← #31728821
Subgroups — #31728821
Order 17152.
1790 conjugacy classes of subgroups.
The subgroup lattice has 600 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22573600 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22571675 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22571671 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22571650 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22571648 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22571633 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #22571626 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #22569996 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #22569820 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #22569792 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #22569667 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #424×D67 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C67×#3261 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C2×#14524066 | C22 | 1 | 2 | yes | — |
| 15 | C2×#14524066 | C22 | 1 | 2 | yes | — |
| 16 | C2×M16×D67 | C22 | 1 | 1 | yes | characteristic |
| 17 | C22×C8×D67 | C22 | 1 | 1 | yes | characteristic |
| 18 | #16864019 | C22 | 1 | 4 | yes | — |
| 19 | #16864018 | C22 | 1 | 4 | yes | — |
| 20 | #16864007 | C22 | 1 | 2 | yes | — |
| 21 | #16864002 | C22 | 1 | 2 | yes | — |
| 22 | #16864001 | C22 | 1 | 2 | yes | — |
| 23 | #16863994 | — | 2 | 4 | no | — |
| 24 | #16863985 | — | 2 | 4 | no | — |
| 25 | #16863952 | C22 | 1 | 2 | yes | — |
| 26 | #16863947 | C22 | 1 | 2 | yes | — |
| 27 | #16863931 | — | 2 | 4 | no | — |
| 28 | #16863929 | — | 2 | 4 | no | — |
| 29 | #16863909 | C22 | 1 | 4 | yes | — |
| 30 | C4×#11761629 | C22 | 1 | 4 | yes | — |
| 31 | #117×D67 | C22 | 1 | 1 | yes | characteristic |
| 32 | #16863703 | C22 | 1 | 4 | yes | complemented |
| 33 | #16863697 | C22 | 1 | 4 | yes | complemented |
| 34 | #16863693 | C22 | 1 | 4 | yes | complemented |
| 35 | #16863689 | C22 | 1 | 4 | yes | complemented |
| 36 | #16863685 | C22 | 1 | 4 | yes | complemented |
| 37 | #16863679 | C22 | 1 | 4 | yes | complemented |
| 38 | #16863675 | C22 | 1 | 4 | yes | complemented |
| 39 | #16863651 | C22 | 1 | 2 | yes | — |
| 40 | #16863650 | C22 | 1 | 2 | yes | — |
| 41 | #16863649 | C22 | 1 | 2 | yes | — |
| 42 | #16863645 | C22 | 1 | 4 | yes | — |
| 43 | #16863644 | C22 | 1 | 4 | yes | — |
| 44 | #16863634 | C22 | 1 | 2 | yes | — |
| 45 | #16863633 | C22 | 1 | 2 | yes | — |
| 46 | #16863632 | C22 | 1 | 2 | yes | — |
| 47 | #16863628 | C22 | 1 | 4 | yes | — |
| 48 | #16863627 | C22 | 1 | 4 | yes | — |
| 49 | #16863620 | C22 | 1 | 4 | yes | complemented |
| 50 | #16863620 | C22 | 1 | 4 | yes | complemented |
| 51 | #16863614 | C22 | 1 | 4 | yes | complemented |
| 52 | #16863614 | C22 | 1 | 4 | yes | complemented |
| 53 | #16863598 | C22 | 1 | 4 | yes | complemented |
| 54 | #16863596 | C22 | 1 | 4 | yes | complemented |
| 55 | #16863592 | C22 | 1 | 4 | yes | complemented |
| 56 | #16863433 | C22 | 1 | 2 | yes | — |
| 57 | #16863431 | C22 | 1 | 2 | yes | — |
| 58 | #16863424 | C22 | 1 | 1 | yes | characteristic |
| 59 | #16863423 | C22 | 1 | 1 | yes | characteristic |
