Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
938 conjugacy classes of subgroups.
The subgroup lattice has 548 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#89669 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#89667 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11736658 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11736595 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11736010 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C7×#1952 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11728429 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11728382 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11727641 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11726762 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11726760 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×#6471 | C22 | 1 | 2 | yes | — |
| 13 | C2×#6471 | C22 | 1 | 2 | yes | — |
| 14 | C2×#6470 | C22 | 1 | 2 | yes | — |
| 15 | C2×#6467 | C22 | 1 | 1 | yes | characteristic |
| 16 | C22×D56 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#6464 | C22 | 1 | 1 | yes | characteristic |
| 18 | #90216 | C22 | 1 | 2 | yes | — |
| 19 | #90201 | C22 | 1 | 2 | yes | — |
| 20 | C2×C7×#108 | C22 | 1 | 1 | yes | characteristic |
| 21 | C7×#428 | C22 | 1 | 2 | yes | — |
| 22 | C2×C7×#107 | C22 | 1 | 1 | yes | characteristic |
| 23 | C7×#405 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#6399 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#6399 | C22 | 1 | 2 | yes | — |
| 26 | C2×#6397 | C22 | 1 | 2 | yes | — |
| 27 | C2×C8×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 28 | #89774 | C22 | 1 | 1 | yes | characteristic |
| 29 | #89760 | C22 | 1 | 2 | yes | — |
| 30 | #89738 | C22 | 1 | 2 | yes | — |
| 31 | C2×#6383 | C22 | 1 | 2 | yes | — |
| 32 | #89669 | — | 2 | 4 | no | — |
| 33 | #89667 | — | 2 | 4 | no | — |
| 34 | #89659 | — | 2 | 1 | no | — |
| 35 | #89658 | — | 2 | 2 | no | — |
| 36 | #89658 | — | 2 | 2 | no | — |
| 37 | #89655 | — | 2 | 2 | no | — |
| 38 | #89655 | — | 2 | 1 | no | — |
| 39 | #89637 | — | 2 | 2 | no | — |
| 40 | #89636 | — | 2 | 2 | no | — |
| 41 | #89484 | — | 2 | 2 | no | — |
| 42 | #89468 | — | 2 | 1 | no | — |
| 43 | #89467 | — | 2 | 1 | no | — |
| 44 | C7×#343 | C22 | 1 | 2 | yes | — |
| 45 | #89353 | C22 | 1 | 1 | yes | characteristic |
| 46 | #89327 | C22 | 1 | 1 | yes | characteristic |
| 47 | #25441 | — | 7 | 1 | no | maximal, Sylow |
| 48 | C2×#1157 | C23 | 1 | 1 | yes | characteristic |
| 49 | C2×#1157 | C23 | 1 | 2 | yes | — |
| 50 | C22×D28 | C23 | 1 | 2 | yes | — |
| 51 | C2×C7×M16 | C23 | 1 | 2 | yes | — |
| 52 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 53 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 54 | C7×#117 | C23 | 1 | 1 | yes | characteristic |
| 55 | C2×C7×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 56 | #6493 | — | 4 | 2 | no | — |
