Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1214 conjugacy classes of subgroups.
The subgroup lattice has 434 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#5500 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #83768 | C2 | 1 | 2 | yes | maximal |
| 3 | #82186 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×C3×#343 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #71982 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #68998 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #68995 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #23462 | — | 3 | 1 | no | maximal, Sylow |
| 9 | C22×#235 | C22 | 1 | 1 | yes | characteristic |
| 10 | C22×C3×M16 | C22 | 1 | 2 | yes | — |
| 11 | C22×C3×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#926 | C22 | 1 | 2 | yes | — |
| 13 | C2×#926 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#924 | — | 2 | 2 | no | — |
| 15 | #5500 | — | 2 | 2 | no | — |
| 16 | #5500 | — | 2 | 4 | no | — |
| 17 | #5500 | C22 | 1 | 4 | yes | — |
| 18 | C2×#890 | — | 2 | 2 | no | — |
| 19 | C2×#888 | — | 2 | 2 | no | — |
| 20 | #5213 | — | 2 | 2 | no | — |
| 21 | #5133 | — | 2 | 2 | no | — |
| 22 | #5133 | — | 2 | 2 | no | — |
| 23 | #5131 | C22 | 1 | 4 | yes | — |
| 24 | #5120 | C22 | 1 | 4 | yes | — |
| 25 | #5113 | — | 2 | 4 | no | — |
| 26 | #4988 | C22 | 1 | 2 | yes | — |
| 27 | #4987 | — | 2 | 2 | no | — |
| 28 | #4973 | C22 | 1 | 2 | yes | — |
| 29 | C3×#343 | C22 | 1 | 4 | yes | — |
| 30 | #4555 | C22 | 1 | 8 | yes | — |
| 31 | C2×#544 | — | 3 | 1 | no | — |
| 32 | #2896 | — | 3 | 2 | no | — |
| 33 | #2311 | — | 3 | 1 | no | — |
| 34 | #2028 | — | 3 | 4 | no | — |
| 35 | #2027 | — | 3 | 4 | no | — |
| 36 | C2×#343 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | #1733 | — | 3 | 2 | no | — |
| 38 | C23×C3×C4 | D4 | 1 | 2 | yes | — |
| 39 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 40 | C22×#67 | — | 2 | 1 | no | — |
| 41 | C2×#235 | — | 2 | 2 | no | — |
| 42 | C2×#235 | — | 2 | 2 | no | — |
| 43 | C2×#235 | — | 2 | 2 | no | — |
| 44 | C2×#235 | — | 2 | 4 | no | — |
| 45 | C2×#235 | Q8 | 1 | 4 | yes | complemented |
| 46 | C22×D12 | C23 | 1 | 1 | yes | characteristic |
| 47 | C22×C4×D3 | — | 2 | 1 | no | — |
| 48 | C22×Dic6 | — | 2 | 2 | no | — |
| 49 | C22×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×C3×M16 | — | 2 | 2 | no | — |
| 51 | C2×C3×M16 | — | 2 | 4 | no | — |
| 52 | C2×C3×M16 | — | 2 | 4 | no | — |
| 53 | C2×C3×M16 | C23 | 1 | 4 | yes | — |
| 54 | C22×C3×C8 | — | 2 | 2 | no | — |
| 55 | C2×C3×C4⋊C4 | — | 2 | 2 | no | — |
| 56 | C2×C3×C4⋊C4 | — | 2 | 2 | no | — |