| 60 | #16863422 | C22 | 1 | 1 | yes | characteristic |
| 61 | #16863421 | C22 | 1 | 4 | yes | — |
| 62 | C4⋊C8×D67 | C22 | 1 | 4 | yes | — |
| 63 | #16863391 | C22 | 1 | 4 | yes | — |
| 64 | #16863391 | C22 | 1 | 4 | yes | — |
| 65 | #541×C67 | C22 | 1 | 2 | yes | — |
| 66 | #479×C67 | C22 | 1 | 4 | yes | complemented |
| 67 | #470×C67 | C22 | 1 | 2 | yes | — |
| 68 | #467×C67 | C22 | 1 | 2 | yes | — |
| 69 | #462×C67 | C22 | 1 | 4 | yes | complemented |
| 70 | #424×C67 | C22 | 1 | 1 | yes | characteristic |
| 71 | C2×#11761629 | C23 | 1 | 4 | yes | — |
| 72 | C22×C4×D67 | C23 | 1 | 1 | yes | characteristic |
| 73 | #14524066 | — | 4 | 4 | no | — |
| 74 | #14524066 | — | 4 | 4 | no | — |
| 75 | C2×#11761615 | C23 | 1 | 4 | yes | — |
| 76 | C2×#11761615 | C23 | 1 | 4 | yes | — |
| 77 | C2×D536 | C23 | 1 | 2 | yes | — |
| 78 | C2×D536 | C23 | 1 | 2 | yes | — |
| 79 | C2×#11761612 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×#11761611 | C23 | 1 | 2 | yes | — |
| 81 | M16×D67 | — | 4 | 2 | no | — |
| 82 | C22×C67⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 83 | C2×C8×D67 | — | 4 | 2 | no | — |
| 84 | C2×C8×D67 | C23 | 1 | 2 | yes | — |
| 85 | C2×C8×D67 | C23 | 1 | 2 | yes | — |
| 86 | C2×C8×D67 | C23 | 1 | 2 | yes | — |
| 87 | #14524042 | C23 | 1 | 4 | yes | — |
| 88 | #14524040 | C23 | 1 | 2 | yes | — |
| 89 | #14524038 | — | 2 | 4 | no | — |
| 90 | #14524038 | — | 2 | 4 | no | — |
| 91 | #14524037 | — | 2 | 4 | no | — |
| 92 | #14524035 | C23 | 1 | 2 | yes | — |
| 93 | #14524033 | — | 2 | 4 | no | — |
| 94 | #14524032 | C23 | 1 | 4 | yes | — |
| 95 | #14524031 | — | 2 | 4 | no | — |
| 96 | #14524029 | — | 2 | 4 | no | — |
| 97 | #14524028 | — | 2 | 4 | no | — |
| 98 | #14524028 | — | 2 | 4 | no | — |
| 99 | #14524028 | — | 2 | 4 | no | — |
| 100 | #14524028 | — | 2 | 4 | no | — |
| 101 | #14524025 | — | 2 | 4 | no | — |
| 102 | #14524023 | — | 2 | 4 | no | — |
| 103 | #14524021 | — | 2 | 4 | no | — |
| 104 | #14524021 | — | 2 | 4 | no | — |
| 105 | #14524019 | C23 | 1 | 4 | yes | — |
| 106 | #14524018 | — | 2 | 4 | no | — |
| 107 | #14524018 | — | 2 | 4 | no | — |
| 108 | #14524018 | C23 | 1 | 4 | yes | — |
| 109 | #14524017 | C23 | 1 | 4 | yes | — |
| 110 | #14524016 | — | 2 | 4 | no | — |
| 111 | #14524013 | — | 2 | 4 | no | — |
| 112 | Q8×Dic67 | C23 | 1 | 4 | yes | — |
| 113 | #14524008 | — | 2 | 4 | no | — |
| 114 | C4×D268 | — | 2 | 4 | no | — |
| 115 | C4×D268 | C23 | 1 | 4 | yes | — |
| 116 | #14524005 | — | 2 | 4 | no | — |
| 117 | #14524005 | — | 2 | 4 | no | — |
| 118 | #14524005 | — | 2 | 4 | no | — |
| 119 | #14524005 | C23 | 1 | 4 | yes | — |
| 120 | (C22⋊D67)⋊C4 | — | 2 | 4 | no | — |
| 121 | #14524002 | C23 | 1 | 1 | yes | characteristic |
| 122 | #14524001 | — | 2 | 4 | no | — |
| 123 | #14524001 | D4 | 1 | 2 | yes | — |
| 124 | #14524001 | C23 | 1 | 4 | yes | — |
| 125 | #14524000 | C23 | 1 | 2 | yes | — |
| 126 | #14523999 | D4 | 1 | 2 | yes | — |
| 127 | C4⋊C4×D67 | D4 | 1 | 2 | yes | — |
| 128 | C22⋊C4×D67 | D4 | 1 | 2 | yes | — |
| 129 | C42×D67 | — | 2 | 4 | no | — |
| 130 | C42×D67 | C23 | 1 | 2 | yes | — |
| 131 | #14523977 | C23 | 1 | 2 | yes | — |
| 132 | #14523976 | C23 | 1 | 4 | yes | — |
| 133 | #14523975 | C23 | 1 | 2 | yes | — |
