Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1012 conjugacy classes of subgroups.
The subgroup lattice has 686 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#89923 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11741271 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11736531 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11736377 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11736360 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#89521 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C7×#2045 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11728291 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11728078 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11728077 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11727836 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #11727828 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #11727824 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #11726686 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #11726680 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C22×C7×D8 | C22 | 1 | 1 | yes | characteristic |
| 17 | #90496 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#6503 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#6503 | C22 | 1 | 1 | yes | characteristic |
| 20 | #90489 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#6495 | C22 | 1 | 1 | yes | characteristic |
| 22 | C22×#1141 | C22 | 1 | 1 | yes | characteristic |
| 23 | C22×#1141 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#6471 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#6470 | C22 | 1 | 1 | yes | characteristic |
| 26 | C22×D56 | C22 | 1 | 1 | yes | characteristic |
| 27 | #90216 | C22 | 1 | 1 | yes | characteristic |
| 28 | #90212 | C22 | 1 | 1 | yes | characteristic |
| 29 | C7×#424 | C22 | 1 | 1 | yes | characteristic |
| 30 | C7×#418 | C22 | 1 | 1 | yes | characteristic |
| 31 | C7×#418 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×C7×#100 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×C7×#100 | C22 | 1 | 1 | yes | characteristic |
| 34 | #89987 | C22 | 1 | 1 | yes | characteristic |
| 35 | #89925 | — | 2 | 2 | no | — |
| 36 | #89923 | — | 2 | 4 | no | — |
| 37 | #89922 | — | 2 | 2 | no | — |
| 38 | C2×#6399 | C22 | 1 | 1 | yes | characteristic |
| 39 | #89903 | C22 | 1 | 1 | yes | characteristic |
| 40 | #89903 | C22 | 1 | 1 | yes | characteristic |
| 41 | #89903 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×#6397 | C22 | 1 | 1 | yes | characteristic |
| 43 | C2×#6397 | C22 | 1 | 1 | yes | characteristic |
| 44 | C2×#6396 | C22 | 1 | 1 | yes | characteristic |
| 45 | #89894 | C22 | 1 | 1 | yes | characteristic |
| 46 | #89885 | C22 | 1 | 1 | yes | characteristic |
| 47 | #89874 | C22 | 1 | 1 | yes | characteristic |
| 48 | C2×C8×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 49 | #89770 | C22 | 1 | 1 | yes | characteristic |
| 50 | #89616 | — | 2 | 2 | no | — |
| 51 | #89615 | — | 2 | 2 | no | — |
| 52 | #89557 | — | 2 | 2 | no | — |
| 53 | #89554 | — | 2 | 2 | no | — |
| 54 | #89547 | — | 2 | 2 | no | — |
| 55 | #89528 | — | 2 | 2 | no | — |
| 56 | #89521 | — | 2 | 4 | no | — |
| 57 | C7×#341 | C22 | 1 | 1 | yes | characteristic |
| 58 | #89350 | C22 | 1 | 1 | yes | characteristic |
| 59 | #89350 | C22 | 1 | 1 | yes | characteristic |
| 60 | #89327 | C22 | 1 | 1 | yes | characteristic |
| 61 | #25434 | — | 7 | 1 | no | maximal, Sylow |
| 62 | C22×C7×D4 | C23 | 1 | 1 | yes | characteristic |
| 63 | C22×C7×D4 | C23 | 1 | 1 | yes | characteristic |
| 64 | C22×C22⋊D7 | — | 4 | 1 | no | — |
| 65 | C22×C22⋊D7 | — | 4 | 1 | no | — |
