Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2026 conjugacy classes of subgroups.
The subgroup lattice has 720 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D7×#578 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11744271 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C7×#3416 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11741462 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11741453 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11739486 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | D7×#510 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #11739482 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #11739480 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #11739478 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #11739475 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #11739469 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | C2×#89687 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | #11739460 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #11739457 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | D7×2−1+4 | — | 2 | 1 | no | — |
| 17 | #90618 | — | 2 | 1 | no | — |
| 18 | C7×#578 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C7×#576 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #90529 | — | 2 | 1 | no | — |
| 21 | #90527 | — | 2 | 1 | no | — |
| 22 | #90470 | — | 2 | 3 | no | — |
| 23 | D7×#137 | — | 2 | 3 | no | — |
| 24 | #90466 | — | 2 | 3 | no | — |
| 25 | #90464 | — | 2 | 3 | no | — |
| 26 | #90462 | C22 | 1 | 3 | yes | complemented |
| 27 | #90462 | C22 | 1 | 3 | yes | complemented |
| 28 | D7×#135 | C22 | 1 | 3 | yes | — |
| 29 | D7×#135 | C22 | 1 | 3 | yes | complemented |
| 30 | #90457 | C22 | 1 | 3 | yes | complemented |
| 31 | C2×D7×Q16 | C22 | 1 | 3 | yes | complemented |
| 32 | #90448 | C22 | 1 | 3 | yes | complemented |
| 33 | C2×#6475 | C22 | 1 | 3 | yes | — |
| 34 | #90444 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #90444 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | D7×#131 | C22 | 1 | 1 | yes | characteristic |
| 37 | C7×#510 | C22 | 1 | 3 | yes | complemented |
| 38 | C7×#509 | C22 | 1 | 3 | yes | complemented |
| 39 | C7×#508 | C22 | 1 | 3 | yes | complemented |
| 40 | C2×C7×SD32 | C22 | 1 | 3 | yes | complemented |
| 41 | C7×#504 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #89967 | C22 | 1 | 3 | yes | complemented |
| 43 | #89967 | C22 | 1 | 3 | yes | complemented |
| 44 | #89966 | C22 | 1 | 3 | yes | complemented |
| 45 | #89966 | C22 | 1 | 3 | yes | complemented |
| 46 | C2×#6403 | C22 | 1 | 3 | yes | complemented |
| 47 | #89951 | C22 | 1 | 3 | yes | complemented |
| 48 | C2×#6401 | C22 | 1 | 3 | yes | complemented |
| 49 | #89919 | C22 | 1 | 3 | yes | complemented |
| 50 | #89912 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | #89690 | C22 | 1 | 3 | yes | complemented |
| 52 | #89690 | C22 | 1 | 3 | yes | complemented |
| 53 | D7×Q32 | C22 | 1 | 6 | yes | complemented |
| 54 | #89688 | C22 | 1 | 6 | yes | complemented |
| 55 | #89687 | C22 | 1 | 3 | yes | complemented |
| 56 | #89687 | C22 | 1 | 6 | yes | complemented |
| 57 | #89687 | C22 | 1 | 6 | yes | complemented |
| 58 | #89687 | C22 | 1 | 6 | yes | complemented |
| 59 | #89687 | C22 | 1 | 3 | yes | complemented |
| 60 | #89686 | C22 | 1 | 3 | yes | complemented |
| 61 | #89686 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | D7×SD32 | C22 | 1 | 6 | yes | complemented |
| 63 | #89684 | C22 | 1 | 6 | yes | complemented |
| 64 | #89683 | C22 | 1 | 3 | yes | complemented |
| 65 | #89683 | C22 | 1 | 3 | yes | complemented |
| 66 | #89681 | C22 | 1 | 3 | yes | complemented |
| 67 | #89681 | C22 | 1 | 3 | yes | complemented |
| 68 | #89679 | C22 | 1 | 3 | yes | complemented |
| 69 | D7×M32 | C22 | 1 | 3 | yes | complemented |
| 70 | C2×Dic56 | C22 | 1 | 3 | yes | complemented |
| 71 | #89676 | C22 | 1 | 3 | yes | complemented |
| 72 | #89673 | C22 | 1 | 3 | yes | complemented |
