Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1684 conjugacy classes of subgroups.
The subgroup lattice has 732 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C7×#3487 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11744355 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11741526 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11740840 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11740381 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11729898 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11729612 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11729608 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11729469 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11729468 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11729416 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×C7×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 13 | C22×C7×#41 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #90616 | C22 | 1 | 1 | yes | characteristic |
| 15 | C7×#550 | — | 2 | 2 | no | — |
| 16 | C7×#550 | — | 2 | 2 | no | — |
| 17 | C7×#548 | — | 2 | 2 | no | — |
| 18 | C7×#548 | — | 2 | 2 | no | — |
| 19 | C7×#535 | — | 2 | 2 | no | — |
| 20 | C7×#535 | C22 | 1 | 1 | yes | characteristic |
| 21 | C7×#535 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C7×#525 | — | 2 | 2 | no | — |
| 23 | C7×#525 | C22 | 1 | 1 | yes | characteristic |
| 24 | C7×#525 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C7×#519 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #90529 | — | 2 | 4 | no | — |
| 27 | #90528 | — | 2 | 4 | no | — |
| 28 | #90513 | — | 2 | 2 | no | — |
| 29 | #90513 | C22 | 1 | 2 | yes | — |
| 30 | #90510 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#6505 | — | 2 | 2 | no | — |
| 32 | C2×#6505 | C22 | 1 | 2 | yes | — |
| 33 | C2×#6495 | C22 | 1 | 2 | yes | — |
| 34 | #90482 | C22 | 1 | 2 | yes | — |
| 35 | #90012 | C22 | 1 | 1 | yes | characteristic |
| 36 | #90011 | — | 2 | 4 | no | — |
| 37 | #90010 | — | 2 | 4 | no | — |
| 38 | #90009 | C22 | 1 | 1 | yes | characteristic |
| 39 | #90008 | C22 | 1 | 2 | yes | complemented |
| 40 | #89997 | C22 | 1 | 2 | yes | complemented |
| 41 | #89987 | C22 | 1 | 2 | yes | complemented |
| 42 | #89979 | C22 | 1 | 2 | yes | complemented |
| 43 | #89849 | — | 2 | 2 | no | — |
| 44 | #89834 | — | 2 | 2 | no | — |
| 45 | #89825 | — | 2 | 2 | no | — |
| 46 | #89804 | — | 2 | 2 | no | — |
| 47 | #89778 | C22 | 1 | 2 | yes | — |
| 48 | #89777 | C22 | 1 | 2 | yes | — |
| 49 | #89328 | C22 | 1 | 2 | yes | complemented |
| 50 | #89326 | C22 | 1 | 2 | yes | complemented |
| 51 | #23884 | — | 7 | 1 | no | maximal, Sylow |
| 52 | C7×2−1+4 | — | 2 | 4 | no | — |
| 53 | C7×2−1+4 | — | 4 | 2 | no | — |
| 54 | C2×C7×#41 | — | 2 | 2 | no | — |
| 55 | C2×C7×#41 | — | 2 | 2 | no | — |
| 56 | C2×C7×#41 | — | 2 | 2 | no | — |
| 57 | C2×C7×#41 | — | 2 | 1 | no | — |
| 58 | C2×C7×#41 | — | 2 | 4 | no | — |
| 59 | C2×C7×#41 | — | 4 | 2 | no | — |
| 60 | C2×C7×#41 | D4 | 1 | 2 | yes | complemented |
| 61 | C2×C7×#41 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×C7×#41 | C23 | 1 | 1 | yes | characteristic |
| 63 | C22×C7×Q8 | — | 2 | 1 | no | — |
| 64 | C22×C7×Q8 | D4 | 1 | 2 | yes | complemented |
| 65 | C22×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 66 | C22×C7×D4 | — | 2 | 1 | no | — |
| 67 | C22×C7×D4 | C23 | 1 | 1 | yes | characteristic |
| 68 | C23×C4×C7 | — | 2 | 1 | no | — |
| 69 | C23×C4×C7 | C23 | 1 | 1 | yes | characteristic |
| 70 | #6554 | — | 2 | 2 | no | — |
| 71 | #6553 | — | 2 | 2 | no | — |
| 72 | D7×#41 | — | 4 | 2 | no | — |
| 73 | #6551 | — | 2 | 1 | no | — |
| 74 | #6548 | — | 2 | 1 | no | — |
| 75 | #6548 | — | 2 | 2 | no | — |
| 76 | C2×#1157 | — | 2 | 2 | no | — |
| 77 | C2×#1157 | C23 | 1 | 2 | yes | — |
| 78 | C7×#127 | — | 2 | 4 | no | — |
| 79 | C7×#127 | — | 2 | 1 | no | — |
| 80 | C7×#127 | D4 | 1 | 2 | yes | complemented |
