← #13336891
Subgroups — #13336891
Order 1792.
746 conjugacy classes of subgroups.
The subgroup lattice has 396 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #11736471 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #11735912 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11735903 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×C7×#335 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11728186 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11726336 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11726331 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11726330 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C2×#6467 | — | 2 | 1 | no | — |
| 10 | C2×#6467 | — | 2 | 1 | no | — |
| 11 | C2×#6464 | — | 2 | 1 | no | — |
| 12 | #90168 | C22 | 1 | 1 | yes | characteristic |
| 13 | #90168 | C22 | 1 | 2 | yes | — |
| 14 | C2×C7×C4⋊C8 | C22 | 1 | 2 | yes | — |
| 15 | C2×C4×C7×C8 | C22 | 1 | 1 | yes | characteristic |
| 16 | #89887 | — | 2 | 4 | no | — |
| 17 | #89882 | — | 2 | 1 | no | — |
| 18 | #89696 | C22 | 1 | 1 | yes | characteristic |
| 19 | #89618 | — | 2 | 2 | no | — |
| 20 | #89618 | C22 | 1 | 4 | yes | — |
| 21 | #89615 | — | 2 | 2 | no | — |
| 22 | #89615 | C22 | 1 | 4 | yes | — |
| 23 | #89471 | C22 | 1 | 1 | yes | characteristic |
| 24 | #89468 | — | 2 | 1 | no | — |
| 25 | #89468 | — | 2 | 1 | no | — |
| 26 | #89467 | C22 | 1 | 1 | yes | characteristic |
| 27 | #89465 | C22 | 1 | 2 | yes | — |
| 28 | #89460 | — | 2 | 1 | no | — |
| 29 | #89460 | C22 | 1 | 2 | yes | — |
| 30 | C8×D28 | — | 2 | 1 | no | — |
| 31 | C8×D28 | C22 | 1 | 2 | yes | — |
| 32 | C7×#335 | C22 | 1 | 2 | yes | — |
| 33 | C7×#335 | C22 | 1 | 2 | yes | — |
| 34 | #89281 | C22 | 1 | 4 | yes | — |
| 35 | #89280 | C22 | 1 | 4 | yes | — |
| 36 | #19190 | — | 7 | 1 | no | maximal, Sylow |
| 37 | C2×#1157 | — | 2 | 1 | no | — |
| 38 | C2×#1157 | — | 2 | 2 | no | — |
| 39 | C22×C7×C8 | — | 2 | 2 | no | — |
| 40 | C22×C7×C8 | D4 | 1 | 1 | yes | characteristic |
| 41 | C22×C7×C8 | D4 | 1 | 1 | yes | characteristic |
| 42 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 43 | #6493 | — | 2 | 1 | no | — |
| 44 | #6493 | — | 2 | 2 | no | — |
| 45 | #6493 | — | 2 | 2 | no | — |
| 46 | #6493 | D4 | 1 | 2 | yes | — |
| 47 | C2×#1136 | — | 2 | 1 | no | — |
| 48 | C2×Dic28 | — | 2 | 1 | no | — |
| 49 | C2×Dic28 | — | 2 | 1 | no | — |
| 50 | #6467 | — | 4 | 4 | no | — |
| 51 | #6467 | — | 4 | 4 | no | — |
| 52 | C2×D56 | — | 2 | 1 | no | — |
| 53 | C2×D56 | — | 2 | 1 | no | — |
| 54 | C2×D56 | — | 2 | 4 | no | — |
| 55 | C2×#1132 | — | 2 | 2 | no | — |
| 56 | C2×#1132 | — | 2 | 2 | no | — |
| 57 | #6464 | — | 4 | 4 | no | — |
| 58 | C2×#1131 | — | 2 | 2 | no | — |
| 59 | C2×C8×D7 | — | 2 | 2 | no | — |