| 73 | C2×#6372 | C22 | 1 | 3 | yes | complemented |
| 74 | #62637 | — | 7 | 1 | no | maximal, Sylow |
| 75 | C7×2−1+4 | — | 2 | 1 | no | — |
| 76 | C7×H(5,𝔽2) | — | 2 | 1 | no | — |
| 77 | #6554 | — | 2 | 1 | no | — |
| 78 | #6554 | — | 2 | 1 | no | — |
| 79 | #6554 | — | 2 | 3 | no | — |
| 80 | #6554 | — | 2 | 3 | no | — |
| 81 | #6554 | — | 4 | 1 | no | — |
| 82 | #6554 | — | 4 | 3 | no | — |
| 83 | D7×#41 | — | 2 | 3 | no | — |
| 84 | D7×#41 | — | 2 | 3 | no | — |
| 85 | D7×#41 | — | 4 | 1 | no | — |
| 86 | D7×#41 | — | 4 | 3 | no | — |
| 87 | D7×#41 | D4 | 1 | 1 | yes | characteristic |
| 88 | #6551 | — | 2 | 3 | no | — |
| 89 | #6551 | — | 4 | 1 | no | — |
| 90 | C2×Q8×D7 | — | 2 | 3 | no | — |
| 91 | C2×Q8×D7 | — | 4 | 1 | no | — |
| 92 | #6548 | — | 2 | 3 | no | — |
| 93 | #6548 | — | 4 | 3 | no | — |
| 94 | C2×#1159 | — | 2 | 3 | no | — |
| 95 | C2×#1159 | — | 4 | 3 | no | — |
| 96 | C7×#137 | — | 2 | 3 | no | — |
| 97 | C7×AGL(1,ℤ/8) | — | 2 | 3 | no | — |
| 98 | C7×#135 | C23 | 1 | 3 | yes | — |
| 99 | C7×#135 | C23 | 1 | 3 | yes | — |
| 100 | C2×C7×Q16 | C23 | 1 | 3 | yes | — |
| 101 | C2×C7×D8 | C23 | 1 | 3 | yes | — |
| 102 | C7×#131 | C23 | 1 | 1 | yes | characteristic |
| 103 | #6514 | — | 2 | 3 | no | — |
| 104 | #6514 | — | 2 | 3 | no | — |
| 105 | #6513 | — | 2 | 3 | no | — |
| 106 | #6513 | — | 2 | 3 | no | — |
| 107 | #6511 | D4 | 1 | 1 | yes | characteristic |
| 108 | C2×#1144 | — | 2 | 3 | no | — |
| 109 | #6505 | — | 2 | 3 | no | — |
| 110 | C2×#1142 | — | 2 | 3 | no | — |
| 111 | #6495 | — | 2 | 3 | no | — |
| 112 | #6482 | C23 | 1 | 3 | yes | — |
| 113 | #6482 | C23 | 1 | 1 | yes | characteristic |
| 114 | #6481 | — | 2 | 6 | no | — |
| 115 | D7×Q16 | — | 2 | 3 | no | — |
| 116 | D7×Q16 | — | 2 | 3 | no | — |
| 117 | D7×Q16 | C23 | 1 | 6 | yes | — |
| 118 | D7×Q16 | C23 | 1 | 3 | yes | — |
| 119 | D7×Q16 | C23 | 1 | 3 | yes | — |
| 120 | #6479 | — | 2 | 3 | no | — |
| 121 | #6479 | — | 2 | 3 | no | — |
| 122 | #6478 | — | 2 | 6 | no | — |
| 123 | #6478 | — | 2 | 6 | no | — |
| 124 | D7×SD16 | — | 2 | 3 | no | — |
| 125 | D7×SD16 | — | 2 | 3 | no | — |
| 126 | #6475 | — | 2 | 3 | no | — |
| 127 | #6475 | — | 2 | 3 | no | — |
| 128 | #6475 | C23 | 1 | 3 | yes | — |
| 129 | #6475 | C23 | 1 | 6 | yes | — |
| 130 | #6475 | C23 | 1 | 3 | yes | — |
| 131 | #6474 | — | 2 | 6 | no | — |
| 132 | D7×D8 | C23 | 1 | 3 | yes | — |
| 133 | D7×D8 | C23 | 1 | 1 | yes | characteristic |
| 134 | #6472 | — | 2 | 3 | no | — |
| 135 | #6472 | — | 2 | 3 | no | — |
| 136 | #6470 | D4 | 1 | 3 | yes | — |
| 137 | D7×M16 | D4 | 1 | 3 | yes | — |
| 138 | C2×Dic28 | C23 | 1 | 3 | yes | — |
| 139 | C2×Dic28 | C23 | 1 | 3 | yes | — |
| 140 | #6467 | C23 | 1 | 3 | yes | — |
| 141 | #6467 | C23 | 1 | 3 | yes | — |
| 142 | #6464 | C23 | 1 | 3 | yes | — |
| 143 | C2×C8×D7 | C23 | 1 | 3 | yes | — |
| 144 | C7×Q32 | C23 | 1 | 3 | yes | — |
| 145 | C7×SD32 | C23 | 1 | 3 | yes | — |
| 146 | C7×SD32 | C23 | 1 | 6 | yes | — |
| 147 | C7×SD32 | C23 | 1 | 1 | yes | characteristic |
| 148 | C7×D16 | C23 | 1 | 3 | yes | — |
| 149 | C7×M32 | C23 | 1 | 3 | yes | — |
| 150 | C2×C7×C16 | C23 | 1 | 3 | yes | — |
| 151 | #6403 | C23 | 1 | 3 | yes | — |
| 152 | #6403 | C23 | 1 | 6 | yes | — |
| 153 | #6403 | C23 | 1 | 3 | yes | — |
| 154 | #6402 | C23 | 1 | 3 | yes | — |
| 155 | #6402 | C23 | 1 | 1 | yes | characteristic |
| 156 | #6401 | C23 | 1 | 6 | yes | — |
| 157 | #6401 | C23 | 1 | 3 | yes | — |
| 158 | #6401 | C23 | 1 | 3 | yes | — |
| 159 | #6400 | C23 | 1 | 3 | yes | — |
| 160 | #6400 | C23 | 1 | 1 | yes | characteristic |
| 161 | #6386 | C23 | 1 | 3 | yes | — |
| 162 | C2×C7⋊C16 | C23 | 1 | 3 | yes | — |
| 163 | Dic56 | C23 | 1 | 3 | yes | — |
| 164 | Dic56 | C23 | 1 | 6 | yes | — |
| 165 | #6374 | C23 | 1 | 3 | yes | — |
| 166 | #6374 | C23 | 1 | 3 | yes | — |
| 167 | D112 | C23 | 1 | 1 | yes | characteristic |
| 168 | #6372 | C23 | 1 | 1 | yes | characteristic |
| 169 | #6372 | C23 | 1 | 3 | yes | — |
| 170 | #6372 | C23 | 1 | 3 | yes | — |