| 81 | C7×#124 | — | 2 | 4 | no | — |
| 82 | C7×#124 | — | 2 | 1 | no | — |
| 83 | C7×#124 | D4 | 1 | 2 | yes | complemented |
| 84 | C7×#123 | — | 2 | 1 | no | — |
| 85 | C7×#123 | D4 | 1 | 2 | yes | — |
| 86 | C7×C22⋊Q8 | — | 2 | 4 | no | — |
| 87 | C7×C22⋊Q8 | — | 2 | 1 | no | — |
| 88 | C7×C22⋊Q8 | — | 2 | 1 | no | — |
| 89 | C7×#121 | — | 2 | 4 | no | — |
| 90 | C7×#121 | — | 2 | 4 | no | — |
| 91 | C7×#121 | — | 2 | 4 | no | — |
| 92 | C7×#121 | — | 2 | 1 | no | — |
| 93 | C7×#121 | — | 2 | 1 | no | — |
| 94 | C7×#121 | — | 2 | 2 | no | — |
| 95 | C7×#121 | — | 2 | 2 | no | — |
| 96 | C7×#120 | — | 2 | 1 | no | — |
| 97 | C7×#120 | — | 2 | 2 | no | — |
| 98 | C7×#120 | — | 2 | 2 | no | — |
| 99 | C7×#120 | D4 | 1 | 2 | yes | — |
| 100 | C4×C7×Q8 | — | 2 | 2 | no | — |
| 101 | C4×C7×Q8 | — | 2 | 2 | no | — |
| 102 | C4×C7×D4 | — | 2 | 4 | no | — |
| 103 | C4×C7×D4 | — | 2 | 4 | no | — |
| 104 | C4×C7×D4 | — | 2 | 2 | no | — |
| 105 | C4×C7×D4 | — | 2 | 2 | no | — |
| 106 | C7×#117 | — | 2 | 2 | no | — |
| 107 | C7×#117 | C23 | 1 | 1 | yes | characteristic |
| 108 | C7×#117 | C23 | 1 | 1 | yes | characteristic |
| 109 | #6516 | — | 2 | 2 | no | — |
| 110 | #6514 | — | 2 | 4 | no | — |
| 111 | #6514 | — | 2 | 2 | no | — |
| 112 | #6513 | — | 2 | 8 | no | — |
| 113 | #6513 | — | 2 | 4 | no | — |
| 114 | #6512 | — | 2 | 4 | no | — |
| 115 | #6512 | — | 2 | 2 | no | — |
| 116 | #6511 | — | 2 | 4 | no | — |
| 117 | C2×#1144 | — | 2 | 4 | no | — |
| 118 | C2×#1144 | D4 | 1 | 4 | yes | complemented |
| 119 | #6505 | — | 2 | 8 | no | — |
| 120 | #6505 | — | 2 | 2 | no | — |
| 121 | #6505 | — | 2 | 4 | no | — |
| 122 | #6505 | — | 2 | 4 | no | — |
| 123 | C2×#1143 | — | 2 | 4 | no | — |
| 124 | C2×#1143 | D4 | 1 | 4 | yes | complemented |
| 125 | C2×#1142 | — | 2 | 2 | no | — |
| 126 | #6495 | — | 2 | 2 | no | — |
| 127 | #6495 | — | 2 | 4 | no | — |
| 128 | #6495 | — | 4 | 2 | no | — |
| 129 | C2×#1141 | — | 2 | 2 | no | — |
| 130 | #6493 | — | 2 | 2 | no | — |
| 131 | #6492 | — | 2 | 2 | no | — |
| 132 | C4×C22⋊D7 | — | 4 | 2 | no | — |
| 133 | #6489 | C23 | 1 | 2 | yes | — |
| 134 | #6487 | — | 2 | 2 | no | — |
| 135 | C2×#1136 | — | 2 | 2 | no | — |
| 136 | C2×#1136 | C23 | 1 | 2 | yes | — |
| 137 | C2×#1136 | C23 | 1 | 2 | yes | — |
| 138 | #6411 | — | 4 | 2 | no | — |
| 139 | #6410 | — | 2 | 1 | no | — |
| 140 | #6409 | — | 2 | 4 | no | — |
| 141 | #6408 | — | 2 | 2 | no | — |
| 142 | #6407 | — | 2 | 1 | no | — |
| 143 | #6406 | — | 2 | 4 | no | — |
| 144 | C22⋊(C7⋊C8) | — | 2 | 4 | no | — |
| 145 | #6380 | — | 2 | 4 | no | — |
| 146 | #6379 | — | 2 | 4 | no | — |
| 147 | #3586 | — | 7 | 1 | no | — |
| 148 | #3487 | D7 | 1 | 1 | yes | characteristic, complemented |
| 149 | #3025 | — | 7 | 1 | no | — |
| 150 | #3021 | — | 7 | 1 | no | — |
| 151 | #3005 | — | 7 | 2 | no | — |
| 152 | #2010 | — | 7 | 2 | no | — |
| 153 | #2008 | — | 7 | 2 | no | — |
| 154 | #1910 | — | 7 | 1 | no | — |
| 155 | #1905 | — | 7 | 2 | no | — |
| 156 | #1891 | — | 7 | 1 | no | — |
| 157 | #1796 | — | 7 | 1 | no | — |
| 158 | C24×C7 | — | 2 | 1 | no | — |
| 159 | C24×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | C7×#41 | — | 2 | 2 | no | — |
| 161 | C7×#41 | — | 2 | 2 | no | — |
| 162 | C7×#41 | — | 2 | 4 | no | — |
| 163 | C7×#41 | — | 2 | 2 | no | — |
| 164 | C7×#41 | — | 2 | 2 | no | — |
| 165 | C7×#41 | — | 4 | 2 | no | — |
| 166 | C7×#41 | — | 4 | 8 | no | — |
| 167 | C7×#41 | — | 4 | 8 | no | — |
| 168 | C7×#41 | — | 4 | 4 | no | — |
| 169 | C7×#41 | — | 4 | 4 | no | — |
| 170 | C7×#41 | — | 4 | 4 | no | — |
| 171 | C2×C7×Q8 | — | 2 | 2 | no | — |
| 172 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 173 | C2×C7×Q8 | — | 2 | 2 | no | — |
| 174 | C2×C7×Q8 | — | 2 | 4 | no | — |
| 175 | C2×C7×Q8 | — | 4 | 2 | no | — |
| 176 | C2×C7×Q8 | — | 4 | 4 | no | — |
| 177 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C2×C7×Q8 | C2×D4 | 1 | 4 | yes | — |
| 179 | C2×C7×Q8 | C2×D4 | 1 | 2 | yes | — |
