Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1998 conjugacy classes of subgroups.
The subgroup lattice has 628 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #86257 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #86219 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#3135 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #83340 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #83286 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #81728 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #81704 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #81665 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #81664 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #78839 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #78818 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #78497 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C2×#4707 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #60676 | — | 3 | 1 | no | maximal, Sylow |
| 15 | C3×#533 | C22 | 1 | 1 | yes | characteristic |
| 16 | C3×#532 | C22 | 1 | 1 | yes | characteristic |
| 17 | #5828 | C22 | 1 | 2 | yes | — |
| 18 | Dic3×#41 | C22 | 1 | 2 | yes | — |
| 19 | C2×#950 | C22 | 1 | 4 | yes | — |
| 20 | C22×ΓL(1,𝔽25) | C22 | 1 | 2 | yes | — |
| 21 | #5728 | C22 | 1 | 2 | yes | — |
| 22 | #5728 | C22 | 1 | 2 | yes | — |
| 23 | #5725 | C22 | 1 | 2 | yes | — |
| 24 | #5716 | C22 | 1 | 2 | yes | — |
| 25 | #5691 | C22 | 1 | 4 | yes | — |
| 26 | #5680 | C22 | 1 | 4 | yes | — |
| 27 | #5627 | — | 2 | 2 | no | — |
| 28 | #5624 | — | 2 | 2 | no | — |
| 29 | #5606 | — | 2 | 2 | no | — |
| 30 | #5600 | — | 2 | 2 | no | — |
| 31 | #5580 | — | 2 | 2 | no | — |
| 32 | C4×#239 | — | 2 | 2 | no | — |
| 33 | #5557 | — | 2 | 2 | no | — |
| 34 | C4×#237 | — | 2 | 2 | no | — |
| 35 | #5524 | C22 | 1 | 2 | yes | — |
| 36 | #5522 | C22 | 1 | 2 | yes | — |
| 37 | #5477 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×C42×D3 | C22 | 1 | 1 | yes | characteristic |
| 39 | #5470 | C22 | 1 | 1 | yes | characteristic |
| 40 | C3×#491 | C22 | 1 | 2 | yes | complemented |
| 41 | C3×#490 | C22 | 1 | 2 | yes | complemented |
| 42 | C3×#489 | C22 | 1 | 4 | yes | complemented |
| 43 | C3×#416 | C22 | 1 | 4 | yes | — |
| 44 | C2×C3×#97 | C22 | 1 | 1 | yes | characteristic |
| 45 | #5113 | C22 | 1 | 4 | yes | — |
| 46 | C2×C8×Dic3 | C22 | 1 | 2 | yes | — |
| 47 | #5086 | C22 | 1 | 2 | yes | complemented |
| 48 | #5081 | C22 | 1 | 4 | yes | complemented |
| 49 | #5074 | C22 | 1 | 2 | yes | complemented |
| 50 | #5064 | C22 | 1 | 4 | yes | complemented |
| 51 | #5060 | C22 | 1 | 2 | yes | complemented |
| 52 | #5058 | C22 | 1 | 2 | yes | complemented |
| 53 | #4998 | C22 | 1 | 4 | yes | — |
| 54 | C2×#803 | C22 | 1 | 1 | yes | characteristic |
| 55 | #4816 | C22 | 1 | 8 | yes | — |
| 56 | #4812 | C22 | 1 | 8 | yes | — |
| 57 | #4790 | C22 | 1 | 8 | yes | complemented |
| 58 | #4788 | C22 | 1 | 8 | yes | complemented |
| 59 | #4782 | C22 | 1 | 8 | yes | — |
| 60 | #4780 | C22 | 1 | 8 | yes | — |
| 61 | #4758 | C22 | 1 | 8 | yes | complemented |
| 62 | #4756 | C22 | 1 | 8 | yes | complemented |
| 63 | #4714 | C22 | 1 | 4 | yes | complemented |
| 64 | #4713 | C22 | 1 | 2 | yes | complemented |
| 65 | #4707 | C22 | 1 | 4 | yes | — |
| 66 | #4707 | C22 | 1 | 4 | yes | — |
| 67 | #4703 | C22 | 1 | 2 | yes | complemented |
| 68 | #3444 | — | 3 | 1 | no | — |
| 69 | #3444 | — | 3 | 1 | no | — |