| 57 | C2×(C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 58 | C2×C4×Dic7 | C23 | 1 | 1 | yes | characteristic |
| 59 | C2×#1136 | C23 | 1 | 1 | yes | characteristic |
| 60 | C22×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 61 | #6471 | — | 2 | 4 | no | — |
| 62 | #6471 | — | 2 | 4 | no | — |
| 63 | #6471 | — | 4 | 2 | no | — |
| 64 | #6471 | — | 4 | 2 | no | — |
| 65 | #6470 | — | 2 | 4 | no | — |
| 66 | #6470 | — | 4 | 2 | no | — |
| 67 | C2×Dic28 | D4 | 1 | 1 | yes | characteristic |
| 68 | #6467 | — | 2 | 2 | no | — |
| 69 | #6467 | — | 2 | 2 | no | — |
| 70 | C2×D56 | — | 2 | 2 | no | — |
| 71 | C2×D56 | — | 2 | 2 | no | — |
| 72 | C2×D56 | — | 2 | 2 | no | — |
| 73 | C2×D56 | — | 2 | 1 | no | — |
| 74 | C2×D56 | — | 2 | 1 | no | — |
| 75 | C2×D56 | — | 2 | 2 | no | — |
| 76 | C2×D56 | D4 | 1 | 1 | yes | characteristic |
| 77 | C2×#1132 | — | 2 | 2 | no | — |
| 78 | C2×#1132 | — | 2 | 2 | no | — |
| 79 | C2×#1132 | D4 | 1 | 2 | yes | — |
| 80 | #6464 | — | 2 | 2 | no | — |
| 81 | #6464 | — | 2 | 2 | no | — |
| 82 | C2×#1131 | — | 2 | 1 | no | — |
| 83 | C2×#1131 | — | 2 | 2 | no | — |
| 84 | C2×C8×D7 | — | 2 | 1 | no | — |
| 85 | C2×C8×D7 | — | 2 | 2 | no | — |
| 86 | #6460 | — | 2 | 2 | no | — |
| 87 | #6460 | — | 2 | 2 | no | — |
| 88 | #6458 | — | 2 | 2 | no | — |
| 89 | #6458 | — | 2 | 2 | no | — |
| 90 | #6458 | — | 2 | 2 | no | — |
| 91 | #6458 | — | 2 | 2 | no | — |
| 92 | #6445 | — | 4 | 2 | no | — |
| 93 | #6438 | — | 2 | 2 | no | — |
| 94 | #6437 | — | 2 | 2 | no | — |
| 95 | C7×#108 | D4 | 1 | 4 | yes | complemented |
| 96 | C7×#107 | — | 2 | 1 | no | — |
| 97 | C7×#107 | — | 2 | 1 | no | — |
| 98 | C7×#107 | — | 2 | 2 | no | — |
| 99 | C7×#106 | — | 2 | 2 | no | — |
| 100 | C7×#97 | — | 2 | 1 | no | — |
| 101 | C4×C7×C8 | — | 2 | 1 | no | — |
| 102 | #6399 | — | 2 | 4 | no | — |
| 103 | #6399 | — | 2 | 2 | no | — |
| 104 | #6397 | — | 2 | 4 | no | — |
| 105 | C8×Dic7 | — | 2 | 2 | no | — |
| 106 | #6384 | — | 2 | 2 | no | — |
| 107 | #6384 | D4 | 1 | 1 | yes | characteristic |
| 108 | #6384 | D4 | 1 | 1 | yes | characteristic |
| 109 | #6383 | — | 2 | 2 | no | — |
| 110 | #6383 | — | 2 | 2 | no | — |
| 111 | #6383 | — | 2 | 2 | no | — |
| 112 | #6383 | D4 | 1 | 1 | yes | characteristic |
| 113 | #6383 | D4 | 1 | 1 | yes | characteristic |
| 114 | #3155 | — | 7 | 1 | no | — |
| 115 | C2×#472 | — | 7 | 1 | no | — |
| 116 | #3062 | — | 7 | 2 | no | — |
| 117 | #3061 | — | 7 | 1 | no | — |
| 118 | C2×#443 | — | 7 | 1 | no | — |
| 119 | #2037 | — | 7 | 2 | no | — |
| 120 | #2006 | — | 7 | 2 | no | — |
| 121 | #1970 | — | 7 | 1 | no | — |
| 122 | #1952 | D7 | 1 | 1 | yes | characteristic, complemented |
| 123 | #1907 | — | 7 | 2 | no | — |
| 124 | #1764 | — | 7 | 1 | no | — |
| 125 | C23×D7 | — | 2 | 2 | no | — |
| 126 | C22×C4×C7 | — | 2 | 2 | no | — |
| 127 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 128 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 129 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 130 | C22×Dic7 | — | 2 | 1 | no | — |
