Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
930 conjugacy classes of subgroups.
The subgroup lattice has 748 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11744089 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11739381 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11738480 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11737920 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C7×#1648 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11729689 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11729123 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11728879 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11728816 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11726186 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11726177 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #11725998 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #11725998 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #11725992 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #11725988 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C7×#557 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#6482 | — | 2 | 1 | no | — |
| 18 | #90422 | — | 2 | 1 | no | — |
| 19 | #90419 | C22 | 1 | 1 | yes | characteristic |
| 20 | #90417 | — | 2 | 1 | no | — |
| 21 | #90417 | C22 | 1 | 1 | yes | characteristic |
| 22 | #90416 | C22 | 1 | 1 | yes | characteristic |
| 23 | #90386 | — | 2 | 1 | no | — |
| 24 | #90384 | — | 2 | 2 | no | — |
| 25 | #90383 | — | 2 | 2 | no | — |
| 26 | D7×#125 | — | 2 | 1 | no | — |
| 27 | #90272 | — | 2 | 1 | no | — |
| 28 | #90272 | — | 2 | 1 | no | — |
| 29 | #90271 | — | 2 | 1 | no | — |
| 30 | #90271 | C22 | 1 | 1 | yes | characteristic |
| 31 | #90270 | C22 | 1 | 1 | yes | characteristic |
| 32 | #90270 | C22 | 1 | 1 | yes | characteristic |
| 33 | #90265 | — | 2 | 1 | no | — |
| 34 | C4×#1161 | C22 | 1 | 1 | yes | characteristic |
| 35 | C7×#500 | C22 | 1 | 1 | yes | characteristic |
| 36 | C7×#475 | C22 | 1 | 1 | yes | characteristic |
| 37 | C7×#462 | C22 | 1 | 1 | yes | characteristic |
| 38 | #89957 | — | 2 | 1 | no | — |
| 39 | #89865 | C22 | 1 | 1 | yes | characteristic |
| 40 | #89860 | C22 | 1 | 1 | yes | characteristic |
| 41 | #89859 | C22 | 1 | 1 | yes | characteristic |
| 42 | #89855 | C22 | 1 | 1 | yes | characteristic |
| 43 | #89799 | C22 | 1 | 1 | yes | characteristic |
| 44 | #89799 | C22 | 1 | 1 | yes | characteristic |
| 45 | #89661 | — | 2 | 2 | no | — |
| 46 | #89658 | — | 2 | 2 | no | — |
| 47 | #89643 | — | 2 | 1 | no | — |
| 48 | #89637 | — | 2 | 1 | no | — |
| 49 | #89615 | C22 | 1 | 1 | yes | characteristic |
| 50 | #89615 | C22 | 1 | 1 | yes | characteristic |
| 51 | #89609 | C22 | 1 | 1 | yes | characteristic |
| 52 | D7×C4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 53 | #89591 | — | 2 | 1 | no | — |
| 54 | #89591 | — | 2 | 1 | no | — |
| 55 | #89584 | — | 2 | 1 | no | — |
| 56 | #89576 | — | 2 | 1 | no | — |
| 57 | #89465 | C22 | 1 | 1 | yes | characteristic |
| 58 | C4×#1131 | C22 | 1 | 1 | yes | characteristic |
| 59 | C7×#332 | C22 | 1 | 1 | yes | characteristic |
| 60 | C7×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 61 | C7×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 62 | #89342 | C22 | 1 | 1 | yes | characteristic |
| 63 | Q8⋊(C7⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 64 | Q8⋊(C7⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 65 | #89278 | C22 | 1 | 1 | yes | characteristic |
| 66 | #89278 | C22 | 1 | 1 | yes | characteristic |
| 67 | #89276 | C22 | 1 | 1 | yes | characteristic |
| 68 | #89276 | C22 | 1 | 1 | yes | characteristic |
| 69 | #89254 | C22 | 1 | 1 | yes | characteristic |
| 70 | #89254 | C22 | 1 | 1 | yes | characteristic |
| 71 | #18596 | — | 7 | 1 | no | maximal, Sylow |
| 72 | C2×#1161 | — | 2 | 1 | no | — |
| 73 | C2×#1161 | — | 2 | 1 | no | — |
| 74 | C2×#1161 | D4 | 1 | 1 | yes | characteristic |
| 75 | C2×C7×Q16 | — | 2 | 1 | no | — |
| 76 | C7×C4⋊Q8 | — | 2 | 1 | no | — |
