Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1302 conjugacy classes of subgroups.
The subgroup lattice has 374 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C3×#401 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#4676 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #69429 | C2 | 1 | 3 | yes | maximal |
| 4 | #69414 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #69408 | C2 | 1 | 3 | yes | maximal |
| 6 | #69405 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | Dic3×#95 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #15171 | — | 3 | 1 | no | maximal, Sylow |
| 9 | C22×(C2×D3)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 10 | C22×(C2×D3)⋊C4 | C22 | 1 | 3 | yes | — |
| 11 | C22×(C2×D3)⋊C4 | C22 | 1 | 3 | yes | — |
| 12 | C22×Dic3⋊C4 | C22 | 1 | 3 | yes | — |
| 13 | C22×C4×Dic3 | C22 | 1 | 3 | yes | — |
| 14 | C3×#401 | — | 2 | 4 | no | — |
| 15 | C2×C3×#95 | C22 | 1 | 3 | yes | — |
| 16 | C2×C3×#95 | C22 | 1 | 3 | yes | — |
| 17 | C2×C3×#95 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C3⋊#95 | C22 | 1 | 3 | yes | — |
| 19 | C2×C3⋊#95 | C22 | 1 | 3 | yes | — |
| 20 | C2×C3⋊#95 | C22 | 1 | 3 | yes | — |
| 21 | C2×C3⋊#95 | C22 | 1 | 3 | yes | — |
| 22 | C2×C3⋊#95 | C22 | 1 | 3 | yes | — |
| 23 | #4676 | — | 2 | 4 | no | — |
| 24 | C2×#401 | D3 | 1 | 1 | yes | characteristic, complemented |
| 25 | C2×#396 | — | 3 | 1 | no | — |
| 26 | #1442 | — | 3 | 3 | no | — |
| 27 | #1440 | — | 3 | 3 | no | — |
| 28 | #1437 | — | 3 | 3 | no | — |
| 29 | #1436 | — | 3 | 3 | no | — |
| 30 | C4×#95 | — | 3 | 1 | no | — |
| 31 | C24×D3 | C23 | 1 | 1 | yes | characteristic |
| 32 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 33 | C23×C3×C4 | C23 | 1 | 3 | yes | — |
| 34 | C23×C3×C4 | C23 | 1 | 3 | yes | — |
| 35 | C23×Dic3 | C23 | 1 | 3 | yes | — |
| 36 | C23×Dic3 | C23 | 1 | 3 | yes | — |
| 37 | C23×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 38 | C2×(C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 39 | C2×(C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 40 | C2×(C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 41 | C2×(C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 42 | C2×(C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 43 | C2×(C2×D3)⋊C4 | — | 4 | 3 | no | — |
| 44 | C2×(C2×D3)⋊C4 | — | 4 | 3 | no | — |
| 45 | C2×Dic3⋊C4 | — | 2 | 6 | no | — |
| 46 | C2×Dic3⋊C4 | — | 2 | 6 | no | — |
| 47 | C2×Dic3⋊C4 | — | 4 | 3 | no | — |
| 48 | C2×C4×Dic3 | — | 2 | 6 | no | — |
| 49 | C2×C4×Dic3 | — | 4 | 3 | no | — |
| 50 | C2×C4×Dic3 | — | 4 | 3 | no | — |
| 51 | C3×#95 | — | 2 | 6 | no | — |
| 52 | C3×#95 | — | 2 | 6 | no | — |
| 53 | C3×#95 | D4 | 1 | 4 | yes | — |