| 66 | C2×#1157 | C23 | 1 | 1 | yes | characteristic |
| 67 | C22×D28 | C23 | 1 | 1 | yes | characteristic |
| 68 | C22×D28 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×C7×D8 | — | 2 | 2 | no | — |
| 70 | C2×C7×D8 | — | 2 | 2 | no | — |
| 71 | C2×C7×D8 | — | 4 | 1 | no | — |
| 72 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 73 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 75 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 76 | C7×#117 | C23 | 1 | 1 | yes | characteristic |
| 77 | #6516 | — | 4 | 1 | no | — |
| 78 | C2×C22⋊Dic7 | — | 4 | 1 | no | — |
| 79 | #6503 | — | 2 | 2 | no | — |
| 80 | #6503 | — | 2 | 1 | no | — |
| 81 | #6503 | — | 2 | 2 | no | — |
| 82 | #6503 | — | 2 | 2 | no | — |
| 83 | #6503 | — | 2 | 2 | no | — |
| 84 | #6501 | — | 2 | 2 | no | — |
| 85 | #6499 | — | 2 | 1 | no | — |
| 86 | D4×Dic7 | — | 2 | 2 | no | — |
| 87 | D4×Dic7 | — | 2 | 2 | no | — |
| 88 | C2×#1142 | — | 2 | 1 | no | — |
| 89 | #6495 | — | 2 | 2 | no | — |
| 90 | #6495 | — | 4 | 1 | no | — |
| 91 | C2×#1141 | — | 2 | 1 | no | — |
| 92 | C2×#1141 | — | 2 | 1 | no | — |
| 93 | C2×#1141 | — | 2 | 1 | no | — |
| 94 | C2×#1141 | — | 2 | 2 | no | — |
| 95 | C2×#1141 | — | 2 | 1 | no | — |
| 96 | C2×#1141 | — | 2 | 1 | no | — |
| 97 | C2×#1141 | — | 2 | 2 | no | — |
| 98 | C2×#1141 | — | 2 | 2 | no | — |
| 99 | C2×#1141 | D4 | 1 | 4 | yes | complemented |
| 100 | #6489 | C23 | 1 | 1 | yes | characteristic |
| 101 | #6489 | C23 | 1 | 1 | yes | characteristic |
| 102 | C2×C4×Dic7 | C23 | 1 | 1 | yes | characteristic |
| 103 | C2×#1136 | C23 | 1 | 1 | yes | characteristic |
| 104 | C22×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 105 | #6471 | — | 2 | 2 | no | — |
| 106 | #6471 | — | 4 | 1 | no | — |
| 107 | #6470 | — | 2 | 2 | no | — |
| 108 | #6470 | — | 2 | 2 | no | — |
| 109 | C2×D56 | — | 2 | 1 | no | — |
| 110 | C2×D56 | — | 2 | 2 | no | — |
| 111 | C2×D56 | — | 2 | 2 | no | — |
| 112 | C2×D56 | — | 4 | 1 | no | — |
| 113 | C2×#1132 | — | 2 | 1 | no | — |
| 114 | C2×#1131 | — | 2 | 1 | no | — |
| 115 | C2×C8×D7 | — | 2 | 1 | no | — |
| 116 | #6458 | — | 2 | 2 | no | — |
| 117 | #6456 | — | 2 | 2 | no | — |
| 118 | #6445 | — | 4 | 1 | no | — |
| 119 | D7×C22⋊C4 | — | 4 | 1 | no | — |
| 120 | #6438 | — | 2 | 1 | no | — |
| 121 | #6437 | — | 2 | 1 | no | — |
| 122 | C4×D28 | — | 2 | 2 | no | — |
| 123 | C7×C4⋊C8 | — | 2 | 2 | no | — |
| 124 | C7×#102 | — | 2 | 2 | no | — |
| 125 | C7×#102 | — | 2 | 2 | no | — |
| 126 | C7×#100 | — | 2 | 2 | no | — |
| 127 | C7×#100 | — | 4 | 1 | no | — |
| 128 | #6406 | — | 2 | 2 | no | — |
| 129 | #6399 | — | 2 | 2 | no | — |
| 130 | #6397 | — | 2 | 2 | no | — |
| 131 | #6397 | — | 4 | 1 | no | — |
| 132 | #6396 | — | 2 | 2 | no | — |
| 133 | #6395 | — | 2 | 2 | no | — |
| 134 | #6395 | — | 2 | 2 | no | — |
| 135 | #6395 | — | 2 | 2 | no | — |
| 136 | #6395 | D4 | 1 | 2 | yes | complemented |
| 137 | #6390 | D4 | 1 | 2 | yes | complemented |
| 138 | #6389 | — | 2 | 1 | no | — |
| 139 | Dic7⋊C8 | — | 2 | 2 | no | — |
| 140 | C8×Dic7 | — | 2 | 2 | no | — |
| 141 | C8×Dic7 | — | 2 | 1 | no | — |
| 142 | #6382 | D4 | 1 | 2 | yes | complemented |
| 143 | #6381 | D4 | 1 | 2 | yes | complemented |
| 144 | C2×#493 | — | 7 | 1 | no | — |
| 145 | C2×#472 | — | 7 | 1 | no | — |
| 146 | #3058 | — | 7 | 1 | no | — |
| 147 | #3041 | — | 7 | 1 | no | — |
| 148 | #3041 | — | 7 | 1 | no | — |
| 149 | #2948 | — | 7 | 1 | no | — |
| 150 | #2045 | — | 7 | 1 | no | — |
| 151 | #2045 | D7 | 1 | 1 | yes | characteristic, complemented |
| 152 | #2002 | — | 7 | 1 | no | — |
| 153 | #2002 | — | 7 | 1 | no | — |
| 154 | #1978 | — | 7 | 1 | no | — |
| 155 | #1945 | — | 7 | 1 | no | — |
