Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
5006 conjugacy classes of subgroups.
The subgroup lattice has 632 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×#937 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C22×#885 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×C3×#392 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#5223 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×#5221 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C2×#4955 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×#4961 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C2×#4947 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #76767 | C2 | 1 | 16 | yes | maximal, direct product factor |
| 10 | C2×#4670 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C2×#2670 | — | 3 | 1 | no | maximal, Sylow |
| 12 | C25×D3 | C22 | 1 | 1 | yes | characteristic |
| 13 | C23×C3×D4 | C22 | 1 | 2 | yes | — |
| 14 | C23×C3×D4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C23×#67 | C22 | 1 | 2 | yes | — |
| 16 | C23×#67 | C22 | 1 | 2 | yes | — |
| 17 | C23×Dic6 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C22×C3×C22⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 19 | C22×C3×C22⋊C4 | C22 | 1 | 2 | yes | complemented |
| 20 | C22×#217 | C22 | 1 | 2 | yes | — |
| 21 | C22×#217 | C22 | 1 | 1 | yes | characteristic |
| 22 | C22×#217 | C22 | 1 | 2 | yes | complemented |
| 23 | C22×#217 | C22 | 1 | 2 | yes | complemented |
| 24 | C2×#937 | — | 2 | 16 | no | — |
| 25 | C2×#937 | C22 | 1 | 16 | yes | complemented |
| 26 | C22×(C2×D3)⋊C4 | C22 | 1 | 2 | yes | — |
| 27 | C22×(C2×D3)⋊C4 | C22 | 1 | 2 | yes | — |
| 28 | C22×(C2×D3)⋊C4 | C22 | 1 | 2 | yes | — |
| 29 | C22×(C2×D3)⋊C4 | C22 | 1 | 2 | yes | — |
| 30 | C22×C4⋊Dic3 | C22 | 1 | 2 | yes | complemented |
| 31 | C22×C4×Dic3 | C22 | 1 | 2 | yes | complemented |
| 32 | C2×#885 | — | 2 | 16 | no | — |
| 33 | C2×#885 | C22 | 1 | 16 | yes | complemented |
| 34 | C3×#392 | C22 | 1 | 8 | yes | complemented |
| 35 | C2×C3×#95 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #5223 | C22 | 1 | 16 | yes | complemented |
| 37 | #5221 | C22 | 1 | 16 | yes | complemented |
| 38 | C2×C3⋊#95 | C22 | 1 | 2 | yes | complemented |
| 39 | C2×C3⋊#95 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #4961 | C22 | 1 | 16 | yes | complemented |
| 41 | #4955 | C22 | 1 | 8 | yes | complemented |
| 42 | #4947 | C22 | 1 | 8 | yes | complemented |
| 43 | #4670 | C22 | 1 | 16 | yes | complemented |
| 44 | C22×#124 | — | 3 | 2 | no | — |
| 45 | C22×#120 | — | 3 | 2 | no | — |
| 46 | #2670 | — | 3 | 16 | no | — |
| 47 | C2×#394 | — | 3 | 2 | no | — |
| 48 | C2×#393 | — | 3 | 1 | no | — |
| 49 | C2×#392 | — | 3 | 2 | no | — |
| 50 | C2×#392 | D3 | 1 | 1 | yes | characteristic, complemented |
| 51 | C2×#390 | — | 3 | 2 | no | — |
| 52 | C2×#388 | — | 3 | 2 | no | — |
| 53 | C2×#379 | — | 3 | 1 | no | — |
| 54 | C25×C3 | C23 | 1 | 2 | yes | — |
| 55 | C25×C3 | C23 | 1 | 1 | yes | characteristic |
| 56 | C24×D3 | — | 2 | 4 | no | — |
| 57 | C24×D3 | — | 2 | 8 | no | — |
| 58 | C24×D3 | — | 4 | 4 | no | — |
| 59 | C24×D3 | — | 4 | 2 | no | — |
| 60 | C24×D3 | — | 4 | 2 | no | — |
| 61 | C24×D3 | C23 | 1 | 2 | yes | — |
| 62 | C24×D3 | C23 | 1 | 4 | yes | — |
| 63 | C22×C3×D4 | — | 2 | 8 | no | — |
| 64 | C22×C3×D4 | — | 2 | 8 | no | — |
| 65 | C22×C3×D4 | — | 4 | 4 | no | — |
| 66 | C22×C3×D4 | — | 4 | 4 | no | — |
| 67 | C22×C3×D4 | — | 4 | 2 | no | — |
| 68 | C22×C3×D4 | C23 | 1 | 8 | yes | — |
| 69 | C22×C3×D4 | C23 | 1 | 4 | yes | complemented |
