← #32053058
Subgroups — #32053058
Order 18176.
1402 conjugacy classes of subgroups.
The subgroup lattice has 462 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22598835 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22597995 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22597746 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22597719 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22589397 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #22589239 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22588140 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C71×#3584 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | C2×#14556158 | C22 | 1 | 4 | yes | complemented |
| 10 | C22×Dic284 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #17986570 | C22 | 1 | 2 | yes | — |
| 12 | #17986570 | C22 | 1 | 4 | yes | complemented |
| 13 | #17986390 | — | 2 | 4 | no | — |
| 14 | #17986382 | — | 2 | 2 | no | — |
| 15 | #17986377 | — | 2 | 2 | no | — |
| 16 | #17986257 | — | 2 | 2 | no | — |
| 17 | #17986240 | — | 2 | 2 | no | — |
| 18 | #17986189 | — | 2 | 8 | no | — |
| 19 | #17986182 | — | 2 | 4 | no | — |
| 20 | #17986177 | — | 2 | 4 | no | — |
| 21 | #17986037 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #17986016 | C22 | 1 | 4 | yes | complemented |
| 23 | #17986009 | C22 | 1 | 2 | yes | complemented |
| 24 | #17985983 | C22 | 1 | 1 | yes | characteristic |
| 25 | #17985973 | C22 | 1 | 1 | yes | characteristic |
| 26 | #17985973 | C22 | 1 | 4 | yes | complemented |
| 27 | #17985954 | C22 | 1 | 2 | yes | complemented |
| 28 | #17985770 | C22 | 1 | 2 | yes | complemented |
| 29 | #585×C71 | C22 | 1 | 2 | yes | — |
| 30 | #578×C71 | — | 2 | 2 | no | — |
| 31 | #577×C71 | — | 2 | 4 | no | — |
| 32 | #576×C71 | — | 2 | 2 | no | — |
| 33 | #575×C71 | — | 2 | 2 | no | — |
| 34 | #575×C71 | C22 | 1 | 2 | yes | — |
| 35 | C2×#135×C71 | — | 2 | 2 | no | — |
| 36 | C2×#135×C71 | C22 | 1 | 2 | yes | — |
| 37 | C2×#131×C71 | C22 | 1 | 1 | yes | characteristic |
| 38 | C22×Dic142 | C23 | 1 | 2 | yes | — |
| 39 | #14556158 | — | 2 | 8 | no | — |
| 40 | #14556158 | — | 4 | 4 | no | — |
| 41 | C2×Dic284 | — | 2 | 2 | no | — |
| 42 | C2×Dic284 | — | 2 | 2 | no | — |
| 43 | C2×Dic284 | — | 2 | 1 | no | — |
| 44 | C2×Dic284 | — | 2 | 1 | no | — |
| 45 | C2×#11765855 | — | 2 | 4 | no | — |
| 46 | C2×#11765853 | — | 2 | 4 | no | — |
| 47 | C2×#11765849 | C23 | 1 | 2 | yes | — |
| 48 | #14556126 | — | 2 | 2 | no | — |
| 49 | #14556126 | — | 2 | 4 | no | — |
| 50 | #14556115 | — | 2 | 2 | no | — |
| 51 | #14556115 | — | 2 | 4 | no | — |
| 52 | #14556109 | — | 2 | 8 | no | — |
| 53 | #14556109 | — | 2 | 4 | no | — |
| 54 | #14556107 | — | 2 | 4 | no | — |
| 55 | #14556107 | — | 4 | 4 | no | — |