| 180 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C2×C7×D4 | — | 2 | 4 | no | — |
| 182 | C2×C7×D4 | — | 2 | 2 | no | — |
| 183 | C2×C7×D4 | — | 2 | 1 | no | — |
| 184 | C2×C7×D4 | — | 2 | 4 | no | — |
| 185 | C2×C7×D4 | — | 2 | 2 | no | — |
| 186 | C2×C7×D4 | — | 2 | 4 | no | — |
| 187 | C2×C7×D4 | — | 2 | 2 | no | — |
| 188 | C2×C7×D4 | — | 2 | 2 | no | — |
| 189 | C2×C7×D4 | — | 2 | 1 | no | — |
| 190 | C2×C7×D4 | — | 2 | 2 | no | — |
| 191 | C2×C7×D4 | — | 4 | 4 | no | — |
| 192 | C2×C7×D4 | C2×D4 | 1 | 2 | yes | — |
| 193 | C2×C7×D4 | C2×D4 | 1 | 2 | yes | — |
| 194 | C2×C7×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | C2×C7×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 196 | C22×C4×C7 | — | 2 | 1 | no | — |
| 197 | C22×C4×C7 | — | 2 | 4 | no | — |
| 198 | C22×C4×C7 | — | 2 | 2 | no | — |
| 199 | C22×C4×C7 | — | 2 | 2 | no | — |
| 200 | C22×C4×C7 | — | 2 | 2 | no | — |
| 201 | C22×C4×C7 | — | 2 | 1 | no | — |
| 202 | C22×C4×C7 | — | 2 | 1 | no | — |
| 203 | C22×C4×C7 | — | 2 | 1 | no | — |
| 204 | C22×C4×C7 | — | 2 | 2 | no | — |
| 205 | C22×C4×C7 | — | 4 | 4 | no | — |
| 206 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | C22×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 208 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 209 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 210 | C2×C22⋊D7 | — | 4 | 2 | no | — |
| 211 | C2×C22⋊D7 | — | 4 | 2 | no | — |
| 212 | #1161 | — | 4 | 2 | no | — |
| 213 | Q8×D7 | — | 4 | 2 | no | — |
| 214 | #1159 | — | 4 | 2 | no | — |
| 215 | #1159 | — | 4 | 4 | no | — |
| 216 | D4×D7 | — | 4 | 2 | no | — |
| 217 | D4×D7 | — | 4 | 4 | no | — |
| 218 | #1157 | — | 2 | 4 | no | — |
| 219 | #1157 | — | 2 | 2 | no | — |
| 220 | #1157 | — | 2 | 2 | no | — |
| 221 | #1157 | — | 2 | 2 | no | — |
| 222 | #1157 | — | 2 | 2 | no | — |
| 223 | #1157 | — | 4 | 2 | no | — |
| 224 | #1157 | — | 4 | 2 | no | — |
| 225 | C2×D28 | — | 2 | 2 | no | — |
| 226 | C2×D28 | C2×D4 | 1 | 2 | yes | — |
| 227 | C2×C4×D7 | — | 2 | 2 | no | — |
| 228 | C2×C4×D7 | — | 4 | 2 | no | — |
| 229 | C2×Dic14 | — | 2 | 2 | no | — |
| 230 | C2×Dic14 | C2×D4 | 1 | 2 | yes | — |
| 231 | C7×C4⋊C4 | — | 2 | 4 | no | — |
| 232 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 233 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 234 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 235 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 236 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 237 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 238 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 239 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 240 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 241 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 242 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 243 | C7×C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 244 | C42×C7 | — | 2 | 4 | no | — |
| 245 | C42×C7 | — | 2 | 1 | no | — |
| 246 | C42×C7 | C2×D4 | 1 | 2 | yes | — |
| 247 | C22⋊Dic7 | — | 2 | 2 | no | — |
| 248 | C22⋊Dic7 | — | 4 | 2 | no | — |
| 249 | #1144 | — | 2 | 4 | no | — |
| 250 | #1144 | — | 2 | 8 | no | — |
| 251 | #1143 | — | 2 | 4 | no | — |
| 252 | #1143 | — | 2 | 8 | no | — |
| 253 | #1142 | — | 2 | 4 | no | — |
| 254 | #1142 | — | 4 | 4 | no | — |
| 255 | #1141 | — | 2 | 4 | no | — |
| 256 | #1141 | — | 4 | 4 | no | — |
| 257 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 258 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 259 | Dic7⋊C4 | — | 4 | 2 | no | — |
| 260 | C4×Dic7 | — | 2 | 2 | no | — |
| 261 | #1136 | — | 2 | 4 | no | — |
| 262 | #1136 | — | 2 | 2 | no | — |
| 263 | #1136 | — | 2 | 2 | no | — |
| 264 | #1136 | — | 2 | 2 | no | — |
| 265 | #1136 | — | 2 | 2 | no | — |
| 266 | C2×C7⋊C8 | — | 2 | 4 | no | — |
| 267 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 268 | C2×C7⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 269 | #585 | — | 7 | 1 | no | — |