| 57 | C2×C3×C4⋊C4 | D4 | 1 | 2 | yes | — |
| 58 | C2×C3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 59 | C2×#217 | — | 2 | 2 | no | — |
| 60 | C2×#217 | — | 2 | 1 | no | — |
| 61 | C2×(C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 62 | #926 | — | 2 | 2 | no | — |
| 63 | #926 | — | 2 | 2 | no | — |
| 64 | #926 | — | 2 | 4 | no | — |
| 65 | #926 | D4 | 1 | 4 | yes | — |
| 66 | #926 | C23 | 1 | 4 | yes | — |
| 67 | C2×C4⋊Dic3 | — | 2 | 2 | no | — |
| 68 | C2×C4⋊Dic3 | — | 2 | 1 | no | — |
| 69 | C2×C4⋊Dic3 | D4 | 1 | 2 | yes | — |
| 70 | C2×C4⋊Dic3 | D4 | 1 | 2 | yes | — |
| 71 | #924 | — | 2 | 8 | no | — |
| 72 | #924 | — | 2 | 8 | no | — |
| 73 | C2×Dic3⋊C4 | — | 2 | 4 | no | — |
| 74 | C2×C4×Dic3 | — | 2 | 2 | no | — |
| 75 | C2×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 76 | #890 | — | 2 | 8 | no | — |
| 77 | #890 | — | 2 | 8 | no | — |
| 78 | #888 | — | 2 | 8 | no | — |
| 79 | #888 | — | 2 | 8 | no | — |
| 80 | C3⋊#95 | — | 2 | 4 | no | — |
| 81 | #821 | — | 2 | 4 | no | — |
| 82 | #821 | — | 2 | 4 | no | — |
| 83 | #816 | — | 2 | 4 | no | — |
| 84 | #816 | — | 2 | 4 | no | — |
| 85 | C22×#41 | — | 3 | 1 | no | — |
| 86 | C22×M16 | C2×D3 | 1 | 2 | yes | — |
| 87 | #544 | — | 3 | 4 | no | — |
| 88 | #544 | — | 6 | 4 | no | — |
| 89 | #544 | — | 6 | 2 | no | — |
| 90 | C2×C4⋊Q8 | — | 6 | 2 | no | — |
| 91 | C2×#125 | — | 6 | 2 | no | — |
| 92 | C2×C22⋊Q8 | — | 6 | 2 | no | — |
| 93 | C2×#117 | — | 3 | 1 | no | — |
| 94 | C2×#117 | — | 3 | 2 | no | — |
| 95 | C22×C4⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 96 | #419 | — | 3 | 4 | no | — |
| 97 | #418 | — | 3 | 4 | no | — |
| 98 | #417 | — | 6 | 2 | no | — |
| 99 | #417 | — | 6 | 2 | no | — |
| 100 | #416 | — | 6 | 4 | no | — |
| 101 | #391 | — | 3 | 2 | no | — |
| 102 | #390 | — | 3 | 2 | no | — |
| 103 | #386 | — | 6 | 2 | no | — |
| 104 | #380 | — | 6 | 2 | no | — |
| 105 | #343 | C2×D3 | 1 | 4 | yes | — |
| 106 | #339 | — | 3 | 8 | no | — |
| 107 | C24×C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | C23×D3 | — | 2 | 1 | no | — |
| 109 | C22×C3×C4 | — | 2 | 2 | no | — |
| 110 | C22×C3×C4 | — | 2 | 2 | no | — |
| 111 | C22×C3×C4 | — | 8 | 2 | no | — |
| 112 | C22×C3×C4 | C2×D4 | 1 | 4 | yes | — |
| 113 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 115 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 116 | C22×C3×C4 | C2×Q8 | 1 | 2 | yes | — |
| 117 | C22×C3×C4 | #41 | 1 | 4 | yes | — |
| 118 | C22×C3×C4 | #41 | 1 | 2 | yes | — |
| 119 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 120 | C2×#67 | — | 2 | 4 | no | — |
| 121 | C2×#67 | — | 4 | 1 | no | — |
| 122 | C2×#67 | — | 4 | 1 | no | — |