| 70 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 71 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 72 | C23×C3×C4 | C23 | 1 | 2 | yes | — |
| 73 | C22×#67 | — | 2 | 8 | no | — |
| 74 | C22×#67 | — | 2 | 8 | no | — |
| 75 | C22×#67 | — | 2 | 8 | no | — |
| 76 | C22×#67 | — | 4 | 4 | no | — |
| 77 | C22×#67 | — | 4 | 4 | no | — |
| 78 | C22×#67 | — | 4 | 4 | no | — |
| 79 | C22×#67 | C23 | 1 | 8 | yes | — |
| 80 | C22×#67 | C23 | 1 | 8 | yes | — |
| 81 | C23×Dic3 | C23 | 1 | 2 | yes | — |
| 82 | C23×Dic3 | C23 | 1 | 2 | yes | — |
| 83 | C23×Dic3 | C23 | 1 | 2 | yes | — |
| 84 | C22×Dic6 | — | 2 | 8 | no | — |
| 85 | C22×Dic6 | — | 4 | 2 | no | — |
| 86 | C22×Dic6 | C23 | 1 | 4 | yes | complemented |
| 87 | C2×C3×C22⋊C4 | — | 2 | 8 | no | — |
| 88 | C2×C3×C22⋊C4 | — | 4 | 2 | no | — |
| 89 | C2×C3×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 90 | C2×C3×C22⋊C4 | C23 | 1 | 8 | yes | complemented |
| 91 | C2×#217 | — | 2 | 8 | no | — |
| 92 | C2×#217 | — | 2 | 8 | no | — |
| 93 | C2×#217 | — | 4 | 2 | no | — |
| 94 | C2×#217 | — | 4 | 4 | no | — |
| 95 | C2×#217 | C23 | 1 | 8 | yes | — |
| 96 | C2×#217 | C23 | 1 | 4 | yes | — |
| 97 | C2×#217 | C23 | 1 | 8 | yes | complemented |
| 98 | C2×#217 | C23 | 1 | 8 | yes | complemented |
| 99 | #937 | — | 2 | 64 | no | — |
| 100 | C2×(C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 101 | C2×(C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 102 | C2×(C2×D3)⋊C4 | — | 4 | 4 | no | — |
| 103 | C2×(C2×D3)⋊C4 | D4 | 1 | 16 | yes | complemented |
| 104 | C2×(C2×D3)⋊C4 | C23 | 1 | 8 | yes | — |
| 105 | C2×(C2×D3)⋊C4 | C23 | 1 | 8 | yes | — |
| 106 | C2×(C2×D3)⋊C4 | C23 | 1 | 8 | yes | — |
| 107 | C2×(C2×D3)⋊C4 | C23 | 1 | 8 | yes | — |
| 108 | C2×C4⋊Dic3 | — | 4 | 4 | no | — |
| 109 | C2×C4⋊Dic3 | C23 | 1 | 8 | yes | complemented |
| 110 | C2×C4×Dic3 | — | 2 | 8 | no | — |
| 111 | C2×C4×Dic3 | C23 | 1 | 8 | yes | complemented |
| 112 | #885 | — | 2 | 64 | no | — |
| 113 | C3×#95 | C23 | 1 | 4 | yes | complemented |
| 114 | C3⋊#95 | C23 | 1 | 8 | yes | complemented |
| 115 | C3⋊#95 | C23 | 1 | 4 | yes | complemented |
| 116 | C26 | — | 3 | 1 | no | — |
| 117 | C23×Q8 | — | 3 | 1 | no | — |
| 118 | C23×D4 | — | 3 | 2 | no | — |
| 119 | C23×D4 | — | 3 | 2 | no | — |
| 120 | C23×D4 | C2×D3 | 1 | 2 | yes | — |
| 121 | C23×D4 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 122 | C2×#124 | — | 3 | 16 | no | — |
| 123 | C2×#124 | — | 6 | 16 | no | — |
| 124 | C2×#120 | — | 3 | 16 | no | — |
| 125 | C2×#120 | — | 6 | 16 | no | — |
| 126 | C22×C4⋊C4 | — | 3 | 2 | no | — |
| 127 | C22×C22⋊C4 | — | 3 | 2 | no | — |
| 128 | C22×C22⋊C4 | — | 3 | 2 | no | — |
| 129 | C22×C22⋊C4 | — | 3 | 2 | no | — |
| 130 | C22×C22⋊C4 | — | 3 | 2 | no | — |
| 131 | C22×C22⋊C4 | — | 3 | 2 | no | — |
| 132 | C22×C22⋊C4 | — | 3 | 2 | no | — |
| 133 | C22×C22⋊C4 | — | 3 | 1 | no | — |
| 134 | C22×C22⋊C4 | — | 3 | 2 | no | — |
| 135 | C22×C22⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 136 | C22×C22⋊C4 | C2×D3 | 1 | 2 | yes | complemented |
| 137 | C22×C42 | — | 3 | 2 | no | — |
| 138 | #394 | — | 3 | 16 | no | — |
| 139 | #393 | — | 3 | 8 | no | — |
| 140 | #392 | — | 3 | 16 | no | — |
| 141 | #392 | C2×D3 | 1 | 8 | yes | complemented |
| 142 | #390 | — | 3 | 16 | no | — |
| 143 | #388 | — | 3 | 16 | no | — |
| 144 | #379 | — | 3 | 8 | no | — |
| 145 | C2×#95 | — | 3 | 2 | no | — |
| 146 | C2×#95 | — | 3 | 1 | no | — |
| 147 | C2×#95 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 148 | C24×C3 | — | 2 | 4 | no | — |
| 149 | C24×C3 | — | 2 | 2 | no | — |
