Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
3326 conjugacy classes of subgroups.
The subgroup lattice has 604 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×#916 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C22×#912 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×#5716 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#5668 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×C3×#496 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#5167 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C2×#5154 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C2×#5074 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#5060 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #81844 | C2 | 1 | 16 | yes | maximal, direct product factor |
| 11 | C2×#4715 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×D3×#97 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C2×#3150 | — | 3 | 1 | no | maximal, Sylow |
| 14 | C22×#239 | C22 | 1 | 1 | yes | characteristic |
| 15 | C22×#237 | C22 | 1 | 1 | yes | characteristic |
| 16 | C22×#237 | C22 | 1 | 2 | yes | — |
| 17 | C22×C3×SD16 | C22 | 1 | 2 | yes | — |
| 18 | C22×C3×D8 | C22 | 1 | 2 | yes | — |
| 19 | C2×C3×#127 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×C3×#124 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#944 | C22 | 1 | 1 | yes | characteristic |
| 22 | C22×#216 | C22 | 1 | 2 | yes | — |
| 23 | C2×#940 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#938 | — | 2 | 2 | no | — |
| 25 | C2×#936 | C22 | 1 | 2 | yes | — |
| 26 | C2×D4×Dic3 | — | 2 | 2 | no | — |
| 27 | C22×#214 | C22 | 1 | 2 | yes | — |
| 28 | C22×#214 | C22 | 1 | 2 | yes | — |
| 29 | C22×#213 | C22 | 1 | 2 | yes | — |
| 30 | C2×#916 | — | 2 | 16 | no | — |
| 31 | C2×#916 | C22 | 1 | 16 | yes | complemented |
| 32 | C2×#912 | — | 2 | 16 | no | — |
| 33 | C2×#912 | C22 | 1 | 16 | yes | complemented |
| 34 | C22×Dic12 | C22 | 1 | 2 | yes | — |
| 35 | C22×#204 | C22 | 1 | 2 | yes | — |
| 36 | C22×D3×C8 | C22 | 1 | 2 | yes | — |
| 37 | #5716 | — | 2 | 4 | no | — |
| 38 | #5716 | C22 | 1 | 8 | yes | complemented |
| 39 | #5668 | — | 2 | 4 | no | — |
| 40 | #5668 | C22 | 1 | 8 | yes | complemented |
| 41 | C2×#884 | — | 2 | 2 | no | — |
| 42 | C2×#67⋊C4 | — | 2 | 2 | no | — |
| 43 | C2×#875 | C22 | 1 | 1 | yes | characteristic |
| 44 | C2×C42×D3 | C22 | 1 | 1 | yes | characteristic |
| 45 | C2×#869 | C22 | 1 | 1 | yes | characteristic |
| 46 | C3×#496 | C22 | 1 | 8 | yes | complemented |
| 47 | C2×C3×#97 | C22 | 1 | 1 | yes | characteristic |
| 48 | #5167 | C22 | 1 | 16 | yes | complemented |
| 49 | #5154 | C22 | 1 | 16 | yes | complemented |
| 50 | C2×#815 | C22 | 1 | 2 | yes | — |
| 51 | #5074 | C22 | 1 | 8 | yes | complemented |
| 52 | #5060 | C22 | 1 | 8 | yes | complemented |
| 53 | C2×#803 | C22 | 1 | 1 | yes | characteristic |
| 54 | #4715 | C22 | 1 | 8 | yes | complemented |
| 55 | D3×#97 | C22 | 1 | 8 | yes | complemented |
| 56 | C22×#135 | — | 3 | 2 | no | — |
| 57 | C22×#135 | — | 3 | 2 | no | — |
| 58 | C2×#532 | — | 3 | 1 | no | — |
| 59 | C2×#532 | — | 3 | 1 | no | — |
| 60 | #3150 | — | 3 | 16 | no | — |
| 61 | C2×#497 | — | 3 | 1 | no | — |
| 62 | C2×#497 | — | 3 | 2 | no | — |
| 63 | C2×#497 | — | 3 | 1 | no | — |