| 270 | C2×2−1+4 | C2×D7 | 1 | 1 | yes | characteristic |
| 271 | C22×#41 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 272 | #578 | — | 14 | 4 | no | — |
| 273 | #577 | — | 14 | 4 | no | — |
| 274 | #575 | — | 7 | 2 | no | — |
| 275 | #575 | — | 14 | 2 | no | — |
| 276 | C2×#137 | — | 7 | 2 | no | — |
| 277 | C2×#137 | — | 14 | 2 | no | — |
| 278 | C2×AGL(1,ℤ/8) | — | 7 | 2 | no | — |
| 279 | #568 | — | 7 | 1 | no | — |
| 280 | #550 | — | 2 | 2 | no | — |
| 281 | #550 | — | 2 | 2 | no | — |
| 282 | #548 | — | 2 | 2 | no | — |
| 283 | #548 | — | 2 | 2 | no | — |
| 284 | #535 | — | 2 | 2 | no | — |
| 285 | #535 | C2×D7 | 1 | 1 | yes | characteristic |
| 286 | #535 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 287 | #525 | — | 2 | 2 | no | — |
| 288 | #525 | — | 7 | 2 | no | — |
| 289 | #525 | C2×D7 | 1 | 1 | yes | characteristic |
| 290 | #525 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 291 | #519 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 292 | #458 | — | 14 | 2 | no | — |
| 293 | B(4,𝔽2) | — | 14 | 2 | no | — |
| 294 | #454 | — | 14 | 2 | no | — |
| 295 | #453 | — | 14 | 2 | no | — |
| 296 | #452 | — | 14 | 4 | no | — |
| 297 | #449 | — | 14 | 4 | no | — |
| 298 | #421 | — | 7 | 2 | no | — |
| 299 | #421 | — | 7 | 2 | no | — |
| 300 | #419 | — | 7 | 2 | no | — |
| 301 | #418 | — | 7 | 2 | no | — |
| 302 | #413 | — | 7 | 1 | no | — |
| 303 | #410 | — | 7 | 1 | no | — |
| 304 | #410 | — | 7 | 2 | no | — |
| 305 | #407 | — | 7 | 2 | no | — |
| 306 | #344 | — | 7 | 2 | no | — |
| 307 | H(3,ℤ/4) | — | 7 | 2 | no | — |
| 308 | C23×C7 | — | 2 | 1 | no | — |
| 309 | C23×C7 | — | 2 | 2 | no | — |
| 310 | C23×C7 | — | 2 | 1 | no | — |
| 311 | C23×C7 | — | 2 | 2 | no | — |
| 312 | C23×C7 | — | 4 | 2 | no | — |
| 313 | C23×C7 | — | 8 | 1 | no | — |
| 314 | C23×C7 | — | 8 | 2 | no | — |
| 315 | C23×C7 | #120 | 1 | 2 | yes | — |
| 316 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 317 | C22×D7 | — | 2 | 2 | no | — |
| 318 | C22×D7 | — | 4 | 2 | no | — |
| 319 | C7×Q8 | — | 2 | 2 | no | — |
| 320 | C7×Q8 | — | 2 | 2 | no | — |
| 321 | C7×Q8 | — | 2 | 4 | no | — |
| 322 | C7×Q8 | — | 2 | 1 | no | — |
| 323 | C7×Q8 | — | 2 | 1 | no | — |
| 324 | C7×Q8 | — | 4 | 4 | no | — |
| 325 | C7×Q8 | #120 | 1 | 4 | yes | — |
| 326 | C7×D4 | — | 2 | 4 | no | — |
| 327 | C7×D4 | — | 2 | 1 | no | — |
| 328 | C7×D4 | — | 2 | 1 | no | — |
| 329 | C7×D4 | — | 2 | 2 | no | — |
| 330 | C7×D4 | — | 2 | 4 | no | — |
| 331 | C7×D4 | — | 4 | 4 | no | — |
| 332 | C7×D4 | — | 4 | 8 | no | — |
| 333 | C7×D4 | — | 4 | 2 | no | — |
| 334 | C7×D4 | — | 4 | 1 | no | — |
| 335 | C7×D4 | — | 4 | 1 | no | — |
| 336 | C7×D4 | — | 8 | 4 | no | — |
| 337 | C7×D4 | — | 8 | 2 | no | — |
| 338 | C7×D4 | — | 8 | 4 | no | — |
| 339 | C7×D4 | — | 8 | 2 | no | — |
| 340 | C2×C4×C7 | — | 2 | 2 | no | — |
| 341 | C2×C4×C7 | — | 2 | 4 | no | — |
| 342 | C2×C4×C7 | — | 2 | 2 | no | — |
| 343 | C2×C4×C7 | — | 2 | 2 | no | — |
| 344 | C2×C4×C7 | — | 2 | 2 | no | — |
| 345 | C2×C4×C7 | — | 2 | 2 | no | — |
| 346 | C2×C4×C7 | — | 2 | 1 | no | — |
| 347 | C2×C4×C7 | — | 2 | 1 | no | — |
| 348 | C2×C4×C7 | — | 2 | 2 | no | — |
| 349 | C2×C4×C7 | — | 4 | 4 | no | — |
| 350 | C2×C4×C7 | — | 4 | 4 | no | — |
| 351 | C2×C4×C7 | — | 4 | 8 | no | — |
| 352 | C2×C4×C7 | — | 4 | 1 | no | — |
| 353 | C2×C4×C7 | — | 4 | 1 | no | — |
| 354 | C2×C4×C7 | — | 4 | 2 | no | — |
| 355 | C2×C4×C7 | — | 4 | 2 | no | — |
| 356 | C2×C4×C7 | #120 | 1 | 2 | yes | — |
| 357 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 358 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 359 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 360 | C2×C4×C7 | H(5,𝔽2) | 1 | 2 | yes | — |
| 361 | C22⋊D7 | — | 4 | 4 | no | — |
| 362 | C22⋊D7 | — | 4 | 2 | no | — |
| 363 | C22⋊D7 | — | 4 | 2 | no | — |
| 364 | C22⋊D7 | — | 8 | 4 | no | — |
| 365 | C2×Dic7 | — | 2 | 2 | no | — |
| 366 | C2×Dic7 | — | 4 | 2 | no | — |