| 156 | #1887 | — | 7 | 1 | no | — |
| 157 | #1887 | — | 7 | 1 | no | — |
| 158 | #1764 | — | 7 | 1 | no | — |
| 159 | C24×C7 | — | 2 | 1 | no | — |
| 160 | C24×C7 | — | 2 | 1 | no | — |
| 161 | C23×D7 | — | 2 | 1 | no | — |
| 162 | C23×D7 | — | 2 | 1 | no | — |
| 163 | C2×C7×D4 | — | 2 | 1 | no | — |
| 164 | C2×C7×D4 | — | 2 | 1 | no | — |
| 165 | C2×C7×D4 | — | 2 | 1 | no | — |
| 166 | C2×C7×D4 | — | 2 | 1 | no | — |
| 167 | C2×C7×D4 | — | 2 | 1 | no | — |
| 168 | C2×C7×D4 | — | 2 | 1 | no | — |
| 169 | C2×C7×D4 | — | 2 | 1 | no | — |
| 170 | C2×C7×D4 | — | 2 | 1 | no | — |
| 171 | C2×C7×D4 | — | 2 | 1 | no | — |
| 172 | C2×C7×D4 | — | 2 | 1 | no | — |
| 173 | C2×C7×D4 | — | 2 | 1 | no | — |
| 174 | C2×C7×D4 | C2×D4 | 1 | 2 | yes | — |
| 175 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 176 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 177 | C2×C22⋊D7 | — | 4 | 4 | no | — |
| 178 | C2×C22⋊D7 | — | 4 | 4 | no | — |
| 179 | C2×C22⋊D7 | — | 4 | 2 | no | — |
| 180 | C2×C22⋊D7 | — | 8 | 4 | no | — |
| 181 | C2×C22⋊D7 | — | 8 | 4 | no | — |
| 182 | C22×Dic7 | — | 2 | 1 | no | — |
| 183 | C22×Dic7 | — | 4 | 2 | no | — |
| 184 | #1157 | — | 2 | 1 | no | — |
| 185 | #1157 | — | 2 | 1 | no | — |
| 186 | #1157 | — | 2 | 1 | no | — |
| 187 | #1157 | — | 2 | 1 | no | — |
| 188 | C2×D28 | — | 2 | 1 | no | — |
| 189 | C2×D28 | — | 2 | 1 | no | — |
| 190 | C2×D28 | — | 2 | 1 | no | — |
| 191 | C2×D28 | — | 2 | 1 | no | — |
| 192 | C2×D28 | — | 2 | 1 | no | — |
| 193 | C2×D28 | — | 2 | 1 | no | — |
| 194 | C2×D28 | — | 2 | 1 | no | — |
| 195 | C2×D28 | — | 2 | 1 | no | — |
| 196 | C2×D28 | — | 2 | 1 | no | — |
| 197 | C2×D28 | — | 2 | 1 | no | — |
| 198 | C2×D28 | — | 2 | 1 | no | — |
| 199 | C2×D28 | — | 4 | 2 | no | — |
| 200 | C2×D28 | C2×D4 | 1 | 1 | yes | characteristic |
| 201 | C2×D28 | C2×D4 | 1 | 2 | yes | — |
| 202 | C2×C4×D7 | — | 2 | 1 | no | — |
| 203 | C2×C4×D7 | — | 4 | 2 | no | — |
| 204 | C2×Dic14 | C2×D4 | 1 | 1 | yes | characteristic |
| 205 | C7×D8 | — | 4 | 4 | no | — |
| 206 | C7×M16 | — | 2 | 1 | no | — |
| 207 | C7×M16 | — | 2 | 1 | no | — |
| 208 | C7×M16 | — | 2 | 1 | no | — |
| 209 | C7×M16 | — | 2 | 1 | no | — |
| 210 | C7×M16 | — | 2 | 1 | no | — |
| 211 | C7×M16 | — | 2 | 1 | no | — |
| 212 | C2×C7×C8 | — | 2 | 1 | no | — |
| 213 | C2×C7×C8 | — | 2 | 1 | no | — |
| 214 | C2×C7×C8 | — | 2 | 1 | no | — |
| 215 | C2×C7×C8 | — | 2 | 1 | no | — |
| 216 | C2×C7×C8 | — | 2 | 1 | no | — |
| 217 | C2×C7×C8 | C2×D4 | 1 | 2 | yes | — |
| 218 | C7×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 219 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 220 | C42×C7 | — | 2 | 1 | no | — |
| 221 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 222 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 223 | C22⋊Dic7 | — | 4 | 2 | no | — |
| 224 | C22⋊Dic7 | — | 4 | 2 | no | — |
| 225 | #1142 | — | 4 | 2 | no | — |
| 226 | #1141 | — | 2 | 4 | no | — |
| 227 | #1141 | — | 2 | 4 | no | — |
| 228 | #1141 | — | 4 | 2 | no | — |
| 229 | #1141 | — | 4 | 2 | no | — |
| 230 | #1141 | — | 4 | 2 | no | — |
| 231 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 232 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 233 | C4⋊Dic7 | C2×D4 | 1 | 2 | yes | — |
| 234 | C4⋊Dic7 | C2×D4 | 1 | 2 | yes | — |
| 235 | C4×Dic7 | — | 2 | 1 | no | — |
| 236 | C4×Dic7 | — | 2 | 1 | no | — |
| 237 | C4×Dic7 | — | 2 | 1 | no | — |
| 238 | C4×Dic7 | #41 | 1 | 2 | yes | — |
| 239 | #1136 | — | 2 | 1 | no | — |
| 240 | #1136 | — | 2 | 1 | no | — |
| 241 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 242 | C2×C7⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 243 | C2×C7⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 244 | C2×C7⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 245 | C2×C7⋊C8 | #41 | 1 | 2 | yes | — |
