← #14223307
Subgroups — #14223307
Order 1792.
3194 conjugacy classes of subgroups.
The subgroup lattice has 420 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#90439 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C22×#6467 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #11742803 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C2×C7×#405 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11736021 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #11736010 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11736009 | C2 | 1 | 8 | yes | maximal, complemented |
| 8 | #11735944 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #11735912 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | C22×#1157 | C22 | 1 | 4 | yes | — |
| 11 | C22×C7×M16 | C22 | 1 | 1 | yes | characteristic |
| 12 | C23×C7×C8 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C7×#117 | C22 | 1 | 1 | yes | characteristic |
| 14 | #90439 | — | 2 | 16 | no | — |
| 15 | C2×#6472 | C22 | 1 | 8 | yes | complemented |
| 16 | C2×#6471 | C22 | 1 | 8 | yes | complemented |
| 17 | C22×Dic28 | C22 | 1 | 2 | yes | complemented |
| 18 | C2×#6467 | — | 2 | 16 | no | — |
| 19 | C2×#6467 | C22 | 1 | 4 | yes | — |
| 20 | C2×#6467 | C22 | 1 | 4 | yes | — |
| 21 | C2×#6467 | C22 | 1 | 4 | yes | complemented |
| 22 | C2×#6467 | C22 | 1 | 8 | yes | complemented |
| 23 | C2×#6467 | C22 | 1 | 4 | yes | complemented |
| 24 | C22×D56 | C22 | 1 | 2 | yes | complemented |
| 25 | C22×#1132 | C22 | 1 | 4 | yes | complemented |
| 26 | #90217 | C22 | 1 | 8 | yes | complemented |
| 27 | #90216 | C22 | 1 | 8 | yes | complemented |
| 28 | #90215 | — | 2 | 8 | no | — |
| 29 | #90201 | — | 2 | 4 | no | — |
| 30 | #90184 | — | 2 | 4 | no | — |
| 31 | #90168 | C22 | 1 | 8 | yes | complemented |
| 32 | C7×#405 | C22 | 1 | 4 | yes | complemented |
| 33 | C7×#405 | C22 | 1 | 4 | yes | complemented |
| 34 | C2×C7×#97 | C22 | 1 | 2 | yes | complemented |
| 35 | C2×C4×C7×C8 | C22 | 1 | 2 | yes | complemented |
| 36 | #89487 | C22 | 1 | 16 | yes | complemented |
| 37 | #89484 | C22 | 1 | 16 | yes | complemented |
| 38 | #89471 | C22 | 1 | 4 | yes | complemented |
| 39 | #89468 | C22 | 1 | 8 | yes | complemented |
| 40 | #89468 | C22 | 1 | 8 | yes | complemented |
| 41 | #89467 | C22 | 1 | 4 | yes | complemented |
| 42 | #89465 | C22 | 1 | 8 | yes | complemented |
| 43 | #60643 | — | 7 | 1 | no | maximal, Sylow |
| 44 | C23×C4×C7 | C23 | 1 | 1 | yes | characteristic |
| 45 | C22×C22⋊D7 | — | 2 | 4 | no | — |
| 46 | C2×#1157 | — | 2 | 4 | no | — |
| 47 | C2×#1157 | — | 2 | 4 | no | — |