| 123 | C2×#67 | — | 4 | 2 | no | — |
| 124 | C22×Dic3 | — | 2 | 2 | no | — |
| 125 | C22×Dic3 | — | 2 | 2 | no | — |
| 126 | C22×Dic3 | — | 2 | 1 | no | — |
| 127 | C22×Dic3 | — | 2 | 2 | no | — |
| 128 | #235 | — | 2 | 8 | no | — |
| 129 | #235 | — | 2 | 8 | no | — |
| 130 | #235 | — | 4 | 4 | no | — |
| 131 | #235 | — | 4 | 4 | no | — |
| 132 | C2×D12 | — | 2 | 2 | no | — |
| 133 | C2×D12 | — | 2 | 2 | no | — |
| 134 | C2×D12 | — | 2 | 1 | no | — |
| 135 | C2×D12 | C2×Q8 | 1 | 2 | yes | complemented |
| 136 | C2×C4×D3 | — | 2 | 4 | no | — |
| 137 | C2×C4×D3 | — | 4 | 2 | no | — |
| 138 | C2×C4×D3 | — | 4 | 2 | no | — |
| 139 | C2×Dic6 | — | 2 | 2 | no | — |
| 140 | C2×Dic6 | — | 2 | 2 | no | — |
| 141 | C2×Dic6 | — | 2 | 1 | no | — |
| 142 | C2×Dic6 | — | 2 | 8 | no | — |
| 143 | C2×Dic6 | — | 8 | 4 | no | — |
| 144 | C2×Dic6 | C2×Q8 | 1 | 2 | yes | complemented |
| 145 | C3×M16 | — | 2 | 4 | no | — |
| 146 | C3×M16 | — | 2 | 4 | no | — |
| 147 | C3×M16 | — | 4 | 4 | no | — |
| 148 | C2×C3×C8 | — | 2 | 4 | no | — |
| 149 | C2×C3×C8 | — | 4 | 4 | no | — |
| 150 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 151 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 152 | #217 | — | 2 | 4 | no | — |
| 153 | #217 | — | 2 | 4 | no | — |
| 154 | #217 | — | 4 | 2 | no | — |
| 155 | (C2×D3)⋊C4 | — | 8 | 4 | no | — |
| 156 | C4⋊Dic3 | — | 2 | 8 | no | — |
| 157 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 158 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 159 | C4⋊Dic3 | — | 4 | 2 | no | — |
| 160 | C4⋊Dic3 | C2×D4 | 1 | 4 | yes | — |
| 161 | C4⋊Dic3 | C2×D4 | 1 | 4 | yes | — |
| 162 | Dic3⋊C4 | — | 2 | 16 | no | — |
| 163 | C4×Dic3 | — | 2 | 4 | no | — |
| 164 | C4×Dic3 | — | 2 | 4 | no | — |
| 165 | C4×Dic3 | — | 2 | 4 | no | — |
| 166 | C2×#41 | — | 3 | 4 | no | — |
| 167 | C2×#41 | — | 6 | 2 | no | — |
| 168 | C2×#41 | — | 6 | 4 | no | — |
| 169 | C2×#41 | — | 6 | 2 | no | — |
| 170 | C2×#41 | — | 6 | 2 | no | — |
| 171 | C22×Q8 | — | 3 | 1 | no | — |
| 172 | C22×Q8 | — | 6 | 2 | no | — |
| 173 | C22×D4 | — | 3 | 1 | no | — |
| 174 | C22×D4 | — | 6 | 1 | no | — |
| 175 | C23×C4 | — | 6 | 1 | no | — |
| 176 | C23×C4 | D12 | 1 | 2 | yes | — |
| 177 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 178 | C2×M16 | — | 2 | 2 | no | — |
| 179 | C2×M16 | — | 2 | 4 | no | — |
| 180 | C2×M16 | — | 2 | 4 | no | — |
| 181 | C2×M16 | C22×D3 | 1 | 4 | yes | — |
| 182 | C22×C8 | — | 2 | 2 | no | — |
| 183 | C4⋊Q8 | — | 6 | 8 | no | — |
| 184 | C4⋊Q8 | — | 6 | 8 | no | — |
| 185 | #125 | — | 6 | 8 | no | — |
| 186 | #125 | — | 6 | 8 | no | — |
| 187 | C22⋊Q8 | — | 6 | 8 | no | — |