| 77 | C7×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 78 | C7×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 79 | C7×#125 | — | 2 | 1 | no | — |
| 80 | C7×#125 | — | 2 | 2 | no | — |
| 81 | C4×C7×Q8 | — | 2 | 1 | no | — |
| 82 | C4×C7×Q8 | — | 2 | 1 | no | — |
| 83 | C4×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 84 | C4×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 85 | #6510 | — | 2 | 1 | no | — |
| 86 | #6510 | D4 | 1 | 1 | yes | characteristic |
| 87 | #6509 | — | 2 | 1 | no | — |
| 88 | #6509 | — | 2 | 1 | no | — |
| 89 | #6509 | — | 2 | 1 | no | — |
| 90 | #6509 | — | 2 | 1 | no | — |
| 91 | #6509 | D4 | 1 | 1 | yes | characteristic |
| 92 | Q8×Dic7 | — | 2 | 1 | no | — |
| 93 | Q8×Dic7 | D4 | 1 | 1 | yes | characteristic |
| 94 | C2×#1143 | — | 2 | 1 | no | — |
| 95 | C2×#1143 | — | 2 | 1 | no | — |
| 96 | C2×#1143 | — | 2 | 1 | no | — |
| 97 | #6482 | — | 4 | 4 | no | — |
| 98 | C2×D56 | — | 2 | 1 | no | — |
| 99 | C2×D56 | — | 2 | 1 | no | — |
| 100 | C2×#1132 | — | 2 | 2 | no | — |
| 101 | C2×#1131 | — | 2 | 1 | no | — |
| 102 | C2×#1131 | — | 2 | 1 | no | — |
| 103 | C2×C8×D7 | — | 2 | 1 | no | — |
| 104 | #6461 | — | 2 | 2 | no | — |
| 105 | #6461 | — | 2 | 2 | no | — |
| 106 | #6461 | — | 2 | 1 | no | — |
| 107 | #6460 | D4 | 1 | 2 | yes | — |
| 108 | #6459 | — | 2 | 2 | no | — |
| 109 | #6459 | — | 2 | 2 | no | — |
| 110 | #6458 | — | 2 | 2 | no | — |
| 111 | #6458 | — | 2 | 1 | no | — |
| 112 | #6458 | — | 2 | 1 | no | — |
| 113 | #6458 | — | 2 | 1 | no | — |
| 114 | #6458 | D4 | 1 | 1 | yes | characteristic |
| 115 | #6457 | — | 2 | 2 | no | — |
| 116 | #6457 | — | 2 | 2 | no | — |
| 117 | #6457 | — | 2 | 2 | no | — |
| 118 | #6457 | — | 2 | 1 | no | — |
| 119 | #6457 | — | 2 | 2 | no | — |
| 120 | #6456 | — | 2 | 2 | no | — |
| 121 | #6456 | — | 2 | 1 | no | — |
| 122 | #6456 | — | 2 | 1 | no | — |
| 123 | #6456 | — | 2 | 1 | no | — |
| 124 | #6456 | D4 | 1 | 1 | yes | characteristic |
| 125 | #6455 | — | 2 | 1 | no | — |
| 126 | #6455 | — | 2 | 1 | no | — |
| 127 | #6455 | D4 | 1 | 1 | yes | characteristic |
| 128 | D7×C4⋊C4 | — | 2 | 2 | no | — |
| 129 | D7×C4⋊C4 | — | 2 | 2 | no | — |
| 130 | D7×C4⋊C4 | — | 2 | 1 | no | — |
| 131 | D7×C4⋊C4 | — | 2 | 1 | no | — |
| 132 | D7×C4⋊C4 | — | 2 | 1 | no | — |
| 133 | #6453 | — | 2 | 1 | no | — |
| 134 | #6453 | D4 | 1 | 1 | yes | characteristic |
| 135 | #6452 | — | 2 | 2 | no | — |
| 136 | #6452 | — | 2 | 2 | no | — |
| 137 | #6452 | — | 2 | 2 | no | — |
| 138 | #6450 | D4 | 1 | 2 | yes | — |
| 139 | #6439 | — | 2 | 2 | no | — |
| 140 | #6437 | C23 | 1 | 1 | yes | characteristic |
| 141 | C4×D28 | — | 2 | 2 | no | — |
| 142 | C4×D28 | — | 2 | 1 | no | — |
| 143 | C4×D28 | — | 2 | 1 | no | — |
| 144 | C4×D28 | — | 2 | 1 | no | — |
| 145 | C4×D28 | — | 2 | 1 | no | — |
| 146 | C4×D28 | C23 | 1 | 1 | yes | characteristic |
| 147 | C4×D28 | C23 | 1 | 1 | yes | characteristic |
| 148 | #6435 | — | 2 | 2 | no | — |
| 149 | #6435 | — | 2 | 2 | no | — |
| 150 | #6435 | — | 2 | 1 | no | — |
| 151 | C42×D7 | — | 2 | 1 | no | — |
| 152 | C42×D7 | C23 | 1 | 1 | yes | characteristic |
| 153 | #6433 | — | 2 | 1 | no | — |
| 154 | #6433 | — | 2 | 1 | no | — |
| 155 | #6432 | C23 | 1 | 1 | yes | characteristic |
| 156 | C7×#107 | — | 2 | 2 | no | — |
| 157 | C7×#106 | — | 2 | 1 | no | — |
| 158 | C7×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 159 | C7×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 160 | C7×#103 | — | 2 | 1 | no | — |
| 161 | C7×#103 | — | 2 | 1 | no | — |
| 162 | C4×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 163 | #6409 | — | 2 | 1 | no | — |
| 164 | #6395 | — | 2 | 1 | no | — |
| 165 | #6395 | — | 2 | 1 | no | — |
| 166 | #6389 | — | 2 | 1 | no | — |
| 167 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 168 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 169 | #6384 | — | 2 | 2 | no | — |
| 170 | #6383 | — | 2 | 1 | no | — |
| 171 | #6383 | — | 2 | 2 | no | — |
| 172 | #6383 | — | 2 | 1 | no | — |
| 173 | #6383 | — | 2 | 1 | no | — |
| 174 | #6381 | — | 2 | 1 | no | — |
