Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1998 conjugacy classes of subgroups.
The subgroup lattice has 650 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #87292 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #85890 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#2898 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #84111 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #83806 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #83782 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #82570 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #78953 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #78952 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #78879 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #78877 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #78828 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #78826 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | #78785 | C2 | 1 | 3 | yes | maximal, complemented |
| 15 | C2×#4797 | C2 | 1 | 3 | yes | maximal, complemented |
| 16 | #60627 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C2×C3×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#1010 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C3×#131 | C22 | 1 | 1 | yes | characteristic |
| 20 | C3×#520 | C22 | 1 | 1 | yes | characteristic |
| 21 | #5832 | C22 | 1 | 3 | yes | — |
| 22 | #5827 | C22 | 1 | 1 | yes | characteristic |
| 23 | Dic3×#41 | C22 | 1 | 1 | yes | characteristic |
| 24 | #5825 | C22 | 1 | 3 | yes | — |
| 25 | #5824 | — | 2 | 3 | no | — |
| 26 | #5824 | — | 2 | 3 | no | — |
| 27 | C2×#948 | C22 | 1 | 1 | yes | characteristic |
| 28 | #5816 | C22 | 1 | 3 | yes | — |
| 29 | Q8×#67 | — | 2 | 1 | no | — |
| 30 | Q8×#67 | — | 2 | 1 | no | — |
| 31 | C2×#944 | C22 | 1 | 3 | yes | — |
| 32 | #5570 | — | 2 | 1 | no | — |
| 33 | #5569 | — | 2 | 1 | no | — |
| 34 | #5543 | — | 2 | 3 | no | — |
| 35 | #5539 | — | 2 | 3 | no | — |
| 36 | #5519 | C22 | 1 | 3 | yes | — |
| 37 | #5517 | C22 | 1 | 3 | yes | — |
| 38 | #5500 | C22 | 1 | 3 | yes | — |
| 39 | C2×#890 | C22 | 1 | 3 | yes | — |
| 40 | C3×#419 | C22 | 1 | 3 | yes | — |
| 41 | C3×#417 | C22 | 1 | 3 | yes | — |
| 42 | C3×#416 | C22 | 1 | 3 | yes | — |
| 43 | C2×C3×#103 | C22 | 1 | 3 | yes | — |
| 44 | #5233 | C22 | 1 | 3 | yes | — |
| 45 | #5232 | C22 | 1 | 3 | yes | — |
| 46 | #5225 | C22 | 1 | 3 | yes | — |
| 47 | C2×#835 | C22 | 1 | 3 | yes | — |
| 48 | #5133 | C22 | 1 | 3 | yes | — |
| 49 | #5122 | C22 | 1 | 3 | yes | — |
| 50 | #5120 | C22 | 1 | 3 | yes | — |
| 51 | Dic3×M16 | C22 | 1 | 3 | yes | — |
| 52 | #5113 | C22 | 1 | 3 | yes | — |
| 53 | C2×#816 | C22 | 1 | 3 | yes | — |
| 54 | #5101 | C22 | 1 | 3 | yes | — |
| 55 | C2×#815 | C22 | 1 | 3 | yes | — |
| 56 | #5004 | C22 | 1 | 3 | yes | — |
| 57 | #5002 | C22 | 1 | 3 | yes | — |
| 58 | C2×#810 | C22 | 1 | 3 | yes | — |
| 59 | #4966 | C22 | 1 | 3 | yes | — |
| 60 | #4800 | C22 | 1 | 6 | yes | — |
| 61 | #4797 | C22 | 1 | 6 | yes | — |
| 62 | #4797 | C22 | 1 | 6 | yes | — |
| 63 | #4797 | C22 | 1 | 3 | yes | — |
| 64 | #4797 | C22 | 1 | 3 | yes | — |
| 65 | #4797 | C22 | 1 | 6 | yes | — |
| 66 | #4794 | C22 | 1 | 3 | yes | — |
| 67 | #4794 | C22 | 1 | 3 | yes | — |
| 68 | #4792 | C22 | 1 | 6 | yes | — |
| 69 | #4792 | C22 | 1 | 6 | yes | — |
| 70 | #4768 | C22 | 1 | 6 | yes | — |
| 71 | #4765 | C22 | 1 | 3 | yes | — |
| 72 | #4765 | C22 | 1 | 3 | yes | — |