| 60 | #6438 | — | 2 | 1 | no | — |
| 61 | #6438 | — | 2 | 2 | no | — |
| 62 | #6437 | D4 | 1 | 1 | yes | characteristic |
| 63 | #6437 | C23 | 1 | 2 | yes | — |
| 64 | C4×D28 | — | 2 | 1 | no | — |
| 65 | C4×D28 | — | 2 | 2 | no | — |
| 66 | C4×D28 | — | 2 | 2 | no | — |
| 67 | C4×D28 | C23 | 1 | 2 | yes | — |
| 68 | #6432 | D4 | 1 | 1 | yes | characteristic |
| 69 | #6432 | C23 | 1 | 2 | yes | — |
| 70 | C7×C4⋊C8 | — | 2 | 2 | no | — |
| 71 | C7×C4⋊C8 | C23 | 1 | 4 | yes | — |
| 72 | C4×C7×C8 | D4 | 1 | 1 | yes | characteristic |
| 73 | C4×C7×C8 | D4 | 1 | 1 | yes | characteristic |
| 74 | C4×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 75 | C4×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 76 | #6395 | — | 2 | 4 | no | — |
| 77 | #6395 | — | 2 | 4 | no | — |
| 78 | (C2×D7)⋊C8 | — | 2 | 2 | no | — |
| 79 | (C2×D7)⋊C8 | — | 2 | 2 | no | — |
| 80 | #6392 | — | 2 | 4 | no | — |
| 81 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 82 | C4⋊(C7⋊C8) | C23 | 1 | 2 | yes | — |
| 83 | #3245 | — | 7 | 2 | no | — |
| 84 | #3147 | — | 7 | 1 | no | — |
| 85 | #2931 | — | 7 | 1 | no | — |
| 86 | #1685 | — | 7 | 4 | no | — |
| 87 | #1669 | — | 7 | 2 | no | — |
| 88 | #1667 | — | 7 | 2 | no | — |
| 89 | C2×#335 | D7 | 1 | 1 | yes | characteristic, complemented |
| 90 | #1547 | — | 7 | 2 | no | — |
| 91 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 92 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 93 | C22×C4×C7 | #41 | 1 | 1 | yes | characteristic |
| 94 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 95 | C2×C22⋊D7 | — | 4 | 2 | no | — |
| 96 | #1157 | — | 4 | 2 | no | — |
| 97 | #1157 | — | 4 | 2 | no | — |
| 98 | #1157 | — | 4 | 4 | no | — |
| 99 | #1157 | — | 4 | 4 | no | — |
| 100 | C2×D28 | — | 2 | 1 | no | — |
| 101 | C2×D28 | — | 2 | 1 | no | — |
| 102 | C2×D28 | — | 2 | 2 | no | — |
| 103 | C2×D28 | — | 2 | 2 | no | — |
| 104 | C2×D28 | — | 2 | 2 | no | — |
| 105 | C2×D28 | C2×D4 | 1 | 2 | yes | — |
| 106 | C2×C4×D7 | — | 2 | 2 | no | — |
| 107 | C2×C4×D7 | — | 4 | 2 | no | — |
| 108 | C2×Dic14 | — | 2 | 1 | no | — |
| 109 | C2×Dic14 | — | 2 | 2 | no | — |
| 110 | C2×C7×C8 | — | 2 | 2 | no | — |
| 111 | C2×C7×C8 | — | 2 | 4 | no | — |
| 112 | C2×C7×C8 | — | 8 | 2 | no | — |
| 113 | C2×C7×C8 | D8 | 1 | 4 | yes | complemented |
| 114 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 117 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | C42×C7 | #41 | 1 | 1 | yes | characteristic |
| 121 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 122 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 123 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 124 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 125 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 126 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 127 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 128 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 129 | C4⋊Dic7 | C2×D4 | 1 | 2 | yes | — |