| 70 | #3172 | — | 3 | 4 | no | — |
| 71 | #3172 | — | 3 | 4 | no | — |
| 72 | #3171 | — | 3 | 4 | no | — |
| 73 | #3171 | — | 3 | 4 | no | — |
| 74 | #3162 | — | 3 | 1 | no | — |
| 75 | #3150 | — | 3 | 1 | no | — |
| 76 | #3135 | — | 3 | 1 | no | — |
| 77 | #3135 | D3 | 1 | 1 | yes | characteristic, complemented |
| 78 | #3054 | — | 3 | 4 | no | — |
| 79 | C4×#135 | — | 3 | 4 | no | — |
| 80 | C2×C4×M16 | — | 3 | 1 | no | — |
| 81 | C2×C3×#41 | C23 | 1 | 2 | yes | — |
| 82 | C2×#239 | — | 2 | 2 | no | — |
| 83 | C2×#237 | — | 2 | 2 | no | — |
| 84 | C2×#235 | C23 | 1 | 2 | yes | — |
| 85 | C22×C4×D3 | D4 | 1 | 2 | yes | — |
| 86 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 87 | C22×C3×C8 | C23 | 1 | 2 | yes | — |
| 88 | C3×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 89 | C3×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 90 | C3×#127 | C23 | 1 | 1 | yes | characteristic |
| 91 | C3×#125 | C23 | 1 | 2 | yes | — |
| 92 | C3×#124 | C23 | 1 | 2 | yes | — |
| 93 | C3×C22⋊Q8 | — | 2 | 2 | no | — |
| 94 | C3×#121 | — | 2 | 2 | no | — |
| 95 | C3×C4×Q8 | — | 2 | 2 | no | — |
| 96 | C3×C4×D4 | — | 2 | 2 | no | — |
| 97 | C3×#117 | C23 | 1 | 2 | yes | — |
| 98 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 99 | #950 | — | 2 | 16 | no | — |
| 100 | #947 | — | 2 | 2 | no | — |
| 101 | #946 | — | 2 | 2 | no | — |
| 102 | #946 | C23 | 1 | 4 | yes | — |
| 103 | Q8×Dic3 | — | 2 | 2 | no | — |
| 104 | Q8×Dic3 | C23 | 1 | 4 | yes | — |
| 105 | C2×#216 | C23 | 1 | 4 | yes | — |
| 106 | C2×#215 | C23 | 1 | 4 | yes | — |
| 107 | #938 | — | 2 | 2 | no | — |
| 108 | #938 | C23 | 1 | 4 | yes | — |
| 109 | #937 | — | 2 | 2 | no | — |
| 110 | #936 | — | 2 | 2 | no | — |
| 111 | #935 | — | 2 | 2 | no | — |
| 112 | D4×Dic3 | — | 2 | 4 | no | — |
| 113 | D4×Dic3 | — | 2 | 2 | no | — |
| 114 | D4×Dic3 | C23 | 1 | 4 | yes | — |
| 115 | C2×#214 | C23 | 1 | 4 | yes | — |
| 116 | C2×#213 | C23 | 1 | 4 | yes | — |
| 117 | #930 | — | 2 | 2 | no | — |
| 118 | C4×#67 | — | 2 | 4 | no | — |
| 119 | #926 | — | 2 | 2 | no | — |
| 120 | #926 | C23 | 1 | 2 | yes | — |
| 121 | #924 | — | 2 | 2 | no | — |
| 122 | C2×C4×Dic3 | — | 2 | 2 | no | — |
| 123 | C2×C4×Dic3 | D4 | 1 | 2 | yes | — |
| 124 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 125 | C22×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 126 | C2×ΓL(1,𝔽25) | — | 2 | 8 | no | — |
| 127 | C2×ΓL(1,𝔽25) | C23 | 1 | 8 | yes | — |
| 128 | #898 | — | 2 | 4 | no | — |
| 129 | #897 | — | 2 | 2 | no | — |
| 130 | #897 | C23 | 1 | 4 | yes | — |
| 131 | #895 | — | 2 | 2 | no | — |
| 132 | #895 | C23 | 1 | 4 | yes | — |
| 133 | #894 | — | 2 | 4 | no | — |
| 134 | #893 | — | 2 | 4 | no | — |
| 135 | #893 | — | 2 | 2 | no | — |
| 136 | #893 | C23 | 1 | 4 | yes | — |
| 137 | #892 | — | 2 | 2 | no | — |
| 138 | #892 | — | 2 | 2 | no | — |
| 139 | #892 | — | 2 | 4 | no | — |
| 140 | #890 | — | 2 | 2 | no | — |
| 141 | #890 | — | 2 | 2 | no | — |
| 142 | #887 | — | 2 | 2 | no | — |
| 143 | #887 | C23 | 1 | 4 | yes | — |
| 144 | #886 | — | 2 | 2 | no | — |
| 145 | #883 | — | 2 | 4 | no | — |
| 146 | #882 | — | 2 | 2 | no | — |
| 147 | #67⋊C4 | — | 2 | 4 | no | — |
| 148 | #67⋊C4 | — | 2 | 4 | no | — |
| 149 | #879 | — | 2 | 4 | no | — |
| 150 | #877 | — | 2 | 4 | no | — |
| 151 | #875 | C23 | 1 | 2 | yes | — |
| 152 | #874 | C23 | 1 | 1 | yes | characteristic |
| 153 | C4×D12 | — | 2 | 4 | no | — |
| 154 | C4×D12 | — | 2 | 2 | no | — |
