Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1300 conjugacy classes of subgroups.
The subgroup lattice has 590 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11744355 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C7×#2889 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11741558 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11741259 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11736162 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11729774 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11727897 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11727891 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11727889 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11727871 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11727864 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×C7×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 13 | #90616 | C22 | 1 | 1 | yes | characteristic |
| 14 | C7×#568 | C22 | 1 | 2 | yes | complemented |
| 15 | #90529 | — | 2 | 4 | no | — |
| 16 | #90528 | — | 2 | 4 | no | — |
| 17 | #90521 | C22 | 1 | 1 | yes | characteristic |
| 18 | #90513 | — | 2 | 2 | no | — |
| 19 | #90513 | C22 | 1 | 2 | yes | — |
| 20 | C2×#6512 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #90510 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#6505 | — | 2 | 2 | no | — |
| 23 | C2×#6505 | C22 | 1 | 2 | yes | — |
| 24 | C22×#1143 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C2×#6471 | C22 | 1 | 2 | yes | — |
| 26 | C7×#413 | — | 2 | 2 | no | — |
| 27 | C7×#413 | C22 | 1 | 1 | yes | characteristic |
| 28 | C7×#413 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×C7×#101 | — | 2 | 2 | no | — |
| 30 | C2×C7×#101 | C22 | 1 | 2 | yes | complemented |
| 31 | #90010 | — | 2 | 2 | no | — |
| 32 | #90006 | C22 | 1 | 1 | yes | characteristic |
| 33 | #90005 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #89999 | — | 2 | 2 | no | — |
| 35 | #89997 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #89914 | — | 2 | 4 | no | — |
| 37 | #89913 | — | 2 | 4 | no | — |
| 38 | #89911 | C22 | 1 | 2 | yes | — |
| 39 | #89904 | C22 | 1 | 2 | yes | — |
| 40 | C2×#6397 | C22 | 1 | 2 | yes | complemented |
| 41 | #89901 | C22 | 1 | 2 | yes | — |
| 42 | #89897 | C22 | 1 | 2 | yes | complemented |
| 43 | #89525 | — | 2 | 2 | no | — |
| 44 | #89519 | — | 2 | 2 | no | — |
| 45 | #89353 | C22 | 1 | 2 | yes | complemented |
| 46 | #89351 | C22 | 1 | 2 | yes | complemented |
| 47 | #24422 | — | 7 | 1 | no | maximal, Sylow |
| 48 | C7×2−1+4 | — | 2 | 4 | no | — |
| 49 | C7×2−1+4 | — | 4 | 2 | no | — |
| 50 | C2×C7×#41 | — | 2 | 1 | no | — |
| 51 | C2×C7×#41 | — | 2 | 2 | no | — |
| 52 | C2×C7×#41 | D4 | 1 | 2 | yes | — |
| 53 | C2×C7×#41 | C23 | 1 | 1 | yes | characteristic |
| 54 | C2×C7×#41 | C23 | 1 | 1 | yes | characteristic |
| 55 | C22×C7×Q8 | — | 2 | 1 | no | — |
| 56 | C22×C7×Q8 | D4 | 1 | 2 | yes | — |
| 57 | C22×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 58 | #6554 | — | 2 | 2 | no | — |
| 59 | #6553 | — | 2 | 2 | no | — |
| 60 | D7×#41 | — | 4 | 2 | no | — |
| 61 | #6551 | — | 2 | 1 | no | — |
