 4 | 4 | no | — |
| 467 | Q8 | — | 8 | 2 | no | — |
| 468 | Q8 | — | 268 | 4 | no | — |
| 469 | Q8 | — | 134 | 4 | no | — |
| 470 | Q8 | — | 134 | 4 | no | — |
| 471 | Q8 | — | 134 | 4 | no | — |
| 472 | D4 | — | 268 | 2 | no | — |
| 473 | D4 | — | 134 | 8 | no | — |
| 474 | D4 | — | 134 | 4 | no | — |
| 475 | D4 | — | 134 | 4 | no | — |
| 476 | C2×C4 | — | 2 | 2 | no | — |
| 477 | C2×C4 | — | 2 | 4 | no | — |
| 478 | C2×C4 | — | 2 | 4 | no | — |
| 479 | C2×C4 | — | 4 | 1 | no | — |
| 480 | C2×C4 | — | 268 | 4 | no | — |
| 481 | C2×C4 | — | 536 | 8 | no | — |
| 482 | C2×C4 | — | 536 | 2 | no | — |
| 483 | C2×C4 | — | 67 | 4 | no | — |
| 484 | C2×C4 | — | 134 | 4 | no | — |
| 485 | C2×C4 | — | 134 | 4 | no | — |
| 486 | C2×C4 | — | 134 | 4 | no | — |
| 487 | C2×C4 | — | 134 | 4 | no | — |
| 488 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 489 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 490 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 491 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 492 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 493 | C2×C4 | C2×#11761629 | 1 | 2 | yes | — |
| 494 | C2×C4 | #14524091 | 1 | 2 | yes | — |
| 495 | C2×C4 | C24×D67 | 1 | 1 | yes | characteristic |
| 496 | C8 | — | 2 | 1 | no | — |
| 497 | C8 | — | 2 | 1 | no | — |
| 498 | C8 | — | 134 | 4 | no | — |
| 499 | C8 | C2×#11761629 | 1 | 2 | yes | — |
| 500 | C8 | C2×#11761629 | 1 | 2 | yes | — |
| 501 | C22 | — | 2 | 1 | no | — |
| 502 | C22 | — | 2 | 1 | no | — |
| 503 | C22 | — | 134 | 4 | no | — |
| 504 | C22 | — | 134 | 4 | no | — |
| 505 | C22 | — | 134 | 4 | no | — |
| 506 | C22 | #16864049 | 1 | 2 | yes | — |
| 507 | C22 | C22×D4×D67 | 1 | 1 | yes | characteristic |
| 508 | C4 | — | 2 | 1 | no | — |
| 509 | C4 | — | 2 | 1 | no | — |
| 510 | C4 | — | 2 | 1 | no | — |
| 511 | C4 | — | 4 | 4 | no | — |
| 512 | C4 | — | 4 | 4 | no | — |
| 513 | C4 | — | 268 | 4 | no | — |
| 514 | C4 | — | 268 | 4 | no | — |
| 515 | C4 | — | 134 | 4 | no | — |
| 516 | C4 | #16864049 | 1 | 2 | yes | — |
| 517 | C4 | #16864210 | 1 | 2 | yes | — |
| 518 | C4 | C22×#11761629 | 1 | 1 | yes | characteristic |
| 519 | C4 | C2×#14524091 | 1 | 1 | yes | characteristic |
| 520 | C2 | — | 2 | 2 | no | — |
| 521 | C2 | — | 268 | 4 | no | — |
| 522 | C2 | C2×#16864049 | 1 | 1 | yes | characteristic |
| 523 | C2 | C2×#16864210 | 1 | 1 | yes | characteristic |
| 524 | C2 | #22574978 | 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