| 56 | #14556087 | C23 | 1 | 2 | yes | — |
| 57 | #14556087 | C23 | 1 | 2 | yes | — |
| 58 | #14556062 | — | 2 | 1 | no | — |
| 59 | #14556060 | — | 2 | 1 | no | — |
| 60 | #14556055 | — | 2 | 8 | no | — |
| 61 | #14556053 | — | 2 | 4 | no | — |
| 62 | #14556047 | D4 | 1 | 2 | yes | — |
| 63 | #14556045 | D4 | 1 | 2 | yes | — |
| 64 | #14556043 | — | 2 | 8 | no | — |
| 65 | #14556043 | D4 | 1 | 4 | yes | — |
| 66 | #14556038 | — | 2 | 2 | no | — |
| 67 | C8×Dic71 | — | 2 | 2 | no | — |
| 68 | 2−1+4×C71 | — | 2 | 4 | no | — |
| 69 | 2−1+4×C71 | — | 2 | 2 | no | — |
| 70 | H(5,𝔽2)×C71 | — | 2 | 4 | no | — |
| 71 | H(5,𝔽2)×C71 | — | 2 | 4 | no | — |
| 72 | H(5,𝔽2)×C71 | — | 2 | 2 | no | — |
| 73 | C2×#41×C71 | — | 2 | 4 | no | — |
| 74 | C2×#41×C71 | — | 4 | 4 | no | — |
| 75 | C2×#41×C71 | C23 | 1 | 4 | yes | — |
| 76 | C2×#41×C71 | C23 | 1 | 1 | yes | characteristic |
| 77 | #137×C71 | — | 2 | 8 | no | — |
| 78 | #137×C71 | — | 2 | 4 | no | — |
| 79 | AGL(1,ℤ/8)×C71 | — | 2 | 8 | no | — |
| 80 | AGL(1,ℤ/8)×C71 | — | 2 | 4 | no | — |
| 81 | #135×C71 | — | 2 | 4 | no | — |
| 82 | #135×C71 | — | 2 | 4 | no | — |
| 83 | #135×C71 | — | 2 | 2 | no | — |
| 84 | #135×C71 | — | 2 | 4 | no | — |
| 85 | #135×C71 | — | 2 | 2 | no | — |
| 86 | #135×C71 | — | 2 | 2 | no | — |
| 87 | #135×C71 | — | 2 | 2 | no | — |
| 88 | C2×Q16×C71 | — | 2 | 2 | no | — |
| 89 | C2×Q16×C71 | D4 | 1 | 2 | yes | — |
| 90 | C2×SD16×C71 | — | 2 | 4 | no | — |
| 91 | C2×SD16×C71 | D4 | 1 | 4 | yes | — |
| 92 | C2×D8×C71 | — | 2 | 2 | no | — |
| 93 | C2×D8×C71 | D4 | 1 | 2 | yes | — |
| 94 | #131×C71 | — | 2 | 2 | no | — |
| 95 | #131×C71 | — | 2 | 2 | no | — |
| 96 | C2×M16×C71 | D4 | 1 | 2 | yes | — |
| 97 | C2×M16×C71 | C23 | 1 | 1 | yes | characteristic |
| 98 | C22×C8×C71 | D4 | 1 | 2 | yes | — |
| 99 | C22×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 100 | C2×Dic142 | — | 2 | 2 | no | — |
| 101 | C2×Dic142 | — | 2 | 4 | no | — |
| 102 | C2×Dic142 | — | 2 | 2 | no | — |
| 103 | C2×Dic142 | — | 2 | 4 | no | — |
| 104 | C22×Dic71 | — | 2 | 2 | no | — |
| 105 | Dic284 | — | 4 | 1 | no | — |
| 106 | Dic284 | — | 4 | 1 | no | — |
| 107 | Dic284 | — | 4 | 2 | no | — |
| 108 | #11765855 | — | 4 | 8 | no | — |
| 109 | #11765853 | — | 4 | 8 | no | — |
| 110 | #11765849 | — | 2 | 2 | no | — |
| 111 | #11765849 | C2×D4 | 1 | 4 | yes | — |
| 112 | C2×C71⋊C8 | — | 2 | 2 | no | — |
| 113 | C4⋊Dic71 | — | 2 | 2 | no | — |
| 114 | C4⋊Dic71 | — | 2 | 2 | no | — |
| 115 | Dic71⋊C4 | — | 4 | 8 | no | — |
| 116 | Dic71⋊C4 | — | 4 | 4 | no | — |
| 117 | C22⋊Dic71 | — | 2 | 2 | no | — |
| 118 | C22⋊Dic71 | — | 4 | 8 | no | — |
| 119 | C22⋊Dic71 | — | 4 | 4 | no | — |
| 120 | C22⋊Dic71 | C2×D4 | 1 | 4 | yes | — |
| 121 | C4×Dic71 | — | 2 | 2 | no | — |
| 122 | C4×Dic71 | — | 2 | 2 | no | — |