| 73 | #4764 | C22 | 1 | 3 | yes | — |
| 74 | #4764 | C22 | 1 | 1 | yes | characteristic |
| 75 | #3504 | — | 3 | 1 | no | — |
| 76 | #3499 | — | 3 | 1 | no | — |
| 77 | #3142 | — | 3 | 3 | no | — |
| 78 | #3139 | — | 3 | 3 | no | — |
| 79 | #3137 | — | 3 | 3 | no | — |
| 80 | #3137 | — | 3 | 3 | no | — |
| 81 | #3137 | — | 3 | 3 | no | — |
| 82 | #3137 | — | 3 | 3 | no | — |
| 83 | #3135 | — | 3 | 3 | no | — |
| 84 | C2×#491 | — | 3 | 3 | no | — |
| 85 | #2898 | — | 3 | 1 | no | — |
| 86 | #2898 | — | 3 | 1 | no | — |
| 87 | #2898 | — | 3 | 1 | no | — |
| 88 | #2898 | D3 | 1 | 1 | yes | characteristic, complemented |
| 89 | #2875 | — | 3 | 1 | no | — |
| 90 | C3×2−1+4 | — | 2 | 4 | no | — |
| 91 | C3×2−1+4 | — | 2 | 4 | no | — |
| 92 | C2×C3×#41 | — | 2 | 3 | no | — |
| 93 | C2×C3×#41 | C23 | 1 | 3 | yes | — |
| 94 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 95 | C22×C3×Q8 | — | 2 | 1 | no | — |
| 96 | C22×C3×Q8 | C23 | 1 | 3 | yes | — |
| 97 | #1010 | — | 2 | 4 | no | — |
| 98 | #1010 | — | 2 | 4 | no | — |
| 99 | C2×D3×Q8 | — | 2 | 1 | no | — |
| 100 | C2×#237 | — | 2 | 3 | no | — |
| 101 | C2×#235 | C23 | 1 | 3 | yes | — |
| 102 | C22×Dic6 | C23 | 1 | 3 | yes | — |
| 103 | C3×#131 | — | 2 | 4 | no | — |
| 104 | C2×C3×M16 | C23 | 1 | 3 | yes | — |
| 105 | C22×C3×C8 | C23 | 1 | 3 | yes | — |
| 106 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 107 | C3×C4×D4 | — | 2 | 3 | no | — |
| 108 | C3×#117 | C23 | 1 | 3 | yes | — |
| 109 | C2×C3×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 110 | #948 | — | 2 | 4 | no | — |
| 111 | #947 | C23 | 1 | 3 | yes | — |
| 112 | #946 | — | 2 | 3 | no | — |
| 113 | #946 | — | 2 | 3 | no | — |
| 114 | Q8×Dic3 | — | 2 | 1 | no | — |
| 115 | Q8×Dic3 | D4 | 1 | 1 | yes | characteristic |
| 116 | Q8×Dic3 | D4 | 1 | 1 | yes | characteristic |
| 117 | #944 | — | 2 | 3 | no | — |
| 118 | #944 | — | 2 | 3 | no | — |
| 119 | #944 | C23 | 1 | 3 | yes | — |
| 120 | #944 | C23 | 1 | 6 | yes | — |
| 121 | #940 | C23 | 1 | 1 | yes | characteristic |
| 122 | #939 | — | 2 | 3 | no | — |
| 123 | #939 | — | 2 | 3 | no | — |
| 124 | #936 | C23 | 1 | 3 | yes | — |
| 125 | #935 | — | 2 | 6 | no | — |
| 126 | D4×Dic3 | — | 2 | 3 | no | — |
| 127 | D4×Dic3 | D4 | 1 | 3 | yes | — |
| 128 | D4×Dic3 | D4 | 1 | 3 | yes | — |
| 129 | #929 | — | 2 | 6 | no | — |
| 130 | C4×#67 | — | 2 | 3 | no | — |
| 131 | C4×#67 | — | 2 | 3 | no | — |
| 132 | #926 | C23 | 1 | 3 | yes | — |
| 133 | #926 | C23 | 1 | 3 | yes | — |
| 134 | C2×C4⋊Dic3 | — | 2 | 3 | no | — |
| 135 | C2×C4⋊Dic3 | C23 | 1 | 3 | yes | — |
| 136 | #924 | — | 2 | 6 | no | — |
| 137 | #924 | — | 2 | 3 | no | — |
| 138 | #924 | — | 2 | 3 | no | — |
| 139 | C2×Dic3⋊C4 | — | 2 | 3 | no | — |
| 140 | C2×Dic3⋊C4 | — | 2 | 3 | no | — |
| 141 | C2×Dic3⋊C4 | — | 2 | 3 | no | — |
| 142 | C2×C4×Dic3 | C23 | 1 | 3 | yes | — |
| 143 | C2×#208 | C23 | 1 | 3 | yes | — |
| 144 | C22×C3⋊C8 | C23 | 1 | 3 | yes | — |
| 145 | #890 | — | 2 | 3 | no | — |
| 146 | #890 | — | 2 | 3 | no | — |
| 147 | #890 | — | 2 | 3 | no | — |
| 148 | #890 | C23 | 1 | 3 | yes | — |
| 149 | #890 | C23 | 1 | 6 | yes | — |
| 150 | #890 | C23 | 1 | 1 | yes | characteristic |
| 151 | #888 | — | 2 | 3 | no | — |
| 152 | #888 | C23 | 1 | 3 | yes | — |
| 153 | #888 | C23 | 1 | 3 | yes | — |
| 154 | #878 | — | 2 | 3 | no | — |
| 155 | #878 | — | 2 | 3 | no | — |
| 156 | #878 | — | 2 | 6 | no | — |
| 157 | #870 | — | 2 | 3 | no | — |