| 155 | #872 | — | 2 | 2 | no | — |
| 156 | C42×D3 | — | 2 | 2 | no | — |
| 157 | C42×D3 | D4 | 1 | 2 | yes | — |
| 158 | C42×D3 | D4 | 1 | 2 | yes | — |
| 159 | C42×D3 | C23 | 1 | 2 | yes | — |
| 160 | C42×D3 | C23 | 1 | 2 | yes | — |
| 161 | #870 | C23 | 1 | 2 | yes | — |
| 162 | #869 | C23 | 1 | 1 | yes | characteristic |
| 163 | #869 | C23 | 1 | 2 | yes | — |
| 164 | C4×Dic6 | — | 2 | 2 | no | — |
| 165 | C3×#103 | C23 | 1 | 8 | yes | — |
| 166 | C3×#102 | C23 | 1 | 8 | yes | — |
| 167 | C3×#97 | C23 | 1 | 2 | yes | — |
| 168 | C3×#97 | C23 | 1 | 2 | yes | — |
| 169 | #821 | C23 | 1 | 8 | yes | — |
| 170 | #816 | C23 | 1 | 8 | yes | — |
| 171 | C8×Dic3 | C23 | 1 | 8 | yes | — |
| 172 | #808 | C23 | 1 | 8 | yes | — |
| 173 | #807 | C23 | 1 | 8 | yes | — |
| 174 | #803 | C23 | 1 | 2 | yes | — |
| 175 | #803 | C23 | 1 | 2 | yes | — |
| 176 | C2×#135 | — | 3 | 4 | no | — |
| 177 | C22×M16 | — | 3 | 2 | no | — |
| 178 | #533 | — | 3 | 2 | no | — |
| 179 | #533 | — | 3 | 2 | no | — |
| 180 | #533 | — | 3 | 1 | no | — |
| 181 | #533 | C2×D3 | 1 | 1 | yes | characteristic |
| 182 | #532 | — | 3 | 2 | no | — |
| 183 | #532 | — | 3 | 2 | no | — |
| 184 | #532 | — | 3 | 1 | no | — |
| 185 | #532 | C2×D3 | 1 | 1 | yes | characteristic |
| 186 | #529 | — | 3 | 4 | no | — |
| 187 | #529 | — | 3 | 4 | no | — |
| 188 | #529 | — | 6 | 2 | no | — |
| 189 | #529 | — | 6 | 2 | no | — |
| 190 | #529 | — | 6 | 2 | no | — |
| 191 | #529 | — | 6 | 2 | no | — |
| 192 | #525 | — | 3 | 2 | no | — |
| 193 | #525 | — | 3 | 2 | no | — |
| 194 | #525 | — | 6 | 2 | no | — |
| 195 | #525 | — | 6 | 2 | no | — |
| 196 | C4×#41 | — | 3 | 2 | no | — |
| 197 | C4×#41 | — | 3 | 2 | no | — |
| 198 | C4×#41 | — | 6 | 2 | no | — |
| 199 | C4×#41 | — | 6 | 2 | no | — |
| 200 | C22×C42 | — | 3 | 1 | no | — |
| 201 | #501 | — | 3 | 4 | no | — |
| 202 | #501 | — | 3 | 4 | no | — |
| 203 | #497 | — | 3 | 2 | no | — |
| 204 | #497 | — | 3 | 2 | no | — |
| 205 | #496 | — | 3 | 2 | no | — |
| 206 | #496 | — | 3 | 2 | no | — |
| 207 | #491 | — | 3 | 2 | no | — |
| 208 | #491 | C2×D3 | 1 | 2 | yes | complemented |
| 209 | #490 | — | 3 | 2 | no | — |
| 210 | #490 | C2×D3 | 1 | 2 | yes | complemented |
| 211 | #489 | — | 3 | 4 | no | — |
| 212 | #489 | C2×D3 | 1 | 4 | yes | complemented |
| 213 | #470 | — | 3 | 8 | no | — |
| 214 | #469 | — | 3 | 8 | no | — |
| 215 | #468 | — | 3 | 8 | no | — |
| 216 | #468 | — | 3 | 8 | no | — |
| 217 | C4×Q16 | — | 3 | 8 | no | — |
| 218 | C4×SD16 | — | 3 | 8 | no | — |
| 219 | C4×SD16 | — | 3 | 8 | no | — |
| 220 | C4×D8 | — | 3 | 8 | no | — |
| 221 | #427 | — | 3 | 4 | no | — |
| 222 | #416 | — | 3 | 4 | no | — |
| 223 | #416 | C2×D3 | 1 | 4 | yes | — |
| 224 | C4×M16 | — | 3 | 4 | no | — |
| 225 | C4×M16 | — | 3 | 4 | no | — |
| 226 | C2×#97 | — | 3 | 1 | no | — |
| 227 | C2×#97 | C2×D3 | 1 | 1 | yes | characteristic |
| 228 | C2×C4×C8 | — | 3 | 2 | no | — |
| 229 | C23×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 230 | C3×#41 | — | 2 | 8 | no | — |
| 231 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 232 | C2×C3×Q8 | C24 | 1 | 2 | yes | — |
| 233 | C2×C3×D4 | — | 2 | 2 | no | — |
| 234 | C2×C3×D4 | — | 2 | 2 | no | — |
| 235 | C2×C3×D4 | C24 | 1 | 2 | yes | — |
| 236 | C22×C3×C4 | — | 2 | 2 | no | — |
| 237 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 238 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 239 | C2×#67 | — | 2 | 2 | no | — |