| 150 | C24×C3 | — | 2 | 2 | no | — |
| 151 | C24×C3 | — | 2 | 4 | no | — |
| 152 | C24×C3 | — | 2 | 4 | no | — |
| 153 | C24×C3 | — | 2 | 4 | no | — |
| 154 | C24×C3 | — | 2 | 4 | no | — |
| 155 | C24×C3 | — | 2 | 4 | no | — |
| 156 | C24×C3 | — | 2 | 4 | no | — |
| 157 | C24×C3 | — | 2 | 4 | no | — |
| 158 | C24×C3 | — | 2 | 4 | no | — |
| 159 | C24×C3 | #41 | 1 | 4 | yes | — |
| 160 | C24×C3 | C24 | 1 | 4 | yes | — |
| 161 | C24×C3 | C24 | 1 | 2 | yes | — |
| 162 | C24×C3 | C24 | 1 | 1 | yes | characteristic |
| 163 | C23×D3 | — | 2 | 4 | no | — |
| 164 | C23×D3 | — | 2 | 4 | no | — |
| 165 | C23×D3 | — | 2 | 4 | no | — |
| 166 | C23×D3 | — | 2 | 4 | no | — |
| 167 | C23×D3 | — | 2 | 4 | no | — |
| 168 | C23×D3 | — | 2 | 4 | no | — |
| 169 | C23×D3 | — | 2 | 8 | no | — |
| 170 | C23×D3 | — | 2 | 16 | no | — |
| 171 | C23×D3 | — | 4 | 8 | no | — |
| 172 | C23×D3 | — | 4 | 4 | no | — |
| 173 | C23×D3 | — | 4 | 4 | no | — |
| 174 | C23×D3 | — | 4 | 16 | no | — |
| 175 | C23×D3 | — | 4 | 32 | no | — |
| 176 | C23×D3 | — | 4 | 32 | no | — |
| 177 | C23×D3 | — | 4 | 16 | no | — |
| 178 | C23×D3 | — | 4 | 16 | no | — |
| 179 | C23×D3 | C2×D4 | 1 | 8 | yes | — |
| 180 | C23×D3 | C24 | 1 | 4 | yes | — |
| 181 | C2×C3×D4 | — | 2 | 16 | no | — |
| 182 | C2×C3×D4 | — | 2 | 16 | no | — |
| 183 | C2×C3×D4 | — | 4 | 8 | no | — |
| 184 | C2×C3×D4 | — | 4 | 8 | no | — |
| 185 | C2×C3×D4 | — | 4 | 4 | no | — |
| 186 | C2×C3×D4 | — | 4 | 32 | no | — |
| 187 | C2×C3×D4 | — | 4 | 16 | no | — |
| 188 | C22×C3×C4 | — | 2 | 4 | no | — |
| 189 | C22×C3×C4 | — | 2 | 4 | no | — |
| 190 | C22×C3×C4 | — | 2 | 4 | no | — |
| 191 | C22×C3×C4 | — | 2 | 4 | no | — |
| 192 | C22×C3×C4 | — | 2 | 2 | no | — |
| 193 | C22×C3×C4 | — | 2 | 2 | no | — |
| 194 | C22×C3×C4 | C2×D4 | 1 | 8 | yes | — |
| 195 | C22×C3×C4 | C24 | 1 | 2 | yes | — |
| 196 | C22×C3×C4 | C24 | 1 | 2 | yes | — |
| 197 | C22×C3×C4 | C24 | 1 | 4 | yes | — |
| 198 | C2×#67 | — | 2 | 16 | no | — |
| 199 | C2×#67 | — | 2 | 16 | no | — |
| 200 | C2×#67 | — | 2 | 16 | no | — |
| 201 | C2×#67 | — | 4 | 8 | no | — |
| 202 | C2×#67 | — | 4 | 8 | no | — |
| 203 | C2×#67 | — | 4 | 8 | no | — |
| 204 | C2×#67 | — | 4 | 32 | no | — |
| 205 | C2×#67 | — | 4 | 32 | no | — |
| 206 | C22×Dic3 | — | 2 | 4 | no | — |
| 207 | C22×Dic3 | — | 2 | 4 | no | — |
| 208 | C22×Dic3 | — | 2 | 4 | no | — |
| 209 | C22×Dic3 | — | 2 | 4 | no | — |
| 210 | C22×Dic3 | — | 2 | 4 | no | — |
| 211 | C22×Dic3 | — | 2 | 4 | no | — |
| 212 | C22×Dic3 | — | 2 | 4 | no | — |
| 213 | C22×Dic3 | — | 2 | 4 | no | — |
| 214 | C22×Dic3 | C2×D4 | 1 | 8 | yes | — |
| 215 | C22×Dic3 | C24 | 1 | 4 | yes | — |
| 216 | C22×Dic3 | C24 | 1 | 4 | yes | — |
| 217 | C22×Dic3 | C24 | 1 | 4 | yes | — |
| 218 | C2×Dic6 | — | 2 | 16 | no | — |
| 219 | C2×Dic6 | — | 4 | 4 | no | — |
| 220 | C2×Dic6 | — | 4 | 16 | no | — |
| 221 | C3×C22⋊C4 | — | 2 | 16 | no | — |
| 222 | C3×C22⋊C4 | — | 4 | 4 | no | — |
| 223 | #217 | — | 2 | 16 | no | — |
| 224 | #217 | — | 2 | 16 | no | — |
| 225 | #217 | — | 4 | 4 | no | — |
| 226 | #217 | — | 4 | 8 | no | — |
| 227 | (C2×D3)⋊C4 | — | 2 | 16 | no | — |
| 228 | (C2×D3)⋊C4 | — | 2 | 16 | no | — |
| 229 | (C2×D3)⋊C4 | — | 4 | 8 | no | — |
| 230 | (C2×D3)⋊C4 | C2×D4 | 1 | 32 | yes | complemented |
| 231 | C4⋊Dic3 | — | 4 | 8 | no | — |
| 232 | C4×Dic3 | — | 2 | 16 | no | — |
| 233 | C25 | — | 3 | 2 | no | — |
| 234 | C25 | — | 3 | 4 | no | — |
| 235 | C25 | — | 6 | 8 | no | — |
| 236 | C25 | — | 6 | 4 | no | — |
| 237 | C25 | — | 12 | 2 | no | — |
| 238 | C25 | — | 12 | 4 | no | — |
