Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1314 conjugacy classes of subgroups.
The subgroup lattice has 582 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11743263 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#89848 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11736714 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11736505 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C7×#1545 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11728508 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11728252 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11726159 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #11726145 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | C2×#6548 | — | 2 | 1 | no | — |
| 11 | C2×C7×#127 | C22 | 1 | 1 | yes | characteristic |
| 12 | #90496 | — | 2 | 1 | no | — |
| 13 | D4×C22⋊D7 | — | 2 | 2 | no | — |
| 14 | D4×C22⋊D7 | — | 2 | 2 | no | — |
| 15 | C22×#1142 | — | 2 | 2 | no | — |
| 16 | #90409 | — | 2 | 1 | no | — |
| 17 | #90409 | C22 | 1 | 2 | yes | — |
| 18 | #90408 | — | 2 | 1 | no | — |
| 19 | #90408 | C22 | 1 | 2 | yes | — |
| 20 | #90407 | — | 2 | 1 | no | — |
| 21 | #90406 | — | 2 | 2 | no | — |
| 22 | D7×#127 | — | 2 | 1 | no | — |
| 23 | #90168 | C22 | 1 | 1 | yes | characteristic |
| 24 | C4×#1157 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#6432 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C7×#431 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C7×#423 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #89905 | — | 2 | 1 | no | — |
| 29 | #89893 | — | 2 | 1 | no | — |
| 30 | #89848 | — | 2 | 2 | no | — |
| 31 | #89848 | C22 | 1 | 4 | yes | complemented |
| 32 | C2×C4×C7⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #89623 | — | 2 | 1 | no | — |
| 34 | #89622 | C22 | 1 | 2 | yes | complemented |
| 35 | #89618 | — | 2 | 1 | no | — |
| 36 | #89614 | C22 | 1 | 2 | yes | complemented |
| 37 | #89614 | C22 | 1 | 4 | yes | complemented |
| 38 | #89507 | — | 2 | 2 | no | — |
| 39 | #89466 | — | 2 | 1 | no | — |
| 40 | #89452 | — | 2 | 1 | no | — |
| 41 | C7×#331 | C22 | 1 | 4 | yes | complemented |
| 42 | #89279 | C22 | 1 | 2 | yes | complemented |
| 43 | #89278 | C22 | 1 | 2 | yes | complemented |
| 44 | #89278 | C22 | 1 | 4 | yes | complemented |
| 45 | #18621 | — | 7 | 1 | no | maximal, Sylow |
| 46 | C22×C7×D4 | — | 2 | 1 | no | — |
| 47 | C22×C7×D4 | — | 2 | 1 | no | — |
| 48 | C22×C7×D4 | D4 | 1 | 2 | yes | — |
| 49 | C22×C22⋊D7 | — | 2 | 4 | no | — |
| 50 | #6548 | — | 4 | 4 | no | — |
| 51 | #6548 | — | 4 | 4 | no | — |
| 52 | C2×#1159 | — | 2 | 2 | no | — |
| 53 | C2×#1159 | — | 2 | 2 | no | — |
| 54 | C2×D4×D7 | — | 2 | 2 | no | — |
| 55 | C2×D4×D7 | — | 2 | 2 | no | — |
| 56 | C2×D4×D7 | — | 2 | 2 | no | — |
| 57 | C2×D4×D7 | — | 2 | 2 | no | — |
| 58 | C2×#1157 | — | 2 | 1 | no | — |
| 59 | C2×#1157 | D4 | 1 | 1 | yes | characteristic |
| 60 | C22×Dic14 | — | 2 | 1 | no | — |
| 61 | C2×C7×M16 | — | 2 | 1 | no | — |
| 62 | C7×#127 | — | 2 | 1 | no | — |
| 63 | C7×#127 | — | 2 | 1 | no | — |
| 64 | C7×#127 | D4 | 1 | 2 | yes | — |
| 65 | C7×#127 | C23 | 1 | 2 | yes | — |