| 246 | D56 | — | 4 | 4 | no | — |
| 247 | D56 | — | 4 | 2 | no | — |
| 248 | #1132 | — | 4 | 2 | no | — |
| 249 | #1131 | — | 4 | 2 | no | — |
| 250 | C8×D7 | — | 4 | 2 | no | — |
| 251 | C2×AGL(1,ℤ/8) | — | 7 | 1 | no | — |
| 252 | C2×AGL(1,ℤ/8) | — | 7 | 1 | no | — |
| 253 | C22×D8 | — | 7 | 1 | no | — |
| 254 | C22×D8 | — | 7 | 1 | no | — |
| 255 | C22×D8 | — | 7 | 1 | no | — |
| 256 | C22×D8 | C2×D7 | 1 | 1 | yes | characteristic |
| 257 | C2×#131 | — | 7 | 1 | no | — |
| 258 | #535 | — | 7 | 1 | no | — |
| 259 | #535 | — | 7 | 1 | no | — |
| 260 | C2×#127 | — | 7 | 1 | no | — |
| 261 | C2×#127 | — | 7 | 1 | no | — |
| 262 | #518 | — | 7 | 1 | no | — |
| 263 | #518 | — | 7 | 1 | no | — |
| 264 | #493 | — | 14 | 4 | no | — |
| 265 | #472 | — | 14 | 4 | no | — |
| 266 | #469 | — | 14 | 2 | no | — |
| 267 | #466 | — | 14 | 2 | no | — |
| 268 | #463 | — | 14 | 2 | no | — |
| 269 | #463 | — | 14 | 2 | no | — |
| 270 | #459 | — | 14 | 2 | no | — |
| 271 | #459 | — | 14 | 2 | no | — |
| 272 | #442 | — | 14 | 2 | no | — |
| 273 | C4×D8 | — | 14 | 2 | no | — |
| 274 | C2×#108 | — | 7 | 1 | no | — |
| 275 | #427 | — | 7 | 1 | no | — |
| 276 | #424 | — | 7 | 1 | no | — |
| 277 | #424 | C2×D7 | 1 | 1 | yes | characteristic |
| 278 | C2×#104 | — | 7 | 1 | no | — |
| 279 | #418 | — | 7 | 1 | no | — |
| 280 | #418 | — | 7 | 1 | no | — |
| 281 | #418 | — | 7 | 1 | no | — |
| 282 | #418 | — | 7 | 1 | no | — |
| 283 | #418 | C2×D7 | 1 | 1 | yes | characteristic |
| 284 | #418 | C2×D7 | 1 | 1 | yes | characteristic |
| 285 | #416 | — | 7 | 1 | no | — |
| 286 | C2×#100 | — | 7 | 1 | no | — |
| 287 | C2×#100 | — | 7 | 1 | no | — |
| 288 | C2×#100 | C2×D7 | 1 | 1 | yes | characteristic |
| 289 | C2×#100 | C2×D7 | 1 | 1 | yes | characteristic |
| 290 | #405 | — | 7 | 1 | no | — |
| 291 | C2×C4×C8 | — | 7 | 1 | no | — |
| 292 | #341 | C2×D7 | 1 | 1 | yes | characteristic |
| 293 | #339 | — | 7 | 1 | no | — |
| 294 | #339 | — | 7 | 1 | no | — |
| 295 | #339 | — | 7 | 1 | no | — |
| 296 | C23×C7 | — | 2 | 2 | no | — |
| 297 | C23×C7 | — | 4 | 1 | no | — |
| 298 | C23×C7 | — | 4 | 1 | no | — |
| 299 | C23×C7 | — | 4 | 1 | no | — |
| 300 | C23×C7 | — | 4 | 1 | no | — |
| 301 | C23×C7 | — | 4 | 1 | no | — |
| 302 | C23×C7 | — | 8 | 2 | no | — |
| 303 | C23×C7 | — | 8 | 2 | no | — |
| 304 | C23×C7 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 305 | C22×D7 | — | 2 | 1 | no | — |
| 306 | C22×D7 | — | 2 | 2 | no | — |
| 307 | C22×D7 | — | 4 | 1 | no | — |
| 308 | C22×D7 | — | 4 | 1 | no | — |
| 309 | C22×D7 | — | 4 | 1 | no | — |
| 310 | C22×D7 | — | 4 | 1 | no | — |
| 311 | C22×D7 | — | 4 | 1 | no | — |
| 312 | C22×D7 | — | 8 | 2 | no | — |
| 313 | C22×D7 | — | 8 | 2 | no | — |
| 314 | C7×D4 | — | 2 | 2 | no | — |
| 315 | C7×D4 | — | 2 | 2 | no | — |
| 316 | C7×D4 | — | 4 | 1 | no | — |
| 317 | C7×D4 | — | 4 | 1 | no | — |
| 318 | C7×D4 | — | 4 | 1 | no | — |
| 319 | C7×D4 | — | 4 | 1 | no | — |
| 320 | C7×D4 | — | 4 | 1 | no | — |
| 321 | C7×D4 | — | 4 | 1 | no | — |
| 322 | C2×C4×C7 | — | 2 | 2 | no | — |
| 323 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 324 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 325 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 326 | C2×C4×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 327 | C2×C4×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 328 | C2×C4×C7 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 329 | C22⋊D7 | — | 4 | 1 | no | — |
| 330 | C22⋊D7 | — | 4 | 1 | no | — |
| 331 | C22⋊D7 | — | 8 | 8 | no | — |