| 188 | C22⋊Q8 | — | 6 | 8 | no | — |
| 189 | #117 | — | 3 | 4 | no | — |
| 190 | #117 | — | 3 | 4 | no | — |
| 191 | #117 | — | 6 | 2 | no | — |
| 192 | #117 | — | 6 | 2 | no | — |
| 193 | #117 | — | 6 | 4 | no | — |
| 194 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 195 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 196 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 197 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 198 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 199 | C2×C4⋊C4 | — | 6 | 4 | no | — |
| 200 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 201 | C2×C4⋊C4 | D12 | 1 | 2 | yes | — |
| 202 | C2×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 203 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 204 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 205 | C2×C22⋊C4 | — | 6 | 4 | no | — |
| 206 | C2×C42 | — | 3 | 2 | no | — |
| 207 | C2×C42 | — | 6 | 2 | no | — |
| 208 | #103 | — | 6 | 4 | no | — |
| 209 | #103 | — | 6 | 4 | no | — |
| 210 | #102 | — | 6 | 4 | no | — |
| 211 | #102 | — | 6 | 4 | no | — |
| 212 | #95 | — | 6 | 4 | no | — |
| 213 | C23×C3 | — | 4 | 1 | no | — |
| 214 | C23×C3 | — | 4 | 1 | no | — |
| 215 | C23×C3 | #120 | 1 | 1 | yes | characteristic |
| 216 | C23×C3 | #120 | 1 | 1 | yes | characteristic |
| 217 | C23×C3 | C22⋊Q8 | 1 | 2 | yes | — |
| 218 | C23×C3 | #124 | 1 | 2 | yes | — |
| 219 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 220 | C22×D3 | — | 2 | 2 | no | — |
| 221 | C22×D3 | — | 4 | 2 | no | — |
| 222 | C22×D3 | — | 4 | 2 | no | — |
| 223 | C22×D3 | — | 4 | 1 | no | — |
| 224 | C22×D3 | — | 4 | 1 | no | — |
| 225 | C2×C3×C4 | — | 2 | 4 | no | — |
| 226 | C2×C3×C4 | — | 4 | 4 | no | — |
| 227 | C2×C3×C4 | — | 4 | 4 | no | — |
| 228 | C2×C3×C4 | — | 8 | 2 | no | — |
| 229 | C2×C3×C4 | #120 | 1 | 2 | yes | — |
| 230 | C2×C3×C4 | C22⋊Q8 | 1 | 4 | yes | — |
| 231 | C2×C3×C4 | C22⋊Q8 | 1 | 4 | yes | — |
| 232 | C2×C3×C4 | C22⋊Q8 | 1 | 2 | yes | — |
| 233 | C2×C3×C4 | #124 | 1 | 2 | yes | — |
| 234 | C2×C3×C4 | #124 | 1 | 4 | yes | — |
| 235 | C2×C3×C4 | #124 | 1 | 4 | yes | — |
| 236 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 237 | C2×C3×C4 | C22×Q8 | 1 | 1 | yes | characteristic |
| 238 | C2×C3×C4 | C2×#41 | 1 | 2 | yes | — |
| 239 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 240 | #67 | — | 4 | 4 | no | — |
| 241 | #67 | — | 4 | 4 | no | — |
| 242 | C2×Dic3 | — | 2 | 4 | no | — |
| 243 | C2×Dic3 | — | 2 | 4 | no | — |
| 244 | C2×Dic3 | — | 2 | 2 | no | — |
| 245 | C2×Dic3 | — | 4 | 4 | no | — |
| 246 | C2×Dic3 | — | 4 | 4 | no | — |
