Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
996 conjugacy classes of subgroups.
The subgroup lattice has 586 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11743320 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C7×#3254 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11740811 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11740779 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11729556 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11728863 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11728862 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11728801 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11728798 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11728259 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11728252 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C7×#533 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C7×#532 | C22 | 1 | 1 | yes | characteristic |
| 14 | #90521 | — | 2 | 2 | no | — |
| 15 | #90425 | — | 2 | 1 | no | — |
| 16 | #90408 | — | 2 | 1 | no | — |
| 17 | #90374 | — | 2 | 2 | no | — |
| 18 | #90298 | — | 2 | 2 | no | — |
| 19 | #90298 | — | 2 | 2 | no | — |
| 20 | #90254 | — | 2 | 1 | no | — |
| 21 | #90254 | C22 | 1 | 2 | yes | — |
| 22 | D4×D28 | — | 2 | 1 | no | — |
| 23 | D4×D28 | C22 | 1 | 2 | yes | — |
| 24 | #90168 | C22 | 1 | 1 | yes | characteristic |
| 25 | #90168 | C22 | 1 | 1 | yes | characteristic |
| 26 | C7×#477 | — | 2 | 1 | no | — |
| 27 | C7×#474 | C22 | 1 | 2 | yes | complemented |
| 28 | C7×#468 | — | 2 | 2 | no | — |
| 29 | C7×#461 | C22 | 1 | 2 | yes | complemented |
| 30 | C7×#460 | — | 2 | 1 | no | — |
| 31 | C7×#423 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #89865 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #89865 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #89860 | C22 | 1 | 1 | yes | characteristic |
| 35 | #89860 | C22 | 1 | 1 | yes | characteristic |
| 36 | #89859 | C22 | 1 | 2 | yes | complemented |
| 37 | #89855 | C22 | 1 | 2 | yes | complemented |
| 38 | #89840 | — | 2 | 2 | no | — |
| 39 | #89821 | — | 2 | 2 | no | — |
| 40 | #89799 | — | 2 | 1 | no | — |
| 41 | #89793 | — | 2 | 1 | no | — |
| 42 | #89774 | — | 2 | 2 | no | — |
| 43 | #89696 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | C2×C4×C7⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | D4⋊(C7⋊C8) | C22 | 1 | 2 | yes | complemented |
| 46 | D4⋊(C7⋊C8) | C22 | 1 | 2 | yes | complemented |
| 47 | #89280 | C22 | 1 | 2 | yes | — |
| 48 | #89278 | C22 | 1 | 2 | yes | complemented |
| 49 | #89278 | C22 | 1 | 2 | yes | complemented |
| 50 | #89276 | C22 | 1 | 2 | yes | complemented |
| 51 | #18691 | — | 7 | 1 | no | maximal, Sylow |
| 52 | C2×C7×#41 | — | 2 | 1 | no | — |
| 53 | C2×D4×D7 | — | 2 | 2 | no | — |
| 54 | C2×D4×D7 | — | 2 | 2 | no | — |
| 55 | C2×#1157 | — | 2 | 1 | no | — |
| 56 | C2×#1157 | D4 | 1 | 2 | yes | — |
| 57 | C22×D28 | — | 2 | 2 | no | — |
| 58 | C2×C7×SD16 | — | 2 | 2 | no | — |
| 59 | C2×C7×M16 | — | 2 | 1 | no | — |
| 60 | C7×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 61 | C7×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 62 | C7×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 63 | C7×#127 | D4 | 1 | 1 | yes | characteristic |