| 332 | C22⋊D7 | — | 8 | 8 | no | — |
| 333 | C22⋊D7 | — | 16 | 2 | no | — |
| 334 | C2×Dic7 | — | 2 | 4 | no | — |
| 335 | C2×Dic7 | — | 2 | 2 | no | — |
| 336 | C2×Dic7 | — | 2 | 2 | no | — |
| 337 | C2×Dic7 | — | 2 | 2 | no | — |
| 338 | C2×Dic7 | — | 2 | 1 | no | — |
| 339 | C2×Dic7 | — | 16 | 2 | no | — |
| 340 | D28 | — | 2 | 2 | no | — |
| 341 | D28 | — | 2 | 1 | no | — |
| 342 | D28 | — | 2 | 2 | no | — |
| 343 | D28 | — | 2 | 1 | no | — |
| 344 | D28 | — | 4 | 1 | no | — |
| 345 | D28 | — | 4 | 1 | no | — |
| 346 | D28 | — | 4 | 1 | no | — |
| 347 | D28 | — | 4 | 1 | no | — |
| 348 | D28 | — | 4 | 1 | no | — |
| 349 | D28 | — | 4 | 1 | no | — |
| 350 | D28 | — | 16 | 2 | no | — |
| 351 | C4×D7 | — | 4 | 1 | no | — |
| 352 | C4×D7 | — | 4 | 1 | no | — |
| 353 | C4×D7 | — | 16 | 2 | no | — |
| 354 | Dic14 | — | 2 | 1 | no | — |
| 355 | Dic14 | — | 2 | 1 | no | — |
| 356 | C7×C8 | — | 2 | 2 | no | — |
| 357 | C7×C8 | — | 4 | 1 | no | — |
| 358 | C7×C8 | — | 4 | 1 | no | — |
| 359 | C7×C8 | — | 4 | 1 | no | — |
| 360 | C7⋊C8 | — | 4 | 1 | no | — |
| 361 | C7⋊C8 | #121 | 1 | 2 | yes | — |
| 362 | C7⋊C8 | #121 | 1 | 2 | yes | — |
| 363 | C2×#41 | — | 7 | 1 | no | — |
| 364 | C22×D4 | — | 7 | 1 | no | — |
| 365 | C22×D4 | — | 7 | 1 | no | — |
| 366 | C22×D4 | — | 28 | 1 | no | — |
| 367 | C22×D4 | — | 28 | 1 | no | — |
| 368 | C22×D4 | C22×D7 | 1 | 1 | yes | characteristic |
| 369 | C22×D4 | C22×D7 | 1 | 1 | yes | characteristic |
| 370 | AGL(1,ℤ/8) | — | 14 | 2 | no | — |
| 371 | AGL(1,ℤ/8) | — | 14 | 2 | no | — |
| 372 | AGL(1,ℤ/8) | — | 28 | 1 | no | — |
| 373 | AGL(1,ℤ/8) | — | 28 | 1 | no | — |
| 374 | C2×SD16 | — | 14 | 1 | no | — |
| 375 | C2×SD16 | — | 14 | 1 | no | — |
| 376 | C2×D8 | — | 2 | 2 | no | — |
| 377 | C2×D8 | — | 2 | 2 | no | — |
| 378 | C2×D8 | — | 4 | 1 | no | — |
| 379 | C2×D8 | — | 7 | 4 | no | — |
| 380 | C2×D8 | — | 14 | 2 | no | — |
| 381 | C2×D8 | — | 14 | 1 | no | — |
| 382 | C2×D8 | — | 14 | 2 | no | — |
| 383 | C2×D8 | — | 14 | 1 | no | — |
| 384 | C2×D8 | — | 14 | 1 | no | — |
| 385 | C2×D8 | — | 14 | 2 | no | — |
| 386 | C2×D8 | — | 14 | 1 | no | — |
| 387 | C2×D8 | — | 14 | 1 | no | — |
| 388 | C2×D8 | — | 14 | 2 | no | — |
| 389 | C2×D8 | — | 14 | 1 | no | — |
| 390 | C2×D8 | — | 14 | 2 | no | — |
| 391 | C2×D8 | — | 28 | 1 | no | — |
| 392 | #131 | — | 14 | 2 | no | — |
| 393 | #131 | — | 14 | 2 | no | — |
| 394 | C2×M16 | — | 7 | 1 | no | — |
| 395 | C2×M16 | — | 14 | 1 | no | — |
| 396 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 397 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 398 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 399 | C22×C8 | — | 7 | 1 | no | — |
| 400 | C22×C8 | — | 14 | 1 | no | — |
| 401 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 402 | #127 | — | 14 | 1 | no | — |
| 403 | #127 | — | 14 | 2 | no | — |
| 404 | #127 | — | 14 | 2 | no | — |
| 405 | #127 | — | 14 | 2 | no | — |
| 406 | #127 | — | 14 | 1 | no | — |
| 407 | #127 | — | 14 | 2 | no | — |
| 408 | #124 | — | 14 | 1 | no | — |
| 409 | #124 | — | 14 | 1 | no | — |
| 410 | #121 | — | 14 | 2 | no | — |
| 411 | #121 | — | 14 | 2 | no | — |
| 412 | #120 | — | 28 | 1 | no | — |
| 413 | #120 | — | 28 | 1 | no | — |
| 414 | C4×D4 | — | 14 | 2 | no | — |
| 415 | C4×D4 | — | 14 | 2 | no | — |
| 416 | C4×D4 | — | 14 | 2 | no | — |
| 417 | C4×D4 | — | 14 | 2 | no | — |
| 418 | #117 | — | 7 | 1 | no | — |
| 419 | #117 | — | 7 | 1 | no | — |
| 420 | #117 | C22×D7 | 1 | 1 | yes | characteristic |
| 421 | C2×C22⋊C4 | — | 28 | 1 | no | — |
| 422 | C2×C22⋊C4 | — | 28 | 1 | no | — |
| 423 | C2×C42 | — | 7 | 1 | no | — |
| 424 | #108 | — | 14 | 2 | no | — |
| 425 | #107 | — | 7 | 2 | no | — |