| 171 | #6372 | C23 | 1 | 3 | yes | — |
| 172 | D7×C16 | C23 | 1 | 6 | yes | — |
| 173 | #3584 | — | 7 | 1 | no | — |
| 174 | C2×#578 | — | 7 | 1 | no | — |
| 175 | #3417 | — | 7 | 3 | no | — |
| 176 | #3417 | — | 7 | 3 | no | — |
| 177 | #3417 | — | 7 | 1 | no | — |
| 178 | #3417 | — | 7 | 1 | no | — |
| 179 | #3416 | — | 7 | 3 | no | — |
| 180 | #3416 | — | 7 | 3 | no | — |
| 181 | #3416 | — | 7 | 1 | no | — |
| 182 | #3416 | D7 | 1 | 1 | yes | characteristic, complemented |
| 183 | #3414 | — | 7 | 3 | no | — |
| 184 | #3414 | — | 7 | 3 | no | — |
| 185 | C2×#510 | — | 7 | 3 | no | — |
| 186 | C2×#510 | — | 7 | 3 | no | — |
| 187 | #3407 | — | 7 | 1 | no | — |
| 188 | C7×#41 | — | 2 | 3 | no | — |
| 189 | C7×#41 | — | 2 | 3 | no | — |
| 190 | C7×#41 | — | 4 | 1 | no | — |
| 191 | C7×#41 | — | 4 | 3 | no | — |
| 192 | C7×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C2×C7×Q8 | — | 2 | 3 | no | — |
| 194 | C2×C7×Q8 | — | 4 | 1 | no | — |
| 195 | C2×C7×D4 | — | 2 | 3 | no | — |
| 196 | C2×C7×D4 | — | 4 | 3 | no | — |
| 197 | C2×C22⋊D7 | — | 4 | 3 | no | — |
| 198 | C2×C22⋊D7 | — | 4 | 6 | no | — |
| 199 | C22×Dic7 | — | 4 | 3 | no | — |
| 200 | #1161 | — | 2 | 1 | no | — |
| 201 | #1161 | — | 2 | 3 | no | — |
| 202 | #1161 | — | 4 | 3 | no | — |
| 203 | #1161 | D8 | 1 | 1 | yes | characteristic |
| 204 | Q8×D7 | — | 2 | 3 | no | — |
| 205 | Q8×D7 | — | 2 | 3 | no | — |
| 206 | Q8×D7 | — | 2 | 6 | no | — |
| 207 | Q8×D7 | — | 4 | 1 | no | — |
| 208 | Q8×D7 | — | 4 | 1 | no | — |
| 209 | Q8×D7 | — | 4 | 3 | no | — |
| 210 | Q8×D7 | — | 4 | 3 | no | — |
| 211 | Q8×D7 | — | 4 | 3 | no | — |
| 212 | Q8×D7 | D8 | 1 | 1 | yes | characteristic |
| 213 | #1159 | — | 2 | 6 | no | — |
| 214 | #1159 | — | 2 | 3 | no | — |
| 215 | #1159 | — | 2 | 3 | no | — |
| 216 | #1159 | — | 4 | 3 | no | — |
| 217 | #1159 | — | 4 | 3 | no | — |
| 218 | #1159 | — | 4 | 6 | no | — |
| 219 | #1159 | — | 4 | 6 | no | — |
| 220 | #1159 | — | 4 | 3 | no | — |
| 221 | #1159 | — | 4 | 3 | no | — |
| 222 | #1159 | — | 4 | 3 | no | — |
| 223 | #1159 | — | 4 | 3 | no | — |
| 224 | #1159 | — | 4 | 3 | no | — |
| 225 | #1159 | D8 | 1 | 3 | yes | — |
| 226 | D4×D7 | — | 2 | 3 | no | — |
| 227 | D4×D7 | — | 2 | 1 | no | — |
| 228 | D4×D7 | — | 4 | 3 | no | — |
| 229 | D4×D7 | — | 4 | 3 | no | — |
| 230 | D4×D7 | — | 4 | 3 | no | — |
| 231 | D4×D7 | D8 | 1 | 3 | yes | — |
| 232 | #1157 | — | 2 | 3 | no | — |
| 233 | #1157 | — | 2 | 3 | no | — |
| 234 | #1157 | — | 4 | 6 | no | — |
| 235 | #1157 | — | 4 | 3 | no | — |
| 236 | #1157 | — | 4 | 3 | no | — |
| 237 | #1157 | — | 4 | 3 | no | — |
| 238 | #1157 | — | 4 | 3 | no | — |
| 239 | #1157 | C2×D4 | 1 | 3 | yes | — |
| 240 | C2×C4×D7 | — | 4 | 3 | no | — |
| 241 | C2×C4×D7 | — | 4 | 3 | no | — |
| 242 | C2×C4×D7 | — | 4 | 3 | no | — |
| 243 | C2×C4×D7 | C2×D4 | 1 | 3 | yes | — |
| 244 | C2×Dic14 | — | 2 | 3 | no | — |
| 245 | C2×Dic14 | — | 2 | 3 | no | — |
| 246 | C2×Dic14 | — | 4 | 3 | no | — |
| 247 | C2×Dic14 | — | 4 | 3 | no | — |
| 248 | C2×Dic14 | — | 4 | 3 | no | — |
| 249 | C7×Q16 | — | 2 | 3 | no | — |
| 250 | C7×Q16 | C24 | 1 | 3 | yes | — |
| 251 | C7×Q16 | C24 | 1 | 1 | yes | characteristic |
| 252 | C7×SD16 | — | 2 | 3 | no | — |
| 253 | C7×SD16 | — | 2 | 3 | no | — |
| 254 | C7×D8 | — | 2 | 3 | no | — |
| 255 | C7×D8 | C24 | 1 | 1 | yes | characteristic |
| 256 | C7×D8 | C24 | 1 | 3 | yes | — |
| 257 | C7×M16 | C2×D4 | 1 | 3 | yes | — |
| 258 | C2×C7×C8 | C24 | 1 | 3 | yes | — |
| 259 | #1144 | — | 2 | 3 | no | — |
| 260 | #1144 | — | 2 | 6 | no | — |
| 261 | #1144 | — | 2 | 3 | no | — |
| 262 | #1143 | — | 2 | 1 | no | — |
| 263 | #1143 | — | 2 | 3 | no | — |
| 264 | #1142 | — | 2 | 6 | no | — |
| 265 | #1142 | — | 2 | 3 | no | — |
| 266 | #1142 | — | 2 | 3 | no | — |
| 267 | #1141 | — | 2 | 3 | no | — |
| 268 | #1141 | — | 2 | 1 | no | — |
| 269 | #1136 | C2×D4 | 1 | 3 | yes | — |
| 270 | C2×C7⋊C8 | C2×D4 | 1 | 3 | yes | — |
| 271 | Dic28 | — | 2 | 3 | no | — |
| 272 | Dic28 | — | 2 | 3 | no | — |