| 54 | C3⋊#95 | — | 2 | 6 | no | — |
| 55 | C3⋊#95 | — | 2 | 6 | no | — |
| 56 | C3⋊#95 | — | 2 | 6 | no | — |
| 57 | C3⋊#95 | — | 2 | 6 | no | — |
| 58 | C3⋊#95 | — | 4 | 3 | no | — |
| 59 | C22×C4⋊C4 | — | 3 | 3 | no | — |
| 60 | C22×C22⋊C4 | — | 3 | 1 | no | — |
| 61 | C22×C22⋊C4 | — | 3 | 3 | no | — |
| 62 | C22×C22⋊C4 | — | 3 | 3 | no | — |
| 63 | C22×C42 | — | 3 | 3 | no | — |
| 64 | #401 | — | 2 | 4 | no | — |
| 65 | #396 | — | 6 | 4 | no | — |
| 66 | C2×#95 | — | 3 | 3 | no | — |
| 67 | C2×#95 | — | 3 | 3 | no | — |
| 68 | C2×#95 | — | 3 | 3 | no | — |
| 69 | C2×#95 | — | 3 | 3 | no | — |
| 70 | C2×#95 | — | 3 | 3 | no | — |
| 71 | C2×#95 | C2×D3 | 1 | 3 | yes | — |
| 72 | C2×#95 | C2×D3 | 1 | 3 | yes | — |
| 73 | C2×#95 | C2×D3 | 1 | 1 | yes | characteristic |
| 74 | C24×C3 | C24 | 1 | 1 | yes | characteristic |
| 75 | C23×D3 | — | 2 | 1 | no | — |
| 76 | C23×D3 | — | 2 | 3 | no | — |
| 77 | C23×D3 | — | 2 | 3 | no | — |
| 78 | C23×D3 | — | 2 | 3 | no | — |
| 79 | C23×D3 | — | 2 | 3 | no | — |
| 80 | C23×D3 | — | 2 | 1 | no | — |
| 81 | C23×D3 | #41 | 1 | 2 | yes | — |
| 82 | C22×C3×C4 | — | 2 | 3 | no | — |
| 83 | C22×C3×C4 | — | 2 | 3 | no | — |
| 84 | C22×C3×C4 | — | 2 | 3 | no | — |
| 85 | C22×C3×C4 | — | 2 | 3 | no | — |
| 86 | C22×C3×C4 | — | 2 | 3 | no | — |
| 87 | C22×C3×C4 | — | 2 | 3 | no | — |
| 88 | C22×C3×C4 | — | 2 | 1 | no | — |
| 89 | C22×C3×C4 | — | 2 | 3 | no | — |
| 90 | C22×C3×C4 | — | 2 | 3 | no | — |
| 91 | C22×C3×C4 | — | 2 | 3 | no | — |
| 92 | C22×C3×C4 | — | 2 | 3 | no | — |
| 93 | C22×C3×C4 | — | 2 | 3 | no | — |
| 94 | C22×C3×C4 | — | 2 | 3 | no | — |
| 95 | C22×C3×C4 | — | 2 | 3 | no | — |
| 96 | C22×C3×C4 | — | 2 | 3 | no | — |
| 97 | C22×C3×C4 | — | 2 | 3 | no | — |
| 98 | C22×C3×C4 | C2×D4 | 1 | 6 | yes | — |
| 99 | C22×Dic3 | — | 2 | 3 | no | — |
| 100 | C22×Dic3 | — | 2 | 1 | no | — |
| 101 | C22×Dic3 | — | 2 | 3 | no | — |
| 102 | C22×Dic3 | — | 2 | 3 | no | — |
| 103 | C22×Dic3 | — | 2 | 3 | no | — |
| 104 | C22×Dic3 | — | 2 | 3 | no | — |
| 105 | C22×Dic3 | — | 2 | 3 | no | — |
| 106 | C22×Dic3 | — | 2 | 3 | no | — |
| 107 | C22×Dic3 | — | 2 | 3 | no | — |
| 108 | C22×Dic3 | — | 2 | 3 | no | — |
| 109 | C22×Dic3 | — | 2 | 3 | no | — |
| 110 | C22×Dic3 | — | 2 | 3 | no | — |
| 111 | C22×Dic3 | — | 2 | 3 | no | — |
| 112 | C22×Dic3 | — | 2 | 3 | no | — |
| 113 | C22×Dic3 | #41 | 1 | 6 | yes | — |
| 114 | C22×Dic3 | #41 | 1 | 6 | yes | — |
| 115 | C22×Dic3 | #41 | 1 | 6 | yes | — |
| 116 | (C2×D3)⋊C4 | — | 4 | 12 | no | — |
| 117 | (C2×D3)⋊C4 | — | 4 | 12 | no | — |
| 118 | (C2×D3)⋊C4 | — | 4 | 4 | no | — |
| 119 | Dic3⋊C4 | — | 4 | 12 | no | — |
| 120 | C4×Dic3 | — | 4 | 12 | no | — |
| 121 | C25 | — | 3 | 1 | no | — |