| 130 | #1136 | — | 4 | 2 | no | — |
| 131 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 132 | Dic28 | — | 4 | 2 | no | — |
| 133 | Dic28 | — | 4 | 2 | no | — |
| 134 | D56 | — | 4 | 2 | no | — |
| 135 | D56 | — | 4 | 2 | no | — |
| 136 | D56 | — | 8 | 4 | no | — |
| 137 | #1132 | — | 4 | 4 | no | — |
| 138 | #1132 | — | 4 | 4 | no | — |
| 139 | #1131 | — | 4 | 4 | no | — |
| 140 | C8×D7 | — | 4 | 4 | no | — |
| 141 | C2×#135 | — | 14 | 1 | no | — |
| 142 | C2×#135 | — | 14 | 1 | no | — |
| 143 | C2×#131 | — | 14 | 1 | no | — |
| 144 | #532 | — | 7 | 1 | no | — |
| 145 | #532 | — | 7 | 2 | no | — |
| 146 | #495 | — | 14 | 1 | no | — |
| 147 | #495 | — | 14 | 1 | no | — |
| 148 | #494 | — | 7 | 1 | no | — |
| 149 | #493 | — | 7 | 1 | no | — |
| 150 | #492 | — | 7 | 2 | no | — |
| 151 | #474 | — | 7 | 4 | no | — |
| 152 | #474 | — | 14 | 2 | no | — |
| 153 | #466 | — | 14 | 4 | no | — |
| 154 | #459 | — | 7 | 4 | no | — |
| 155 | #459 | — | 14 | 2 | no | — |
| 156 | #436 | — | 7 | 2 | no | — |
| 157 | #436 | — | 14 | 1 | no | — |
| 158 | C8×D4 | — | 7 | 2 | no | — |
| 159 | C8×D4 | — | 14 | 1 | no | — |
| 160 | #423 | — | 7 | 1 | no | — |
| 161 | C2×C4⋊C8 | C2×D7 | 1 | 2 | yes | — |
| 162 | #408 | — | 14 | 1 | no | — |
| 163 | C2×C4×C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 164 | #335 | C2×D7 | 1 | 2 | yes | — |
| 165 | #335 | C2×D7 | 1 | 2 | yes | — |
| 166 | #332 | — | 7 | 4 | no | — |
| 167 | #331 | — | 7 | 4 | no | — |
| 168 | C23×C7 | #121 | 1 | 1 | yes | characteristic |
| 169 | C22×D7 | — | 2 | 2 | no | — |
| 170 | C22×D7 | — | 4 | 2 | no | — |
| 171 | C2×C4×C7 | — | 2 | 1 | no | — |
| 172 | C2×C4×C7 | — | 2 | 1 | no | — |
| 173 | C2×C4×C7 | — | 4 | 1 | no | — |
| 174 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 175 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 176 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 177 | C2×C4×C7 | C2×D8 | 1 | 2 | yes | — |
| 178 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 179 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 180 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 181 | C2×C4×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 182 | C22⋊D7 | — | 4 | 4 | no | — |
| 183 | C22⋊D7 | — | 8 | 4 | no | — |
| 184 | C2×Dic7 | — | 2 | 2 | no | — |
| 185 | C2×Dic7 | — | 4 | 2 | no | — |
| 186 | D28 | — | 2 | 2 | no | — |
| 187 | D28 | — | 2 | 2 | no | — |
| 188 | D28 | — | 4 | 2 | no | — |
| 189 | D28 | — | 4 | 2 | no | — |
| 190 | D28 | — | 4 | 2 | no | — |
| 191 | D28 | — | 4 | 2 | no | — |
| 192 | D28 | — | 4 | 2 | no | — |
| 193 | D28 | — | 4 | 2 | no | — |
