Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1054 conjugacy classes of subgroups.
The subgroup lattice has 1052 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | A4×#126 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #85313 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #85312 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #85311 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #85305 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #85304 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #85303 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #85301 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #85300 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #85298 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #85294 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #85293 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #85293 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #85291 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #85283 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #45971 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C2×GL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic |
| 18 | C22×SL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C4×S4 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×A4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×A4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×A4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 23 | #5712 | — | 4 | 1 | no | maximal |
| 24 | A4×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 25 | A4×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 26 | A4×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 27 | A4×C22⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 28 | A4×C22⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 29 | A4×C22⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 30 | C42×A4 | C22 | 1 | 1 | yes | characteristic |
| 31 | #5432 | C22 | 1 | 1 | yes | characteristic |
| 32 | #5432 | C22 | 1 | 1 | yes | characteristic |
| 33 | (C2×S4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 34 | (C2×S4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 35 | (C2×S4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 36 | (C2×S4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 37 | (C2×S4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 38 | C4⋊SL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic |
| 39 | C4⋊SL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic |
| 40 | C4⋊SL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic |
| 41 | C4⋊SL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic |
| 42 | C4⋊SL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic |
| 43 | C4⋊SL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic |
| 44 | SL(2,ℤ/4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 45 | SL(2,ℤ/4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 46 | SL(2,ℤ/4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 47 | SL(2,ℤ/4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 48 | SL(2,ℤ/4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 49 | SL(2,ℤ/4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 50 | SL(2,ℤ/4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 51 | C4×SL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic |
| 52 | C4×SL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic |
| 53 | C2×#563 | — | 3 | 1 | no | — |
| 54 | C22×#126 | D3 | 1 | 1 | yes | characteristic, complemented |
| 55 | #2857 | — | 3 | 1 | no | — |
| 56 | #2852 | — | 3 | 1 | no | — |
| 57 | #2823 | — | 3 | 1 | no | — |
| 58 | #2821 | — | 3 | 1 | no | — |
| 59 | #2727 | — | 3 | 1 | no | — |
| 60 | #2725 | — | 3 | 1 | no | — |
| 61 | #2723 | — | 3 | 1 | no | — |
| 62 | #2722 | — | 3 | 1 | no | — |
| 63 | #2721 | — | 3 | 1 | no | — |
| 64 | #2718 | — | 3 | 1 | no | — |
| 65 | #2716 | — | 3 | 1 | no | — |
| 66 | #2715 | — | 3 | 1 | no | — |
| 67 | #2702 | — | 3 | 1 | no | — |
| 68 | #2698 | — | 3 | 1 | no | — |
| 69 | #2695 | — | 3 | 1 | no | — |
| 70 | #2689 | — | 3 | 1 | no | — |
| 71 | #2481 | — | 3 | 1 | no | — |
| 72 | #2480 | — | 3 | 1 | no | — |
| 73 | #2473 | — | 3 | 1 | no | — |
| 74 | #2472 | — | 3 | 1 | no | — |
| 75 | #2449 | — | 3 | 1 | no | — |
| 76 | #2442 | — | 3 | 1 | no | — |
| 77 | #2440 | — | 3 | 1 | no | — |
| 78 | #2437 | — | 3 | 1 | no | — |
| 79 | #2437 | — | 3 | 1 | no | — |
| 80 | #2418 | — | 3 | 1 | no | — |
| 81 | #2417 | — | 3 | 1 | no | — |
| 82 | #2412 | — | 3 | 1 | no | — |
| 83 | #2383 | — | 3 | 1 | no | — |
| 84 | C23×A4 | C23 | 1 | 1 | yes | characteristic |
| 85 | C22×S4 | C23 | 1 | 1 | yes | characteristic |
| 86 | C2×C4×A4 | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×C4×A4 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×C4×A4 | C23 | 1 | 1 | yes | characteristic |
| 89 | C2×C4×A4 | C23 | 1 | 1 | yes | characteristic |
| 90 | C2×C4×A4 | C23 | 1 | 1 | yes | characteristic |
| 91 | C2×C4×A4 | C23 | 1 | 1 | yes | characteristic |
| 92 | GL(2,ℤ/4) | — | 4 | 1 | no | — |
| 93 | C2×SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 94 | C2×SL(2,ℤ/4) | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×SL(2,ℤ/4) | C23 | 1 | 1 | yes | characteristic |
| 96 | C2×SL(2,ℤ/4) | C23 | 1 | 1 | yes | characteristic |
| 97 | C2×SL(2,ℤ/4) | C23 | 1 | 1 | yes | characteristic |
| 98 | C2×SL(2,ℤ/4) | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×SL(2,ℤ/4) | C23 | 1 | 1 | yes | characteristic |
| 100 | C2×SL(2,ℤ/4) | C23 | 1 | 1 | yes | characteristic |
| 101 | C4×S4 | — | 4 | 1 | no | — |
| 102 | A4⋊Q8 | — | 4 | 1 | no | — |