| 158 | #869 | — | 2 | 3 | no | — |
| 159 | C4×Dic6 | — | 2 | 3 | no | — |
| 160 | C4×Dic6 | — | 2 | 3 | no | — |
| 161 | C3×#103 | C23 | 1 | 3 | yes | — |
| 162 | C3×#103 | C23 | 1 | 6 | yes | — |
| 163 | C3×#103 | C23 | 1 | 3 | yes | — |
| 164 | C3×#102 | C23 | 1 | 1 | yes | characteristic |
| 165 | C3×#102 | C23 | 1 | 3 | yes | — |
| 166 | #835 | C23 | 1 | 3 | yes | — |
| 167 | #835 | C23 | 1 | 6 | yes | — |
| 168 | #835 | C23 | 1 | 3 | yes | — |
| 169 | #832 | C23 | 1 | 3 | yes | — |
| 170 | #832 | C23 | 1 | 1 | yes | characteristic |
| 171 | #821 | C23 | 1 | 3 | yes | — |
| 172 | #821 | C23 | 1 | 1 | yes | characteristic |
| 173 | #816 | C23 | 1 | 3 | yes | — |
| 174 | #816 | C23 | 1 | 6 | yes | — |
| 175 | #816 | C23 | 1 | 3 | yes | — |
| 176 | #815 | C23 | 1 | 3 | yes | — |
| 177 | #815 | C23 | 1 | 1 | yes | characteristic |
| 178 | #815 | C23 | 1 | 3 | yes | — |
| 179 | #815 | C23 | 1 | 3 | yes | — |
| 180 | C8×Dic3 | C23 | 1 | 6 | yes | — |
| 181 | #810 | C23 | 1 | 6 | yes | — |
| 182 | #810 | C23 | 1 | 3 | yes | — |
| 183 | #810 | C23 | 1 | 3 | yes | — |
| 184 | #809 | C23 | 1 | 3 | yes | — |
| 185 | #809 | C23 | 1 | 1 | yes | characteristic |
| 186 | C2×2−1+4 | — | 3 | 1 | no | — |
| 187 | C2×2−1+4 | C2×D3 | 1 | 1 | yes | characteristic |
| 188 | C2×#131 | — | 3 | 1 | no | — |
| 189 | C2×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 190 | #557 | — | 6 | 1 | no | — |
| 191 | #557 | — | 6 | 1 | no | — |
| 192 | #554 | — | 6 | 3 | no | — |
| 193 | #554 | — | 6 | 3 | no | — |
| 194 | D4×Q8 | — | 6 | 1 | no | — |
| 195 | D4×Q8 | — | 6 | 1 | no | — |
| 196 | #547 | — | 6 | 3 | no | — |
| 197 | #547 | — | 6 | 3 | no | — |
| 198 | #544 | — | 3 | 3 | no | — |
| 199 | #544 | — | 3 | 3 | no | — |
| 200 | #536 | — | 3 | 3 | no | — |
| 201 | #536 | — | 3 | 3 | no | — |
| 202 | #533 | — | 3 | 3 | no | — |
| 203 | #532 | — | 3 | 3 | no | — |
| 204 | C2×C4⋊Q8 | — | 3 | 3 | no | — |
| 205 | C2×#125 | — | 3 | 3 | no | — |
| 206 | #520 | — | 3 | 1 | no | — |
| 207 | #520 | C2×D3 | 1 | 1 | yes | characteristic |
| 208 | C4×#41 | — | 3 | 1 | no | — |
| 209 | #491 | — | 3 | 3 | no | — |
| 210 | #491 | — | 3 | 6 | no | — |
| 211 | #491 | — | 3 | 6 | no | — |
| 212 | #491 | — | 3 | 6 | no | — |
| 213 | #491 | — | 3 | 3 | no | — |
| 214 | #490 | — | 3 | 1 | no | — |
| 215 | #490 | — | 3 | 3 | no | — |
| 216 | #489 | — | 3 | 3 | no | — |
| 217 | #489 | — | 3 | 3 | no | — |
| 218 | #489 | — | 3 | 3 | no | — |
| 219 | #489 | — | 3 | 3 | no | — |
| 220 | #488 | — | 3 | 6 | no | — |
| 221 | #488 | — | 3 | 6 | no | — |
| 222 | #487 | — | 3 | 6 | no | — |
| 223 | #487 | — | 3 | 6 | no | — |
| 224 | #419 | — | 3 | 3 | no | — |
| 225 | #419 | — | 3 | 3 | no | — |
| 226 | #419 | — | 3 | 3 | no | — |
| 227 | #419 | C2×D3 | 1 | 3 | yes | — |
| 228 | #417 | — | 3 | 3 | no | — |
| 229 | #417 | — | 3 | 3 | no | — |
| 230 | #417 | — | 3 | 3 | no | — |
| 231 | #417 | C2×D3 | 1 | 3 | yes | — |
| 232 | #416 | — | 3 | 3 | no | — |
| 233 | #416 | — | 3 | 3 | no | — |
| 234 | #416 | — | 3 | 3 | no | — |
| 235 | #416 | C2×D3 | 1 | 3 | yes | — |
| 236 | C2×#103 | — | 3 | 3 | no | — |
| 237 | C2×#103 | — | 3 | 3 | no | — |
| 238 | C2×#103 | — | 3 | 3 | no | — |
| 239 | C2×#103 | C2×D3 | 1 | 3 | yes | — |
| 240 | #405 | — | 3 | 3 | no | — |
| 241 | #405 | — | 3 | 3 | no | — |
| 242 | C4×M16 | — | 3 | 3 | no | — |
| 243 | C2×#97 | — | 3 | 3 | no | — |
| 244 | C3×#41 | — | 2 | 6 | no | — |