| 273 | Dic28 | C24 | 1 | 3 | yes | — |
| 274 | Dic28 | C24 | 1 | 3 | yes | — |
| 275 | D56 | C24 | 1 | 1 | yes | characteristic |
| 276 | D56 | C24 | 1 | 1 | yes | characteristic |
| 277 | #1132 | — | 2 | 3 | no | — |
| 278 | #1132 | — | 2 | 3 | no | — |
| 279 | #1131 | C2×D4 | 1 | 6 | yes | — |
| 280 | C8×D7 | C2×D4 | 1 | 3 | yes | — |
| 281 | C8×D7 | C2×D4 | 1 | 3 | yes | — |
| 282 | C8×D7 | C24 | 1 | 1 | yes | characteristic |
| 283 | C8×D7 | C24 | 1 | 3 | yes | — |
| 284 | C7×C16 | C24 | 1 | 1 | yes | characteristic |
| 285 | C7×C16 | C24 | 1 | 3 | yes | — |
| 286 | C7⋊C16 | C24 | 1 | 3 | yes | — |
| 287 | C7⋊C16 | C24 | 1 | 1 | yes | characteristic |
| 288 | #585 | — | 14 | 1 | no | — |
| 289 | C2×2−1+4 | — | 14 | 1 | no | — |
| 290 | #578 | — | 7 | 3 | no | — |
| 291 | #578 | — | 7 | 3 | no | — |
| 292 | #578 | — | 7 | 3 | no | — |
| 293 | #578 | — | 7 | 1 | no | — |
| 294 | #578 | — | 7 | 1 | no | — |
| 295 | #578 | — | 14 | 3 | no | — |
| 296 | #578 | — | 14 | 1 | no | — |
| 297 | #578 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 298 | #577 | — | 14 | 3 | no | — |
| 299 | #577 | — | 14 | 1 | no | — |
| 300 | #576 | — | 7 | 3 | no | — |
| 301 | #576 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 302 | #575 | — | 14 | 3 | no | — |
| 303 | C2×#137 | — | 14 | 3 | no | — |
| 304 | C2×#135 | — | 7 | 3 | no | — |
| 305 | C2×#135 | — | 7 | 3 | no | — |
| 306 | C2×#135 | — | 7 | 3 | no | — |
| 307 | C22×Q16 | — | 7 | 3 | no | — |
| 308 | C2×#131 | — | 7 | 1 | no | — |
| 309 | #510 | — | 7 | 3 | no | — |
| 310 | #510 | — | 7 | 3 | no | — |
| 311 | #510 | — | 7 | 3 | no | — |
| 312 | #510 | — | 7 | 3 | no | — |
| 313 | #510 | — | 7 | 3 | no | — |
| 314 | #510 | — | 7 | 6 | no | — |
| 315 | #510 | — | 7 | 3 | no | — |
| 316 | #510 | — | 7 | 6 | no | — |
| 317 | #510 | — | 7 | 6 | no | — |
| 318 | #510 | — | 7 | 3 | no | — |
| 319 | #510 | — | 7 | 3 | no | — |
| 320 | #510 | — | 7 | 3 | no | — |
| 321 | #510 | C2×D7 | 1 | 3 | yes | complemented |
| 322 | #509 | — | 7 | 3 | no | — |
| 323 | #509 | — | 7 | 1 | no | — |
| 324 | #509 | — | 7 | 3 | no | — |
| 325 | #509 | — | 7 | 3 | no | — |
| 326 | #509 | — | 7 | 3 | no | — |
| 327 | #509 | C2×D7 | 1 | 3 | yes | complemented |
| 328 | #508 | — | 7 | 3 | no | — |
| 329 | #508 | — | 7 | 3 | no | — |
| 330 | #508 | — | 7 | 6 | no | — |
| 331 | #508 | — | 7 | 6 | no | — |
| 332 | #508 | — | 7 | 3 | no | — |
| 333 | #508 | C2×D7 | 1 | 3 | yes | complemented |
| 334 | C2×Q32 | — | 7 | 3 | no | — |
| 335 | C2×Q32 | — | 7 | 6 | no | — |
| 336 | C2×Q32 | — | 7 | 3 | no | — |
| 337 | C2×SD32 | — | 7 | 3 | no | — |
| 338 | C2×SD32 | — | 7 | 6 | no | — |
| 339 | C2×SD32 | C2×D7 | 1 | 3 | yes | complemented |
| 340 | #504 | — | 7 | 1 | no | — |
| 341 | #504 | — | 7 | 3 | no | — |
| 342 | #504 | — | 7 | 3 | no | — |
| 343 | #504 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 344 | C2×M32 | — | 7 | 3 | no | — |
| 345 | C2×M32 | — | 7 | 3 | no | — |
| 346 | C23×C7 | — | 4 | 3 | no | — |
| 347 | C22×D7 | — | 4 | 1 | no | — |
| 348 | C22×D7 | — | 4 | 3 | no | — |
| 349 | C22×D7 | C2×D8 | 1 | 3 | yes | — |
| 350 | C7×Q8 | — | 2 | 1 | no | — |
| 351 | C7×Q8 | — | 2 | 3 | no | — |
| 352 | C7×Q8 | — | 4 | 3 | no | — |
| 353 | C7×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 354 | C7×D4 | — | 2 | 3 | no | — |
| 355 | C7×D4 | — | 2 | 1 | no | — |
| 356 | C7×D4 | — | 4 | 3 | no | — |
| 357 | C7×D4 | — | 4 | 3 | no | — |
| 358 | C7×D4 | — | 4 | 3 | no | — |
| 359 | C7×D4 | C2×D8 | 1 | 3 | yes | — |
| 360 | C2×C4×C7 | — | 4 | 3 | no | — |
| 361 | C2×C4×C7 | — | 4 | 3 | no | — |
| 362 | C2×C4×C7 | — | 4 | 3 | no | — |
| 363 | C2×C4×C7 | C22×D4 | 1 | 3 | yes | — |
| 364 | C22⋊D7 | — | 4 | 3 | no | — |
| 365 | C22⋊D7 | — | 4 | 3 | no | — |
| 366 | C22⋊D7 | — | 4 | 3 | no | — |
| 367 | C22⋊D7 | — | 4 | 3 | no | — |
| 368 | C22⋊D7 | — | 4 | 6 | no | — |
| 369 | C22⋊D7 | — | 4 | 1 | no | — |
| 370 | C22⋊D7 | — | 4 | 3 | no | — |
| 371 | C22⋊D7 | C2×D8 | 1 | 6 | yes | — |
| 372 | C2×Dic7 | — | 4 | 3 | no | — |