| 123 | #41×C71 | — | 2 | 2 | no | — |
| 124 | #41×C71 | — | 2 | 2 | no | — |
| 125 | #41×C71 | — | 2 | 8 | no | — |
| 126 | #41×C71 | — | 2 | 4 | no | — |
| 127 | #41×C71 | — | 2 | 4 | no | — |
| 128 | #41×C71 | — | 2 | 4 | no | — |
| 129 | #41×C71 | — | 2 | 4 | no | — |
| 130 | #41×C71 | — | 4 | 8 | no | — |
| 131 | #41×C71 | — | 4 | 4 | no | — |
| 132 | #41×C71 | — | 4 | 4 | no | — |
| 133 | #41×C71 | — | 4 | 4 | no | — |
| 134 | #41×C71 | — | 4 | 4 | no | — |
| 135 | C2×Q8×C71 | — | 2 | 4 | no | — |
| 136 | C2×Q8×C71 | — | 4 | 4 | no | — |
| 137 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | C2×Q8×C71 | C2×D4 | 1 | 4 | yes | — |
| 139 | C2×D4×C71 | — | 2 | 4 | no | — |
| 140 | C2×D4×C71 | — | 2 | 4 | no | — |
| 141 | C2×D4×C71 | — | 4 | 4 | no | — |
| 142 | C2×D4×C71 | — | 4 | 8 | no | — |
| 143 | C2×D4×C71 | — | 4 | 4 | no | — |
| 144 | C2×D4×C71 | C2×D4 | 1 | 2 | yes | — |
| 145 | C2×D4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 146 | C2×D4×C71 | C2×D4 | 1 | 4 | yes | — |
| 147 | C22×C4×C71 | — | 2 | 4 | no | — |
| 148 | C22×C4×C71 | — | 4 | 4 | no | — |
| 149 | C22×C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 150 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 151 | Q16×C71 | — | 2 | 4 | no | — |
| 152 | Q16×C71 | — | 2 | 2 | no | — |
| 153 | Q16×C71 | — | 2 | 2 | no | — |
| 154 | SD16×C71 | — | 2 | 8 | no | — |
| 155 | SD16×C71 | — | 2 | 4 | no | — |
| 156 | SD16×C71 | — | 2 | 4 | no | — |
| 157 | D8×C71 | — | 2 | 4 | no | — |
| 158 | D8×C71 | — | 2 | 2 | no | — |
| 159 | D8×C71 | — | 2 | 2 | no | — |
| 160 | M16×C71 | — | 2 | 2 | no | — |
| 161 | M16×C71 | — | 2 | 4 | no | — |
| 162 | C2×C8×C71 | — | 2 | 2 | no | — |
| 163 | C2×C8×C71 | — | 2 | 2 | no | — |
| 164 | C2×C8×C71 | C2×D4 | 1 | 2 | yes | — |
| 165 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 166 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C2×C8×C71 | C2×D4 | 1 | 2 | yes | — |
| 168 | C2×C8×C71 | C2×D4 | 1 | 2 | yes | — |
| 169 | C23×C71 | — | 2 | 4 | no | — |
| 170 | C23×C71 | — | 4 | 4 | no | — |
| 171 | C23×C71 | #127 | 1 | 2 | yes | — |
| 172 | C23×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 173 | Q8×C71 | — | 2 | 2 | no | — |
| 174 | Q8×C71 | — | 2 | 4 | no | — |
| 175 | Q8×C71 | — | 2 | 4 | no | — |
| 176 | Q8×C71 | — | 4 | 4 | no | — |
| 177 | D4×C71 | — | 2 | 4 | no | — |
| 178 | D4×C71 | — | 2 | 4 | no | — |
| 179 | D4×C71 | — | 2 | 2 | no | — |
| 180 | D4×C71 | — | 2 | 4 | no | — |
| 181 | D4×C71 | — | 4 | 4 | no | — |
| 182 | D4×C71 | — | 4 | 8 | no | — |
| 183 | D4×C71 | — | 4 | 4 | no | — |
| 184 | D4×C71 | — | 4 | 4 | no | — |
| 185 | C2×C4×C71 | — | 2 | 2 | no | — |
| 186 | C2×C4×C71 | — | 2 | 2 | no | — |
| 187 | C2×C4×C71 | — | 2 | 4 | no | — |
| 188 | C2×C4×C71 | — | 4 | 8 | no | — |