| 175 | C4⋊(C7⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 176 | C4⋊(C7⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 177 | C4×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 178 | #3515 | — | 7 | 1 | no | — |
| 179 | #3251 | — | 7 | 1 | no | — |
| 180 | #3182 | — | 7 | 1 | no | — |
| 181 | #3035 | — | 7 | 1 | no | — |
| 182 | #1648 | D7 | 1 | 1 | yes | characteristic, complemented |
| 183 | #1647 | — | 7 | 1 | no | — |
| 184 | #1644 | — | 7 | 1 | no | — |
| 185 | #1643 | — | 7 | 1 | no | — |
| 186 | #1626 | — | 7 | 1 | no | — |
| 187 | #1625 | — | 7 | 1 | no | — |
| 188 | #1622 | — | 7 | 1 | no | — |
| 189 | #1622 | — | 7 | 1 | no | — |
| 190 | #1550 | — | 7 | 1 | no | — |
| 191 | #1489 | — | 7 | 1 | no | — |
| 192 | #1483 | — | 7 | 1 | no | — |
| 193 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 194 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 195 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 196 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 197 | #1161 | — | 2 | 2 | no | — |
| 198 | #1161 | — | 4 | 1 | no | — |
| 199 | #1161 | — | 4 | 2 | no | — |
| 200 | #1161 | — | 4 | 2 | no | — |
| 201 | #1161 | — | 4 | 2 | no | — |
| 202 | #1161 | — | 4 | 2 | no | — |
| 203 | C2×D28 | — | 2 | 2 | no | — |
| 204 | C2×D28 | — | 2 | 1 | no | — |
| 205 | C2×D28 | — | 2 | 1 | no | — |
| 206 | C2×D28 | — | 2 | 1 | no | — |
| 207 | C2×D28 | — | 2 | 1 | no | — |
| 208 | C2×D28 | — | 2 | 1 | no | — |
| 209 | C2×D28 | — | 4 | 1 | no | — |
| 210 | C2×D28 | C2×D4 | 1 | 1 | yes | characteristic |
| 211 | C2×D28 | C2×D4 | 1 | 1 | yes | characteristic |
| 212 | C2×C4×D7 | — | 2 | 2 | no | — |
| 213 | C2×C4×D7 | — | 2 | 1 | no | — |
| 214 | C2×C4×D7 | — | 2 | 1 | no | — |
| 215 | C2×C4×D7 | — | 2 | 1 | no | — |
| 216 | C2×C4×D7 | — | 2 | 2 | no | — |
| 217 | C2×C4×D7 | — | 2 | 2 | no | — |
| 218 | C2×C4×D7 | — | 2 | 1 | no | — |
| 219 | C2×C4×D7 | — | 4 | 1 | no | — |
| 220 | C2×C4×D7 | C2×D4 | 1 | 1 | yes | characteristic |
| 221 | C2×C4×D7 | C2×D4 | 1 | 1 | yes | characteristic |
| 222 | C2×C4×D7 | C2×D4 | 1 | 1 | yes | characteristic |
| 223 | C2×Dic14 | C2×D4 | 1 | 2 | yes | — |
| 224 | C7×Q16 | — | 4 | 2 | no | — |
| 225 | C2×C7×C8 | — | 2 | 1 | no | — |
| 226 | C2×C7×C8 | — | 2 | 1 | no | — |
| 227 | C2×C7×C8 | — | 2 | 1 | no | — |
| 228 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 229 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 230 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 231 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 232 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 233 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 234 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 235 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 236 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | C7×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 239 | C42×C7 | — | 2 | 2 | no | — |
| 240 | C42×C7 | — | 2 | 1 | no | — |
| 241 | C42×C7 | — | 2 | 1 | no | — |
| 242 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 243 | #1143 | — | 4 | 2 | no | — |
| 244 | #1143 | — | 4 | 2 | no | — |
| 245 | #1143 | — | 8 | 1 | no | — |
| 246 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 247 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 248 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 249 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 250 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 251 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 252 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 253 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 254 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 255 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 256 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 257 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 258 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 259 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 260 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 261 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 262 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 263 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 