| 240 | C2×#67 | — | 2 | 4 | no | — |
| 241 | C22×Dic3 | — | 2 | 4 | no | — |
| 242 | C22×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 243 | C22×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 244 | #239 | — | 4 | 8 | no | — |
| 245 | #237 | — | 4 | 8 | no | — |
| 246 | #235 | — | 2 | 8 | no | — |
| 247 | C2×D12 | — | 2 | 4 | no | — |
| 248 | C2×D12 | — | 2 | 2 | no | — |
| 249 | C2×D12 | C24 | 1 | 2 | yes | — |
| 250 | C2×C4×D3 | — | 2 | 4 | no | — |
| 251 | C2×C4×D3 | — | 2 | 2 | no | — |
| 252 | C2×C4×D3 | — | 2 | 4 | no | — |
| 253 | C2×C4×D3 | — | 4 | 4 | no | — |
| 254 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 255 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 256 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 257 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 258 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 259 | C2×C4×D3 | C24 | 1 | 2 | yes | — |
| 260 | C2×Dic6 | — | 2 | 2 | no | — |
| 261 | C2×Dic6 | C24 | 1 | 2 | yes | — |
| 262 | C2×C3×C8 | — | 2 | 4 | no | — |
| 263 | C2×C3×C8 | C24 | 1 | 4 | yes | — |
| 264 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 265 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 266 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 267 | C3×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 268 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 269 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 270 | C3×C42 | — | 2 | 2 | no | — |
| 271 | C3×C42 | C2×D4 | 1 | 2 | yes | — |
| 272 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 273 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 274 | #217 | — | 2 | 2 | no | — |
| 275 | #217 | — | 2 | 4 | no | — |
| 276 | #217 | — | 2 | 4 | no | — |
| 277 | #216 | — | 2 | 8 | no | — |
| 278 | #215 | — | 2 | 8 | no | — |
| 279 | #214 | — | 2 | 8 | no | — |
| 280 | #213 | — | 2 | 8 | no | — |
| 281 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 282 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 283 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 284 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 285 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 286 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 287 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 288 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 289 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 290 | C4⋊Dic3 | C24 | 1 | 4 | yes | — |
| 291 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 292 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 293 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 294 | C4×Dic3 | — | 2 | 2 | no | — |
| 295 | C4×Dic3 | — | 2 | 4 | no | — |
| 296 | C4×Dic3 | — | 2 | 4 | no | — |
| 297 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 298 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 299 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 300 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 301 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 302 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 303 | C4×Dic3 | C24 | 1 | 2 | yes | — |
| 304 | C2×C3⋊C8 | #41 | 1 | 8 | yes | complemented |
| 305 | C2×C3⋊C8 | C24 | 1 | 4 | yes | — |
| 306 | ΓL(1,𝔽25) | — | 2 | 16 | no | — |
| 307 | C2×#41 | — | 3 | 2 | no | — |
| 308 | C2×#41 | — | 6 | 2 | no | — |
| 309 | C2×#41 | — | 6 | 2 | no | — |
| 310 | C2×#41 | C22×D3 | 1 | 2 | yes | — |