| 189 | C2×C4×C71 | — | 4 | 4 | no | — |
| 190 | C2×C4×C71 | — | 4 | 4 | no | — |
| 191 | C2×C4×C71 | — | 4 | 4 | no | — |
| 192 | C2×C4×C71 | #127 | 1 | 2 | yes | — |
| 193 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 194 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 195 | C2×C4×C71 | C22×D4 | 1 | 2 | yes | — |
| 196 | C2×C4×C71 | H(5,𝔽2) | 1 | 2 | yes | — |
| 197 | C2×Dic71 | — | 2 | 4 | no | — |
| 198 | C2×Dic71 | — | 4 | 2 | no | — |
| 199 | C2×Dic71 | — | 4 | 2 | no | — |
| 200 | C2×Dic71 | — | 4 | 4 | no | — |
| 201 | Dic142 | — | 4 | 2 | no | — |
| 202 | Dic142 | — | 4 | 2 | no | — |
| 203 | Dic142 | — | 4 | 4 | no | — |
| 204 | C8×C71 | — | 2 | 2 | no | — |
| 205 | C8×C71 | #120 | 1 | 1 | yes | characteristic |
| 206 | C8×C71 | #120 | 1 | 1 | yes | characteristic |
| 207 | C8×C71 | #120 | 1 | 2 | yes | — |
| 208 | C71⋊C8 | — | 2 | 4 | no | — |
| 209 | C22×C71 | — | 2 | 2 | no | — |
| 210 | C22×C71 | — | 4 | 1 | no | — |
| 211 | C22×C71 | — | 4 | 2 | no | — |
| 212 | C22×C71 | — | 4 | 4 | no | — |
| 213 | C22×C71 | — | 8 | 4 | no | — |
| 214 | C22×C71 | — | 16 | 4 | no | — |
| 215 | C22×C71 | C2×#127 | 1 | 1 | yes | characteristic |
| 216 | C22×C71 | D42 | 1 | 2 | yes | — |
| 217 | C4×C71 | — | 2 | 2 | no | — |
| 218 | C4×C71 | — | 4 | 4 | no | — |
| 219 | C4×C71 | C2×#120 | 1 | 1 | yes | characteristic |
| 220 | C4×C71 | #535 | 1 | 1 | yes | characteristic |
| 221 | C4×C71 | D42 | 1 | 2 | yes | — |
| 222 | Dic71 | — | 4 | 4 | no | — |
| 223 | Dic71 | — | 8 | 2 | no | — |
| 224 | Dic71 | — | 8 | 2 | no | — |
| 225 | #25800 | — | 71 | 1 | no | maximal, Sylow |
| 226 | C2×C71 | — | 2 | 2 | no | — |
| 227 | C2×C71 | — | 2 | 1 | no | — |
| 228 | C2×C71 | — | 4 | 2 | no | — |
| 229 | C2×C71 | — | 8 | 4 | no | — |
| 230 | C2×C71 | #2433 | 1 | 1 | yes | characteristic |
| 231 | #3584 | D71 | 1 | 1 | yes | characteristic |
| 232 | #3156 | — | 71 | 2 | no | — |
| 233 | #3059 | — | 71 | 1 | no | — |
| 234 | #3028 | — | 71 | 2 | no | — |
| 235 | #3022 | — | 71 | 2 | no | — |
| 236 | #2009 | — | 71 | 4 | no | — |
| 237 | #1976 | — | 71 | 2 | no | — |
| 238 | #1757 | — | 71 | 1 | no | — |
| 239 | C71 | #25800 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 240 | #585 | C2×D71 | 1 | 2 | yes | — |
| 241 | #578 | — | 2 | 2 | no | — |
| 242 | #577 | — | 2 | 4 | no | — |
| 243 | #576 | — | 2 | 2 | no | — |
| 244 | #575 | — | 2 | 2 | no | — |
| 245 | #575 | C2×D71 | 1 | 2 | yes | — |
| 246 | C2×#137 | — | 71 | 4 | no | — |
| 247 | C2×#135 | — | 2 | 2 | no | — |
| 248 | C2×#135 | C2×D71 | 1 | 2 | yes | — |
| 249 | C22×Q16 | — | 71 | 1 | no | — |
| 250 | C2×#131 | C2×D71 | 1 | 1 | yes | characteristic |
| 251 | #536 | — | 71 | 4 | no | — |
| 252 | #536 | — | 71 | 2 | no | — |
| 253 | #497 | — | 142 | 4 | no | — |