| 48 | C2×#1157 | — | 2 | 16 | no | — |
| 49 | C2×#1157 | — | 2 | 16 | no | — |
| 50 | C2×#1157 | C23 | 1 | 8 | yes | — |
| 51 | C2×#1157 | C23 | 1 | 8 | yes | — |
| 52 | C22×D28 | C23 | 1 | 4 | yes | — |
| 53 | C22×C4×D7 | — | 2 | 4 | no | — |
| 54 | C22×Dic14 | C23 | 1 | 4 | yes | — |
| 55 | C2×C7×M16 | D4 | 1 | 8 | yes | complemented |
| 56 | C2×C7×M16 | C23 | 1 | 4 | yes | — |
| 57 | C22×C7×C8 | D4 | 1 | 8 | yes | complemented |
| 58 | C22×C7×C8 | C23 | 1 | 2 | yes | — |
| 59 | C22×C7×C8 | C23 | 1 | 2 | yes | — |
| 60 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 61 | C22×C7×C8 | C23 | 1 | 2 | yes | — |
| 62 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 63 | C7×#117 | D4 | 1 | 4 | yes | — |
| 64 | C7×#117 | C23 | 1 | 4 | yes | — |
| 65 | C2×C7×C4⋊C4 | D4 | 1 | 2 | yes | — |
| 66 | C2×C7×C22⋊C4 | D4 | 1 | 2 | yes | — |
| 67 | C2×C42×C7 | C23 | 1 | 2 | yes | — |
| 68 | #6493 | — | 2 | 16 | no | — |
| 69 | #6472 | — | 2 | 32 | no | — |
| 70 | #6471 | — | 2 | 32 | no | — |
| 71 | C2×Dic28 | — | 2 | 8 | no | — |
| 72 | C2×Dic28 | C23 | 1 | 4 | yes | — |
| 73 | C2×Dic28 | C23 | 1 | 4 | yes | — |
| 74 | C2×Dic28 | C23 | 1 | 8 | yes | — |
| 75 | #6467 | — | 2 | 16 | no | — |
| 76 | #6467 | — | 2 | 16 | no | — |
| 77 | #6467 | — | 2 | 16 | no | — |
| 78 | #6467 | — | 2 | 16 | no | — |
| 79 | #6467 | — | 2 | 32 | no | — |
| 80 | C2×D56 | — | 2 | 8 | no | — |
| 81 | C2×D56 | C23 | 1 | 4 | yes | — |
| 82 | C2×D56 | C23 | 1 | 4 | yes | — |
| 83 | C2×D56 | C23 | 1 | 8 | yes | — |
| 84 | C2×#1132 | — | 2 | 16 | no | — |
| 85 | C2×#1132 | C23 | 1 | 8 | yes | — |
| 86 | C2×#1132 | C23 | 1 | 8 | yes | — |
| 87 | C2×#1132 | C23 | 1 | 16 | yes | — |
| 88 | #6460 | — | 2 | 16 | no | — |
| 89 | #6458 | — | 2 | 16 | no | — |
| 90 | #6449 | — | 2 | 16 | no | — |
| 91 | #6445 | — | 2 | 16 | no | — |
| 92 | #6438 | C23 | 1 | 16 | yes | — |
| 93 | #6437 | C23 | 1 | 8 | yes | — |
| 94 | C4×D28 | — | 2 | 16 | no | — |
| 95 | #6432 | C23 | 1 | 8 | yes | — |
| 96 | C7×#97 | C23 | 1 | 8 | yes | — |
| 97 | C4×C7×C8 | C23 | 1 | 4 | yes | — |
| 98 | C4×C7×C8 | C23 | 1 | 4 | yes | — |
| 99 | C2×#575 | — | 7 | 2 | no | — |
| 100 | C22×#135 | — | 7 | 2 | no | — |
| 101 | #3449 | — | 7 | 2 | no | — |
| 102 | #3156 | — | 7 | 4 | no | — |
| 103 | #3155 | — | 7 | 4 | no | — |
| 104 | #3154 | — | 7 | 8 | no | — |
| 105 | #3150 | — | 7 | 4 | no | — |
| 106 | #3147 | — | 7 | 4 | no | — |
| 107 | C2×#405 | D7 | 1 | 1 | yes | characteristic, complemented |
| 108 | C24×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C23×D7 | — | 2 | 4 | no | — |