| 66 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 67 | #6516 | — | 2 | 4 | no | — |
| 68 | #6503 | — | 2 | 2 | no | — |
| 69 | #6503 | — | 2 | 2 | no | — |
| 70 | #6503 | — | 2 | 2 | no | — |
| 71 | #6502 | — | 2 | 4 | no | — |
| 72 | #6502 | — | 2 | 4 | no | — |
| 73 | #6501 | — | 2 | 2 | no | — |
| 74 | #6501 | — | 2 | 2 | no | — |
| 75 | #6501 | — | 2 | 2 | no | — |
| 76 | #6501 | — | 2 | 2 | no | — |
| 77 | #6500 | — | 2 | 4 | no | — |
| 78 | #6500 | — | 2 | 4 | no | — |
| 79 | #6499 | — | 2 | 2 | no | — |
| 80 | D4×Dic7 | — | 2 | 2 | no | — |
| 81 | D4×Dic7 | — | 2 | 2 | no | — |
| 82 | C2×#1142 | — | 2 | 8 | no | — |
| 83 | C2×#1142 | — | 4 | 8 | no | — |
| 84 | #6493 | — | 2 | 1 | no | — |
| 85 | #6493 | D4 | 1 | 2 | yes | — |
| 86 | C4×C22⋊D7 | — | 2 | 1 | no | — |
| 87 | C4×C22⋊D7 | — | 2 | 1 | no | — |
| 88 | #6489 | D4 | 1 | 1 | yes | characteristic |
| 89 | C2×C4⋊Dic7 | — | 2 | 1 | no | — |
| 90 | C2×C4⋊Dic7 | — | 2 | 1 | no | — |
| 91 | C22×C7⋊C8 | — | 2 | 1 | no | — |
| 92 | #6438 | — | 2 | 1 | no | — |
| 93 | #6437 | D4 | 1 | 1 | yes | characteristic |
| 94 | C4×D28 | — | 2 | 1 | no | — |
| 95 | C4×D28 | D4 | 1 | 1 | yes | characteristic |
| 96 | C4×D28 | C23 | 1 | 1 | yes | characteristic |
| 97 | C4×D28 | C23 | 1 | 2 | yes | — |
| 98 | #6435 | — | 2 | 1 | no | — |
| 99 | C42×D7 | — | 2 | 1 | no | — |
| 100 | #6432 | — | 2 | 1 | no | — |
| 101 | #6432 | — | 2 | 1 | no | — |
| 102 | #6432 | — | 2 | 1 | no | — |
| 103 | #6432 | D4 | 1 | 1 | yes | characteristic |
| 104 | #6432 | C23 | 1 | 2 | yes | — |
| 105 | C4×Dic14 | D4 | 1 | 1 | yes | characteristic |
| 106 | C4×Dic14 | C23 | 1 | 1 | yes | characteristic |
| 107 | C7×C4⋊C8 | — | 2 | 1 | no | — |
| 108 | C7×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 109 | C7×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 110 | C7×C22⋊C8 | — | 2 | 1 | no | — |
| 111 | C4×C7×C8 | — | 2 | 1 | no | — |
| 112 | #6395 | — | 2 | 2 | no | — |
| 113 | #6395 | — | 2 | 4 | no | — |
| 114 | #6392 | — | 2 | 2 | no | — |
| 115 | #6391 | — | 2 | 2 | no | — |
| 116 | #6391 | — | 2 | 4 | no | — |
| 117 | #6390 | — | 2 | 2 | no | — |
| 118 | C4×C7⋊C8 | — | 2 | 1 | no | — |
| 119 | C4×C7⋊C8 | C23 | 1 | 2 | yes | — |
| 120 | #3498 | — | 7 | 1 | no | — |
| 121 | #3227 | — | 7 | 1 | no | — |
| 122 | C2×#492 | — | 7 | 1 | no | — |
| 123 | #3079 | — | 7 | 1 | no | — |
| 124 | #1631 | — | 7 | 4 | no | — |
| 125 | #1629 | — | 7 | 4 | no | — |
| 126 | #1545 | D7 | 1 | 1 | yes | characteristic, complemented |
| 127 | #1492 | — | 7 | 1 | no | — |
| 128 | #1476 | — | 7 | 1 | no | — |
| 129 | C24×C7 | — | 2 | 2 | no | — |
| 130 | C23×D7 | — | 2 | 4 | no | — |
| 131 | C2×C7×D4 | — | 2 | 2 | no | — |
| 132 | C2×C7×D4 | — | 2 | 2 | no | — |
| 133 | C2×C7×D4 | — | 2 | 2 | no | — |
| 134 | C2×C7×D4 | — | 2 | 2 | no | — |
| 135 | C2×C7×D4 | — | 2 | 2 | no | — |
| 136 | C2×C7×D4 | — | 4 | 4 | no | — |
| 137 | C2×C7×D4 | — | 4 | 2 | no | — |
| 138 | C2×C7×D4 | — | 4 | 2 | no | — |
| 139 | C2×C7×D4 | — | 8 | 2 | no | — |
| 140 | C2×C7×D4 | C2×D4 | 1 | 4 | yes | — |