| 62 | #6548 | — | 2 | 1 | no | — |
| 63 | #6548 | — | 2 | 2 | no | — |
| 64 | C2×#1157 | — | 2 | 2 | no | — |
| 65 | C2×#1157 | C23 | 1 | 2 | yes | — |
| 66 | C22×D28 | C23 | 1 | 1 | yes | characteristic |
| 67 | C7×#131 | — | 2 | 4 | no | — |
| 68 | C7×#131 | — | 4 | 2 | no | — |
| 69 | C2×C7×M16 | — | 2 | 4 | no | — |
| 70 | C2×C7×M16 | C23 | 1 | 2 | yes | — |
| 71 | C2×C7×M16 | C23 | 1 | 2 | yes | — |
| 72 | #6514 | — | 2 | 4 | no | — |
| 73 | #6514 | D4 | 1 | 4 | yes | complemented |
| 74 | #6513 | — | 2 | 8 | no | — |
| 75 | #6513 | — | 2 | 4 | no | — |
| 76 | #6512 | — | 2 | 4 | no | — |
| 77 | #6512 | — | 2 | 4 | no | — |
| 78 | #6512 | D4 | 1 | 4 | yes | complemented |
| 79 | #6511 | — | 2 | 4 | no | — |
| 80 | #6510 | — | 2 | 1 | no | — |
| 81 | C2×#1144 | — | 2 | 4 | no | — |
| 82 | C2×#1144 | — | 2 | 2 | no | — |
| 83 | #6505 | — | 2 | 8 | no | — |
| 84 | #6505 | — | 2 | 2 | no | — |
| 85 | #6505 | — | 2 | 4 | no | — |
| 86 | #6505 | — | 2 | 4 | no | — |
| 87 | C2×#1143 | — | 2 | 4 | no | — |
| 88 | C2×#1143 | — | 2 | 2 | no | — |
| 89 | C2×#1143 | — | 2 | 2 | no | — |
| 90 | C2×#1143 | — | 2 | 1 | no | — |
| 91 | C2×#1143 | — | 4 | 2 | no | — |
| 92 | #6503 | — | 2 | 1 | no | — |
| 93 | #6500 | — | 2 | 2 | no | — |
| 94 | #6495 | — | 2 | 2 | no | — |
| 95 | C2×#1141 | — | 2 | 1 | no | — |
| 96 | #6493 | — | 2 | 2 | no | — |
| 97 | #6489 | C23 | 1 | 1 | yes | characteristic |
| 98 | C2×#1136 | — | 2 | 2 | no | — |
| 99 | C2×#1136 | C23 | 1 | 1 | yes | characteristic |
| 100 | C2×#1136 | C23 | 1 | 2 | yes | — |
| 101 | C22×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 102 | #6471 | — | 2 | 4 | no | — |
| 103 | #6471 | — | 4 | 2 | no | — |
| 104 | C2×D56 | — | 2 | 2 | no | — |
| 105 | C2×#1132 | — | 2 | 2 | no | — |
| 106 | C7×#101 | — | 2 | 1 | no | — |
| 107 | C7×#101 | — | 2 | 4 | no | — |
| 108 | C7×#101 | D4 | 1 | 2 | yes | — |
| 109 | C7×#100 | — | 2 | 1 | no | — |
| 110 | C7×#100 | D4 | 1 | 2 | yes | — |
| 111 | #6409 | — | 2 | 2 | no | — |
| 112 | #6409 | — | 2 | 1 | no | — |
| 113 | #6406 | — | 2 | 1 | no | — |
| 114 | C22⋊(C7⋊C8) | — | 2 | 2 | no | — |
| 115 | #6399 | — | 2 | 4 | no | — |
| 116 | #6398 | — | 2 | 2 | no | — |
| 117 | #6397 | — | 2 | 2 | no | — |
| 118 | #6397 | — | 2 | 4 | no | — |
| 119 | (C2×D7)⋊C8 | — | 4 | 2 | no | — |
| 120 | #6393 | — | 2 | 4 | no | — |
| 121 | #3586 | — | 7 | 1 | no | — |
| 122 | #3068 | — | 7 | 2 | no | — |
| 123 | #3021 | — | 7 | 1 | no | — |
| 124 | #3010 | — | 7 | 1 | no | — |
| 125 | #2889 | D7 | 1 | 1 | yes | characteristic, complemented |
| 126 | #2049 | — | 7 | 2 | no | — |
| 127 | #2019 | — | 7 | 2 | no | — |
| 128 | #1914 | — | 7 | 1 | no | — |
| 129 | #1881 | — | 7 | 2 | no | — |
| 130 | #1858 | — | 7 | 1 | no | — |
| 131 | #1791 | — | 7 | 1 | no | — |
| 132 | C23×D7 | — | 2 | 1 | no | — |
| 133 | C7×#41 | — | 2 | 2 | no | — |
| 134 | C7×#41 | — | 2 | 2 | no | — |
| 135 | C7×#41 | — | 2 | 2 | no | — |
| 136 | C7×#41 | — | 2 | 4 | no | — |
| 137 | C7×#41 | — | 4 | 2 | no | — |
| 138 | C7×#41 | — | 4 | 4 | no | — |
| 139 | C7×#41 | — | 4 | 8 | no | — |
| 140 | C7×#41 | C2×D4 | 1 | 4 | yes | — |
| 141 | C2×C7×Q8 | — | 2 | 2 | no | — |