| 134 | #14523974 | C23 | 1 | 4 | yes | — |
| 135 | C4⋊(C67⋊C8) | C23 | 1 | 4 | yes | — |
| 136 | Dic67⋊C8 | C23 | 1 | 4 | yes | — |
| 137 | Dic67⋊C8 | C23 | 1 | 4 | yes | — |
| 138 | #14523967 | C23 | 1 | 4 | yes | — |
| 139 | #14523967 | C23 | 1 | 4 | yes | — |
| 140 | #14523965 | C23 | 1 | 4 | yes | — |
| 141 | #14523965 | C23 | 1 | 4 | yes | — |
| 142 | #14523963 | C23 | 1 | 4 | yes | — |
| 143 | #14523963 | C23 | 1 | 4 | yes | — |
| 144 | C2×Q16×C67 | C23 | 1 | 2 | yes | — |
| 145 | C2×Q16×C67 | C23 | 1 | 2 | yes | — |
| 146 | C2×M16×C67 | C23 | 1 | 1 | yes | characteristic |
| 147 | C22×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 148 | C4⋊Q8×C67 | C23 | 1 | 2 | yes | — |
| 149 | #126×C67 | — | 2 | 4 | no | — |
| 150 | #125×C67 | — | 2 | 4 | no | — |
| 151 | #125×C67 | C23 | 1 | 2 | yes | — |
| 152 | C22⋊Q8×C67 | C23 | 1 | 4 | yes | — |
| 153 | C4×Q8×C67 | C23 | 1 | 4 | yes | — |
| 154 | #117×C67 | C23 | 1 | 1 | yes | characteristic |
| 155 | #107×C67 | C23 | 1 | 2 | yes | — |
| 156 | #106×C67 | C23 | 1 | 2 | yes | — |
| 157 | C4⋊C8×C67 | C23 | 1 | 4 | yes | — |
| 158 | #103×C67 | C23 | 1 | 4 | yes | — |
| 159 | #103×C67 | C23 | 1 | 4 | yes | — |
| 160 | C23×D67 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | #11761629 | — | 2 | 8 | no | — |
| 162 | #11761629 | — | 2 | 8 | no | — |
| 163 | C2×Dic134 | — | 2 | 4 | no | — |
| 164 | C2×D268 | — | 2 | 4 | no | — |
| 165 | C2×D268 | — | 2 | 4 | no | — |
| 166 | C2×D268 | — | 2 | 4 | no | — |
| 167 | C2×D268 | C24 | 1 | 4 | yes | — |
| 168 | C2×C22⋊D67 | — | 2 | 4 | no | — |
| 169 | C22×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C2×C4×D67 | — | 2 | 2 | no | — |
| 171 | C2×C4×D67 | — | 2 | 2 | no | — |
| 172 | C2×C4×D67 | — | 2 | 4 | no | — |
| 173 | C2×C4×D67 | — | 2 | 4 | no | — |
| 174 | C2×C4×D67 | — | 2 | 4 | no | — |
| 175 | C2×C4×D67 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C2×C4×D67 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | C2×C4×D67 | C2×D4 | 1 | 4 | yes | — |
| 178 | C2×C4×D67 | C24 | 1 | 1 | yes | characteristic |
| 179 | C2×C4×D67 | C24 | 1 | 1 | yes | characteristic |
| 180 | #11761615 | — | 4 | 4 | no | — |
| 181 | #11761615 | — | 4 | 4 | no | — |
| 182 | D536 | — | 4 | 2 | no | — |
| 183 | D536 | — | 4 | 2 | no | — |
| 184 | #11761612 | — | 4 | 1 | no | — |
| 185 | #11761611 | — | 4 | 2 | no | — |
| 186 | C2×C67⋊C8 | — | 4 | 1 | no | — |
| 187 | C2×C67⋊C8 | C24 | 1 | 2 | yes | — |
| 188 | C2×C67⋊C8 | C24 | 1 | 2 | yes | — |
| 189 | C8×D67 | — | 2 | 4 | no | — |
| 190 | C8×D67 | — | 2 | 4 | no | — |
| 191 | C8×D67 | — | 4 | 2 | no | — |
| 192 | C4⋊Dic67 | — | 2 | 4 | no | — |
| 193 | C4⋊Dic67 | C2×D4 | 1 | 2 | yes | — |
| 194 | C4⋊Dic67 | C24 | 1 | 4 | yes | — |
| 195 | Dic67⋊C4 | — | 2 | 4 | no | — |
| 196 | Dic67⋊C4 | — | 2 | 4 | no | — |
| 197 | Dic67⋊C4 | — | 2 | 4 | no | — |
| 198 | Dic67⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 199 | C22⋊Dic67 | C2×D4 | 1 | 2 | yes | — |