| 110 | C22×C4×C7 | C2×D4 | 1 | 4 | yes | — |
| 111 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 112 | C22×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 113 | C22×C4×C7 | C2×D4 | 1 | 4 | yes | — |
| 114 | C22×C4×C7 | C2×D4 | 1 | 4 | yes | — |
| 115 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 116 | C22×C4×C7 | C24 | 1 | 2 | yes | — |
| 117 | C2×C22⋊D7 | — | 2 | 8 | no | — |
| 118 | C2×C22⋊D7 | — | 2 | 8 | no | — |
| 119 | C2×C22⋊D7 | — | 4 | 16 | no | — |
| 120 | C22×Dic7 | — | 2 | 4 | no | — |
| 121 | #1157 | — | 2 | 16 | no | — |
| 122 | #1157 | — | 2 | 16 | no | — |
| 123 | #1157 | — | 2 | 16 | no | — |
| 124 | #1157 | — | 2 | 16 | no | — |
| 125 | #1157 | — | 4 | 16 | no | — |
| 126 | #1157 | — | 4 | 16 | no | — |
| 127 | C2×D28 | — | 2 | 8 | no | — |
| 128 | C2×D28 | — | 2 | 8 | no | — |
| 129 | C2×D28 | — | 2 | 4 | no | — |
| 130 | C2×D28 | — | 2 | 16 | no | — |
| 131 | C2×D28 | C24 | 1 | 8 | yes | — |
| 132 | C2×C4×D7 | — | 2 | 8 | no | — |
| 133 | C2×C4×D7 | — | 2 | 8 | no | — |
| 134 | C2×C4×D7 | — | 4 | 16 | no | — |
| 135 | C2×Dic14 | — | 2 | 8 | no | — |
| 136 | C2×Dic14 | — | 2 | 8 | no | — |
| 137 | C2×Dic14 | — | 2 | 4 | no | — |
| 138 | C2×Dic14 | C24 | 1 | 8 | yes | — |
| 139 | C7×M16 | C2×D4 | 1 | 16 | yes | — |
| 140 | C2×C7×C8 | C2×D4 | 1 | 8 | yes | — |
| 141 | C2×C7×C8 | C2×D4 | 1 | 8 | yes | — |
| 142 | C2×C7×C8 | C2×D4 | 1 | 4 | yes | — |
| 143 | C2×C7×C8 | C2×D4 | 1 | 4 | yes | — |
| 144 | C2×C7×C8 | C2×D4 | 1 | 8 | yes | — |
| 145 | C2×C7×C8 | C24 | 1 | 1 | yes | characteristic |
| 146 | C2×C7×C8 | C24 | 1 | 1 | yes | characteristic |
| 147 | C2×C7×C8 | C24 | 1 | 4 | yes | — |
| 148 | C2×C7×C8 | C24 | 1 | 2 | yes | — |
| 149 | C7×C4⋊C4 | C2×D4 | 1 | 8 | yes | — |
| 150 | C7×C22⋊C4 | C2×D4 | 1 | 8 | yes | — |
| 151 | C42×C7 | C2×D4 | 1 | 4 | yes | — |
| 152 | C42×C7 | C24 | 1 | 4 | yes | — |
| 153 | (C2×D7)⋊C4 | — | 2 | 32 | no | — |
| 154 | C4⋊Dic7 | — | 2 | 16 | no | — |
| 155 | Dic28 | — | 2 | 8 | no | — |
| 156 | Dic28 | — | 2 | 8 | no | — |
| 157 | Dic28 | — | 2 | 16 | no | — |
| 158 | D56 | — | 2 | 8 | no | — |
| 159 | D56 | — | 2 | 8 | no | — |
| 160 | D56 | — | 2 | 16 | no | — |
| 161 | #1132 | — | 2 | 16 | no | — |
| 162 | #1132 | — | 2 | 16 | no | — |
| 163 | #1132 | — | 2 | 32 | no | — |
| 164 | C22×#41 | — | 7 | 4 | no | — |
| 165 | #575 | — | 14 | 16 | no | — |
| 166 | C2×#137 | — | 7 | 8 | no | — |
| 167 | C2×AGL(1,ℤ/8) | — | 7 | 8 | no | — |
| 168 | C2×#135 | — | 7 | 4 | no | — |
| 169 | C2×#135 | — | 7 | 4 | no | — |
| 170 | C2×#135 | — | 7 | 4 | no | — |
| 171 | C2×#135 | — | 7 | 8 | no | — |