| 239 | C25 | — | 12 | 2 | no | — |
| 240 | C25 | C22×D3 | 1 | 2 | yes | — |
| 241 | C25 | C22×D3 | 1 | 1 | yes | characteristic |
| 242 | C22×Q8 | — | 3 | 4 | no | — |
| 243 | C22×Q8 | — | 6 | 8 | no | — |
| 244 | C22×Q8 | — | 12 | 2 | no | — |
| 245 | C22×D4 | — | 2 | 8 | no | — |
| 246 | C22×D4 | — | 2 | 8 | no | — |
| 247 | C22×D4 | — | 3 | 8 | no | — |
| 248 | C22×D4 | — | 3 | 8 | no | — |
| 249 | C22×D4 | — | 4 | 4 | no | — |
| 250 | C22×D4 | — | 4 | 2 | no | — |
| 251 | C22×D4 | — | 4 | 4 | no | — |
| 252 | C22×D4 | — | 6 | 8 | no | — |
| 253 | C22×D4 | — | 6 | 8 | no | — |
| 254 | C22×D4 | — | 6 | 8 | no | — |
| 255 | C22×D4 | — | 12 | 4 | no | — |
| 256 | C22×D4 | — | 12 | 4 | no | — |
| 257 | C22×D4 | — | 12 | 4 | no | — |
| 258 | C22×D4 | C22×D3 | 1 | 8 | yes | — |
| 259 | C22×D4 | C22×D3 | 1 | 4 | yes | complemented |
| 260 | C23×C4 | — | 3 | 2 | no | — |
| 261 | C23×C4 | — | 3 | 2 | no | — |
| 262 | C23×C4 | — | 3 | 2 | no | — |
| 263 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 264 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 265 | C23×C4 | C22×D3 | 1 | 2 | yes | — |
| 266 | #124 | — | 6 | 64 | no | — |
| 267 | #120 | — | 6 | 64 | no | — |
| 268 | C2×C4⋊C4 | — | 3 | 8 | no | — |
| 269 | C2×C4⋊C4 | — | 12 | 4 | no | — |
| 270 | C2×C22⋊C4 | — | 2 | 8 | no | — |
| 271 | C2×C22⋊C4 | — | 3 | 16 | no | — |
| 272 | C2×C22⋊C4 | — | 3 | 8 | no | — |
| 273 | C2×C22⋊C4 | — | 3 | 8 | no | — |
| 274 | C2×C22⋊C4 | — | 3 | 8 | no | — |
| 275 | C2×C22⋊C4 | — | 3 | 8 | no | — |
| 276 | C2×C22⋊C4 | — | 3 | 8 | no | — |
| 277 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 278 | C2×C22⋊C4 | — | 3 | 8 | no | — |
| 279 | C2×C22⋊C4 | — | 3 | 8 | no | — |
| 280 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 281 | C2×C22⋊C4 | — | 6 | 8 | no | — |
| 282 | C2×C22⋊C4 | — | 6 | 8 | no | — |
| 283 | C2×C22⋊C4 | — | 6 | 8 | no | — |
| 284 | C2×C22⋊C4 | — | 6 | 8 | no | — |
| 285 | C2×C22⋊C4 | — | 12 | 4 | no | — |
| 286 | C2×C22⋊C4 | — | 12 | 2 | no | — |
| 287 | C2×C22⋊C4 | — | 12 | 4 | no | — |
| 288 | C2×C22⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 289 | C2×C22⋊C4 | C22×D3 | 1 | 8 | yes | complemented |
| 290 | C2×C42 | — | 3 | 8 | no | — |
| 291 | C2×C42 | — | 6 | 8 | no | — |
| 292 | #95 | — | 3 | 8 | no | — |
| 293 | #95 | — | 3 | 4 | no | — |
| 294 | #95 | C22×D3 | 1 | 4 | yes | complemented |
| 295 | C23×C3 | — | 2 | 8 | no | — |
| 296 | C23×C3 | — | 2 | 16 | no | — |
| 297 | C23×C3 | — | 2 | 4 | no | — |
| 298 | C23×C3 | — | 2 | 2 | no | — |
| 299 | C23×C3 | — | 2 | 2 | no | — |
| 300 | C23×C3 | — | 2 | 4 | no | — |
| 301 | C23×C3 | — | 2 | 4 | no | — |
| 302 | C23×C3 | — | 2 | 4 | no | — |
| 303 | C23×C3 | — | 2 | 4 | no | — |
| 304 | C23×C3 | — | 2 | 4 | no | — |
| 305 | C23×C3 | — | 2 | 4 | no | — |
| 306 | C23×C3 | — | 2 | 4 | no | — |
| 307 | C23×C3 | — | 2 | 4 | no | — |
| 308 | C23×C3 | — | 4 | 8 | no | — |
| 309 | C23×C3 | — | 4 | 4 | no | — |
| 310 | C23×C3 | — | 4 | 4 | no | — |
| 311 | C23×C3 | — | 4 | 8 | no | — |
| 312 | C23×C3 | — | 4 | 8 | no | — |
| 313 | C23×C3 | — | 4 | 8 | no | — |
| 314 | C23×C3 | — | 4 | 8 | no | — |
| 315 | C23×C3 | — | 4 | 8 | no | — |
| 316 | C23×C3 | — | 4 | 8 | no | — |
| 317 | C23×C3 | — | 4 | 8 | no | — |
| 318 | C23×C3 | C22×D4 | 1 | 4 | yes | — |
| 319 | C23×C3 | C2×#41 | 1 | 4 | yes | — |
| 320 | C23×C3 | C2×#41 | 1 | 2 | yes | — |
| 321 | C23×C3 | H(5,𝔽2) | 1 | 4 | yes | — |
| 322 | C23×C3 | H(5,𝔽2) | 1 | 2 | yes | — |
| 323 | C23×C3 | H(5,𝔽2) | 1 | 2 | yes | — |
| 324 | C23×C3 | C25 | 1 | 1 | yes | characteristic |
