Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
4770 conjugacy classes of subgroups.
The subgroup lattice has 498 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C7×H(7,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11744367 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #11744351 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11741568 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #11741566 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #11741565 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C2×#90014 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #11741549 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #11741545 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C7×#585 | — | 2 | 8 | no | — |
| 11 | C7×#585 | — | 2 | 2 | no | — |
| 12 | C7×#585 | C22 | 1 | 6 | yes | — |
| 13 | C7×#585 | C22 | 1 | 2 | yes | — |
| 14 | C2×C7×H(5,𝔽2) | — | 2 | 8 | no | — |
| 15 | C2×C7×H(5,𝔽2) | — | 2 | 6 | no | — |
| 16 | C2×C7×H(5,𝔽2) | C22 | 1 | 6 | yes | — |
| 17 | C2×C7×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#6554 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #90529 | — | 2 | 8 | no | — |
| 20 | #90527 | — | 2 | 8 | no | — |
| 21 | #90523 | C22 | 1 | 3 | yes | complemented |
| 22 | #90522 | — | 2 | 2 | no | — |
| 23 | #41×Dic7 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #90516 | C22 | 1 | 3 | yes | complemented |
| 25 | C2×#6514 | C22 | 1 | 12 | yes | complemented |
| 26 | #90513 | C22 | 1 | 12 | yes | complemented |
| 27 | #90510 | C22 | 1 | 2 | yes | complemented |
| 28 | #90497 | — | 2 | 6 | no | — |
| 29 | #90496 | C22 | 1 | 3 | yes | complemented |
| 30 | C2×#6499 | C22 | 1 | 3 | yes | complemented |
| 31 | #90018 | C22 | 1 | 12 | yes | complemented |
| 32 | #90017 | C22 | 1 | 4 | yes | complemented |
| 33 | #90014 | C22 | 1 | 24 | yes | complemented |
| 34 | #90014 | C22 | 1 | 12 | yes | complemented |
| 35 | #90013 | C22 | 1 | 12 | yes | complemented |
| 36 | #90009 | C22 | 1 | 6 | yes | complemented |
| 37 | #90008 | C22 | 1 | 12 | yes | complemented |
| 38 | C2×#6411 | C22 | 1 | 12 | yes | complemented |
| 39 | C2×#6407 | C22 | 1 | 6 | yes | complemented |
| 40 | #60389 | — | 7 | 1 | no | maximal, Sylow |
| 41 | C7×2−1+4 | — | 2 | 8 | no | — |
| 42 | C7×2−1+4 | — | 2 | 12 | no | — |
| 43 | C7×2−1+4 | — | 2 | 2 | no | — |
| 44 | C7×2−1+4 | D4 | 1 | 8 | yes | complemented |
| 45 | C7×2−1+4 | C23 | 1 | 4 | yes | — |
| 46 | C7×H(5,𝔽2) | — | 2 | 8 | no | — |
| 47 | C7×H(5,𝔽2) | — | 2 | 48 | no | — |
| 48 | C7×H(5,𝔽2) | — | 2 | 24 | no | — |
| 49 | C7×H(5,𝔽2) | — | 2 | 8 | no | — |
| 50 | C7×H(5,𝔽2) | — | 2 | 12 | no | — |
| 51 | C7×H(5,𝔽2) | — | 2 | 12 | no | — |
| 52 | C7×H(5,𝔽2) | — | 2 | 6 | no | — |
| 53 | C7×H(5,𝔽2) | — | 2 | 12 | no | — |
| 54 | C7×H(5,𝔽2) | D4 | 1 | 8 | yes | complemented |