| 103 | A4⋊Q8 | — | 4 | 1 | no | — |
| 104 | A4⋊Q8 | — | 4 | 1 | no | — |
| 105 | C3×#126 | — | 4 | 1 | no | — |
| 106 | #898 | — | 4 | 1 | no | — |
| 107 | #897 | — | 4 | 1 | no | — |
| 108 | #896 | — | 4 | 1 | no | — |
| 109 | #890 | — | 4 | 1 | no | — |
| 110 | #889 | — | 4 | 1 | no | — |
| 111 | #888 | — | 4 | 1 | no | — |
| 112 | #886 | — | 4 | 1 | no | — |
| 113 | #885 | — | 4 | 1 | no | — |
| 114 | #883 | — | 4 | 1 | no | — |
| 115 | #879 | — | 4 | 1 | no | — |
| 116 | #878 | — | 4 | 1 | no | — |
| 117 | #878 | — | 4 | 1 | no | — |
| 118 | #876 | — | 4 | 1 | no | — |
| 119 | #869 | — | 4 | 1 | no | — |
| 120 | #563 | — | 6 | 1 | no | — |
| 121 | #563 | — | 6 | 1 | no | — |
| 122 | #563 | — | 6 | 1 | no | — |
| 123 | #563 | — | 6 | 1 | no | — |
| 124 | #563 | — | 6 | 1 | no | — |
| 125 | #563 | — | 6 | 1 | no | — |
| 126 | #563 | — | 6 | 1 | no | — |
| 127 | #563 | — | 6 | 1 | no | — |
| 128 | C2×C4⋊Q8 | — | 3 | 1 | no | — |
| 129 | C2×C4⋊Q8 | — | 3 | 1 | no | — |
| 130 | C2×#126 | — | 3 | 1 | no | — |
| 131 | C2×#126 | — | 3 | 1 | no | — |
| 132 | C2×#126 | — | 3 | 1 | no | — |
| 133 | C2×#126 | — | 3 | 1 | no | — |
| 134 | C2×#126 | — | 3 | 1 | no | — |
| 135 | C2×#126 | — | 3 | 1 | no | — |
| 136 | C2×#126 | — | 3 | 1 | no | — |
| 137 | C2×#126 | — | 3 | 1 | no | — |
| 138 | C2×#126 | — | 3 | 1 | no | — |
| 139 | C2×#126 | — | 3 | 1 | no | — |
| 140 | C2×#126 | — | 3 | 1 | no | — |
| 141 | C2×#125 | — | 3 | 1 | no | — |
| 142 | C2×#125 | — | 3 | 1 | no | — |
| 143 | C2×#124 | — | 3 | 1 | no | — |
| 144 | C2×#123 | — | 3 | 1 | no | — |
| 145 | C2×#123 | — | 3 | 1 | no | — |
| 146 | C2×C22⋊Q8 | — | 3 | 1 | no | — |
| 147 | C2×C22⋊Q8 | — | 3 | 1 | no | — |
| 148 | C2×C22⋊Q8 | — | 3 | 1 | no | — |
| 149 | C2×C22⋊Q8 | — | 3 | 1 | no | — |
| 150 | C2×C22⋊Q8 | — | 3 | 1 | no | — |
| 151 | C2×C22⋊Q8 | — | 3 | 1 | no | — |
| 152 | C2×C22⋊Q8 | — | 3 | 1 | no | — |
| 153 | C2×#120 | — | 3 | 1 | no | — |
| 154 | C2×C4×D4 | — | 3 | 1 | no | — |
| 155 | C22×C4⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 156 | C22×C4⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 157 | C22×C4⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 158 | C22×C22⋊C4 | — | 3 | 1 | no | — |
| 159 | C22×C22⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 160 | C22×C22⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 161 | C22×C22⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 162 | C22×C42 | C2×D3 | 1 | 1 | yes | characteristic |
| 163 | #400 | — | 3 | 1 | no | — |
| 164 | #400 | — | 3 | 1 | no | — |
| 165 | #400 | — | 3 | 1 | no | — |
| 166 | #400 | — | 3 | 1 | no | — |
| 167 | #400 | — | 3 | 1 | no | — |
| 168 | #399 | — | 3 | 1 | no | — |
| 169 | #399 | — | 3 | 1 | no | — |
| 170 | #399 | — | 3 | 1 | no | — |
| 171 | #399 | — | 3 | 1 | no | — |
| 172 | #398 | — | 3 | 1 | no | — |
| 173 | #398 | — | 3 | 1 | no | — |
| 174 | #398 | — | 3 | 1 | no | — |
| 175 | #398 | — | 3 | 1 | no | — |
| 176 | #398 | — | 3 | 1 | no | — |
| 177 | #398 | — | 3 | 1 | no | — |
| 178 | #398 | — | 3 | 1 | no | — |
| 179 | #398 | — | 3 | 1 | no | — |
| 180 | #398 | — | 3 | 1 | no | — |
| 181 | #398 | — | 3 | 1 | no | — |
| 182 | #397 | — | 3 | 1 | no | — |
| 183 | #397 | — | 3 | 1 | no | — |
| 184 | #397 | — | 3 | 1 | no | — |
| 185 | #397 | — | 3 | 1 | no | — |
| 186 | #397 | — | 3 | 1 | no | — |
| 187 | #397 | — | 3 | 1 | no | — |
| 188 | #397 | — | 3 | 1 | no | — |
| 189 | #397 | — | 3 | 1 | no | — |
| 190 | #396 | — | 3 | 1 | no | — |
| 191 | #396 | — | 3 | 1 | no | — |
| 192 | #396 | — | 3 | 1 | no | — |
| 193 | #396 | — | 3 | 1 | no | — |
| 194 | #396 | — | 3 | 1 | no | — |
| 195 | #396 | — | 3 | 1 | no | — |
| 196 | #396 | — | 3 | 1 | no | — |
| 197 | #396 | — | 3 | 1 | no | — |
| 198 | #396 | — | 3 | 1 | no | — |
| 199 | #395 | — | 3 | 1 | no | — |
| 200 | #395 | — | 3 | 1 | no | — |
| 201 | #395 | — | 3 | 1 | no | — |
| 202 | #394 | — | 3 | 1 | no | — |
| 203 | #394 | — | 3 | 1 | no | — |
| 204 | #394 | — | 3 | 1 | no | — |
| 205 | #394 | — | 3 | 1 | no | — |
| 206 | #394 | — | 3 | 1 | no | — |
| 207 | #394 | — | 3 | 1 | no | — |
| 208 | #393 | — | 3 | 1 | no | — |
| 209 | #393 | — | 3 | 1 | no | — |
| 210 | #393 | — | 3 | 1 | no | — |
| 211 | #391 | — | 3 | 1 | no | — |
| 212 | #391 | — | 3 | 1 | no | — |
| 213 | #391 | — | 3 | 1 | no | — |
| 214 | #390 | — | 3 | 1 | no | — |
| 215 | #389 | — | 3 | 1 | no | — |
| 216 | #389 | — | 3 | 1 | no | — |
| 217 | #389 | — | 3 | 1 | no | — |
| 218 | #389 | — | 3 | 1 | no | — |
| 219 | #389 | — | 3 | 1 | no | — |
| 220 | #389 | — | 3 | 1 | no | — |
| 221 | #389 | — | 3 | 1 | no | — |
| 222 | #389 | — | 3 | 1 | no | — |
| 223 | #389 | — | 3 | 1 | no | — |
| 224 | #389 | — | 3 | 1 | no | — |
| 225 | #389 | — | 3 | 1 | no | — |
| 226 | #388 | — | 3 | 1 | no | — |
| 227 | #388 | — | 3 | 1 | no | — |
| 228 | #388 | — | 3 | 1 | no | — |
| 229 | #388 | — | 3 | 1 | no | — |
| 230 | #388 | — | 3 | 1 | no | — |
| 231 | #388 | — | 3 | 1 | no | — |
| 232 | #388 | — | 3 | 1 | no | — |
| 233 | #388 | — | 3 | 1 | no | — |
| 234 | #388 | — | 3 | 1 | no | — |
| 235 | #388 | — | 3 | 1 | no | — |
| 236 | #388 | — | 3 | 1 | no | — |
| 237 | #387 | — | 3 | 1 | no | — |
| 238 | #387 | — | 3 | 1 | no | — |
| 239 | #387 | — | 3 | 1 | no | — |
| 240 | #387 | — | 3 | 1 | no | — |
| 241 | #387 | — | 3 | 1 | no | — |
| 242 | #387 | — | 3 | 1 | no | — |
| 243 | #387 | — | 3 | 1 | no | — |
| 244 | #387 | — | 3 | 1 | no | — |
| 245 | #386 | — | 3 | 1 | no | — |
| 246 | #386 | — | 3 | 1 | no | — |
| 247 | #386 | — | 3 | 1 | no | — |
| 248 | #386 | — | 3 | 1 | no | — |
| 249 | #386 | — | 3 | 1 | no | — |