| 325 | C22×D3 | — | 2 | 16 | no | — |
| 326 | C22×D3 | — | 2 | 16 | no | — |
| 327 | C22×D3 | — | 2 | 16 | no | — |
| 328 | C22×D3 | — | 2 | 4 | no | — |
| 329 | C22×D3 | — | 2 | 4 | no | — |
| 330 | C22×D3 | — | 2 | 4 | no | — |
| 331 | C22×D3 | — | 2 | 4 | no | — |
| 332 | C22×D3 | — | 2 | 4 | no | — |
| 333 | C22×D3 | — | 2 | 4 | no | — |
| 334 | C22×D3 | — | 4 | 16 | no | — |
| 335 | C22×D3 | — | 4 | 32 | no | — |
| 336 | C22×D3 | — | 4 | 32 | no | — |
| 337 | C22×D3 | — | 4 | 16 | no | — |
| 338 | C22×D3 | — | 4 | 128 | no | — |
| 339 | C22×D3 | — | 4 | 16 | no | — |
| 340 | C22×D3 | — | 4 | 8 | no | — |
| 341 | C22×D3 | — | 4 | 8 | no | — |
| 342 | C22×D3 | — | 4 | 8 | no | — |
| 343 | C22×D3 | — | 4 | 8 | no | — |
| 344 | C22×D3 | C22×D4 | 1 | 8 | yes | — |
| 345 | C3×D4 | — | 4 | 32 | no | — |
| 346 | C3×D4 | — | 4 | 16 | no | — |
| 347 | C2×C3×C4 | — | 2 | 16 | no | — |
| 348 | C2×C3×C4 | — | 2 | 4 | no | — |
| 349 | C2×C3×C4 | — | 2 | 4 | no | — |
| 350 | C2×C3×C4 | — | 2 | 4 | no | — |
| 351 | C2×C3×C4 | — | 2 | 4 | no | — |
| 352 | C2×C3×C4 | — | 2 | 2 | no | — |
| 353 | C2×C3×C4 | — | 2 | 2 | no | — |
| 354 | C2×C3×C4 | — | 4 | 4 | no | — |
| 355 | C2×C3×C4 | — | 4 | 4 | no | — |
| 356 | C2×C3×C4 | C22×D4 | 1 | 8 | yes | — |
| 357 | #67 | — | 4 | 32 | no | — |
| 358 | #67 | — | 4 | 32 | no | — |
| 359 | C2×Dic3 | — | 2 | 16 | no | — |
| 360 | C2×Dic3 | — | 2 | 4 | no | — |
| 361 | C2×Dic3 | — | 2 | 4 | no | — |
| 362 | C2×Dic3 | — | 2 | 4 | no | — |
| 363 | C2×Dic3 | — | 2 | 4 | no | — |
| 364 | C2×Dic3 | — | 2 | 4 | no | — |
| 365 | C2×Dic3 | — | 2 | 4 | no | — |
| 366 | C2×Dic3 | — | 2 | 4 | no | — |
| 367 | C2×Dic3 | — | 2 | 4 | no | — |
| 368 | C2×Dic3 | — | 4 | 8 | no | — |
| 369 | C2×Dic3 | — | 4 | 8 | no | — |
| 370 | C2×Dic3 | C22×D4 | 1 | 8 | yes | — |
| 371 | Dic6 | — | 4 | 16 | no | — |
| 372 | C24 | — | 2 | 4 | no | — |
| 373 | C24 | — | 2 | 2 | no | — |
| 374 | C24 | — | 2 | 4 | no | — |
| 375 | C24 | — | 2 | 2 | no | — |
| 376 | C24 | — | 2 | 4 | no | — |
| 377 | C24 | — | 2 | 4 | no | — |
| 378 | C24 | — | 2 | 4 | no | — |
| 379 | C24 | — | 2 | 4 | no | — |
| 380 | C24 | — | 2 | 4 | no | — |
| 381 | C24 | — | 2 | 4 | no | — |
| 382 | C24 | — | 2 | 4 | no | — |
| 383 | C24 | — | 3 | 8 | no | — |
| 384 | C24 | — | 3 | 4 | no | — |
| 385 | C24 | — | 6 | 16 | no | — |
| 386 | C24 | — | 6 | 4 | no | — |
| 387 | C24 | — | 6 | 4 | no | — |
| 388 | C24 | — | 6 | 4 | no | — |
| 389 | C24 | — | 6 | 4 | no | — |
| 390 | C24 | — | 6 | 4 | no | — |
| 391 | C24 | — | 6 | 4 | no | — |
| 392 | C24 | — | 6 | 8 | no | — |
| 393 | C24 | — | 12 | 4 | no | — |
| 394 | C24 | — | 12 | 8 | no | — |
| 395 | C24 | — | 12 | 4 | no | — |
| 396 | C24 | — | 12 | 32 | no | — |
| 397 | C24 | — | 12 | 16 | no | — |
| 398 | C24 | — | 12 | 16 | no | — |
| 399 | C24 | — | 12 | 32 | no | — |
| 400 | C24 | — | 12 | 16 | no | — |
| 401 | C24 | #237 | 1 | 4 | yes | — |
| 402 | C24 | C23×D3 | 1 | 4 | yes | — |
| 403 | C24 | C23×D3 | 1 | 2 | yes | — |
| 404 | C24 | C23×D3 | 1 | 1 | yes | characteristic |
| 405 | C2×Q8 | — | 6 | 16 | no | — |
| 406 | C2×Q8 | — | 12 | 4 | no | — |
| 407 | C2×Q8 | — | 12 | 16 | no | — |
| 408 | C2×D4 | — | 2 | 16 | no | — |
| 409 | C2×D4 | — | 2 | 16 | no | — |
| 410 | C2×D4 | — | 4 | 8 | no | — |
| 411 | C2×D4 | — | 4 | 4 | no | — |
| 412 | C2×D4 | — | 4 | 8 | no | — |
| 413 | C2×D4 | — | 4 | 32 | no | — |
| 414 | C2×D4 | — | 4 | 16 | no | — |
| 415 | C2×D4 | — | 6 | 16 | no | — |
| 416 | C2×D4 | — | 6 | 16 | no | — |
| 417 | C2×D4 | — | 6 | 16 | no | — |
| 418 | C2×D4 | — | 12 | 8 | no | — |