| 55 | C7×H(5,𝔽2) | C23 | 1 | 12 | yes | — |
| 56 | C2×C7×#41 | — | 2 | 16 | no | — |
| 57 | C2×C7×#41 | — | 2 | 24 | no | — |
| 58 | C2×C7×#41 | — | 2 | 24 | no | — |
| 59 | C2×C7×#41 | — | 2 | 8 | no | — |
| 60 | C2×C7×#41 | — | 2 | 12 | no | — |
| 61 | C2×C7×#41 | — | 2 | 12 | no | — |
| 62 | C2×C7×#41 | D4 | 1 | 2 | yes | — |
| 63 | C2×C7×#41 | C23 | 1 | 12 | yes | — |
| 64 | C2×C7×#41 | C23 | 1 | 3 | yes | — |
| 65 | C2×C7×#41 | C23 | 1 | 1 | yes | characteristic |
| 66 | C22×C7×D4 | — | 2 | 24 | no | — |
| 67 | C22×C7×D4 | — | 2 | 12 | no | — |
| 68 | C22×C7×D4 | — | 2 | 12 | no | — |
| 69 | C22×C7×D4 | D4 | 1 | 6 | yes | — |
| 70 | C22×C7×D4 | C23 | 1 | 3 | yes | — |
| 71 | #6554 | — | 2 | 8 | no | — |
| 72 | C2×Q8×D7 | — | 2 | 1 | no | — |
| 73 | C2×#1159 | — | 2 | 3 | no | — |
| 74 | C2×#1157 | C23 | 1 | 3 | yes | complemented |
| 75 | C22×Dic14 | C23 | 1 | 3 | yes | complemented |
| 76 | #6516 | — | 2 | 6 | no | — |
| 77 | C2×C22⋊Dic7 | — | 2 | 6 | no | — |
| 78 | #6514 | — | 2 | 24 | no | — |
| 79 | #6514 | C23 | 1 | 24 | yes | complemented |
| 80 | #6513 | — | 2 | 24 | no | — |
| 81 | #6512 | C23 | 1 | 8 | yes | complemented |
| 82 | #6511 | — | 2 | 8 | no | — |
| 83 | #6510 | C23 | 1 | 1 | yes | characteristic, complemented |
| 84 | Q8×Dic7 | — | 2 | 1 | no | — |
| 85 | #6507 | C23 | 1 | 3 | yes | complemented |
| 86 | C2×#1144 | — | 2 | 12 | no | — |
| 87 | #6505 | — | 2 | 12 | no | — |
| 88 | #6503 | C23 | 1 | 3 | yes | complemented |
| 89 | #6502 | — | 2 | 6 | no | — |
| 90 | #6501 | — | 2 | 6 | no | — |
| 91 | #6499 | — | 2 | 6 | no | — |
| 92 | #6499 | C23 | 1 | 3 | yes | complemented |
| 93 | #6499 | C23 | 1 | 6 | yes | complemented |
| 94 | #6498 | — | 2 | 6 | no | — |
| 95 | D4×Dic7 | — | 2 | 3 | no | — |
| 96 | C2×#1142 | — | 2 | 12 | no | — |
| 97 | #6495 | — | 2 | 12 | no | — |
| 98 | C4×C22⋊D7 | — | 2 | 6 | no | — |
| 99 | #6489 | C23 | 1 | 3 | yes | complemented |
| 100 | #6487 | — | 2 | 6 | no | — |
| 101 | C2×C4×Dic7 | C23 | 1 | 3 | yes | complemented |
| 102 | C2×#1136 | C23 | 1 | 12 | yes | complemented |
| 103 | #6411 | C23 | 1 | 8 | yes | complemented |
| 104 | #6411 | C23 | 1 | 24 | yes | complemented |
| 105 | #6410 | C23 | 1 | 4 | yes | complemented |
| 106 | #6407 | C23 | 1 | 12 | yes | complemented |
| 107 | H(7,𝔽2) | D7 | 1 | 1 | yes | characteristic, complemented |
| 108 | #3586 | — | 7 | 2 | no | — |
| 109 | #3500 | — | 7 | 1 | no | — |
| 110 | #3022 | — | 7 | 6 | no | — |
| 111 | #3019 | — | 7 | 6 | no | — |
| 112 | #3018 | — | 7 | 6 | no | — |
| 113 | C2×#455 | — | 7 | 6 | no | — |
| 114 | #2901 | — | 7 | 2 | no | — |
| 115 | #2888 | — | 7 | 1 | no | — |
| 116 | C24×C7 | — | 2 | 12 | no | — |
| 117 | C24×C7 | C2×D4 | 1 | 6 | yes | — |
| 118 | C7×#41 | — | 2 | 48 | no | — |
| 119 | C7×#41 | — | 2 | 48 | no | — |