| 131 | #1157 | — | 2 | 1 | no | — |
| 132 | #1157 | — | 2 | 2 | no | — |
| 133 | #1157 | — | 2 | 1 | no | — |
| 134 | #1157 | — | 2 | 2 | no | — |
| 135 | #1157 | — | 2 | 2 | no | — |
| 136 | #1157 | — | 2 | 1 | no | — |
| 137 | #1157 | — | 2 | 2 | no | — |
| 138 | #1157 | — | 2 | 1 | no | — |
| 139 | C2×D28 | — | 2 | 2 | no | — |
| 140 | C2×D28 | — | 2 | 2 | no | — |
| 141 | C2×D28 | — | 2 | 2 | no | — |
| 142 | C2×D28 | — | 2 | 2 | no | — |
| 143 | C2×D28 | — | 2 | 2 | no | — |
| 144 | C2×D28 | — | 2 | 2 | no | — |
| 145 | C2×D28 | — | 4 | 2 | no | — |
| 146 | C2×D28 | — | 4 | 2 | no | — |
| 147 | C2×D28 | — | 4 | 2 | no | — |
| 148 | C2×D28 | C2×D4 | 1 | 2 | yes | — |
| 149 | C2×D28 | C2×D4 | 1 | 1 | yes | characteristic |
| 150 | C2×C4×D7 | — | 2 | 2 | no | — |
| 151 | C2×C4×D7 | — | 2 | 1 | no | — |
| 152 | C2×Dic14 | C2×D4 | 1 | 2 | yes | — |
| 153 | C2×Dic14 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C7×M16 | — | 2 | 2 | no | — |
| 155 | C7×M16 | — | 2 | 1 | no | — |
| 156 | C7×M16 | C2×D4 | 1 | 4 | yes | — |
| 157 | C7×M16 | #41 | 1 | 2 | yes | — |
| 158 | C2×C7×C8 | — | 2 | 1 | no | — |
| 159 | C2×C7×C8 | — | 2 | 2 | no | — |
| 160 | C2×C7×C8 | C2×D4 | 1 | 2 | yes | — |
| 161 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | C2×C7×C8 | #41 | 1 | 2 | yes | — |
| 164 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 165 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 166 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 169 | C42×C7 | — | 2 | 1 | no | — |
| 170 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 171 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 172 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 173 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 174 | (C2×D7)⋊C4 | — | 8 | 4 | no | — |
| 175 | C4⋊Dic7 | — | 4 | 2 | no | — |
| 176 | C4×Dic7 | — | 2 | 1 | no | — |
| 177 | C4×Dic7 | — | 2 | 1 | no | — |
| 178 | #1136 | — | 2 | 1 | no | — |
| 179 | #1136 | — | 2 | 1 | no | — |
| 180 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 181 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 182 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 183 | C2×C7⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | C2×C7⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 185 | Dic28 | — | 2 | 2 | no | — |
| 186 | D56 | — | 2 | 2 | no | — |
| 187 | D56 | — | 4 | 4 | no | — |
| 188 | D56 | — | 4 | 4 | no | — |
| 189 | D56 | — | 4 | 2 | no | — |
| 190 | D56 | — | 4 | 2 | no | — |
| 191 | #1132 | — | 2 | 4 | no | — |
| 192 | #1132 | — | 4 | 4 | no | — |
| 193 | #1132 | — | 4 | 4 | no | — |
| 194 | #1131 | — | 4 | 4 | no | — |
| 195 | #1131 | — | 4 | 2 | no | — |
| 196 | C8×D7 | — | 4 | 4 | no | — |
| 197 | C8×D7 | — | 4 | 2 | no | — |
| 198 | C2×AGL(1,ℤ/8) | — | 7 | 2 | no | — |
| 199 | C2×AGL(1,ℤ/8) | — | 7 | 2 | no | — |