| 311 | C23×C4 | — | 3 | 1 | no | — |
| 312 | C23×C4 | — | 3 | 2 | no | — |
| 313 | #135 | — | 6 | 16 | no | — |
| 314 | C2×Q16 | — | 3 | 4 | no | — |
| 315 | C2×SD16 | — | 3 | 4 | no | — |
| 316 | C2×SD16 | — | 3 | 4 | no | — |
| 317 | C2×D8 | — | 3 | 4 | no | — |
| 318 | C2×M16 | — | 3 | 8 | no | — |
| 319 | C2×M16 | — | 6 | 8 | no | — |
| 320 | C22×C8 | — | 3 | 2 | no | — |
| 321 | C22×C8 | C22×D3 | 1 | 2 | yes | — |
| 322 | C4⋊Q8 | — | 3 | 2 | no | — |
| 323 | C4⋊Q8 | — | 3 | 1 | no | — |
| 324 | C4⋊Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 325 | C4⋊Q8 | C22×D3 | 1 | 2 | yes | — |
| 326 | #127 | — | 3 | 1 | no | — |
| 327 | #127 | C22×D3 | 1 | 1 | yes | characteristic |
| 328 | #126 | — | 6 | 4 | no | — |
| 329 | #126 | — | 6 | 4 | no | — |
| 330 | #125 | — | 3 | 2 | no | — |
| 331 | #125 | — | 6 | 2 | no | — |
| 332 | #125 | — | 6 | 2 | no | — |
| 333 | #125 | C22×D3 | 1 | 2 | yes | — |
| 334 | #124 | — | 3 | 2 | no | — |
| 335 | #124 | — | 6 | 2 | no | — |
| 336 | #124 | — | 6 | 2 | no | — |
| 337 | #124 | C22×D3 | 1 | 2 | yes | — |
| 338 | #123 | — | 6 | 2 | no | — |
| 339 | #123 | — | 6 | 4 | no | — |
| 340 | #123 | — | 6 | 4 | no | — |
| 341 | #123 | — | 6 | 2 | no | — |
| 342 | C22⋊Q8 | — | 2 | 2 | no | — |
| 343 | C22⋊Q8 | — | 3 | 4 | no | — |
| 344 | C22⋊Q8 | — | 3 | 4 | no | — |
| 345 | C22⋊Q8 | — | 6 | 2 | no | — |
| 346 | C22⋊Q8 | — | 6 | 2 | no | — |
| 347 | C22⋊Q8 | — | 6 | 2 | no | — |
| 348 | #121 | — | 2 | 2 | no | — |
| 349 | #121 | — | 3 | 4 | no | — |
| 350 | #121 | — | 3 | 4 | no | — |
| 351 | #121 | — | 6 | 2 | no | — |
| 352 | #121 | — | 6 | 2 | no | — |
| 353 | #121 | — | 6 | 2 | no | — |
| 354 | #120 | — | 6 | 2 | no | — |
| 355 | #120 | — | 6 | 2 | no | — |
| 356 | C4×Q8 | — | 2 | 2 | no | — |
| 357 | C4×Q8 | — | 3 | 4 | no | — |
| 358 | C4×Q8 | — | 3 | 4 | no | — |
| 359 | C4×Q8 | — | 6 | 2 | no | — |
| 360 | C4×Q8 | — | 6 | 2 | no | — |
| 361 | C4×Q8 | — | 6 | 2 | no | — |
| 362 | C4×D4 | — | 2 | 2 | no | — |
| 363 | C4×D4 | — | 3 | 4 | no | — |
| 364 | C4×D4 | — | 3 | 4 | no | — |
| 365 | C4×D4 | — | 6 | 4 | no | — |
| 366 | C4×D4 | — | 6 | 2 | no | — |
| 367 | C4×D4 | — | 6 | 2 | no | — |
| 368 | C4×D4 | — | 6 | 4 | no | — |
| 369 | C4×D4 | — | 6 | 4 | no | — |
| 370 | C4×D4 | — | 6 | 4 | no | — |
| 371 | C4×D4 | — | 6 | 4 | no | — |
| 372 | C4×D4 | — | 6 | 4 | no | — |
| 373 | C4×D4 | — | 6 | 2 | no | — |
| 374 | #117 | — | 3 | 2 | no | — |
| 375 | #117 | — | 6 | 2 | no | — |
| 376 | #117 | — | 6 | 4 | no | — |
| 377 | #117 | — | 6 | 4 | no | — |
| 378 | #117 | — | 6 | 2 | no | — |
| 379 | #117 | — | 6 | 2 | no | — |
| 380 | #117 | — | 6 | 2 | no | — |
| 381 | #117 | C22×D3 | 1 | 2 | yes | — |
| 382 | C2×C42 | — | 3 | 2 | no | — |
| 383 | C2×C42 | — | 3 | 1 | no | — |
| 384 | C2×C42 | — | 3 | 2 | no | — |
| 385 | C2×C42 | — | 3 | 2 | no | — |
| 386 | C2×C42 | — | 3 | 2 | no | — |
| 387 | C2×C42 | — | 3 | 2 | no | — |
| 388 | C2×C42 | — | 6 | 2 | no | — |
| 389 | C2×C42 | — | 6 | 2 | no | — |
| 390 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 391 | #107 | — | 3 | 8 | no | — |
| 392 | #106 | — | 3 | 8 | no | — |
| 393 | #103 | — | 3 | 8 | no | — |
| 394 | #103 | C22×D3 | 1 | 8 | yes | — |
| 395 | #102 | — | 3 | 8 | no | — |
| 396 | #102 | C22×D3 | 1 | 8 | yes | — |
| 397 | #97 | — | 3 | 2 | no | — |
| 398 | #97 | — | 3 | 2 | no | — |
| 399 | #97 | C22×D3 | 1 | 2 | yes | — |
| 400 | #97 | C22×D3 | 1 | 2 | yes | — |