| 141 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 145 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 146 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 147 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 148 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 149 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 150 | C2×C22⋊D7 | — | 4 | 16 | no | — |
| 151 | C22×Dic7 | — | 2 | 4 | no | — |
| 152 | C22×Dic7 | — | 4 | 1 | no | — |
| 153 | #1159 | — | 4 | 4 | no | — |
| 154 | #1159 | — | 4 | 8 | no | — |
| 155 | #1159 | — | 4 | 4 | no | — |
| 156 | D4×D7 | — | 4 | 8 | no | — |
| 157 | D4×D7 | — | 4 | 4 | no | — |
| 158 | D4×D7 | — | 4 | 4 | no | — |
| 159 | D4×D7 | — | 8 | 4 | no | — |
| 160 | D4×D7 | — | 8 | 4 | no | — |
| 161 | #1157 | — | 2 | 2 | no | — |
| 162 | #1157 | — | 4 | 2 | no | — |
| 163 | #1157 | — | 4 | 2 | no | — |
| 164 | #1157 | SD16 | 1 | 4 | yes | complemented |
| 165 | C2×D28 | — | 2 | 1 | no | — |
| 166 | C2×D28 | — | 2 | 1 | no | — |
| 167 | C2×D28 | C2×D4 | 1 | 2 | yes | — |
| 168 | C2×D28 | C2×D4 | 1 | 1 | yes | characteristic |
| 169 | C2×C4×D7 | — | 2 | 1 | no | — |
| 170 | C2×C4×D7 | — | 2 | 1 | no | — |
| 171 | C2×C4×D7 | — | 2 | 1 | no | — |
| 172 | C2×C4×D7 | — | 2 | 2 | no | — |
| 173 | C2×Dic14 | — | 2 | 1 | no | — |
| 174 | C2×Dic14 | — | 2 | 2 | no | — |
| 175 | C2×Dic14 | — | 4 | 4 | no | — |
| 176 | C2×Dic14 | — | 4 | 1 | no | — |
| 177 | C2×Dic14 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C7×M16 | — | 4 | 2 | no | — |
| 179 | C2×C7×C8 | — | 2 | 2 | no | — |
| 180 | C2×C7×C8 | — | 2 | 2 | no | — |
| 181 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 183 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 185 | C22⋊Dic7 | — | 2 | 4 | no | — |
| 186 | C22⋊Dic7 | — | 2 | 4 | no | — |
| 187 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 188 | #1142 | — | 4 | 16 | no | — |
| 189 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 190 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 191 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 192 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 193 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 194 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 195 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 196 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 197 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 198 | C4⋊Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 199 | C4⋊Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 200 | C4⋊Dic7 | C2×D4 | 1 | 2 | yes | — |
| 201 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 202 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 203 | C4×Dic7 | — | 2 | 1 | no | — |
| 204 | C4×Dic7 | — | 2 | 1 | no | — |
| 205 | C4×Dic7 | — | 2 | 1 | no | — |
| 206 | C2×C7⋊C8 | — | 2 | 4 | no | — |
| 207 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 208 | C2×H(5,𝔽2) | — | 14 | 1 | no | — |
| 209 | C22×SD16 | — | 14 | 2 | no | — |
| 210 | #550 | — | 7 | 2 | no | — |
| 211 | #550 | — | 14 | 1 | no | — |
| 212 | D42 | — | 7 | 2 | no | — |
| 213 | D42 | — | 14 | 1 | no | — |
| 214 | D42 | — | 14 | 2 | no | — |
| 215 | D42 | — | 14 | 2 | no | — |