| 200 | C2×#135 | — | 7 | 1 | no | — |
| 201 | C22×D8 | — | 7 | 1 | no | — |
| 202 | C2×#131 | — | 7 | 2 | no | — |
| 203 | C2×#131 | — | 7 | 1 | no | — |
| 204 | #537 | — | 7 | 2 | no | — |
| 205 | #535 | — | 7 | 2 | no | — |
| 206 | #496 | — | 14 | 2 | no | — |
| 207 | #495 | — | 14 | 1 | no | — |
| 208 | #493 | — | 14 | 1 | no | — |
| 209 | #472 | — | 14 | 4 | no | — |
| 210 | #469 | — | 14 | 2 | no | — |
| 211 | #468 | — | 14 | 2 | no | — |
| 212 | #468 | — | 14 | 2 | no | — |
| 213 | #467 | — | 14 | 1 | no | — |
| 214 | #466 | — | 14 | 2 | no | — |
| 215 | #466 | — | 14 | 1 | no | — |
| 216 | #465 | — | 14 | 2 | no | — |
| 217 | #443 | — | 14 | 4 | no | — |
| 218 | C2×#108 | C2×D7 | 1 | 1 | yes | characteristic |
| 219 | #428 | C2×D7 | 1 | 2 | yes | — |
| 220 | C2×#107 | C2×D7 | 1 | 1 | yes | characteristic |
| 221 | C2×#104 | — | 7 | 2 | no | — |
| 222 | C2×#104 | — | 7 | 1 | no | — |
| 223 | #417 | — | 7 | 2 | no | — |
| 224 | #416 | — | 7 | 1 | no | — |
| 225 | C2×#102 | — | 7 | 2 | no | — |
| 226 | C2×#100 | — | 7 | 2 | no | — |
| 227 | #405 | C2×D7 | 1 | 1 | yes | characteristic |
| 228 | C2×C4×C8 | — | 7 | 1 | no | — |
| 229 | #390 | — | 7 | 2 | no | — |
| 230 | #343 | C2×D7 | 1 | 2 | yes | — |
| 231 | #341 | — | 7 | 1 | no | — |
| 232 | #339 | — | 7 | 1 | no | — |
| 233 | C23×C7 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 234 | C22×D7 | — | 2 | 1 | no | — |
| 235 | C22×D7 | — | 2 | 2 | no | — |
| 236 | C22×D7 | — | 4 | 2 | no | — |
| 237 | C22×D7 | — | 4 | 2 | no | — |
| 238 | C22×D7 | — | 4 | 2 | no | — |
| 239 | C22×D7 | — | 8 | 2 | no | — |
| 240 | C22×D7 | — | 8 | 2 | no | — |
| 241 | C2×C4×C7 | — | 2 | 1 | no | — |
| 242 | C2×C4×C7 | — | 2 | 1 | no | — |
| 243 | C2×C4×C7 | — | 4 | 2 | no | — |
| 244 | C2×C4×C7 | — | 8 | 2 | no | — |
| 245 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 246 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 247 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 248 | C2×C4×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 249 | C2×C4×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 250 | C2×C4×C7 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 251 | C22⋊D7 | — | 4 | 1 | no | — |
| 252 | C22⋊D7 | — | 4 | 2 | no | — |
| 253 | C22⋊D7 | — | 4 | 1 | no | — |
| 254 | C22⋊D7 | — | 4 | 2 | no | — |
| 255 | C2×Dic7 | — | 2 | 2 | no | — |
| 256 | C2×Dic7 | — | 2 | 1 | no | — |
| 257 | C2×Dic7 | — | 2 | 2 | no | — |
| 258 | C2×Dic7 | — | 4 | 1 | no | — |
| 259 | C2×Dic7 | — | 4 | 1 | no | — |
| 260 | D28 | — | 2 | 2 | no | — |
| 261 | D28 | — | 2 | 1 | no | — |
| 262 | D28 | — | 2 | 1 | no | — |
| 263 | D28 | — | 2 | 2 | no | — |
| 264 | D28 | — | 4 | 2 | no | — |
| 265 | D28 | — | 4 | 2 | no | — |
| 266 | D28 | — | 4 | 2 | no | — |
| 267 | D28 | — | 4 | 2 | no | — |
| 268 | D28 | — | 16 | 2 | no | — |
| 269 | D28 | — | 16 | 2 | no | — |
| 270 | D28 | — | 16 | 2 | no | — |