| 64 | C7×#125 | — | 2 | 1 | no | — |
| 65 | C7×#124 | — | 2 | 1 | no | — |
| 66 | C7×C22⋊Q8 | — | 2 | 1 | no | — |
| 67 | C7×C22⋊Q8 | — | 2 | 1 | no | — |
| 68 | C7×#121 | — | 2 | 1 | no | — |
| 69 | C7×#121 | D4 | 1 | 2 | yes | — |
| 70 | C4×C7×Q8 | — | 2 | 1 | no | — |
| 71 | C4×C7×Q8 | — | 2 | 1 | no | — |
| 72 | C4×C7×D4 | — | 2 | 1 | no | — |
| 73 | C4×C7×D4 | C23 | 1 | 2 | yes | — |
| 74 | C7×#117 | — | 2 | 1 | no | — |
| 75 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 76 | #6510 | — | 2 | 4 | no | — |
| 77 | C2×#1143 | — | 2 | 2 | no | — |
| 78 | #6503 | — | 2 | 4 | no | — |
| 79 | #6501 | — | 2 | 2 | no | — |
| 80 | #6501 | — | 2 | 2 | no | — |
| 81 | #6500 | — | 2 | 4 | no | — |
| 82 | #6500 | — | 2 | 4 | no | — |
| 83 | #6493 | — | 2 | 1 | no | — |
| 84 | #6493 | — | 2 | 1 | no | — |
| 85 | #6493 | — | 2 | 1 | no | — |
| 86 | #6493 | — | 2 | 2 | no | — |
| 87 | #6493 | — | 2 | 2 | no | — |
| 88 | #6493 | D4 | 1 | 2 | yes | — |
| 89 | #6489 | — | 2 | 2 | no | — |
| 90 | C2×#1136 | — | 2 | 1 | no | — |
| 91 | C22×C7⋊C8 | — | 2 | 1 | no | — |
| 92 | #6458 | — | 2 | 2 | no | — |
| 93 | #6458 | — | 2 | 2 | no | — |
| 94 | #6455 | — | 2 | 2 | no | — |
| 95 | #6455 | — | 2 | 2 | no | — |
| 96 | #6448 | — | 2 | 4 | no | — |
| 97 | #6448 | — | 2 | 4 | no | — |
| 98 | #6445 | — | 2 | 4 | no | — |
| 99 | #6445 | — | 2 | 4 | no | — |
| 100 | #6438 | — | 2 | 1 | no | — |
| 101 | #6438 | D4 | 1 | 2 | yes | — |
| 102 | #6437 | D4 | 1 | 1 | yes | characteristic |
| 103 | #6437 | C23 | 1 | 1 | yes | characteristic |
| 104 | C4×D28 | — | 2 | 1 | no | — |
| 105 | C4×D28 | — | 2 | 1 | no | — |
| 106 | C4×D28 | — | 2 | 1 | no | — |
| 107 | C4×D28 | C23 | 1 | 2 | yes | — |
| 108 | #6432 | D4 | 1 | 1 | yes | characteristic |
| 109 | #6432 | C23 | 1 | 1 | yes | characteristic |
| 110 | C7×#107 | — | 2 | 2 | no | — |
| 111 | C7×C4⋊C8 | — | 2 | 1 | no | — |
| 112 | C7×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 113 | C7×#103 | — | 2 | 2 | no | — |
| 114 | C7×#102 | — | 2 | 2 | no | — |
| 115 | #6409 | — | 2 | 2 | no | — |
| 116 | #6384 | — | 2 | 2 | no | — |
| 117 | #6384 | — | 2 | 2 | no | — |
| 118 | #6383 | — | 2 | 2 | no | — |
| 119 | #6383 | — | 2 | 2 | no | — |
| 120 | #6383 | — | 2 | 2 | no | — |
| 121 | #6381 | — | 2 | 2 | no | — |
| 122 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 123 | C4⋊(C7⋊C8) | C23 | 1 | 2 | yes | — |
| 124 | C4×C7⋊C8 | — | 2 | 1 | no | — |
| 125 | C4×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 126 | C4×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 127 | #3549 | — | 7 | 1 | no | — |
| 128 | #3254 | — | 7 | 1 | no | — |
| 129 | #3254 | D7 | 1 | 1 | yes | characteristic, complemented |
| 130 | #3131 | — | 7 | 1 | no | — |
| 131 | #1646 | — | 7 | 2 | no | — |
| 132 | #1646 | — | 7 | 2 | no | — |
| 133 | #1639 | — | 7 | 2 | no | — |
| 134 | #1639 | — | 7 | 2 | no | — |
| 135 | #1560 | — | 7 | 1 | no | — |
| 136 | #1492 | — | 7 | 1 | no | — |
| 137 | #1492 | — | 7 | 1 | no | — |
| 138 | C23×D7 | — | 2 | 4 | no | — |
| 139 | C7×#41 | — | 8 | 1 | no | — |
| 140 | C7×#41 | — | 8 | 1 | no | — |