| 419 | C2×D4 | — | 12 | 8 | no | — |
| 420 | C2×D4 | — | 12 | 8 | no | — |
| 421 | C2×D4 | — | 12 | 32 | no | — |
| 422 | C2×D4 | — | 12 | 32 | no | — |
| 423 | C22×C4 | — | 2 | 4 | no | — |
| 424 | C22×C4 | — | 2 | 4 | no | — |
| 425 | C22×C4 | — | 2 | 4 | no | — |
| 426 | C22×C4 | — | 2 | 2 | no | — |
| 427 | C22×C4 | — | 2 | 2 | no | — |
| 428 | C22×C4 | — | 2 | 4 | no | — |
| 429 | C22×C4 | — | 3 | 8 | no | — |
| 430 | C22×C4 | — | 3 | 4 | no | — |
| 431 | C22×C4 | — | 3 | 4 | no | — |
| 432 | C22×C4 | — | 3 | 4 | no | — |
| 433 | C22×C4 | — | 6 | 4 | no | — |
| 434 | C22×C4 | — | 6 | 4 | no | — |
| 435 | C22×C4 | — | 6 | 4 | no | — |
| 436 | C22×C4 | — | 6 | 4 | no | — |
| 437 | C22×C4 | — | 6 | 4 | no | — |
| 438 | C22×C4 | — | 6 | 4 | no | — |
| 439 | C22×C4 | — | 6 | 4 | no | — |
| 440 | C22×C4 | — | 6 | 4 | no | — |
| 441 | C22×C4 | D3×D4 | 1 | 8 | yes | — |
| 442 | C22×C4 | C23×D3 | 1 | 2 | yes | — |
| 443 | C22×C4 | C23×D3 | 1 | 2 | yes | — |
| 444 | C22×C4 | C23×D3 | 1 | 4 | yes | — |
| 445 | C4⋊C4 | — | 12 | 8 | no | — |
| 446 | C22⋊C4 | — | 2 | 16 | no | — |
| 447 | C22⋊C4 | — | 3 | 32 | no | — |
| 448 | C22⋊C4 | — | 4 | 4 | no | — |
| 449 | C22⋊C4 | — | 6 | 16 | no | — |
| 450 | C22⋊C4 | — | 6 | 16 | no | — |
| 451 | C22⋊C4 | — | 6 | 16 | no | — |
| 452 | C22⋊C4 | — | 6 | 16 | no | — |
| 453 | C22⋊C4 | — | 12 | 8 | no | — |
| 454 | C22⋊C4 | — | 12 | 4 | no | — |
| 455 | C22⋊C4 | — | 12 | 8 | no | — |
| 456 | C42 | — | 6 | 16 | no | — |
| 457 | C22×C3 | — | 2 | 4 | no | — |
| 458 | C22×C3 | — | 2 | 8 | no | — |
| 459 | C22×C3 | — | 4 | 16 | no | — |
| 460 | C22×C3 | — | 4 | 4 | no | — |
| 461 | C22×C3 | — | 4 | 2 | no | — |
| 462 | C22×C3 | — | 4 | 2 | no | — |
| 463 | C22×C3 | — | 4 | 4 | no | — |
| 464 | C22×C3 | — | 4 | 4 | no | — |
| 465 | C22×C3 | — | 4 | 4 | no | — |
| 466 | C22×C3 | — | 4 | 4 | no | — |
| 467 | C22×C3 | — | 4 | 4 | no | — |
| 468 | C22×C3 | — | 4 | 4 | no | — |
| 469 | C22×C3 | — | 4 | 4 | no | — |
| 470 | C22×C3 | — | 8 | 16 | no | — |
| 471 | C22×C3 | #535 | 1 | 8 | yes | — |
| 472 | C22×C3 | #538 | 1 | 4 | yes | — |
| 473 | C22×C3 | D42 | 1 | 4 | yes | — |
| 474 | C22×C3 | #546 | 1 | 8 | yes | — |
| 475 | C22×C3 | H(3,𝔽4) | 1 | 4 | yes | — |
| 476 | C22×C3 | C23×D4 | 1 | 2 | yes | — |
| 477 | C22×C3 | C22×#41 | 1 | 1 | yes | characteristic |
| 478 | C22×C3 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 479 | C22×C3 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 480 | C22×C3 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 481 | C2×D3 | — | 2 | 8 | no | — |
| 482 | C2×D3 | — | 2 | 8 | no | — |
| 483 | C2×D3 | — | 2 | 8 | no | — |
| 484 | C2×D3 | — | 4 | 64 | no | — |
| 485 | C2×D3 | — | 4 | 32 | no | — |
| 486 | C2×D3 | — | 4 | 4 | no | — |
| 487 | C2×D3 | — | 4 | 4 | no | — |
| 488 | C2×D3 | — | 4 | 4 | no | — |
| 489 | C2×D3 | — | 4 | 4 | no | — |
| 490 | C3×C4 | — | 2 | 8 | no | — |
| 491 | C3×C4 | — | 4 | 2 | no | — |
| 492 | C3×C4 | — | 4 | 2 | no | — |
| 493 | Dic3 | — | 2 | 8 | no | — |
| 494 | Dic3 | — | 4 | 4 | no | — |
| 495 | Dic3 | — | 4 | 4 | no | — |
| 496 | C23 | — | 2 | 4 | no | — |
| 497 | C23 | — | 2 | 2 | no | — |
| 498 | C23 | — | 2 | 4 | no | — |
| 499 | C23 | — | 2 | 2 | no | — |
| 500 | C23 | — | 2 | 16 | no | — |
| 501 | C23 | — | 2 | 8 | no | — |
| 502 | C23 | — | 2 | 4 | no | — |
| 503 | C23 | — | 2 | 4 | no | — |
| 504 | C23 | — | 2 | 4 | no | — |
| 505 | C23 | — | 2 | 4 | no | — |
| 506 | C23 | — | 2 | 4 | no | — |
| 507 | C23 | — | 2 | 4 | no | — |
| 508 | C23 | — | 2 | 4 | no | — |
| 509 | C23 | — | 3 | 8 | no | — |