| 172 | C2×#135 | — | 7 | 4 | no | — |
| 173 | C2×#135 | — | 14 | 16 | no | — |
| 174 | C22×Q16 | — | 7 | 2 | no | — |
| 175 | C22×SD16 | — | 7 | 4 | no | — |
| 176 | C22×D8 | — | 7 | 2 | no | — |
| 177 | C22×M16 | C2×D7 | 1 | 1 | yes | characteristic |
| 178 | C23×C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 179 | #537 | — | 14 | 4 | no | — |
| 180 | #536 | — | 7 | 8 | no | — |
| 181 | #535 | — | 7 | 8 | no | — |
| 182 | #534 | — | 14 | 4 | no | — |
| 183 | #532 | — | 7 | 8 | no | — |
| 184 | #525 | — | 14 | 8 | no | — |
| 185 | C2×#117 | C2×D7 | 1 | 1 | yes | characteristic |
| 186 | #497 | — | 7 | 16 | no | — |
| 187 | #496 | — | 7 | 16 | no | — |
| 188 | #495 | — | 7 | 8 | no | — |
| 189 | #495 | — | 7 | 8 | no | — |
| 190 | #494 | — | 7 | 4 | no | — |
| 191 | #493 | — | 7 | 4 | no | — |
| 192 | #492 | — | 7 | 8 | no | — |
| 193 | #405 | C2×D7 | 1 | 4 | yes | complemented |
| 194 | #405 | C2×D7 | 1 | 4 | yes | complemented |
| 195 | C2×#97 | C2×D7 | 1 | 2 | yes | complemented |
| 196 | C2×C4×C8 | C2×D7 | 1 | 2 | yes | complemented |
| 197 | C23×C7 | — | 4 | 2 | no | — |
| 198 | C23×C7 | #127 | 1 | 4 | yes | — |
| 199 | C23×C7 | C22×D4 | 1 | 2 | yes | — |
| 200 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 201 | C22×D7 | — | 2 | 8 | no | — |
| 202 | C22×D7 | — | 4 | 8 | no | — |
| 203 | C22×D7 | — | 8 | 8 | no | — |
| 204 | C2×C4×C7 | — | 4 | 4 | no | — |
| 205 | C2×C4×C7 | #127 | 1 | 8 | yes | — |
| 206 | C2×C4×C7 | #127 | 1 | 4 | yes | — |
| 207 | C2×C4×C7 | C22×D4 | 1 | 8 | yes | — |
| 208 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 209 | C2×C4×C7 | C22×D4 | 1 | 4 | yes | — |
| 210 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 211 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 212 | C2×C4×C7 | C22×D4 | 1 | 4 | yes | — |
| 213 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 214 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 215 | C22⋊D7 | — | 4 | 16 | no | — |
| 216 | C22⋊D7 | — | 4 | 16 | no | — |
| 217 | C2×Dic7 | — | 2 | 8 | no | — |
| 218 | C2×Dic7 | — | 4 | 8 | no | — |
| 219 | D28 | — | 2 | 8 | no | — |
| 220 | D28 | — | 2 | 8 | no | — |
| 221 | D28 | — | 4 | 8 | no | — |
| 222 | D28 | — | 8 | 16 | no | — |
| 223 | C4×D7 | — | 4 | 16 | no | — |
| 224 | C4×D7 | — | 4 | 16 | no | — |
| 225 | Dic14 | — | 2 | 8 | no | — |
| 226 | Dic14 | — | 2 | 8 | no | — |
| 227 | Dic14 | — | 4 | 8 | no | — |
| 228 | C7×C8 | C22×D4 | 1 | 2 | yes | — |
| 229 | C7×C8 | C22×D4 | 1 | 4 | yes | — |
| 230 | C7×C8 | C22×D4 | 1 | 8 | yes | — |
| 231 | C7×C8 | C22×D4 | 1 | 2 | yes | — |