| 120 | C7×#41 | — | 2 | 24 | no | — |
| 121 | C7×#41 | — | 2 | 24 | no | — |
| 122 | C7×#41 | — | 2 | 8 | no | — |
| 123 | C7×#41 | — | 2 | 8 | no | — |
| 124 | C7×#41 | — | 2 | 24 | no | — |
| 125 | C7×#41 | — | 2 | 24 | no | — |
| 126 | C7×#41 | — | 2 | 8 | no | — |
| 127 | C7×#41 | — | 2 | 8 | no | — |
| 128 | C7×#41 | — | 2 | 12 | no | — |
| 129 | C7×#41 | — | 2 | 12 | no | — |
| 130 | C7×#41 | — | 2 | 12 | no | — |
| 131 | C7×#41 | C2×D4 | 1 | 24 | yes | — |
| 132 | C7×#41 | C2×D4 | 1 | 8 | yes | — |
| 133 | C7×#41 | C24 | 1 | 8 | yes | — |
| 134 | C2×C7×Q8 | — | 2 | 12 | no | — |
| 135 | C2×C7×Q8 | — | 2 | 8 | no | — |
| 136 | C2×C7×Q8 | — | 2 | 8 | no | — |
| 137 | C2×C7×Q8 | C2×D4 | 1 | 12 | yes | — |
| 138 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C2×C7×Q8 | C24 | 1 | 1 | yes | characteristic |
| 140 | C2×C7×D4 | — | 2 | 48 | no | — |
| 141 | C2×C7×D4 | — | 2 | 48 | no | — |
| 142 | C2×C7×D4 | — | 2 | 24 | no | — |
| 143 | C2×C7×D4 | — | 2 | 48 | no | — |
| 144 | C2×C7×D4 | — | 2 | 12 | no | — |
| 145 | C2×C7×D4 | — | 2 | 24 | no | — |
| 146 | C2×C7×D4 | — | 2 | 12 | no | — |
| 147 | C2×C7×D4 | — | 2 | 24 | no | — |
| 148 | C2×C7×D4 | — | 2 | 24 | no | — |
| 149 | C2×C7×D4 | — | 2 | 24 | no | — |
| 150 | C2×C7×D4 | — | 2 | 12 | no | — |
| 151 | C2×C7×D4 | C2×D4 | 1 | 6 | yes | — |
| 152 | C2×C7×D4 | C2×D4 | 1 | 6 | yes | — |
| 153 | C2×C7×D4 | C2×D4 | 1 | 12 | yes | — |
| 154 | C2×C7×D4 | C2×D4 | 1 | 3 | yes | — |
| 155 | C2×C7×D4 | C24 | 1 | 3 | yes | — |
| 156 | C22×C4×C7 | — | 2 | 12 | no | — |
| 157 | C22×C4×C7 | — | 2 | 24 | no | — |
| 158 | C22×C4×C7 | — | 2 | 12 | no | — |
| 159 | C22×C4×C7 | C2×D4 | 1 | 6 | yes | — |
| 160 | C22×C4×C7 | C24 | 1 | 3 | yes | — |
| 161 | C2×C22⋊D7 | — | 2 | 3 | no | — |
| 162 | C2×C22⋊D7 | — | 2 | 6 | no | — |
| 163 | C22×Dic7 | — | 2 | 3 | no | — |
| 164 | C22×Dic7 | — | 2 | 3 | no | — |
| 165 | Q8×D7 | — | 4 | 4 | no | — |
| 166 | #1159 | — | 4 | 12 | no | — |
| 167 | #1157 | — | 2 | 12 | no | — |
| 168 | C2×D28 | C24 | 1 | 1 | yes | characteristic |
| 169 | C2×C4×D7 | — | 2 | 3 | no | — |
| 170 | C2×Dic14 | — | 2 | 12 | no | — |
| 171 | C2×Dic14 | — | 2 | 3 | no | — |
| 172 | C2×Dic14 | C24 | 1 | 3 | yes | — |
| 173 | C22⋊Dic7 | — | 2 | 12 | no | — |
| 174 | C22⋊Dic7 | — | 2 | 3 | no | — |
| 175 | C22⋊Dic7 | — | 2 | 6 | no | — |
| 176 | #1144 | — | 2 | 24 | no | — |
| 177 | #1143 | — | 2 | 8 | no | — |
| 178 | #1142 | — | 2 | 24 | no | — |
| 179 | #1141 | — | 2 | 8 | no | — |
| 180 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 181 | C4⋊Dic7 | — | 2 | 3 | no | — |
| 182 | Dic7⋊C4 | — | 2 | 6 | no | — |
| 183 | C4×Dic7 | — | 2 | 3 | no | — |
| 184 | C4×Dic7 | C24 | 1 | 1 | yes | characteristic |
| 185 | C4×Dic7 | C24 | 1 | 3 | yes | — |
| 186 | #1136 | — | 2 | 12 | no | — |
| 187 | #1136 | C24 | 1 | 8 | yes | — |