| 510 | C23 | — | 4 | 4 | no | — |
| 511 | C23 | — | 4 | 4 | no | — |
| 512 | C23 | — | 4 | 8 | no | — |
| 513 | C23 | — | 4 | 8 | no | — |
| 514 | C23 | — | 4 | 8 | no | — |
| 515 | C23 | — | 4 | 8 | no | — |
| 516 | C23 | — | 4 | 8 | no | — |
| 517 | C23 | — | 4 | 8 | no | — |
| 518 | C23 | — | 4 | 8 | no | — |
| 519 | C23 | — | 4 | 8 | no | — |
| 520 | C23 | — | 6 | 4 | no | — |
| 521 | C23 | — | 6 | 4 | no | — |
| 522 | C23 | — | 6 | 4 | no | — |
| 523 | C23 | — | 6 | 4 | no | — |
| 524 | C23 | — | 6 | 4 | no | — |
| 525 | C23 | — | 6 | 4 | no | — |
| 526 | C23 | — | 6 | 16 | no | — |
| 527 | C23 | — | 6 | 16 | no | — |
| 528 | C23 | — | 6 | 16 | no | — |
| 529 | C23 | — | 12 | 32 | no | — |
| 530 | C23 | — | 12 | 16 | no | — |
| 531 | C23 | — | 12 | 16 | no | — |
| 532 | C23 | — | 12 | 32 | no | — |
| 533 | C23 | — | 12 | 16 | no | — |
| 534 | C23 | — | 12 | 128 | no | — |
| 535 | C23 | — | 12 | 8 | no | — |
| 536 | C23 | — | 12 | 8 | no | — |
| 537 | C23 | — | 12 | 8 | no | — |
| 538 | C23 | — | 12 | 8 | no | — |
| 539 | C23 | C2×D3×D4 | 1 | 4 | yes | — |
| 540 | C23 | C2×#237 | 1 | 4 | yes | — |
| 541 | C23 | C2×#237 | 1 | 2 | yes | — |
| 542 | C23 | #1004 | 1 | 2 | yes | — |
| 543 | C23 | #1004 | 1 | 4 | yes | — |
| 544 | C23 | #1009 | 1 | 2 | yes | — |
| 545 | C23 | C24×D3 | 1 | 1 | yes | characteristic |
| 546 | Q8 | — | 12 | 16 | no | — |
| 547 | D4 | — | 4 | 32 | no | — |
| 548 | D4 | — | 4 | 16 | no | — |
| 549 | D4 | — | 12 | 32 | no | — |
| 550 | D4 | — | 12 | 32 | no | — |
| 551 | C2×C4 | — | 2 | 4 | no | — |
| 552 | C2×C4 | — | 2 | 4 | no | — |
| 553 | C2×C4 | — | 2 | 16 | no | — |
| 554 | C2×C4 | — | 2 | 4 | no | — |
| 555 | C2×C4 | — | 2 | 2 | no | — |
| 556 | C2×C4 | — | 2 | 2 | no | — |
| 557 | C2×C4 | — | 2 | 4 | no | — |
| 558 | C2×C4 | — | 3 | 8 | no | — |
| 559 | C2×C4 | — | 4 | 4 | no | — |
| 560 | C2×C4 | — | 4 | 4 | no | — |
| 561 | C2×C4 | — | 6 | 4 | no | — |
| 562 | C2×C4 | — | 6 | 4 | no | — |
| 563 | C2×C4 | — | 6 | 16 | no | — |
| 564 | C2×C4 | — | 6 | 4 | no | — |
| 565 | C2×C4 | — | 6 | 4 | no | — |
| 566 | C2×C4 | — | 6 | 4 | no | — |
| 567 | C2×C4 | — | 6 | 4 | no | — |
| 568 | C2×C4 | — | 6 | 4 | no | — |
| 569 | C2×C4 | — | 6 | 4 | no | — |
| 570 | C2×C4 | — | 12 | 8 | no | — |
| 571 | C2×C4 | — | 12 | 8 | no | — |
| 572 | C2×C4 | C2×D3×D4 | 1 | 8 | yes | — |
| 573 | C2×C3 | — | 4 | 4 | no | — |
| 574 | C2×C3 | — | 8 | 4 | no | — |
| 575 | C2×C3 | #2670 | 1 | 8 | yes | complemented |
| 576 | C2×C3 | C2×#535 | 1 | 2 | yes | — |
| 577 | C2×C3 | C2×#538 | 1 | 1 | yes | characteristic |
| 578 | C2×C3 | C2×D42 | 1 | 1 | yes | characteristic |
| 579 | C2×C3 | C2×#546 | 1 | 2 | yes | — |
| 580 | C2×C3 | C2×H(3,𝔽4) | 1 | 1 | yes | characteristic |
| 581 | D3 | — | 4 | 8 | no | — |
| 582 | C22 | — | 2 | 8 | no | — |
| 583 | C22 | — | 2 | 4 | no | — |
| 584 | C22 | — | 4 | 2 | no | — |
| 585 | C22 | — | 4 | 2 | no | — |
| 586 | C22 | — | 4 | 4 | no | — |
| 587 | C22 | — | 4 | 16 | no | — |
| 588 | C22 | — | 4 | 4 | no | — |
| 589 | C22 | — | 4 | 4 | no | — |
| 590 | C22 | — | 4 | 4 | no | — |
| 591 | C22 | — | 4 | 4 | no | — |
| 592 | C22 | — | 4 | 4 | no | — |
| 593 | C22 | — | 4 | 4 | no | — |
| 594 | C22 | — | 4 | 4 | no | — |
| 595 | C22 | — | 6 | 8 | no | — |
| 596 | C22 | — | 6 | 8 | no | — |
| 597 | C22 | — | 6 | 8 | no | — |
| 598 | C22 | — | 8 | 16 | no | — |
| 599 | C22 | — | 12 | 64 | no | — |
| 600 | C22 | — | 12 | 4 | no | — |
| 601 | C22 | — | 12 | 4 | no | — |
| 602 | C22 | — | 12 | 4 | no | — |
| 603 | C22 | — | 12 | 4 | no | — |
| 604 | C22 | — | 12 | 32 | no | — |