| 232 | C2×#41 | — | 7 | 8 | no | — |
| 233 | C2×#41 | — | 7 | 8 | no | — |
| 234 | C2×#41 | — | 14 | 4 | no | — |
| 235 | C2×#41 | — | 14 | 4 | no | — |
| 236 | C2×#41 | — | 14 | 16 | no | — |
| 237 | C2×#41 | — | 14 | 16 | no | — |
| 238 | C22×Q8 | — | 7 | 4 | no | — |
| 239 | C22×D4 | — | 7 | 4 | no | — |
| 240 | C22×D4 | — | 14 | 4 | no | — |
| 241 | C23×C4 | — | 14 | 4 | no | — |
| 242 | C23×C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 243 | #137 | — | 14 | 32 | no | — |
| 244 | AGL(1,ℤ/8) | — | 14 | 32 | no | — |
| 245 | #135 | — | 14 | 16 | no | — |
| 246 | #135 | — | 14 | 16 | no | — |
| 247 | #135 | — | 14 | 16 | no | — |
| 248 | #135 | — | 14 | 16 | no | — |
| 249 | #135 | — | 14 | 32 | no | — |
| 250 | C2×Q16 | — | 7 | 4 | no | — |
| 251 | C2×Q16 | — | 7 | 4 | no | — |
| 252 | C2×Q16 | — | 7 | 8 | no | — |
| 253 | C2×Q16 | — | 14 | 8 | no | — |
| 254 | C2×SD16 | — | 7 | 8 | no | — |
| 255 | C2×SD16 | — | 7 | 8 | no | — |
| 256 | C2×SD16 | — | 7 | 16 | no | — |
| 257 | C2×SD16 | — | 14 | 16 | no | — |
| 258 | C2×D8 | — | 7 | 4 | no | — |
| 259 | C2×D8 | — | 7 | 4 | no | — |
| 260 | C2×D8 | — | 7 | 8 | no | — |
| 261 | C2×D8 | — | 14 | 8 | no | — |
| 262 | C2×M16 | D28 | 1 | 8 | yes | complemented |
| 263 | C2×M16 | C22×D7 | 1 | 4 | yes | — |
| 264 | C22×C8 | D28 | 1 | 8 | yes | complemented |
| 265 | C22×C8 | C22×D7 | 1 | 2 | yes | — |
| 266 | C22×C8 | C22×D7 | 1 | 2 | yes | — |
| 267 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 268 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 269 | C22×C8 | C22×D7 | 1 | 2 | yes | — |
| 270 | C4⋊Q8 | — | 7 | 8 | no | — |
| 271 | #127 | — | 7 | 8 | no | — |
| 272 | #124 | — | 7 | 16 | no | — |
| 273 | #123 | — | 14 | 16 | no | — |
| 274 | C22⋊Q8 | — | 14 | 16 | no | — |
| 275 | #121 | — | 14 | 16 | no | — |
| 276 | #121 | — | 14 | 16 | no | — |
| 277 | #120 | — | 14 | 16 | no | — |
| 278 | C4×D4 | — | 14 | 16 | no | — |
| 279 | #117 | D28 | 1 | 4 | yes | — |
| 280 | #117 | C22×D7 | 1 | 4 | yes | — |
| 281 | C2×C4⋊C4 | D28 | 1 | 2 | yes | — |
| 282 | C2×C22⋊C4 | D28 | 1 | 2 | yes | — |
| 283 | C2×C42 | C22×D7 | 1 | 2 | yes | — |
| 284 | #97 | C22×D7 | 1 | 8 | yes | — |
| 285 | C4×C8 | C22×D7 | 1 | 4 | yes | — |
| 286 | C4×C8 | C22×D7 | 1 | 4 | yes | — |
| 287 | C22×C7 | — | 2 | 2 | no | — |
| 288 | C22×C7 | — | 2 | 4 | no | — |
| 289 | C22×C7 | — | 4 | 4 | no | — |
| 290 | C22×C7 | C2×#127 | 1 | 4 | yes | — |
| 291 | C22×C7 | C2×#127 | 1 | 2 | yes | — |
| 292 | C22×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 293 | C2×D7 | — | 4 | 16 | no | — |
| 294 | C2×D7 | — | 4 | 8 | no | — |