| 188 | C2×C7⋊C8 | — | 2 | 12 | no | — |
| 189 | #585 | — | 2 | 8 | no | — |
| 190 | #585 | — | 2 | 2 | no | — |
| 191 | #585 | C2×D7 | 1 | 6 | yes | — |
| 192 | #585 | C2×D7 | 1 | 2 | yes | — |
| 193 | C2×2−1+4 | — | 7 | 1 | no | — |
| 194 | C2×H(5,𝔽2) | — | 2 | 8 | no | — |
| 195 | C2×H(5,𝔽2) | — | 2 | 6 | no | — |
| 196 | C2×H(5,𝔽2) | C2×D7 | 1 | 6 | yes | — |
| 197 | C2×H(5,𝔽2) | C2×D7 | 1 | 1 | yes | characteristic |
| 198 | #578 | — | 14 | 8 | no | — |
| 199 | #577 | — | 14 | 8 | no | — |
| 200 | #575 | — | 7 | 12 | no | — |
| 201 | C2×#137 | — | 7 | 12 | no | — |
| 202 | #568 | — | 7 | 2 | no | — |
| 203 | #548 | — | 14 | 2 | no | — |
| 204 | #546 | — | 14 | 6 | no | — |
| 205 | #536 | — | 7 | 3 | no | — |
| 206 | #535 | — | 7 | 3 | no | — |
| 207 | #532 | — | 7 | 3 | no | — |
| 208 | C2×#124 | — | 7 | 3 | no | — |
| 209 | C4×#41 | — | 7 | 1 | no | — |
| 210 | #456 | — | 7 | 12 | no | — |
| 211 | #455 | — | 7 | 12 | no | — |
| 212 | #455 | — | 7 | 24 | no | — |
| 213 | #454 | — | 7 | 4 | no | — |
| 214 | #453 | — | 7 | 12 | no | — |
| 215 | #421 | — | 7 | 12 | no | — |
| 216 | C2×#104 | — | 7 | 12 | no | — |
| 217 | #413 | — | 7 | 6 | no | — |
| 218 | C2×#100 | — | 7 | 6 | no | — |
| 219 | C23×C7 | — | 2 | 24 | no | — |
| 220 | C23×C7 | — | 2 | 12 | no | — |
| 221 | C23×C7 | — | 2 | 12 | no | — |
| 222 | C23×C7 | — | 8 | 6 | no | — |
| 223 | C23×C7 | — | 16 | 12 | no | — |
| 224 | C23×C7 | C22×D4 | 1 | 6 | yes | — |
| 225 | C23×C7 | C22×D4 | 1 | 3 | yes | — |
| 226 | C22×D7 | — | 2 | 1 | no | — |
| 227 | C7×Q8 | — | 2 | 8 | no | — |
| 228 | C7×Q8 | — | 2 | 12 | no | — |
| 229 | C7×Q8 | — | 2 | 2 | no | — |
| 230 | C7×Q8 | #120 | 1 | 4 | yes | — |
| 231 | C7×Q8 | C22×D4 | 1 | 8 | yes | — |
| 232 | C7×D4 | — | 2 | 48 | no | — |
| 233 | C7×D4 | — | 2 | 8 | no | — |
| 234 | C7×D4 | — | 2 | 24 | no | — |
| 235 | C7×D4 | — | 2 | 12 | no | — |
| 236 | C7×D4 | — | 2 | 8 | no | — |
| 237 | C7×D4 | — | 2 | 12 | no | — |
| 238 | C7×D4 | — | 2 | 12 | no | — |
| 239 | C7×D4 | — | 2 | 6 | no | — |
| 240 | C7×D4 | #120 | 1 | 12 | yes | — |
| 241 | C7×D4 | C22×D4 | 1 | 8 | yes | — |
| 242 | C2×C4×C7 | — | 2 | 24 | no | — |
| 243 | C2×C4×C7 | — | 2 | 16 | no | — |
| 244 | C2×C4×C7 | — | 2 | 12 | no | — |
| 245 | C2×C4×C7 | — | 2 | 24 | no | — |
| 246 | C2×C4×C7 | — | 2 | 12 | no | — |
| 247 | C2×C4×C7 | — | 2 | 8 | no | — |
| 248 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 249 | C2×C4×C7 | C22×D4 | 1 | 3 | yes | — |
| 250 | C2×C4×C7 | C22×D4 | 1 | 12 | yes | — |
| 251 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 252 | C22⋊D7 | — | 4 | 6 | no | — |
| 253 | C22⋊D7 | — | 8 | 6 | no | — |
| 254 | C2×Dic7 | — | 2 | 1 | no | — |
| 255 | C2×Dic7 | — | 2 | 3 | no | — |
| 256 | C2×Dic7 | — | 2 | 3 | no | — |
| 257 | C2×Dic7 | — | 4 | 6 | no | — |
| 258 | C2×Dic7 | — | 8 | 3 | no | — |