| 141 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 142 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 143 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 144 | C2×C7×D4 | — | 2 | 2 | no | — |
| 145 | C2×C7×D4 | — | 2 | 1 | no | — |
| 146 | C2×C7×D4 | — | 2 | 1 | no | — |
| 147 | C2×C7×D4 | C2×D4 | 1 | 2 | yes | — |
| 148 | C22×C4×C7 | — | 2 | 2 | no | — |
| 149 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 150 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 151 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 152 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 153 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 154 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 155 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 156 | D4×D7 | — | 8 | 2 | no | — |
| 157 | D4×D7 | — | 8 | 2 | no | — |
| 158 | D4×D7 | — | 8 | 4 | no | — |
| 159 | #1157 | — | 4 | 4 | no | — |
| 160 | #1157 | — | 8 | 1 | no | — |
| 161 | #1157 | — | 8 | 1 | no | — |
| 162 | C2×D28 | — | 2 | 1 | no | — |
| 163 | C2×D28 | — | 2 | 1 | no | — |
| 164 | C2×D28 | — | 2 | 1 | no | — |
| 165 | C2×D28 | — | 2 | 4 | no | — |
| 166 | C2×D28 | — | 2 | 1 | no | — |
| 167 | C2×D28 | — | 8 | 2 | no | — |
| 168 | C2×D28 | — | 8 | 2 | no | — |
| 169 | C2×D28 | C2×D4 | 1 | 2 | yes | — |
| 170 | C2×D28 | C2×D4 | 1 | 2 | yes | — |
| 171 | C2×C4×D7 | — | 2 | 2 | no | — |
| 172 | C2×C4×D7 | — | 2 | 2 | no | — |
| 173 | C2×Dic14 | — | 2 | 1 | no | — |
| 174 | C2×Dic14 | C2×D4 | 1 | 2 | yes | — |
| 175 | C7×SD16 | — | 8 | 2 | no | — |
| 176 | C7×M16 | — | 8 | 1 | no | — |
| 177 | C2×C7×C8 | — | 2 | 2 | no | — |
| 178 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 179 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 180 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 181 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 182 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 183 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 184 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 185 | C7×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 186 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 187 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 188 | C7×C22⋊C4 | — | 4 | 1 | no | — |
| 189 | C42×C7 | — | 4 | 1 | no | — |
| 190 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 194 | C22⋊Dic7 | — | 2 | 4 | no | — |
| 195 | #1143 | — | 8 | 2 | no | — |
| 196 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 197 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 198 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 199 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 200 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 201 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 202 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 203 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 204 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 205 | C4⋊Dic7 | C2×D4 | 1 | 2 | yes | — |
| 206 | C4×Dic7 | — | 2 | 4 | no | — |
| 207 | #1136 | — | 8 | 1 | no | — |
| 208 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 209 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 210 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 211 | C2×C7⋊C8 | — | 4 | 2 | no | — |