| 64 | C2×#496 | — | 3 | 2 | no | — |
| 65 | C2×#496 | — | 3 | 1 | no | — |
| 66 | C2×#496 | D3 | 1 | 1 | yes | characteristic, complemented |
| 67 | C22×#97 | — | 3 | 1 | no | — |
| 68 | C22×C3×Q8 | C23 | 1 | 1 | yes | characteristic |
| 69 | C22×C3×D4 | — | 2 | 2 | no | — |
| 70 | C22×C3×D4 | C23 | 1 | 1 | yes | characteristic |
| 71 | C22×C3×D4 | C23 | 1 | 2 | yes | — |
| 72 | C22×#67 | — | 2 | 1 | no | — |
| 73 | C22×#67 | — | 2 | 2 | no | — |
| 74 | C22×#67 | — | 2 | 2 | no | — |
| 75 | C23×Dic3 | — | 2 | 1 | no | — |
| 76 | C23×Dic3 | — | 2 | 2 | no | — |
| 77 | C2×#239 | — | 2 | 2 | no | — |
| 78 | C2×#239 | — | 2 | 8 | no | — |
| 79 | C2×#239 | C23 | 1 | 4 | yes | — |
| 80 | C2×#237 | — | 2 | 8 | no | — |
| 81 | C2×#237 | — | 2 | 8 | no | — |
| 82 | C2×#237 | — | 2 | 8 | no | — |
| 83 | C2×#237 | — | 2 | 2 | no | — |
| 84 | C2×#237 | — | 2 | 4 | no | — |
| 85 | C2×#237 | C23 | 1 | 4 | yes | — |
| 86 | C2×#237 | C23 | 1 | 8 | yes | — |
| 87 | C22×D12 | — | 2 | 1 | no | — |
| 88 | C22×D12 | C23 | 1 | 1 | yes | characteristic |
| 89 | C22×C4×D3 | — | 2 | 1 | no | — |
| 90 | C22×C4×D3 | D4 | 1 | 2 | yes | — |
| 91 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 92 | C22×Dic6 | C23 | 1 | 2 | yes | — |
| 93 | C22×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×C3×SD16 | — | 2 | 8 | no | — |
| 95 | C2×C3×SD16 | C23 | 1 | 8 | yes | — |
| 96 | C2×C3×D8 | — | 2 | 8 | no | — |
| 97 | C2×C3×D8 | C23 | 1 | 8 | yes | — |
| 98 | C22×C3×C8 | C23 | 1 | 2 | yes | — |
| 99 | C3×#127 | — | 2 | 2 | no | — |
| 100 | C3×#127 | C23 | 1 | 4 | yes | — |
| 101 | C3×#124 | — | 2 | 2 | no | — |
| 102 | C3×#124 | C23 | 1 | 4 | yes | — |
| 103 | C2×C3×C22⋊C4 | — | 2 | 2 | no | — |
| 104 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 105 | C2×#217 | — | 2 | 4 | no | — |
| 106 | #944 | — | 2 | 2 | no | — |
| 107 | #944 | C23 | 1 | 4 | yes | — |
| 108 | C2×#216 | — | 2 | 8 | no | — |
| 109 | C2×#216 | C23 | 1 | 8 | yes | — |
| 110 | #940 | — | 2 | 2 | no | — |
| 111 | #940 | C23 | 1 | 4 | yes | — |
| 112 | #938 | — | 2 | 16 | no | — |
| 113 | #936 | — | 2 | 4 | no | — |
| 114 | #936 | C23 | 1 | 8 | yes | — |
| 115 | D4×Dic3 | — | 2 | 16 | no | — |
| 116 | C2×#214 | — | 2 | 8 | no | — |
| 117 | C2×#214 | — | 2 | 8 | no | — |
| 118 | C2×#214 | C23 | 1 | 8 | yes | — |
| 119 | C2×#214 | C23 | 1 | 8 | yes | — |
| 120 | C2×#213 | — | 2 | 8 | no | — |
| 121 | C2×#213 | C23 | 1 | 8 | yes | — |
| 122 | C2×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 123 | C2×C4⋊Dic3 | — | 2 | 2 | no | — |
| 124 | C2×Dic3⋊C4 | — | 2 | 2 | no | — |
| 125 | C2×C4×Dic3 | D4 | 1 | 2 | yes | — |
| 126 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 127 | C22×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 128 | #916 | — | 2 | 64 | no | — |
| 129 | #912 | — | 2 | 64 | no | — |
| 130 | C2×Dic12 | — | 2 | 8 | no | — |
| 131 | C2×Dic12 | C23 | 1 | 8 | yes | — |
| 132 | C2×#204 | — | 2 | 8 | no | — |
| 133 | C2×#204 | C23 | 1 | 8 | yes | — |
| 134 | C2×D3×C8 | D4 | 1 | 16 | yes | complemented |
| 135 | C2×D3×C8 | C23 | 1 | 8 | yes | — |
| 136 | #884 | — | 2 | 16 | no | — |
| 137 | #67⋊C4 | — | 2 | 16 | no | — |
| 138 | #875 | — | 2 | 2 | no | — |
| 139 | #875 | C23 | 1 | 4 | yes | — |
| 140 | C42×D3 | D4 | 1 | 4 | yes | — |