| 254 | #495 | — | 142 | 2 | no | — |
| 255 | #494 | — | 142 | 2 | no | — |
| 256 | #470 | — | 142 | 2 | no | — |
| 257 | #467 | — | 142 | 2 | no | — |
| 258 | #458 | — | 142 | 8 | no | — |
| 259 | #456 | — | 142 | 4 | no | — |
| 260 | #455 | — | 142 | 4 | no | — |
| 261 | #427 | — | 71 | 1 | no | — |
| 262 | #421 | — | 71 | 4 | no | — |
| 263 | #419 | — | 71 | 2 | no | — |
| 264 | #413 | — | 71 | 1 | no | — |
| 265 | #410 | — | 71 | 1 | no | — |
| 266 | #410 | — | 71 | 4 | no | — |
| 267 | #405 | — | 71 | 2 | no | — |
| 268 | #344 | — | 71 | 2 | no | — |
| 269 | 2−1+4 | — | 2 | 4 | no | — |
| 270 | 2−1+4 | — | 2 | 2 | no | — |
| 271 | H(5,𝔽2) | — | 2 | 4 | no | — |
| 272 | H(5,𝔽2) | — | 2 | 4 | no | — |
| 273 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 274 | C2×#41 | — | 2 | 4 | no | — |
| 275 | C2×#41 | — | 4 | 4 | no | — |
| 276 | C2×#41 | C22×D71 | 1 | 4 | yes | — |
| 277 | C2×#41 | C22×D71 | 1 | 1 | yes | characteristic |
| 278 | C22×Q8 | — | 71 | 2 | no | — |
| 279 | #137 | — | 2 | 8 | no | — |
| 280 | #137 | — | 2 | 4 | no | — |
| 281 | #137 | — | 284 | 4 | no | — |
| 282 | #137 | — | 142 | 8 | no | — |
| 283 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 284 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 285 | #135 | — | 2 | 4 | no | — |
| 286 | #135 | — | 2 | 4 | no | — |
| 287 | #135 | — | 2 | 2 | no | — |
| 288 | #135 | — | 2 | 4 | no | — |
| 289 | #135 | — | 2 | 2 | no | — |
| 290 | #135 | — | 2 | 2 | no | — |
| 291 | #135 | — | 2 | 2 | no | — |
| 292 | C2×Q16 | — | 2 | 2 | no | — |
| 293 | C2×Q16 | — | 142 | 4 | no | — |
| 294 | C2×Q16 | — | 142 | 1 | no | — |
| 295 | C2×Q16 | — | 142 | 1 | no | — |
| 296 | C2×Q16 | — | 142 | 2 | no | — |
| 297 | C2×Q16 | — | 142 | 2 | no | — |
| 298 | C2×Q16 | C22⋊D71 | 1 | 2 | yes | — |
| 299 | C2×SD16 | — | 2 | 4 | no | — |
| 300 | C2×SD16 | — | 142 | 4 | no | — |
| 301 | C2×SD16 | C22⋊D71 | 1 | 4 | yes | — |
| 302 | C2×D8 | — | 2 | 2 | no | — |
| 303 | C2×D8 | C22⋊D71 | 1 | 2 | yes | — |
| 304 | #131 | — | 2 | 2 | no | — |
| 305 | #131 | — | 2 | 2 | no | — |
| 306 | C2×M16 | — | 71 | 2 | no | — |
| 307 | C2×M16 | C22⋊D71 | 1 | 2 | yes | — |
| 308 | C2×M16 | C22×D71 | 1 | 1 | yes | characteristic |
| 309 | C22×C8 | C22⋊D71 | 1 | 2 | yes | — |
| 310 | C22×C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 311 | C4⋊Q8 | — | 142 | 2 | no | — |
| 312 | C4⋊Q8 | — | 142 | 4 | no | — |
| 313 | #124 | — | 142 | 2 | no | — |
| 314 | #124 | — | 142 | 4 | no | — |
| 315 | #123 | — | 142 | 8 | no | — |
| 316 | #123 | — | 142 | 4 | no | — |
| 317 | C22⋊Q8 | — | 284 | 4 | no | — |
| 318 | C22⋊Q8 | — | 142 | 4 | no | — |
| 319 | #117 | — | 71 | 2 | no | — |
| 320 | #117 | — | 71 | 2 | no | — |
| 321 | #107 | — | 142 | 1 | no | — |
| 322 | #106 | — | 142 | 1 | no | — |