| 245 | C3×#41 | — | 2 | 6 | no | — |
| 246 | C3×#41 | — | 4 | 12 | no | — |
| 247 | C3×#41 | #41 | 1 | 4 | yes | — |
| 248 | C3×#41 | #41 | 1 | 4 | yes | — |
| 249 | C2×C3×Q8 | — | 2 | 3 | no | — |
| 250 | C2×C3×Q8 | — | 2 | 6 | no | — |
| 251 | C2×C3×Q8 | — | 2 | 6 | no | — |
| 252 | C2×C3×Q8 | — | 4 | 4 | no | — |
| 253 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 254 | C2×C3×Q8 | C24 | 1 | 3 | yes | — |
| 255 | C2×C3×D4 | — | 2 | 3 | no | — |
| 256 | C2×C3×D4 | C2×D4 | 1 | 3 | yes | — |
| 257 | C2×C3×D4 | C24 | 1 | 1 | yes | characteristic |
| 258 | C22×C3×C4 | — | 2 | 3 | no | — |
| 259 | C22×C3×C4 | — | 2 | 3 | no | — |
| 260 | C22×C3×C4 | — | 2 | 3 | no | — |
| 261 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 262 | C2×#67 | — | 2 | 3 | no | — |
| 263 | C2×#67 | — | 2 | 1 | no | — |
| 264 | C2×#67 | — | 2 | 1 | no | — |
| 265 | C22×Dic3 | — | 2 | 3 | no | — |
| 266 | C22×Dic3 | — | 2 | 3 | no | — |
| 267 | C22×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 268 | C22×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 269 | D3×Q8 | — | 4 | 4 | no | — |
| 270 | #237 | — | 4 | 12 | no | — |
| 271 | #235 | — | 2 | 6 | no | — |
| 272 | #235 | — | 2 | 6 | no | — |
| 273 | C2×D12 | C24 | 1 | 1 | yes | characteristic |
| 274 | C2×C4×D3 | — | 2 | 3 | no | — |
| 275 | C2×Dic6 | — | 2 | 6 | no | — |
| 276 | C2×Dic6 | — | 2 | 6 | no | — |
| 277 | C2×Dic6 | — | 2 | 3 | no | — |
| 278 | C2×Dic6 | — | 2 | 3 | no | — |
| 279 | C2×Dic6 | — | 2 | 3 | no | — |
| 280 | C2×Dic6 | C24 | 1 | 3 | yes | — |
| 281 | C3×M16 | — | 2 | 6 | no | — |
| 282 | C2×C3×C8 | — | 2 | 6 | no | — |
| 283 | C2×C3×C8 | C24 | 1 | 3 | yes | — |
| 284 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 285 | C3×C4⋊C4 | — | 2 | 3 | no | — |
| 286 | C3×C4⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 287 | C3×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 288 | C3×C22⋊C4 | — | 2 | 3 | no | — |
| 289 | C3×C42 | — | 2 | 3 | no | — |
| 290 | #217 | — | 2 | 3 | no | — |
| 291 | #217 | — | 2 | 3 | no | — |
| 292 | #217 | — | 2 | 3 | no | — |
| 293 | #217 | C2×D4 | 1 | 6 | yes | — |
| 294 | (C2×D3)⋊C4 | — | 2 | 3 | no | — |
| 295 | (C2×D3)⋊C4 | — | 2 | 3 | no | — |
| 296 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 297 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 298 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 299 | C4⋊Dic3 | — | 2 | 6 | no | — |
| 300 | C4⋊Dic3 | C2×D4 | 1 | 3 | yes | — |
| 301 | C4⋊Dic3 | C2×D4 | 1 | 3 | yes | — |
| 302 | C4⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 303 | C4⋊Dic3 | C24 | 1 | 3 | yes | — |
| 304 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 305 | Dic3⋊C4 | — | 2 | 3 | no | — |
| 306 | Dic3⋊C4 | — | 2 | 3 | no | — |
| 307 | Dic3⋊C4 | — | 2 | 3 | no | — |
| 308 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 309 | Dic3⋊C4 | — | 2 | 3 | no | — |
| 310 | Dic3⋊C4 | — | 2 | 3 | no | — |
| 311 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 312 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 313 | C4×Dic3 | — | 2 | 3 | no | — |
| 314 | C4×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 315 | C4×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 316 | C4×Dic3 | C24 | 1 | 3 | yes | — |
| 317 | C4×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 318 | #208 | — | 2 | 6 | no | — |
| 319 | C2×C3⋊C8 | — | 2 | 6 | no | — |
| 320 | C2×C3⋊C8 | C24 | 1 | 3 | yes | — |