| 250 | #386 | — | 3 | 1 | no | — |
| 251 | #386 | — | 3 | 1 | no | — |
| 252 | #385 | — | 3 | 1 | no | — |
| 253 | #385 | — | 3 | 1 | no | — |
| 254 | #385 | — | 3 | 1 | no | — |
| 255 | #385 | — | 3 | 1 | no | — |
| 256 | #385 | — | 3 | 1 | no | — |
| 257 | #385 | — | 3 | 1 | no | — |
| 258 | #385 | — | 3 | 1 | no | — |
| 259 | #385 | — | 3 | 1 | no | — |
| 260 | #385 | — | 3 | 1 | no | — |
| 261 | #385 | — | 3 | 1 | no | — |
| 262 | #385 | — | 3 | 1 | no | — |
| 263 | #385 | — | 3 | 1 | no | — |
| 264 | #385 | — | 3 | 1 | no | — |
| 265 | #384 | — | 3 | 1 | no | — |
| 266 | #384 | — | 3 | 1 | no | — |
| 267 | #383 | — | 3 | 1 | no | — |
| 268 | #382 | — | 3 | 1 | no | — |
| 269 | #381 | — | 3 | 1 | no | — |
| 270 | #380 | — | 3 | 1 | no | — |
| 271 | #380 | — | 3 | 1 | no | — |
| 272 | #380 | — | 3 | 1 | no | — |
| 273 | #380 | — | 3 | 1 | no | — |
| 274 | #380 | — | 3 | 1 | no | — |
| 275 | #380 | — | 3 | 1 | no | — |
| 276 | #380 | — | 3 | 1 | no | — |
| 277 | #380 | — | 3 | 1 | no | — |
| 278 | #380 | — | 3 | 1 | no | — |
| 279 | #379 | — | 3 | 1 | no | — |
| 280 | #379 | — | 3 | 1 | no | — |
| 281 | C4×C22⋊C4 | — | 3 | 1 | no | — |
| 282 | C4×C22⋊C4 | — | 3 | 1 | no | — |
| 283 | C22×A4 | — | 2 | 1 | no | — |
| 284 | C22×A4 | — | 2 | 1 | no | — |
| 285 | C22×A4 | — | 2 | 1 | no | — |
| 286 | C22×A4 | C24 | 1 | 1 | yes | characteristic |
| 287 | C2×S4 | — | 2 | 1 | no | — |
| 288 | C2×S4 | — | 2 | 1 | no | — |
| 289 | C2×S4 | — | 2 | 1 | no | — |
| 290 | C2×#67 | — | 4 | 1 | no | — |
| 291 | C22×Dic3 | — | 4 | 1 | no | — |
| 292 | C2×C4×D3 | — | 4 | 1 | no | — |
| 293 | C2×Dic6 | — | 4 | 1 | no | — |
| 294 | C2×Dic6 | — | 4 | 1 | no | — |
| 295 | C2×Dic6 | — | 4 | 1 | no | — |
| 296 | C4×A4 | — | 2 | 1 | no | — |
| 297 | C4×A4 | — | 2 | 1 | no | — |
| 298 | C4×A4 | — | 2 | 1 | no | — |
| 299 | C4×A4 | — | 2 | 1 | no | — |
| 300 | C4×A4 | — | 2 | 1 | no | — |
| 301 | C4×A4 | — | 2 | 1 | no | — |
| 302 | SL(2,ℤ/4) | — | 2 | 1 | no | — |
| 303 | SL(2,ℤ/4) | — | 2 | 1 | no | — |
| 304 | SL(2,ℤ/4) | — | 2 | 1 | no | — |
| 305 | SL(2,ℤ/4) | — | 2 | 1 | no | — |
| 306 | SL(2,ℤ/4) | — | 2 | 1 | no | — |
| 307 | SL(2,ℤ/4) | — | 2 | 1 | no | — |
| 308 | SL(2,ℤ/4) | — | 2 | 1 | no | — |
| 309 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 310 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 311 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 312 | C3×C22⋊C4 | — | 4 | 1 | no | — |
| 313 | C3×C22⋊C4 | — | 4 | 1 | no | — |
| 314 | C3×C22⋊C4 | — | 4 | 1 | no | — |
| 315 | C3×C42 | — | 4 | 1 | no | — |
| 316 | #217 | — | 4 | 1 | no | — |
| 317 | #217 | — | 4 | 1 | no | — |
| 318 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 319 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 320 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 321 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 322 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 323 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 324 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 325 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 326 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 327 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 328 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 329 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 330 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 331 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 332 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 333 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 334 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 335 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 336 | C4×Dic3 | — | 4 | 1 | no | — |
| 337 | C4×Dic3 | — | 4 | 1 | no | — |
| 338 | C25 | C22×D3 | 1 | 1 | yes | characteristic |
| 339 | C22×Q8 | — | 3 | 1 | no | — |
| 340 | C22×Q8 | — | 3 | 1 | no | — |
| 341 | C22×Q8 | — | 3 | 1 | no | — |
| 342 | C22×D4 | — | 3 | 1 | no | — |
| 343 | C22×D4 | — | 3 | 1 | no | — |
| 344 | C22×D4 | — | 3 | 1 | no | — |
| 345 | C23×C4 | — | 3 | 1 | no | — |
| 346 | C23×C4 | — | 3 | 1 | no | — |
| 347 | C23×C4 | — | 3 | 1 | no | — |
| 348 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 349 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 350 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 351 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 352 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 353 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 354 | C4⋊Q8 | — | 6 | 1 | no | — |
| 355 | C4⋊Q8 | — | 6 | 1 | no | — |
| 356 | C4⋊Q8 | — | 6 | 1 | no | — |
| 357 | C4⋊Q8 | — | 6 | 1 | no | — |
| 358 | C4⋊Q8 | — | 6 | 1 | no | — |
| 359 | C4⋊Q8 | — | 6 | 1 | no | — |
| 360 | C4⋊Q8 | — | 6 | 1 | no | — |
| 361 | C4⋊Q8 | — | 6 | 1 | no | — |
| 362 | #126 | — | 3 | 1 | no | — |
| 363 | #126 | — | 3 | 1 | no | — |
| 364 | #126 | — | 3 | 1 | no | — |
| 365 | #126 | — | 3 | 1 | no | — |
| 366 | #126 | — | 3 | 1 | no | — |
| 367 | #126 | — | 3 | 1 | no | — |
| 368 | #126 | — | 3 | 1 | no | — |
| 369 | #126 | — | 6 | 1 | no | — |
| 370 | #126 | — | 6 | 1 | no | — |
| 371 | #126 | — | 6 | 1 | no | — |
| 372 | #126 | — | 6 | 1 | no | — |
| 373 | #126 | — | 6 | 1 | no | — |
| 374 | #126 | — | 6 | 1 | no | — |
| 375 | #126 | — | 6 | 1 | no | — |
| 376 | #126 | — | 6 | 1 | no | — |
| 377 | #126 | — | 6 | 1 | no | — |
| 378 | #126 | — | 6 | 1 | no | — |
| 379 | #126 | — | 6 | 1 | no | — |
| 380 | #126 | — | 6 | 1 | no | — |
| 381 | #126 | — | 6 | 1 | no | — |
| 382 | #126 | — | 6 | 1 | no | — |
| 383 | #126 | — | 6 | 1 | no | — |
| 384 | #126 | — | 6 | 1 | no | — |
| 385 | #126 | — | 6 | 1 | no | — |