| 373 | C2×Dic7 | — | 4 | 3 | no | — |
| 374 | C2×Dic7 | — | 4 | 3 | no | — |
| 375 | C2×Dic7 | — | 4 | 6 | no | — |
| 376 | C2×Dic7 | — | 4 | 3 | no | — |
| 377 | C2×Dic7 | C2×D8 | 1 | 3 | yes | — |
| 378 | D28 | — | 2 | 1 | no | — |
| 379 | D28 | — | 2 | 1 | no | — |
| 380 | D28 | — | 4 | 1 | no | — |
| 381 | D28 | — | 4 | 3 | no | — |
| 382 | D28 | C2×D8 | 1 | 3 | yes | — |
| 383 | C4×D7 | — | 4 | 3 | no | — |
| 384 | C4×D7 | — | 4 | 3 | no | — |
| 385 | C4×D7 | — | 4 | 6 | no | — |
| 386 | C4×D7 | — | 4 | 3 | no | — |
| 387 | C4×D7 | — | 4 | 3 | no | — |
| 388 | C4×D7 | — | 4 | 1 | no | — |
| 389 | C4×D7 | — | 4 | 3 | no | — |
| 390 | C4×D7 | C2×D8 | 1 | 3 | yes | — |
| 391 | C4×D7 | C2×D8 | 1 | 3 | yes | — |
| 392 | C4×D7 | C22×D4 | 1 | 1 | yes | characteristic |
| 393 | C4×D7 | C22×D4 | 1 | 3 | yes | — |
| 394 | Dic14 | — | 2 | 3 | no | — |
| 395 | Dic14 | — | 2 | 3 | no | — |
| 396 | Dic14 | — | 4 | 3 | no | — |
| 397 | Dic14 | — | 4 | 3 | no | — |
| 398 | Dic14 | — | 4 | 3 | no | — |
| 399 | Dic14 | — | 4 | 6 | no | — |
| 400 | Dic14 | — | 4 | 3 | no | — |
| 401 | Dic14 | C2×D8 | 1 | 3 | yes | — |
| 402 | C7×C8 | C22×D4 | 1 | 3 | yes | — |
| 403 | C7×C8 | C25 | 1 | 1 | yes | characteristic |
| 404 | C7⋊C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 405 | C7⋊C8 | C22×D4 | 1 | 3 | yes | — |
| 406 | 2−1+4 | — | 2 | 1 | no | — |
| 407 | 2−1+4 | — | 14 | 3 | no | — |
| 408 | 2−1+4 | — | 14 | 3 | no | — |
| 409 | 2−1+4 | — | 14 | 3 | no | — |
| 410 | 2−1+4 | — | 14 | 1 | no | — |
| 411 | 2−1+4 | — | 14 | 1 | no | — |
| 412 | 2−1+4 | — | 28 | 1 | no | — |
| 413 | 2−1+4 | — | 28 | 1 | no | — |
| 414 | 2−1+4 | — | 28 | 3 | no | — |
| 415 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 416 | H(5,𝔽2) | — | 14 | 3 | no | — |
| 417 | H(5,𝔽2) | — | 28 | 3 | no | — |
| 418 | C2×#41 | — | 7 | 1 | no | — |
| 419 | C2×#41 | — | 14 | 3 | no | — |
| 420 | C2×#41 | — | 14 | 3 | no | — |
| 421 | C2×#41 | — | 14 | 3 | no | — |
| 422 | C2×#41 | — | 28 | 3 | no | — |
| 423 | C2×#41 | — | 28 | 3 | no | — |
| 424 | C2×#41 | — | 28 | 1 | no | — |
| 425 | C22×Q8 | — | 14 | 3 | no | — |
| 426 | C22×Q8 | — | 28 | 1 | no | — |
| 427 | #137 | — | 2 | 3 | no | — |
| 428 | #137 | — | 14 | 6 | no | — |
| 429 | #137 | — | 14 | 6 | no | — |
| 430 | #137 | — | 14 | 6 | no | — |
| 431 | #137 | — | 14 | 3 | no | — |
| 432 | #137 | — | 14 | 3 | no | — |
| 433 | #137 | — | 14 | 3 | no | — |
| 434 | #137 | — | 14 | 3 | no | — |
| 435 | #137 | — | 14 | 3 | no | — |
| 436 | AGL(1,ℤ/8) | — | 2 | 3 | no | — |
| 437 | AGL(1,ℤ/8) | — | 14 | 6 | no | — |
| 438 | AGL(1,ℤ/8) | — | 14 | 3 | no | — |
| 439 | #135 | — | 7 | 1 | no | — |
| 440 | #135 | — | 7 | 3 | no | — |
| 441 | #135 | — | 7 | 3 | no | — |
| 442 | #135 | — | 7 | 6 | no | — |
| 443 | #135 | — | 7 | 3 | no | — |
| 444 | #135 | — | 7 | 3 | no | — |
| 445 | #135 | — | 7 | 3 | no | — |
| 446 | #135 | — | 14 | 3 | no | — |
| 447 | #135 | — | 14 | 3 | no | — |
| 448 | #135 | — | 14 | 3 | no | — |
| 449 | #135 | — | 14 | 3 | no | — |
| 450 | #135 | — | 14 | 3 | no | — |
| 451 | #135 | — | 14 | 3 | no | — |
| 452 | #135 | C22×D7 | 1 | 3 | yes | — |
| 453 | #135 | C22×D7 | 1 | 3 | yes | — |
| 454 | C2×Q16 | — | 7 | 3 | no | — |
| 455 | C2×Q16 | — | 7 | 6 | no | — |
| 456 | C2×Q16 | — | 7 | 3 | no | — |
| 457 | C2×Q16 | — | 7 | 3 | no | — |
| 458 | C2×Q16 | — | 7 | 3 | no | — |
| 459 | C2×Q16 | — | 14 | 3 | no | — |
| 460 | C2×Q16 | — | 14 | 3 | no | — |
| 461 | C2×Q16 | — | 14 | 3 | no | — |
| 462 | C2×Q16 | C22×D7 | 1 | 3 | yes | — |
| 463 | C2×SD16 | — | 14 | 3 | no | — |
| 464 | C2×SD16 | — | 14 | 3 | no | — |
| 465 | C2×SD16 | — | 14 | 3 | no | — |
| 466 | C2×D8 | — | 7 | 1 | no | — |
| 467 | C2×D8 | — | 7 | 3 | no | — |
| 468 | C2×D8 | C22×D7 | 1 | 3 | yes | — |
| 469 | #131 | — | 7 | 1 | no | — |
| 470 | #131 | — | 7 | 3 | no | — |
| 471 | #131 | — | 7 | 3 | no | — |
| 472 | #131 | C22×D7 | 1 | 1 | yes | characteristic |
| 473 | C2×M16 | — | 7 | 3 | no | — |
| 474 | C22×C8 | — | 7 | 3 | no | — |