| 367 | C2×Dic7 | — | 4 | 2 | no | — |
| 368 | D28 | — | 2 | 2 | no | — |
| 369 | D28 | — | 2 | 2 | no | — |
| 370 | D28 | — | 4 | 2 | no | — |
| 371 | C4×D7 | — | 4 | 4 | no | — |
| 372 | C4×D7 | — | 4 | 2 | no | — |
| 373 | C4×D7 | — | 4 | 2 | no | — |
| 374 | Dic14 | — | 2 | 2 | no | — |
| 375 | Dic14 | — | 2 | 2 | no | — |
| 376 | Dic14 | — | 4 | 2 | no | — |
| 377 | C7⋊C8 | — | 2 | 4 | no | — |
| 378 | C7⋊C8 | — | 4 | 2 | no | — |
| 379 | 2−1+4 | — | 2 | 4 | no | — |
| 380 | 2−1+4 | — | 4 | 2 | no | — |
| 381 | 2−1+4 | — | 14 | 2 | no | — |
| 382 | 2−1+4 | — | 14 | 1 | no | — |
| 383 | H(5,𝔽2) | — | 14 | 2 | no | — |
| 384 | H(5,𝔽2) | — | 14 | 2 | no | — |
| 385 | H(5,𝔽2) | — | 14 | 1 | no | — |
| 386 | C2×#41 | — | 2 | 2 | no | — |
| 387 | C2×#41 | — | 2 | 2 | no | — |
| 388 | C2×#41 | — | 2 | 2 | no | — |
| 389 | C2×#41 | — | 2 | 1 | no | — |
| 390 | C2×#41 | — | 2 | 4 | no | — |
| 391 | C2×#41 | — | 4 | 2 | no | — |
| 392 | C2×#41 | — | 7 | 2 | no | — |
| 393 | C2×#41 | — | 14 | 2 | no | — |
| 394 | C2×#41 | — | 28 | 2 | no | — |
| 395 | C2×#41 | C22⋊D7 | 1 | 2 | yes | complemented |
| 396 | C2×#41 | C22×D7 | 1 | 1 | yes | characteristic |
| 397 | C2×#41 | C22×D7 | 1 | 1 | yes | characteristic |
| 398 | C22×Q8 | — | 2 | 1 | no | — |
| 399 | C22×Q8 | C22⋊D7 | 1 | 2 | yes | complemented |
| 400 | C22×Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 401 | C22×D4 | — | 2 | 1 | no | — |
| 402 | C22×D4 | C22×D7 | 1 | 1 | yes | characteristic |
| 403 | C23×C4 | — | 2 | 1 | no | — |
| 404 | C23×C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 405 | #137 | — | 14 | 8 | no | — |
| 406 | #137 | — | 14 | 2 | no | — |
| 407 | #137 | — | 14 | 4 | no | — |
| 408 | #137 | — | 14 | 4 | no | — |
| 409 | #137 | — | 14 | 4 | no | — |
| 410 | #137 | — | 14 | 2 | no | — |
| 411 | AGL(1,ℤ/8) | — | 14 | 2 | no | — |
| 412 | AGL(1,ℤ/8) | — | 14 | 4 | no | — |
| 413 | AGL(1,ℤ/8) | — | 14 | 2 | no | — |
| 414 | AGL(1,ℤ/8) | — | 14 | 4 | no | — |
| 415 | AGL(1,ℤ/8) | — | 28 | 2 | no | — |
| 416 | #135 | — | 14 | 4 | no | — |
| 417 | #135 | — | 14 | 8 | no | — |
| 418 | C2×Q16 | — | 7 | 4 | no | — |
| 419 | C2×Q16 | — | 14 | 4 | no | — |
| 420 | C2×SD16 | — | 7 | 4 | no | — |
| 421 | C2×SD16 | — | 14 | 4 | no | — |
| 422 | C2×SD16 | — | 14 | 2 | no | — |
| 423 | C2×D8 | — | 14 | 2 | no | — |
| 424 | #131 | — | 14 | 4 | no | — |
| 425 | C2×M16 | — | 7 | 2 | no | — |
| 426 | C2×M16 | — | 7 | 2 | no | — |
| 427 | C2×M16 | — | 14 | 2 | no | — |
| 428 | #127 | — | 2 | 4 | no | — |
| 429 | #127 | — | 2 | 1 | no | — |
| 430 | #127 | C22⋊D7 | 1 | 2 | yes | complemented |
| 431 | #124 | — | 2 | 4 | no | — |
| 432 | #124 | — | 2 | 1 | no | — |
| 433 | #124 | C22⋊D7 | 1 | 2 | yes | complemented |
| 434 | #123 | — | 2 | 1 | no | — |
| 435 | #123 | — | 14 | 2 | no | — |
| 436 | #123 | C22⋊D7 | 1 | 2 | yes | — |
| 437 | C22⋊Q8 | — | 2 | 4 | no | — |
| 438 | C22⋊Q8 | — | 2 | 1 | no | — |
| 439 | C22⋊Q8 | — | 2 | 1 | no | — |
| 440 | C22⋊Q8 | — | 14 | 2 | no | — |
| 441 | #121 | — | 2 | 4 | no | — |
| 442 | #121 | — | 2 | 4 | no | — |
| 443 | #121 | — | 2 | 4 | no | — |
| 444 | #121 | — | 2 | 1 | no | — |
| 445 | #121 | — | 2 | 1 | no | — |
| 446 | #121 | — | 2 | 2 | no | — |
| 447 | #121 | — | 2 | 2 | no | — |
| 448 | #121 | — | 14 | 2 | no | — |
| 449 | #120 | — | 2 | 1 | no | — |
| 450 | #120 | — | 2 | 2 | no | — |
| 451 | #120 | — | 2 | 2 | no | — |
| 452 | #120 | — | 14 | 2 | no | — |
| 453 | #120 | C22⋊D7 | 1 | 2 | yes | — |
| 454 | C4×Q8 | — | 2 | 2 | no | — |
| 455 | C4×Q8 | — | 2 | 2 | no | — |
| 456 | C4×D4 | — | 2 | 4 | no | — |
| 457 | C4×D4 | — | 2 | 4 | no | — |
| 458 | C4×D4 | — | 2 | 2 | no | — |
| 459 | C4×D4 | — | 2 | 2 | no | — |
| 460 | C4×D4 | — | 28 | 2 | no | — |
| 461 | #117 | — | 2 | 2 | no | — |
| 462 | #117 | — | 7 | 2 | no | — |
| 463 | #117 | C22×D7 | 1 | 1 | yes | characteristic |
| 464 | #117 | C22×D7 | 1 | 1 | yes | characteristic |
| 465 | #104 | — | 14 | 4 | no | — |
| 466 | #104 | — | 28 | 2 | no | — |