| 426 | #106 | — | 7 | 2 | no | — |
| 427 | C4⋊C8 | — | 2 | 2 | no | — |
| 428 | C4⋊C8 | — | 14 | 2 | no | — |
| 429 | #104 | — | 14 | 2 | no | — |
| 430 | #103 | — | 7 | 2 | no | — |
| 431 | #102 | — | 2 | 2 | no | — |
| 432 | #102 | — | 2 | 2 | no | — |
| 433 | #102 | — | 7 | 2 | no | — |
| 434 | #102 | — | 14 | 2 | no | — |
| 435 | #102 | — | 14 | 2 | no | — |
| 436 | #102 | — | 14 | 2 | no | — |
| 437 | #102 | — | 14 | 2 | no | — |
| 438 | #100 | — | 2 | 2 | no | — |
| 439 | #100 | — | 4 | 1 | no | — |
| 440 | #100 | — | 14 | 2 | no | — |
| 441 | #100 | — | 28 | 1 | no | — |
| 442 | #97 | — | 14 | 1 | no | — |
| 443 | C4×C8 | — | 14 | 2 | no | — |
| 444 | C4×C8 | — | 14 | 1 | no | — |
| 445 | C22×C7 | — | 2 | 2 | no | — |
| 446 | C22×C7 | — | 4 | 2 | no | — |
| 447 | C22×C7 | — | 8 | 2 | no | — |
| 448 | C22×C7 | — | 8 | 2 | no | — |
| 449 | C22×C7 | — | 8 | 2 | no | — |
| 450 | C22×C7 | — | 8 | 1 | no | — |
| 451 | C22×C7 | — | 8 | 2 | no | — |
| 452 | C22×C7 | — | 16 | 1 | no | — |
| 453 | C22×C7 | — | 16 | 1 | no | — |
| 454 | C22×C7 | #540 | 1 | 1 | yes | characteristic |
| 455 | C22×C7 | D42 | 1 | 1 | yes | characteristic |
| 456 | C22×C7 | #546 | 1 | 1 | yes | characteristic |
| 457 | C2×D7 | — | 4 | 1 | no | — |
| 458 | C2×D7 | — | 4 | 2 | no | — |
| 459 | C2×D7 | — | 4 | 2 | no | — |
| 460 | C2×D7 | — | 8 | 2 | no | — |
| 461 | C2×D7 | — | 8 | 2 | no | — |
| 462 | C2×D7 | — | 8 | 2 | no | — |
| 463 | C2×D7 | — | 8 | 1 | no | — |
| 464 | C2×D7 | — | 8 | 2 | no | — |
| 465 | C2×D7 | — | 16 | 1 | no | — |
| 466 | C2×D7 | — | 16 | 1 | no | — |
| 467 | C4×C7 | — | 4 | 2 | no | — |
| 468 | C4×C7 | C2×#121 | 1 | 1 | yes | characteristic |
| 469 | C4×C7 | #532 | 1 | 1 | yes | characteristic |
| 470 | C4×C7 | D42 | 1 | 1 | yes | characteristic |
| 471 | C4×C7 | #550 | 1 | 1 | yes | characteristic |
| 472 | Dic7 | — | 2 | 4 | no | — |
| 473 | Dic7 | — | 4 | 1 | no | — |
| 474 | Dic7 | — | 4 | 2 | no | — |
| 475 | Dic7 | — | 4 | 2 | no | — |
| 476 | C24 | — | 2 | 1 | no | — |
| 477 | C24 | — | 2 | 1 | no | — |
| 478 | C24 | — | 14 | 1 | no | — |
| 479 | C24 | — | 14 | 1 | no | — |
| 480 | #41 | — | 14 | 1 | no | — |
| 481 | #41 | — | 14 | 1 | no | — |
| 482 | #41 | — | 14 | 1 | no | — |
| 483 | #41 | — | 14 | 1 | no | — |
| 484 | C2×Q8 | — | 7 | 1 | no | — |
| 485 | C2×D4 | — | 2 | 1 | no | — |
| 486 | C2×D4 | — | 2 | 1 | no | — |
| 487 | C2×D4 | — | 2 | 1 | no | — |
| 488 | C2×D4 | — | 2 | 1 | no | — |
| 489 | C2×D4 | — | 2 | 1 | no | — |
| 490 | C2×D4 | — | 2 | 1 | no | — |
| 491 | C2×D4 | — | 2 | 1 | no | — |
| 492 | C2×D4 | — | 2 | 1 | no | — |
| 493 | C2×D4 | — | 2 | 1 | no | — |
| 494 | C2×D4 | — | 2 | 1 | no | — |
| 495 | C2×D4 | — | 2 | 1 | no | — |
| 496 | C2×D4 | — | 7 | 2 | no | — |
| 497 | C2×D4 | — | 7 | 1 | no | — |
| 498 | C2×D4 | — | 14 | 1 | no | — |
| 499 | C2×D4 | — | 14 | 1 | no | — |
| 500 | C2×D4 | — | 14 | 1 | no | — |
| 501 | C2×D4 | — | 14 | 1 | no | — |
| 502 | C2×D4 | — | 14 | 1 | no | — |
| 503 | C2×D4 | — | 14 | 1 | no | — |
| 504 | C2×D4 | — | 14 | 1 | no | — |
| 505 | C2×D4 | — | 14 | 1 | no | — |
| 506 | C2×D4 | — | 14 | 1 | no | — |
| 507 | C2×D4 | — | 14 | 1 | no | — |
| 508 | C2×D4 | — | 14 | 1 | no | — |
| 509 | C2×D4 | — | 14 | 1 | no | — |
| 510 | C2×D4 | — | 28 | 2 | no | — |
| 511 | C2×D4 | — | 28 | 4 | no | — |
| 512 | C2×D4 | — | 28 | 4 | no | — |
| 513 | C2×D4 | — | 28 | 2 | no | — |
| 514 | C2×D4 | — | 56 | 4 | no | — |
| 515 | C2×D4 | — | 56 | 4 | no | — |
| 516 | C2×D4 | D4×D7 | 1 | 2 | yes | — |
| 517 | C22×C4 | — | 14 | 1 | no | — |
| 518 | C22×C4 | — | 14 | 1 | no | — |
| 519 | C22×C4 | — | 28 | 2 | no | — |
| 520 | C22×C4 | — | 28 | 2 | no | — |