| 212 | H(3,𝔽4) | — | 14 | 2 | no | — |
| 213 | #555 | — | 7 | 2 | no | — |
| 214 | #555 | — | 14 | 1 | no | — |
| 215 | #555 | — | 14 | 1 | no | — |
| 216 | D42 | — | 7 | 2 | no | — |
| 217 | D42 | — | 14 | 1 | no | — |
| 218 | D42 | — | 14 | 1 | no | — |
| 219 | #535 | — | 14 | 2 | no | — |
| 220 | #535 | — | 14 | 2 | no | — |
| 221 | #535 | — | 14 | 2 | no | — |
| 222 | #533 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 223 | #532 | — | 7 | 1 | no | — |
| 224 | #532 | — | 7 | 1 | no | — |
| 225 | #532 | C2×D7 | 1 | 1 | yes | characteristic |
| 226 | #488 | — | 14 | 2 | no | — |
| 227 | #487 | — | 7 | 1 | no | — |
| 228 | #487 | — | 7 | 1 | no | — |
| 229 | #486 | — | 7 | 1 | no | — |
| 230 | #486 | — | 7 | 1 | no | — |
| 231 | #477 | — | 2 | 1 | no | — |
| 232 | #477 | — | 14 | 1 | no | — |
| 233 | #474 | — | 7 | 2 | no | — |
| 234 | #474 | C2×D7 | 1 | 2 | yes | complemented |
| 235 | #468 | — | 2 | 2 | no | — |
| 236 | #468 | — | 14 | 2 | no | — |
| 237 | #461 | — | 7 | 2 | no | — |
| 238 | #461 | C2×D7 | 1 | 2 | yes | complemented |
| 239 | #460 | — | 2 | 1 | no | — |
| 240 | #460 | — | 14 | 1 | no | — |
| 241 | #423 | — | 7 | 1 | no | — |
| 242 | #423 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 243 | #416 | — | 14 | 2 | no | — |
| 244 | C2×C4×C8 | — | 7 | 1 | no | — |
| 245 | #333 | — | 7 | 2 | no | — |
| 246 | #331 | — | 7 | 2 | no | — |
| 247 | D4⋊C8 | — | 7 | 2 | no | — |
| 248 | D4⋊C8 | — | 7 | 2 | no | — |
| 249 | D4⋊C8 | — | 7 | 2 | no | — |
| 250 | D4⋊C8 | — | 7 | 2 | no | — |
| 251 | C23×C7 | — | 2 | 2 | no | — |
| 252 | C23×C7 | #120 | 1 | 1 | yes | characteristic |
| 253 | C22×D7 | — | 2 | 2 | no | — |
| 254 | C22×D7 | — | 2 | 2 | no | — |
| 255 | C22×D7 | — | 8 | 4 | no | — |
| 256 | C22×D7 | — | 8 | 4 | no | — |
| 257 | C22×D7 | — | 8 | 4 | no | — |
| 258 | C7×Q8 | — | 4 | 1 | no | — |
| 259 | C7×Q8 | — | 4 | 1 | no | — |
| 260 | C7×Q8 | — | 4 | 1 | no | — |
| 261 | C7×Q8 | — | 4 | 1 | no | — |
| 262 | C7×Q8 | — | 8 | 1 | no | — |
| 263 | C7×D4 | — | 2 | 2 | no | — |
| 264 | C7×D4 | — | 2 | 2 | no | — |
| 265 | C7×D4 | — | 4 | 2 | no | — |
| 266 | C7×D4 | — | 8 | 1 | no | — |
| 267 | C7×D4 | — | 8 | 2 | no | — |
| 268 | C2×C4×C7 | — | 2 | 1 | no | — |
| 269 | C2×C4×C7 | — | 2 | 1 | no | — |
| 270 | C2×C4×C7 | — | 2 | 1 | no | — |
| 271 | C2×C4×C7 | — | 2 | 1 | no | — |
| 272 | C2×C4×C7 | — | 2 | 2 | no | — |
| 273 | C2×C4×C7 | — | 2 | 2 | no | — |
| 274 | C2×C4×C7 | — | 4 | 2 | no | — |
| 275 | C2×C4×C7 | — | 4 | 2 | no | — |
| 276 | C2×C4×C7 | — | 4 | 1 | no | — |
| 277 | C2×C4×C7 | — | 4 | 1 | no | — |
| 278 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 279 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 280 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 281 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 282 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 283 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 284 | C22⋊D7 | — | 8 | 2 | no | — |
| 285 | C22⋊D7 | — | 8 | 2 | no | — |
| 286 | C22⋊D7 | — | 8 | 4 | no | — |
| 287 | C22⋊D7 | — | 8 | 4 | no | — |
| 288 | C2×Dic7 | — | 2 | 2 | no | — |
| 289 | C2×Dic7 | — | 2 | 2 | no | — |
| 290 | D28 | — | 2 | 2 | no | — |
| 291 | D28 | — | 2 | 2 | no | — |