| 467 | #103 | — | 14 | 4 | no | — |
| 468 | #102 | — | 14 | 4 | no | — |
| 469 | #101 | — | 14 | 1 | no | — |
| 470 | #100 | — | 14 | 1 | no | — |
| 471 | #99 | — | 14 | 2 | no | — |
| 472 | #99 | — | 14 | 4 | no | — |
| 473 | C22⋊C8 | — | 14 | 4 | no | — |
| 474 | C22×C7 | — | 2 | 2 | no | — |
| 475 | C22×C7 | — | 4 | 1 | no | — |
| 476 | C22×C7 | — | 4 | 2 | no | — |
| 477 | C22×C7 | — | 4 | 2 | no | — |
| 478 | C22×C7 | — | 4 | 2 | no | — |
| 479 | C22×C7 | — | 4 | 1 | no | — |
| 480 | C22×C7 | — | 4 | 1 | no | — |
| 481 | C22×C7 | — | 4 | 4 | no | — |
| 482 | C22×C7 | — | 4 | 2 | no | — |
| 483 | C22×C7 | — | 4 | 1 | no | — |
| 484 | C22×C7 | — | 4 | 2 | no | — |
| 485 | C22×C7 | — | 4 | 1 | no | — |
| 486 | C22×C7 | — | 8 | 4 | no | — |
| 487 | C22×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 488 | C22×C7 | D42 | 1 | 2 | yes | — |
| 489 | C2×D7 | — | 4 | 2 | no | — |
| 490 | C2×D7 | — | 8 | 2 | no | — |
| 491 | C2×D7 | — | 16 | 2 | no | — |
| 492 | C4×C7 | — | 2 | 2 | no | — |
| 493 | C4×C7 | — | 2 | 4 | no | — |
| 494 | C4×C7 | — | 4 | 2 | no | — |
| 495 | C4×C7 | — | 4 | 2 | no | — |
| 496 | C4×C7 | — | 4 | 1 | no | — |
| 497 | C4×C7 | — | 4 | 1 | no | — |
| 498 | C4×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 499 | C4×C7 | #534 | 1 | 1 | yes | characteristic |
| 500 | C4×C7 | D42 | 1 | 2 | yes | — |
| 501 | Dic7 | — | 4 | 2 | no | — |
| 502 | Dic7 | — | 8 | 2 | no | — |
| 503 | C24 | — | 2 | 1 | no | — |
| 504 | C24 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 505 | #41 | — | 2 | 2 | no | — |
| 506 | #41 | — | 2 | 2 | no | — |
| 507 | #41 | — | 2 | 4 | no | — |
| 508 | #41 | — | 2 | 2 | no | — |
| 509 | #41 | — | 2 | 2 | no | — |
| 510 | #41 | — | 4 | 2 | no | — |
| 511 | #41 | — | 4 | 8 | no | — |
| 512 | #41 | — | 4 | 8 | no | — |
| 513 | #41 | — | 4 | 4 | no | — |
| 514 | #41 | — | 4 | 4 | no | — |
| 515 | #41 | — | 4 | 4 | no | — |
| 516 | #41 | — | 14 | 4 | no | — |
| 517 | #41 | — | 14 | 2 | no | — |
| 518 | #41 | — | 14 | 2 | no | — |
| 519 | #41 | — | 14 | 2 | no | — |
| 520 | #41 | — | 14 | 2 | no | — |
| 521 | #41 | — | 28 | 2 | no | — |
| 522 | #41 | — | 28 | 4 | no | — |
| 523 | #41 | — | 28 | 2 | no | — |
| 524 | #41 | — | 28 | 2 | no | — |
| 525 | #41 | — | 28 | 2 | no | — |
| 526 | C2×Q8 | — | 2 | 2 | no | — |
| 527 | C2×Q8 | — | 2 | 2 | no | — |
| 528 | C2×Q8 | — | 2 | 1 | no | — |
| 529 | C2×Q8 | — | 2 | 4 | no | — |
| 530 | C2×Q8 | — | 4 | 2 | no | — |
| 531 | C2×Q8 | — | 4 | 4 | no | — |
| 532 | C2×Q8 | — | 7 | 2 | no | — |
| 533 | C2×Q8 | — | 14 | 2 | no | — |
| 534 | C2×Q8 | — | 28 | 2 | no | — |
| 535 | C2×Q8 | D4×D7 | 1 | 4 | yes | — |
| 536 | C2×Q8 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 537 | C2×Q8 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 538 | C2×Q8 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 539 | C2×D4 | — | 2 | 4 | no | — |
| 540 | C2×D4 | — | 2 | 2 | no | — |
| 541 | C2×D4 | — | 2 | 1 | no | — |
| 542 | C2×D4 | — | 2 | 4 | no | — |
| 543 | C2×D4 | — | 2 | 2 | no | — |
| 544 | C2×D4 | — | 2 | 4 | no | — |
| 545 | C2×D4 | — | 2 | 2 | no | — |
| 546 | C2×D4 | — | 2 | 2 | no | — |
| 547 | C2×D4 | — | 2 | 2 | no | — |
| 548 | C2×D4 | — | 2 | 1 | no | — |
| 549 | C2×D4 | — | 4 | 4 | no | — |
| 550 | C2×D4 | — | 7 | 2 | no | — |
| 551 | C2×D4 | — | 14 | 2 | no | — |
| 552 | C2×D4 | — | 14 | 2 | no | — |
| 553 | C2×D4 | — | 28 | 2 | no | — |
| 554 | C2×D4 | — | 28 | 4 | no | — |
| 555 | C2×D4 | — | 28 | 2 | no | — |
| 556 | C2×D4 | — | 28 | 2 | no | — |
| 557 | C2×D4 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 558 | C2×D4 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 559 | C2×D4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 560 | C2×D4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 561 | C22×C4 | — | 2 | 1 | no | — |
| 562 | C22×C4 | — | 2 | 4 | no | — |
| 563 | C22×C4 | — | 2 | 2 | no | — |
| 564 | C22×C4 | — | 2 | 2 | no | — |