| 141 | C42×D3 | C23 | 1 | 4 | yes | — |
| 142 | #869 | — | 2 | 2 | no | — |
| 143 | #869 | C23 | 1 | 4 | yes | — |
| 144 | C3×#97 | C23 | 1 | 4 | yes | — |
| 145 | #815 | C23 | 1 | 8 | yes | — |
| 146 | #803 | C23 | 1 | 4 | yes | — |
| 147 | C22×#41 | — | 3 | 1 | no | — |
| 148 | C22×#41 | — | 3 | 2 | no | — |
| 149 | C22×#41 | — | 3 | 1 | no | — |
| 150 | C2×#135 | — | 3 | 16 | no | — |
| 151 | C2×#135 | — | 3 | 16 | no | — |
| 152 | C2×#135 | — | 6 | 16 | no | — |
| 153 | C2×#135 | — | 6 | 16 | no | — |
| 154 | C22×Q16 | — | 3 | 2 | no | — |
| 155 | C22×Q16 | — | 3 | 2 | no | — |
| 156 | C22×SD16 | — | 3 | 2 | no | — |
| 157 | C22×SD16 | — | 3 | 2 | no | — |
| 158 | C22×SD16 | — | 3 | 2 | no | — |
| 159 | C22×SD16 | C2×D3 | 1 | 2 | yes | — |
| 160 | C22×D8 | — | 3 | 2 | no | — |
| 161 | C22×D8 | C2×D3 | 1 | 2 | yes | — |
| 162 | C23×C8 | — | 3 | 2 | no | — |
| 163 | #532 | — | 3 | 8 | no | — |
| 164 | #532 | — | 3 | 8 | no | — |
| 165 | #532 | — | 6 | 4 | no | — |
| 166 | #532 | — | 6 | 4 | no | — |
| 167 | C2×C4⋊Q8 | — | 3 | 1 | no | — |
| 168 | C2×C4⋊Q8 | — | 3 | 1 | no | — |
| 169 | C2×#127 | — | 3 | 1 | no | — |
| 170 | C2×#127 | C2×D3 | 1 | 1 | yes | characteristic |
| 171 | C2×#124 | — | 3 | 2 | no | — |
| 172 | C2×#124 | — | 3 | 1 | no | — |
| 173 | C2×#124 | C2×D3 | 1 | 1 | yes | characteristic |
| 174 | C2×#121 | — | 6 | 2 | no | — |
| 175 | C2×#121 | — | 6 | 2 | no | — |
| 176 | C2×C4×D4 | — | 6 | 2 | no | — |
| 177 | C2×C4×D4 | — | 6 | 2 | no | — |
| 178 | C22×C42 | — | 3 | 1 | no | — |
| 179 | #497 | — | 3 | 16 | no | — |
| 180 | #497 | — | 3 | 8 | no | — |
| 181 | #497 | — | 3 | 8 | no | — |
| 182 | #496 | — | 3 | 16 | no | — |
| 183 | #496 | — | 3 | 8 | no | — |
| 184 | #496 | C2×D3 | 1 | 8 | yes | complemented |
| 185 | C2×#97 | — | 3 | 2 | no | — |
| 186 | C2×#97 | — | 3 | 1 | no | — |
| 187 | C2×#97 | — | 3 | 8 | no | — |
| 188 | C2×#97 | C2×D3 | 1 | 1 | yes | characteristic |
| 189 | C24×C3 | — | 2 | 2 | no | — |
| 190 | C24×C3 | — | 2 | 1 | no | — |
| 191 | C23×D3 | — | 2 | 1 | no | — |
| 192 | C23×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 194 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 195 | C2×C3×Q8 | C24 | 1 | 2 | yes | — |
| 196 | C2×C3×D4 | — | 2 | 4 | no | — |
| 197 | C2×C3×D4 | — | 2 | 4 | no | — |
| 198 | C2×C3×D4 | — | 2 | 4 | no | — |
| 199 | C2×C3×D4 | — | 2 | 8 | no | — |
| 200 | C2×C3×D4 | — | 2 | 2 | no | — |
| 201 | C2×C3×D4 | — | 2 | 1 | no | — |
| 202 | C2×C3×D4 | — | 4 | 8 | no | — |
| 203 | C2×C3×D4 | C24 | 1 | 4 | yes | — |
| 204 | C2×C3×D4 | C24 | 1 | 2 | yes | — |
| 205 | C22×C3×C4 | — | 2 | 1 | no | — |
| 206 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 207 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 208 | C2×#67 | — | 2 | 4 | no | — |
| 209 | C2×#67 | — | 2 | 8 | no | — |
| 210 | C2×#67 | — | 2 | 8 | no | — |
| 211 | C2×#67 | — | 4 | 8 | no | — |
| 212 | C2×#67 | — | 4 | 4 | no | — |
| 213 | C2×#67 | — | 4 | 8 | no | — |
| 214 | C22×Dic3 | — | 2 | 1 | no | — |
| 215 | C22×Dic3 | — | 2 | 2 | no | — |
| 216 | C22×Dic3 | — | 2 | 4 | no | — |
| 217 | C22×Dic3 | — | 2 | 8 | no | — |
| 218 | C22×Dic3 | — | 4 | 4 | no | — |
| 219 | C22×Dic3 | — | 4 | 8 | no | — |