| 142 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 143 | C2×C7×Q8 | — | 2 | 4 | no | — |
| 144 | C2×C7×Q8 | — | 2 | 2 | no | — |
| 145 | C2×C7×Q8 | — | 2 | 2 | no | — |
| 146 | C2×C7×Q8 | — | 4 | 2 | no | — |
| 147 | C2×C7×Q8 | — | 4 | 4 | no | — |
| 148 | C2×C7×Q8 | C2×D4 | 1 | 2 | yes | — |
| 149 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 150 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 151 | C2×C7×D4 | — | 2 | 1 | no | — |
| 152 | C2×C7×D4 | — | 2 | 2 | no | — |
| 153 | C2×C7×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C2×C7×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C2×C7×D4 | #41 | 1 | 2 | yes | — |
| 156 | C22×C4×C7 | — | 2 | 1 | no | — |
| 157 | C22×C4×C7 | — | 2 | 2 | no | — |
| 158 | C22×C4×C7 | — | 2 | 1 | no | — |
| 159 | C22×C4×C7 | — | 2 | 2 | no | — |
| 160 | C22×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 161 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 162 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 163 | C2×C22⋊D7 | — | 4 | 2 | no | — |
| 164 | C2×C22⋊D7 | — | 4 | 2 | no | — |
| 165 | #1161 | — | 4 | 2 | no | — |
| 166 | Q8×D7 | — | 4 | 2 | no | — |
| 167 | #1159 | — | 4 | 2 | no | — |
| 168 | #1159 | — | 4 | 4 | no | — |
| 169 | D4×D7 | — | 4 | 2 | no | — |
| 170 | D4×D7 | — | 4 | 4 | no | — |
| 171 | #1157 | — | 2 | 4 | no | — |
| 172 | #1157 | — | 2 | 2 | no | — |
| 173 | #1157 | — | 2 | 2 | no | — |
| 174 | #1157 | — | 2 | 2 | no | — |
| 175 | #1157 | — | 2 | 2 | no | — |
| 176 | #1157 | — | 4 | 2 | no | — |
| 177 | #1157 | — | 4 | 2 | no | — |
| 178 | C2×D28 | — | 2 | 2 | no | — |
| 179 | C2×D28 | — | 2 | 2 | no | — |
| 180 | C2×D28 | — | 2 | 1 | no | — |
| 181 | C2×D28 | — | 2 | 1 | no | — |
| 182 | C2×D28 | — | 2 | 2 | no | — |
| 183 | C2×D28 | C2×D4 | 1 | 2 | yes | — |
| 184 | C2×C4×D7 | — | 2 | 2 | no | — |
| 185 | C2×C4×D7 | — | 4 | 2 | no | — |
| 186 | C2×Dic14 | — | 2 | 2 | no | — |
| 187 | C2×Dic14 | C2×D4 | 1 | 2 | yes | — |
| 188 | C7×M16 | — | 2 | 2 | no | — |
| 189 | C7×M16 | — | 2 | 2 | no | — |
| 190 | C7×M16 | — | 2 | 2 | no | — |
| 191 | C7×M16 | — | 4 | 4 | no | — |
| 192 | C7×M16 | C2×D4 | 1 | 4 | yes | — |
| 193 | C2×C7×C8 | — | 2 | 2 | no | — |
| 194 | C2×C7×C8 | — | 2 | 2 | no | — |
| 195 | C2×C7×C8 | — | 4 | 4 | no | — |
| 196 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 197 | #1144 | — | 2 | 8 | no | — |
| 198 | #1144 | — | 2 | 4 | no | — |
| 199 | #1143 | — | 2 | 8 | no | — |
| 200 | #1143 | — | 2 | 4 | no | — |
| 201 | #1143 | — | 4 | 4 | no | — |
| 202 | #1143 | — | 4 | 2 | no | — |
| 203 | #1142 | — | 2 | 4 | no | — |
| 204 | #1141 | — | 2 | 4 | no | — |
| 205 | #1141 | — | 4 | 2 | no | — |
| 206 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 207 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 208 | C4×Dic7 | — | 2 | 1 | no | — |
| 209 | #1136 | — | 2 | 4 | no | — |
| 210 | #1136 | — | 2 | 2 | no | — |
| 211 | #1136 | — | 2 | 2 | no | — |
| 212 | #1136 | C2×D4 | 1 | 4 | yes | — |
| 213 | C2×C7⋊C8 | — | 2 | 4 | no | — |