| 216 | #535 | — | 14 | 1 | no | — |
| 217 | #535 | — | 14 | 2 | no | — |
| 218 | #532 | — | 7 | 1 | no | — |
| 219 | #532 | — | 14 | 1 | no | — |
| 220 | C2×C4⋊Q8 | — | 7 | 1 | no | — |
| 221 | C2×#127 | — | 14 | 1 | no | — |
| 222 | C2×#127 | C2×D7 | 1 | 1 | yes | characteristic |
| 223 | C4×#41 | — | 7 | 1 | no | — |
| 224 | #498 | — | 14 | 1 | no | — |
| 225 | #492 | — | 7 | 4 | no | — |
| 226 | #492 | — | 14 | 2 | no | — |
| 227 | #486 | — | 14 | 1 | no | — |
| 228 | #481 | — | 14 | 2 | no | — |
| 229 | #477 | — | 7 | 2 | no | — |
| 230 | #476 | — | 7 | 2 | no | — |
| 231 | #476 | — | 7 | 4 | no | — |
| 232 | #475 | — | 14 | 1 | no | — |
| 233 | #474 | — | 14 | 1 | no | — |
| 234 | #431 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 235 | #428 | — | 14 | 1 | no | — |
| 236 | #423 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 237 | #417 | — | 14 | 1 | no | — |
| 238 | C2×C4×C8 | — | 7 | 1 | no | — |
| 239 | #331 | C2×D7 | 1 | 4 | yes | complemented |
| 240 | Q8⋊C8 | — | 7 | 2 | no | — |
| 241 | D4⋊C8 | — | 7 | 2 | no | — |
| 242 | D4⋊C8 | — | 7 | 4 | no | — |
| 243 | C23×C7 | — | 2 | 4 | no | — |
| 244 | C23×C7 | — | 4 | 4 | no | — |
| 245 | C23×C7 | — | 8 | 2 | no | — |
| 246 | C23×C7 | — | 8 | 2 | no | — |
| 247 | C23×C7 | #120 | 1 | 1 | yes | characteristic |
| 248 | C22×D7 | — | 2 | 1 | no | — |
| 249 | C22×D7 | — | 2 | 2 | no | — |
| 250 | C22×D7 | — | 4 | 8 | no | — |
| 251 | C22×D7 | — | 8 | 4 | no | — |
| 252 | C22×D7 | — | 8 | 4 | no | — |
| 253 | C7×D4 | — | 4 | 4 | no | — |
| 254 | C7×D4 | — | 4 | 2 | no | — |
| 255 | C7×D4 | — | 4 | 2 | no | — |
| 256 | C7×D4 | — | 4 | 4 | no | — |
| 257 | C7×D4 | — | 4 | 4 | no | — |
| 258 | C7×D4 | — | 4 | 4 | no | — |
| 259 | C7×D4 | — | 8 | 2 | no | — |
| 260 | C2×C4×C7 | — | 2 | 2 | no | — |
| 261 | C2×C4×C7 | — | 2 | 2 | no | — |
| 262 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 263 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 264 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 265 | C2×C4×C7 | C2×SD16 | 1 | 2 | yes | — |
| 266 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 267 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 268 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 269 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 270 | C22⋊D7 | — | 2 | 4 | no | — |
| 271 | C22⋊D7 | — | 4 | 8 | no | — |
| 272 | C22⋊D7 | — | 4 | 8 | no | — |
| 273 | C22⋊D7 | — | 4 | 4 | no | — |
| 274 | C22⋊D7 | — | 8 | 4 | no | — |
| 275 | C22⋊D7 | — | 8 | 4 | no | — |
| 276 | C2×Dic7 | — | 2 | 1 | no | — |
| 277 | C2×Dic7 | — | 2 | 1 | no | — |
| 278 | C2×Dic7 | — | 2 | 1 | no | — |
| 279 | C2×Dic7 | — | 2 | 2 | no | — |
| 280 | C2×Dic7 | — | 4 | 8 | no | — |
| 281 | C2×Dic7 | — | 4 | 2 | no | — |
| 282 | C2×Dic7 | — | 8 | 2 | no | — |
| 283 | D28 | — | 2 | 1 | no | — |
| 284 | D28 | — | 2 | 4 | no | — |
| 285 | D28 | — | 4 | 2 | no | — |
| 286 | D28 | — | 4 | 2 | no | — |
| 287 | D28 | C2×SD16 | 1 | 2 | yes | complemented |
| 288 | C4×D7 | — | 2 | 4 | no | — |
| 289 | C4×D7 | — | 4 | 2 | no | — |
| 290 | C4×D7 | — | 4 | 2 | no | — |
| 291 | C4×D7 | — | 4 | 2 | no | — |