| 292 | D28 | — | 4 | 2 | no | — |
| 293 | D28 | — | 4 | 1 | no | — |
| 294 | D28 | — | 4 | 1 | no | — |
| 295 | D28 | — | 4 | 1 | no | — |
| 296 | D28 | — | 4 | 1 | no | — |
| 297 | D28 | — | 4 | 2 | no | — |
| 298 | D28 | — | 8 | 1 | no | — |
| 299 | D28 | — | 8 | 4 | no | — |
| 300 | C4×D7 | — | 4 | 2 | no | — |
| 301 | C4×D7 | — | 4 | 2 | no | — |
| 302 | C4×D7 | — | 4 | 4 | no | — |
| 303 | Dic14 | — | 4 | 2 | no | — |
| 304 | Dic14 | — | 8 | 1 | no | — |
| 305 | C7×C8 | — | 4 | 2 | no | — |
| 306 | C7⋊C8 | — | 4 | 1 | no | — |
| 307 | C7⋊C8 | — | 4 | 1 | no | — |
| 308 | C7⋊C8 | — | 4 | 2 | no | — |
| 309 | C2×#41 | — | 2 | 1 | no | — |
| 310 | C2×#41 | — | 7 | 2 | no | — |
| 311 | C2×#41 | — | 14 | 1 | no | — |
| 312 | C22×D4 | — | 14 | 2 | no | — |
| 313 | C22×D4 | — | 14 | 2 | no | — |
| 314 | C22×D4 | — | 14 | 2 | no | — |
| 315 | C2×SD16 | — | 2 | 2 | no | — |
| 316 | C2×SD16 | — | 14 | 2 | no | — |
| 317 | C2×M16 | — | 2 | 1 | no | — |
| 318 | C2×M16 | — | 14 | 1 | no | — |
| 319 | C22×C8 | — | 14 | 1 | no | — |
| 320 | C4⋊Q8 | — | 7 | 1 | no | — |
| 321 | C4⋊Q8 | — | 7 | 1 | no | — |
| 322 | C4⋊Q8 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 323 | C4⋊Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 324 | C4⋊Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 325 | #127 | — | 7 | 1 | no | — |
| 326 | #127 | — | 7 | 1 | no | — |
| 327 | #127 | — | 14 | 4 | no | — |
| 328 | #127 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 329 | #125 | — | 2 | 1 | no | — |
| 330 | #124 | — | 2 | 1 | no | — |
| 331 | #124 | — | 7 | 2 | no | — |
| 332 | #124 | — | 14 | 4 | no | — |
| 333 | #124 | — | 14 | 4 | no | — |
| 334 | #124 | — | 14 | 4 | no | — |
| 335 | #124 | — | 14 | 1 | no | — |
| 336 | C22⋊Q8 | — | 2 | 1 | no | — |
| 337 | C22⋊Q8 | — | 2 | 1 | no | — |
| 338 | #121 | — | 2 | 1 | no | — |
| 339 | #121 | — | 7 | 2 | no | — |
| 340 | #121 | — | 14 | 2 | no | — |
| 341 | #121 | — | 14 | 2 | no | — |
| 342 | #121 | — | 14 | 2 | no | — |
| 343 | #121 | — | 14 | 2 | no | — |
| 344 | #121 | — | 14 | 2 | no | — |
| 345 | #121 | — | 14 | 1 | no | — |
| 346 | #121 | — | 14 | 1 | no | — |
| 347 | #121 | — | 14 | 1 | no | — |
| 348 | #121 | — | 14 | 2 | no | — |
| 349 | #121 | C22⋊D7 | 1 | 2 | yes | — |
| 350 | #120 | — | 14 | 4 | no | — |
| 351 | #120 | — | 14 | 4 | no | — |
| 352 | #120 | — | 14 | 4 | no | — |
| 353 | #120 | — | 14 | 4 | no | — |
| 354 | C4×Q8 | — | 2 | 1 | no | — |
| 355 | C4×Q8 | — | 2 | 1 | no | — |
| 356 | C4×D4 | — | 2 | 1 | no | — |
| 357 | C4×D4 | — | 7 | 2 | no | — |
| 358 | C4×D4 | — | 14 | 1 | no | — |
| 359 | C4×D4 | — | 14 | 1 | no | — |
| 360 | C4×D4 | — | 14 | 1 | no | — |
| 361 | C4×D4 | C22×D7 | 1 | 2 | yes | — |
| 362 | #117 | — | 2 | 1 | no | — |
| 363 | #117 | — | 14 | 2 | no | — |
| 364 | #117 | — | 14 | 2 | no | — |
| 365 | #117 | — | 14 | 2 | no | — |
| 366 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 367 | #107 | — | 2 | 2 | no | — |
| 368 | #107 | — | 14 | 2 | no | — |
| 369 | C4⋊C8 | — | 2 | 1 | no | — |
| 370 | C4⋊C8 | — | 7 | 2 | no | — |
| 371 | C4⋊C8 | — | 14 | 1 | no | — |
| 372 | C4⋊C8 | C22×D7 | 1 | 2 | yes | — |
| 373 | #103 | — | 2 | 2 | no | — |
| 374 | #103 | — | 14 | 2 | no | — |
| 375 | #103 | — | 14 | 2 | no | — |