| 521 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 522 | SD16 | — | 28 | 2 | no | — |
| 523 | SD16 | — | 28 | 2 | no | — |
| 524 | D8 | — | 4 | 4 | no | — |
| 525 | D8 | — | 14 | 4 | no | — |
| 526 | D8 | — | 14 | 4 | no | — |
| 527 | D8 | — | 28 | 4 | no | — |
| 528 | D8 | — | 28 | 2 | no | — |
| 529 | D8 | — | 28 | 2 | no | — |
| 530 | D8 | — | 28 | 2 | no | — |
| 531 | D8 | — | 28 | 2 | no | — |
| 532 | M16 | — | 2 | 1 | no | — |
| 533 | M16 | — | 2 | 1 | no | — |
| 534 | M16 | — | 2 | 1 | no | — |
| 535 | M16 | — | 2 | 1 | no | — |
| 536 | M16 | — | 2 | 1 | no | — |
| 537 | M16 | — | 2 | 1 | no | — |
| 538 | M16 | — | 14 | 1 | no | — |
| 539 | M16 | — | 14 | 1 | no | — |
| 540 | M16 | — | 28 | 2 | no | — |
| 541 | C2×C8 | — | 2 | 1 | no | — |
| 542 | C2×C8 | — | 2 | 1 | no | — |
| 543 | C2×C8 | — | 2 | 1 | no | — |
| 544 | C2×C8 | — | 2 | 1 | no | — |
| 545 | C2×C8 | — | 2 | 1 | no | — |
| 546 | C2×C8 | — | 7 | 1 | no | — |
| 547 | C2×C8 | — | 7 | 2 | no | — |
| 548 | C2×C8 | — | 7 | 1 | no | — |
| 549 | C2×C8 | — | 7 | 2 | no | — |
| 550 | C2×C8 | — | 14 | 1 | no | — |
| 551 | C2×C8 | — | 28 | 2 | no | — |
| 552 | C2×C8 | D4×D7 | 1 | 2 | yes | — |
| 553 | C4⋊C4 | — | 7 | 2 | no | — |
| 554 | C4⋊C4 | — | 7 | 2 | no | — |
| 555 | C4⋊C4 | D4×D7 | 1 | 2 | yes | — |
| 556 | C22⋊C4 | — | 2 | 1 | no | — |
| 557 | C22⋊C4 | — | 14 | 1 | no | — |
| 558 | C22⋊C4 | — | 14 | 1 | no | — |
| 559 | C22⋊C4 | — | 28 | 2 | no | — |
| 560 | C22⋊C4 | — | 28 | 2 | no | — |
| 561 | C22⋊C4 | — | 28 | 2 | no | — |
| 562 | C22⋊C4 | — | 28 | 2 | no | — |
| 563 | C42 | — | 2 | 1 | no | — |
| 564 | C42 | — | 7 | 2 | no | — |
| 565 | C42 | — | 14 | 1 | no | — |
| 566 | C42 | — | 14 | 1 | no | — |
| 567 | C42 | — | 14 | 1 | no | — |
| 568 | C2×C7 | — | 2 | 1 | no | — |
| 569 | C2×C7 | — | 2 | 1 | no | — |
| 570 | C2×C7 | — | 8 | 2 | no | — |
| 571 | C2×C7 | — | 16 | 1 | no | — |
| 572 | C2×C7 | #2428 | 1 | 1 | yes | characteristic |
| 573 | C2×C7 | #3292 | 1 | 2 | yes | — |
| 574 | D7 | — | 8 | 1 | no | — |
| 575 | D7 | — | 8 | 2 | no | — |
| 576 | D7 | — | 16 | 1 | no | — |
| 577 | C23 | — | 2 | 2 | no | — |
| 578 | C23 | — | 4 | 1 | no | — |
| 579 | C23 | — | 4 | 1 | no | — |
| 580 | C23 | — | 4 | 1 | no | — |
| 581 | C23 | — | 4 | 1 | no | — |
| 582 | C23 | — | 4 | 1 | no | — |
| 583 | C23 | — | 8 | 2 | no | — |
| 584 | C23 | — | 8 | 2 | no | — |
| 585 | C23 | — | 14 | 1 | no | — |
| 586 | C23 | — | 14 | 2 | no | — |
| 587 | C23 | — | 28 | 1 | no | — |
| 588 | C23 | — | 28 | 1 | no | — |
| 589 | C23 | — | 28 | 1 | no | — |
| 590 | C23 | — | 28 | 1 | no | — |
| 591 | C23 | — | 28 | 1 | no | — |
| 592 | C23 | — | 56 | 2 | no | — |
| 593 | C23 | — | 56 | 2 | no | — |
| 594 | C23 | #6553 | 1 | 1 | yes | characteristic |
| 595 | Q8 | — | 14 | 1 | no | — |
| 596 | Q8 | — | 14 | 1 | no | — |
| 597 | D4 | — | 2 | 2 | no | — |
| 598 | D4 | — | 2 | 2 | no | — |
| 599 | D4 | — | 4 | 1 | no | — |
| 600 | D4 | — | 4 | 1 | no | — |
| 601 | D4 | — | 4 | 1 | no | — |
| 602 | D4 | — | 4 | 1 | no | — |
| 603 | D4 | — | 4 | 1 | no | — |
| 604 | D4 | — | 4 | 1 | no | — |
| 605 | D4 | — | 14 | 1 | no | — |
| 606 | D4 | — | 14 | 2 | no | — |
| 607 | D4 | — | 14 | 2 | no | — |
| 608 | D4 | — | 14 | 1 | no | — |
| 609 | D4 | — | 28 | 1 | no | — |
| 610 | D4 | — | 28 | 1 | no | — |
| 611 | D4 | — | 28 | 1 | no | — |
| 612 | D4 | — | 28 | 1 | no | — |
| 613 | D4 | — | 28 | 1 | no | — |
| 614 | D4 | — | 28 | 1 | no | — |
| 615 | D4 | — | 28 | 1 | no | — |
| 616 | D4 | — | 28 | 1 | no | — |
| 617 | D4 | — | 56 | 8 | no | — |
| 618 | D4 | — | 56 | 8 | no | — |
| 619 | D4 | — | 112 | 2 | no | — |
| 620 | D4 | — | 112 | 2 | no | — |
| 621 | C2×C4 | — | 2 | 2 | no | — |