| 292 | C4×D7 | — | 4 | 2 | no | — |
| 293 | Dic14 | — | 2 | 1 | no | — |
| 294 | Dic14 | — | 4 | 2 | no | — |
| 295 | Dic14 | — | 4 | 4 | no | — |
| 296 | Dic14 | — | 8 | 2 | no | — |
| 297 | Dic14 | C2×SD16 | 1 | 2 | yes | complemented |
| 298 | C7×C8 | — | 4 | 2 | no | — |
| 299 | C7×C8 | — | 4 | 2 | no | — |
| 300 | C7⋊C8 | — | 2 | 4 | no | — |
| 301 | H(5,𝔽2) | — | 28 | 4 | no | — |
| 302 | H(5,𝔽2) | — | 28 | 4 | no | — |
| 303 | C2×#41 | — | 7 | 1 | no | — |
| 304 | C2×#41 | — | 14 | 2 | no | — |
| 305 | C2×#41 | — | 14 | 2 | no | — |
| 306 | C2×#41 | — | 14 | 1 | no | — |
| 307 | C22×Q8 | — | 14 | 1 | no | — |
| 308 | C22×D4 | — | 2 | 1 | no | — |
| 309 | C22×D4 | — | 2 | 1 | no | — |
| 310 | C22×D4 | — | 14 | 2 | no | — |
| 311 | C22×D4 | — | 14 | 2 | no | — |
| 312 | C22×D4 | — | 14 | 2 | no | — |
| 313 | C22×D4 | — | 14 | 2 | no | — |
| 314 | C22×D4 | — | 14 | 4 | no | — |
| 315 | C22×D4 | D28 | 1 | 2 | yes | — |
| 316 | C2×SD16 | — | 14 | 8 | no | — |
| 317 | C2×SD16 | — | 28 | 8 | no | — |
| 318 | C2×M16 | — | 2 | 1 | no | — |
| 319 | C22×C8 | — | 14 | 1 | no | — |
| 320 | C4⋊Q8 | — | 7 | 1 | no | — |
| 321 | C4⋊Q8 | — | 7 | 2 | no | — |
| 322 | C4⋊Q8 | — | 14 | 1 | no | — |
| 323 | C4⋊Q8 | — | 14 | 1 | no | — |
| 324 | C4⋊Q8 | — | 14 | 1 | no | — |
| 325 | #127 | — | 2 | 1 | no | — |
| 326 | #127 | — | 2 | 1 | no | — |
| 327 | #127 | — | 7 | 1 | no | — |
| 328 | #127 | — | 14 | 2 | no | — |
| 329 | #127 | — | 14 | 2 | no | — |
| 330 | #127 | — | 14 | 2 | no | — |
| 331 | #127 | D28 | 1 | 2 | yes | — |
| 332 | #127 | C22×D7 | 1 | 2 | yes | — |
| 333 | #124 | — | 14 | 2 | no | — |
| 334 | #124 | — | 14 | 1 | no | — |
| 335 | #121 | — | 7 | 2 | no | — |
| 336 | #121 | — | 14 | 2 | no | — |
| 337 | #121 | — | 14 | 2 | no | — |
| 338 | #121 | — | 14 | 2 | no | — |
| 339 | #121 | — | 14 | 2 | no | — |
| 340 | #121 | — | 14 | 4 | no | — |
| 341 | #121 | — | 14 | 4 | no | — |
| 342 | #121 | — | 14 | 1 | no | — |
| 343 | #120 | — | 14 | 4 | no | — |
| 344 | #120 | — | 14 | 4 | no | — |
| 345 | #120 | — | 14 | 4 | no | — |
| 346 | C4×Q8 | — | 7 | 1 | no | — |
| 347 | C4×Q8 | — | 7 | 1 | no | — |
| 348 | C4×D4 | — | 7 | 1 | no | — |
| 349 | C4×D4 | — | 7 | 1 | no | — |
| 350 | C4×D4 | — | 7 | 2 | no | — |
| 351 | C4×D4 | — | 14 | 2 | no | — |
| 352 | C4×D4 | — | 14 | 2 | no | — |
| 353 | C4×D4 | — | 14 | 1 | no | — |
| 354 | C4×D4 | — | 14 | 1 | no | — |
| 355 | C4×D4 | — | 14 | 1 | no | — |
| 356 | #117 | — | 7 | 1 | no | — |
| 357 | #117 | — | 14 | 1 | no | — |
| 358 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 359 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 360 | C2×C42 | — | 14 | 1 | no | — |
| 361 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 362 | #107 | — | 14 | 2 | no | — |
| 363 | #106 | — | 14 | 2 | no | — |
| 364 | #106 | — | 14 | 4 | no | — |
| 365 | C4⋊C8 | — | 2 | 1 | no | — |
| 366 | C4⋊C8 | C22×D7 | 1 | 2 | yes | — |
| 367 | C4⋊C8 | C22×D7 | 1 | 2 | yes | — |
| 368 | #103 | — | 14 | 2 | no | — |
| 369 | #102 | — | 14 | 2 | no | — |
| 370 | #102 | — | 14 | 4 | no | — |
| 371 | C22⋊C8 | — | 2 | 1 | no | — |
| 372 | C4×C8 | — | 2 | 1 | no | — |