| 401 | C4×C8 | — | 3 | 8 | no | — |
| 402 | C23×C3 | — | 2 | 2 | no | — |
| 403 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 404 | C22×D3 | — | 2 | 2 | no | — |
| 405 | C22×D3 | — | 2 | 2 | no | — |
| 406 | C22×D3 | — | 4 | 2 | no | — |
| 407 | C22×D3 | C22×D4 | 1 | 2 | yes | — |
| 408 | C3×Q8 | — | 2 | 4 | no | — |
| 409 | C3×Q8 | — | 4 | 4 | no | — |
| 410 | C3×D4 | — | 2 | 4 | no | — |
| 411 | C3×D4 | — | 4 | 4 | no | — |
| 412 | C3×D4 | — | 4 | 4 | no | — |
| 413 | C2×C3×C4 | — | 2 | 2 | no | — |
| 414 | C2×C3×C4 | — | 2 | 4 | no | — |
| 415 | C2×C3×C4 | — | 4 | 2 | no | — |
| 416 | C2×C3×C4 | — | 4 | 4 | no | — |
| 417 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 418 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 419 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 420 | C2×C3×C4 | C2×#41 | 1 | 4 | yes | — |
| 421 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 422 | #67 | — | 4 | 8 | no | — |
| 423 | #67 | — | 4 | 4 | no | — |
| 424 | C2×Dic3 | — | 2 | 2 | no | — |
| 425 | C2×Dic3 | — | 2 | 4 | no | — |
| 426 | C2×Dic3 | — | 2 | 4 | no | — |
| 427 | C2×Dic3 | — | 2 | 2 | no | — |
| 428 | C2×Dic3 | — | 4 | 8 | no | — |
| 429 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 430 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 431 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 432 | D12 | — | 2 | 4 | no | — |
| 433 | D12 | — | 4 | 4 | no | — |
| 434 | D12 | — | 4 | 8 | no | — |
| 435 | C4×D3 | — | 2 | 4 | no | — |
| 436 | C4×D3 | — | 2 | 4 | no | — |
| 437 | C4×D3 | — | 2 | 4 | no | — |
| 438 | C4×D3 | — | 2 | 4 | no | — |
| 439 | C4×D3 | — | 4 | 2 | no | — |
| 440 | C4×D3 | — | 4 | 2 | no | — |
| 441 | C4×D3 | — | 4 | 4 | no | — |
| 442 | C4×D3 | — | 4 | 8 | no | — |
| 443 | Dic6 | — | 2 | 4 | no | — |
| 444 | Dic6 | — | 4 | 4 | no | — |
| 445 | C3×C8 | — | 2 | 4 | no | — |
| 446 | C3⋊C8 | C2×#41 | 1 | 8 | yes | — |
| 447 | C24 | — | 3 | 1 | no | — |
| 448 | #41 | — | 2 | 8 | no | — |
| 449 | #41 | — | 6 | 8 | no | — |
| 450 | #41 | — | 12 | 8 | no | — |
| 451 | #41 | — | 12 | 8 | no | — |
| 452 | C2×Q8 | — | 2 | 2 | no | — |
| 453 | C2×Q8 | — | 3 | 2 | no | — |
| 454 | C2×Q8 | — | 6 | 2 | no | — |
| 455 | C2×Q8 | C23×D3 | 1 | 2 | yes | — |
| 456 | C2×D4 | — | 2 | 2 | no | — |
| 457 | C2×D4 | — | 2 | 2 | no | — |
| 458 | C2×D4 | — | 3 | 2 | no | — |
| 459 | C2×D4 | — | 6 | 4 | no | — |
| 460 | C2×D4 | — | 6 | 4 | no | — |
| 461 | C2×D4 | — | 6 | 2 | no | — |
| 462 | C2×D4 | — | 6 | 2 | no | — |
| 463 | C2×D4 | C23×D3 | 1 | 2 | yes | — |
| 464 | C22×C4 | — | 2 | 2 | no | — |
| 465 | C22×C4 | — | 3 | 2 | no | — |
| 466 | C22×C4 | — | 3 | 1 | no | — |
| 467 | C22×C4 | — | 3 | 2 | no | — |
| 468 | C22×C4 | — | 3 | 2 | no | — |
| 469 | C22×C4 | — | 3 | 2 | no | — |
| 470 | C22×C4 | — | 3 | 2 | no | — |
| 471 | C22×C4 | — | 3 | 2 | no | — |
| 472 | C22×C4 | — | 3 | 2 | no | — |
| 473 | C22×C4 | — | 6 | 4 | no | — |
| 474 | C22×C4 | — | 6 | 4 | no | — |
| 475 | C22×C4 | — | 6 | 4 | no | — |
| 476 | C22×C4 | — | 6 | 2 | no | — |
| 477 | C22×C4 | — | 12 | 4 | no | — |
| 478 | C22×C4 | D3×D4 | 1 | 2 | yes | — |
| 479 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 480 | Q16 | — | 6 | 8 | no | — |
| 481 | SD16 | — | 6 | 8 | no | — |
| 482 | SD16 | — | 6 | 8 | no | — |
| 483 | D8 | — | 6 | 8 | no | — |
| 484 | M16 | — | 6 | 16 | no | — |
| 485 | C2×C8 | — | 2 | 4 | no | — |
| 486 | C2×C8 | — | 3 | 8 | no | — |