| 475 | Q32 | — | 7 | 3 | no | — |
| 476 | Q32 | — | 7 | 3 | no | — |
| 477 | Q32 | — | 7 | 6 | no | — |
| 478 | Q32 | — | 7 | 6 | no | — |
| 479 | Q32 | — | 7 | 3 | no | — |
| 480 | Q32 | C22×D7 | 1 | 3 | yes | — |
| 481 | SD32 | — | 7 | 3 | no | — |
| 482 | SD32 | — | 7 | 1 | no | — |
| 483 | SD32 | — | 7 | 6 | no | — |
| 484 | SD32 | — | 7 | 3 | no | — |
| 485 | SD32 | — | 7 | 3 | no | — |
| 486 | SD32 | — | 7 | 3 | no | — |
| 487 | SD32 | — | 7 | 3 | no | — |
| 488 | SD32 | C22×D7 | 1 | 6 | yes | — |
| 489 | SD32 | C22×D7 | 1 | 3 | yes | — |
| 490 | SD32 | C22×D7 | 1 | 1 | yes | characteristic |
| 491 | D16 | — | 7 | 3 | no | — |
| 492 | D16 | — | 7 | 1 | no | — |
| 493 | D16 | — | 7 | 1 | no | — |
| 494 | D16 | C22×D7 | 1 | 3 | yes | — |
| 495 | M32 | — | 7 | 3 | no | — |
| 496 | M32 | — | 7 | 3 | no | — |
| 497 | M32 | — | 7 | 1 | no | — |
| 498 | M32 | — | 7 | 3 | no | — |
| 499 | M32 | — | 7 | 3 | no | — |
| 500 | M32 | C22×D7 | 1 | 3 | yes | — |
| 501 | C2×C16 | — | 7 | 3 | no | — |
| 502 | C2×C16 | — | 7 | 6 | no | — |
| 503 | C2×C16 | C22×D7 | 1 | 3 | yes | — |
| 504 | C22×C7 | — | 4 | 1 | no | — |
| 505 | C22×C7 | — | 4 | 3 | no | — |
| 506 | C22×C7 | — | 16 | 3 | no | — |
| 507 | C22×C7 | C22×D8 | 1 | 3 | yes | — |
| 508 | C2×D7 | — | 4 | 3 | no | — |
| 509 | C2×D7 | — | 4 | 1 | no | — |
| 510 | C2×D7 | — | 4 | 1 | no | — |
| 511 | C2×D7 | — | 8 | 2 | no | — |
| 512 | C2×D7 | — | 16 | 3 | no | — |
| 513 | C2×D7 | C22×D8 | 1 | 1 | yes | characteristic |
| 514 | C2×D7 | C22×D8 | 1 | 3 | yes | — |
| 515 | C4×C7 | — | 4 | 1 | no | — |
| 516 | C4×C7 | — | 4 | 3 | no | — |
| 517 | C4×C7 | C22×D8 | 1 | 3 | yes | — |
| 518 | C4×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 519 | Dic7 | — | 4 | 3 | no | — |
| 520 | Dic7 | — | 4 | 3 | no | — |
| 521 | Dic7 | C22×D8 | 1 | 3 | yes | — |
| 522 | Dic7 | C22×D8 | 1 | 1 | yes | characteristic |
| 523 | #41 | — | 2 | 3 | no | — |
| 524 | #41 | — | 2 | 3 | no | — |
| 525 | #41 | — | 4 | 1 | no | — |
| 526 | #41 | — | 4 | 3 | no | — |
| 527 | #41 | — | 7 | 1 | no | — |
| 528 | #41 | — | 7 | 3 | no | — |
| 529 | #41 | — | 7 | 3 | no | — |
| 530 | #41 | — | 14 | 3 | no | — |
| 531 | #41 | — | 14 | 6 | no | — |
| 532 | #41 | — | 14 | 3 | no | — |
| 533 | #41 | — | 14 | 1 | no | — |
| 534 | #41 | — | 14 | 3 | no | — |
| 535 | #41 | — | 14 | 3 | no | — |
| 536 | #41 | — | 14 | 3 | no | — |
| 537 | #41 | — | 28 | 3 | no | — |
| 538 | #41 | — | 28 | 3 | no | — |
| 539 | #41 | — | 28 | 3 | no | — |
| 540 | #41 | — | 28 | 6 | no | — |
| 541 | #41 | — | 28 | 3 | no | — |
| 542 | #41 | — | 28 | 3 | no | — |
| 543 | #41 | — | 28 | 3 | no | — |
| 544 | #41 | — | 28 | 3 | no | — |
| 545 | #41 | — | 28 | 3 | no | — |
| 546 | #41 | — | 28 | 6 | no | — |
| 547 | #41 | — | 28 | 6 | no | — |
| 548 | #41 | — | 28 | 3 | no | — |
| 549 | #41 | — | 28 | 3 | no | — |
| 550 | #41 | — | 28 | 3 | no | — |
| 551 | #41 | — | 28 | 3 | no | — |
| 552 | #41 | D4×D7 | 1 | 1 | yes | characteristic |
| 553 | C2×Q8 | — | 2 | 3 | no | — |
| 554 | C2×Q8 | — | 4 | 1 | no | — |
| 555 | C2×Q8 | — | 7 | 1 | no | — |
| 556 | C2×Q8 | — | 14 | 3 | no | — |
| 557 | C2×Q8 | — | 14 | 3 | no | — |
| 558 | C2×Q8 | — | 14 | 6 | no | — |
| 559 | C2×Q8 | — | 14 | 3 | no | — |
| 560 | C2×Q8 | — | 14 | 3 | no | — |
| 561 | C2×Q8 | — | 28 | 3 | no | — |
| 562 | C2×Q8 | — | 28 | 3 | no | — |
| 563 | C2×Q8 | — | 28 | 3 | no | — |
| 564 | C2×Q8 | — | 28 | 3 | no | — |
| 565 | C2×Q8 | — | 28 | 3 | no | — |
| 566 | C2×Q8 | — | 28 | 3 | no | — |
| 567 | C2×Q8 | — | 28 | 1 | no | — |
| 568 | C2×Q8 | — | 28 | 1 | no | — |
| 569 | C2×D4 | — | 2 | 3 | no | — |
| 570 | C2×D4 | — | 4 | 3 | no | — |
| 571 | C2×D4 | — | 7 | 3 | no | — |
| 572 | C2×D4 | — | 14 | 1 | no | — |
| 573 | C2×D4 | — | 14 | 3 | no | — |
| 574 | C2×D4 | — | 28 | 3 | no | — |
| 575 | C2×D4 | — | 28 | 3 | no | — |
| 576 | C2×D4 | — | 28 | 3 | no | — |
| 577 | C2×D4 | — | 28 | 6 | no | — |
| 578 | C2×D4 | — | 28 | 3 | no | — |
| 579 | C22×C4 | — | 7 | 3 | no | — |