| 122 | C23×C4 | — | 3 | 1 | no | — |
| 123 | C23×C4 | — | 3 | 3 | no | — |
| 124 | C23×C4 | — | 3 | 3 | no | — |
| 125 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 126 | C23×C4 | C22×D3 | 1 | 3 | yes | — |
| 127 | C23×C4 | C22×D3 | 1 | 3 | yes | — |
| 128 | C2×C4⋊C4 | — | 6 | 6 | no | — |
| 129 | C2×C4⋊C4 | — | 6 | 6 | no | — |
| 130 | C2×C4⋊C4 | — | 12 | 3 | no | — |
| 131 | C2×C22⋊C4 | — | 6 | 6 | no | — |
| 132 | C2×C22⋊C4 | — | 6 | 6 | no | — |
| 133 | C2×C22⋊C4 | — | 6 | 6 | no | — |
| 134 | C2×C22⋊C4 | — | 6 | 6 | no | — |
| 135 | C2×C22⋊C4 | — | 6 | 6 | no | — |
| 136 | C2×C22⋊C4 | — | 12 | 3 | no | — |
| 137 | C2×C22⋊C4 | — | 12 | 3 | no | — |
| 138 | C2×C42 | — | 6 | 6 | no | — |
| 139 | C2×C42 | — | 12 | 3 | no | — |
| 140 | C2×C42 | — | 12 | 3 | no | — |
| 141 | #95 | — | 2 | 6 | no | — |
| 142 | #95 | — | 2 | 6 | no | — |
| 143 | #95 | — | 6 | 6 | no | — |
| 144 | #95 | — | 6 | 6 | no | — |
| 145 | #95 | — | 6 | 6 | no | — |
| 146 | #95 | — | 6 | 6 | no | — |
| 147 | #95 | — | 12 | 3 | no | — |
| 148 | #95 | #67 | 1 | 4 | yes | — |
| 149 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 150 | C23×C3 | C2×#41 | 1 | 3 | yes | — |
| 151 | C23×C3 | C2×#41 | 1 | 3 | yes | — |
| 152 | C23×C3 | C2×#41 | 1 | 1 | yes | characteristic |
| 153 | C23×C3 | C2×#41 | 1 | 3 | yes | — |
| 154 | C23×C3 | H(5,𝔽2) | 1 | 3 | yes | — |
| 155 | C23×C3 | 2−1+4 | 1 | 1 | yes | characteristic |
| 156 | C22×D3 | — | 2 | 6 | no | — |
| 157 | C22×D3 | — | 2 | 2 | no | — |
| 158 | C22×D3 | — | 2 | 6 | no | — |
| 159 | C22×D3 | — | 4 | 1 | no | — |
| 160 | C22×D3 | — | 4 | 3 | no | — |
| 161 | C22×D3 | — | 4 | 3 | no | — |
| 162 | C22×D3 | — | 4 | 3 | no | — |
| 163 | C22×D3 | — | 4 | 3 | no | — |
| 164 | C22×D3 | — | 4 | 3 | no | — |
| 165 | C22×D3 | — | 4 | 3 | no | — |
| 166 | C22×D3 | — | 4 | 3 | no | — |
| 167 | C22×D3 | — | 4 | 3 | no | — |
| 168 | C22×D3 | — | 4 | 3 | no | — |
| 169 | C2×C3×C4 | — | 2 | 6 | no | — |
| 170 | C2×C3×C4 | — | 2 | 6 | no | — |
| 171 | C2×C3×C4 | — | 2 | 6 | no | — |
| 172 | C2×C3×C4 | — | 4 | 3 | no | — |
| 173 | C2×C3×C4 | — | 4 | 3 | no | — |
| 174 | C2×C3×C4 | — | 4 | 3 | no | — |
| 175 | C2×C3×C4 | — | 4 | 3 | no | — |
| 176 | C2×C3×C4 | — | 4 | 1 | no | — |
| 177 | C2×C3×C4 | — | 4 | 3 | no | — |
| 178 | C2×C3×C4 | — | 4 | 3 | no | — |
| 179 | C2×C3×C4 | — | 4 | 3 | no | — |
| 180 | C2×C3×C4 | — | 4 | 3 | no | — |
| 181 | C2×C3×C4 | — | 4 | 3 | no | — |
| 182 | C2×C3×C4 | — | 4 | 3 | no | — |
| 183 | C2×C3×C4 | — | 4 | 3 | no | — |
| 184 | C2×C3×C4 | — | 4 | 3 | no | — |
| 185 | C2×C3×C4 | — | 4 | 3 | no | — |
| 186 | C2×Dic3 | — | 2 | 6 | no | — |
| 187 | C2×Dic3 | — | 2 | 6 | no | — |