| 565 | C22×C4 | — | 2 | 2 | no | — |
| 566 | C22×C4 | — | 2 | 2 | no | — |
| 567 | C22×C4 | — | 2 | 1 | no | — |
| 568 | C22×C4 | — | 2 | 1 | no | — |
| 569 | C22×C4 | — | 2 | 1 | no | — |
| 570 | C22×C4 | — | 4 | 4 | no | — |
| 571 | C22×C4 | — | 14 | 2 | no | — |
| 572 | C22×C4 | — | 28 | 2 | no | — |
| 573 | C22×C4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 574 | C22×C4 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 575 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 576 | Q16 | — | 14 | 4 | no | — |
| 577 | Q16 | — | 14 | 8 | no | — |
| 578 | SD16 | — | 14 | 4 | no | — |
| 579 | SD16 | — | 14 | 4 | no | — |
| 580 | SD16 | — | 14 | 8 | no | — |
| 581 | SD16 | — | 28 | 4 | no | — |
| 582 | D8 | — | 14 | 4 | no | — |
| 583 | D8 | — | 28 | 4 | no | — |
| 584 | M16 | — | 14 | 4 | no | — |
| 585 | M16 | — | 14 | 2 | no | — |
| 586 | M16 | — | 14 | 2 | no | — |
| 587 | M16 | — | 14 | 2 | no | — |
| 588 | M16 | — | 14 | 2 | no | — |
| 589 | C2×C8 | — | 7 | 4 | no | — |
| 590 | C2×C8 | — | 14 | 4 | no | — |
| 591 | C2×C8 | — | 14 | 2 | no | — |
| 592 | C4⋊C4 | — | 2 | 4 | no | — |
| 593 | C4⋊C4 | — | 2 | 2 | no | — |
| 594 | C4⋊C4 | — | 2 | 2 | no | — |
| 595 | C4⋊C4 | — | 2 | 1 | no | — |
| 596 | C4⋊C4 | — | 2 | 1 | no | — |
| 597 | C4⋊C4 | — | 14 | 2 | no | — |
| 598 | C4⋊C4 | — | 28 | 2 | no | — |
| 599 | C22⋊C4 | — | 2 | 2 | no | — |
| 600 | C22⋊C4 | — | 2 | 4 | no | — |
| 601 | C22⋊C4 | — | 2 | 2 | no | — |
| 602 | C22⋊C4 | — | 2 | 2 | no | — |
| 603 | C22⋊C4 | — | 2 | 1 | no | — |
| 604 | C22⋊C4 | — | 2 | 4 | no | — |
| 605 | C22⋊C4 | — | 2 | 2 | no | — |
| 606 | C22⋊C4 | — | 14 | 2 | no | — |
| 607 | C22⋊C4 | — | 28 | 2 | no | — |
| 608 | C22⋊C4 | — | 28 | 2 | no | — |
| 609 | C22⋊C4 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 610 | C42 | — | 2 | 4 | no | — |
| 611 | C42 | — | 2 | 1 | no | — |
| 612 | C42 | — | 14 | 2 | no | — |
| 613 | C42 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 614 | C2×C7 | — | 2 | 2 | no | — |
| 615 | C2×C7 | — | 2 | 1 | no | — |
| 616 | C2×C7 | — | 4 | 2 | no | — |
| 617 | C2×C7 | — | 8 | 1 | no | — |
| 618 | C2×C7 | — | 8 | 1 | no | — |
| 619 | C2×C7 | — | 8 | 2 | no | — |
| 620 | C2×C7 | #2403 | 1 | 1 | yes | characteristic |
| 621 | D7 | — | 8 | 2 | no | — |
| 622 | C23 | — | 2 | 2 | no | — |
| 623 | C23 | — | 2 | 1 | no | — |
| 624 | C23 | — | 2 | 2 | no | — |
| 625 | C23 | — | 2 | 1 | no | — |
| 626 | C23 | — | 4 | 2 | no | — |
| 627 | C23 | — | 8 | 1 | no | — |
| 628 | C23 | — | 8 | 2 | no | — |
| 629 | C23 | — | 14 | 2 | no | — |
| 630 | C23 | — | 28 | 2 | no | — |
| 631 | C23 | #6516 | 1 | 2 | yes | — |
| 632 | C23 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 633 | Q8 | — | 2 | 4 | no | — |
| 634 | Q8 | — | 2 | 2 | no | — |
| 635 | Q8 | — | 2 | 2 | no | — |
| 636 | Q8 | — | 2 | 1 | no | — |
| 637 | Q8 | — | 2 | 1 | no | — |
| 638 | Q8 | — | 4 | 4 | no | — |
| 639 | Q8 | — | 14 | 2 | no | — |
| 640 | Q8 | — | 14 | 2 | no | — |
| 641 | Q8 | — | 28 | 2 | no | — |
| 642 | Q8 | #6500 | 1 | 4 | yes | — |
| 643 | D4 | — | 2 | 4 | no | — |
| 644 | D4 | — | 2 | 1 | no | — |
| 645 | D4 | — | 2 | 2 | no | — |
| 646 | D4 | — | 2 | 4 | no | — |
| 647 | D4 | — | 2 | 1 | no | — |
| 648 | D4 | — | 4 | 4 | no | — |
| 649 | D4 | — | 4 | 8 | no | — |
| 650 | D4 | — | 4 | 2 | no | — |
| 651 | D4 | — | 4 | 1 | no | — |
| 652 | D4 | — | 4 | 1 | no | — |
| 653 | D4 | — | 8 | 4 | no | — |
| 654 | D4 | — | 8 | 2 | no | — |
| 655 | D4 | — | 8 | 4 | no | — |
| 656 | D4 | — | 8 | 2 | no | — |
| 657 | D4 | — | 14 | 2 | no | — |
| 658 | D4 | — | 14 | 2 | no | — |
| 659 | D4 | — | 28 | 2 | no | — |
| 660 | D4 | — | 28 | 4 | no | — |
| 661 | D4 | — | 28 | 2 | no | — |
| 662 | D4 | — | 28 | 2 | no | — |
| 663 | D4 | — | 56 | 4 | no | — |
| 664 | C2×C4 | — | 2 | 4 | no | — |
| 665 | C2×C4 | — | 2 | 2 | no | — |
| 666 | C2×C4 | — | 2 | 2 | no | — |
| 667 | C2×C4 | — | 2 | 2 | no | — |
| 668 | C2×C4 | — | 2 | 2 | no | — |
| 669 | C2×C4 | — | 2 | 2 | no | — |