| 295 | C2×D7 | — | 8 | 16 | no | — |
| 296 | C4×C7 | — | 2 | 8 | no | — |
| 297 | C4×C7 | C2×#127 | 1 | 4 | yes | — |
| 298 | C4×C7 | C2×#127 | 1 | 2 | yes | — |
| 299 | C4×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 300 | C4×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 301 | Dic7 | — | 4 | 8 | no | — |
| 302 | C24 | — | 14 | 4 | no | — |
| 303 | C24 | C2×D28 | 1 | 1 | yes | characteristic |
| 304 | #41 | — | 14 | 16 | no | — |
| 305 | #41 | — | 14 | 16 | no | — |
| 306 | #41 | — | 14 | 16 | no | — |
| 307 | #41 | — | 14 | 16 | no | — |
| 308 | #41 | — | 28 | 16 | no | — |
| 309 | #41 | — | 28 | 16 | no | — |
| 310 | C2×Q8 | — | 7 | 8 | no | — |
| 311 | C2×Q8 | — | 14 | 4 | no | — |
| 312 | C2×Q8 | — | 14 | 8 | no | — |
| 313 | C2×Q8 | — | 14 | 8 | no | — |
| 314 | C2×D4 | — | 7 | 8 | no | — |
| 315 | C2×D4 | — | 14 | 8 | no | — |
| 316 | C2×D4 | — | 14 | 8 | no | — |
| 317 | C2×D4 | — | 14 | 8 | no | — |
| 318 | C2×D4 | — | 14 | 8 | no | — |
| 319 | C2×D4 | — | 14 | 4 | no | — |
| 320 | C2×D4 | — | 14 | 16 | no | — |
| 321 | C2×D4 | — | 28 | 16 | no | — |
| 322 | C22×C4 | — | 14 | 4 | no | — |
| 323 | C22×C4 | — | 14 | 8 | no | — |
| 324 | C22×C4 | — | 14 | 8 | no | — |
| 325 | C22×C4 | — | 28 | 16 | no | — |
| 326 | C22×C4 | C2×D28 | 1 | 4 | yes | — |
| 327 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 328 | C22×C4 | C2×D28 | 1 | 2 | yes | — |
| 329 | C22×C4 | C2×D28 | 1 | 4 | yes | — |
| 330 | C22×C4 | C2×D28 | 1 | 4 | yes | — |
| 331 | C22×C4 | C23×D7 | 1 | 2 | yes | — |
| 332 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 333 | Q16 | — | 14 | 8 | no | — |
| 334 | Q16 | — | 14 | 8 | no | — |
| 335 | Q16 | — | 14 | 16 | no | — |
| 336 | SD16 | — | 14 | 16 | no | — |
| 337 | SD16 | — | 14 | 16 | no | — |
| 338 | SD16 | — | 14 | 32 | no | — |
| 339 | D8 | — | 14 | 8 | no | — |
| 340 | D8 | — | 14 | 8 | no | — |
| 341 | D8 | — | 14 | 16 | no | — |
| 342 | M16 | C2×D28 | 1 | 16 | yes | — |
| 343 | C2×C8 | C2×D28 | 1 | 8 | yes | — |
| 344 | C2×C8 | C2×D28 | 1 | 8 | yes | — |
| 345 | C2×C8 | C2×D28 | 1 | 4 | yes | — |
| 346 | C2×C8 | C2×D28 | 1 | 4 | yes | — |
| 347 | C2×C8 | C2×D28 | 1 | 8 | yes | — |
| 348 | C2×C8 | C23×D7 | 1 | 1 | yes | characteristic |
| 349 | C2×C8 | C23×D7 | 1 | 1 | yes | characteristic |
| 350 | C2×C8 | C23×D7 | 1 | 4 | yes | — |
| 351 | C2×C8 | C23×D7 | 1 | 2 | yes | — |
| 352 | C4⋊C4 | — | 14 | 16 | no | — |
| 353 | C4⋊C4 | C2×D28 | 1 | 8 | yes | — |
| 354 | C22⋊C4 | — | 14 | 32 | no | — |
| 355 | C22⋊C4 | C2×D28 | 1 | 8 | yes | — |
| 356 | C42 | C2×D28 | 1 | 4 | yes | — |