| 194 | D28 | — | 8 | 2 | no | — |
| 195 | C4×D7 | — | 4 | 2 | no | — |
| 196 | C4×D7 | — | 4 | 2 | no | — |
| 197 | C4×D7 | — | 8 | 4 | no | — |
| 198 | Dic14 | — | 4 | 2 | no | — |
| 199 | Dic14 | — | 4 | 2 | no | — |
| 200 | Dic14 | — | 4 | 2 | no | — |
| 201 | C7×C8 | — | 2 | 1 | no | — |
| 202 | C7×C8 | — | 2 | 1 | no | — |
| 203 | C7×C8 | — | 4 | 4 | no | — |
| 204 | C7×C8 | C2×D8 | 1 | 2 | yes | — |
| 205 | C7×C8 | C2×D8 | 1 | 2 | yes | — |
| 206 | C7⋊C8 | — | 4 | 2 | no | — |
| 207 | C2×#41 | — | 14 | 1 | no | — |
| 208 | C2×#41 | — | 14 | 2 | no | — |
| 209 | #135 | — | 28 | 4 | no | — |
| 210 | #135 | — | 28 | 4 | no | — |
| 211 | C2×Q16 | — | 14 | 1 | no | — |
| 212 | C2×Q16 | — | 14 | 1 | no | — |
| 213 | C2×SD16 | — | 14 | 2 | no | — |
| 214 | C2×SD16 | — | 14 | 2 | no | — |
| 215 | C2×D8 | — | 14 | 4 | no | — |
| 216 | C2×D8 | — | 14 | 1 | no | — |
| 217 | C2×D8 | — | 14 | 1 | no | — |
| 218 | #131 | — | 28 | 4 | no | — |
| 219 | C2×M16 | — | 14 | 1 | no | — |
| 220 | C2×M16 | — | 14 | 2 | no | — |
| 221 | C22×C8 | — | 2 | 2 | no | — |
| 222 | C22×C8 | — | 14 | 2 | no | — |
| 223 | C22×C8 | D28 | 1 | 1 | yes | characteristic |
| 224 | C22×C8 | D28 | 1 | 1 | yes | characteristic |
| 225 | C4⋊Q8 | — | 7 | 1 | no | — |
| 226 | C4⋊Q8 | — | 7 | 2 | no | — |
| 227 | #127 | — | 7 | 1 | no | — |
| 228 | #127 | — | 7 | 2 | no | — |
| 229 | #124 | — | 14 | 2 | no | — |
| 230 | #124 | — | 14 | 1 | no | — |
| 231 | #121 | — | 7 | 2 | no | — |
| 232 | #121 | — | 14 | 1 | no | — |
| 233 | #121 | — | 14 | 2 | no | — |
| 234 | #121 | — | 14 | 2 | no | — |
| 235 | C4×D4 | — | 7 | 2 | no | — |
| 236 | C4×D4 | — | 14 | 1 | no | — |
| 237 | C4×D4 | — | 14 | 2 | no | — |
| 238 | C4×D4 | — | 14 | 2 | no | — |
| 239 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 240 | #107 | — | 14 | 4 | no | — |
| 241 | C4⋊C8 | — | 2 | 2 | no | — |
| 242 | C4⋊C8 | — | 7 | 2 | no | — |
| 243 | C4⋊C8 | — | 14 | 1 | no | — |
| 244 | C4⋊C8 | C22×D7 | 1 | 4 | yes | — |
| 245 | #102 | — | 14 | 4 | no | — |
| 246 | #102 | — | 14 | 4 | no | — |
| 247 | C22⋊C8 | — | 14 | 2 | no | — |
| 248 | C22⋊C8 | — | 14 | 2 | no | — |
| 249 | C4×C8 | D28 | 1 | 1 | yes | characteristic |
| 250 | C4×C8 | D28 | 1 | 1 | yes | characteristic |
| 251 | C4×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 252 | C4×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 253 | C22×C7 | — | 2 | 1 | no | — |
| 254 | C22×C7 | — | 2 | 1 | no | — |
| 255 | C22×C7 | #459 | 1 | 2 | yes | — |
| 256 | C22×C7 | C2×#121 | 1 | 1 | yes | characteristic |
| 257 | C2×D7 | — | 4 | 2 | no | — |
| 258 | C2×D7 | — | 4 | 2 | no | — |
| 259 | C2×D7 | — | 4 | 2 | no | — |
| 260 | C2×D7 | — | 8 | 2 | no | — |
| 261 | C2×D7 | — | 8 | 2 | no | — |
| 262 | C2×D7 | — | 8 | 2 | no | — |