| 271 | C4×D7 | — | 4 | 1 | no | — |
| 272 | C4×D7 | — | 4 | 2 | no | — |
| 273 | C4×D7 | — | 4 | 2 | no | — |
| 274 | C4×D7 | — | 4 | 1 | no | — |
| 275 | Dic14 | — | 2 | 2 | no | — |
| 276 | Dic14 | — | 2 | 1 | no | — |
| 277 | Dic14 | — | 2 | 1 | no | — |
| 278 | Dic14 | — | 2 | 2 | no | — |
| 279 | C7×C8 | — | 2 | 4 | no | — |
| 280 | C7×C8 | — | 2 | 2 | no | — |
| 281 | C7×C8 | #121 | 1 | 2 | yes | — |
| 282 | C7×C8 | #121 | 1 | 2 | yes | — |
| 283 | C7⋊C8 | — | 2 | 1 | no | — |
| 284 | C7⋊C8 | — | 2 | 1 | no | — |
| 285 | C7⋊C8 | — | 4 | 1 | no | — |
| 286 | C2×#41 | — | 7 | 2 | no | — |
| 287 | C2×#41 | — | 7 | 1 | no | — |
| 288 | C22×D4 | — | 7 | 2 | no | — |
| 289 | AGL(1,ℤ/8) | — | 14 | 4 | no | — |
| 290 | AGL(1,ℤ/8) | — | 14 | 4 | no | — |
| 291 | AGL(1,ℤ/8) | — | 28 | 2 | no | — |
| 292 | AGL(1,ℤ/8) | — | 28 | 2 | no | — |
| 293 | #135 | — | 14 | 2 | no | — |
| 294 | #135 | — | 14 | 2 | no | — |
| 295 | C2×Q16 | — | 7 | 1 | no | — |
| 296 | C2×SD16 | — | 7 | 2 | no | — |
| 297 | C2×SD16 | — | 14 | 2 | no | — |
| 298 | C2×SD16 | — | 14 | 2 | no | — |
| 299 | C2×D8 | — | 7 | 1 | no | — |
| 300 | C2×D8 | — | 14 | 2 | no | — |
| 301 | C2×D8 | — | 14 | 2 | no | — |
| 302 | C2×D8 | — | 14 | 2 | no | — |
| 303 | C2×D8 | — | 14 | 1 | no | — |
| 304 | C2×D8 | — | 14 | 1 | no | — |
| 305 | C2×D8 | — | 14 | 2 | no | — |
| 306 | #131 | — | 14 | 4 | no | — |
| 307 | #131 | — | 14 | 2 | no | — |
| 308 | #131 | — | 14 | 2 | no | — |
| 309 | #131 | — | 28 | 2 | no | — |
| 310 | C2×M16 | — | 7 | 1 | no | — |
| 311 | C2×M16 | — | 14 | 2 | no | — |
| 312 | C2×M16 | — | 14 | 1 | no | — |
| 313 | C2×M16 | C22×D7 | 1 | 2 | yes | — |
| 314 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 315 | C22×C8 | — | 7 | 1 | no | — |
| 316 | C22×C8 | — | 14 | 2 | no | — |
| 317 | C22×C8 | — | 14 | 1 | no | — |
| 318 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 319 | #127 | — | 14 | 2 | no | — |
| 320 | #124 | — | 14 | 2 | no | — |
| 321 | C22⋊Q8 | — | 14 | 2 | no | — |
| 322 | C22⋊Q8 | — | 14 | 2 | no | — |
| 323 | #121 | — | 14 | 2 | no | — |
| 324 | #121 | — | 14 | 2 | no | — |
| 325 | #121 | — | 14 | 2 | no | — |
| 326 | #121 | — | 14 | 2 | no | — |
| 327 | #121 | — | 28 | 2 | no | — |
| 328 | #120 | — | 28 | 2 | no | — |
| 329 | #117 | C22×D7 | 1 | 1 | yes | characteristic |
| 330 | C2×C4⋊C4 | C22×D7 | 1 | 2 | yes | — |
| 331 | C2×C22⋊C4 | — | 28 | 2 | no | — |
| 332 | C2×C42 | — | 7 | 1 | no | — |
| 333 | #108 | D28 | 1 | 4 | yes | complemented |
| 334 | #107 | — | 2 | 1 | no | — |
| 335 | #107 | — | 2 | 1 | no | — |
| 336 | #107 | — | 2 | 2 | no | — |
| 337 | #106 | — | 2 | 2 | no | — |
| 338 | #104 | — | 14 | 4 | no | — |
| 339 | #104 | — | 14 | 2 | no | — |
| 340 | #103 | — | 7 | 1 | no | — |
| 341 | #103 | — | 7 | 1 | no | — |
| 342 | #103 | — | 14 | 2 | no | — |
| 343 | #102 | — | 7 | 1 | no | — |
| 344 | #102 | — | 7 | 1 | no | — |
| 345 | #102 | — | 14 | 2 | no | — |