| 373 | C4×C8 | — | 7 | 2 | no | — |
| 374 | C4×C8 | — | 14 | 1 | no | — |
| 375 | C22×C7 | — | 2 | 1 | no | — |
| 376 | C22×C7 | — | 2 | 1 | no | — |
| 377 | C22×C7 | — | 4 | 4 | no | — |
| 378 | C22×C7 | — | 4 | 4 | no | — |
| 379 | C22×C7 | — | 4 | 4 | no | — |
| 380 | C22×C7 | — | 16 | 4 | no | — |
| 381 | C22×C7 | #450 | 1 | 2 | yes | — |
| 382 | C22×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 383 | C2×D7 | — | 2 | 2 | no | — |
| 384 | C2×D7 | — | 4 | 1 | no | — |
| 385 | C2×D7 | — | 4 | 1 | no | — |
| 386 | C2×D7 | — | 4 | 2 | no | — |
| 387 | C2×D7 | — | 4 | 2 | no | — |
| 388 | C2×D7 | — | 4 | 2 | no | — |
| 389 | C2×D7 | — | 16 | 8 | no | — |
| 390 | C4×C7 | — | 2 | 1 | no | — |
| 391 | C4×C7 | — | 2 | 1 | no | — |
| 392 | C4×C7 | #450 | 1 | 2 | yes | — |
| 393 | C4×C7 | #453 | 1 | 2 | yes | — |
| 394 | C4×C7 | C22×SD16 | 1 | 1 | yes | characteristic |
| 395 | C4×C7 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 396 | C4×C7 | #577 | 1 | 2 | yes | — |
| 397 | Dic7 | — | 2 | 2 | no | — |
| 398 | Dic7 | — | 4 | 2 | no | — |
| 399 | Dic7 | — | 4 | 1 | no | — |
| 400 | Dic7 | — | 4 | 1 | no | — |
| 401 | Dic7 | — | 8 | 2 | no | — |
| 402 | C24 | — | 2 | 2 | no | — |
| 403 | C24 | — | 14 | 4 | no | — |
| 404 | #41 | — | 7 | 4 | no | — |
| 405 | #41 | — | 14 | 2 | no | — |
| 406 | #41 | — | 28 | 8 | no | — |
| 407 | #41 | — | 28 | 4 | no | — |
| 408 | #41 | — | 28 | 4 | no | — |
| 409 | #41 | — | 28 | 2 | no | — |
| 410 | #41 | — | 28 | 2 | no | — |
| 411 | C2×Q8 | — | 7 | 1 | no | — |
| 412 | C2×Q8 | — | 14 | 1 | no | — |
| 413 | C2×Q8 | — | 14 | 2 | no | — |
| 414 | C2×Q8 | — | 28 | 4 | no | — |
| 415 | C2×Q8 | — | 28 | 1 | no | — |
| 416 | C2×D4 | — | 2 | 2 | no | — |
| 417 | C2×D4 | — | 2 | 2 | no | — |
| 418 | C2×D4 | — | 2 | 2 | no | — |
| 419 | C2×D4 | — | 2 | 2 | no | — |
| 420 | C2×D4 | — | 2 | 2 | no | — |
| 421 | C2×D4 | — | 4 | 4 | no | — |
| 422 | C2×D4 | — | 4 | 2 | no | — |
| 423 | C2×D4 | — | 4 | 2 | no | — |
| 424 | C2×D4 | — | 7 | 1 | no | — |
| 425 | C2×D4 | — | 7 | 2 | no | — |
| 426 | C2×D4 | — | 8 | 2 | no | — |
| 427 | C2×D4 | — | 14 | 1 | no | — |
| 428 | C2×D4 | — | 14 | 4 | no | — |
| 429 | C2×D4 | — | 14 | 4 | no | — |
| 430 | C2×D4 | — | 14 | 2 | no | — |
| 431 | C2×D4 | — | 14 | 4 | no | — |
| 432 | C2×D4 | — | 14 | 4 | no | — |
| 433 | C2×D4 | — | 14 | 1 | no | — |
| 434 | C2×D4 | — | 14 | 1 | no | — |
| 435 | C2×D4 | — | 28 | 8 | no | — |
| 436 | C2×D4 | — | 28 | 4 | no | — |
| 437 | C2×D4 | — | 28 | 4 | no | — |
| 438 | C2×D4 | — | 28 | 16 | no | — |
| 439 | C2×D4 | — | 56 | 4 | no | — |
| 440 | C2×D4 | — | 56 | 4 | no | — |
| 441 | C2×D4 | C2×D28 | 1 | 4 | yes | — |
| 442 | C22×C4 | — | 14 | 1 | no | — |
| 443 | C22×C4 | — | 14 | 4 | no | — |
| 444 | C22×C4 | — | 14 | 1 | no | — |
| 445 | C22×C4 | — | 14 | 1 | no | — |
| 446 | C22×C4 | — | 14 | 2 | no | — |
| 447 | C22×C4 | — | 28 | 1 | no | — |
| 448 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 449 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 450 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 451 | SD16 | — | 28 | 16 | no | — |
| 452 | M16 | — | 4 | 2 | no | — |