| 263 | C4×C7 | — | 2 | 1 | no | — |
| 264 | C4×C7 | — | 2 | 1 | no | — |
| 265 | C4×C7 | — | 2 | 1 | no | — |
| 266 | C4×C7 | #459 | 1 | 2 | yes | — |
| 267 | C4×C7 | C22×D8 | 1 | 1 | yes | characteristic |
| 268 | C4×C7 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 269 | C4×C7 | #576 | 1 | 1 | yes | characteristic |
| 270 | C4×C7 | #578 | 1 | 1 | yes | characteristic |
| 271 | Dic7 | — | 4 | 2 | no | — |
| 272 | Dic7 | — | 8 | 2 | no | — |
| 273 | #41 | — | 28 | 2 | no | — |
| 274 | #41 | — | 28 | 2 | no | — |
| 275 | #41 | — | 28 | 4 | no | — |
| 276 | #41 | — | 28 | 4 | no | — |
| 277 | C2×Q8 | — | 14 | 1 | no | — |
| 278 | C2×Q8 | — | 14 | 2 | no | — |
| 279 | C2×D4 | — | 7 | 2 | no | — |
| 280 | C2×D4 | — | 14 | 2 | no | — |
| 281 | C2×D4 | — | 14 | 1 | no | — |
| 282 | C2×D4 | — | 14 | 1 | no | — |
| 283 | C2×D4 | — | 14 | 2 | no | — |
| 284 | C2×D4 | — | 14 | 2 | no | — |
| 285 | C2×D4 | — | 14 | 2 | no | — |
| 286 | C2×D4 | — | 28 | 2 | no | — |
| 287 | C22×C4 | — | 14 | 2 | no | — |
| 288 | C22×C4 | — | 28 | 2 | no | — |
| 289 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 290 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 291 | C22×C4 | #1161 | 1 | 1 | yes | characteristic |
| 292 | Q16 | — | 28 | 2 | no | — |
| 293 | Q16 | — | 28 | 2 | no | — |
| 294 | SD16 | — | 28 | 4 | no | — |
| 295 | SD16 | — | 28 | 4 | no | — |
| 296 | D8 | — | 28 | 2 | no | — |
| 297 | D8 | — | 28 | 2 | no | — |
| 298 | D8 | — | 56 | 4 | no | — |
| 299 | M16 | — | 28 | 2 | no | — |
| 300 | M16 | — | 28 | 4 | no | — |
| 301 | C2×C8 | — | 2 | 2 | no | — |
| 302 | C2×C8 | — | 2 | 4 | no | — |
| 303 | C2×C8 | — | 8 | 2 | no | — |
| 304 | C2×C8 | — | 14 | 2 | no | — |
| 305 | C2×C8 | — | 28 | 4 | no | — |
| 306 | C2×C8 | D56 | 1 | 4 | yes | complemented |
| 307 | C2×C8 | C2×D28 | 1 | 1 | yes | characteristic |
| 308 | C2×C8 | C2×D28 | 1 | 1 | yes | characteristic |
| 309 | C2×C8 | C2×D28 | 1 | 1 | yes | characteristic |
| 310 | C2×C8 | C2×D28 | 1 | 1 | yes | characteristic |
| 311 | C4⋊C4 | — | 7 | 2 | no | — |
| 312 | C4⋊C4 | — | 14 | 1 | no | — |
| 313 | C4⋊C4 | — | 14 | 2 | no | — |
| 314 | C4⋊C4 | — | 14 | 2 | no | — |
| 315 | C22⋊C4 | — | 14 | 2 | no | — |
| 316 | C22⋊C4 | — | 14 | 2 | no | — |
| 317 | C22⋊C4 | — | 28 | 2 | no | — |
| 318 | C22⋊C4 | — | 28 | 2 | no | — |
| 319 | C42 | C2×D28 | 1 | 1 | yes | characteristic |
| 320 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 321 | C42 | #1161 | 1 | 1 | yes | characteristic |
| 322 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 323 | C2×C7 | — | 2 | 2 | no | — |
| 324 | C2×C7 | C2×#459 | 1 | 1 | yes | characteristic |
| 325 | C2×C7 | #3061 | 1 | 1 | yes | characteristic |
| 326 | C2×C7 | #3067 | 1 | 1 | yes | characteristic |
| 327 | D7 | — | 8 | 2 | no | — |