| 580 | C22×C4 | — | 28 | 3 | no | — |
| 581 | C22×C4 | — | 28 | 3 | no | — |
| 582 | C22×C4 | — | 28 | 3 | no | — |
| 583 | C22×C4 | — | 28 | 3 | no | — |
| 584 | Q16 | — | 2 | 3 | no | — |
| 585 | Q16 | — | 7 | 3 | no | — |
| 586 | Q16 | — | 7 | 3 | no | — |
| 587 | Q16 | — | 14 | 3 | no | — |
| 588 | Q16 | — | 14 | 6 | no | — |
| 589 | Q16 | — | 14 | 3 | no | — |
| 590 | Q16 | — | 14 | 3 | no | — |
| 591 | Q16 | — | 14 | 3 | no | — |
| 592 | Q16 | C23×D7 | 1 | 3 | yes | — |
| 593 | Q16 | C23×D7 | 1 | 1 | yes | characteristic |
| 594 | SD16 | — | 2 | 3 | no | — |
| 595 | SD16 | — | 2 | 3 | no | — |
| 596 | SD16 | — | 14 | 3 | no | — |
| 597 | SD16 | — | 14 | 6 | no | — |
| 598 | SD16 | — | 14 | 3 | no | — |
| 599 | SD16 | — | 14 | 1 | no | — |
| 600 | SD16 | — | 14 | 3 | no | — |
| 601 | SD16 | — | 14 | 3 | no | — |
| 602 | SD16 | — | 14 | 3 | no | — |
| 603 | D8 | — | 2 | 3 | no | — |
| 604 | D8 | — | 7 | 1 | no | — |
| 605 | D8 | — | 7 | 1 | no | — |
| 606 | D8 | — | 14 | 1 | no | — |
| 607 | D8 | — | 14 | 3 | no | — |
| 608 | D8 | C23×D7 | 1 | 1 | yes | characteristic |
| 609 | D8 | C23×D7 | 1 | 3 | yes | — |
| 610 | M16 | — | 7 | 3 | no | — |
| 611 | M16 | — | 7 | 6 | no | — |
| 612 | M16 | D4×D7 | 1 | 3 | yes | — |
| 613 | C2×C8 | — | 7 | 3 | no | — |
| 614 | C2×C8 | — | 7 | 3 | no | — |
| 615 | C2×C8 | — | 7 | 3 | no | — |
| 616 | C2×C8 | — | 7 | 3 | no | — |
| 617 | C2×C8 | — | 7 | 1 | no | — |
| 618 | C2×C8 | C23×D7 | 1 | 3 | yes | — |
| 619 | C16 | — | 7 | 3 | no | — |
| 620 | C16 | — | 7 | 1 | no | — |
| 621 | C16 | C23×D7 | 1 | 3 | yes | — |
| 622 | C16 | C23×D7 | 1 | 1 | yes | characteristic |
| 623 | C2×C7 | — | 2 | 3 | no | — |
| 624 | C2×C7 | — | 8 | 1 | no | — |
| 625 | C2×C7 | — | 8 | 3 | no | — |
| 626 | C2×C7 | C23×D8 | 1 | 1 | yes | characteristic |
| 627 | D7 | — | 2 | 1 | no | — |
| 628 | D7 | — | 2 | 3 | no | — |
| 629 | D7 | — | 8 | 1 | no | — |
| 630 | D7 | — | 8 | 1 | no | — |
| 631 | C23 | — | 4 | 3 | no | — |
| 632 | C23 | — | 7 | 3 | no | — |
| 633 | C23 | — | 28 | 1 | no | — |
| 634 | C23 | — | 28 | 3 | no | — |
| 635 | Q8 | — | 2 | 1 | no | — |
| 636 | Q8 | — | 2 | 3 | no | — |
| 637 | Q8 | — | 4 | 3 | no | — |
| 638 | Q8 | — | 7 | 3 | no | — |
| 639 | Q8 | — | 14 | 3 | no | — |
| 640 | Q8 | — | 14 | 3 | no | — |
| 641 | Q8 | — | 28 | 3 | no | — |
| 642 | Q8 | — | 28 | 6 | no | — |
| 643 | Q8 | — | 28 | 3 | no | — |
| 644 | Q8 | — | 28 | 3 | no | — |
| 645 | Q8 | — | 28 | 3 | no | — |
| 646 | Q8 | D7×D8 | 1 | 1 | yes | characteristic |
| 647 | D4 | — | 2 | 3 | no | — |
| 648 | D4 | — | 2 | 1 | no | — |
| 649 | D4 | — | 4 | 3 | no | — |
| 650 | D4 | — | 4 | 3 | no | — |
| 651 | D4 | — | 4 | 3 | no | — |
| 652 | D4 | — | 7 | 6 | no | — |
| 653 | D4 | — | 7 | 3 | no | — |
| 654 | D4 | — | 14 | 1 | no | — |
| 655 | D4 | — | 14 | 1 | no | — |
| 656 | D4 | — | 28 | 1 | no | — |
| 657 | D4 | — | 28 | 3 | no | — |
| 658 | D4 | — | 28 | 3 | no | — |
| 659 | D4 | — | 28 | 1 | no | — |
| 660 | D4 | — | 28 | 3 | no | — |
| 661 | D4 | — | 28 | 6 | no | — |
| 662 | D4 | — | 28 | 3 | no | — |
| 663 | D4 | — | 28 | 3 | no | — |
| 664 | D4 | — | 28 | 3 | no | — |
| 665 | D4 | D7×D8 | 1 | 3 | yes | — |
| 666 | C2×C4 | — | 4 | 3 | no | — |
| 667 | C2×C4 | — | 4 | 3 | no | — |
| 668 | C2×C4 | — | 4 | 3 | no | — |
| 669 | C2×C4 | — | 7 | 3 | no | — |
| 670 | C2×C4 | — | 7 | 3 | no | — |
| 671 | C2×C4 | — | 7 | 3 | no | — |
| 672 | C2×C4 | — | 7 | 1 | no | — |
| 673 | C2×C4 | — | 7 | 3 | no | — |
| 674 | C2×C4 | — | 28 | 1 | no | — |
| 675 | C2×C4 | — | 28 | 3 | no | — |
| 676 | C2×C4 | — | 28 | 3 | no | — |
| 677 | C2×C4 | — | 28 | 3 | no | — |
| 678 | C2×C4 | — | 28 | 6 | no | — |
| 679 | C2×C4 | — | 28 | 3 | no | — |
| 680 | C2×C4 | — | 28 | 6 | no | — |
| 681 | C2×C4 | — | 28 | 3 | no | — |
| 682 | C2×C4 | — | 28 | 3 | no | — |
| 683 | C2×C4 | — | 28 | 3 | no | — |
| 684 | C2×C4 | — | 28 | 3 | no | — |
| 685 | C2×C4 | — | 28 | 3 | no | — |
| 686 | C2×C4 | C2×D4×D7 | 1 | 3 | yes | — |
| 687 | C8 | — | 7 | 1 | no | — |