264 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 265 | C4⋊Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 266 | C4⋊Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 267 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 268 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 269 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 270 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 271 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 272 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 273 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 274 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 275 | C4×Dic7 | — | 2 | 1 | no | — |
| 276 | C4×Dic7 | — | 2 | 1 | no | — |
| 277 | C4×Dic7 | — | 2 | 2 | no | — |
| 278 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 279 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 280 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 281 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 282 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 283 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 284 | D56 | — | 4 | 2 | no | — |
| 285 | D56 | — | 8 | 1 | no | — |
| 286 | #1132 | — | 4 | 4 | no | — |
| 287 | #1131 | — | 4 | 2 | no | — |
| 288 | #1131 | — | 8 | 1 | no | — |
| 289 | C8×D7 | — | 4 | 2 | no | — |
| 290 | C2×#135 | — | 14 | 1 | no | — |
| 291 | #557 | C2×D7 | 1 | 1 | yes | characteristic |
| 292 | #554 | — | 7 | 1 | no | — |
| 293 | #554 | — | 7 | 1 | no | — |
| 294 | #553 | — | 14 | 1 | no | — |
| 295 | #552 | — | 14 | 1 | no | — |
| 296 | #552 | — | 14 | 1 | no | — |
| 297 | #552 | — | 14 | 2 | no | — |
| 298 | #547 | — | 7 | 1 | no | — |
| 299 | #547 | — | 14 | 1 | no | — |
| 300 | #541 | — | 14 | 1 | no | — |
| 301 | #539 | — | 14 | 2 | no | — |
| 302 | #533 | — | 7 | 1 | no | — |
| 303 | #532 | — | 7 | 1 | no | — |
| 304 | #529 | — | 7 | 1 | no | — |
| 305 | #529 | — | 14 | 1 | no | — |
| 306 | C2×#125 | — | 14 | 1 | no | — |
| 307 | #520 | — | 14 | 1 | no | — |
| 308 | C4×#41 | — | 7 | 1 | no | — |
| 309 | #500 | C2×D7 | 1 | 1 | yes | characteristic |
| 310 | #492 | — | 7 | 1 | no | — |
| 311 | #487 | — | 7 | 1 | no | — |
| 312 | #486 | — | 7 | 1 | no | — |
| 313 | #478 | — | 14 | 1 | no | — |
| 314 | #475 | C2×D7 | 1 | 1 | yes | characteristic |
| 315 | #474 | — | 7 | 1 | no | — |
| 316 | #469 | — | 14 | 1 | no | — |
| 317 | #468 | — | 14 | 1 | no | — |
| 318 | #468 | — | 14 | 2 | no | — |
| 319 | #464 | — | 14 | 1 | no | — |
| 320 | #463 | — | 14 | 1 | no | — |
| 321 | #463 | — | 14 | 1 | no | — |
| 322 | #462 | C2×D7 | 1 | 1 | yes | characteristic |
| 323 | #461 | — | 7 | 1 | no | — |
| 324 | #460 | — | 7 | 1 | no | — |
| 325 | #460 | — | 7 | 1 | no | — |
| 326 | #459 | — | 7 | 1 | no | — |
| 327 | #459 | — | 7 | 1 | no | — |
| 328 | #440 | — | 14 | 2 | no | — |
| 329 | #423 | — | 7 | 1 | no | — |
| 330 | C2×C4⋊C8 | — | 7 | 1 | no | — |
| 331 | #416 | — | 14 | 1 | no | — |
| 332 | C4×M16 | — | 7 | 1 | no | — |
| 333 | #333 | — | 7 | 1 | no | — |
| 334 | #333 | — | 7 | 1 | no | — |
| 335 | #332 | — | 7 | 1 | no | — |
| 336 | #332 | C2×D7 | 1 | 1 | yes | characteristic |
| 337 | Q8⋊C8 | — | 7 | 1 | no | — |
| 338 | Q8⋊C8 | — | 7 | 1 | no | — |
| 339 | Q8⋊C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 340 | Q8⋊C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 341 | D4⋊C8 | — | 7 | 1 | no | — |
| 342 | D4⋊C8 | — | 7 | 1 | no | — |
| 343 | D4⋊C8 | — | 7 | 1 | no | — |
| 344 | D4⋊C8 | — | 7 | 1 | no | — |
| 345 | C22×D7 | — | 2 | 1 | no | — |
| 346 | C22×D7 | — | 2 | 1 | no | — |
| 347 | C22×D7 | — | 4 | 1 | no | — |
| 348 | C22×D7 | #120 | 1 | 1 | yes | characteristic |
| 349 | C7×Q8 | — | 2 | 1 | no | — |
| 350 | C7×Q8 | — | 2 | 1 | no | — |
| 351 | C7×Q8 | — | 2 | 1 | no | — |
| 352 | C7×Q8 | — | 2 | 1 | no | — |
| 353 | C7×Q8 | — | 4 | 1 | no | — |
| 354 | C7×Q8 | — | 4 | 1 | no | — |
| 355 | C7×Q8 | — | 4 | 1 | no | — |
| 356 | C7×Q8 | — | 4 | 1 | no | — |
| 357 | C2×C4×C7 | — | 2 | 1 | no | — |
| 358 | C2×C4×C7 | — | 2 | 2 | no | — |
| 359 | C2×C4×C7 | — | 2 | 1 | no | — |