| 386 | #126 | — | 6 | 1 | no | — |
| 387 | #126 | — | 6 | 1 | no | — |
| 388 | #126 | S4 | 1 | 1 | yes | characteristic, complemented |
| 389 | #125 | — | 6 | 1 | no | — |
| 390 | #125 | — | 6 | 1 | no | — |
| 391 | #125 | — | 6 | 1 | no | — |
| 392 | #125 | — | 6 | 1 | no | — |
| 393 | #125 | — | 6 | 1 | no | — |
| 394 | #125 | — | 6 | 1 | no | — |
| 395 | #125 | — | 6 | 1 | no | — |
| 396 | #125 | — | 6 | 1 | no | — |
| 397 | #124 | — | 6 | 1 | no | — |
| 398 | #124 | — | 6 | 1 | no | — |
| 399 | #124 | — | 6 | 1 | no | — |
| 400 | #124 | — | 6 | 1 | no | — |
| 401 | #123 | — | 6 | 1 | no | — |
| 402 | #123 | — | 6 | 1 | no | — |
| 403 | #123 | — | 6 | 1 | no | — |
| 404 | #123 | — | 6 | 1 | no | — |
| 405 | #123 | — | 6 | 1 | no | — |
| 406 | #123 | — | 6 | 1 | no | — |
| 407 | #123 | — | 6 | 1 | no | — |
| 408 | #123 | — | 6 | 1 | no | — |
| 409 | C22⋊Q8 | — | 6 | 1 | no | — |
| 410 | C22⋊Q8 | — | 6 | 1 | no | — |
| 411 | C22⋊Q8 | — | 6 | 1 | no | — |
| 412 | C22⋊Q8 | — | 6 | 1 | no | — |
| 413 | C22⋊Q8 | — | 6 | 1 | no | — |
| 414 | C22⋊Q8 | — | 6 | 1 | no | — |
| 415 | C22⋊Q8 | — | 6 | 1 | no | — |
| 416 | C22⋊Q8 | — | 6 | 1 | no | — |
| 417 | C22⋊Q8 | — | 6 | 1 | no | — |
| 418 | C22⋊Q8 | — | 6 | 1 | no | — |
| 419 | C22⋊Q8 | — | 6 | 1 | no | — |
| 420 | C22⋊Q8 | — | 6 | 1 | no | — |
| 421 | C22⋊Q8 | — | 6 | 1 | no | — |
| 422 | C22⋊Q8 | — | 6 | 1 | no | — |
| 423 | C22⋊Q8 | — | 6 | 1 | no | — |
| 424 | C22⋊Q8 | — | 6 | 1 | no | — |
| 425 | C22⋊Q8 | — | 12 | 1 | no | — |
| 426 | C22⋊Q8 | — | 12 | 1 | no | — |
| 427 | C22⋊Q8 | — | 12 | 1 | no | — |
| 428 | C22⋊Q8 | — | 12 | 1 | no | — |
| 429 | C22⋊Q8 | — | 12 | 1 | no | — |
| 430 | C22⋊Q8 | — | 12 | 1 | no | — |
| 431 | #120 | — | 12 | 1 | no | — |
| 432 | #120 | — | 12 | 1 | no | — |
| 433 | C4×D4 | — | 12 | 1 | no | — |
| 434 | C4×D4 | — | 12 | 1 | no | — |
| 435 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 436 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 437 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 438 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 439 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 440 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 441 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 442 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 443 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 444 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 445 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 446 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 447 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 448 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 449 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 450 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 451 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 452 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 453 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 454 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 455 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 456 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 457 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 458 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 459 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 460 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 461 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 462 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 463 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 464 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 465 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 466 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 467 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 468 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 469 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 470 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 471 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 472 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 473 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 474 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 475 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 476 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 477 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 478 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 479 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 480 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 481 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 482 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 483 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 484 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 485 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 486 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 487 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 488 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 489 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 490 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 491 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 492 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 493 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 494 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 495 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 496 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 497 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 498 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 499 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 