| 214 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 215 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 216 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 217 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 218 | D56 | — | 4 | 4 | no | — |
| 219 | #1132 | — | 4 | 4 | no | — |
| 220 | #585 | — | 7 | 1 | no | — |
| 221 | C2×2−1+4 | C2×D7 | 1 | 1 | yes | characteristic |
| 222 | #578 | — | 14 | 4 | no | — |
| 223 | #577 | — | 14 | 4 | no | — |
| 224 | #575 | — | 7 | 2 | no | — |
| 225 | #575 | — | 14 | 2 | no | — |
| 226 | C2×#137 | — | 7 | 2 | no | — |
| 227 | C2×#137 | — | 14 | 2 | no | — |
| 228 | C2×AGL(1,ℤ/8) | — | 7 | 1 | no | — |
| 229 | C2×AGL(1,ℤ/8) | — | 7 | 2 | no | — |
| 230 | C22×SD16 | — | 7 | 1 | no | — |
| 231 | #568 | — | 7 | 1 | no | — |
| 232 | #568 | C2×D7 | 1 | 2 | yes | complemented |
| 233 | #535 | — | 7 | 1 | no | — |
| 234 | #472 | — | 14 | 4 | no | — |
| 235 | #471 | — | 14 | 4 | no | — |
| 236 | #454 | — | 14 | 2 | no | — |
| 237 | #453 | — | 14 | 2 | no | — |
| 238 | #449 | — | 14 | 2 | no | — |
| 239 | #448 | — | 14 | 2 | no | — |
| 240 | #430 | — | 7 | 2 | no | — |
| 241 | #421 | — | 7 | 2 | no | — |
| 242 | #419 | — | 7 | 1 | no | — |
| 243 | #416 | — | 7 | 1 | no | — |
| 244 | #413 | — | 2 | 2 | no | — |
| 245 | #413 | — | 7 | 2 | no | — |
| 246 | #413 | C2×D7 | 1 | 1 | yes | characteristic |
| 247 | #413 | C2×D7 | 1 | 1 | yes | characteristic |
| 248 | C2×#101 | — | 2 | 2 | no | — |
| 249 | C2×#101 | C2×D7 | 1 | 2 | yes | complemented |
| 250 | C2×#100 | — | 7 | 2 | no | — |
| 251 | #408 | — | 7 | 1 | no | — |
| 252 | #408 | — | 7 | 2 | no | — |
| 253 | #344 | — | 7 | 2 | no | — |
| 254 | #341 | — | 7 | 2 | no | — |
| 255 | C23×C7 | — | 2 | 1 | no | — |
| 256 | C23×C7 | #121 | 1 | 2 | yes | — |
| 257 | C23×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 258 | C22×D7 | — | 2 | 2 | no | — |
| 259 | C22×D7 | — | 4 | 2 | no | — |
| 260 | C22×D7 | — | 4 | 1 | no | — |
| 261 | C22×D7 | — | 4 | 2 | no | — |
| 262 | C22×D7 | — | 16 | 1 | no | — |
| 263 | C7×Q8 | — | 2 | 1 | no | — |
| 264 | C7×Q8 | — | 2 | 2 | no | — |
| 265 | C7×Q8 | — | 2 | 2 | no | — |
| 266 | C7×Q8 | — | 2 | 2 | no | — |
| 267 | C7×Q8 | — | 4 | 4 | no | — |
| 268 | C7×Q8 | — | 4 | 2 | no | — |
| 269 | C7×Q8 | #120 | 1 | 2 | yes | — |
| 270 | C7×D4 | — | 2 | 4 | no | — |
| 271 | C7×D4 | — | 2 | 4 | no | — |
| 272 | C7×D4 | — | 2 | 1 | no | — |
| 273 | C7×D4 | — | 2 | 2 | no | — |
| 274 | C7×D4 | — | 4 | 4 | no | — |
| 275 | C7×D4 | #120 | 1 | 2 | yes | — |
| 276 | C2×C4×C7 | — | 2 | 1 | no | — |
| 277 | C2×C4×C7 | — | 2 | 2 | no | — |
| 278 | C2×C4×C7 | — | 2 | 2 | no | — |
| 279 | C2×C4×C7 | — | 2 | 4 | no | — |
| 280 | C2×C4×C7 | — | 2 | 2 | no | — |
| 281 | C2×C4×C7 | — | 4 | 4 | no | — |
| 282 | C2×C4×C7 | — | 4 | 4 | no | — |
| 283 | C2×C4×C7 | — | 4 | 2 | no | — |
| 284 | C2×C4×C7 | #121 | 1 | 2 | yes | — |
| 285 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 286 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 287 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 288 | C2×C4×C7 | H(5,𝔽2) | 1 | 2 | yes | — |
| 289 | C22⋊D7 | — | 4 | 4 | no | — |
| 290 | C22⋊D7 | — | 4 | 2 | no | — |
| 291 | C22⋊D7 | — | 4 | 2 | no | — |
| 292 | C22⋊D7 | — | 16 | 2 | no | — |
| 293 | C2×Dic7 | — | 2 | 2 | no | — |