| 200 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 201 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 202 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 203 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 204 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 205 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 206 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 207 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 208 | (C2×D67)⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 209 | C4×Dic67 | — | 2 | 4 | no | — |
| 210 | C4×Dic67 | — | 2 | 4 | no | — |
| 211 | C4×Dic67 | C2×D4 | 1 | 4 | yes | — |
| 212 | C4×Dic67 | C24 | 1 | 2 | yes | — |
| 213 | C2×Q8×C67 | C24 | 1 | 4 | yes | — |
| 214 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 215 | Q16×C67 | — | 4 | 2 | no | — |
| 216 | Q16×C67 | — | 4 | 2 | no | — |
| 217 | M16×C67 | — | 4 | 1 | no | — |
| 218 | C2×C8×C67 | — | 4 | 1 | no | — |
| 219 | C2×C8×C67 | C24 | 1 | 2 | yes | — |
| 220 | C2×C8×C67 | C24 | 1 | 2 | yes | — |
| 221 | C4⋊C4×C67 | — | 2 | 4 | no | — |
| 222 | C4⋊C4×C67 | — | 2 | 4 | no | — |
| 223 | C4⋊C4×C67 | — | 2 | 4 | no | — |
| 224 | C4⋊C4×C67 | — | 2 | 4 | no | — |
| 225 | C4⋊C4×C67 | C2×D4 | 1 | 2 | yes | — |
| 226 | C4⋊C4×C67 | C24 | 1 | 4 | yes | — |
| 227 | C22⋊C4×C67 | — | 2 | 4 | no | — |
| 228 | C22⋊C4×C67 | C2×D4 | 1 | 2 | yes | — |
| 229 | C42×C67 | — | 2 | 4 | no | — |
| 230 | C42×C67 | C24 | 1 | 2 | yes | — |
| 231 | C23×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 232 | C22×D67 | — | 2 | 2 | no | — |
| 233 | C22×D67 | — | 2 | 4 | no | — |
| 234 | C22×D67 | — | 4 | 2 | no | — |
| 235 | C22×D67 | C22×D4 | 1 | 1 | yes | characteristic |
| 236 | C22×D67 | C22×D4 | 1 | 1 | yes | characteristic |
| 237 | Q8×C67 | — | 2 | 4 | no | — |
| 238 | Q8×C67 | — | 2 | 4 | no | — |
| 239 | C2×C4×C67 | — | 2 | 1 | no | — |
| 240 | C2×C4×C67 | — | 2 | 1 | no | — |
| 241 | C2×C4×C67 | — | 2 | 4 | no | — |
| 242 | C2×C4×C67 | — | 2 | 4 | no | — |
| 243 | C2×C4×C67 | C22×D4 | 1 | 4 | yes | — |
| 244 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 245 | C2×C4×C67 | C25 | 1 | 1 | yes | characteristic |
| 246 | C22⋊D67 | — | 8 | 4 | no | — |
| 247 | C2×Dic67 | — | 2 | 2 | no | — |
| 248 | C2×Dic67 | — | 2 | 4 | no | — |
| 249 | C2×Dic67 | C22×D4 | 1 | 4 | yes | — |
| 250 | C2×Dic67 | C22×D4 | 1 | 1 | yes | characteristic |
| 251 | C2×Dic67 | C22×D4 | 1 | 1 | yes | characteristic |
| 252 | D268 | — | 2 | 4 | no | — |
| 253 | D268 | — | 2 | 4 | no | — |
| 254 | D268 | — | 4 | 8 | no | — |
| 255 | D268 | — | 8 | 4 | no | — |
| 256 | D268 | — | 8 | 4 | no | — |
| 257 | C4×D67 | — | 2 | 2 | no | — |
| 258 | C4×D67 | — | 2 | 1 | no | — |
| 259 | C4×D67 | — | 2 | 1 | no | — |
| 260 | C4×D67 | — | 2 | 2 | no | — |
| 261 | C4×D67 | — | 4 | 4 | no | — |
| 262 | C4×D67 | — | 4 | 8 | no | — |
| 263 | C4×D67 | — | 8 | 4 | no | — |
| 264 | C4×D67 | — | 8 | 4 | no | — |
| 265 | C4×D67 | H(5,𝔽2) | 1 | 2 | yes | — |
| 266 | C4×D67 | 2−1+4 | 1 | 2 | yes | — |
| 267 | Dic134 | — | 8 | 4 | no | — |
| 268 | C8×C67 | — | 2 | 2 | no | — |
| 269 | C8×C67 | — | 2 | 2 | no | — |
| 270 | C67⋊C8 | — | 2 | 2 | no | — |
| 271 | C67⋊C8 | — | 2 | 2 | no | — |
| 272 | C22×C67 | — | 2 | 2 | no | — |
| 273 | C22×C67 | — | 2 | 1 | no | — |
| 274 | C22×C67 | C23×D4 | 1 | 1 | yes | characteristic |
| 275 | C2×D67 | — | 2 | 2 | no | — |