500 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 501 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 502 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 503 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 504 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 505 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 506 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 507 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 508 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 509 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 510 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 511 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 512 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 513 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 514 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 515 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 516 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 517 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 518 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 519 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 520 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 521 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 522 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 523 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 524 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 525 | C2×C22⋊C4 | — | 12 | 1 | no | — |
| 526 | C2×C22⋊C4 | — | 12 | 1 | no | — |
| 527 | C2×C42 | — | 3 | 1 | no | — |
| 528 | C2×C42 | — | 3 | 1 | no | — |
| 529 | C2×C42 | — | 3 | 1 | no | — |
| 530 | C2×C42 | — | 3 | 1 | no | — |
| 531 | C2×C42 | — | 3 | 1 | no | — |
| 532 | C2×C42 | — | 3 | 1 | no | — |
| 533 | C2×C42 | — | 3 | 1 | no | — |
| 534 | C2×C42 | — | 3 | 1 | no | — |
| 535 | C2×C42 | — | 3 | 1 | no | — |
| 536 | #95 | — | 3 | 1 | no | — |
| 537 | #95 | — | 3 | 1 | no | — |
| 538 | #95 | — | 3 | 1 | no | — |
| 539 | #95 | — | 3 | 1 | no | — |
| 540 | #95 | — | 3 | 1 | no | — |
| 541 | #95 | — | 3 | 1 | no | — |
| 542 | #95 | — | 3 | 1 | no | — |
| 543 | #95 | — | 3 | 1 | no | — |
| 544 | #95 | — | 3 | 1 | no | — |
| 545 | #95 | — | 3 | 1 | no | — |
| 546 | #95 | — | 3 | 1 | no | — |
| 547 | #95 | — | 3 | 1 | no | — |
| 548 | #95 | — | 3 | 1 | no | — |
| 549 | #95 | — | 3 | 1 | no | — |
| 550 | #95 | — | 3 | 1 | no | — |
| 551 | #95 | — | 3 | 1 | no | — |
| 552 | #95 | — | 3 | 1 | no | — |
| 553 | #95 | — | 3 | 1 | no | — |
| 554 | #95 | — | 3 | 1 | no | — |
| 555 | #95 | — | 3 | 1 | no | — |
| 556 | #95 | — | 3 | 1 | no | — |
| 557 | #95 | — | 3 | 1 | no | — |
| 558 | #95 | — | 3 | 1 | no | — |
| 559 | #95 | — | 3 | 1 | no | — |
| 560 | #95 | — | 3 | 1 | no | — |
| 561 | #95 | — | 3 | 1 | no | — |
| 562 | #95 | — | 3 | 1 | no | — |
| 563 | #95 | — | 3 | 1 | no | — |
| 564 | #95 | — | 3 | 1 | no | — |
| 565 | #95 | — | 3 | 1 | no | — |
| 566 | #95 | — | 3 | 1 | no | — |
| 567 | #95 | — | 3 | 1 | no | — |
| 568 | #95 | — | 3 | 1 | no | — |
| 569 | #95 | — | 3 | 1 | no | — |
| 570 | #95 | — | 3 | 1 | no | — |
| 571 | #95 | — | 3 | 1 | no | — |
| 572 | #95 | — | 3 | 1 | no | — |
| 573 | #95 | — | 3 | 1 | no | — |
| 574 | #95 | — | 3 | 1 | no | — |
| 575 | #95 | — | 3 | 1 | no | — |
| 576 | C23×C3 | — | 4 | 1 | no | — |
| 577 | C22×D3 | — | 4 | 1 | no | — |
| 578 | C2×A4 | — | 4 | 1 | no | — |
| 579 | C2×A4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 580 | C2×A4 | 2−1+4 | 1 | 1 | yes | characteristic |
| 581 | C2×A4 | 2−1+4 | 1 | 1 | yes | characteristic |
| 582 | S4 | — | 4 | 1 | no | — |
| 583 | C2×C3×C4 | — | 4 | 1 | no | — |
| 584 | C2×C3×C4 | — | 4 | 1 | no | — |
| 585 | C2×C3×C4 | — | 4 | 1 | no | — |
| 586 | C2×C3×C4 | — | 4 | 1 | no | — |
| 587 | C2×C3×C4 | — | 4 | 1 | no | — |
| 588 | C2×C3×C4 | — | 4 | 1 | no | — |
| 589 | #67 | — | 16 | 1 | no | — |
| 590 | C2×Dic3 | — | 4 | 1 | no | — |
| 591 | C2×Dic3 | — | 4 | 1 | no | — |
| 592 | C2×Dic3 | — | 4 | 1 | no | — |
| 593 | C2×Dic3 | — | 4 | 1 | no | — |
| 594 | C2×Dic3 | — | 4 | 1 | no | — |
| 595 | C2×Dic3 | — | 4 | 1 | no | — |
| 596 | C2×Dic3 | — | 4 | 1 | no | — |
| 597 | C2×Dic3 | — | 16 | 1 | no | — |
| 598 | C4×D3 | — | 16 | 1 | no | — |
| 599 | Dic6 | — | 16 | 1 | no | — |
| 600 | Dic6 | — | 16 | 1 | no | — |
| 601 | Dic6 | — | 16 | 1 | no | — |
| 602 | C24 | — | 2 | 1 | no | — |
| 603 | C24 | — | 2 | 1 | no | — |
| 604 | C24 | — | 2 | 1 | no | — |
| 605 | C24 | — | 3 | 1 | no | — |
| 606 | C24 | — | 3 | 1 | no | — |
| 607 | C24 | — | 3 | 1 | no | — |
| 608 | C24 | — | 6 | 1 | no | — |
| 609 | C24 | — | 6 | 1 | no | — |
| 610 | C24 | — | 6 | 1 | no | — |
| 611 | C24 | C23×D3 | 1 | 1 | yes | characteristic |
| 612 | C2×Q8 | — | 6 | 1 | no | — |
| 613 | C2×Q8 | — | 6 | 1 | no | — |
| 614 | C2×Q8 | — | 6 | 1 | no | — |
| 615 | C2×Q8 | — | 6 | 1 | no | — |
| 616 | C2×Q8 | — | 6 | 1 | no | — |
| 617 | C2×Q8 | — | 6 | 1 | no | — |
| 618 | C2×Q8 | — | 12 | 1 | no | — |
| 619 | C2×Q8 | — | 12 | 1 | no | — |
| 620 | C2×Q8 | — | 12 | 1 | no | — |
| 621 | C2×Q8 | — | 12 | 1 | no | — |
| 622 | C2×Q8 | — | 12 | 1 | no | — |
| 623 | C2×Q8 | — | 12 | 1 | no | — |
| 624 | C2×D4 | — | 6 | 1 | no | — |
| 625 | C2×D4 | — | 6 | 1 | no | — |
| 626 | C2×D4 | — | 6 | 1 | no | — |
| 627 | C2×D4 | — | 6 | 1 | no | — |
| 628 | C2×D4 | — | 6 | 1 | no | — |
| 629 | C2×D4 | — | 6 | 1 | no | — |
| 630 | C2×D4 | — | 6 | 1 | no | — |
| 631 | C2×D4 | — | 6 | 1 | no | — |
| 632 | C2×D4 | — | 12 | 1 | no | — |
| 633 | C2×D4 | — | 12 | 1 | no | — |
| 634 | C2×D4 | — | 12 | 1 | no | — |
| 635 | C2×D4 | — | 12 | 1 | no | — |
| 636 | C2×D4 | — | 12 | 1 | no | — |