| 346 | #102 | — | 14 | 2 | no | — |
| 347 | #102 | — | 14 | 2 | no | — |
| 348 | #100 | — | 14 | 4 | no | — |
| 349 | #97 | — | 2 | 1 | no | — |
| 350 | C4×C8 | — | 2 | 1 | no | — |
| 351 | C4×C8 | — | 14 | 2 | no | — |
| 352 | C22×C7 | — | 2 | 1 | no | — |
| 353 | C22×C7 | — | 2 | 1 | no | — |
| 354 | C22×C7 | #540 | 1 | 1 | yes | characteristic |
| 355 | C22×C7 | D42 | 1 | 1 | yes | characteristic |
| 356 | C22×C7 | #550 | 1 | 1 | yes | characteristic |
| 357 | C2×D7 | — | 4 | 1 | no | — |
| 358 | C2×D7 | — | 4 | 2 | no | — |
| 359 | C2×D7 | — | 4 | 2 | no | — |
| 360 | C2×D7 | — | 4 | 1 | no | — |
| 361 | C2×D7 | — | 4 | 2 | no | — |
| 362 | C2×D7 | — | 4 | 1 | no | — |
| 363 | C2×D7 | — | 8 | 4 | no | — |
| 364 | C2×D7 | — | 8 | 2 | no | — |
| 365 | C2×D7 | — | 8 | 2 | no | — |
| 366 | C2×D7 | — | 8 | 2 | no | — |
| 367 | C2×D7 | — | 16 | 2 | no | — |
| 368 | C4×C7 | — | 4 | 1 | no | — |
| 369 | C4×C7 | — | 4 | 1 | no | — |
| 370 | C4×C7 | — | 8 | 2 | no | — |
| 371 | C4×C7 | C2×#121 | 1 | 1 | yes | characteristic |
| 372 | C4×C7 | #532 | 1 | 1 | yes | characteristic |
| 373 | C4×C7 | D42 | 1 | 1 | yes | characteristic |
| 374 | C4×C7 | #546 | 1 | 1 | yes | characteristic |
| 375 | Dic7 | — | 4 | 2 | no | — |
| 376 | Dic7 | — | 4 | 2 | no | — |
| 377 | Dic7 | — | 4 | 1 | no | — |
| 378 | C24 | — | 14 | 2 | no | — |
| 379 | #41 | — | 14 | 2 | no | — |
| 380 | #41 | — | 14 | 1 | no | — |
| 381 | #41 | — | 14 | 1 | no | — |
| 382 | #41 | — | 14 | 1 | no | — |
| 383 | #41 | — | 14 | 2 | no | — |
| 384 | #41 | — | 14 | 2 | no | — |
| 385 | #41 | — | 14 | 2 | no | — |
| 386 | #41 | — | 14 | 1 | no | — |
| 387 | C2×Q8 | — | 7 | 1 | no | — |
| 388 | C2×Q8 | — | 7 | 2 | no | — |
| 389 | C2×D4 | — | 7 | 1 | no | — |
| 390 | C2×D4 | — | 7 | 2 | no | — |
| 391 | C2×D4 | — | 14 | 2 | no | — |
| 392 | C2×D4 | — | 14 | 1 | no | — |
| 393 | C2×D4 | — | 14 | 2 | no | — |
| 394 | C2×D4 | — | 14 | 2 | no | — |
| 395 | C2×D4 | — | 14 | 2 | no | — |
| 396 | C2×D4 | — | 14 | 2 | no | — |
| 397 | C2×D4 | — | 14 | 2 | no | — |
| 398 | C2×D4 | — | 14 | 2 | no | — |
| 399 | C2×D4 | — | 28 | 2 | no | — |
| 400 | C2×D4 | — | 28 | 2 | no | — |
| 401 | C2×D4 | — | 28 | 2 | no | — |
| 402 | C22×C4 | — | 2 | 2 | no | — |
| 403 | C22×C4 | — | 14 | 1 | no | — |
| 404 | C22×C4 | — | 14 | 2 | no | — |
| 405 | C22×C4 | — | 14 | 1 | no | — |
| 406 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 407 | Q16 | — | 14 | 2 | no | — |
| 408 | SD16 | — | 14 | 4 | no | — |
| 409 | SD16 | — | 28 | 4 | no | — |
| 410 | SD16 | — | 28 | 4 | no | — |
| 411 | D8 | — | 14 | 2 | no | — |
| 412 | D8 | — | 28 | 4 | no | — |
| 413 | D8 | — | 28 | 4 | no | — |
| 414 | D8 | — | 28 | 2 | no | — |
| 415 | D8 | — | 28 | 2 | no | — |
| 416 | M16 | — | 2 | 2 | no | — |
| 417 | M16 | — | 2 | 1 | no | — |
| 418 | M16 | — | 14 | 1 | no | — |
| 419 | M16 | — | 14 | 1 | no | — |
| 420 | M16 | — | 28 | 4 | no | — |
| 421 | M16 | — | 28 | 2 | no | — |