| 276 | C2×D67 | — | 2 | 2 | no | — |
| 277 | C2×D67 | — | 2 | 1 | no | — |
| 278 | C2×D67 | — | 4 | 4 | no | — |
| 279 | C2×D67 | — | 4 | 4 | no | — |
| 280 | C2×D67 | — | 4 | 4 | no | — |
| 281 | C2×D67 | — | 4 | 4 | no | — |
| 282 | C2×D67 | #537 | 1 | 2 | yes | — |
| 283 | C4×C67 | — | 2 | 4 | no | — |
| 284 | C4×C67 | — | 2 | 1 | no | — |
| 285 | C4×C67 | — | 4 | 4 | no | — |
| 286 | C4×C67 | — | 4 | 4 | no | — |
| 287 | C4×C67 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 288 | C4×C67 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 289 | Dic67 | — | 2 | 4 | no | — |
| 290 | Dic67 | — | 2 | 1 | no | — |
| 291 | Dic67 | — | 4 | 4 | no | — |
| 292 | Dic67 | #537 | 1 | 2 | yes | — |
| 293 | #60915 | — | 67 | 1 | no | maximal, Sylow |
| 294 | C2×C67 | — | 4 | 1 | no | — |
| 295 | C2×C67 | C2×#537 | 1 | 1 | yes | characteristic |
| 296 | C2×C67 | #3584 | 1 | 2 | yes | — |
| 297 | D67 | — | 2 | 2 | no | — |
| 298 | D67 | — | 4 | 1 | no | — |
| 299 | D67 | — | 8 | 4 | no | — |
| 300 | #3455 | — | 67 | 2 | no | — |
| 301 | #3263 | — | 67 | 2 | no | — |
| 302 | #3262 | — | 67 | 2 | no | — |
| 303 | #3261 | D67 | 1 | 1 | yes | characteristic, complemented |
| 304 | #3260 | — | 67 | 2 | no | — |
| 305 | #3259 | — | 67 | 1 | no | — |
| 306 | #3258 | — | 67 | 4 | no | — |
| 307 | #3257 | — | 67 | 4 | no | — |
| 308 | #3076 | — | 67 | 4 | no | — |
| 309 | #3054 | — | 67 | 2 | no | — |
| 310 | #3050 | — | 67 | 2 | no | — |
| 311 | #3035 | — | 67 | 4 | no | — |
| 312 | C2×#424 | — | 67 | 1 | no | — |
| 313 | C67 | #60915 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 314 | C2×#135 | — | 67 | 2 | no | — |
| 315 | C2×#135 | — | 67 | 2 | no | — |
| 316 | C22×M16 | — | 67 | 1 | no | — |
| 317 | C23×C8 | — | 67 | 1 | no | — |
| 318 | #542 | — | 67 | 4 | no | — |
| 319 | #542 | — | 67 | 4 | no | — |
| 320 | #541 | — | 67 | 2 | no | — |
| 321 | #541 | C2×D67 | 1 | 2 | yes | — |
| 322 | #540 | — | 67 | 2 | no | — |
| 323 | #540 | — | 67 | 2 | no | — |
| 324 | #539 | — | 134 | 4 | no | — |
| 325 | #538 | — | 134 | 4 | no | — |
| 326 | #533 | — | 67 | 2 | no | — |
| 327 | #532 | — | 67 | 2 | no | — |
| 328 | #529 | — | 134 | 4 | no | — |
| 329 | #529 | — | 134 | 4 | no | — |
| 330 | #525 | — | 67 | 4 | no | — |
| 331 | C4×#41 | — | 67 | 4 | no | — |
| 332 | C2×#117 | — | 67 | 1 | no | — |
| 333 | #479 | — | 67 | 4 | no | — |
| 334 | #479 | C2×D67 | 1 | 4 | yes | complemented |
| 335 | #478 | — | 67 | 4 | no | — |
| 336 | #478 | — | 67 | 4 | no | — |
| 337 | #477 | — | 67 | 4 | no | — |
| 338 | #476 | — | 67 | 4 | no | — |
| 339 | #475 | — | 67 | 4 | no | — |
| 340 | #474 | — | 67 | 4 | no | — |
| 341 | #470 | — | 67 | 2 | no | — |
| 342 | #470 | C2×D67 | 1 | 2 | yes | — |
| 343 | #469 | — | 67 | 2 | no | — |
| 344 | #469 | — | 67 | 2 | no | — |
| 345 | #468 | — | 67 | 4 | no | — |
| 346 | #468 | — | 67 | 4 | no | — |
| 347 | #467 | — | 67 | 2 | no | — |
| 348 | #467 | C2×D67 | 1 | 2 | yes | — |
| 349 | #466 | — | 67 | 2 | no | — |
| 350 | #466 | — | 67 | 2 | no | — |
| 351 | #465 | — | 67 | 4 | no | — |
| 352 | #465 | — | 67 | 4 | no | — |
| 353 | #464 | — | 67 | 4 | no | — |
| 354 | #464 | — | 67 | 4 | no | — |
| 355 | #463 | — | 67 | 4 | no | — |