| 670 | C2×C4 | — | 2 | 2 | no | — |
| 671 | C2×C4 | — | 2 | 1 | no | — |
| 672 | C2×C4 | — | 2 | 1 | no | — |
| 673 | C2×C4 | — | 4 | 4 | no | — |
| 674 | C2×C4 | — | 4 | 4 | no | — |
| 675 | C2×C4 | — | 4 | 8 | no | — |
| 676 | C2×C4 | — | 4 | 1 | no | — |
| 677 | C2×C4 | — | 4 | 2 | no | — |
| 678 | C2×C4 | — | 4 | 2 | no | — |
| 679 | C2×C4 | — | 4 | 1 | no | — |
| 680 | C2×C4 | — | 14 | 2 | no | — |
| 681 | C2×C4 | — | 28 | 4 | no | — |
| 682 | C2×C4 | — | 28 | 2 | no | — |
| 683 | C2×C4 | — | 28 | 2 | no | — |
| 684 | C2×C4 | — | 28 | 2 | no | — |
| 685 | C2×C4 | — | 28 | 2 | no | — |
| 686 | C2×C4 | #6516 | 1 | 2 | yes | — |
| 687 | C2×C4 | C2×D4×D7 | 1 | 2 | yes | — |
| 688 | C2×C4 | #6548 | 1 | 2 | yes | — |
| 689 | C2×C4 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 690 | C2×C4 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 691 | C8 | — | 14 | 4 | no | — |
| 692 | C8 | — | 28 | 2 | no | — |
| 693 | C7 | #23884 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 694 | C22 | — | 2 | 2 | no | — |
| 695 | C22 | — | 4 | 1 | no | — |
| 696 | C22 | — | 4 | 2 | no | — |
| 697 | C22 | — | 4 | 2 | no | — |
| 698 | C22 | — | 4 | 1 | no | — |
| 699 | C22 | — | 4 | 1 | no | — |
| 700 | C22 | — | 4 | 4 | no | — |
| 701 | C22 | — | 4 | 2 | no | — |
| 702 | C22 | — | 4 | 2 | no | — |
| 703 | C22 | — | 4 | 1 | no | — |
| 704 | C22 | — | 4 | 2 | no | — |
| 705 | C22 | — | 4 | 1 | no | — |
| 706 | C22 | — | 8 | 4 | no | — |
| 707 | C22 | — | 28 | 2 | no | — |
| 708 | C22 | — | 56 | 2 | no | — |
| 709 | C22 | — | 112 | 2 | no | — |
| 710 | C22 | D4×C22⋊D7 | 1 | 2 | yes | — |
| 711 | C22 | C2×#6516 | 1 | 1 | yes | characteristic |
| 712 | C4 | — | 2 | 4 | no | — |
| 713 | C4 | — | 2 | 2 | no | — |
| 714 | C4 | — | 4 | 2 | no | — |
| 715 | C4 | — | 4 | 2 | no | — |
| 716 | C4 | — | 4 | 1 | no | — |
| 717 | C4 | — | 4 | 1 | no | — |
| 718 | C4 | — | 28 | 2 | no | — |
| 719 | C4 | — | 56 | 2 | no | — |
| 720 | C4 | C2×#6500 | 1 | 1 | yes | characteristic |
| 721 | C4 | D4×C22⋊D7 | 1 | 2 | yes | — |
| 722 | C4 | #90495 | 1 | 1 | yes | characteristic |
| 723 | C2 | — | 2 | 1 | no | — |
| 724 | C2 | — | 2 | 2 | no | — |
| 725 | C2 | — | 4 | 2 | no | — |
| 726 | C2 | — | 8 | 1 | no | — |
| 727 | C2 | — | 8 | 2 | no | — |
| 728 | C2 | — | 8 | 1 | no | — |
| 729 | C2 | — | 56 | 2 | no | — |
| 730 | C2 | #11741497 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#3487 | C2 | semidirect |
| 2. #11744355 | C2 | semidirect |
| 3. #11741526 | C2 | semidirect |
| 4. #11740840 | C2 | semidirect |
| 5. #11740381 | C2 | semidirect |
| 6. #11729898 | C2 | semidirect |
| 7. #11729612 | C2 | semidirect |
| 8. #11729608 | C2 | semidirect |
| 9. #11729469 | C2 | semidirect |
| 10. #11729468 | C2 | semidirect |
| 11. #11729416 | C2 | semidirect |
| 13. C22×C7×#41 | C22 | semidirect |
| 21. C7×#535 | C22 | semidirect |
| 24. C7×#525 | C22 | semidirect |
| 25. C7×#519 | C22 | semidirect |
| 39. #90008 | C22 | semidirect |
| 40. #89997 | C22 | semidirect |
| 41. #89987 | C22 | semidirect |
| 42. #89979 | C22 | semidirect |
| 49. #89328 | C22 | semidirect |
| 50. #89326 | C22 | semidirect |
| 60. C2×C7×#41 | D4 | semidirect |
| 64. C22×C7×Q8 | D4 | semidirect |
| 80. C7×#127 | D4 | semidirect |
| 83. C7×#124 | D4 | semidirect |
| 118. C2×#1144 | D4 | semidirect |
| 124. C2×#1143 | D4 | semidirect |
| 148. #3487 | D7 | semidirect |
| 271. C22×#41 | C2×D7 | semidirect |
| 286. #535 | C2×D7 | semidirect |
| 290. #525 | C2×D7 | semidirect |
| 291. #519 | C2×D7 | semidirect |
| 395. C2×#41 | C22⋊D7 | semidirect |
| 399. C22×Q8 | C22⋊D7 | semidirect |
| 430. #127 | C22⋊D7 | semidirect |
| 433. #124 | C22⋊D7 | semidirect |
| 693. C7 | #23884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3487 | 2 |
| #11744355 | 2 |
| #11741526 | 2 |
| #11740840 | 2 |
| #11740381 | 2 |
| #11729898 | 2 |
| #11729612 | 2 |
| #11729608 | 2 |
| #11729469 | 2 |
| #11729468 | 2 |
| #11729416 | 2 |
| #23884 | 7 |