| 422 | M16 | C2×D28 | 1 | 4 | yes | — |
| 423 | M16 | #1161 | 1 | 2 | yes | — |
| 424 | C2×C8 | — | 2 | 1 | no | — |
| 425 | C2×C8 | — | 2 | 2 | no | — |
| 426 | C2×C8 | — | 7 | 1 | no | — |
| 427 | C2×C8 | — | 7 | 1 | no | — |
| 428 | C2×C8 | — | 14 | 1 | no | — |
| 429 | C2×C8 | — | 14 | 1 | no | — |
| 430 | C2×C8 | — | 14 | 1 | no | — |
| 431 | C2×C8 | — | 28 | 4 | no | — |
| 432 | C2×C8 | — | 28 | 2 | no | — |
| 433 | C2×C8 | C2×D28 | 1 | 2 | yes | — |
| 434 | C2×C8 | D4×D7 | 1 | 1 | yes | characteristic |
| 435 | C2×C8 | D4×D7 | 1 | 1 | yes | characteristic |
| 436 | C2×C8 | #1161 | 1 | 2 | yes | — |
| 437 | C4⋊C4 | — | 2 | 2 | no | — |
| 438 | C4⋊C4 | — | 2 | 2 | no | — |
| 439 | C4⋊C4 | — | 28 | 2 | no | — |
| 440 | C4⋊C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 441 | C4⋊C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 442 | C22⋊C4 | — | 2 | 1 | no | — |
| 443 | C22⋊C4 | — | 28 | 2 | no | — |
| 444 | C22⋊C4 | — | 28 | 2 | no | — |
| 445 | C22⋊C4 | — | 28 | 2 | no | — |
| 446 | C22⋊C4 | — | 28 | 2 | no | — |
| 447 | C22⋊C4 | — | 56 | 4 | no | — |
| 448 | C42 | — | 2 | 1 | no | — |
| 449 | C42 | — | 14 | 1 | no | — |
| 450 | C42 | — | 14 | 1 | no | — |
| 451 | C2×C7 | — | 2 | 1 | no | — |
| 452 | C2×C7 | — | 2 | 1 | no | — |
| 453 | C2×C7 | #2428 | 1 | 1 | yes | characteristic |
| 454 | C2×C7 | #3290 | 1 | 1 | yes | characteristic |
| 455 | C2×C7 | #3292 | 1 | 1 | yes | characteristic |
| 456 | D7 | — | 8 | 2 | no | — |
| 457 | D7 | — | 8 | 1 | no | — |
| 458 | D7 | — | 16 | 2 | no | — |
| 459 | C23 | — | 14 | 1 | no | — |
| 460 | C23 | — | 14 | 2 | no | — |
| 461 | C23 | — | 28 | 2 | no | — |
| 462 | C23 | — | 28 | 2 | no | — |
| 463 | C23 | — | 28 | 2 | no | — |
| 464 | C23 | — | 56 | 2 | no | — |
| 465 | C23 | — | 56 | 2 | no | — |
| 466 | C23 | #6553 | 1 | 1 | yes | characteristic |
| 467 | Q8 | — | 14 | 1 | no | — |
| 468 | Q8 | — | 14 | 2 | no | — |
| 469 | Q8 | — | 14 | 1 | no | — |
| 470 | Q8 | — | 14 | 2 | no | — |
| 471 | D4 | — | 14 | 1 | no | — |
| 472 | D4 | — | 14 | 2 | no | — |
| 473 | D4 | — | 14 | 1 | no | — |
| 474 | D4 | — | 14 | 2 | no | — |
| 475 | D4 | — | 28 | 2 | no | — |
| 476 | D4 | — | 28 | 1 | no | — |
| 477 | D4 | — | 28 | 2 | no | — |
| 478 | D4 | — | 28 | 1 | no | — |
| 479 | D4 | — | 28 | 2 | no | — |
| 480 | D4 | — | 28 | 2 | no | — |
| 481 | D4 | — | 28 | 2 | no | — |
| 482 | D4 | — | 28 | 2 | no | — |
| 483 | D4 | — | 112 | 2 | no | — |
| 484 | D4 | — | 112 | 2 | no | — |
| 485 | D4 | — | 112 | 2 | no | — |
| 486 | C2×C4 | — | 2 | 1 | no | — |
| 487 | C2×C4 | — | 2 | 1 | no | — |
| 488 | C2×C4 | — | 4 | 2 | no | — |
| 489 | C2×C4 | — | 8 | 2 | no | — |
| 490 | C2×C4 | — | 14 | 2 | no | — |
| 491 | C2×C4 | — | 14 | 2 | no | — |
| 492 | C2×C4 | — | 14 | 1 | no | — |
| 493 | C2×C4 | — | 28 | 1 | no | — |
| 494 | C2×C4 | — | 28 | 1 | no | — |
| 495 | C2×C4 | — | 28 | 2 | no | — |
| 496 | C2×C4 | — | 28 | 1 | no | — |