| 360 | C2×C4×C7 | — | 2 | 1 | no | — |
| 361 | C2×C4×C7 | — | 2 | 1 | no | — |
| 362 | C2×C4×C7 | — | 4 | 1 | no | — |
| 363 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 364 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 365 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 366 | C2×Dic7 | — | 2 | 1 | no | — |
| 367 | C2×Dic7 | — | 2 | 2 | no | — |
| 368 | C2×Dic7 | — | 2 | 1 | no | — |
| 369 | C2×Dic7 | #120 | 1 | 1 | yes | characteristic |
| 370 | C2×Dic7 | #120 | 1 | 1 | yes | characteristic |
| 371 | C2×Dic7 | #120 | 1 | 1 | yes | characteristic |
| 372 | D28 | — | 2 | 1 | no | — |
| 373 | D28 | — | 2 | 1 | no | — |
| 374 | D28 | — | 2 | 1 | no | — |
| 375 | D28 | — | 4 | 2 | no | — |
| 376 | D28 | — | 4 | 2 | no | — |
| 377 | D28 | — | 4 | 4 | no | — |
| 378 | D28 | — | 4 | 1 | no | — |
| 379 | D28 | — | 4 | 1 | no | — |
| 380 | D28 | — | 4 | 1 | no | — |
| 381 | D28 | — | 4 | 1 | no | — |
| 382 | D28 | — | 8 | 1 | no | — |
| 383 | D28 | — | 8 | 2 | no | — |
| 384 | D28 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 385 | C4×D7 | — | 2 | 1 | no | — |
| 386 | C4×D7 | — | 2 | 1 | no | — |
| 387 | C4×D7 | — | 2 | 1 | no | — |
| 388 | C4×D7 | — | 2 | 1 | no | — |
| 389 | C4×D7 | — | 4 | 1 | no | — |
| 390 | C4×D7 | — | 4 | 2 | no | — |
| 391 | C4×D7 | — | 4 | 4 | no | — |
| 392 | C4×D7 | — | 4 | 1 | no | — |
| 393 | C4×D7 | — | 4 | 1 | no | — |
| 394 | C4×D7 | — | 4 | 1 | no | — |
| 395 | C4×D7 | — | 4 | 1 | no | — |
| 396 | C4×D7 | — | 8 | 1 | no | — |
| 397 | C4×D7 | — | 8 | 2 | no | — |
| 398 | C4×D7 | — | 8 | 2 | no | — |
| 399 | C4×D7 | — | 8 | 2 | no | — |
| 400 | Dic14 | — | 4 | 2 | no | — |
| 401 | C7×C8 | — | 2 | 2 | no | — |
| 402 | C7×C8 | — | 4 | 1 | no | — |
| 403 | C7×C8 | — | 4 | 1 | no | — |
| 404 | C7⋊C8 | — | 4 | 1 | no | — |
| 405 | C7⋊C8 | — | 4 | 1 | no | — |
| 406 | C7⋊C8 | — | 4 | 1 | no | — |
| 407 | C2×#41 | — | 7 | 1 | no | — |
| 408 | C2×#41 | — | 14 | 1 | no | — |
| 409 | C2×#41 | — | 14 | 1 | no | — |
| 410 | #135 | — | 28 | 4 | no | — |
| 411 | C2×Q16 | — | 2 | 1 | no | — |
| 412 | C2×SD16 | — | 14 | 2 | no | — |
| 413 | C2×SD16 | — | 14 | 1 | no | — |
| 414 | C2×SD16 | — | 14 | 1 | no | — |
| 415 | C2×SD16 | — | 14 | 1 | no | — |
| 416 | C2×D8 | — | 14 | 1 | no | — |
| 417 | C2×D8 | — | 14 | 1 | no | — |
| 418 | C2×M16 | — | 14 | 1 | no | — |
| 419 | C2×M16 | — | 14 | 1 | no | — |
| 420 | C22×C8 | — | 14 | 1 | no | — |
| 421 | C4⋊Q8 | — | 2 | 1 | no | — |
| 422 | C4⋊Q8 | — | 7 | 1 | no | — |
| 423 | C4⋊Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 424 | C4⋊Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 425 | #127 | — | 7 | 1 | no | — |
| 426 | #126 | — | 14 | 2 | no | — |
| 427 | #126 | — | 14 | 1 | no | — |
| 428 | #126 | — | 14 | 2 | no | — |
| 429 | #126 | — | 14 | 2 | no | — |
| 430 | #125 | — | 2 | 1 | no | — |
| 431 | #125 | — | 2 | 2 | no | — |
| 432 | #125 | — | 7 | 1 | no | — |
| 433 | #125 | — | 14 | 1 | no | — |
| 434 | #125 | — | 14 | 1 | no | — |
| 435 | #125 | — | 14 | 1 | no | — |
| 436 | #125 | — | 14 | 2 | no | — |
| 437 | #125 | — | 14 | 2 | no | — |
| 438 | #125 | — | 14 | 2 | no | — |
| 439 | #124 | — | 7 | 1 | no | — |
| 440 | #124 | — | 14 | 1 | no | — |
| 441 | #123 | — | 14 | 1 | no | — |
| 442 | #123 | — | 14 | 2 | no | — |
| 443 | #123 | — | 14 | 2 | no | — |
| 444 | #123 | — | 14 | 2 | no | — |
| 445 | #123 | — | 14 | 2 | no | — |
| 446 | C22⋊Q8 | — | 7 | 1 | no | — |
| 447 | C22⋊Q8 | — | 7 | 2 | no | — |
| 448 | C22⋊Q8 | — | 14 | 2 | no | — |
| 449 | C22⋊Q8 | — | 14 | 2 | no | — |
| 450 | C22⋊Q8 | — | 14 | 1 | no | — |
| 451 | C22⋊Q8 | — | 14 | 1 | no | — |
| 452 | C22⋊Q8 | — | 14 | 1 | no | — |
| 453 | C22⋊Q8 | — | 14 | 1 | no | — |
| 454 | #121 | — | 7 | 1 | no | — |
| 455 | #121 | — | 14 | 1 | no | — |
| 456 | #121 | — | 14 | 2 | no | — |
| 457 | #121 | — | 14 | 1 | no | — |
| 458 | #121 | — | 14 | 1 | no | — |
| 459 | C4×Q8 | — | 2 | 1 | no | — |
| 460 | C4×Q8 | — | 2 | 1 | no | — |
| 461 | C4×Q8 | — | 7 | 1 | no | — |
| 462 | C4×Q8 | — | 7 | 2 | no | — |
| 463 | C4×Q8 | — | 14 | 1 | no | — |