| 259 | D28 | — | 2 | 2 | no | — |
| 260 | C4×D7 | — | 4 | 6 | no | — |
| 261 | Dic14 | — | 2 | 6 | no | — |
| 262 | Dic14 | — | 4 | 6 | no | — |
| 263 | C7⋊C8 | — | 2 | 8 | no | — |
| 264 | 2−1+4 | — | 2 | 8 | no | — |
| 265 | 2−1+4 | — | 2 | 12 | no | — |
| 266 | 2−1+4 | — | 2 | 2 | no | — |
| 267 | 2−1+4 | — | 14 | 8 | no | — |
| 268 | 2−1+4 | C22⋊D7 | 1 | 8 | yes | complemented |
| 269 | 2−1+4 | C22×D7 | 1 | 4 | yes | — |
| 270 | H(5,𝔽2) | — | 2 | 8 | no | — |
| 271 | H(5,𝔽2) | — | 2 | 48 | no | — |
| 272 | H(5,𝔽2) | — | 2 | 24 | no | — |
| 273 | H(5,𝔽2) | — | 2 | 8 | no | — |
| 274 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 275 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 276 | H(5,𝔽2) | — | 2 | 6 | no | — |
| 277 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 278 | H(5,𝔽2) | C22⋊D7 | 1 | 8 | yes | complemented |
| 279 | H(5,𝔽2) | C22×D7 | 1 | 12 | yes | — |
| 280 | C2×#41 | — | 2 | 16 | no | — |
| 281 | C2×#41 | — | 2 | 24 | no | — |
| 282 | C2×#41 | — | 2 | 24 | no | — |
| 283 | C2×#41 | — | 2 | 8 | no | — |
| 284 | C2×#41 | — | 2 | 12 | no | — |
| 285 | C2×#41 | — | 2 | 12 | no | — |
| 286 | C2×#41 | — | 7 | 3 | no | — |
| 287 | C2×#41 | — | 14 | 3 | no | — |
| 288 | C2×#41 | C22⋊D7 | 1 | 2 | yes | — |
| 289 | C2×#41 | C22×D7 | 1 | 12 | yes | — |
| 290 | C2×#41 | C22×D7 | 1 | 3 | yes | — |
| 291 | C2×#41 | C22×D7 | 1 | 1 | yes | characteristic |
| 292 | C22×Q8 | — | 7 | 3 | no | — |
| 293 | C22×Q8 | — | 14 | 1 | no | — |
| 294 | C22×D4 | — | 2 | 24 | no | — |
| 295 | C22×D4 | — | 2 | 12 | no | — |
| 296 | C22×D4 | — | 2 | 12 | no | — |
| 297 | C22×D4 | C22⋊D7 | 1 | 6 | yes | — |
| 298 | C22×D4 | C22×D7 | 1 | 3 | yes | — |
| 299 | #137 | — | 7 | 24 | no | — |
| 300 | #137 | — | 14 | 24 | no | — |
| 301 | #137 | — | 14 | 12 | no | — |
| 302 | AGL(1,ℤ/8) | — | 7 | 8 | no | — |
| 303 | AGL(1,ℤ/8) | — | 14 | 12 | no | — |
| 304 | #135 | — | 14 | 24 | no | — |
| 305 | C2×Q16 | — | 14 | 12 | no | — |
| 306 | C2×SD16 | — | 14 | 12 | no | — |
| 307 | #131 | — | 14 | 8 | no | — |
| 308 | C2×M16 | — | 7 | 12 | no | — |
| 309 | C4⋊Q8 | — | 7 | 3 | no | — |
| 310 | #127 | — | 7 | 3 | no | — |
| 311 | #124 | — | 7 | 1 | no | — |
| 312 | #124 | — | 7 | 3 | no | — |
| 313 | #124 | — | 7 | 6 | no | — |
| 314 | #124 | — | 14 | 6 | no | — |
| 315 | #123 | — | 14 | 6 | no | — |
| 316 | C22⋊Q8 | — | 14 | 6 | no | — |
| 317 | #121 | — | 14 | 6 | no | — |
| 318 | #121 | — | 14 | 6 | no | — |
| 319 | #120 | — | 14 | 6 | no | — |
| 320 | C4×Q8 | — | 14 | 1 | no | — |
| 321 | C4×D4 | — | 14 | 3 | no | — |
| 322 | C4×D4 | — | 14 | 6 | no | — |
| 323 | #117 | — | 7 | 3 | no | — |
| 324 | C2×C22⋊C4 | — | 14 | 6 | no | — |
| 325 | C2×C42 | — | 7 | 3 | no | — |
| 326 | #104 | — | 7 | 8 | no | — |
| 327 | #104 | — | 7 | 24 | no | — |
| 328 | #101 | — | 7 | 4 | no | — |