| 376 | #103 | — | 14 | 2 | no | — |
| 377 | #102 | — | 2 | 2 | no | — |
| 378 | #102 | — | 14 | 2 | no | — |
| 379 | #102 | — | 14 | 2 | no | — |
| 380 | #102 | — | 14 | 2 | no | — |
| 381 | C4×C8 | — | 7 | 1 | no | — |
| 382 | C4×C8 | — | 7 | 1 | no | — |
| 383 | C4×C8 | — | 14 | 1 | no | — |
| 384 | C22×C7 | — | 2 | 1 | no | — |
| 385 | C22×C7 | — | 2 | 1 | no | — |
| 386 | C22×C7 | — | 2 | 1 | no | — |
| 387 | C22×C7 | — | 4 | 2 | no | — |
| 388 | C22×C7 | — | 4 | 2 | no | — |
| 389 | C22×C7 | — | 4 | 2 | no | — |
| 390 | C22×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 391 | C2×D7 | — | 4 | 2 | no | — |
| 392 | C2×D7 | — | 4 | 2 | no | — |
| 393 | C2×D7 | — | 4 | 2 | no | — |
| 394 | C2×D7 | — | 4 | 2 | no | — |
| 395 | C2×D7 | — | 4 | 2 | no | — |
| 396 | C2×D7 | — | 4 | 2 | no | — |
| 397 | C2×D7 | — | 16 | 8 | no | — |
| 398 | C4×C7 | — | 2 | 1 | no | — |
| 399 | C4×C7 | — | 2 | 1 | no | — |
| 400 | C4×C7 | — | 2 | 1 | no | — |
| 401 | C4×C7 | — | 4 | 2 | no | — |
| 402 | C4×C7 | — | 8 | 1 | no | — |
| 403 | C4×C7 | — | 8 | 1 | no | — |
| 404 | C4×C7 | #455 | 1 | 2 | yes | — |
| 405 | C4×C7 | #576 | 1 | 1 | yes | characteristic |
| 406 | C4×C7 | #576 | 1 | 1 | yes | characteristic |
| 407 | C4×C7 | #577 | 1 | 1 | yes | characteristic |
| 408 | C4×C7 | #577 | 1 | 1 | yes | characteristic |
| 409 | Dic7 | — | 4 | 2 | no | — |
| 410 | Dic7 | — | 4 | 2 | no | — |
| 411 | C24 | — | 14 | 4 | no | — |
| 412 | #41 | — | 8 | 1 | no | — |
| 413 | #41 | — | 8 | 1 | no | — |
| 414 | #41 | — | 28 | 4 | no | — |
| 415 | #41 | — | 56 | 1 | no | — |
| 416 | #41 | — | 56 | 1 | no | — |
| 417 | C2×Q8 | — | 2 | 1 | no | — |
| 418 | C2×Q8 | — | 2 | 1 | no | — |
| 419 | C2×Q8 | — | 2 | 1 | no | — |
| 420 | C2×Q8 | — | 7 | 2 | no | — |
| 421 | C2×Q8 | — | 14 | 1 | no | — |
| 422 | C2×D4 | — | 2 | 2 | no | — |
| 423 | C2×D4 | — | 2 | 1 | no | — |
| 424 | C2×D4 | — | 2 | 1 | no | — |
| 425 | C2×D4 | — | 7 | 2 | no | — |
| 426 | C2×D4 | — | 7 | 2 | no | — |
| 427 | C2×D4 | — | 14 | 4 | no | — |
| 428 | C2×D4 | — | 14 | 4 | no | — |
| 429 | C2×D4 | — | 14 | 4 | no | — |
| 430 | C2×D4 | — | 14 | 2 | no | — |
| 431 | C2×D4 | — | 14 | 2 | no | — |
| 432 | C2×D4 | — | 14 | 1 | no | — |
| 433 | C2×D4 | — | 14 | 1 | no | — |
| 434 | C2×D4 | — | 14 | 1 | no | — |
| 435 | C2×D4 | — | 14 | 1 | no | — |
| 436 | C2×D4 | — | 56 | 2 | no | — |
| 437 | C2×D4 | — | 56 | 2 | no | — |
| 438 | C2×D4 | — | 56 | 2 | no | — |
| 439 | C2×D4 | — | 56 | 2 | no | — |
| 440 | C2×D4 | — | 56 | 4 | no | — |
| 441 | C2×D4 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 442 | C22×C4 | — | 2 | 2 | no | — |
| 443 | C22×C4 | — | 14 | 2 | no | — |
| 444 | C22×C4 | — | 14 | 2 | no | — |
| 445 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 446 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 447 | C22×C4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 448 | SD16 | — | 8 | 2 | no | — |
| 449 | SD16 | — | 56 | 2 | no | — |
| 450 | M16 | — | 8 | 1 | no | — |
| 451 | M16 | — | 56 | 1 | no | — |
| 452 | C2×C8 | — | 2 | 2 | no | — |
| 453 | C2×C8 | — | 14 | 1 | no | — |
| 454 | C2×C8 | — | 14 | 1 | no | — |
| 455 | C2×C8 | — | 14 | 2 | no | — |
| 456 | C2×C8 | — | 28 | 2 | no | — |