| 220 | C22×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 221 | C22×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 222 | #239 | — | 2 | 16 | no | — |
| 223 | #239 | — | 4 | 8 | no | — |
| 224 | #237 | — | 2 | 16 | no | — |
| 225 | #237 | — | 2 | 16 | no | — |
| 226 | #237 | — | 2 | 16 | no | — |
| 227 | #237 | — | 4 | 8 | no | — |
| 228 | #237 | — | 4 | 16 | no | — |
| 229 | C2×D12 | — | 2 | 4 | no | — |
| 230 | C2×D12 | — | 2 | 4 | no | — |
| 231 | C2×D12 | — | 2 | 1 | no | — |
| 232 | C2×D12 | — | 4 | 4 | no | — |
| 233 | C2×D12 | C24 | 1 | 2 | yes | — |
| 234 | C2×C4×D3 | — | 2 | 4 | no | — |
| 235 | C2×C4×D3 | — | 4 | 4 | no | — |
| 236 | C2×C4×D3 | — | 4 | 4 | no | — |
| 237 | C2×C4×D3 | C2×D4 | 1 | 8 | yes | — |
| 238 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 239 | C2×C4×D3 | C2×D4 | 1 | 8 | yes | — |
| 240 | C2×C4×D3 | C24 | 1 | 2 | yes | — |
| 241 | C2×Dic6 | — | 2 | 4 | no | — |
| 242 | C2×Dic6 | — | 2 | 4 | no | — |
| 243 | C2×Dic6 | — | 2 | 4 | no | — |
| 244 | C2×Dic6 | — | 2 | 2 | no | — |
| 245 | C2×Dic6 | — | 2 | 1 | no | — |
| 246 | C2×Dic6 | C24 | 1 | 4 | yes | — |
| 247 | C2×Dic6 | C24 | 1 | 2 | yes | — |
| 248 | C3×SD16 | — | 2 | 16 | no | — |
| 249 | C3×D8 | — | 2 | 16 | no | — |
| 250 | C2×C3×C8 | C2×D4 | 1 | 8 | yes | — |
| 251 | C2×C3×C8 | C24 | 1 | 4 | yes | — |
| 252 | C3×C22⋊C4 | — | 2 | 8 | no | — |
| 253 | C3×C42 | C2×D4 | 1 | 2 | yes | — |
| 254 | C3×C42 | C24 | 1 | 2 | yes | — |
| 255 | #217 | — | 2 | 16 | no | — |
| 256 | #216 | — | 2 | 16 | no | — |
| 257 | #214 | — | 2 | 16 | no | — |
| 258 | #214 | — | 2 | 16 | no | — |
| 259 | #213 | — | 2 | 16 | no | — |
| 260 | (C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 261 | C4⋊Dic3 | — | 2 | 8 | no | — |
| 262 | Dic3⋊C4 | — | 2 | 8 | no | — |
| 263 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 264 | C4×Dic3 | C2×D4 | 1 | 8 | yes | — |
| 265 | C4×Dic3 | C24 | 1 | 2 | yes | — |
| 266 | C2×C3⋊C8 | C2×D4 | 1 | 8 | yes | — |
| 267 | C2×C3⋊C8 | C24 | 1 | 4 | yes | — |
| 268 | Dic12 | — | 2 | 16 | no | — |
| 269 | #204 | — | 2 | 16 | no | — |
| 270 | D3×C8 | C2×D4 | 1 | 32 | yes | complemented |
| 271 | C2×#41 | — | 3 | 4 | no | — |
| 272 | C2×#41 | — | 3 | 8 | no | — |
| 273 | C2×#41 | — | 3 | 4 | no | — |
| 274 | C2×#41 | — | 6 | 2 | no | — |
| 275 | C2×#41 | — | 6 | 4 | no | — |
| 276 | C2×#41 | — | 6 | 2 | no | — |
| 277 | C2×#41 | — | 6 | 8 | no | — |
| 278 | C2×#41 | — | 6 | 8 | no | — |
| 279 | C2×#41 | — | 6 | 8 | no | — |
| 280 | C2×#41 | — | 6 | 8 | no | — |
| 281 | C22×Q8 | — | 3 | 2 | no | — |
| 282 | C22×Q8 | — | 3 | 1 | no | — |
| 283 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 284 | C22×D4 | — | 2 | 2 | no | — |
| 285 | C22×D4 | — | 3 | 1 | no | — |
| 286 | C22×D4 | — | 6 | 1 | no | — |
| 287 | C22×D4 | — | 6 | 2 | no | — |
| 288 | C22×D4 | — | 6 | 1 | no | — |
| 289 | C22×D4 | — | 6 | 2 | no | — |
| 290 | C22×D4 | C22×D3 | 1 | 2 | yes | — |
| 291 | C22×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 292 | C23×C4 | — | 3 | 1 | no | — |
| 293 | C23×C4 | — | 3 | 2 | no | — |
| 294 | C23×C4 | — | 6 | 1 | no | — |
| 295 | C23×C4 | — | 6 | 1 | no | — |
| 296 | C23×C4 | — | 6 | 2 | no | — |
| 297 | #135 | — | 6 | 64 | no | — |
| 298 | #135 | — | 6 | 64 | no | — |
| 299 | C2×Q16 | — | 3 | 8 | no | — |
| 300 | C2×Q16 | — | 3 | 8 | no | — |