| 294 | C2×Dic7 | — | 4 | 2 | no | — |
| 295 | C2×Dic7 | — | 4 | 1 | no | — |
| 296 | D28 | — | 2 | 2 | no | — |
| 297 | D28 | — | 2 | 2 | no | — |
| 298 | D28 | — | 4 | 2 | no | — |
| 299 | D28 | — | 4 | 1 | no | — |
| 300 | D28 | — | 4 | 1 | no | — |
| 301 | D28 | — | 4 | 2 | no | — |
| 302 | C4×D7 | — | 4 | 4 | no | — |
| 303 | C4×D7 | — | 4 | 2 | no | — |
| 304 | C4×D7 | — | 4 | 2 | no | — |
| 305 | Dic14 | — | 2 | 2 | no | — |
| 306 | Dic14 | — | 2 | 2 | no | — |
| 307 | Dic14 | — | 4 | 2 | no | — |
| 308 | C7×C8 | — | 2 | 4 | no | — |
| 309 | C7×C8 | — | 4 | 2 | no | — |
| 310 | C7⋊C8 | — | 2 | 4 | no | — |
| 311 | C7⋊C8 | — | 4 | 1 | no | — |
| 312 | C7⋊C8 | — | 4 | 1 | no | — |
| 313 | 2−1+4 | — | 2 | 4 | no | — |
| 314 | 2−1+4 | — | 4 | 2 | no | — |
| 315 | 2−1+4 | — | 14 | 2 | no | — |
| 316 | 2−1+4 | — | 14 | 1 | no | — |
| 317 | H(5,𝔽2) | — | 14 | 2 | no | — |
| 318 | H(5,𝔽2) | — | 14 | 2 | no | — |
| 319 | H(5,𝔽2) | — | 14 | 1 | no | — |
| 320 | C2×#41 | — | 2 | 2 | no | — |
| 321 | C2×#41 | — | 2 | 1 | no | — |
| 322 | C2×#41 | — | 7 | 2 | no | — |
| 323 | C2×#41 | — | 14 | 2 | no | — |
| 324 | C2×#41 | — | 28 | 2 | no | — |
| 325 | C2×#41 | D28 | 1 | 2 | yes | — |
| 326 | C2×#41 | C22×D7 | 1 | 1 | yes | characteristic |
| 327 | C2×#41 | C22×D7 | 1 | 1 | yes | characteristic |
| 328 | C22×Q8 | — | 2 | 1 | no | — |
| 329 | C22×Q8 | D28 | 1 | 2 | yes | — |
| 330 | C22×Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 331 | C22×D4 | — | 7 | 1 | no | — |
| 332 | #137 | — | 7 | 4 | no | — |
| 333 | #137 | — | 14 | 4 | no | — |
| 334 | #137 | — | 14 | 8 | no | — |
| 335 | #137 | — | 14 | 4 | no | — |
| 336 | #137 | — | 14 | 4 | no | — |
| 337 | #137 | — | 14 | 2 | no | — |
| 338 | AGL(1,ℤ/8) | — | 7 | 4 | no | — |
| 339 | AGL(1,ℤ/8) | — | 14 | 4 | no | — |
| 340 | AGL(1,ℤ/8) | — | 14 | 2 | no | — |
| 341 | AGL(1,ℤ/8) | — | 14 | 4 | no | — |
| 342 | AGL(1,ℤ/8) | — | 14 | 4 | no | — |
| 343 | AGL(1,ℤ/8) | — | 28 | 2 | no | — |
| 344 | #135 | — | 14 | 8 | no | — |
| 345 | #135 | — | 14 | 4 | no | — |
| 346 | C2×Q16 | — | 14 | 2 | no | — |
| 347 | C2×Q16 | — | 14 | 4 | no | — |
| 348 | C2×SD16 | — | 14 | 2 | no | — |
| 349 | C2×SD16 | — | 14 | 2 | no | — |
| 350 | C2×SD16 | — | 14 | 4 | no | — |
| 351 | C2×SD16 | — | 14 | 2 | no | — |
| 352 | C2×SD16 | — | 14 | 1 | no | — |
| 353 | C2×SD16 | — | 28 | 2 | no | — |
| 354 | C2×D8 | — | 14 | 2 | no | — |
| 355 | C2×D8 | — | 14 | 1 | no | — |
| 356 | #131 | — | 2 | 4 | no | — |
| 357 | #131 | — | 4 | 2 | no | — |
| 358 | #131 | — | 14 | 4 | no | — |
| 359 | C2×M16 | — | 2 | 4 | no | — |
| 360 | C2×M16 | — | 7 | 2 | no | — |
| 361 | C2×M16 | — | 7 | 1 | no | — |
| 362 | C2×M16 | — | 14 | 2 | no | — |
| 363 | C2×M16 | C22×D7 | 1 | 2 | yes | — |
| 364 | C2×M16 | C22×D7 | 1 | 2 | yes | — |
| 365 | C22×C8 | — | 7 | 1 | no | — |
| 366 | #127 | — | 14 | 1 | no | — |
| 367 | #124 | — | 14 | 1 | no | — |
| 368 | #121 | — | 14 | 2 | no | — |
| 369 | #120 | — | 14 | 2 | no | — |
| 370 | #117 | — | 7 | 1 | no | — |
| 371 | #108 | — | 14 | 4 | no | — |
| 372 | #104 | — | 14 | 4 | no | — |
| 373 | #103 | — | 14 | 1 | no | — |