| 357 | C42 | C23×D7 | 1 | 4 | yes | — |
| 358 | C2×C7 | — | 2 | 4 | no | — |
| 359 | C2×C7 | — | 2 | 2 | no | — |
| 360 | C2×C7 | C22×#127 | 1 | 1 | yes | characteristic |
| 361 | C2×C7 | #3584 | 1 | 2 | yes | — |
| 362 | D7 | — | 8 | 8 | no | — |
| 363 | C23 | — | 4 | 2 | no | — |
| 364 | C23 | — | 14 | 8 | no | — |
| 365 | C23 | — | 28 | 8 | no | — |
| 366 | C23 | — | 56 | 8 | no | — |
| 367 | C23 | #6437 | 1 | 4 | yes | — |
| 368 | C23 | C22×D28 | 1 | 2 | yes | — |
| 369 | C23 | C22×D28 | 1 | 1 | yes | characteristic |
| 370 | Q8 | — | 14 | 8 | no | — |
| 371 | Q8 | — | 14 | 8 | no | — |
| 372 | Q8 | — | 28 | 8 | no | — |
| 373 | D4 | — | 14 | 8 | no | — |
| 374 | D4 | — | 14 | 8 | no | — |
| 375 | D4 | — | 28 | 16 | no | — |
| 376 | D4 | — | 28 | 16 | no | — |
| 377 | D4 | — | 28 | 8 | no | — |
| 378 | D4 | — | 56 | 16 | no | — |
| 379 | C2×C4 | — | 4 | 4 | no | — |
| 380 | C2×C4 | — | 14 | 8 | no | — |
| 381 | C2×C4 | — | 28 | 8 | no | — |
| 382 | C2×C4 | — | 28 | 16 | no | — |
| 383 | C2×C4 | — | 28 | 16 | no | — |
| 384 | C2×C4 | #6437 | 1 | 8 | yes | — |
| 385 | C2×C4 | #6437 | 1 | 4 | yes | — |
| 386 | C2×C4 | C22×D28 | 1 | 8 | yes | — |
| 387 | C2×C4 | C22×D28 | 1 | 2 | yes | — |
| 388 | C2×C4 | C22×D28 | 1 | 4 | yes | — |
| 389 | C2×C4 | C22×D28 | 1 | 2 | yes | — |
| 390 | C2×C4 | C22×D28 | 1 | 2 | yes | — |
| 391 | C2×C4 | C22×D28 | 1 | 4 | yes | — |
| 392 | C2×C4 | C22×D28 | 1 | 1 | yes | characteristic |
| 393 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 394 | C8 | C22×D28 | 1 | 2 | yes | — |
| 395 | C8 | C22×D28 | 1 | 4 | yes | — |
| 396 | C8 | C22×D28 | 1 | 2 | yes | — |
| 397 | C8 | C22×D28 | 1 | 8 | yes | — |
| 398 | C7 | #60643 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 399 | C22 | — | 2 | 2 | no | — |
| 400 | C22 | — | 2 | 4 | no | — |
| 401 | C22 | — | 4 | 4 | no | — |
| 402 | C22 | — | 28 | 8 | no | — |
| 403 | C22 | — | 28 | 16 | no | — |
| 404 | C22 | — | 56 | 16 | no | — |
| 405 | C22 | C2×#6437 | 1 | 4 | yes | — |
| 406 | C22 | C2×#6437 | 1 | 2 | yes | — |
| 407 | C22 | C23×D28 | 1 | 1 | yes | characteristic |
| 408 | C4 | — | 2 | 8 | no | — |
| 409 | C4 | — | 28 | 8 | no | — |
| 410 | C4 | C2×#6437 | 1 | 2 | yes | — |
| 411 | C4 | C2×#6437 | 1 | 4 | yes | — |
| 412 | C4 | C23×D28 | 1 | 1 | yes | characteristic |
| 413 | C4 | C23×D28 | 1 | 1 | yes | characteristic |
| 414 | C2 | — | 2 | 4 | no | — |
| 415 | C2 | — | 2 | 2 | no | — |
| 416 | C2 | — | 56 | 8 | no | — |
| 417 | C2 | C22×#6437 | 1 | 1 | yes | characteristic |
| 418 | C2 | #11744231 | 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