| 329 | #100 | — | 7 | 12 | no | — |
| 330 | C22×C7 | — | 2 | 6 | no | — |
| 331 | C22×C7 | — | 2 | 8 | no | — |
| 332 | C22×C7 | — | 4 | 3 | no | — |
| 333 | C22×C7 | — | 4 | 6 | no | — |
| 334 | C22×C7 | — | 8 | 12 | no | — |
| 335 | C22×C7 | — | 8 | 12 | no | — |
| 336 | C22×C7 | — | 8 | 24 | no | — |
| 337 | C22×C7 | C2×#120 | 1 | 6 | yes | — |
| 338 | C22×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 339 | C2×D7 | — | 4 | 2 | no | — |
| 340 | C2×D7 | — | 4 | 1 | no | — |
| 341 | C4×C7 | — | 2 | 8 | no | — |
| 342 | C4×C7 | — | 2 | 2 | no | — |
| 343 | C4×C7 | C2×#120 | 1 | 6 | yes | — |
| 344 | C4×C7 | C23×D4 | 1 | 2 | yes | — |
| 345 | Dic7 | — | 4 | 1 | no | — |
| 346 | Dic7 | — | 4 | 3 | no | — |
| 347 | Dic7 | — | 4 | 3 | no | — |
| 348 | C24 | — | 2 | 12 | no | — |
| 349 | C24 | C2×C22⋊D7 | 1 | 6 | yes | — |
| 350 | #41 | — | 2 | 48 | no | — |
| 351 | #41 | — | 2 | 48 | no | — |
| 352 | #41 | — | 2 | 24 | no | — |
| 353 | #41 | — | 2 | 24 | no | — |
| 354 | #41 | — | 2 | 8 | no | — |
| 355 | #41 | — | 2 | 8 | no | — |
| 356 | #41 | — | 2 | 24 | no | — |
| 357 | #41 | — | 2 | 24 | no | — |
| 358 | #41 | — | 2 | 8 | no | — |
| 359 | #41 | — | 2 | 8 | no | — |
| 360 | #41 | — | 2 | 12 | no | — |
| 361 | #41 | — | 2 | 12 | no | — |
| 362 | #41 | — | 2 | 12 | no | — |
| 363 | #41 | — | 14 | 12 | no | — |
| 364 | #41 | — | 28 | 12 | no | — |
| 365 | #41 | C2×C22⋊D7 | 1 | 24 | yes | — |
| 366 | #41 | C2×C22⋊D7 | 1 | 8 | yes | — |
| 367 | #41 | C23×D7 | 1 | 8 | yes | — |
| 368 | C2×Q8 | — | 2 | 12 | no | — |
| 369 | C2×Q8 | — | 2 | 8 | no | — |
| 370 | C2×Q8 | — | 2 | 8 | no | — |
| 371 | C2×Q8 | — | 7 | 3 | no | — |
| 372 | C2×Q8 | — | 14 | 3 | no | — |
| 373 | C2×Q8 | — | 14 | 12 | no | — |
| 374 | C2×Q8 | — | 28 | 4 | no | — |
| 375 | C2×Q8 | C2×C22⋊D7 | 1 | 12 | yes | — |
| 376 | C2×Q8 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 377 | C2×Q8 | C23×D7 | 1 | 1 | yes | characteristic |
| 378 | C2×D4 | — | 2 | 48 | no | — |
| 379 | C2×D4 | — | 2 | 48 | no | — |
| 380 | C2×D4 | — | 2 | 24 | no | — |
| 381 | C2×D4 | — | 2 | 48 | no | — |
| 382 | C2×D4 | — | 2 | 12 | no | — |
| 383 | C2×D4 | — | 2 | 24 | no | — |
| 384 | C2×D4 | — | 2 | 12 | no | — |
| 385 | C2×D4 | — | 2 | 24 | no | — |
| 386 | C2×D4 | — | 2 | 24 | no | — |
| 387 | C2×D4 | — | 2 | 24 | no | — |
| 388 | C2×D4 | — | 2 | 12 | no | — |
| 389 | C2×D4 | — | 7 | 1 | no | — |
| 390 | C2×D4 | — | 14 | 3 | no | — |
| 391 | C2×D4 | — | 14 | 6 | no | — |
| 392 | C2×D4 | C2×C22⋊D7 | 1 | 6 | yes | — |
| 393 | C2×D4 | C2×C22⋊D7 | 1 | 6 | yes | — |
| 394 | C2×D4 | C2×C22⋊D7 | 1 | 12 | yes | — |
| 395 | C2×D4 | C2×C22⋊D7 | 1 | 3 | yes | — |
| 396 | C2×D4 | C23×D7 | 1 | 3 | yes | — |
| 397 | C22×C4 | — | 2 | 12 | no | — |
| 398 | C22×C4 | — | 2 | 24 | no | — |
| 399 | C22×C4 | — | 2 | 12 | no | — |