| 356 | #463 | — | 67 | 4 | no | — |
| 357 | #462 | C2×D67 | 1 | 4 | yes | complemented |
| 358 | #461 | — | 67 | 4 | no | — |
| 359 | #460 | — | 67 | 4 | no | — |
| 360 | #459 | — | 67 | 4 | no | — |
| 361 | #427 | — | 67 | 2 | no | — |
| 362 | #427 | — | 67 | 2 | no | — |
| 363 | #424 | — | 67 | 1 | no | — |
| 364 | #424 | — | 67 | 1 | no | — |
| 365 | #424 | — | 67 | 1 | no | — |
| 366 | #424 | — | 67 | 4 | no | — |
| 367 | #424 | C2×D67 | 1 | 1 | yes | characteristic |
| 368 | C2×C4⋊C8 | — | 67 | 4 | no | — |
| 369 | #416 | — | 67 | 4 | no | — |
| 370 | #416 | — | 67 | 4 | no | — |
| 371 | C2×#41 | — | 67 | 4 | no | — |
| 372 | C23×C4 | — | 67 | 1 | no | — |
| 373 | #135 | — | 268 | 4 | no | — |
| 374 | #135 | — | 268 | 4 | no | — |
| 375 | C2×Q16 | C22×D67 | 1 | 2 | yes | — |
| 376 | C2×Q16 | C22×D67 | 1 | 2 | yes | — |
| 377 | C2×SD16 | — | 67 | 4 | no | — |
| 378 | C2×SD16 | — | 67 | 4 | no | — |
| 379 | C2×D8 | — | 67 | 2 | no | — |
| 380 | C2×D8 | — | 67 | 2 | no | — |
| 381 | C2×M16 | — | 268 | 2 | no | — |
| 382 | C2×M16 | — | 67 | 1 | no | — |
| 383 | C2×M16 | — | 67 | 2 | no | — |
| 384 | C2×M16 | C22×D67 | 1 | 1 | yes | characteristic |
| 385 | C22×C8 | — | 268 | 2 | no | — |
| 386 | C22×C8 | — | 67 | 1 | no | — |
| 387 | C22×C8 | — | 67 | 2 | no | — |
| 388 | C22×C8 | — | 67 | 2 | no | — |
| 389 | C22×C8 | — | 67 | 2 | no | — |
| 390 | C22×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 391 | C4⋊Q8 | — | 67 | 4 | no | — |
| 392 | C4⋊Q8 | C22×D67 | 1 | 2 | yes | — |
| 393 | #127 | — | 67 | 2 | no | — |
| 394 | #126 | — | 2 | 4 | no | — |
| 395 | #126 | — | 134 | 4 | no | — |
| 396 | #126 | — | 134 | 4 | no | — |
| 397 | #126 | — | 134 | 4 | no | — |
| 398 | #125 | — | 2 | 4 | no | — |
| 399 | #125 | — | 67 | 2 | no | — |
| 400 | #125 | — | 134 | 4 | no | — |
| 401 | #125 | C22×D67 | 1 | 2 | yes | — |
| 402 | #124 | — | 67 | 4 | no | — |
| 403 | #124 | — | 134 | 4 | no | — |
| 404 | #124 | — | 134 | 4 | no | — |
| 405 | #123 | — | 134 | 4 | no | — |
| 406 | #123 | — | 134 | 4 | no | — |
| 407 | #123 | — | 134 | 4 | no | — |
| 408 | #123 | — | 134 | 4 | no | — |
| 409 | #123 | — | 134 | 4 | no | — |
| 410 | C22⋊Q8 | — | 67 | 4 | no | — |
| 411 | C22⋊Q8 | — | 134 | 4 | no | — |
| 412 | C22⋊Q8 | — | 134 | 4 | no | — |
| 413 | C22⋊Q8 | — | 134 | 4 | no | — |
| 414 | C22⋊Q8 | C22×D67 | 1 | 4 | yes | — |
| 415 | #121 | — | 67 | 4 | no | — |
| 416 | #121 | — | 67 | 4 | no | — |
| 417 | #121 | — | 134 | 4 | no | — |
| 418 | #121 | — | 134 | 4 | no | — |
| 419 | #121 | — | 134 | 4 | no | — |
| 420 | #120 | — | 134 | 4 | no | — |
| 421 | C4×Q8 | — | 67 | 4 | no | — |
| 422 | C4×Q8 | — | 134 | 4 | no | — |
| 423 | C4×Q8 | C22×D67 | 1 | 4 | yes | — |
| 424 | C4×D4 | — | 67 | 4 | no | — |
| 425 | C4×D4 | — | 67 | 4 | no | — |
| 426 | C4×D4 | — | 134 | 4 | no | — |
| 427 | C4×D4 | — | 134 | 4 | no | — |
| 428 | C4×D4 | — | 134 | 4 | no | — |
| 429 | C4×D4 | — | 134 | 4 | no | — |
| 430 | C4×D4 | — | 134 | 4 | no | — |
| 431 | #117 | — | 67 | 1 | no | — |
| 432 | #117 | — | 67 | 2 | no | — |
| 433 | #117 | — | 67 | 2 | no | — |
| 434 | #117 | — | 67 | 2 | no | — |
| 435 | #117 | — | 67 | 4 | no | — |
| 436 | #117 | — | 134 | 4 | no | — |