| 637 | C22×C4 | — | 2 | 1 | no | — |
| 638 | C22×C4 | — | 2 | 1 | no | — |
| 639 | C22×C4 | — | 2 | 1 | no | — |
| 640 | C22×C4 | — | 2 | 1 | no | — |
| 641 | C22×C4 | — | 2 | 1 | no | — |
| 642 | C22×C4 | — | 2 | 1 | no | — |
| 643 | C22×C4 | — | 3 | 1 | no | — |
| 644 | C22×C4 | — | 3 | 1 | no | — |
| 645 | C22×C4 | — | 3 | 1 | no | — |
| 646 | C22×C4 | — | 3 | 1 | no | — |
| 647 | C22×C4 | — | 3 | 1 | no | — |
| 648 | C22×C4 | — | 3 | 1 | no | — |
| 649 | C22×C4 | — | 3 | 1 | no | — |
| 650 | C22×C4 | — | 3 | 1 | no | — |
| 651 | C22×C4 | — | 3 | 1 | no | — |
| 652 | C22×C4 | — | 3 | 1 | no | — |
| 653 | C22×C4 | — | 3 | 1 | no | — |
| 654 | C22×C4 | — | 3 | 1 | no | — |
| 655 | C22×C4 | — | 3 | 1 | no | — |
| 656 | C22×C4 | — | 3 | 1 | no | — |
| 657 | C22×C4 | — | 3 | 1 | no | — |
| 658 | C22×C4 | — | 3 | 1 | no | — |
| 659 | C22×C4 | — | 3 | 1 | no | — |
| 660 | C22×C4 | — | 3 | 1 | no | — |
| 661 | C22×C4 | — | 3 | 1 | no | — |
| 662 | C22×C4 | — | 3 | 1 | no | — |
| 663 | C22×C4 | — | 3 | 1 | no | — |
| 664 | C22×C4 | — | 3 | 1 | no | — |
| 665 | C22×C4 | — | 3 | 1 | no | — |
| 666 | C22×C4 | — | 3 | 1 | no | — |
| 667 | C22×C4 | — | 3 | 1 | no | — |
| 668 | C22×C4 | — | 3 | 1 | no | — |
| 669 | C22×C4 | — | 3 | 1 | no | — |
| 670 | C22×C4 | — | 6 | 1 | no | — |
| 671 | C22×C4 | — | 6 | 1 | no | — |
| 672 | C22×C4 | — | 6 | 1 | no | — |
| 673 | C22×C4 | — | 6 | 1 | no | — |
| 674 | C22×C4 | — | 6 | 1 | no | — |
| 675 | C22×C4 | — | 6 | 1 | no | — |
| 676 | C22×C4 | — | 6 | 1 | no | — |
| 677 | C22×C4 | — | 6 | 1 | no | — |
| 678 | C22×C4 | — | 6 | 1 | no | — |
| 679 | C22×C4 | — | 6 | 1 | no | — |
| 680 | C22×C4 | — | 12 | 1 | no | — |
| 681 | C22×C4 | — | 12 | 1 | no | — |
| 682 | C22×C4 | — | 12 | 1 | no | — |
| 683 | C22×C4 | — | 12 | 1 | no | — |
| 684 | C22×C4 | — | 12 | 1 | no | — |
| 685 | C22×C4 | — | 12 | 1 | no | — |
| 686 | C22×C4 | — | 12 | 1 | no | — |
| 687 | C4⋊C4 | — | 3 | 1 | no | — |
| 688 | C4⋊C4 | — | 3 | 1 | no | — |
| 689 | C4⋊C4 | — | 3 | 1 | no | — |
| 690 | C4⋊C4 | — | 3 | 1 | no | — |
| 691 | C4⋊C4 | — | 3 | 1 | no | — |
| 692 | C4⋊C4 | — | 3 | 1 | no | — |
| 693 | C4⋊C4 | — | 3 | 1 | no | — |
| 694 | C4⋊C4 | — | 3 | 1 | no | — |
| 695 | C4⋊C4 | — | 3 | 1 | no | — |
| 696 | C4⋊C4 | — | 6 | 1 | no | — |
| 697 | C4⋊C4 | — | 6 | 1 | no | — |
| 698 | C4⋊C4 | — | 6 | 1 | no | — |
| 699 | C4⋊C4 | — | 6 | 1 | no | — |
| 700 | C4⋊C4 | — | 6 | 1 | no | — |
| 701 | C4⋊C4 | — | 6 | 1 | no | — |
| 702 | C4⋊C4 | — | 6 | 1 | no | — |
| 703 | C4⋊C4 | — | 6 | 1 | no | — |
| 704 | C4⋊C4 | — | 6 | 1 | no | — |
| 705 | C4⋊C4 | — | 6 | 1 | no | — |
| 706 | C4⋊C4 | — | 6 | 1 | no | — |
| 707 | C4⋊C4 | — | 6 | 1 | no | — |
| 708 | C4⋊C4 | — | 6 | 1 | no | — |
| 709 | C4⋊C4 | — | 6 | 1 | no | — |
| 710 | C4⋊C4 | — | 6 | 1 | no | — |
| 711 | C4⋊C4 | — | 6 | 1 | no | — |
| 712 | C4⋊C4 | — | 6 | 1 | no | — |
| 713 | C4⋊C4 | — | 6 | 1 | no | — |
| 714 | C4⋊C4 | — | 6 | 1 | no | — |
| 715 | C4⋊C4 | — | 6 | 1 | no | — |
| 716 | C4⋊C4 | — | 6 | 1 | no | — |
| 717 | C4⋊C4 | — | 6 | 1 | no | — |
| 718 | C4⋊C4 | — | 6 | 1 | no | — |
| 719 | C4⋊C4 | — | 6 | 1 | no | — |
| 720 | C4⋊C4 | — | 6 | 1 | no | — |
| 721 | C4⋊C4 | — | 6 | 1 | no | — |
| 722 | C4⋊C4 | — | 6 | 1 | no | — |
| 723 | C4⋊C4 | — | 6 | 1 | no | — |
| 724 | C4⋊C4 | — | 6 | 1 | no | — |
| 725 | C4⋊C4 | — | 12 | 1 | no | — |
| 726 | C4⋊C4 | — | 12 | 1 | no | — |
| 727 | C4⋊C4 | — | 12 | 1 | no | — |
| 728 | C4⋊C4 | — | 12 | 1 | no | — |
| 729 | C4⋊C4 | — | 12 | 1 | no | — |
| 730 | C4⋊C4 | — | 12 | 1 | no | — |
| 731 | C4⋊C4 | — | 12 | 1 | no | — |
| 732 | C4⋊C4 | — | 12 | 1 | no | — |
| 733 | C4⋊C4 | — | 12 | 1 | no | — |
| 734 | C4⋊C4 | — | 12 | 1 | no | — |
| 735 | C4⋊C4 | — | 12 | 1 | no | — |
| 736 | C4⋊C4 | — | 12 | 1 | no | — |
| 737 | C4⋊C4 | — | 12 | 1 | no | — |
| 738 | C4⋊C4 | — | 12 | 1 | no | — |
| 739 | C4⋊C4 | — | 12 | 1 | no | — |
| 740 | C4⋊C4 | — | 12 | 1 | no | — |
| 741 | C4⋊C4 | — | 12 | 1 | no | — |
| 742 | C4⋊C4 | — | 12 | 1 | no | — |
| 743 | C4⋊C4 | — | 12 | 1 | no | — |
| 744 | C4⋊C4 | — | 12 | 1 | no | — |
| 745 | C4⋊C4 | — | 12 | 1 | no | — |
| 746 | C4⋊C4 | — | 12 | 1 | no | — |
| 747 | C4⋊C4 | — | 12 | 1 | no | — |
| 748 | C4⋊C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 749 | C4⋊C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 750 | C4⋊C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 751 | C22⋊C4 | — | 3 | 1 | no | — |
| 752 | C22⋊C4 | — | 3 | 1 | no | — |
| 753 | C22⋊C4 | — | 3 | 1 | no | — |
| 754 | C22⋊C4 | — | 3 | 1 | no | — |
| 755 | C22⋊C4 | — | 3 | 1 | no | — |
| 756 | C22⋊C4 | — | 3 | 1 | no | — |
| 757 | C22⋊C4 | — | 3 | 1 | no | — |
| 758 | C22⋊C4 | — | 3 | 1 | no | — |
| 759 | C22⋊C4 | — | 3 | 1 | no | — |
| 760 | C22⋊C4 | — | 6 | 1 | no | — |
| 761 | C22⋊C4 | — | 6 | 1 | no | — |
| 762 | C22⋊C4 | — | 6 | 1 | no | — |
| 763 | C22⋊C4 | — | 6 | 1 | no | — |
| 764 | C22⋊C4 | — | 6 | 1 | no | — |
| 765 | C22⋊C4 | — | 6 | 1 | no | — |
| 766 | C22⋊C4 | — | 6 | 1 | no | — |
| 767 | C22⋊C4 | — | 6 | 1 | no | — |
| 768 | C22⋊C4 | — | 6 | 1 | no | — |
| 769 | C22⋊C4 | — | 6 | 1 | no | — |
| 770 | C22⋊C4 | — | 6 | 1 | no | — |
| 771 | C22⋊C4 | — | 6 | 1 | no | — |
| 772 | C22⋊C4 | — | 6 | 1 | no | — |
| 773 | C22⋊C4 | — | 6 | 1 | no | — |
| 774 | C22⋊C4 | — | 6 | 1 | no | — |
| 775 | C22⋊C4 | — | 6 | 1 | no | — |
| 776 | C22⋊C4 | — | 6 | 1 | no | — |
| 777 | C22⋊C4 | — | 6 | 1 | no | — |
| 778 | C22⋊C4 | — | 6 | 1 | no | — |
| 779 | C22⋊C4 | — | 6 | 1 | no | — |
| 780 | C22⋊C4 | — | 6 | 1 | no | — |
| 781 | C22⋊C4 | — | 6 | 1 | no | — |
| 782 | C22⋊C4 | — | 6 | 1 | no | — |