| 487 | C2×C8 | — | 3 | 4 | no | — |
| 488 | C2×C8 | C23×D3 | 1 | 4 | yes | — |
| 489 | C4⋊C4 | — | 2 | 2 | no | — |
| 490 | C4⋊C4 | — | 2 | 2 | no | — |
| 491 | C4⋊C4 | — | 2 | 4 | no | — |
| 492 | C4⋊C4 | — | 3 | 4 | no | — |
| 493 | C4⋊C4 | — | 6 | 4 | no | — |
| 494 | C4⋊C4 | — | 6 | 4 | no | — |
| 495 | C4⋊C4 | — | 6 | 4 | no | — |
| 496 | C4⋊C4 | — | 6 | 4 | no | — |
| 497 | C4⋊C4 | — | 6 | 2 | no | — |
| 498 | C4⋊C4 | — | 6 | 2 | no | — |
| 499 | C4⋊C4 | — | 6 | 4 | no | — |
| 500 | C4⋊C4 | C23×D3 | 1 | 4 | yes | — |
| 501 | C22⋊C4 | — | 2 | 2 | no | — |
| 502 | C22⋊C4 | — | 2 | 4 | no | — |
| 503 | C22⋊C4 | — | 6 | 4 | no | — |
| 504 | C22⋊C4 | — | 6 | 4 | no | — |
| 505 | C22⋊C4 | — | 6 | 4 | no | — |
| 506 | C22⋊C4 | — | 6 | 4 | no | — |
| 507 | C22⋊C4 | — | 6 | 4 | no | — |
| 508 | C22⋊C4 | — | 6 | 4 | no | — |
| 509 | C22⋊C4 | — | 6 | 2 | no | — |
| 510 | C22⋊C4 | — | 6 | 4 | no | — |
| 511 | C42 | — | 2 | 2 | no | — |
| 512 | C42 | — | 3 | 2 | no | — |
| 513 | C42 | — | 3 | 2 | no | — |
| 514 | C42 | — | 3 | 2 | no | — |
| 515 | C42 | — | 3 | 2 | no | — |
| 516 | C42 | — | 3 | 1 | no | — |
| 517 | C42 | — | 3 | 1 | no | — |
| 518 | C42 | — | 3 | 2 | no | — |
| 519 | C42 | — | 6 | 4 | no | — |
| 520 | C42 | — | 6 | 4 | no | — |
| 521 | C42 | — | 6 | 2 | no | — |
| 522 | C42 | D3×D4 | 1 | 2 | yes | — |
| 523 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 524 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 525 | C22×C3 | — | 2 | 2 | no | — |
| 526 | C22×C3 | — | 4 | 2 | no | — |
| 527 | C22×C3 | — | 4 | 4 | no | — |
| 528 | C22×C3 | #532 | 1 | 2 | yes | — |
| 529 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 530 | C2×D3 | — | 2 | 2 | no | — |
| 531 | C2×D3 | — | 2 | 2 | no | — |
| 532 | C2×D3 | — | 2 | 2 | no | — |
| 533 | C2×D3 | — | 4 | 4 | no | — |
| 534 | C2×D3 | — | 4 | 2 | no | — |
| 535 | C2×D3 | — | 4 | 4 | no | — |
| 536 | C3×C4 | — | 2 | 2 | no | — |
| 537 | C3×C4 | — | 2 | 2 | no | — |
| 538 | C3×C4 | — | 4 | 2 | no | — |
| 539 | C3×C4 | — | 4 | 4 | no | — |
| 540 | C3×C4 | #532 | 1 | 2 | yes | — |
| 541 | C3×C4 | C22×#41 | 1 | 2 | yes | — |
| 542 | Dic3 | — | 2 | 2 | no | — |
| 543 | Dic3 | — | 2 | 2 | no | — |
| 544 | Dic3 | — | 4 | 2 | no | — |
| 545 | Dic3 | — | 4 | 4 | no | — |
| 546 | Dic3 | #575 | 1 | 4 | yes | — |
| 547 | C23 | — | 2 | 2 | no | — |
| 548 | C23 | — | 3 | 2 | no | — |
| 549 | C23 | — | 6 | 2 | no | — |
| 550 | C23 | — | 6 | 2 | no | — |
| 551 | C23 | — | 12 | 2 | no | — |
| 552 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 553 | Q8 | — | 2 | 4 | no | — |
| 554 | Q8 | — | 4 | 4 | no | — |
| 555 | Q8 | — | 6 | 4 | no | — |
| 556 | Q8 | — | 12 | 4 | no | — |
| 557 | D4 | — | 2 | 4 | no | — |
| 558 | D4 | — | 4 | 4 | no | — |
| 559 | D4 | — | 4 | 4 | no | — |
| 560 | D4 | — | 6 | 4 | no | — |
| 561 | D4 | — | 12 | 4 | no | — |
| 562 | D4 | — | 12 | 8 | no | — |
| 563 | D4 | — | 12 | 8 | no | — |
| 564 | D4 | — | 12 | 4 | no | — |
| 565 | C2×C4 | — | 2 | 4 | no | — |
| 566 | C2×C4 | — | 2 | 2 | no | — |
| 567 | C2×C4 | — | 3 | 2 | no | — |
| 568 | C2×C4 | — | 3 | 2 | no | — |
| 569 | C2×C4 | — | 3 | 2 | no | — |
| 570 | C2×C4 | — | 4 | 2 | no | — |
| 571 | C2×C4 | — | 4 | 4 | no | — |
| 572 | C2×C4 | — | 6 | 4 | no | — |
| 573 | C2×C4 | — | 6 | 4 | no | — |
| 574 | C2×C4 | — | 6 | 4 | no | — |
| 575 | C2×C4 | — | 6 | 2 | no | — |
| 576 | C2×C4 | — | 6 | 4 | no | — |