| 301 | C2×Q16 | — | 6 | 8 | no | — |
| 302 | C2×Q16 | — | 6 | 8 | no | — |
| 303 | C2×SD16 | — | 2 | 8 | no | — |
| 304 | C2×SD16 | — | 3 | 8 | no | — |
| 305 | C2×SD16 | — | 3 | 8 | no | — |
| 306 | C2×SD16 | — | 3 | 8 | no | — |
| 307 | C2×SD16 | — | 6 | 8 | no | — |
| 308 | C2×SD16 | — | 6 | 8 | no | — |
| 309 | C2×SD16 | — | 6 | 8 | no | — |
| 310 | C2×SD16 | C22×D3 | 1 | 8 | yes | — |
| 311 | C2×D8 | — | 2 | 8 | no | — |
| 312 | C2×D8 | — | 3 | 8 | no | — |
| 313 | C2×D8 | — | 6 | 8 | no | — |
| 314 | C2×D8 | C22×D3 | 1 | 8 | yes | — |
| 315 | C22×C8 | — | 3 | 2 | no | — |
| 316 | C22×C8 | — | 3 | 16 | no | — |
| 317 | C22×C8 | — | 3 | 8 | no | — |
| 318 | C22×C8 | C22×D3 | 1 | 2 | yes | — |
| 319 | C4⋊Q8 | — | 3 | 4 | no | — |
| 320 | C4⋊Q8 | — | 3 | 4 | no | — |
| 321 | C4⋊Q8 | — | 6 | 2 | no | — |
| 322 | C4⋊Q8 | — | 6 | 2 | no | — |
| 323 | #127 | — | 2 | 2 | no | — |
| 324 | #127 | — | 3 | 4 | no | — |
| 325 | #127 | — | 6 | 2 | no | — |
| 326 | #127 | C22×D3 | 1 | 4 | yes | — |
| 327 | #124 | — | 2 | 2 | no | — |
| 328 | #124 | — | 3 | 8 | no | — |
| 329 | #124 | — | 3 | 4 | no | — |
| 330 | #124 | — | 6 | 4 | no | — |
| 331 | #124 | — | 6 | 2 | no | — |
| 332 | #124 | C22×D3 | 1 | 4 | yes | — |
| 333 | #121 | — | 6 | 16 | no | — |
| 334 | #121 | — | 6 | 16 | no | — |
| 335 | C4×D4 | — | 6 | 16 | no | — |
| 336 | C4×D4 | — | 6 | 16 | no | — |
| 337 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 338 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 339 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 340 | C2×C22⋊C4 | — | 6 | 4 | no | — |
| 341 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 342 | C2×C42 | — | 3 | 2 | no | — |
| 343 | C2×C42 | — | 3 | 1 | no | — |
| 344 | C2×C42 | — | 3 | 4 | no | — |
| 345 | C2×C42 | — | 3 | 4 | no | — |
| 346 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 347 | #97 | — | 3 | 8 | no | — |
| 348 | #97 | — | 3 | 4 | no | — |
| 349 | #97 | C22×D3 | 1 | 4 | yes | — |
| 350 | C23×C3 | — | 2 | 4 | no | — |
| 351 | C23×C3 | — | 2 | 2 | no | — |
| 352 | C23×C3 | — | 4 | 4 | no | — |
| 353 | C23×C3 | — | 4 | 2 | no | — |
| 354 | C23×C3 | — | 4 | 4 | no | — |
| 355 | C23×C3 | — | 4 | 8 | no | — |
| 356 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 357 | C22×D3 | — | 2 | 4 | no | — |
| 358 | C22×D3 | — | 2 | 2 | no | — |
| 359 | C22×D3 | — | 4 | 2 | no | — |
| 360 | C22×D3 | — | 4 | 4 | no | — |
| 361 | C22×D3 | #127 | 1 | 4 | yes | — |
| 362 | C22×D3 | C22×D4 | 1 | 2 | yes | — |
| 363 | C3×Q8 | — | 2 | 4 | no | — |
| 364 | C3×Q8 | — | 4 | 2 | no | — |
| 365 | C3×D4 | — | 2 | 4 | no | — |
| 366 | C3×D4 | — | 2 | 4 | no | — |
| 367 | C3×D4 | — | 2 | 4 | no | — |
| 368 | C3×D4 | — | 4 | 16 | no | — |
| 369 | C3×D4 | — | 4 | 4 | no | — |
| 370 | C3×D4 | — | 4 | 2 | no | — |
| 371 | C2×C3×C4 | — | 2 | 4 | no | — |
| 372 | C2×C3×C4 | — | 2 | 2 | no | — |
| 373 | C2×C3×C4 | — | 4 | 2 | no | — |
| 374 | C2×C3×C4 | C22×D4 | 1 | 4 | yes | — |
| 375 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 376 | C2×C3×C4 | C22×D4 | 1 | 4 | yes | — |
| 377 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 378 | #67 | — | 4 | 16 | no | — |
| 379 | #67 | — | 4 | 8 | no | — |
| 380 | #67 | — | 4 | 16 | no | — |
| 381 | C2×Dic3 | — | 2 | 4 | no | — |