| 247 | C2×Dic3 | — | 4 | 1 | no | — |
| 248 | C2×Dic3 | — | 4 | 1 | no | — |
| 249 | C2×Dic3 | — | 4 | 2 | no | — |
| 250 | C2×Dic3 | — | 4 | 2 | no | — |
| 251 | C2×Dic3 | — | 4 | 2 | no | — |
| 252 | D12 | — | 2 | 4 | no | — |
| 253 | D12 | — | 4 | 2 | no | — |
| 254 | C4×D3 | — | 4 | 8 | no | — |
| 255 | Dic6 | — | 2 | 4 | no | — |
| 256 | Dic6 | — | 4 | 2 | no | — |
| 257 | Dic6 | — | 8 | 8 | no | — |
| 258 | C3×C8 | — | 4 | 4 | no | — |
| 259 | C24 | — | 6 | 1 | no | — |
| 260 | C24 | C2×D12 | 1 | 1 | yes | characteristic |
| 261 | #41 | — | 6 | 8 | no | — |
| 262 | #41 | — | 6 | 8 | no | — |
| 263 | #41 | — | 12 | 4 | no | — |
| 264 | #41 | — | 12 | 4 | no | — |
| 265 | C2×Q8 | — | 3 | 2 | no | — |
| 266 | C2×Q8 | — | 6 | 8 | no | — |
| 267 | C2×Q8 | — | 6 | 1 | no | — |
| 268 | C2×Q8 | — | 6 | 2 | no | — |
| 269 | C2×Q8 | — | 6 | 2 | no | — |
| 270 | C2×Q8 | — | 24 | 4 | no | — |
| 271 | C2×D4 | — | 3 | 2 | no | — |
| 272 | C2×D4 | — | 6 | 4 | no | — |
| 273 | C2×D4 | — | 6 | 2 | no | — |
| 274 | C2×D4 | — | 6 | 2 | no | — |
| 275 | C2×D4 | — | 6 | 1 | no | — |
| 276 | C2×D4 | — | 12 | 2 | no | — |
| 277 | C2×D4 | — | 12 | 1 | no | — |
| 278 | C2×D4 | — | 12 | 1 | no | — |
| 279 | C22×C4 | — | 2 | 2 | no | — |
| 280 | C22×C4 | — | 2 | 2 | no | — |
| 281 | C22×C4 | — | 6 | 2 | no | — |
| 282 | C22×C4 | — | 6 | 2 | no | — |
| 283 | C22×C4 | — | 6 | 1 | no | — |
| 284 | C22×C4 | — | 6 | 4 | no | — |
| 285 | C22×C4 | — | 6 | 2 | no | — |
| 286 | C22×C4 | — | 8 | 2 | no | — |
| 287 | C22×C4 | — | 12 | 2 | no | — |
| 288 | C22×C4 | — | 12 | 2 | no | — |
| 289 | C22×C4 | C2×D12 | 1 | 4 | yes | — |
| 290 | C22×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 291 | C22×C4 | #235 | 1 | 4 | yes | — |
| 292 | C22×C4 | D3×D4 | 1 | 2 | yes | — |
| 293 | C22×C4 | D3×D4 | 1 | 2 | yes | — |
| 294 | C22×C4 | #237 | 1 | 2 | yes | — |
| 295 | C22×C4 | D3×Q8 | 1 | 2 | yes | — |
| 296 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 297 | M16 | — | 2 | 4 | no | — |
| 298 | M16 | — | 2 | 4 | no | — |
| 299 | M16 | — | 4 | 4 | no | — |
| 300 | C2×C8 | — | 2 | 4 | no | — |
| 301 | C2×C8 | — | 4 | 4 | no | — |
| 302 | C4⋊C4 | — | 2 | 4 | no | — |
| 303 | C4⋊C4 | — | 2 | 4 | no | — |
| 304 | C4⋊C4 | — | 3 | 4 | no | — |
| 305 | C4⋊C4 | — | 3 | 4 | no | — |
| 306 | C4⋊C4 | — | 6 | 8 | no | — |
| 307 | C4⋊C4 | — | 6 | 16 | no | — |
| 308 | C4⋊C4 | — | 6 | 2 | no | — |
| 309 | C4⋊C4 | — | 6 | 2 | no | — |
| 310 | C4⋊C4 | — | 12 | 2 | no | — |
| 311 | C22⋊C4 | — | 6 | 4 | no | — |
| 312 | C22⋊C4 | — | 6 | 4 | no | — |
| 313 | C22⋊C4 | — | 12 | 2 | no | — |
| 314 | C22⋊C4 | — | 24 | 4 | no | — |