| 374 | #103 | — | 14 | 2 | no | — |
| 375 | #102 | — | 14 | 1 | no | — |
| 376 | #101 | — | 2 | 1 | no | — |
| 377 | #101 | — | 2 | 4 | no | — |
| 378 | #101 | — | 14 | 2 | no | — |
| 379 | #101 | C22⋊D7 | 1 | 2 | yes | — |
| 380 | #100 | — | 2 | 1 | no | — |
| 381 | #100 | — | 14 | 4 | no | — |
| 382 | #100 | — | 14 | 2 | no | — |
| 383 | #100 | C22⋊D7 | 1 | 2 | yes | — |
| 384 | C22⋊C8 | — | 14 | 2 | no | — |
| 385 | C22⋊C8 | — | 28 | 2 | no | — |
| 386 | C22×C7 | — | 2 | 2 | no | — |
| 387 | C22×C7 | — | 2 | 2 | no | — |
| 388 | C22×C7 | — | 4 | 1 | no | — |
| 389 | C22×C7 | — | 4 | 2 | no | — |
| 390 | C22×C7 | — | 8 | 1 | no | — |
| 391 | C22×C7 | C2×#121 | 1 | 1 | yes | characteristic |
| 392 | C22×C7 | #546 | 1 | 2 | yes | — |
| 393 | C2×D7 | — | 4 | 2 | no | — |
| 394 | C2×D7 | — | 8 | 2 | no | — |
| 395 | C2×D7 | — | 8 | 2 | no | — |
| 396 | C2×D7 | — | 8 | 1 | no | — |
| 397 | C2×D7 | — | 16 | 2 | no | — |
| 398 | C2×D7 | — | 16 | 2 | no | — |
| 399 | C4×C7 | — | 2 | 2 | no | — |
| 400 | C4×C7 | — | 2 | 2 | no | — |
| 401 | C4×C7 | — | 4 | 2 | no | — |
| 402 | C4×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 403 | C4×C7 | #534 | 1 | 1 | yes | characteristic |
| 404 | C4×C7 | D42 | 1 | 2 | yes | — |
| 405 | Dic7 | — | 4 | 2 | no | — |
| 406 | Dic7 | — | 8 | 1 | no | — |
| 407 | C24 | — | 14 | 1 | no | — |
| 408 | #41 | — | 2 | 2 | no | — |
| 409 | #41 | — | 2 | 2 | no | — |
| 410 | #41 | — | 2 | 2 | no | — |
| 411 | #41 | — | 2 | 4 | no | — |
| 412 | #41 | — | 4 | 2 | no | — |
| 413 | #41 | — | 4 | 4 | no | — |
| 414 | #41 | — | 4 | 8 | no | — |
| 415 | #41 | — | 14 | 4 | no | — |
| 416 | #41 | — | 14 | 2 | no | — |
| 417 | #41 | — | 14 | 2 | no | — |
| 418 | #41 | — | 14 | 2 | no | — |
| 419 | #41 | — | 14 | 2 | no | — |
| 420 | #41 | — | 28 | 2 | no | — |
| 421 | #41 | — | 28 | 4 | no | — |
| 422 | #41 | — | 28 | 2 | no | — |
| 423 | #41 | — | 28 | 2 | no | — |
| 424 | #41 | — | 28 | 2 | no | — |
| 425 | #41 | D4×D7 | 1 | 4 | yes | — |
| 426 | C2×Q8 | — | 2 | 2 | no | — |
| 427 | C2×Q8 | — | 2 | 1 | no | — |
| 428 | C2×Q8 | — | 2 | 4 | no | — |
| 429 | C2×Q8 | — | 2 | 2 | no | — |
| 430 | C2×Q8 | — | 2 | 2 | no | — |
| 431 | C2×Q8 | — | 4 | 2 | no | — |
| 432 | C2×Q8 | — | 4 | 4 | no | — |
| 433 | C2×Q8 | — | 7 | 2 | no | — |
| 434 | C2×Q8 | — | 14 | 2 | no | — |
| 435 | C2×Q8 | — | 28 | 2 | no | — |
| 436 | C2×Q8 | C2×D28 | 1 | 2 | yes | — |
| 437 | C2×Q8 | C2×D28 | 1 | 1 | yes | characteristic |
| 438 | C2×Q8 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 439 | C2×D4 | — | 2 | 1 | no | — |
| 440 | C2×D4 | — | 2 | 2 | no | — |
| 441 | C2×D4 | — | 7 | 2 | no | — |
| 442 | C2×D4 | — | 14 | 2 | no | — |
| 443 | C2×D4 | — | 14 | 2 | no | — |
| 444 | C2×D4 | — | 14 | 1 | no | — |
| 445 | C2×D4 | — | 14 | 2 | no | — |
| 446 | C2×D4 | — | 14 | 2 | no | — |
| 447 | C2×D4 | — | 14 | 1 | no | — |
| 448 | C2×D4 | — | 28 | 2 | no | — |
| 449 | C2×D4 | — | 28 | 4 | no | — |
| 450 | C2×D4 | — | 28 | 2 | no | — |
| 451 | C2×D4 | — | 28 | 2 | no | — |
| 452 | C2×D4 | C2×D28 | 1 | 1 | yes | characteristic |
| 453 | C2×D4 | #1157 | 1 | 2 | yes | — |
| 454 | C2×D4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 455 | C22×C4 | — | 2 | 1 | no | — |