| 382 | C2×Dic3 | — | 2 | 2 | no | — |
| 383 | C2×Dic3 | — | 2 | 4 | no | — |
| 384 | C2×Dic3 | — | 4 | 4 | no | — |
| 385 | C2×Dic3 | — | 4 | 2 | no | — |
| 386 | C2×Dic3 | — | 4 | 8 | no | — |
| 387 | C2×Dic3 | — | 4 | 16 | no | — |
| 388 | C2×Dic3 | #127 | 1 | 4 | yes | — |
| 389 | C2×Dic3 | C22×D4 | 1 | 4 | yes | — |
| 390 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 391 | D12 | — | 2 | 4 | no | — |
| 392 | D12 | — | 4 | 8 | no | — |
| 393 | D12 | — | 4 | 2 | no | — |
| 394 | C4×D3 | — | 4 | 8 | no | — |
| 395 | C4×D3 | — | 4 | 8 | no | — |
| 396 | C4×D3 | #127 | 1 | 8 | yes | — |
| 397 | C4×D3 | C22×D4 | 1 | 8 | yes | — |
| 398 | Dic6 | — | 2 | 4 | no | — |
| 399 | Dic6 | — | 2 | 4 | no | — |
| 400 | Dic6 | — | 2 | 4 | no | — |
| 401 | Dic6 | — | 4 | 4 | no | — |
| 402 | Dic6 | — | 4 | 2 | no | — |
| 403 | C3×C8 | C22×D4 | 1 | 8 | yes | — |
| 404 | C3⋊C8 | C22×D4 | 1 | 8 | yes | — |
| 405 | C24 | — | 2 | 1 | no | — |
| 406 | C24 | — | 2 | 2 | no | — |
| 407 | C24 | — | 3 | 1 | no | — |
| 408 | C24 | — | 6 | 1 | no | — |
| 409 | #41 | — | 6 | 16 | no | — |
| 410 | #41 | — | 6 | 16 | no | — |
| 411 | #41 | — | 6 | 16 | no | — |
| 412 | #41 | — | 6 | 16 | no | — |
| 413 | #41 | — | 12 | 8 | no | — |
| 414 | #41 | — | 12 | 16 | no | — |
| 415 | #41 | — | 12 | 8 | no | — |
| 416 | C2×Q8 | — | 2 | 1 | no | — |
| 417 | C2×Q8 | — | 2 | 4 | no | — |
| 418 | C2×Q8 | — | 3 | 4 | no | — |
| 419 | C2×Q8 | — | 3 | 2 | no | — |
| 420 | C2×Q8 | — | 6 | 2 | no | — |
| 421 | C2×Q8 | — | 6 | 1 | no | — |
| 422 | C2×Q8 | — | 6 | 4 | no | — |
| 423 | C2×Q8 | — | 6 | 4 | no | — |
| 424 | C2×Q8 | — | 6 | 4 | no | — |
| 425 | C2×Q8 | C23×D3 | 1 | 2 | yes | — |
| 426 | C2×D4 | — | 2 | 4 | no | — |
| 427 | C2×D4 | — | 2 | 4 | no | — |
| 428 | C2×D4 | — | 2 | 4 | no | — |
| 429 | C2×D4 | — | 2 | 8 | no | — |
| 430 | C2×D4 | — | 2 | 1 | no | — |
| 431 | C2×D4 | — | 2 | 2 | no | — |
| 432 | C2×D4 | — | 3 | 2 | no | — |
| 433 | C2×D4 | — | 4 | 8 | no | — |
| 434 | C2×D4 | — | 6 | 4 | no | — |
| 435 | C2×D4 | — | 6 | 8 | no | — |
| 436 | C2×D4 | — | 6 | 4 | no | — |
| 437 | C2×D4 | — | 6 | 8 | no | — |
| 438 | C2×D4 | — | 6 | 4 | no | — |
| 439 | C2×D4 | — | 6 | 1 | no | — |
| 440 | C2×D4 | — | 12 | 4 | no | — |
| 441 | C2×D4 | — | 12 | 8 | no | — |
| 442 | C2×D4 | — | 12 | 4 | no | — |
| 443 | C2×D4 | — | 12 | 8 | no | — |
| 444 | C2×D4 | C23×D3 | 1 | 4 | yes | — |
| 445 | C2×D4 | C23×D3 | 1 | 2 | yes | — |
| 446 | C22×C4 | — | 2 | 1 | no | — |
| 447 | C22×C4 | — | 3 | 1 | no | — |
| 448 | C22×C4 | — | 3 | 2 | no | — |
| 449 | C22×C4 | — | 3 | 8 | no | — |
| 450 | C22×C4 | — | 3 | 2 | no | — |
| 451 | C22×C4 | — | 3 | 2 | no | — |
| 452 | C22×C4 | — | 3 | 8 | no | — |
| 453 | C22×C4 | — | 6 | 4 | no | — |
| 454 | C22×C4 | — | 6 | 4 | no | — |
| 455 | C22×C4 | — | 6 | 8 | no | — |
| 456 | C22×C4 | — | 6 | 2 | no | — |
| 457 | C22×C4 | — | 6 | 1 | no | — |
| 458 | C22×C4 | — | 12 | 4 | no | — |
| 459 | C22×C4 | — | 12 | 4 | no | — |
| 460 | C22×C4 | — | 12 | 4 | no | — |
| 461 | C22×C4 | — | 12 | 8 | no | — |
| 462 | C22×C4 | D3×D4 | 1 | 2 | yes | — |
| 463 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 464 | Q16 | — | 6 | 16 | no | — |
| 465 | Q16 | — | 6 | 16 | no | — |
| 466 | SD16 | — | 2 | 16 | no | — |
| 467 | SD16 | — | 6 | 16 | no | — |