| 577 | C2×C4 | — | 6 | 4 | no | — |
| 578 | C2×C4 | — | 6 | 4 | no | — |
| 579 | C2×C4 | — | 6 | 2 | no | — |
| 580 | C2×C4 | — | 12 | 2 | no | — |
| 581 | C2×C4 | — | 12 | 2 | no | — |
| 582 | C2×C4 | — | 12 | 8 | no | — |
| 583 | C2×C4 | — | 12 | 8 | no | — |
| 584 | C2×C4 | — | 12 | 4 | no | — |
| 585 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 586 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 587 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 588 | C2×C4 | D3×#41 | 1 | 4 | yes | — |
| 589 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 590 | C8 | — | 2 | 4 | no | — |
| 591 | C8 | — | 3 | 8 | no | — |
| 592 | C2×C3 | — | 2 | 2 | no | — |
| 593 | C2×C3 | — | 8 | 2 | no | — |
| 594 | C2×C3 | C2×#532 | 1 | 1 | yes | characteristic |
| 595 | C2×C3 | C2×#575 | 1 | 2 | yes | — |
| 596 | D3 | — | 4 | 2 | no | — |
| 597 | D3 | — | 8 | 2 | no | — |
| 598 | C22 | — | 2 | 2 | no | — |
| 599 | C22 | — | 4 | 2 | no | — |
| 600 | C22 | — | 4 | 4 | no | — |
| 601 | C22 | — | 6 | 2 | no | — |
| 602 | C22 | — | 6 | 2 | no | — |
| 603 | C22 | — | 6 | 2 | no | — |
| 604 | C22 | — | 12 | 4 | no | — |
| 605 | C22 | — | 12 | 2 | no | — |
| 606 | C22 | — | 12 | 4 | no | — |
| 607 | C22 | #5668 | 1 | 2 | yes | — |
| 608 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 609 | C4 | — | 2 | 2 | no | — |
| 610 | C4 | — | 2 | 2 | no | — |
| 611 | C4 | — | 3 | 4 | no | — |
| 612 | C4 | — | 4 | 2 | no | — |
| 613 | C4 | — | 4 | 4 | no | — |
| 614 | C4 | — | 6 | 2 | no | — |
| 615 | C4 | — | 6 | 2 | no | — |
| 616 | C4 | — | 12 | 2 | no | — |
| 617 | C4 | — | 12 | 4 | no | — |
| 618 | C4 | #5668 | 1 | 2 | yes | — |
| 619 | C4 | C2×D3×#41 | 1 | 2 | yes | — |
| 620 | C3 | #60676 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 621 | C2 | — | 2 | 2 | no | — |
| 622 | C2 | — | 8 | 2 | no | — |
| 623 | C2 | — | 12 | 2 | no | — |
| 624 | C2 | — | 24 | 2 | no | — |
| 625 | C2 | C2×#5668 | 1 | 1 | yes | characteristic |
| 626 | C2 | D3×#575 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #86257 | C2 | semidirect |
| 2. #86219 | C2 | semidirect |
| 3. C3×#3135 | C2 | semidirect |
| 4. #83340 | C2 | semidirect |
| 5. #83286 | C2 | semidirect |
| 6. #81728 | C2 | semidirect |
| 7. #81704 | C2 | semidirect |
| 8. #81665 | C2 | semidirect |
| 9. #81664 | C2 | semidirect |
| 10. #78839 | C2 | semidirect |
| 11. #78818 | C2 | semidirect |
| 12. #78497 | C2 | semidirect |
| 13. C2×#4707 | C2 | semidirect |
| 40. C3×#491 | C22 | semidirect |
| 41. C3×#490 | C22 | semidirect |
| 42. C3×#489 | C22 | semidirect |
| 47. #5086 | C22 | semidirect |
| 48. #5081 | C22 | semidirect |
| 49. #5074 | C22 | semidirect |
| 50. #5064 | C22 | semidirect |
| 51. #5060 | C22 | semidirect |
| 52. #5058 | C22 | semidirect |
| 57. #4790 | C22 | semidirect |
| 58. #4788 | C22 | semidirect |
| 61. #4758 | C22 | semidirect |
| 62. #4756 | C22 | semidirect |
| 63. #4714 | C22 | semidirect |
| 64. #4713 | C22 | semidirect |
| 67. #4703 | C22 | semidirect |
| 77. #3135 | D3 | semidirect |
| 208. #491 | C2×D3 | semidirect |
| 210. #490 | C2×D3 | semidirect |
| 212. #489 | C2×D3 | semidirect |
| 304. C2×C3⋊C8 | #41 | semidirect |
| 620. C3 | #60676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #86257 | 2 |
| #86219 | 2 |
| C3×#3135 | 2 |
| #83340 | 2 |
| #83286 | 2 |
| #81728 | 2 |
| #81704 | 2 |
| #81665 | 2 |
| #81664 | 2 |
| #78839 | 2 |
| #78818 | 2 |
| #78497 | 2 |
| C2×#4707 | 2 |
| #60676 | 3 |