| 453 | C2×C8 | — | 2 | 2 | no | — |
| 454 | C2×C8 | — | 2 | 2 | no | — |
| 455 | C2×C8 | — | 14 | 4 | no | — |
| 456 | C2×C8 | — | 14 | 2 | no | — |
| 457 | C4⋊C4 | — | 7 | 1 | no | — |
| 458 | C4⋊C4 | — | 7 | 2 | no | — |
| 459 | C4⋊C4 | — | 7 | 1 | no | — |
| 460 | C4⋊C4 | — | 14 | 1 | no | — |
| 461 | C4⋊C4 | — | 14 | 1 | no | — |
| 462 | C4⋊C4 | — | 14 | 1 | no | — |
| 463 | C4⋊C4 | — | 14 | 2 | no | — |
| 464 | C4⋊C4 | — | 14 | 2 | no | — |
| 465 | C4⋊C4 | — | 28 | 1 | no | — |
| 466 | C4⋊C4 | — | 28 | 1 | no | — |
| 467 | C22⋊C4 | — | 14 | 4 | no | — |
| 468 | C22⋊C4 | — | 14 | 4 | no | — |
| 469 | C22⋊C4 | — | 14 | 1 | no | — |
| 470 | C22⋊C4 | — | 14 | 1 | no | — |
| 471 | C22⋊C4 | — | 14 | 2 | no | — |
| 472 | C22⋊C4 | — | 14 | 1 | no | — |
| 473 | C22⋊C4 | — | 14 | 2 | no | — |
| 474 | C42 | — | 14 | 1 | no | — |
| 475 | C42 | — | 14 | 1 | no | — |
| 476 | C42 | — | 14 | 1 | no | — |
| 477 | C42 | C2×D28 | 1 | 1 | yes | characteristic |
| 478 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 479 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 480 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 481 | C2×C7 | — | 2 | 2 | no | — |
| 482 | C2×C7 | — | 8 | 4 | no | — |
| 483 | C2×C7 | C2×#450 | 1 | 1 | yes | characteristic |
| 484 | C2×C7 | #3009 | 1 | 1 | yes | characteristic |
| 485 | C2×C7 | C2×#453 | 1 | 1 | yes | characteristic |
| 486 | D7 | — | 4 | 2 | no | — |
| 487 | D7 | — | 8 | 2 | no | — |
| 488 | C23 | — | 2 | 4 | no | — |
| 489 | C23 | — | 4 | 4 | no | — |
| 490 | C23 | — | 8 | 2 | no | — |
| 491 | C23 | — | 8 | 2 | no | — |
| 492 | C23 | — | 14 | 1 | no | — |
| 493 | C23 | — | 14 | 2 | no | — |
| 494 | C23 | — | 28 | 8 | no | — |
| 495 | C23 | — | 56 | 4 | no | — |
| 496 | C23 | — | 56 | 4 | no | — |
| 497 | C23 | #6445 | 1 | 1 | yes | characteristic |
| 498 | Q8 | — | 7 | 2 | no | — |
| 499 | Q8 | — | 14 | 1 | no | — |
| 500 | Q8 | — | 28 | 4 | no | — |
| 501 | Q8 | — | 28 | 2 | no | — |
| 502 | Q8 | — | 56 | 2 | no | — |
| 503 | D4 | — | 4 | 4 | no | — |
| 504 | D4 | — | 4 | 2 | no | — |
| 505 | D4 | — | 4 | 2 | no | — |
| 506 | D4 | — | 4 | 4 | no | — |
| 507 | D4 | — | 4 | 4 | no | — |
| 508 | D4 | — | 4 | 4 | no | — |
| 509 | D4 | — | 7 | 2 | no | — |
| 510 | D4 | — | 8 | 2 | no | — |
| 511 | D4 | — | 14 | 4 | no | — |
| 512 | D4 | — | 14 | 1 | no | — |
| 513 | D4 | — | 14 | 4 | no | — |
| 514 | D4 | — | 28 | 8 | no | — |
| 515 | D4 | — | 28 | 8 | no | — |
| 516 | D4 | — | 28 | 4 | no | — |
| 517 | D4 | — | 28 | 2 | no | — |
| 518 | D4 | — | 28 | 2 | no | — |
| 519 | D4 | — | 56 | 4 | no | — |
| 520 | D4 | — | 56 | 4 | no | — |
| 521 | C2×C4 | — | 2 | 2 | no | — |
| 522 | C2×C4 | — | 2 | 2 | no | — |
| 523 | C2×C4 | — | 14 | 1 | no | — |
| 524 | C2×C4 | — | 14 | 4 | no | — |
| 525 | C2×C4 | — | 14 | 1 | no | — |
| 526 | C2×C4 | — | 14 | 1 | no | — |
| 527 | C2×C4 | — | 14 | 2 | no | — |
| 528 | C2×C4 | — | 28 | 8 | no | — |
| 529 | C2×C4 | — | 28 | 2 | no | — |
| 530 | C2×C4 | — | 28 | 2 | no | — |
| 531 | C2×C4 | — | 28 | 2 | no | — |
| 532 | C2×C4 | — | 28 | 2 | no | — |
| 533 | C2×C4 | — | 28 | 2 | no | — |
| 534 | C2×C4 | — | 56 | 2 | no | — |