| 783 | C22⋊C4 | — | 6 | 1 | no | — |
| 784 | C22⋊C4 | — | 6 | 1 | no | — |
| 785 | C22⋊C4 | — | 6 | 1 | no | — |
| 786 | C22⋊C4 | — | 6 | 1 | no | — |
| 787 | C22⋊C4 | — | 6 | 1 | no | — |
| 788 | C22⋊C4 | — | 6 | 1 | no | — |
| 789 | C22⋊C4 | — | 6 | 1 | no | — |
| 790 | C22⋊C4 | — | 6 | 1 | no | — |
| 791 | C22⋊C4 | — | 12 | 1 | no | — |
| 792 | C22⋊C4 | — | 12 | 1 | no | — |
| 793 | C22⋊C4 | — | 12 | 1 | no | — |
| 794 | C22⋊C4 | — | 12 | 1 | no | — |
| 795 | C22⋊C4 | — | 12 | 1 | no | — |
| 796 | C22⋊C4 | — | 12 | 1 | no | — |
| 797 | C22⋊C4 | — | 12 | 1 | no | — |
| 798 | C22⋊C4 | — | 12 | 1 | no | — |
| 799 | C22⋊C4 | — | 12 | 1 | no | — |
| 800 | C22⋊C4 | — | 12 | 1 | no | — |
| 801 | C22⋊C4 | — | 12 | 1 | no | — |
| 802 | C22⋊C4 | — | 12 | 1 | no | — |
| 803 | C22⋊C4 | — | 12 | 1 | no | — |
| 804 | C22⋊C4 | — | 12 | 1 | no | — |
| 805 | C22⋊C4 | — | 12 | 1 | no | — |
| 806 | C22⋊C4 | — | 12 | 1 | no | — |
| 807 | C22⋊C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 808 | C22⋊C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 809 | C22⋊C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 810 | C42 | — | 3 | 1 | no | — |
| 811 | C42 | — | 3 | 1 | no | — |
| 812 | C42 | — | 3 | 1 | no | — |
| 813 | C42 | — | 6 | 1 | no | — |
| 814 | C42 | — | 6 | 1 | no | — |
| 815 | C42 | — | 6 | 1 | no | — |
| 816 | C42 | — | 6 | 1 | no | — |
| 817 | C42 | — | 6 | 1 | no | — |
| 818 | C42 | — | 12 | 1 | no | — |
| 819 | C42 | — | 12 | 1 | no | — |
| 820 | C42 | — | 12 | 1 | no | — |
| 821 | C42 | C2×S4 | 1 | 1 | yes | characteristic |
| 822 | C22×C3 | — | 4 | 1 | no | — |
| 823 | C22×C3 | — | 8 | 1 | no | — |
| 824 | C22×C3 | — | 8 | 1 | no | — |
| 825 | C22×C3 | — | 8 | 1 | no | — |
| 826 | C2×D3 | — | 8 | 1 | no | — |
| 827 | C2×D3 | — | 8 | 1 | no | — |
| 828 | C2×D3 | — | 8 | 1 | no | — |
| 829 | A4 | #563 | 1 | 1 | yes | characteristic, complemented |
| 830 | C3×C4 | — | 8 | 1 | no | — |
| 831 | C3×C4 | — | 8 | 1 | no | — |
| 832 | C3×C4 | — | 8 | 1 | no | — |
| 833 | C3×C4 | — | 8 | 1 | no | — |
| 834 | C3×C4 | — | 8 | 1 | no | — |
| 835 | C3×C4 | — | 8 | 1 | no | — |
| 836 | Dic3 | — | 8 | 1 | no | — |
| 837 | Dic3 | — | 8 | 1 | no | — |
| 838 | Dic3 | — | 8 | 1 | no | — |
| 839 | Dic3 | — | 8 | 1 | no | — |
| 840 | Dic3 | — | 8 | 1 | no | — |
| 841 | Dic3 | — | 8 | 1 | no | — |
| 842 | Dic3 | — | 8 | 1 | no | — |
| 843 | C23 | — | 3 | 1 | no | — |
| 844 | C23 | — | 3 | 1 | no | — |
| 845 | C23 | — | 3 | 1 | no | — |
| 846 | C23 | — | 3 | 1 | no | — |
| 847 | C23 | — | 3 | 1 | no | — |
| 848 | C23 | — | 4 | 1 | no | — |
| 849 | C23 | — | 6 | 1 | no | — |
| 850 | C23 | — | 6 | 1 | no | — |
| 851 | C23 | — | 6 | 1 | no | — |
| 852 | C23 | — | 6 | 1 | no | — |
| 853 | C23 | — | 6 | 1 | no | — |
| 854 | C23 | — | 6 | 1 | no | — |
| 855 | C23 | — | 6 | 1 | no | — |
| 856 | C23 | — | 6 | 1 | no | — |
| 857 | C23 | — | 6 | 1 | no | — |
| 858 | C23 | — | 6 | 1 | no | — |
| 859 | C23 | — | 6 | 1 | no | — |
| 860 | C23 | — | 6 | 1 | no | — |
| 861 | C23 | — | 6 | 1 | no | — |
| 862 | C23 | — | 6 | 1 | no | — |
| 863 | C23 | — | 6 | 1 | no | — |
| 864 | C23 | — | 6 | 1 | no | — |
| 865 | C23 | — | 6 | 1 | no | — |
| 866 | C23 | — | 6 | 1 | no | — |
| 867 | C23 | — | 6 | 1 | no | — |
| 868 | C23 | — | 12 | 1 | no | — |
| 869 | C23 | — | 12 | 1 | no | — |
| 870 | C23 | — | 12 | 1 | no | — |
| 871 | C23 | — | 24 | 1 | no | — |
| 872 | C23 | #1009 | 1 | 1 | yes | characteristic |
| 873 | C23 | #1010 | 1 | 1 | yes | characteristic |
| 874 | C23 | #1010 | 1 | 1 | yes | characteristic |
| 875 | C23 | C22×S4 | 1 | 1 | yes | characteristic |
| 876 | Q8 | — | 24 | 1 | no | — |
| 877 | Q8 | — | 24 | 1 | no | — |
| 878 | Q8 | — | 24 | 1 | no | — |
| 879 | Q8 | — | 24 | 1 | no | — |
| 880 | Q8 | — | 24 | 1 | no | — |
| 881 | Q8 | — | 24 | 1 | no | — |
| 882 | D4 | — | 12 | 1 | no | — |
| 883 | D4 | — | 12 | 1 | no | — |
| 884 | D4 | — | 12 | 1 | no | — |
| 885 | D4 | — | 12 | 1 | no | — |
| 886 | D4 | — | 24 | 1 | no | — |
| 887 | D4 | — | 24 | 1 | no | — |
| 888 | D4 | — | 24 | 2 | no | — |
| 889 | C2×C4 | — | 3 | 1 | no | — |
| 890 | C2×C4 | — | 3 | 1 | no | — |
| 891 | C2×C4 | — | 3 | 1 | no | — |
| 892 | C2×C4 | — | 3 | 1 | no | — |
| 893 | C2×C4 | — | 3 | 1 | no | — |
| 894 | C2×C4 | — | 3 | 1 | no | — |
| 895 | C2×C4 | — | 6 | 1 | no | — |
| 896 | C2×C4 | — | 6 | 1 | no | — |
| 897 | C2×C4 | — | 6 | 1 | no | — |
| 898 | C2×C4 | — | 6 | 1 | no | — |
| 899 | C2×C4 | — | 6 | 1 | no | — |
| 900 | C2×C4 | — | 6 | 1 | no | — |
| 901 | C2×C4 | — | 6 | 1 | no | — |
| 902 | C2×C4 | — | 6 | 1 | no | — |
| 903 | C2×C4 | — | 6 | 1 | no | — |
| 904 | C2×C4 | — | 6 | 1 | no | — |
| 905 | C2×C4 | — | 6 | 1 | no | — |
| 906 | C2×C4 | — | 6 | 1 | no | — |
| 907 | C2×C4 | — | 6 | 1 | no | — |
| 908 | C2×C4 | — | 6 | 1 | no | — |
| 909 | C2×C4 | — | 6 | 1 | no | — |
| 910 | C2×C4 | — | 6 | 1 | no | — |
| 911 | C2×C4 | — | 6 | 1 | no | — |
| 912 | C2×C4 | — | 6 | 1 | no | — |
| 913 | C2×C4 | — | 6 | 1 | no | — |
| 914 | C2×C4 | — | 6 | 1 | no | — |
| 915 | C2×C4 | — | 6 | 1 | no | — |
| 916 | C2×C4 | — | 6 | 1 | no | — |
| 917 | C2×C4 | — | 6 | 1 | no | — |
| 918 | C2×C4 | — | 6 | 1 | no | — |
| 919 | C2×C4 | — | 6 | 1 | no | — |
| 920 | C2×C4 | — | 6 | 1 | no | — |
| 921 | C2×C4 | — | 6 | 1 | no | — |
| 922 | C2×C4 | — | 6 | 1 | no | — |
| 923 | C2×C4 | — | 6 | 1 | no | — |
| 924 | C2×C4 | — | 6 | 1 | no | — |
| 925 | C2×C4 | — | 6 | 1 | no | — |
| 926 | C2×C4 | — | 6 | 1 | no | — |
| 927 | C2×C4 | — | 6 | 1 | no | — |
| 928 | C2×C4 | — | 6 | 1 | no | — |
| 929 | C2×C4 | — | 6 | 1 | no | — |
| 930 | C2×C4 | — | 6 | 1 | no | — |
| 931 | C2×C4 | — | 6 | 1 | no | — |