| 457 | C4⋊C4 | — | 2 | 1 | no | — |
| 458 | C4⋊C4 | — | 2 | 1 | no | — |
| 459 | C4⋊C4 | — | 2 | 1 | no | — |
| 460 | C4⋊C4 | — | 2 | 1 | no | — |
| 461 | C4⋊C4 | — | 2 | 1 | no | — |
| 462 | C4⋊C4 | — | 4 | 1 | no | — |
| 463 | C4⋊C4 | — | 4 | 1 | no | — |
| 464 | C4⋊C4 | — | 7 | 2 | no | — |
| 465 | C4⋊C4 | — | 14 | 1 | no | — |
| 466 | C4⋊C4 | — | 14 | 1 | no | — |
| 467 | C4⋊C4 | — | 14 | 1 | no | — |
| 468 | C4⋊C4 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 469 | C22⋊C4 | — | 2 | 2 | no | — |
| 470 | C22⋊C4 | — | 2 | 2 | no | — |
| 471 | C22⋊C4 | — | 4 | 1 | no | — |
| 472 | C22⋊C4 | — | 14 | 4 | no | — |
| 473 | C22⋊C4 | — | 14 | 4 | no | — |
| 474 | C22⋊C4 | — | 14 | 4 | no | — |
| 475 | C22⋊C4 | — | 14 | 2 | no | — |
| 476 | C22⋊C4 | — | 14 | 2 | no | — |
| 477 | C22⋊C4 | — | 14 | 2 | no | — |
| 478 | C22⋊C4 | — | 14 | 2 | no | — |
| 479 | C42 | — | 4 | 1 | no | — |
| 480 | C42 | — | 14 | 4 | no | — |
| 481 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 482 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 483 | C42 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 484 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 485 | C2×C7 | — | 4 | 1 | no | — |
| 486 | C2×C7 | — | 8 | 2 | no | — |
| 487 | C2×C7 | #3012 | 1 | 1 | yes | characteristic |
| 488 | C2×C7 | #3012 | 1 | 1 | yes | characteristic |
| 489 | C2×C7 | C2×#455 | 1 | 1 | yes | characteristic |
| 490 | D7 | — | 8 | 2 | no | — |
| 491 | D7 | — | 8 | 2 | no | — |
| 492 | C23 | — | 2 | 2 | no | — |
| 493 | C23 | — | 14 | 2 | no | — |
| 494 | C23 | — | 14 | 2 | no | — |
| 495 | C23 | — | 56 | 4 | no | — |
| 496 | C23 | — | 56 | 4 | no | — |
| 497 | C23 | — | 56 | 4 | no | — |
| 498 | C23 | #6500 | 1 | 1 | yes | characteristic |
| 499 | Q8 | — | 4 | 1 | no | — |
| 500 | Q8 | — | 4 | 1 | no | — |
| 501 | Q8 | — | 4 | 1 | no | — |
| 502 | Q8 | — | 4 | 1 | no | — |
| 503 | Q8 | — | 8 | 1 | no | — |
| 504 | Q8 | — | 28 | 2 | no | — |
| 505 | Q8 | — | 56 | 1 | no | — |
| 506 | D4 | — | 2 | 2 | no | — |
| 507 | D4 | — | 2 | 2 | no | — |
| 508 | D4 | — | 4 | 2 | no | — |
| 509 | D4 | — | 8 | 1 | no | — |
| 510 | D4 | — | 8 | 2 | no | — |
| 511 | D4 | — | 14 | 2 | no | — |
| 512 | D4 | — | 14 | 2 | no | — |
| 513 | D4 | — | 28 | 2 | no | — |
| 514 | D4 | — | 28 | 1 | no | — |
| 515 | D4 | — | 28 | 1 | no | — |
| 516 | D4 | — | 28 | 2 | no | — |
| 517 | D4 | — | 28 | 1 | no | — |
| 518 | D4 | — | 28 | 1 | no | — |
| 519 | D4 | — | 56 | 1 | no | — |
| 520 | D4 | — | 56 | 4 | no | — |
| 521 | D4 | — | 56 | 2 | no | — |
| 522 | D4 | — | 56 | 2 | no | — |
| 523 | D4 | — | 56 | 4 | no | — |
| 524 | D4 | — | 56 | 4 | no | — |
| 525 | C2×C4 | — | 2 | 1 | no | — |
| 526 | C2×C4 | — | 2 | 1 | no | — |
| 527 | C2×C4 | — | 2 | 2 | no | — |
| 528 | C2×C4 | — | 2 | 1 | no | — |
| 529 | C2×C4 | — | 2 | 1 | no | — |
| 530 | C2×C4 | — | 2 | 2 | no | — |
| 531 | C2×C4 | — | 4 | 2 | no | — |
| 532 | C2×C4 | — | 4 | 2 | no | — |
| 533 | C2×C4 | — | 4 | 1 | no | — |
| 534 | C2×C4 | — | 4 | 1 | no | — |
| 535 | C2×C4 | — | 14 | 2 | no | — |
| 536 | C2×C4 | — | 14 | 2 | no | — |
| 537 | C2×C4 | — | 28 | 4 | no | — |
| 538 | C2×C4 | — | 28 | 2 | no | — |
| 539 | C2×C4 | — | 28 | 2 | no | — |