| 437 | #117 | C22×D67 | 1 | 1 | yes | characteristic |
| 438 | C2×C4⋊C4 | — | 67 | 2 | no | — |
| 439 | C2×C22⋊C4 | — | 67 | 2 | no | — |
| 440 | C2×C42 | — | 67 | 2 | no | — |
| 441 | C2×C42 | — | 134 | 4 | no | — |
| 442 | #107 | — | 67 | 2 | no | — |
| 443 | #107 | — | 67 | 4 | no | — |
| 444 | #107 | C22×D67 | 1 | 2 | yes | — |
| 445 | #106 | — | 67 | 2 | no | — |
| 446 | #106 | — | 67 | 4 | no | — |
| 447 | #106 | C22×D67 | 1 | 2 | yes | — |
| 448 | C4⋊C8 | — | 67 | 4 | no | — |
| 449 | C4⋊C8 | — | 67 | 4 | no | — |
| 450 | C4⋊C8 | — | 67 | 4 | no | — |
| 451 | C4⋊C8 | C22×D67 | 1 | 4 | yes | — |
| 452 | #103 | — | 67 | 4 | no | — |
| 453 | #103 | — | 67 | 4 | no | — |
| 454 | #103 | C22×D67 | 1 | 4 | yes | — |
| 455 | #103 | C22×D67 | 1 | 4 | yes | — |
| 456 | #102 | — | 67 | 4 | no | — |
| 457 | #102 | — | 67 | 4 | no | — |
| 458 | #102 | — | 67 | 4 | no | — |
| 459 | #102 | — | 67 | 4 | no | — |
| 460 | C24 | — | 67 | 1 | no | — |
| 461 | #41 | — | 134 | 8 | no | — |
| 462 | #41 | — | 134 | 8 | no | — |
| 463 | C2×Q8 | — | 134 | 4 | no | — |
| 464 | C2×Q8 | C23×D67 | 1 | 4 | yes | — |
| 465 | C2×D4 | — | 67 | 4 | no | — |
| 466 | C2×D4 | — | 134 | 4 | no | — |
| 467 | C2×D4 | — | 134 | 4 | no | — |
| 468 | C2×D4 | — | 134 | 4 | no | — |
| 469 | C2×D4 | — | 134 | 4 | no | — |
| 470 | C22×C4 | — | 67 | 4 | no | — |
| 471 | C22×C4 | — | 67 | 1 | no | — |
| 472 | C22×C4 | — | 67 | 1 | no | — |
| 473 | C22×C4 | — | 67 | 1 | no | — |
| 474 | C22×C4 | — | 67 | 1 | no | — |
| 475 | C22×C4 | — | 67 | 1 | no | — |
| 476 | C22×C4 | — | 134 | 4 | no | — |
| 477 | C22×C4 | — | 134 | 4 | no | — |
| 478 | C22×C4 | — | 134 | 2 | no | — |
| 479 | C22×C4 | — | 134 | 2 | no | — |
| 480 | C22×C4 | — | 134 | 4 | no | — |
| 481 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 482 | Q16 | — | 4 | 2 | no | — |
| 483 | Q16 | — | 4 | 2 | no | — |
| 484 | SD16 | — | 268 | 4 | no | — |
| 485 | SD16 | — | 268 | 4 | no | — |
| 486 | D8 | — | 268 | 2 | no | — |
| 487 | D8 | — | 268 | 2 | no | — |
| 488 | M16 | — | 4 | 1 | no | — |
| 489 | M16 | — | 268 | 2 | no | — |
| 490 | M16 | — | 268 | 1 | no | — |
| 491 | C2×C8 | — | 4 | 1 | no | — |
| 492 | C2×C8 | — | 268 | 2 | no | — |
| 493 | C2×C8 | — | 268 | 1 | no | — |
| 494 | C2×C8 | — | 67 | 2 | no | — |
| 495 | C2×C8 | — | 67 | 2 | no | — |
| 496 | C2×C8 | — | 134 | 4 | no | — |
| 497 | C2×C8 | — | 134 | 4 | no | — |
| 498 | C2×C8 | C23×D67 | 1 | 2 | yes | — |
| 499 | C2×C8 | C23×D67 | 1 | 2 | yes | — |
| 500 | C4⋊C4 | — | 2 | 4 | no | — |
| 501 | C4⋊C4 | — | 2 | 4 | no | — |
| 502 | C4⋊C4 | — | 2 | 4 | no | — |
| 503 | C4⋊C4 | — | 2 | 4 | no | — |
| 504 | C4⋊C4 | — | 67 | 2 | no | — |
| 505 | C4⋊C4 | — | 67 | 4 | no | — |
| 506 | C4⋊C4 | — | 67 | 4 | no | — |
| 507 | C4⋊C4 | — | 134 | 4 | no | — |
| 508 | C4⋊C4 | — | 134 | 4 | no | — |
| 509 | C4⋊C4 | — | 134 | 4 | no | — |
| 510 | C4⋊C4 | — | 134 | 4 | no | — |
| 511 | C4⋊C4 | D4×D67 | 1 | 2 | yes | — |
| 512 | C4⋊C4 | C23×D67 | 1 | 4 | yes | — |
| 513 | C22⋊C4 | — | 2 | 4 | no | — |
| 514 | C22⋊C4 | — | 67 | 2 | no | — |
| 515 | C22⋊C4 | — | 67 | 4 | no | — |
| 516 | C22⋊C4 | — | 134 | 4 | no | — |
| 517 | C22⋊C4 | — | 134 | 4 | no | — |