| 315 | C42 | — | 6 | 4 | no | — |
| 316 | C42 | — | 6 | 4 | no | — |
| 317 | C42 | — | 6 | 4 | no | — |
| 318 | C22×C3 | — | 2 | 1 | no | — |
| 319 | C22×C3 | — | 2 | 1 | no | — |
| 320 | C22×C3 | — | 2 | 1 | no | — |
| 321 | C22×C3 | — | 2 | 1 | no | — |
| 322 | C22×C3 | — | 2 | 1 | no | — |
| 323 | C22×C3 | — | 2 | 1 | no | — |
| 324 | C22×C3 | — | 4 | 2 | no | — |
| 325 | C22×C3 | — | 4 | 2 | no | — |
| 326 | C22×C3 | #393 | 1 | 2 | yes | — |
| 327 | C22×C3 | #393 | 1 | 2 | yes | — |
| 328 | C22×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 329 | C22×C3 | C2×C22⋊Q8 | 1 | 1 | yes | characteristic |
| 330 | C22×C3 | C2×#124 | 1 | 1 | yes | characteristic |
| 331 | C2×D3 | — | 4 | 4 | no | — |
| 332 | C2×D3 | — | 4 | 2 | no | — |
| 333 | C2×D3 | — | 8 | 2 | no | — |
| 334 | C2×D3 | — | 8 | 1 | no | — |
| 335 | C2×D3 | — | 8 | 1 | no | — |
| 336 | C3×C4 | — | 4 | 4 | no | — |
| 337 | C3×C4 | #393 | 1 | 4 | yes | — |
| 338 | C3×C4 | C2×C22⋊Q8 | 1 | 2 | yes | — |
| 339 | C3×C4 | C2×#124 | 1 | 2 | yes | — |
| 340 | Dic3 | — | 4 | 2 | no | — |
| 341 | Dic3 | — | 4 | 4 | no | — |
| 342 | Dic3 | — | 4 | 4 | no | — |
| 343 | Dic3 | — | 8 | 2 | no | — |
| 344 | C23 | — | 4 | 1 | no | — |
| 345 | C23 | — | 4 | 1 | no | — |
| 346 | C23 | — | 6 | 2 | no | — |
| 347 | C23 | — | 12 | 2 | no | — |
| 348 | C23 | — | 12 | 2 | no | — |
| 349 | C23 | — | 12 | 1 | no | — |
| 350 | C23 | — | 12 | 1 | no | — |
| 351 | C23 | #875 | 1 | 2 | yes | — |
| 352 | C23 | #882 | 1 | 1 | yes | characteristic |
| 353 | C23 | #882 | 1 | 1 | yes | characteristic |
| 354 | C23 | #897 | 1 | 2 | yes | — |
| 355 | C23 | C22×D12 | 1 | 1 | yes | characteristic |
| 356 | Q8 | — | 6 | 4 | no | — |
| 357 | Q8 | — | 12 | 2 | no | — |
| 358 | Q8 | — | 24 | 8 | no | — |
| 359 | D4 | — | 6 | 4 | no | — |
| 360 | D4 | — | 12 | 4 | no | — |
| 361 | D4 | — | 12 | 4 | no | — |
| 362 | D4 | — | 12 | 2 | no | — |
| 363 | C2×C4 | — | 2 | 4 | no | — |
| 364 | C2×C4 | — | 4 | 4 | no | — |
| 365 | C2×C4 | — | 4 | 4 | no | — |
| 366 | C2×C4 | — | 6 | 4 | no | — |
| 367 | C2×C4 | — | 6 | 4 | no | — |
| 368 | C2×C4 | — | 6 | 2 | no | — |
| 369 | C2×C4 | — | 8 | 2 | no | — |
| 370 | C2×C4 | — | 12 | 4 | no | — |
| 371 | C2×C4 | — | 12 | 4 | no | — |
| 372 | C2×C4 | — | 12 | 1 | no | — |
| 373 | C2×C4 | — | 12 | 1 | no | — |
| 374 | C2×C4 | — | 12 | 8 | no | — |
| 375 | C2×C4 | — | 12 | 2 | no | — |
| 376 | C2×C4 | — | 12 | 2 | no | — |
| 377 | C2×C4 | — | 12 | 2 | no | — |
| 378 | C2×C4 | #875 | 1 | 2 | yes | — |
| 379 | C2×C4 | #882 | 1 | 2 | yes | — |
| 380 | C2×C4 | #885 | 1 | 4 | yes | — |
| 381 | C2×C4 | #885 | 1 | 4 | yes | — |