| 464 | C4×Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 465 | C4×Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 466 | C4×D4 | — | 7 | 1 | no | — |
| 467 | C4×D4 | — | 7 | 1 | no | — |
| 468 | C4×D4 | — | 7 | 1 | no | — |
| 469 | C4×D4 | — | 14 | 1 | no | — |
| 470 | C4×D4 | — | 14 | 1 | no | — |
| 471 | C4×D4 | — | 14 | 1 | no | — |
| 472 | C4×D4 | — | 14 | 1 | no | — |
| 473 | C4×D4 | — | 14 | 2 | no | — |
| 474 | C4×D4 | — | 14 | 1 | no | — |
| 475 | C4×D4 | — | 14 | 1 | no | — |
| 476 | C4×D4 | — | 14 | 1 | no | — |
| 477 | C4×D4 | — | 14 | 2 | no | — |
| 478 | #117 | — | 7 | 1 | no | — |
| 479 | #117 | — | 14 | 1 | no | — |
| 480 | #117 | — | 14 | 2 | no | — |
| 481 | #117 | — | 14 | 2 | no | — |
| 482 | #117 | — | 14 | 1 | no | — |
| 483 | #117 | — | 14 | 1 | no | — |
| 484 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 485 | C2×C4⋊C4 | — | 14 | 2 | no | — |
| 486 | C2×C4⋊C4 | — | 14 | 2 | no | — |
| 487 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 488 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 489 | C2×C42 | — | 7 | 1 | no | — |
| 490 | C2×C42 | — | 14 | 1 | no | — |
| 491 | #107 | — | 2 | 2 | no | — |
| 492 | #107 | — | 14 | 1 | no | — |
| 493 | #106 | — | 2 | 1 | no | — |
| 494 | C4⋊C8 | — | 7 | 1 | no | — |
| 495 | C4⋊C8 | — | 7 | 1 | no | — |
| 496 | C4⋊C8 | — | 14 | 1 | no | — |
| 497 | C4⋊C8 | — | 14 | 1 | no | — |
| 498 | C4⋊C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 499 | C4⋊C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 500 | #103 | — | 2 | 1 | no | — |
| 501 | #103 | — | 2 | 1 | no | — |
| 502 | #103 | — | 14 | 2 | no | — |
| 503 | #103 | — | 14 | 1 | no | — |
| 504 | #102 | — | 14 | 1 | no | — |
| 505 | #102 | — | 14 | 1 | no | — |
| 506 | #102 | — | 14 | 1 | no | — |
| 507 | #102 | — | 14 | 1 | no | — |
| 508 | #102 | — | 14 | 2 | no | — |
| 509 | #102 | — | 14 | 1 | no | — |
| 510 | #97 | — | 14 | 1 | no | — |
| 511 | C4×C8 | — | 7 | 1 | no | — |
| 512 | C4×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 513 | C22×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 514 | C2×D7 | — | 2 | 1 | no | — |
| 515 | C2×D7 | — | 2 | 2 | no | — |
| 516 | C2×D7 | — | 2 | 1 | no | — |
| 517 | C2×D7 | — | 2 | 1 | no | — |
| 518 | C2×D7 | — | 4 | 1 | no | — |
| 519 | C2×D7 | — | 4 | 1 | no | — |
| 520 | C2×D7 | — | 4 | 1 | no | — |
| 521 | C2×D7 | — | 4 | 1 | no | — |
| 522 | C2×D7 | — | 4 | 1 | no | — |
| 523 | C2×D7 | — | 8 | 1 | no | — |
| 524 | C2×D7 | — | 8 | 1 | no | — |
| 525 | C2×D7 | — | 8 | 1 | no | — |
| 526 | C4×C7 | — | 2 | 1 | no | — |
| 527 | C4×C7 | — | 4 | 1 | no | — |
| 528 | C4×C7 | — | 4 | 2 | no | — |
| 529 | C4×C7 | — | 4 | 1 | no | — |
| 530 | C4×C7 | — | 4 | 1 | no | — |
| 531 | C4×C7 | — | 4 | 1 | no | — |
| 532 | C4×C7 | — | 8 | 1 | no | — |
| 533 | C4×C7 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 534 | C4×C7 | #575 | 1 | 1 | yes | characteristic |
| 535 | C4×C7 | #577 | 1 | 1 | yes | characteristic |
| 536 | C4×C7 | #578 | 1 | 1 | yes | characteristic |
| 537 | Dic7 | — | 2 | 1 | no | — |
| 538 | Dic7 | — | 2 | 1 | no | — |
| 539 | Dic7 | — | 2 | 1 | no | — |
| 540 | Dic7 | — | 4 | 1 | no | — |
| 541 | Dic7 | — | 4 | 1 | no | — |
| 542 | Dic7 | — | 4 | 2 | no | — |
| 543 | #41 | — | 14 | 2 | no | — |
| 544 | #41 | — | 28 | 1 | no | — |
| 545 | #41 | — | 28 | 2 | no | — |
| 546 | #41 | — | 28 | 2 | no | — |
| 547 | #41 | — | 28 | 2 | no | — |
| 548 | #41 | — | 28 | 2 | no | — |
| 549 | C2×Q8 | — | 2 | 1 | no | — |
| 550 | C2×Q8 | — | 2 | 1 | no | — |
| 551 | C2×Q8 | — | 7 | 2 | no | — |
| 552 | C2×Q8 | D4×D7 | 1 | 1 | yes | characteristic |
| 553 | C2×Q8 | D4×D7 | 1 | 1 | yes | characteristic |
| 554 | C2×D4 | — | 7 | 1 | no | — |
| 555 | C2×D4 | — | 7 | 1 | no | — |
| 556 | C2×D4 | — | 14 | 1 | no | — |
| 557 | C2×D4 | — | 14 | 2 | no | — |
| 558 | C2×D4 | — | 14 | 1 | no | — |
| 559 | C2×D4 | — | 14 | 1 | no | — |
| 560 | C2×D4 | — | 14 | 1 | no | — |
| 561 | C2×D4 | — | 14 | 1 | no | — |
| 562 | C2×D4 | — | 28 | 1 | no | — |
| 563 | C22×C4 | — | 7 | 1 | no | — |
| 564 | C22×C4 | — | 7 | 1 | no | — |
| 565 | C22×C4 | — | 7 | 1 | no | — |
| 566 | C22×C4 | — | 14 | 1 | no | — |