| 468 | SD16 | — | 6 | 16 | no | — |
| 469 | SD16 | — | 6 | 16 | no | — |
| 470 | D8 | — | 2 | 16 | no | — |
| 471 | D8 | — | 6 | 16 | no | — |
| 472 | C2×C8 | — | 3 | 8 | no | — |
| 473 | C2×C8 | — | 3 | 4 | no | — |
| 474 | C2×C8 | — | 3 | 32 | no | — |
| 475 | C2×C8 | D3×D4 | 1 | 8 | yes | — |
| 476 | C2×C8 | C23×D3 | 1 | 4 | yes | — |
| 477 | C4⋊C4 | — | 6 | 8 | no | — |
| 478 | C4⋊C4 | — | 6 | 8 | no | — |
| 479 | C22⋊C4 | — | 2 | 8 | no | — |
| 480 | C22⋊C4 | — | 6 | 16 | no | — |
| 481 | C22⋊C4 | — | 6 | 8 | no | — |
| 482 | C42 | — | 3 | 8 | no | — |
| 483 | C42 | — | 3 | 2 | no | — |
| 484 | C42 | — | 3 | 2 | no | — |
| 485 | C42 | D3×D4 | 1 | 2 | yes | — |
| 486 | C42 | C23×D3 | 1 | 2 | yes | — |
| 487 | C22×C3 | — | 4 | 4 | no | — |
| 488 | C22×C3 | — | 4 | 2 | no | — |
| 489 | C22×C3 | — | 4 | 4 | no | — |
| 490 | C22×C3 | — | 4 | 8 | no | — |
| 491 | C22×C3 | — | 8 | 4 | no | — |
| 492 | C22×C3 | — | 8 | 8 | no | — |
| 493 | C22×C3 | C2×#127 | 1 | 2 | yes | — |
| 494 | C22×C3 | #575 | 1 | 4 | yes | — |
| 495 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 496 | C2×D3 | — | 2 | 8 | no | — |
| 497 | C2×D3 | — | 2 | 4 | no | — |
| 498 | C2×D3 | — | 4 | 2 | no | — |
| 499 | C2×D3 | — | 4 | 4 | no | — |
| 500 | C2×D3 | — | 8 | 4 | no | — |
| 501 | C2×D3 | C2×#127 | 1 | 4 | yes | — |
| 502 | C3×C4 | — | 2 | 4 | no | — |
| 503 | C3×C4 | — | 4 | 2 | no | — |
| 504 | C3×C4 | C2×#127 | 1 | 2 | yes | — |
| 505 | C3×C4 | C23×D4 | 1 | 2 | yes | — |
| 506 | Dic3 | — | 2 | 4 | no | — |
| 507 | Dic3 | — | 4 | 4 | no | — |
| 508 | Dic3 | — | 4 | 2 | no | — |
| 509 | Dic3 | C2×#127 | 1 | 4 | yes | — |
| 510 | C23 | — | 2 | 2 | no | — |
| 511 | C23 | — | 2 | 4 | no | — |
| 512 | C23 | — | 3 | 2 | no | — |
| 513 | C23 | — | 3 | 4 | no | — |
| 514 | C23 | — | 4 | 2 | no | — |
| 515 | C23 | — | 4 | 4 | no | — |
| 516 | C23 | — | 4 | 8 | no | — |
| 517 | C23 | — | 4 | 4 | no | — |
| 518 | C23 | — | 6 | 4 | no | — |
| 519 | C23 | — | 6 | 2 | no | — |
| 520 | C23 | — | 12 | 2 | no | — |
| 521 | C23 | — | 12 | 4 | no | — |
| 522 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 523 | Q8 | — | 2 | 4 | no | — |
| 524 | Q8 | — | 4 | 2 | no | — |
| 525 | Q8 | — | 6 | 4 | no | — |
| 526 | Q8 | — | 6 | 4 | no | — |
| 527 | Q8 | — | 6 | 4 | no | — |
| 528 | Q8 | — | 12 | 4 | no | — |
| 529 | Q8 | — | 12 | 2 | no | — |
| 530 | D4 | — | 2 | 4 | no | — |
| 531 | D4 | — | 2 | 4 | no | — |
| 532 | D4 | — | 2 | 4 | no | — |
| 533 | D4 | — | 4 | 16 | no | — |
| 534 | D4 | — | 4 | 2 | no | — |
| 535 | D4 | — | 4 | 4 | no | — |
| 536 | D4 | — | 6 | 4 | no | — |
| 537 | D4 | — | 12 | 8 | no | — |
| 538 | D4 | — | 12 | 16 | no | — |
| 539 | D4 | — | 12 | 8 | no | — |
| 540 | D4 | — | 12 | 16 | no | — |
| 541 | D4 | — | 12 | 2 | no | — |
| 542 | C2×C4 | — | 2 | 4 | no | — |
| 543 | C2×C4 | — | 2 | 2 | no | — |
| 544 | C2×C4 | — | 3 | 2 | no | — |
| 545 | C2×C4 | — | 3 | 4 | no | — |
| 546 | C2×C4 | — | 3 | 8 | no | — |
| 547 | C2×C4 | — | 3 | 8 | no | — |
| 548 | C2×C4 | — | 3 | 4 | no | — |
| 549 | C2×C4 | — | 4 | 2 | no | — |
| 550 | C2×C4 | — | 6 | 4 | no | — |
| 551 | C2×C4 | — | 6 | 4 | no | — |
| 552 | C2×C4 | — | 6 | 2 | no | — |
| 553 | C2×C4 | — | 12 | 8 | no | — |
| 554 | C2×C4 | — | 12 | 8 | no | — |