| 321 | C2×C3⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 322 | 2−1+4 | — | 2 | 4 | no | — |
| 323 | 2−1+4 | — | 2 | 4 | no | — |
| 324 | 2−1+4 | — | 6 | 4 | no | — |
| 325 | 2−1+4 | — | 6 | 4 | no | — |
| 326 | C2×#41 | — | 2 | 3 | no | — |
| 327 | C2×#41 | — | 3 | 3 | no | — |
| 328 | C2×#41 | — | 6 | 3 | no | — |
| 329 | C2×#41 | C22×D3 | 1 | 3 | yes | — |
| 330 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 331 | C22×Q8 | — | 2 | 1 | no | — |
| 332 | C22×Q8 | — | 3 | 3 | no | — |
| 333 | C22×Q8 | — | 6 | 1 | no | — |
| 334 | C22×Q8 | C22×D3 | 1 | 3 | yes | — |
| 335 | #131 | — | 2 | 4 | no | — |
| 336 | #131 | — | 6 | 4 | no | — |
| 337 | C2×M16 | — | 3 | 3 | no | — |
| 338 | C2×M16 | C22×D3 | 1 | 3 | yes | — |
| 339 | C22×C8 | — | 3 | 3 | no | — |
| 340 | C22×C8 | C22×D3 | 1 | 3 | yes | — |
| 341 | C4⋊Q8 | — | 3 | 3 | no | — |
| 342 | C4⋊Q8 | — | 3 | 3 | no | — |
| 343 | C4⋊Q8 | — | 3 | 3 | no | — |
| 344 | C4⋊Q8 | — | 3 | 6 | no | — |
| 345 | C4⋊Q8 | — | 6 | 3 | no | — |
| 346 | C4⋊Q8 | — | 6 | 3 | no | — |
| 347 | C4⋊Q8 | — | 6 | 3 | no | — |
| 348 | C4⋊Q8 | — | 6 | 3 | no | — |
| 349 | #127 | — | 3 | 1 | no | — |
| 350 | #125 | — | 3 | 3 | no | — |
| 351 | #125 | — | 3 | 6 | no | — |
| 352 | #125 | — | 3 | 1 | no | — |
| 353 | #125 | — | 6 | 3 | no | — |
| 354 | #125 | — | 6 | 3 | no | — |
| 355 | #125 | — | 6 | 3 | no | — |
| 356 | #125 | — | 6 | 3 | no | — |
| 357 | #124 | — | 3 | 3 | no | — |
| 358 | #124 | — | 3 | 3 | no | — |
| 359 | #123 | — | 6 | 6 | no | — |
| 360 | #123 | — | 6 | 6 | no | — |
| 361 | C22⋊Q8 | — | 6 | 6 | no | — |
| 362 | C22⋊Q8 | — | 6 | 3 | no | — |
| 363 | C22⋊Q8 | — | 6 | 3 | no | — |
| 364 | C22⋊Q8 | — | 6 | 6 | no | — |
| 365 | C22⋊Q8 | — | 6 | 3 | no | — |
| 366 | C22⋊Q8 | — | 6 | 3 | no | — |
| 367 | C22⋊Q8 | — | 6 | 3 | no | — |
| 368 | C22⋊Q8 | — | 6 | 3 | no | — |
| 369 | #121 | — | 6 | 3 | no | — |
| 370 | #121 | — | 6 | 3 | no | — |
| 371 | C4×Q8 | — | 2 | 1 | no | — |
| 372 | C4×Q8 | — | 3 | 1 | no | — |
| 373 | C4×Q8 | — | 3 | 1 | no | — |
| 374 | C4×Q8 | — | 6 | 3 | no | — |
| 375 | C4×Q8 | — | 6 | 3 | no | — |
| 376 | C4×Q8 | — | 6 | 1 | no | — |
| 377 | C4×D4 | — | 2 | 3 | no | — |
| 378 | C4×D4 | — | 3 | 3 | no | — |
| 379 | C4×D4 | — | 3 | 3 | no | — |
| 380 | C4×D4 | — | 6 | 3 | no | — |
| 381 | C4×D4 | — | 6 | 3 | no | — |
| 382 | C4×D4 | — | 6 | 3 | no | — |
| 383 | #117 | — | 3 | 3 | no | — |
| 384 | #117 | — | 3 | 3 | no | — |
| 385 | #117 | C22×D3 | 1 | 3 | yes | — |
| 386 | C2×C4⋊C4 | — | 3 | 3 | no | — |
| 387 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 388 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 389 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 390 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 391 | C2×C4⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 392 | C2×C42 | — | 3 | 3 | no | — |
| 393 | #103 | — | 3 | 3 | no | — |
| 394 | #103 | — | 3 | 6 | no | — |
| 395 | #103 | — | 3 | 3 | no | — |
| 396 | #103 | — | 3 | 3 | no | — |
| 397 | #103 | — | 3 | 6 | no | — |
| 398 | #103 | — | 3 | 3 | no | — |
| 399 | #103 | — | 3 | 3 | no | — |
| 400 | #103 | — | 3 | 6 | no | — |
| 401 | #103 | — | 3 | 3 | no | — |
| 402 | #103 | C22×D3 | 1 | 3 | yes | — |
| 403 | #103 | C22×D3 | 1 | 6 | yes | — |
| 404 | #103 | C22×D3 | 1 | 3 | yes | — |
| 405 | #102 | — | 3 | 1 | no | — |
| 406 | #102 | — | 3 | 3 | no | — |
| 407 | #102 | — | 3 | 1 | no | — |