| 188 | C2×Dic3 | — | 2 | 6 | no | — |
| 189 | C2×Dic3 | — | 2 | 6 | no | — |
| 190 | C2×Dic3 | — | 2 | 6 | no | — |
| 191 | C2×Dic3 | — | 2 | 6 | no | — |
| 192 | C2×Dic3 | — | 2 | 6 | no | — |
| 193 | C2×Dic3 | — | 2 | 6 | no | — |
| 194 | C2×Dic3 | — | 4 | 3 | no | — |
| 195 | C2×Dic3 | — | 4 | 3 | no | — |
| 196 | C2×Dic3 | — | 4 | 3 | no | — |
| 197 | C2×Dic3 | — | 4 | 3 | no | — |
| 198 | C2×Dic3 | — | 4 | 3 | no | — |
| 199 | C2×Dic3 | — | 4 | 3 | no | — |
| 200 | C2×Dic3 | — | 4 | 3 | no | — |
| 201 | C2×Dic3 | — | 4 | 3 | no | — |
| 202 | C2×Dic3 | #126 | 1 | 4 | yes | — |
| 203 | C24 | — | 3 | 2 | no | — |
| 204 | C24 | — | 6 | 3 | no | — |
| 205 | C24 | — | 6 | 3 | no | — |
| 206 | C24 | — | 6 | 3 | no | — |
| 207 | C24 | — | 6 | 3 | no | — |
| 208 | C24 | — | 6 | 1 | no | — |
| 209 | C24 | — | 6 | 1 | no | — |
| 210 | C24 | C23×D3 | 1 | 1 | yes | characteristic |
| 211 | C22×C4 | — | 2 | 3 | no | — |
| 212 | C22×C4 | — | 2 | 3 | no | — |
| 213 | C22×C4 | — | 2 | 3 | no | — |
| 214 | C22×C4 | — | 2 | 3 | no | — |
| 215 | C22×C4 | — | 2 | 3 | no | — |
| 216 | C22×C4 | — | 2 | 3 | no | — |
| 217 | C22×C4 | — | 2 | 3 | no | — |
| 218 | C22×C4 | — | 2 | 3 | no | — |
| 219 | C22×C4 | — | 2 | 3 | no | — |
| 220 | C22×C4 | — | 2 | 3 | no | — |
| 221 | C22×C4 | — | 2 | 3 | no | — |
| 222 | C22×C4 | — | 2 | 3 | no | — |
| 223 | C22×C4 | — | 2 | 3 | no | — |
| 224 | C22×C4 | — | 2 | 3 | no | — |
| 225 | C22×C4 | — | 2 | 3 | no | — |
| 226 | C22×C4 | — | 2 | 1 | no | — |
| 227 | C22×C4 | — | 3 | 6 | no | — |
| 228 | C22×C4 | — | 3 | 6 | no | — |
| 229 | C22×C4 | — | 3 | 6 | no | — |
| 230 | C22×C4 | — | 6 | 3 | no | — |
| 231 | C22×C4 | — | 6 | 1 | no | — |
| 232 | C22×C4 | — | 6 | 3 | no | — |
| 233 | C22×C4 | — | 6 | 3 | no | — |
| 234 | C22×C4 | — | 6 | 3 | no | — |
| 235 | C22×C4 | — | 6 | 3 | no | — |
| 236 | C22×C4 | — | 6 | 3 | no | — |
| 237 | C22×C4 | — | 6 | 3 | no | — |
| 238 | C22×C4 | — | 6 | 3 | no | — |
| 239 | C22×C4 | — | 6 | 3 | no | — |
| 240 | C22×C4 | — | 6 | 3 | no | — |
| 241 | C22×C4 | — | 6 | 3 | no | — |
| 242 | C22×C4 | — | 6 | 3 | no | — |
| 243 | C22×C4 | — | 6 | 3 | no | — |
| 244 | C22×C4 | C2×#67 | 1 | 6 | yes | — |
| 245 | C4⋊C4 | — | 12 | 12 | no | — |
| 246 | C22⋊C4 | — | 12 | 12 | no | — |
| 247 | C22⋊C4 | — | 12 | 4 | no | — |
| 248 | C22⋊C4 | — | 12 | 12 | no | — |
| 249 | C42 | — | 12 | 12 | no | — |
| 250 | C22×C3 | C2×#126 | 1 | 1 | yes | characteristic |
| 251 | C22×C3 | #529 | 1 | 3 | yes | — |
| 252 | C22×C3 | #529 | 1 | 3 | yes | — |
| 253 | C22×C3 | #529 | 1 | 3 | yes | — |
| 254 | C22×C3 | #532 | 1 | 3 | yes | — |
| 255 | C22×C3 | #538 | 1 | 3 | yes | — |
| 256 | C22×C3 | #539 | 1 | 3 | yes | — |