| 400 | C22×C4 | — | 14 | 3 | no | — |
| 401 | C22×C4 | — | 14 | 3 | no | — |
| 402 | C22×C4 | — | 14 | 3 | no | — |
| 403 | C22×C4 | C2×C22⋊D7 | 1 | 6 | yes | — |
| 404 | C22×C4 | C23×D7 | 1 | 3 | yes | — |
| 405 | Q16 | — | 14 | 24 | no | — |
| 406 | SD16 | — | 14 | 8 | no | — |
| 407 | SD16 | — | 14 | 24 | no | — |
| 408 | D8 | — | 14 | 8 | no | — |
| 409 | M16 | — | 7 | 8 | no | — |
| 410 | M16 | — | 14 | 12 | no | — |
| 411 | C2×C8 | — | 14 | 12 | no | — |
| 412 | C4⋊C4 | — | 14 | 6 | no | — |
| 413 | C4⋊C4 | — | 14 | 3 | no | — |
| 414 | C22⋊C4 | — | 14 | 6 | no | — |
| 415 | C22⋊C4 | — | 14 | 12 | no | — |
| 416 | C22⋊C4 | — | 14 | 3 | no | — |
| 417 | C22⋊C4 | — | 14 | 2 | no | — |
| 418 | C42 | — | 7 | 1 | no | — |
| 419 | C42 | — | 7 | 3 | no | — |
| 420 | C42 | — | 14 | 3 | no | — |
| 421 | C2×C7 | — | 2 | 1 | no | — |
| 422 | C2×C7 | — | 2 | 6 | no | — |
| 423 | C2×C7 | — | 4 | 6 | no | — |
| 424 | C2×C7 | — | 4 | 8 | no | — |
| 425 | C2×C7 | C22×#120 | 1 | 1 | yes | characteristic |
| 426 | D7 | — | 8 | 1 | no | — |
| 427 | C23 | — | 2 | 24 | no | — |
| 428 | C23 | — | 2 | 12 | no | — |
| 429 | C23 | — | 2 | 12 | no | — |
| 430 | C23 | — | 8 | 6 | no | — |
| 431 | C23 | — | 14 | 1 | no | — |
| 432 | C23 | — | 16 | 12 | no | — |
| 433 | C23 | C22×C22⋊D7 | 1 | 6 | yes | — |
| 434 | C23 | C22×C22⋊D7 | 1 | 3 | yes | — |
| 435 | Q8 | — | 2 | 8 | no | — |
| 436 | Q8 | — | 2 | 12 | no | — |
| 437 | Q8 | — | 2 | 2 | no | — |
| 438 | Q8 | — | 14 | 6 | no | — |
| 439 | Q8 | — | 28 | 6 | no | — |
| 440 | Q8 | #6516 | 1 | 4 | yes | — |
| 441 | Q8 | C22×C22⋊D7 | 1 | 8 | yes | — |
| 442 | D4 | — | 2 | 48 | no | — |
| 443 | D4 | — | 2 | 8 | no | — |
| 444 | D4 | — | 2 | 24 | no | — |
| 445 | D4 | — | 2 | 12 | no | — |
| 446 | D4 | — | 2 | 8 | no | — |
| 447 | D4 | — | 2 | 12 | no | — |
| 448 | D4 | — | 2 | 12 | no | — |
| 449 | D4 | — | 2 | 6 | no | — |
| 450 | D4 | — | 14 | 2 | no | — |
| 451 | D4 | — | 28 | 6 | no | — |
| 452 | D4 | — | 56 | 6 | no | — |
| 453 | D4 | #6516 | 1 | 12 | yes | — |
| 454 | D4 | C22×C22⋊D7 | 1 | 8 | yes | — |
| 455 | C2×C4 | — | 2 | 24 | no | — |
| 456 | C2×C4 | — | 2 | 16 | no | — |
| 457 | C2×C4 | — | 2 | 12 | no | — |
| 458 | C2×C4 | — | 2 | 24 | no | — |
| 459 | C2×C4 | — | 2 | 12 | no | — |
| 460 | C2×C4 | — | 2 | 8 | no | — |
| 461 | C2×C4 | — | 14 | 1 | no | — |
| 462 | C2×C4 | — | 14 | 3 | no | — |
| 463 | C2×C4 | — | 14 | 3 | no | — |
| 464 | C2×C4 | — | 28 | 6 | no | — |
| 465 | C2×C4 | — | 28 | 6 | no | — |
| 466 | C2×C4 | — | 56 | 3 | no | — |
| 467 | C2×C4 | C22×C22⋊D7 | 1 | 2 | yes | — |
| 468 | C2×C4 | C22×C22⋊D7 | 1 | 3 | yes | — |
| 469 | C2×C4 | C22×C22⋊D7 | 1 | 12 | yes | — |
| 470 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 471 | C8 | — | 14 | 8 | no | — |
| 472 | C7 | #60389 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 473 | C22 | — | 2 | 6 | no | — |