| 456 | C22×C4 | — | 2 | 2 | no | — |
| 457 | C22×C4 | — | 2 | 1 | no | — |
| 458 | C22×C4 | — | 2 | 2 | no | — |
| 459 | C22×C4 | — | 14 | 2 | no | — |
| 460 | C22×C4 | — | 28 | 2 | no | — |
| 461 | C22×C4 | C2×D28 | 1 | 2 | yes | — |
| 462 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 463 | Q16 | — | 14 | 8 | no | — |
| 464 | Q16 | — | 14 | 4 | no | — |
| 465 | SD16 | — | 14 | 8 | no | — |
| 466 | SD16 | — | 14 | 4 | no | — |
| 467 | SD16 | — | 14 | 4 | no | — |
| 468 | SD16 | — | 28 | 4 | no | — |
| 469 | SD16 | — | 28 | 4 | no | — |
| 470 | SD16 | — | 28 | 2 | no | — |
| 471 | D8 | — | 14 | 4 | no | — |
| 472 | D8 | — | 28 | 4 | no | — |
| 473 | D8 | — | 28 | 2 | no | — |
| 474 | M16 | — | 2 | 2 | no | — |
| 475 | M16 | — | 2 | 2 | no | — |
| 476 | M16 | — | 2 | 2 | no | — |
| 477 | M16 | — | 4 | 4 | no | — |
| 478 | M16 | — | 7 | 4 | no | — |
| 479 | M16 | — | 14 | 4 | no | — |
| 480 | M16 | — | 14 | 2 | no | — |
| 481 | M16 | — | 14 | 2 | no | — |
| 482 | M16 | C2×C22⋊D7 | 1 | 4 | yes | — |
| 483 | C2×C8 | — | 2 | 2 | no | — |
| 484 | C2×C8 | — | 2 | 2 | no | — |
| 485 | C2×C8 | — | 4 | 4 | no | — |
| 486 | C2×C8 | — | 14 | 4 | no | — |
| 487 | C2×C8 | — | 14 | 2 | no | — |
| 488 | C2×C8 | — | 14 | 1 | no | — |
| 489 | C2×C8 | — | 14 | 1 | no | — |
| 490 | C2×C8 | — | 14 | 2 | no | — |
| 491 | C4⋊C4 | — | 14 | 1 | no | — |
| 492 | C22⋊C4 | — | 14 | 1 | no | — |
| 493 | C22⋊C4 | — | 28 | 2 | no | — |
| 494 | C42 | — | 14 | 1 | no | — |
| 495 | C2×C7 | — | 2 | 1 | no | — |
| 496 | C2×C7 | — | 2 | 2 | no | — |
| 497 | C2×C7 | — | 4 | 2 | no | — |
| 498 | C2×C7 | — | 4 | 2 | no | — |
| 499 | C2×C7 | #2410 | 1 | 1 | yes | characteristic |
| 500 | D7 | — | 8 | 2 | no | — |
| 501 | D7 | — | 16 | 1 | no | — |
| 502 | C23 | — | 2 | 1 | no | — |
| 503 | C23 | — | 14 | 2 | no | — |
| 504 | C23 | — | 28 | 2 | no | — |
| 505 | C23 | — | 28 | 1 | no | — |
| 506 | C23 | — | 28 | 2 | no | — |
| 507 | C23 | — | 112 | 1 | no | — |
| 508 | C23 | #6493 | 1 | 2 | yes | — |
| 509 | C23 | C2×#1157 | 1 | 1 | yes | characteristic |
| 510 | Q8 | — | 2 | 1 | no | — |
| 511 | Q8 | — | 2 | 2 | no | — |
| 512 | Q8 | — | 2 | 2 | no | — |
| 513 | Q8 | — | 2 | 2 | no | — |
| 514 | Q8 | — | 4 | 4 | no | — |
| 515 | Q8 | — | 4 | 2 | no | — |
| 516 | Q8 | — | 14 | 2 | no | — |
| 517 | Q8 | — | 14 | 2 | no | — |
| 518 | Q8 | — | 28 | 2 | no | — |
| 519 | Q8 | #6445 | 1 | 2 | yes | — |
| 520 | D4 | — | 2 | 4 | no | — |
| 521 | D4 | — | 2 | 4 | no | — |
| 522 | D4 | — | 2 | 1 | no | — |
| 523 | D4 | — | 2 | 2 | no | — |
| 524 | D4 | — | 4 | 4 | no | — |
| 525 | D4 | — | 14 | 2 | no | — |
| 526 | D4 | — | 14 | 2 | no | — |
| 527 | D4 | — | 28 | 2 | no | — |
| 528 | D4 | — | 28 | 4 | no | — |
| 529 | D4 | — | 28 | 2 | no | — |
| 530 | D4 | — | 28 | 2 | no | — |
| 531 | D4 | — | 28 | 1 | no | — |
| 532 | D4 | — | 28 | 1 | no | — |
| 533 | D4 | — | 28 | 2 | no | — |
| 534 | D4 | — | 112 | 2 | no | — |
| 535 | D4 | #6445 | 1 | 2 | yes | — |
| 536 | C2×C4 | — | 2 | 1 | no | — |
| 537 | C2×C4 | — | 2 | 2 | no | — |
| 538 | C2×C4 | — | 2 | 2 | no | — |
| 539 | C2×C4 | — | 2 | 4 | no | — |