| 328 | D7 | — | 16 | 2 | no | — |
| 329 | C23 | — | 14 | 2 | no | — |
| 330 | C23 | — | 28 | 2 | no | — |
| 331 | C23 | #6458 | 1 | 1 | yes | characteristic |
| 332 | Q8 | — | 28 | 2 | no | — |
| 333 | Q8 | — | 28 | 2 | no | — |
| 334 | Q8 | — | 28 | 2 | no | — |
| 335 | D4 | — | 14 | 2 | no | — |
| 336 | D4 | — | 14 | 2 | no | — |
| 337 | D4 | — | 28 | 2 | no | — |
| 338 | D4 | — | 28 | 4 | no | — |
| 339 | D4 | — | 28 | 2 | no | — |
| 340 | D4 | — | 28 | 2 | no | — |
| 341 | D4 | — | 28 | 2 | no | — |
| 342 | D4 | — | 28 | 2 | no | — |
| 343 | D4 | — | 28 | 2 | no | — |
| 344 | D4 | — | 56 | 2 | no | — |
| 345 | D4 | — | 56 | 4 | no | — |
| 346 | C2×C4 | — | 2 | 1 | no | — |
| 347 | C2×C4 | — | 2 | 1 | no | — |
| 348 | C2×C4 | — | 4 | 1 | no | — |
| 349 | C2×C4 | — | 14 | 2 | no | — |
| 350 | C2×C4 | — | 28 | 2 | no | — |
| 351 | C2×C4 | — | 28 | 2 | no | — |
| 352 | C2×C4 | — | 28 | 2 | no | — |
| 353 | C2×C4 | — | 56 | 4 | no | — |
| 354 | C2×C4 | #6458 | 1 | 1 | yes | characteristic |
| 355 | C2×C4 | #6458 | 1 | 1 | yes | characteristic |
| 356 | C2×C4 | #6458 | 1 | 1 | yes | characteristic |
| 357 | C2×C4 | C2×D56 | 1 | 2 | yes | — |
| 358 | C2×C4 | #6471 | 1 | 2 | yes | — |
| 359 | C2×C4 | C22×D28 | 1 | 1 | yes | characteristic |
| 360 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 361 | C2×C4 | C2×#1161 | 1 | 1 | yes | characteristic |
| 362 | C8 | — | 2 | 1 | no | — |
| 363 | C8 | — | 2 | 1 | no | — |
| 364 | C8 | — | 4 | 4 | no | — |
| 365 | C8 | — | 28 | 2 | no | — |
| 366 | C8 | C2×D56 | 1 | 2 | yes | — |
| 367 | C8 | C2×D56 | 1 | 2 | yes | — |
| 368 | C7 | #19190 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 369 | C22 | — | 2 | 1 | no | — |
| 370 | C22 | — | 2 | 1 | no | — |
| 371 | C22 | — | 28 | 2 | no | — |
| 372 | C22 | — | 28 | 2 | no | — |
| 373 | C22 | — | 28 | 2 | no | — |
| 374 | C22 | — | 56 | 2 | no | — |
| 375 | C22 | — | 56 | 2 | no | — |
| 376 | C22 | — | 56 | 2 | no | — |
| 377 | C22 | #89615 | 1 | 2 | yes | — |
| 378 | C22 | C2×#6458 | 1 | 1 | yes | characteristic |
| 379 | C4 | — | 2 | 1 | no | — |
| 380 | C4 | — | 2 | 1 | no | — |
| 381 | C4 | — | 2 | 1 | no | — |
| 382 | C4 | — | 28 | 2 | no | — |
| 383 | C4 | — | 56 | 2 | no | — |
| 384 | C4 | #89615 | 1 | 2 | yes | — |
| 385 | C4 | C22×D56 | 1 | 1 | yes | characteristic |
| 386 | C4 | C2×#6471 | 1 | 1 | yes | characteristic |
| 387 | C4 | #90448 | 1 | 1 | yes | characteristic |
| 388 | C4 | #90457 | 1 | 1 | yes | characteristic |
| 389 | C2 | — | 2 | 2 | no | — |
| 390 | C2 | — | 56 | 2 | no | — |
| 391 | C2 | — | 112 | 2 | no | — |
| 392 | C2 | C2×#89615 | 1 | 1 | yes | characteristic |
| 393 | C2 | #11736595 | 1 | 1 | yes | characteristic |
| 394 | C2 | #11736701 | 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