| 474 | C22 | — | 2 | 8 | no | — |
| 475 | C22 | — | 4 | 3 | no | — |
| 476 | C22 | — | 4 | 6 | no | — |
| 477 | C22 | — | 8 | 12 | no | — |
| 478 | C22 | — | 8 | 12 | no | — |
| 479 | C22 | — | 8 | 24 | no | — |
| 480 | C22 | — | 28 | 2 | no | — |
| 481 | C22 | — | 28 | 1 | no | — |
| 482 | C22 | C2×#6516 | 1 | 6 | yes | — |
| 483 | C22 | C23×C22⋊D7 | 1 | 1 | yes | characteristic |
| 484 | C4 | — | 2 | 8 | no | — |
| 485 | C4 | — | 2 | 2 | no | — |
| 486 | C4 | — | 28 | 1 | no | — |
| 487 | C4 | — | 28 | 3 | no | — |
| 488 | C4 | — | 28 | 3 | no | — |
| 489 | C4 | C2×#6516 | 1 | 6 | yes | — |
| 490 | C4 | C23×C22⋊D7 | 1 | 2 | yes | — |
| 491 | C2 | — | 2 | 1 | no | — |
| 492 | C2 | — | 2 | 6 | no | — |
| 493 | C2 | — | 4 | 6 | no | — |
| 494 | C2 | — | 4 | 8 | no | — |
| 495 | C2 | — | 56 | 1 | no | — |
| 496 | C2 | C22×#6516 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×H(7,𝔽2) | C2 | semidirect |
| 2. #11744367 | C2 | semidirect |
| 3. #11744351 | C2 | semidirect |
| 4. #11741568 | C2 | semidirect |
| 5. #11741566 | C2 | semidirect |
| 6. #11741565 | C2 | semidirect |
| 7. C2×#90014 | C2 | semidirect |
| 8. #11741549 | C2 | semidirect |
| 9. #11741545 | C2 | semidirect |
| 18. C2×#6554 | C22 | semidirect |
| 21. #90523 | C22 | semidirect |
| 23. #41×Dic7 | C22 | semidirect |
| 24. #90516 | C22 | semidirect |
| 25. C2×#6514 | C22 | semidirect |
| 26. #90513 | C22 | semidirect |
| 27. #90510 | C22 | semidirect |
| 29. #90496 | C22 | semidirect |
| 30. C2×#6499 | C22 | semidirect |
| 31. #90018 | C22 | semidirect |
| 32. #90017 | C22 | semidirect |
| 33. #90014 | C22 | semidirect |
| 34. #90014 | C22 | semidirect |
| 35. #90013 | C22 | semidirect |
| 36. #90009 | C22 | semidirect |
| 37. #90008 | C22 | semidirect |
| 38. C2×#6411 | C22 | semidirect |
| 39. C2×#6407 | C22 | semidirect |
| 44. C7×2−1+4 | D4 | semidirect |
| 54. C7×H(5,𝔽2) | D4 | semidirect |
| 74. C2×#1157 | C23 | semidirect |
| 75. C22×Dic14 | C23 | semidirect |
| 79. #6514 | C23 | semidirect |
| 81. #6512 | C23 | semidirect |
| 83. #6510 | C23 | semidirect |
| 85. #6507 | C23 | semidirect |
| 88. #6503 | C23 | semidirect |
| 92. #6499 | C23 | semidirect |
| 93. #6499 | C23 | semidirect |
| 99. #6489 | C23 | semidirect |
| 101. C2×C4×Dic7 | C23 | semidirect |
| 102. C2×#1136 | C23 | semidirect |
| 103. #6411 | C23 | semidirect |
| 104. #6411 | C23 | semidirect |
| 105. #6410 | C23 | semidirect |
| 106. #6407 | C23 | semidirect |
| 107. H(7,𝔽2) | D7 | semidirect |
| 268. 2−1+4 | C22⋊D7 | semidirect |
| 278. H(5,𝔽2) | C22⋊D7 | semidirect |
| 472. C7 | #60389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×H(7,𝔽2) | 2 |
| #11744367 | 2 |
| #11744351 | 2 |
| #11741568 | 2 |
| #11741566 | 2 |
| #11741565 | 2 |
| C2×#90014 | 2 |
| #11741549 | 2 |
| #11741545 | 2 |
| #60389 | 7 |