| 540 | C2×C4 | #6500 | 1 | 1 | yes | characteristic |
| 541 | C2×C4 | #6500 | 1 | 1 | yes | characteristic |
| 542 | C2×C4 | #6500 | 1 | 1 | yes | characteristic |
| 543 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 544 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 545 | C2×C4 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 546 | C8 | — | 4 | 2 | no | — |
| 547 | C8 | — | 28 | 1 | no | — |
| 548 | C8 | — | 28 | 1 | no | — |
| 549 | C8 | — | 28 | 2 | no | — |
| 550 | C7 | #18691 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 551 | C22 | — | 2 | 1 | no | — |
| 552 | C22 | — | 2 | 1 | no | — |
| 553 | C22 | — | 2 | 1 | no | — |
| 554 | C22 | — | 4 | 2 | no | — |
| 555 | C22 | — | 4 | 2 | no | — |
| 556 | C22 | — | 4 | 2 | no | — |
| 557 | C22 | — | 28 | 2 | no | — |
| 558 | C22 | — | 28 | 2 | no | — |
| 559 | C22 | — | 28 | 2 | no | — |
| 560 | C22 | — | 28 | 2 | no | — |
| 561 | C22 | — | 28 | 2 | no | — |
| 562 | C22 | — | 28 | 2 | no | — |
| 563 | C22 | — | 112 | 8 | no | — |
| 564 | C22 | C2×#6500 | 1 | 1 | yes | characteristic |
| 565 | C4 | — | 2 | 1 | no | — |
| 566 | C4 | — | 2 | 1 | no | — |
| 567 | C4 | — | 2 | 1 | no | — |
| 568 | C4 | — | 4 | 2 | no | — |
| 569 | C4 | — | 8 | 1 | no | — |
| 570 | C4 | — | 8 | 1 | no | — |
| 571 | C4 | — | 28 | 2 | no | — |
| 572 | C4 | — | 28 | 2 | no | — |
| 573 | C4 | #89974 | 1 | 2 | yes | — |
| 574 | C4 | #90465 | 1 | 1 | yes | characteristic |
| 575 | C4 | #90466 | 1 | 1 | yes | characteristic |
| 576 | C4 | #90526 | 1 | 1 | yes | characteristic |
| 577 | C4 | #90528 | 1 | 1 | yes | characteristic |
| 578 | C2 | — | 4 | 1 | no | — |
| 579 | C2 | — | 8 | 2 | no | — |
| 580 | C2 | — | 56 | 2 | no | — |
| 581 | C2 | — | 56 | 2 | no | — |
| 582 | C2 | #11740869 | 1 | 1 | yes | characteristic |
| 583 | C2 | #11741394 | 1 | 1 | yes | characteristic |
| 584 | C2 | C2×#89974 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#3254 | C2 | semidirect |
| 3. #11740811 | C2 | semidirect |
| 4. #11740779 | C2 | semidirect |
| 5. #11729556 | C2 | semidirect |
| 6. #11728863 | C2 | semidirect |
| 7. #11728862 | C2 | semidirect |
| 8. #11728801 | C2 | semidirect |
| 9. #11728798 | C2 | semidirect |
| 10. #11728259 | C2 | semidirect |
| 11. #11728252 | C2 | semidirect |
| 12. C7×#533 | C22 | semidirect |
| 27. C7×#474 | C22 | semidirect |
| 29. C7×#461 | C22 | semidirect |
| 31. C7×#423 | C22 | semidirect |
| 32. #89865 | C22 | semidirect |
| 33. #89865 | C22 | semidirect |
| 36. #89859 | C22 | semidirect |
| 37. #89855 | C22 | semidirect |
| 43. #89696 | C22 | semidirect |
| 44. C2×C4×C7⋊C8 | C22 | semidirect |
| 45. D4⋊(C7⋊C8) | C22 | semidirect |
| 46. D4⋊(C7⋊C8) | C22 | semidirect |
| 48. #89278 | C22 | semidirect |
| 49. #89278 | C22 | semidirect |
| 50. #89276 | C22 | semidirect |
| 129. #3254 | D7 | semidirect |
| 222. #533 | C2×D7 | semidirect |
| 234. #474 | C2×D7 | semidirect |
| 238. #461 | C2×D7 | semidirect |
| 242. #423 | C2×D7 | semidirect |
| 550. C7 | #18691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11743320 | 2 |
| C7×#3254 | 2 |
| #11740811 | 2 |
| #11740779 | 2 |
| #11729556 | 2 |
| #11728863 | 2 |
| #11728862 | 2 |
| #11728801 | 2 |
| #11728798 | 2 |
| #11728259 | 2 |
| #11728252 | 2 |
| #18691 | 7 |