| 382 | C2×C4 | #896 | 1 | 4 | yes | — |
| 383 | C2×C4 | #896 | 1 | 4 | yes | — |
| 384 | C2×C4 | #897 | 1 | 2 | yes | — |
| 385 | C2×C4 | C2×#235 | 1 | 2 | yes | — |
| 386 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 387 | C2×C4 | C2×#237 | 1 | 1 | yes | characteristic |
| 388 | C2×C4 | C2×D3×Q8 | 1 | 1 | yes | characteristic |
| 389 | C8 | — | 4 | 4 | no | — |
| 390 | C2×C3 | — | 2 | 1 | no | — |
| 391 | C2×C3 | — | 2 | 1 | no | — |
| 392 | C2×C3 | — | 2 | 2 | no | — |
| 393 | C2×C3 | — | 2 | 2 | no | — |
| 394 | C2×C3 | C2×#393 | 1 | 1 | yes | characteristic |
| 395 | C2×C3 | #3019 | 1 | 1 | yes | characteristic |
| 396 | C2×C3 | #3020 | 1 | 1 | yes | characteristic |
| 397 | D3 | — | 8 | 2 | no | — |
| 398 | C22 | — | 2 | 1 | no | — |
| 399 | C22 | — | 2 | 1 | no | — |
| 400 | C22 | — | 2 | 1 | no | — |
| 401 | C22 | — | 2 | 1 | no | — |
| 402 | C22 | — | 2 | 1 | no | — |
| 403 | C22 | — | 2 | 1 | no | — |
| 404 | C22 | — | 4 | 2 | no | — |
| 405 | C22 | — | 4 | 2 | no | — |
| 406 | C22 | — | 12 | 4 | no | — |
| 407 | C22 | — | 12 | 2 | no | — |
| 408 | C22 | — | 24 | 2 | no | — |
| 409 | C22 | — | 24 | 1 | no | — |
| 410 | C22 | — | 24 | 1 | no | — |
| 411 | C22 | #4673 | 1 | 2 | yes | — |
| 412 | C22 | #4673 | 1 | 2 | yes | — |
| 413 | C22 | C2×#875 | 1 | 1 | yes | characteristic |
| 414 | C22 | C2×#882 | 1 | 1 | yes | characteristic |
| 415 | C22 | C2×#897 | 1 | 1 | yes | characteristic |
| 416 | C4 | — | 4 | 4 | no | — |
| 417 | C4 | — | 12 | 4 | no | — |
| 418 | C4 | — | 12 | 4 | no | — |
| 419 | C4 | — | 12 | 2 | no | — |
| 420 | C4 | — | 24 | 2 | no | — |
| 421 | C4 | #4673 | 1 | 4 | yes | — |
| 422 | C4 | C2×#885 | 1 | 2 | yes | — |
| 423 | C4 | C2×#896 | 1 | 2 | yes | — |
| 424 | C3 | #23462 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 425 | C2 | — | 2 | 1 | no | — |
| 426 | C2 | — | 2 | 1 | no | — |
| 427 | C2 | — | 2 | 2 | no | — |
| 428 | C2 | — | 2 | 2 | no | — |
| 429 | C2 | — | 24 | 2 | no | — |
| 430 | C2 | C2×#4673 | 1 | 1 | yes | characteristic |
| 431 | C2 | #78700 | 1 | 1 | yes | characteristic |
| 432 | C2 | #78709 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#5500 | C2 | semidirect |
| 4. C2×C3×#343 | C2 | semidirect |
| 5. #71982 | C2 | semidirect |
| 6. #68998 | C2 | semidirect |
| 7. #68995 | C2 | semidirect |
| 36. C2×#343 | D3 | semidirect |
| 45. C2×#235 | Q8 | semidirect |
| 135. C2×D12 | C2×Q8 | semidirect |
| 144. C2×Dic6 | C2×Q8 | semidirect |
| 424. C3 | #23462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5500 | 2 |
| #83768 | 2 |
| #82186 | 2 |
| C2×C3×#343 | 2 |
| #71982 | 2 |
| #68998 | 2 |
| #68995 | 2 |
| #23462 | 3 |