| 932 | C2×C4 | — | 6 | 1 | no | — |
| 933 | C2×C4 | — | 6 | 1 | no | — |
| 934 | C2×C4 | — | 6 | 1 | no | — |
| 935 | C2×C4 | — | 6 | 1 | no | — |
| 936 | C2×C4 | — | 6 | 1 | no | — |
| 937 | C2×C4 | — | 6 | 1 | no | — |
| 938 | C2×C4 | — | 6 | 1 | no | — |
| 939 | C2×C4 | — | 6 | 1 | no | — |
| 940 | C2×C4 | — | 6 | 1 | no | — |
| 941 | C2×C4 | — | 6 | 1 | no | — |
| 942 | C2×C4 | — | 6 | 1 | no | — |
| 943 | C2×C4 | — | 6 | 1 | no | — |
| 944 | C2×C4 | — | 6 | 1 | no | — |
| 945 | C2×C4 | — | 6 | 1 | no | — |
| 946 | C2×C4 | — | 6 | 1 | no | — |
| 947 | C2×C4 | — | 6 | 1 | no | — |
| 948 | C2×C4 | — | 6 | 1 | no | — |
| 949 | C2×C4 | — | 6 | 1 | no | — |
| 950 | C2×C4 | — | 6 | 1 | no | — |
| 951 | C2×C4 | — | 6 | 1 | no | — |
| 952 | C2×C4 | — | 6 | 1 | no | — |
| 953 | C2×C4 | — | 6 | 1 | no | — |
| 954 | C2×C4 | — | 6 | 1 | no | — |
| 955 | C2×C4 | — | 6 | 1 | no | — |
| 956 | C2×C4 | — | 6 | 1 | no | — |
| 957 | C2×C4 | — | 6 | 1 | no | — |
| 958 | C2×C4 | — | 6 | 1 | no | — |
| 959 | C2×C4 | — | 6 | 1 | no | — |
| 960 | C2×C4 | — | 6 | 1 | no | — |
| 961 | C2×C4 | — | 6 | 1 | no | — |
| 962 | C2×C4 | — | 6 | 1 | no | — |
| 963 | C2×C4 | — | 6 | 1 | no | — |
| 964 | C2×C4 | — | 24 | 1 | no | — |
| 965 | C2×C4 | — | 24 | 1 | no | — |
| 966 | C2×C4 | — | 24 | 1 | no | — |
| 967 | C2×C4 | — | 24 | 1 | no | — |
| 968 | C2×C4 | — | 24 | 2 | no | — |
| 969 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 970 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 971 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 972 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 973 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 974 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 975 | C2×C3 | — | 4 | 1 | no | — |
| 976 | C2×C3 | — | 4 | 1 | no | — |
| 977 | C2×C3 | — | 4 | 1 | no | — |
| 978 | C2×C3 | — | 16 | 1 | no | — |
| 979 | D3 | — | 16 | 1 | no | — |
| 980 | C22 | — | 2 | 1 | no | — |
| 981 | C22 | — | 2 | 1 | no | — |
| 982 | C22 | — | 2 | 1 | no | — |
| 983 | C22 | — | 3 | 1 | no | — |
| 984 | C22 | — | 3 | 1 | no | — |
| 985 | C22 | — | 3 | 1 | no | — |
| 986 | C22 | — | 3 | 1 | no | — |
| 987 | C22 | — | 3 | 1 | no | — |
| 988 | C22 | — | 3 | 1 | no | — |
| 989 | C22 | — | 3 | 1 | no | — |
| 990 | C22 | — | 3 | 1 | no | — |
| 991 | C22 | — | 3 | 1 | no | — |
| 992 | C22 | — | 6 | 1 | no | — |
| 993 | C22 | — | 6 | 1 | no | — |
| 994 | C22 | — | 6 | 1 | no | — |
| 995 | C22 | — | 6 | 1 | no | — |
| 996 | C22 | — | 12 | 1 | no | — |
| 997 | C22 | — | 12 | 1 | no | — |
| 998 | C22 | — | 12 | 1 | no | — |
| 999 | C22 | — | 12 | 1 | no | — |
| 1000 | C22 | — | 12 | 1 | no | — |
| 1001 | C22 | — | 12 | 1 | no | — |
| 1002 | C22 | — | 12 | 1 | no | — |
| 1003 | C22 | — | 12 | 1 | no | — |
| 1004 | C22 | — | 12 | 1 | no | — |
| 1005 | C22 | — | 12 | 1 | no | — |
| 1006 | C22 | — | 12 | 1 | no | — |
| 1007 | C22 | — | 12 | 1 | no | — |
| 1008 | C22 | — | 12 | 1 | no | — |
| 1009 | C22 | — | 12 | 1 | no | — |
| 1010 | C22 | — | 12 | 1 | no | — |
| 1011 | C22 | #5712 | 1 | 1 | yes | characteristic, complemented |
| 1012 | C22 | C23×S4 | 1 | 1 | yes | characteristic |
| 1013 | C4 | — | 2 | 1 | no | — |
| 1014 | C4 | — | 2 | 1 | no | — |
| 1015 | C4 | — | 2 | 1 | no | — |
| 1016 | C4 | — | 2 | 1 | no | — |
| 1017 | C4 | — | 2 | 1 | no | — |
| 1018 | C4 | — | 2 | 1 | no | — |
| 1019 | C4 | — | 6 | 1 | no | — |
| 1020 | C4 | — | 6 | 1 | no | — |
| 1021 | C4 | — | 6 | 1 | no | — |
| 1022 | C4 | — | 6 | 1 | no | — |
| 1023 | C4 | — | 6 | 1 | no | — |
| 1024 | C4 | — | 6 | 1 | no | — |
| 1025 | C4 | — | 12 | 1 | no | — |
| 1026 | C4 | — | 12 | 1 | no | — |
| 1027 | C4 | — | 12 | 1 | no | — |
| 1028 | C4 | — | 12 | 1 | no | — |
| 1029 | C4 | — | 12 | 1 | no | — |
| 1030 | C4 | — | 12 | 1 | no | — |
| 1031 | C4 | — | 12 | 1 | no | — |
| 1032 | C4 | — | 12 | 1 | no | — |
| 1033 | C4 | — | 12 | 1 | no | — |
| 1034 | C4 | — | 12 | 1 | no | — |
| 1035 | C4 | — | 12 | 1 | no | — |
| 1036 | C4 | — | 12 | 1 | no | — |
| 1037 | C4 | — | 12 | 1 | no | — |
| 1038 | C4 | — | 12 | 1 | no | — |
| 1039 | C4 | — | 12 | 1 | no | — |
| 1040 | C3 | — | 4 | 1 | no | Sylow |
| 1041 | C2 | — | 3 | 1 | no | — |
| 1042 | C2 | — | 3 | 1 | no | — |
| 1043 | C2 | — | 3 | 1 | no | — |
| 1044 | C2 | — | 3 | 1 | no | — |
| 1045 | C2 | — | 4 | 1 | no | — |
| 1046 | C2 | — | 12 | 1 | no | — |
| 1047 | C2 | — | 24 | 1 | no | — |
| 1048 | C2 | #87489 | 1 | 1 | yes | characteristic |
| 1049 | C2 | #87490 | 1 | 1 | yes | characteristic |
| 1050 | C2 | #87490 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×S4 |
| commutator, cosocle | C22×A4 | C24 |
| Fitting | C22×#126 | D3 |
| socle | C24 | C23×D3 |
| prime radical | C2×GL(2,ℤ/4) | C22 |
| hypercenter | #126 | S4 |
| hypocenter | A4 | #563 |
| LCS | G ▷ C22×A4 ▷ A4 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. A4×#126 | C2 | semidirect |
| 2. #85313 | C2 | semidirect |
| 3. #85312 | C2 | semidirect |
| 4. #85311 | C2 | semidirect |
| 5. #85305 | C2 | semidirect |
| 6. #85304 | C2 | semidirect |
| 7. #85303 | C2 | semidirect |
| 11. #85294 | C2 | semidirect |
| 12. #85293 | C2 | semidirect |
| 13. #85293 | C2 | semidirect |
| 14. #85291 | C2 | semidirect |
| 15. #85283 | C2 | semidirect |
| 54. C22×#126 | D3 | semidirect |
| 388. #126 | S4 | semidirect |
| 829. A4 | #563 | semidirect |
| 1011. C22 | #5712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#126 | 2 |
| #85313 | 2 |
| #85312 | 2 |
| #85311 | 2 |
| #85305 | 2 |
| #85304 | 2 |
| #85303 | 2 |
| #85301 | 2 |
| #85300 | 2 |
| #85298 | 2 |
| #85294 | 2 |
| #85293 | 2 |
| #85291 | 2 |
| #85283 | 2 |
| #45971 | 3 |
| #5712 | 4 |