| 622 | C2×C4 | — | 14 | 4 | no | — |
| 623 | C2×C4 | — | 14 | 2 | no | — |
| 624 | C2×C4 | — | 14 | 2 | no | — |
| 625 | C2×C4 | — | 14 | 2 | no | — |
| 626 | C2×C4 | — | 14 | 1 | no | — |
| 627 | C2×C4 | — | 28 | 1 | no | — |
| 628 | C2×C4 | — | 28 | 1 | no | — |
| 629 | C2×C4 | — | 112 | 2 | no | — |
| 630 | C2×C4 | — | 112 | 2 | no | — |
| 631 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 632 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 633 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 634 | C2×C4 | #6548 | 1 | 1 | yes | characteristic |
| 635 | C2×C4 | D7×#41 | 1 | 1 | yes | characteristic |
| 636 | C2×C4 | D7×#41 | 1 | 1 | yes | characteristic |
| 637 | C8 | — | 2 | 2 | no | — |
| 638 | C8 | — | 4 | 1 | no | — |
| 639 | C8 | — | 4 | 1 | no | — |
| 640 | C8 | — | 4 | 1 | no | — |
| 641 | C8 | — | 7 | 2 | no | — |
| 642 | C8 | — | 7 | 2 | no | — |
| 643 | C8 | — | 28 | 1 | no | — |
| 644 | C7 | #25434 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 645 | C22 | — | 2 | 2 | no | — |
| 646 | C22 | — | 4 | 2 | no | — |
| 647 | C22 | — | 8 | 2 | no | — |
| 648 | C22 | — | 8 | 2 | no | — |
| 649 | C22 | — | 8 | 2 | no | — |
| 650 | C22 | — | 8 | 2 | no | — |
| 651 | C22 | — | 8 | 1 | no | — |
| 652 | C22 | — | 16 | 1 | no | — |
| 653 | C22 | — | 16 | 1 | no | — |
| 654 | C22 | — | 28 | 2 | no | — |
| 655 | C22 | — | 28 | 1 | no | — |
| 656 | C22 | — | 28 | 2 | no | — |
| 657 | C22 | — | 56 | 2 | no | — |
| 658 | C22 | — | 56 | 2 | no | — |
| 659 | C22 | — | 56 | 2 | no | — |
| 660 | C22 | — | 56 | 2 | no | — |
| 661 | C22 | — | 56 | 1 | no | — |
| 662 | C22 | — | 112 | 1 | no | — |
| 663 | C22 | — | 112 | 1 | no | — |
| 664 | C22 | #90300 | 1 | 1 | yes | characteristic |
| 665 | C22 | #90345 | 1 | 1 | yes | characteristic |
| 666 | C22 | #90354 | 1 | 1 | yes | characteristic |
| 667 | C4 | — | 4 | 2 | no | — |
| 668 | C4 | — | 14 | 4 | no | — |
| 669 | C4 | — | 28 | 2 | no | — |
| 670 | C4 | — | 28 | 2 | no | — |
| 671 | C4 | — | 28 | 1 | no | — |
| 672 | C4 | #90281 | 1 | 1 | yes | characteristic |
| 673 | C4 | #90290 | 1 | 1 | yes | characteristic |
| 674 | C4 | D7×#121 | 1 | 1 | yes | characteristic |
| 675 | C4 | #90359 | 1 | 1 | yes | characteristic |
| 676 | C2 | — | 2 | 1 | no | — |
| 677 | C2 | — | 2 | 1 | no | — |
| 678 | C2 | — | 8 | 2 | no | — |
| 679 | C2 | — | 16 | 1 | no | — |
| 680 | C2 | — | 56 | 1 | no | — |
| 681 | C2 | — | 56 | 2 | no | — |
| 682 | C2 | — | 112 | 1 | no | — |
| 683 | C2 | #11734348 | 1 | 1 | yes | characteristic |
| 684 | C2 | #11738386 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#89923 | C2 | semidirect |
| 2. #11741271 | C2 | semidirect |
| 3. #11736531 | C2 | semidirect |
| 4. #11736377 | C2 | semidirect |
| 5. #11736360 | C2 | semidirect |
| 6. C2×#89521 | C2 | semidirect |
| 7. C7×#2045 | C2 | semidirect |
| 8. #11728291 | C2 | semidirect |
| 9. #11728078 | C2 | semidirect |
| 10. #11728077 | C2 | semidirect |
| 11. #11727836 | C2 | semidirect |
| 12. #11727828 | C2 | semidirect |
| 13. #11727824 | C2 | semidirect |
| 14. #11726686 | C2 | semidirect |
| 15. #11726680 | C2 | semidirect |
| 99. C2×#1141 | D4 | semidirect |
| 136. #6395 | D4 | semidirect |
| 137. #6390 | D4 | semidirect |
| 142. #6382 | D4 | semidirect |
| 143. #6381 | D4 | semidirect |
| 151. #2045 | D7 | semidirect |
| 644. C7 | #25434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89923 | 2 |
| #11741271 | 2 |
| #11736531 | 2 |
| #11736377 | 2 |
| #11736360 | 2 |
| C2×#89521 | 2 |
| C7×#2045 | 2 |
| #11728291 | 2 |
| #11728078 | 2 |
| #11728077 | 2 |
| #11727836 | 2 |
| #11727828 | 2 |
| #11727824 | 2 |
| #11726686 | 2 |
| #11726680 | 2 |
| #25434 | 7 |