| 323 | #104 | — | 142 | 8 | no | — |
| 324 | #103 | — | 142 | 4 | no | — |
| 325 | #101 | — | 71 | 2 | no | — |
| 326 | #100 | — | 71 | 2 | no | — |
| 327 | #99 | — | 71 | 4 | no | — |
| 328 | #99 | — | 142 | 8 | no | — |
| 329 | #97 | — | 142 | 2 | no | — |
| 330 | C4×C8 | — | 142 | 2 | no | — |
| 331 | #41 | — | 2 | 2 | no | — |
| 332 | #41 | — | 2 | 2 | no | — |
| 333 | #41 | — | 2 | 8 | no | — |
| 334 | #41 | — | 2 | 4 | no | — |
| 335 | #41 | — | 2 | 4 | no | — |
| 336 | #41 | — | 2 | 4 | no | — |
| 337 | #41 | — | 2 | 4 | no | — |
| 338 | #41 | — | 4 | 8 | no | — |
| 339 | #41 | — | 4 | 4 | no | — |
| 340 | #41 | — | 4 | 4 | no | — |
| 341 | #41 | — | 4 | 4 | no | — |
| 342 | #41 | — | 4 | 4 | no | — |
| 343 | C2×Q8 | — | 2 | 4 | no | — |
| 344 | C2×Q8 | — | 4 | 4 | no | — |
| 345 | C2×Q8 | — | 142 | 2 | no | — |
| 346 | C2×Q8 | — | 142 | 2 | no | — |
| 347 | C2×Q8 | — | 142 | 4 | no | — |
| 348 | C2×Q8 | — | 142 | 4 | no | — |
| 349 | C2×Q8 | D4×D71 | 1 | 1 | yes | characteristic |
| 350 | C2×Q8 | C2×C22⋊D71 | 1 | 4 | yes | — |
| 351 | C2×D4 | — | 2 | 4 | no | — |
| 352 | C2×D4 | — | 2 | 4 | no | — |
| 353 | C2×D4 | — | 4 | 4 | no | — |
| 354 | C2×D4 | — | 4 | 8 | no | — |
| 355 | C2×D4 | — | 4 | 4 | no | — |
| 356 | C2×D4 | D4×D71 | 1 | 1 | yes | characteristic |
| 357 | C2×D4 | D4×D71 | 1 | 2 | yes | — |
| 358 | C2×D4 | C2×C22⋊D71 | 1 | 4 | yes | — |
| 359 | C22×C4 | — | 2 | 4 | no | — |
| 360 | C22×C4 | — | 4 | 4 | no | — |
| 361 | C22×C4 | — | 142 | 2 | no | — |
| 362 | C22×C4 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 363 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 364 | Q16 | — | 2 | 4 | no | — |
| 365 | Q16 | — | 2 | 2 | no | — |
| 366 | Q16 | — | 2 | 2 | no | — |
| 367 | Q16 | — | 284 | 8 | no | — |
| 368 | Q16 | — | 284 | 1 | no | — |
| 369 | Q16 | — | 284 | 1 | no | — |
| 370 | Q16 | — | 284 | 2 | no | — |
| 371 | SD16 | — | 2 | 8 | no | — |
| 372 | SD16 | — | 2 | 4 | no | — |
| 373 | SD16 | — | 2 | 4 | no | — |
| 374 | SD16 | — | 284 | 8 | no | — |
| 375 | D8 | — | 2 | 4 | no | — |
| 376 | D8 | — | 2 | 2 | no | — |
| 377 | D8 | — | 2 | 2 | no | — |
| 378 | M16 | — | 2 | 2 | no | — |
| 379 | M16 | — | 2 | 4 | no | — |
| 380 | M16 | — | 71 | 4 | no | — |
| 381 | M16 | — | 142 | 2 | no | — |
| 382 | C2×C8 | — | 2 | 2 | no | — |
| 383 | C2×C8 | — | 2 | 2 | no | — |
| 384 | C2×C8 | — | 142 | 2 | no | — |
| 385 | C2×C8 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 386 | C2×C8 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 387 | C2×C8 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 388 | C2×C8 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 389 | C2×C8 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 390 | C4⋊C4 | — | 284 | 8 | no | — |
| 391 | C4⋊C4 | — | 284 | 4 | no | — |