| 540 | C2×C4 | — | 2 | 2 | no | — |
| 541 | C2×C4 | — | 4 | 4 | no | — |
| 542 | C2×C4 | — | 4 | 4 | no | — |
| 543 | C2×C4 | — | 4 | 2 | no | — |
| 544 | C2×C4 | — | 14 | 2 | no | — |
| 545 | C2×C4 | — | 28 | 4 | no | — |
| 546 | C2×C4 | — | 28 | 2 | no | — |
| 547 | C2×C4 | — | 28 | 2 | no | — |
| 548 | C2×C4 | — | 28 | 2 | no | — |
| 549 | C2×C4 | — | 28 | 1 | no | — |
| 550 | C2×C4 | #6493 | 1 | 2 | yes | — |
| 551 | C2×C4 | C22×D28 | 1 | 1 | yes | characteristic |
| 552 | C2×C4 | C2×D4×D7 | 1 | 2 | yes | — |
| 553 | C2×C4 | #6548 | 1 | 2 | yes | — |
| 554 | C2×C4 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 555 | C8 | — | 2 | 4 | no | — |
| 556 | C8 | — | 4 | 2 | no | — |
| 557 | C8 | — | 14 | 4 | no | — |
| 558 | C8 | — | 28 | 1 | no | — |
| 559 | C8 | — | 28 | 1 | no | — |
| 560 | C7 | #24422 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 561 | C22 | — | 2 | 2 | no | — |
| 562 | C22 | — | 2 | 2 | no | — |
| 563 | C22 | — | 4 | 1 | no | — |
| 564 | C22 | — | 4 | 2 | no | — |
| 565 | C22 | — | 8 | 1 | no | — |
| 566 | C22 | — | 28 | 2 | no | — |
| 567 | C22 | — | 56 | 2 | no | — |
| 568 | C22 | — | 56 | 2 | no | — |
| 569 | C22 | — | 56 | 1 | no | — |
| 570 | C22 | — | 112 | 2 | no | — |
| 571 | C22 | — | 112 | 2 | no | — |
| 572 | C22 | #90181 | 1 | 2 | yes | — |
| 573 | C22 | C2×#6493 | 1 | 1 | yes | characteristic |
| 574 | C4 | — | 2 | 2 | no | — |
| 575 | C4 | — | 2 | 2 | no | — |
| 576 | C4 | — | 4 | 2 | no | — |
| 577 | C4 | — | 28 | 2 | no | — |
| 578 | C4 | — | 56 | 1 | no | — |
| 579 | C4 | C2×#6445 | 1 | 1 | yes | characteristic |
| 580 | C4 | #90184 | 1 | 1 | yes | characteristic |
| 581 | C4 | D4×C22⋊D7 | 1 | 2 | yes | — |
| 582 | C2 | — | 2 | 1 | no | — |
| 583 | C2 | — | 2 | 2 | no | — |
| 584 | C2 | — | 4 | 2 | no | — |
| 585 | C2 | — | 4 | 2 | no | — |
| 586 | C2 | — | 56 | 2 | no | — |
| 587 | C2 | — | 112 | 1 | no | — |
| 588 | C2 | #11739572 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11744355 | C2 | semidirect |
| 2. C7×#2889 | C2 | semidirect |
| 3. #11741558 | C2 | semidirect |
| 4. #11741259 | C2 | semidirect |
| 5. #11736162 | C2 | semidirect |
| 6. #11729774 | C2 | semidirect |
| 7. #11727897 | C2 | semidirect |
| 8. #11727891 | C2 | semidirect |
| 9. #11727889 | C2 | semidirect |
| 10. #11727871 | C2 | semidirect |
| 11. #11727864 | C2 | semidirect |
| 14. C7×#568 | C22 | semidirect |
| 20. C2×#6512 | C22 | semidirect |
| 24. C22×#1143 | C22 | semidirect |
| 30. C2×C7×#101 | C22 | semidirect |
| 33. #90005 | C22 | semidirect |
| 35. #89997 | C22 | semidirect |
| 40. C2×#6397 | C22 | semidirect |
| 42. #89897 | C22 | semidirect |
| 45. #89353 | C22 | semidirect |
| 46. #89351 | C22 | semidirect |
| 73. #6514 | D4 | semidirect |
| 78. #6512 | D4 | semidirect |
| 125. #2889 | D7 | semidirect |
| 232. #568 | C2×D7 | semidirect |
| 249. C2×#101 | C2×D7 | semidirect |
| 560. C7 | #24422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11744355 | 2 |
| C7×#2889 | 2 |
| #11741558 | 2 |
| #11741259 | 2 |
| #11736162 | 2 |
| #11729774 | 2 |
| #11727897 | 2 |
| #11727891 | 2 |
| #11727889 | 2 |
| #11727871 | 2 |
| #11727864 | 2 |
| #24422 | 7 |