| 567 | C22×C4 | — | 14 | 1 | no | — |
| 568 | C22×C4 | — | 14 | 2 | no | — |
| 569 | C22×C4 | — | 14 | 2 | no | — |
| 570 | C22×C4 | — | 14 | 2 | no | — |
| 571 | C22×C4 | — | 14 | 1 | no | — |
| 572 | C22×C4 | — | 14 | 1 | no | — |
| 573 | C22×C4 | — | 28 | 1 | no | — |
| 574 | Q16 | — | 4 | 2 | no | — |
| 575 | SD16 | — | 28 | 4 | no | — |
| 576 | SD16 | — | 28 | 2 | no | — |
| 577 | SD16 | — | 28 | 2 | no | — |
| 578 | SD16 | — | 56 | 1 | no | — |
| 579 | D8 | — | 28 | 2 | no | — |
| 580 | D8 | — | 56 | 1 | no | — |
| 581 | M16 | — | 28 | 2 | no | — |
| 582 | M16 | — | 56 | 1 | no | — |
| 583 | C2×C8 | — | 2 | 1 | no | — |
| 584 | C2×C8 | — | 2 | 1 | no | — |
| 585 | C2×C8 | — | 2 | 1 | no | — |
| 586 | C2×C8 | — | 14 | 1 | no | — |
| 587 | C2×C8 | — | 14 | 1 | no | — |
| 588 | C2×C8 | — | 14 | 1 | no | — |
| 589 | C2×C8 | — | 28 | 2 | no | — |
| 590 | C4⋊C4 | — | 2 | 2 | no | — |
| 591 | C4⋊C4 | — | 2 | 2 | no | — |
| 592 | C4⋊C4 | — | 2 | 2 | no | — |
| 593 | C4⋊C4 | — | 2 | 1 | no | — |
| 594 | C4⋊C4 | — | 2 | 1 | no | — |
| 595 | C4⋊C4 | — | 2 | 1 | no | — |
| 596 | C4⋊C4 | — | 2 | 1 | no | — |
| 597 | C4⋊C4 | — | 2 | 1 | no | — |
| 598 | C4⋊C4 | — | 7 | 1 | no | — |
| 599 | C4⋊C4 | — | 7 | 1 | no | — |
| 600 | C4⋊C4 | — | 14 | 1 | no | — |
| 601 | C4⋊C4 | — | 14 | 2 | no | — |
| 602 | C4⋊C4 | — | 14 | 1 | no | — |
| 603 | C4⋊C4 | — | 14 | 1 | no | — |
| 604 | C4⋊C4 | — | 14 | 2 | no | — |
| 605 | C4⋊C4 | — | 14 | 1 | no | — |
| 606 | C4⋊C4 | — | 14 | 2 | no | — |
| 607 | C4⋊C4 | — | 14 | 2 | no | — |
| 608 | C4⋊C4 | — | 14 | 2 | no | — |
| 609 | C4⋊C4 | — | 14 | 2 | no | — |
| 610 | C4⋊C4 | — | 14 | 2 | no | — |
| 611 | C4⋊C4 | — | 14 | 1 | no | — |
| 612 | C4⋊C4 | — | 14 | 1 | no | — |
| 613 | C4⋊C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 614 | C4⋊C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 615 | C4⋊C4 | D4×D7 | 1 | 2 | yes | — |
| 616 | C22⋊C4 | — | 14 | 1 | no | — |
| 617 | C22⋊C4 | — | 14 | 1 | no | — |
| 618 | C22⋊C4 | — | 14 | 1 | no | — |
| 619 | C22⋊C4 | — | 14 | 1 | no | — |
| 620 | C22⋊C4 | — | 14 | 1 | no | — |
| 621 | C22⋊C4 | — | 14 | 2 | no | — |
| 622 | C22⋊C4 | — | 14 | 1 | no | — |
| 623 | C22⋊C4 | — | 14 | 2 | no | — |
| 624 | C22⋊C4 | — | 14 | 2 | no | — |
| 625 | C22⋊C4 | — | 14 | 2 | no | — |
| 626 | C22⋊C4 | — | 14 | 1 | no | — |
| 627 | C22⋊C4 | — | 14 | 1 | no | — |
| 628 | C22⋊C4 | — | 28 | 1 | no | — |
| 629 | C22⋊C4 | — | 28 | 1 | no | — |
| 630 | C42 | — | 2 | 2 | no | — |
| 631 | C42 | — | 2 | 1 | no | — |
| 632 | C42 | — | 2 | 1 | no | — |
| 633 | C42 | — | 7 | 1 | no | — |
| 634 | C42 | — | 7 | 1 | no | — |
| 635 | C42 | — | 7 | 1 | no | — |
| 636 | C42 | — | 14 | 1 | no | — |
| 637 | C42 | — | 14 | 1 | no | — |
| 638 | C42 | — | 14 | 2 | no | — |
| 639 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 640 | C2×C7 | #3006 | 1 | 1 | yes | characteristic |
| 641 | C2×C7 | #3013 | 1 | 1 | yes | characteristic |
| 642 | C2×C7 | #3018 | 1 | 1 | yes | characteristic |
| 643 | D7 | — | 4 | 1 | no | — |
| 644 | D7 | — | 4 | 2 | no | — |
| 645 | D7 | — | 8 | 1 | no | — |
| 646 | D7 | — | 16 | 1 | no | — |
| 647 | C23 | — | 7 | 1 | no | — |
| 648 | C23 | — | 14 | 1 | no | — |
| 649 | C23 | — | 14 | 1 | no | — |
| 650 | C23 | — | 28 | 1 | no | — |
| 651 | Q8 | — | 2 | 1 | no | — |
| 652 | Q8 | — | 2 | 1 | no | — |
| 653 | Q8 | — | 2 | 1 | no | — |
| 654 | Q8 | — | 2 | 1 | no | — |
| 655 | Q8 | — | 4 | 1 | no | — |
| 656 | Q8 | — | 4 | 1 | no | — |
| 657 | Q8 | — | 4 | 1 | no | — |
| 658 | Q8 | — | 4 | 1 | no | — |
| 659 | Q8 | — | 28 | 2 | no | — |
| 660 | D4 | — | 7 | 2 | no | — |
| 661 | D4 | — | 14 | 1 | no | — |
| 662 | D4 | — | 14 | 1 | no | — |
| 663 | D4 | — | 14 | 1 | no | — |
| 664 | D4 | — | 28 | 2 | no | — |
| 665 | D4 | — | 28 | 2 | no | — |
| 666 | D4 | — | 28 | 4 | no | — |
| 667 | D4 | — | 28 | 1 | no | — |
| 668 | D4 | — | 28 | 1 | no | — |
| 669 | D4 | — | 28 | 1 | no | — |
| 670 | D4 | — | 28 | 1 | no | — |
| 671 | D4 | — | 56 | 1 | no | — |
| 672 | D4 | — | 56 | 2 | no | — |
| 673 | C2×C4 | — | 2 | 1 | no | — |
| 674 | C2×C4 | — | 2 | 1 | no | — |