| 535 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 536 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 537 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 538 | C2×C4 | #6474 | 1 | 2 | yes | — |
| 539 | C2×C4 | D7×SD16 | 1 | 2 | yes | — |
| 540 | C2×C4 | C22×D28 | 1 | 1 | yes | characteristic |
| 541 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 542 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 543 | C8 | — | 4 | 2 | no | — |
| 544 | C8 | — | 4 | 2 | no | — |
| 545 | C8 | — | 14 | 4 | no | — |
| 546 | C7 | #18621 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 547 | C22 | — | 2 | 1 | no | — |
| 548 | C22 | — | 2 | 1 | no | — |
| 549 | C22 | — | 4 | 4 | no | — |
| 550 | C22 | — | 4 | 4 | no | — |
| 551 | C22 | — | 4 | 4 | no | — |
| 552 | C22 | — | 14 | 2 | no | — |
| 553 | C22 | — | 16 | 4 | no | — |
| 554 | C22 | — | 28 | 1 | no | — |
| 555 | C22 | — | 28 | 1 | no | — |
| 556 | C22 | — | 28 | 2 | no | — |
| 557 | C22 | — | 28 | 2 | no | — |
| 558 | C22 | — | 28 | 2 | no | — |
| 559 | C22 | — | 112 | 8 | no | — |
| 560 | C22 | #89548 | 1 | 2 | yes | — |
| 561 | C22 | C2×#6445 | 1 | 1 | yes | characteristic |
| 562 | C4 | — | 2 | 1 | no | — |
| 563 | C4 | — | 2 | 1 | no | — |
| 564 | C4 | — | 14 | 2 | no | — |
| 565 | C4 | — | 28 | 1 | no | — |
| 566 | C4 | — | 28 | 1 | no | — |
| 567 | C4 | — | 28 | 2 | no | — |
| 568 | C4 | — | 56 | 2 | no | — |
| 569 | C4 | #89519 | 1 | 2 | yes | — |
| 570 | C4 | #89548 | 1 | 2 | yes | — |
| 571 | C4 | C2×#6474 | 1 | 1 | yes | characteristic |
| 572 | C4 | C2×D7×SD16 | 1 | 1 | yes | characteristic |
| 573 | C4 | #90466 | 1 | 2 | yes | — |
| 574 | C2 | — | 2 | 2 | no | — |
| 575 | C2 | — | 8 | 4 | no | — |
| 576 | C2 | — | 28 | 2 | no | — |
| 577 | C2 | — | 56 | 2 | no | — |
| 578 | C2 | C2×#89519 | 1 | 1 | yes | characteristic |
| 579 | C2 | C2×#89548 | 1 | 1 | yes | characteristic |
| 580 | C2 | #11736374 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#89848 | C2 | semidirect |
| 3. #11736714 | C2 | semidirect |
| 4. #11736505 | C2 | semidirect |
| 5. C7×#1545 | C2 | semidirect |
| 6. #11728508 | C2 | semidirect |
| 7. #11728252 | C2 | semidirect |
| 8. #11726159 | C2 | semidirect |
| 9. #11726145 | C2 | semidirect |
| 25. C2×#6432 | C22 | semidirect |
| 26. C7×#431 | C22 | semidirect |
| 27. C7×#423 | C22 | semidirect |
| 31. #89848 | C22 | semidirect |
| 32. C2×C4×C7⋊C8 | C22 | semidirect |
| 34. #89622 | C22 | semidirect |
| 36. #89614 | C22 | semidirect |
| 37. #89614 | C22 | semidirect |
| 41. C7×#331 | C22 | semidirect |
| 42. #89279 | C22 | semidirect |
| 43. #89278 | C22 | semidirect |
| 44. #89278 | C22 | semidirect |
| 126. #1545 | D7 | semidirect |
| 164. #1157 | SD16 | semidirect |
| 234. #431 | C2×D7 | semidirect |
| 236. #423 | C2×D7 | semidirect |
| 239. #331 | C2×D7 | semidirect |
| 287. D28 | C2×SD16 | semidirect |
| 297. Dic14 | C2×SD16 | semidirect |
| 546. C7 | #18621 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11743263 | 2 |
| C2×#89848 | 2 |
| #11736714 | 2 |
| #11736505 | 2 |
| C7×#1545 | 2 |
| #11728508 | 2 |
| #11728252 | 2 |
| #11726159 | 2 |
| #11726145 | 2 |
| #18621 | 7 |