| 408 | #102 | — | 3 | 3 | no | — |
| 409 | #102 | — | 3 | 1 | no | — |
| 410 | #102 | — | 3 | 3 | no | — |
| 411 | #102 | C22×D3 | 1 | 1 | yes | characteristic |
| 412 | #102 | C22×D3 | 1 | 3 | yes | — |
| 413 | #97 | — | 3 | 1 | no | — |
| 414 | #97 | — | 3 | 3 | no | — |
| 415 | #97 | — | 3 | 3 | no | — |
| 416 | #97 | — | 3 | 3 | no | — |
| 417 | C4×C8 | — | 3 | 6 | no | — |
| 418 | C23×C3 | — | 2 | 1 | no | — |
| 419 | C23×C3 | C22×D4 | 1 | 3 | yes | — |
| 420 | C22×D3 | — | 2 | 1 | no | — |
| 421 | C3×Q8 | — | 2 | 3 | no | — |
| 422 | C3×Q8 | — | 2 | 3 | no | — |
| 423 | C3×Q8 | — | 4 | 6 | no | — |
| 424 | C3×Q8 | #124 | 1 | 4 | yes | — |
| 425 | C3×D4 | — | 2 | 1 | no | — |
| 426 | C3×D4 | — | 2 | 1 | no | — |
| 427 | C3×D4 | — | 4 | 6 | no | — |
| 428 | C3×D4 | #124 | 1 | 12 | yes | — |
| 429 | C2×C3×C4 | — | 2 | 3 | no | — |
| 430 | C2×C3×C4 | — | 2 | 3 | no | — |
| 431 | C2×C3×C4 | — | 2 | 1 | no | — |
| 432 | C2×C3×C4 | — | 4 | 6 | no | — |
| 433 | C2×C3×C4 | — | 4 | 6 | no | — |
| 434 | C2×C3×C4 | — | 8 | 3 | no | — |
| 435 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 436 | C2×C3×C4 | C2×#41 | 1 | 6 | yes | — |
| 437 | C2×C3×C4 | C2×#41 | 1 | 6 | yes | — |
| 438 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 439 | #67 | — | 4 | 2 | no | — |
| 440 | #67 | — | 4 | 2 | no | — |
| 441 | #67 | — | 4 | 6 | no | — |
| 442 | C2×Dic3 | — | 2 | 1 | no | — |
| 443 | C2×Dic3 | — | 2 | 3 | no | — |
| 444 | C2×Dic3 | — | 2 | 3 | no | — |
| 445 | C2×Dic3 | — | 4 | 3 | no | — |
| 446 | C2×Dic3 | — | 4 | 3 | no | — |
| 447 | C2×Dic3 | — | 4 | 6 | no | — |
| 448 | C2×Dic3 | — | 8 | 3 | no | — |
| 449 | C2×Dic3 | C22×D4 | 1 | 1 | yes | characteristic |
| 450 | C2×Dic3 | C22×D4 | 1 | 1 | yes | characteristic |
| 451 | C2×Dic3 | C22×D4 | 1 | 3 | yes | — |
| 452 | C2×Dic3 | C22×D4 | 1 | 3 | yes | — |
| 453 | D12 | — | 2 | 1 | no | — |
| 454 | D12 | — | 2 | 1 | no | — |
| 455 | C4×D3 | — | 4 | 6 | no | — |
| 456 | Dic6 | — | 2 | 3 | no | — |
| 457 | Dic6 | — | 2 | 3 | no | — |
| 458 | Dic6 | — | 4 | 6 | no | — |
| 459 | Dic6 | — | 8 | 3 | no | — |
| 460 | Dic6 | — | 8 | 3 | no | — |
| 461 | C3×C8 | — | 2 | 1 | no | — |
| 462 | C3×C8 | — | 2 | 3 | no | — |
| 463 | C3⋊C8 | — | 2 | 1 | no | — |
| 464 | C3⋊C8 | — | 2 | 3 | no | — |
| 465 | #41 | — | 2 | 6 | no | — |
| 466 | #41 | — | 2 | 6 | no | — |
| 467 | #41 | — | 4 | 12 | no | — |
| 468 | #41 | — | 6 | 6 | no | — |
| 469 | #41 | — | 6 | 6 | no | — |
| 470 | #41 | — | 12 | 12 | no | — |
| 471 | #41 | #235 | 1 | 4 | yes | — |
| 472 | #41 | #237 | 1 | 4 | yes | — |
| 473 | C2×Q8 | — | 2 | 3 | no | — |
| 474 | C2×Q8 | — | 2 | 6 | no | — |
| 475 | C2×Q8 | — | 2 | 6 | no | — |
| 476 | C2×Q8 | — | 3 | 3 | no | — |
| 477 | C2×Q8 | — | 4 | 4 | no | — |
| 478 | C2×Q8 | — | 6 | 3 | no | — |
| 479 | C2×Q8 | — | 6 | 3 | no | — |
| 480 | C2×Q8 | — | 6 | 3 | no | — |
| 481 | C2×Q8 | — | 6 | 6 | no | — |
| 482 | C2×Q8 | — | 6 | 6 | no | — |
| 483 | C2×Q8 | — | 12 | 4 | no | — |
| 484 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 485 | C2×Q8 | C23×D3 | 1 | 3 | yes | — |
| 486 | C2×D4 | — | 2 | 3 | no | — |
| 487 | C2×D4 | — | 3 | 1 | no | — |
| 488 | C2×D4 | — | 6 | 1 | no | — |
| 489 | C2×D4 | — | 6 | 1 | no | — |
| 490 | C2×D4 | — | 6 | 3 | no | — |
| 491 | C2×D4 | D3×D4 | 1 | 3 | yes | — |
| 492 | C2×D4 | C23×D3 | 1 | 1 | yes | characteristic |
| 493 | C22×C4 | — | 2 | 3 | no | — |
| 494 | C22×C4 | — | 2 | 3 | no | — |