| 497 | C2×C4 | — | 28 | 2 | no | — |
| 498 | C2×C4 | — | 28 | 1 | no | — |
| 499 | C2×C4 | C22×D28 | 1 | 1 | yes | characteristic |
| 500 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 501 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 502 | C2×C4 | C2×#1161 | 1 | 1 | yes | characteristic |
| 503 | C2×C4 | C2×#1161 | 1 | 1 | yes | characteristic |
| 504 | C2×C4 | #6553 | 1 | 1 | yes | characteristic |
| 505 | C8 | — | 2 | 4 | no | — |
| 506 | C8 | — | 2 | 2 | no | — |
| 507 | C8 | — | 14 | 1 | no | — |
| 508 | C8 | — | 14 | 1 | no | — |
| 509 | C8 | — | 28 | 1 | no | — |
| 510 | C8 | #6458 | 1 | 2 | yes | — |
| 511 | C8 | #6458 | 1 | 2 | yes | — |
| 512 | C7 | #25441 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 513 | C22 | — | 2 | 1 | no | — |
| 514 | C22 | — | 2 | 1 | no | — |
| 515 | C22 | — | 28 | 2 | no | — |
| 516 | C22 | — | 28 | 1 | no | — |
| 517 | C22 | — | 28 | 2 | no | — |
| 518 | C22 | — | 28 | 1 | no | — |
| 519 | C22 | — | 28 | 2 | no | — |
| 520 | C22 | — | 28 | 1 | no | — |
| 521 | C22 | — | 56 | 4 | no | — |
| 522 | C22 | — | 56 | 2 | no | — |
| 523 | C22 | — | 56 | 2 | no | — |
| 524 | C22 | — | 56 | 2 | no | — |
| 525 | C22 | — | 112 | 2 | no | — |
| 526 | C22 | #90268 | 1 | 1 | yes | characteristic |
| 527 | C22 | #90300 | 1 | 1 | yes | characteristic |
| 528 | C22 | #90389 | 1 | 1 | yes | characteristic |
| 529 | C4 | — | 4 | 1 | no | — |
| 530 | C4 | — | 4 | 1 | no | — |
| 531 | C4 | — | 8 | 2 | no | — |
| 532 | C4 | — | 28 | 2 | no | — |
| 533 | C4 | — | 28 | 2 | no | — |
| 534 | C4 | — | 28 | 1 | no | — |
| 535 | C4 | C2×#6458 | 1 | 1 | yes | characteristic |
| 536 | C4 | D4×D28 | 1 | 1 | yes | characteristic |
| 537 | C4 | #90321 | 1 | 1 | yes | characteristic |
| 538 | C4 | #90416 | 1 | 1 | yes | characteristic |
| 539 | C2 | — | 2 | 1 | no | — |
| 540 | C2 | — | 2 | 1 | no | — |
| 541 | C2 | — | 56 | 2 | no | — |
| 542 | C2 | — | 56 | 1 | no | — |
| 543 | C2 | — | 112 | 2 | no | — |
| 544 | C2 | #11733665 | 1 | 1 | yes | characteristic |
| 545 | C2 | #11738386 | 1 | 1 | yes | characteristic |
| 546 | C2 | #11738391 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#89669 | C2 | semidirect |
| 2. C2×#89667 | C2 | semidirect |
| 3. #11736658 | C2 | semidirect |
| 4. #11736595 | C2 | semidirect |
| 5. #11736010 | C2 | semidirect |
| 6. C7×#1952 | C2 | semidirect |
| 7. #11728429 | C2 | semidirect |
| 8. #11728382 | C2 | semidirect |
| 9. #11727641 | C2 | semidirect |
| 10. #11726762 | C2 | semidirect |
| 11. #11726760 | C2 | semidirect |
| 95. C7×#108 | D4 | semidirect |
| 122. #1952 | D7 | semidirect |
| 333. #108 | D28 | semidirect |
| 512. C7 | #25441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89669 | 2 |
| C2×#89667 | 2 |
| #11736658 | 2 |
| #11736595 | 2 |
| #11736010 | 2 |
| C7×#1952 | 2 |
| #11728429 | 2 |
| #11728382 | 2 |
| #11727641 | 2 |
| #11726762 | 2 |
| #11726760 | 2 |
| #25441 | 7 |