| 675 | C2×C4 | — | 2 | 1 | no | — |
| 676 | C2×C4 | — | 2 | 2 | no | — |
| 677 | C2×C4 | — | 2 | 1 | no | — |
| 678 | C2×C4 | — | 4 | 1 | no | — |
| 679 | C2×C4 | — | 7 | 1 | no | — |
| 680 | C2×C4 | — | 7 | 1 | no | — |
| 681 | C2×C4 | — | 7 | 1 | no | — |
| 682 | C2×C4 | — | 14 | 1 | no | — |
| 683 | C2×C4 | — | 14 | 1 | no | — |
| 684 | C2×C4 | — | 14 | 1 | no | — |
| 685 | C2×C4 | — | 14 | 1 | no | — |
| 686 | C2×C4 | — | 14 | 1 | no | — |
| 687 | C2×C4 | — | 14 | 2 | no | — |
| 688 | C2×C4 | — | 14 | 1 | no | — |
| 689 | C2×C4 | — | 28 | 1 | no | — |
| 690 | C2×C4 | — | 28 | 2 | no | — |
| 691 | C2×C4 | — | 28 | 4 | no | — |
| 692 | C2×C4 | — | 28 | 1 | no | — |
| 693 | C2×C4 | — | 28 | 1 | no | — |
| 694 | C2×C4 | — | 28 | 1 | no | — |
| 695 | C2×C4 | — | 28 | 1 | no | — |
| 696 | C2×C4 | — | 56 | 1 | no | — |
| 697 | C2×C4 | — | 56 | 2 | no | — |
| 698 | C2×C4 | — | 56 | 2 | no | — |
| 699 | C2×C4 | — | 56 | 2 | no | — |
| 700 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 701 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 702 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 703 | C8 | — | 2 | 2 | no | — |
| 704 | C8 | — | 4 | 1 | no | — |
| 705 | C8 | — | 4 | 1 | no | — |
| 706 | C8 | — | 28 | 1 | no | — |
| 707 | C8 | — | 28 | 1 | no | — |
| 708 | C8 | — | 28 | 1 | no | — |
| 709 | C7 | #18596 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 710 | C22 | — | 14 | 1 | no | — |
| 711 | C22 | — | 14 | 1 | no | — |
| 712 | C22 | — | 14 | 1 | no | — |
| 713 | C22 | — | 14 | 2 | no | — |
| 714 | C22 | — | 28 | 1 | no | — |
| 715 | C22 | — | 28 | 1 | no | — |
| 716 | C22 | — | 28 | 1 | no | — |
| 717 | C22 | — | 28 | 1 | no | — |
| 718 | C22 | — | 28 | 1 | no | — |
| 719 | C22 | — | 56 | 1 | no | — |
| 720 | C22 | — | 56 | 1 | no | — |
| 721 | C22 | — | 56 | 1 | no | — |
| 722 | C22 | D7×#120 | 1 | 1 | yes | characteristic |
| 723 | C4 | — | 2 | 1 | no | — |
| 724 | C4 | — | 4 | 1 | no | — |
| 725 | C4 | — | 4 | 1 | no | — |
| 726 | C4 | — | 4 | 1 | no | — |
| 727 | C4 | — | 4 | 1 | no | — |
| 728 | C4 | — | 4 | 2 | no | — |
| 729 | C4 | — | 8 | 1 | no | — |
| 730 | C4 | — | 14 | 1 | no | — |
| 731 | C4 | — | 14 | 1 | no | — |
| 732 | C4 | — | 14 | 1 | no | — |
| 733 | C4 | — | 28 | 1 | no | — |
| 734 | C4 | — | 28 | 2 | no | — |
| 735 | C4 | — | 28 | 1 | no | — |
| 736 | C4 | #90457 | 1 | 1 | yes | characteristic |
| 737 | C4 | #90459 | 1 | 1 | yes | characteristic |
| 738 | C4 | D7×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 739 | C4 | #90469 | 1 | 1 | yes | characteristic |
| 740 | C2 | — | 28 | 1 | no | — |
| 741 | C2 | — | 28 | 2 | no | — |
| 742 | C2 | — | 56 | 1 | no | — |
| 743 | C2 | — | 112 | 1 | no | — |
| 744 | C2 | #11737529 | 1 | 1 | yes | characteristic |
| 745 | C2 | #11737631 | 1 | 1 | yes | characteristic |
| 746 | C2 | #11737743 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D7×#120 |
| commutator, cosocle | C42×C7 | C24 |
| Frattini | C42 | C23×D7 |
| Fitting | C7×#1648 | C2 |
| socle | C22×C7 | C2×#120 |
| hypercenter | #1648 | D7 |
| hypocenter | C7 | #18596 |
| LCS | G ▷ C42×C7 ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #1648 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11744089 | C2 | semidirect |
| 2. #11739381 | C2 | semidirect |
| 3. #11738480 | C2 | semidirect |
| 4. #11737920 | C2 | semidirect |
| 5. C7×#1648 | C2 | semidirect |
| 6. #11729689 | C2 | semidirect |
| 7. #11729123 | C2 | semidirect |
| 8. #11728879 | C2 | semidirect |
| 9. #11728816 | C2 | semidirect |
| 10. #11726186 | C2 | semidirect |
| 11. #11726177 | C2 | semidirect |
| 12. #11725998 | C2 | semidirect |
| 13. #11725998 | C2 | semidirect |
| 14. #11725992 | C2 | semidirect |
| 15. #11725988 | C2 | semidirect |
| 182. #1648 | D7 | semidirect |
| 709. C7 | #18596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11744089 | 2 |
| #11739381 | 2 |
| #11738480 | 2 |
| #11737920 | 2 |
| C7×#1648 | 2 |
| #11729689 | 2 |
| #11729123 | 2 |
| #11728879 | 2 |
| #11728816 | 2 |
| #11726186 | 2 |
| #11726177 | 2 |
| #11725998 | 2 |
| #11725992 | 2 |
| #11725988 | 2 |
| #18596 | 7 |