| 495 | C22×C4 | — | 2 | 3 | no | — |
| 496 | C22×C4 | — | 3 | 3 | no | — |
| 497 | C22×C4 | — | 3 | 3 | no | — |
| 498 | C22×C4 | — | 6 | 3 | no | — |
| 499 | C22×C4 | — | 6 | 3 | no | — |
| 500 | C22×C4 | — | 6 | 3 | no | — |
| 501 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 502 | M16 | — | 2 | 6 | no | — |
| 503 | M16 | — | 6 | 6 | no | — |
| 504 | C2×C8 | — | 2 | 6 | no | — |
| 505 | C2×C8 | — | 3 | 3 | no | — |
| 506 | C2×C8 | — | 3 | 1 | no | — |
| 507 | C2×C8 | — | 6 | 6 | no | — |
| 508 | C2×C8 | C23×D3 | 1 | 3 | yes | — |
| 509 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 510 | C4⋊C4 | — | 2 | 3 | no | — |
| 511 | C4⋊C4 | — | 3 | 3 | no | — |
| 512 | C4⋊C4 | — | 3 | 3 | no | — |
| 513 | C4⋊C4 | — | 3 | 3 | no | — |
| 514 | C4⋊C4 | — | 3 | 1 | no | — |
| 515 | C4⋊C4 | — | 6 | 3 | no | — |
| 516 | C4⋊C4 | — | 6 | 3 | no | — |
| 517 | C4⋊C4 | — | 6 | 3 | no | — |
| 518 | C4⋊C4 | — | 6 | 3 | no | — |
| 519 | C4⋊C4 | — | 6 | 6 | no | — |
| 520 | C4⋊C4 | — | 6 | 6 | no | — |
| 521 | C4⋊C4 | — | 6 | 6 | no | — |
| 522 | C4⋊C4 | — | 6 | 6 | no | — |
| 523 | C4⋊C4 | — | 6 | 1 | no | — |
| 524 | C4⋊C4 | — | 6 | 1 | no | — |
| 525 | C4⋊C4 | — | 6 | 3 | no | — |
| 526 | C4⋊C4 | — | 6 | 3 | no | — |
| 527 | C4⋊C4 | — | 6 | 3 | no | — |
| 528 | C4⋊C4 | C23×D3 | 1 | 3 | yes | — |
| 529 | C4⋊C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 530 | C22⋊C4 | — | 2 | 3 | no | — |
| 531 | C22⋊C4 | — | 3 | 6 | no | — |
| 532 | C22⋊C4 | — | 6 | 3 | no | — |
| 533 | C22⋊C4 | — | 6 | 3 | no | — |
| 534 | C22⋊C4 | — | 6 | 3 | no | — |
| 535 | C22⋊C4 | — | 6 | 3 | no | — |
| 536 | C22⋊C4 | — | 6 | 3 | no | — |
| 537 | C42 | — | 2 | 3 | no | — |
| 538 | C42 | — | 3 | 3 | no | — |
| 539 | C42 | — | 3 | 3 | no | — |
| 540 | C42 | — | 3 | 3 | no | — |
| 541 | C42 | — | 3 | 1 | no | — |
| 542 | C42 | — | 6 | 3 | no | — |
| 543 | C22×C3 | — | 2 | 3 | no | — |
| 544 | C22×C3 | — | 2 | 3 | no | — |
| 545 | C22×C3 | — | 4 | 1 | no | — |
| 546 | C22×C3 | — | 4 | 1 | no | — |
| 547 | C22×C3 | — | 4 | 1 | no | — |
| 548 | C22×C3 | C2×#124 | 1 | 6 | yes | — |
| 549 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 550 | C2×D3 | — | 4 | 1 | no | — |
| 551 | C2×D3 | — | 4 | 1 | no | — |
| 552 | C2×D3 | — | 4 | 1 | no | — |
| 553 | C3×C4 | — | 4 | 1 | no | — |
| 554 | C3×C4 | — | 4 | 3 | no | — |
| 555 | C3×C4 | — | 4 | 3 | no | — |
| 556 | C3×C4 | C2×#124 | 1 | 6 | yes | — |
| 557 | C3×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 558 | C3×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 559 | Dic3 | — | 2 | 3 | no | — |
| 560 | Dic3 | — | 2 | 3 | no | — |
| 561 | Dic3 | — | 2 | 1 | no | — |
| 562 | Dic3 | — | 2 | 1 | no | — |
| 563 | Dic3 | — | 4 | 1 | no | — |
| 564 | Dic3 | — | 4 | 3 | no | — |
| 565 | Dic3 | — | 4 | 3 | no | — |
| 566 | C23 | — | 2 | 1 | no | — |
| 567 | C23 | — | 6 | 1 | no | — |
| 568 | C23 | C2×D3×D4 | 1 | 3 | yes | — |
| 569 | Q8 | — | 2 | 3 | no | — |
| 570 | Q8 | — | 2 | 3 | no | — |
| 571 | Q8 | — | 4 | 6 | no | — |
| 572 | Q8 | — | 6 | 3 | no | — |
| 573 | Q8 | — | 6 | 3 | no | — |
| 574 | Q8 | — | 12 | 6 | no | — |
| 575 | Q8 | — | 24 | 3 | no | — |
| 576 | Q8 | — | 24 | 3 | no | — |
| 577 | Q8 | #885 | 1 | 4 | yes | — |
| 578 | D4 | — | 2 | 1 | no | — |
| 579 | D4 | — | 2 | 1 | no | — |
| 580 | D4 | — | 4 | 6 | no | — |
| 581 | D4 | — | 6 | 1 | no | — |
| 582 | D4 | — | 6 | 1 | no | — |
| 583 | D4 | — | 12 | 2 | no | — |