| 392 | C4⋊C4 | — | 142 | 2 | no | — |
| 393 | C4⋊C4 | — | 142 | 2 | no | — |
| 394 | C22⋊C4 | — | 284 | 4 | no | — |
| 395 | C22⋊C4 | — | 284 | 8 | no | — |
| 396 | C22⋊C4 | — | 71 | 4 | no | — |
| 397 | C22⋊C4 | — | 142 | 2 | no | — |
| 398 | C42 | — | 142 | 2 | no | — |
| 399 | C42 | — | 142 | 2 | no | — |
| 400 | C23 | — | 2 | 4 | no | — |
| 401 | C23 | — | 4 | 4 | no | — |
| 402 | C23 | #14556124 | 1 | 2 | yes | — |
| 403 | C23 | C2×D4×D71 | 1 | 1 | yes | characteristic |
| 404 | Q8 | — | 2 | 2 | no | — |
| 405 | Q8 | — | 2 | 4 | no | — |
| 406 | Q8 | — | 2 | 4 | no | — |
| 407 | Q8 | — | 4 | 4 | no | — |
| 408 | Q8 | — | 284 | 2 | no | — |
| 409 | Q8 | — | 284 | 4 | no | — |
| 410 | Q8 | — | 284 | 2 | no | — |
| 411 | D4 | — | 2 | 4 | no | — |
| 412 | D4 | — | 2 | 2 | no | — |
| 413 | D4 | — | 2 | 4 | no | — |
| 414 | D4 | — | 2 | 4 | no | — |
| 415 | D4 | — | 4 | 4 | no | — |
| 416 | D4 | — | 4 | 8 | no | — |
| 417 | D4 | — | 4 | 4 | no | — |
| 418 | D4 | — | 4 | 4 | no | — |
| 419 | C2×C4 | — | 2 | 2 | no | — |
| 420 | C2×C4 | — | 2 | 2 | no | — |
| 421 | C2×C4 | — | 2 | 4 | no | — |
| 422 | C2×C4 | — | 4 | 8 | no | — |
| 423 | C2×C4 | — | 4 | 4 | no | — |
| 424 | C2×C4 | — | 4 | 4 | no | — |
| 425 | C2×C4 | — | 4 | 4 | no | — |
| 426 | C2×C4 | — | 284 | 4 | no | — |
| 427 | C2×C4 | — | 284 | 2 | no | — |
| 428 | C2×C4 | — | 284 | 2 | no | — |
| 429 | C2×C4 | — | 142 | 4 | no | — |
| 430 | C2×C4 | #14556124 | 1 | 2 | yes | — |
| 431 | C2×C4 | C2×D4×D71 | 1 | 1 | yes | characteristic |
| 432 | C2×C4 | C22×C22⋊D71 | 1 | 1 | yes | characteristic |
| 433 | C2×C4 | C22×C22⋊D71 | 1 | 2 | yes | — |
| 434 | C2×C4 | #14556173 | 1 | 2 | yes | — |
| 435 | C8 | — | 2 | 2 | no | — |
| 436 | C8 | — | 142 | 4 | no | — |
| 437 | C8 | #14556097 | 1 | 1 | yes | characteristic |
| 438 | C8 | #14556097 | 1 | 1 | yes | characteristic |
| 439 | C8 | #14556097 | 1 | 2 | yes | — |
| 440 | C22 | — | 2 | 2 | no | — |
| 441 | C22 | — | 4 | 1 | no | — |
| 442 | C22 | — | 4 | 2 | no | — |
| 443 | C22 | — | 4 | 4 | no | — |
| 444 | C22 | — | 8 | 4 | no | — |
| 445 | C22 | — | 16 | 4 | no | — |
| 446 | C22 | C2×#14556124 | 1 | 1 | yes | characteristic |
| 447 | C22 | D4×C22⋊D71 | 1 | 2 | yes | — |
| 448 | C4 | — | 2 | 2 | no | — |
| 449 | C4 | — | 4 | 4 | no | — |
| 450 | C4 | — | 284 | 4 | no | — |
| 451 | C4 | — | 568 | 2 | no | — |
| 452 | C4 | — | 568 | 2 | no | — |
| 453 | C4 | C2×#14556097 | 1 | 1 | yes | characteristic |
| 454 | C4 | #17986566 | 1 | 1 | yes | characteristic |
| 455 | C4 | D4×C22⋊D71 | 1 | 2 | yes | — |
| 456 | C2 | — | 2 | 2 | no | — |
| 457 | C2 | — | 2 | 1 | no | — |
| 458 | C2 | — | 4 | 2 | no | — |
| 459 | C2 | — | 8 | 4 | no | — |
| 460 | C2 | #22591973 | 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