| 605 | C22 | #5591 | 1 | 8 | yes | — |
| 606 | C22 | #5594 | 1 | 4 | yes | — |
| 607 | C22 | #5607 | 1 | 8 | yes | — |
| 608 | C22 | #5617 | 1 | 4 | yes | — |
| 609 | C22 | #5717 | 1 | 4 | yes | — |
| 610 | C22 | C22×D3×D4 | 1 | 2 | yes | — |
| 611 | C22 | C22×#237 | 1 | 1 | yes | characteristic |
| 612 | C22 | C2×#1004 | 1 | 2 | yes | — |
| 613 | C22 | C2×#1004 | 1 | 1 | yes | characteristic |
| 614 | C22 | C2×#1009 | 1 | 1 | yes | characteristic |
| 615 | C4 | — | 2 | 8 | no | — |
| 616 | C4 | — | 4 | 2 | no | — |
| 617 | C4 | — | 4 | 2 | no | — |
| 618 | C4 | — | 6 | 8 | no | — |
| 619 | C4 | — | 12 | 4 | no | — |
| 620 | C4 | — | 12 | 4 | no | — |
| 621 | C3 | C2×#2670 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 622 | C2 | — | 4 | 4 | no | — |
| 623 | C2 | — | 8 | 4 | no | — |
| 624 | C2 | — | 12 | 8 | no | — |
| 625 | C2 | #76767 | 1 | 8 | yes | direct product factor |
| 626 | C2 | C2×#5594 | 1 | 1 | yes | characteristic |
| 627 | C2 | C2×#5591 | 1 | 2 | yes | — |
| 628 | C2 | C2×#5607 | 1 | 2 | yes | — |
| 629 | C2 | C2×#5617 | 1 | 1 | yes | characteristic |
| 630 | C2 | C2×#5717 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D3 |
| commutator, cosocle | C23×C3 | C25 |
| Frattini | C23 | C24×D3 |
| Fitting | C2×C3×#392 | C2 |
| socle | C24×C3 | C24 |
| hypercenter | C2×#392 | D3 |
| hypocenter | C3 | C2×#2670 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C24 ◁ C2×#392 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#937 | C2 | semidirect |
| 2. C22×#885 | C2 | semidirect |
| 3. C2×C3×#392 | C2 | semidirect |
| 4. C2×#5223 | C2 | semidirect |
| 5. C2×#5221 | C2 | semidirect |
| 6. C2×#4955 | C2 | semidirect |
| 7. C2×#4961 | C2 | semidirect |
| 8. C2×#4947 | C2 | semidirect |
| 9. #76767 | C2 | direct (N × H) |
| 10. C2×#4670 | C2 | semidirect |
| 14. C23×C3×D4 | C22 | semidirect |
| 17. C23×Dic6 | C22 | semidirect |
| 19. C22×C3×C22⋊C4 | C22 | semidirect |
| 22. C22×#217 | C22 | semidirect |
| 23. C22×#217 | C22 | semidirect |
| 25. C2×#937 | C22 | semidirect |
| 30. C22×C4⋊Dic3 | C22 | semidirect |
| 31. C22×C4×Dic3 | C22 | semidirect |
| 33. C2×#885 | C22 | semidirect |
| 34. C3×#392 | C22 | semidirect |
| 35. C2×C3×#95 | C22 | semidirect |
| 36. #5223 | C22 | semidirect |
| 37. #5221 | C22 | semidirect |
| 38. C2×C3⋊#95 | C22 | semidirect |
| 39. C2×C3⋊#95 | C22 | semidirect |
| 40. #4961 | C22 | semidirect |
| 41. #4955 | C22 | semidirect |
| 42. #4947 | C22 | semidirect |
| 43. #4670 | C22 | semidirect |
| 50. C2×#392 | D3 | semidirect |
| 69. C22×C3×D4 | C23 | semidirect |
| 86. C22×Dic6 | C23 | semidirect |
| 90. C2×C3×C22⋊C4 | C23 | semidirect |
| 97. C2×#217 | C23 | semidirect |
| 98. C2×#217 | C23 | semidirect |
| 103. C2×(C2×D3)⋊C4 | D4 | semidirect |
| 109. C2×C4⋊Dic3 | C23 | semidirect |
| 111. C2×C4×Dic3 | C23 | semidirect |
| 113. C3×#95 | C23 | semidirect |
| 114. C3⋊#95 | C23 | semidirect |
| 115. C3⋊#95 | C23 | semidirect |
| 121. C23×D4 | C2×D3 | semidirect |
| 136. C22×C22⋊C4 | C2×D3 | semidirect |
| 141. #392 | C2×D3 | semidirect |
| 147. C2×#95 | C2×D3 | semidirect |
| 230. (C2×D3)⋊C4 | C2×D4 | semidirect |
| 259. C22×D4 | C22×D3 | semidirect |
| 289. C2×C22⋊C4 | C22×D3 | semidirect |
| 294. #95 | C22×D3 | semidirect |
| 575. C2×C3 | #2670 | semidirect |
| 621. C3 | C2×#2670 | semidirect |
| 625. C2 | #76767 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#937 | 2 |
| C22×#885 | 2 |
| C2×C3×#392 | 2 |
| C2×#5223 | 2 |
| C2×#5221 | 2 |
| C2×#4955 | 2 |
| C2×#4961 | 2 |
| C2×#4947 | 2 |
| #76767 | 2 |
| C2×#4670 | 2 |
| C2×#2670 | 3 |