| 584 | D4 | — | 12 | 2 | no | — |
| 585 | D4 | — | 12 | 6 | no | — |
| 586 | D4 | #885 | 1 | 12 | yes | — |
| 587 | C2×C4 | — | 2 | 1 | no | — |
| 588 | C2×C4 | — | 2 | 3 | no | — |
| 589 | C2×C4 | — | 2 | 3 | no | — |
| 590 | C2×C4 | — | 3 | 1 | no | — |
| 591 | C2×C4 | — | 3 | 1 | no | — |
| 592 | C2×C4 | — | 3 | 3 | no | — |
| 593 | C2×C4 | — | 3 | 3 | no | — |
| 594 | C2×C4 | — | 4 | 6 | no | — |
| 595 | C2×C4 | — | 4 | 6 | no | — |
| 596 | C2×C4 | — | 6 | 1 | no | — |
| 597 | C2×C4 | — | 6 | 3 | no | — |
| 598 | C2×C4 | — | 6 | 3 | no | — |
| 599 | C2×C4 | — | 8 | 3 | no | — |
| 600 | C2×C4 | — | 12 | 3 | no | — |
| 601 | C2×C4 | — | 12 | 3 | no | — |
| 602 | C2×C4 | — | 12 | 6 | no | — |
| 603 | C2×C4 | — | 12 | 6 | no | — |
| 604 | C2×C4 | — | 24 | 3 | no | — |
| 605 | C2×C4 | C2×#235 | 1 | 6 | yes | — |
| 606 | C2×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 607 | C2×C4 | C2×#237 | 1 | 6 | yes | — |
| 608 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 609 | C8 | — | 2 | 1 | no | — |
| 610 | C8 | — | 2 | 3 | no | — |
| 611 | C8 | — | 6 | 1 | no | — |
| 612 | C8 | — | 6 | 3 | no | — |
| 613 | C2×C3 | — | 2 | 6 | no | — |
| 614 | C2×C3 | — | 8 | 1 | no | — |
| 615 | C2×C3 | C22×#124 | 1 | 1 | yes | characteristic |
| 616 | C2×C3 | #3586 | 1 | 1 | yes | characteristic |
| 617 | C2×C3 | #3586 | 1 | 1 | yes | characteristic |
| 618 | D3 | — | 8 | 1 | no | — |
| 619 | C22 | — | 2 | 3 | no | — |
| 620 | C22 | — | 2 | 3 | no | — |
| 621 | C22 | — | 4 | 1 | no | — |
| 622 | C22 | — | 4 | 1 | no | — |
| 623 | C22 | — | 4 | 1 | no | — |
| 624 | C22 | — | 12 | 1 | no | — |
| 625 | C22 | — | 12 | 1 | no | — |
| 626 | C22 | — | 12 | 1 | no | — |
| 627 | C22 | C2×#885 | 1 | 6 | yes | — |
| 628 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 629 | C4 | — | 4 | 3 | no | — |
| 630 | C4 | — | 4 | 1 | no | — |
| 631 | C4 | — | 4 | 3 | no | — |
| 632 | C4 | — | 6 | 1 | no | — |
| 633 | C4 | — | 6 | 3 | no | — |
| 634 | C4 | — | 6 | 1 | no | — |
| 635 | C4 | — | 6 | 3 | no | — |
| 636 | C4 | — | 12 | 1 | no | — |
| 637 | C4 | — | 12 | 3 | no | — |
| 638 | C4 | — | 12 | 3 | no | — |
| 639 | C4 | C2×#885 | 1 | 6 | yes | — |
| 640 | C4 | C22×#235 | 1 | 1 | yes | characteristic |
| 641 | C4 | C22×#237 | 1 | 1 | yes | characteristic |
| 642 | C3 | #60627 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 643 | C2 | — | 2 | 6 | no | — |
| 644 | C2 | — | 8 | 1 | no | — |
| 645 | C2 | — | 24 | 1 | no | — |
| 646 | C2 | C22×#885 | 1 | 1 | yes | characteristic |
| 647 | C2 | #87208 | 1 | 1 | yes | characteristic |
| 648 | C2 | #87211 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #85890 | C2 | semidirect |
| 3. C3×#2898 | C2 | semidirect |
| 4. #84111 | C2 | semidirect |
| 5. #83806 | C2 | semidirect |
| 6. #83782 | C2 | semidirect |
| 7. #82570 | C2 | semidirect |
| 8. #78953 | C2 | semidirect |
| 9. #78952 | C2 | semidirect |
| 10. #78879 | C2 | semidirect |
| 11. #78877 | C2 | semidirect |
| 12. #78828 | C2 | semidirect |
| 13. #78826 | C2 | semidirect |
| 14. #78785 | C2 | semidirect |
| 15. C2×#4797 | C2 | semidirect |
| 88. #2898 | D3 | semidirect |
| 642. C3 | #60627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #87292 | 2 |
| #85890 | 2 |
| C3×#2898 | 2 |
| #84111 | 2 |
| #83806 | 2 |
| #83782 | 2 |
| #82570 | 2 |
| #78953 | 2 |
| #78952 | 2 |
| #78879 | 2 |
| #78877 | 2 |
| #78828 | 2 |
| #78826 | 2 |
| #78785 | 2 |
| C2×#4797 | 2 |
| #60627 | 3 |