| 555 | C2×C4 | — | 12 | 8 | no | — |
| 556 | C2×C4 | — | 12 | 16 | no | — |
| 557 | C2×C4 | — | 12 | 4 | no | — |
| 558 | C2×C4 | — | 12 | 2 | no | — |
| 559 | C2×C4 | C2×D3×D4 | 1 | 4 | yes | — |
| 560 | C2×C4 | C2×D3×D4 | 1 | 4 | yes | — |
| 561 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 562 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 563 | C8 | — | 3 | 8 | no | — |
| 564 | C8 | C2×D3×D4 | 1 | 8 | yes | — |
| 565 | C2×C3 | — | 8 | 2 | no | — |
| 566 | C2×C3 | — | 8 | 4 | no | — |
| 567 | C2×C3 | #3150 | 1 | 4 | yes | complemented |
| 568 | C2×C3 | C22×#127 | 1 | 1 | yes | characteristic |
| 569 | C2×C3 | C2×#575 | 1 | 2 | yes | — |
| 570 | D3 | — | 2 | 4 | no | — |
| 571 | D3 | — | 8 | 2 | no | — |
| 572 | C22 | — | 3 | 4 | no | — |
| 573 | C22 | — | 4 | 8 | no | — |
| 574 | C22 | — | 4 | 4 | no | — |
| 575 | C22 | — | 4 | 2 | no | — |
| 576 | C22 | — | 4 | 4 | no | — |
| 577 | C22 | — | 6 | 4 | no | — |
| 578 | C22 | — | 6 | 8 | no | — |
| 579 | C22 | — | 8 | 8 | no | — |
| 580 | C22 | — | 8 | 4 | no | — |
| 581 | C22 | — | 12 | 4 | no | — |
| 582 | C22 | — | 12 | 2 | no | — |
| 583 | C22 | — | 24 | 4 | no | — |
| 584 | C22 | D3×#127 | 1 | 2 | yes | — |
| 585 | C22 | #5773 | 1 | 4 | yes | — |
| 586 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 587 | C4 | — | 2 | 4 | no | — |
| 588 | C4 | — | 3 | 4 | no | — |
| 589 | C4 | — | 4 | 2 | no | — |
| 590 | C4 | — | 6 | 4 | no | — |
| 591 | C4 | — | 12 | 4 | no | — |
| 592 | C4 | — | 12 | 2 | no | — |
| 593 | C4 | D3×#127 | 1 | 2 | yes | — |
| 594 | C4 | C22×D3×D4 | 1 | 2 | yes | — |
| 595 | C3 | C2×#3150 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 596 | C2 | — | 6 | 4 | no | — |
| 597 | C2 | — | 8 | 4 | no | — |
| 598 | C2 | — | 8 | 2 | no | — |
| 599 | C2 | — | 24 | 2 | no | — |
| 600 | C2 | #81844 | 1 | 4 | yes | direct product factor |
| 601 | C2 | C2×D3×#127 | 1 | 1 | yes | characteristic |
| 602 | C2 | C2×#5773 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#916 | C2 | semidirect |
| 2. C22×#912 | C2 | semidirect |
| 3. C2×#5716 | C2 | semidirect |
| 4. C2×#5668 | C2 | semidirect |
| 5. C2×C3×#496 | C2 | semidirect |
| 6. C2×#5167 | C2 | semidirect |
| 7. C2×#5154 | C2 | semidirect |
| 8. C2×#5074 | C2 | semidirect |
| 9. C2×#5060 | C2 | semidirect |
| 10. #81844 | C2 | direct (N × H) |
| 11. C2×#4715 | C2 | semidirect |
| 12. C2×D3×#97 | C2 | semidirect |
| 31. C2×#916 | C22 | semidirect |
| 33. C2×#912 | C22 | semidirect |
| 38. #5716 | C22 | semidirect |
| 40. #5668 | C22 | semidirect |
| 46. C3×#496 | C22 | semidirect |
| 48. #5167 | C22 | semidirect |
| 49. #5154 | C22 | semidirect |
| 51. #5074 | C22 | semidirect |
| 52. #5060 | C22 | semidirect |
| 54. #4715 | C22 | semidirect |
| 55. D3×#97 | C22 | semidirect |
| 66. C2×#496 | D3 | semidirect |
| 134. C2×D3×C8 | D4 | semidirect |
| 184. #496 | C2×D3 | semidirect |
| 270. D3×C8 | C2×D4 | semidirect |
| 567. C2×C3 | #3150 | semidirect |
| 595. C3 | C2×#3150 | semidirect |
| 600. C2 | #81844 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#916 | 2 |
| C22×#912 | 2 |
| C2×#5716 | 2 |
| C2×#5668 | 2 |
| C2×C3×#496 | 2 |
| C2×#5167 | 2 |
| C2×#5154 | 2 |
| C2×#5074 | 2 |
| C2×#5060 | 2 |
| #81844 | 2 |
| C2×#4715 | 2 |
| C2×D3×#97 | 2 |
| C2×#3150 | 3 |