| 518 | C22⋊C4 | — | 134 | 4 | no | — |
| 519 | C22⋊C4 | — | 134 | 4 | no | — |
| 520 | C22⋊C4 | — | 134 | 4 | no | — |
| 521 | C22⋊C4 | — | 134 | 4 | no | — |
| 522 | C22⋊C4 | — | 134 | 4 | no | — |
| 523 | C22⋊C4 | — | 134 | 4 | no | — |
| 524 | C22⋊C4 | D4×D67 | 1 | 2 | yes | — |
| 525 | C42 | — | 2 | 4 | no | — |
| 526 | C42 | — | 67 | 4 | no | — |
| 527 | C42 | — | 67 | 2 | no | — |
| 528 | C42 | — | 134 | 4 | no | — |
| 529 | C42 | — | 134 | 4 | no | — |
| 530 | C42 | C23×D67 | 1 | 2 | yes | — |
| 531 | C23 | — | 268 | 2 | no | — |
| 532 | C23 | — | 67 | 1 | no | — |
| 533 | C23 | — | 67 | 1 | no | — |
| 534 | C23 | — | 134 | 2 | no | — |
| 535 | C23 | — | 134 | 4 | no | — |
| 536 | C23 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 537 | Q8 | — | 2 | 4 | no | — |
| 538 | Q8 | — | 2 | 4 | no | — |
| 539 | Q8 | — | 536 | 4 | no | — |
| 540 | D4 | — | 268 | 8 | no | — |
| 541 | D4 | — | 536 | 4 | no | — |
| 542 | D4 | — | 536 | 4 | no | — |
| 543 | D4 | — | 536 | 4 | no | — |
| 544 | D4 | — | 134 | 4 | no | — |
| 545 | D4 | — | 134 | 4 | no | — |
| 546 | C2×C4 | — | 2 | 1 | no | — |
| 547 | C2×C4 | — | 2 | 1 | no | — |
| 548 | C2×C4 | — | 2 | 4 | no | — |
| 549 | C2×C4 | — | 2 | 4 | no | — |
| 550 | C2×C4 | — | 268 | 4 | no | — |
| 551 | C2×C4 | — | 268 | 8 | no | — |
| 552 | C2×C4 | — | 536 | 4 | no | — |
| 553 | C2×C4 | — | 536 | 4 | no | — |
| 554 | C2×C4 | — | 67 | 1 | no | — |
| 555 | C2×C4 | — | 67 | 2 | no | — |
| 556 | C2×C4 | — | 67 | 2 | no | — |
| 557 | C2×C4 | — | 67 | 4 | no | — |
| 558 | C2×C4 | — | 67 | 1 | no | — |
| 559 | C2×C4 | — | 134 | 2 | no | — |
| 560 | C2×C4 | — | 134 | 2 | no | — |
| 561 | C2×C4 | — | 134 | 4 | no | — |
| 562 | C2×C4 | — | 134 | 2 | no | — |
| 563 | C2×C4 | — | 134 | 1 | no | — |
| 564 | C2×C4 | — | 134 | 1 | no | — |
| 565 | C2×C4 | C2×D4×D67 | 1 | 4 | yes | — |
| 566 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 567 | C2×C4 | C24×D67 | 1 | 1 | yes | characteristic |
| 568 | C8 | — | 2 | 2 | no | — |
| 569 | C8 | — | 2 | 2 | no | — |
| 570 | C8 | — | 134 | 2 | no | — |
| 571 | C8 | — | 134 | 2 | no | — |
| 572 | C22 | — | 2 | 2 | no | — |
| 573 | C22 | — | 2 | 1 | no | — |
| 574 | C22 | — | 268 | 4 | no | — |
| 575 | C22 | — | 268 | 4 | no | — |
| 576 | C22 | — | 268 | 4 | no | — |
| 577 | C22 | — | 268 | 4 | no | — |
| 578 | C22 | — | 67 | 2 | no | — |
| 579 | C22 | — | 134 | 2 | no | — |
| 580 | C22 | — | 134 | 1 | no | — |
| 581 | C22 | — | 134 | 2 | no | — |
| 582 | C22 | C22×D4×D67 | 1 | 1 | yes | characteristic |
| 583 | C4 | — | 2 | 4 | no | — |
| 584 | C4 | — | 2 | 1 | no | — |
| 585 | C4 | — | 4 | 4 | no | — |
| 586 | C4 | — | 4 | 4 | no | — |
| 587 | C4 | — | 268 | 4 | no | — |
| 588 | C4 | — | 67 | 2 | no | — |
| 589 | C4 | — | 134 | 4 | no | — |
| 590 | C4 | — | 134 | 1 | no | — |
| 591 | C4 | H(5,𝔽2)×D67 | 1 | 1 | yes | characteristic |
| 592 | C4 | 2−1+4×D67 | 1 | 1 | yes | characteristic |
| 593 | C2 | — | 4 | 1 | no | — |
| 594 | C2 | — | 268 | 1 | no | — |
| 595 | C2 | — | 536 | 4 | no | — |
| 596 | C2 | — | 134 | 2 | no | — |
| 597 | C2 | #537×D67 | 1 | 1 | yes | characteristic |
| 598 | C2 | #22574979 | 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