| 688 | C8 | — | 7 | 3 | no | — |
| 689 | C8 | C2×D4×D7 | 1 | 3 | yes | — |
| 690 | C8 | C24×D7 | 1 | 1 | yes | characteristic |
| 691 | C7 | #62637 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 692 | C22 | — | 4 | 1 | no | — |
| 693 | C22 | — | 4 | 3 | no | — |
| 694 | C22 | — | 7 | 1 | no | — |
| 695 | C22 | — | 7 | 3 | no | — |
| 696 | C22 | — | 16 | 3 | no | — |
| 697 | C22 | — | 28 | 3 | no | — |
| 698 | C22 | — | 28 | 1 | no | — |
| 699 | C22 | — | 28 | 1 | no | — |
| 700 | C22 | — | 56 | 2 | no | — |
| 701 | C22 | — | 112 | 3 | no | — |
| 702 | C22 | C2×D7×D8 | 1 | 3 | yes | — |
| 703 | C4 | — | 4 | 1 | no | — |
| 704 | C4 | — | 4 | 3 | no | — |
| 705 | C4 | — | 7 | 1 | no | — |
| 706 | C4 | — | 7 | 3 | no | — |
| 707 | C4 | — | 28 | 3 | no | — |
| 708 | C4 | — | 28 | 3 | no | — |
| 709 | C4 | C2×D7×D8 | 1 | 3 | yes | — |
| 710 | C4 | C22×D4×D7 | 1 | 1 | yes | characteristic |
| 711 | C2 | — | 2 | 3 | no | — |
| 712 | C2 | — | 8 | 3 | no | — |
| 713 | C2 | — | 8 | 1 | no | — |
| 714 | C2 | — | 14 | 1 | no | — |
| 715 | C2 | — | 14 | 3 | no | — |
| 716 | C2 | — | 56 | 1 | no | — |
| 717 | C2 | — | 56 | 1 | no | — |
| 718 | C2 | C22×D7×D8 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D7×#578 | C2 | semidirect |
| 2. #11744271 | C2 | semidirect |
| 3. C7×#3416 | C2 | semidirect |
| 4. #11741462 | C2 | semidirect |
| 5. #11741453 | C2 | semidirect |
| 6. #11739486 | C2 | semidirect |
| 7. D7×#510 | C2 | semidirect |
| 8. #11739482 | C2 | semidirect |
| 9. #11739480 | C2 | semidirect |
| 10. #11739478 | C2 | semidirect |
| 11. #11739475 | C2 | semidirect |
| 12. #11739469 | C2 | semidirect |
| 13. C2×#89687 | C2 | semidirect |
| 14. #11739460 | C2 | semidirect |
| 15. #11739457 | C2 | semidirect |
| 18. C7×#578 | C22 | semidirect |
| 19. C7×#576 | C22 | semidirect |
| 26. #90462 | C22 | semidirect |
| 27. #90462 | C22 | semidirect |
| 29. D7×#135 | C22 | semidirect |
| 30. #90457 | C22 | semidirect |
| 31. C2×D7×Q16 | C22 | semidirect |
| 32. #90448 | C22 | semidirect |
| 34. #90444 | C22 | semidirect |
| 35. #90444 | C22 | semidirect |
| 37. C7×#510 | C22 | semidirect |
| 38. C7×#509 | C22 | semidirect |
| 39. C7×#508 | C22 | semidirect |
| 40. C2×C7×SD32 | C22 | semidirect |
| 41. C7×#504 | C22 | semidirect |
| 42. #89967 | C22 | semidirect |
| 43. #89967 | C22 | semidirect |
| 44. #89966 | C22 | semidirect |
| 45. #89966 | C22 | semidirect |
| 46. C2×#6403 | C22 | semidirect |
| 47. #89951 | C22 | semidirect |
| 48. C2×#6401 | C22 | semidirect |
| 49. #89919 | C22 | semidirect |
| 50. #89912 | C22 | semidirect |
| 51. #89690 | C22 | semidirect |
| 52. #89690 | C22 | semidirect |
| 53. D7×Q32 | C22 | semidirect |
| 54. #89688 | C22 | semidirect |
| 55. #89687 | C22 | semidirect |
| 56. #89687 | C22 | semidirect |
| 57. #89687 | C22 | semidirect |
| 58. #89687 | C22 | semidirect |
| 59. #89687 | C22 | semidirect |
| 60. #89686 | C22 | semidirect |
| 61. #89686 | C22 | semidirect |
| 62. D7×SD32 | C22 | semidirect |
| 63. #89684 | C22 | semidirect |
| 64. #89683 | C22 | semidirect |
| 65. #89683 | C22 | semidirect |
| 66. #89681 | C22 | semidirect |
| 67. #89681 | C22 | semidirect |
| 68. #89679 | C22 | semidirect |
| 69. D7×M32 | C22 | semidirect |
| 70. C2×Dic56 | C22 | semidirect |
| 71. #89676 | C22 | semidirect |
| 72. #89673 | C22 | semidirect |
| 73. C2×#6372 | C22 | semidirect |
| 182. #3416 | D7 | semidirect |
| 297. #578 | C2×D7 | semidirect |
| 301. #576 | C2×D7 | semidirect |
| 321. #510 | C2×D7 | semidirect |
| 327. #509 | C2×D7 | semidirect |
| 333. #508 | C2×D7 | semidirect |
| 339. C2×SD32 | C2×D7 | semidirect |
| 343. #504 | C2×D7 | semidirect |
| 691. C7 | #62637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×#578 | 2 |
| #11744271 | 2 |
| C7×#3416 | 2 |
| #11741462 | 2 |
| #11741453 | 2 |
| #11739486 | 2 |
| D7×#510 | 2 |
| #11739482 | 2 |
| #11739480 | 2 |
| #11739478 | 2 |
| #11739475 | 2 |
| #11739469 | 2 |
| C2×#89687 | 2 |
| #11739460 | 2 |
| #11739457 | 2 |
| #62637 | 7 |