| 257 | C22×C3 | #546 | 1 | 3 | yes | — |
| 258 | C22×C3 | #548 | 1 | 1 | yes | characteristic |
| 259 | C22×C3 | #551 | 1 | 3 | yes | — |
| 260 | C22×C3 | #553 | 1 | 3 | yes | — |
| 261 | C22×C3 | #553 | 1 | 3 | yes | — |
| 262 | C22×C3 | #556 | 1 | 3 | yes | — |
| 263 | C2×D3 | — | 4 | 6 | no | — |
| 264 | C2×D3 | — | 4 | 6 | no | — |
| 265 | C2×D3 | — | 4 | 2 | no | — |
| 266 | C2×D3 | — | 8 | 3 | no | — |
| 267 | C2×D3 | — | 8 | 1 | no | — |
| 268 | C2×D3 | — | 8 | 1 | no | — |
| 269 | C2×D3 | — | 8 | 3 | no | — |
| 270 | C3×C4 | — | 4 | 6 | no | — |
| 271 | C3×C4 | — | 8 | 3 | no | — |
| 272 | C3×C4 | — | 8 | 1 | no | — |
| 273 | Dic3 | — | 2 | 4 | no | — |
| 274 | Dic3 | — | 4 | 6 | no | — |
| 275 | Dic3 | — | 4 | 6 | no | — |
| 276 | C23 | — | 6 | 6 | no | — |
| 277 | C23 | — | 6 | 6 | no | — |
| 278 | C23 | — | 6 | 2 | no | — |
| 279 | C23 | — | 12 | 3 | no | — |
| 280 | C23 | — | 12 | 1 | no | — |
| 281 | C23 | — | 12 | 3 | no | — |
| 282 | C23 | — | 12 | 3 | no | — |
| 283 | C23 | — | 12 | 3 | no | — |
| 284 | C23 | — | 12 | 3 | no | — |
| 285 | C23 | — | 12 | 3 | no | — |
| 286 | C23 | — | 12 | 3 | no | — |
| 287 | C23 | — | 12 | 3 | no | — |
| 288 | C23 | — | 12 | 3 | no | — |
| 289 | C23 | D3×#41 | 1 | 3 | yes | — |
| 290 | C23 | D3×#41 | 1 | 3 | yes | — |
| 291 | C23 | D3×#41 | 1 | 3 | yes | — |
| 292 | C23 | D3×#41 | 1 | 1 | yes | characteristic |
| 293 | C23 | #1009 | 1 | 3 | yes | — |
| 294 | C23 | #1010 | 1 | 1 | yes | characteristic |
| 295 | C23 | C22×#67 | 1 | 1 | yes | characteristic |
| 296 | C2×C4 | — | 2 | 6 | no | — |
| 297 | C2×C4 | — | 2 | 6 | no | — |
| 298 | C2×C4 | — | 2 | 6 | no | — |
| 299 | C2×C4 | — | 3 | 4 | no | — |
| 300 | C2×C4 | — | 4 | 3 | no | — |
| 301 | C2×C4 | — | 4 | 3 | no | — |
| 302 | C2×C4 | — | 4 | 3 | no | — |
| 303 | C2×C4 | — | 4 | 3 | no | — |
| 304 | C2×C4 | — | 4 | 3 | no | — |
| 305 | C2×C4 | — | 4 | 1 | no | — |
| 306 | C2×C4 | — | 4 | 3 | no | — |
| 307 | C2×C4 | — | 4 | 3 | no | — |
| 308 | C2×C4 | — | 4 | 3 | no | — |
| 309 | C2×C4 | — | 4 | 3 | no | — |
| 310 | C2×C4 | — | 4 | 3 | no | — |
| 311 | C2×C4 | — | 4 | 3 | no | — |
| 312 | C2×C4 | — | 4 | 3 | no | — |
| 313 | C2×C4 | — | 4 | 3 | no | — |
| 314 | C2×C4 | — | 6 | 6 | no | — |
| 315 | C2×C4 | — | 6 | 6 | no | — |
| 316 | C2×C4 | — | 6 | 6 | no | — |
| 317 | C2×C4 | — | 6 | 6 | no | — |
| 318 | C2×C4 | — | 6 | 6 | no | — |
| 319 | C2×C4 | — | 6 | 6 | no | — |
| 320 | C2×C4 | — | 6 | 6 | no | — |
| 321 | C2×C4 | — | 6 | 6 | no | — |
| 322 | C2×C4 | — | 12 | 3 | no | — |
| 323 | C2×C4 | — | 12 | 3 | no | — |
| 324 | C2×C4 | — | 12 | 3 | no | — |
| 325 | C2×C4 | — | 12 | 3 | no | — |
| 326 | C2×C4 | — | 12 | 3 | no | — |
| 327 | C2×C4 | — | 12 | 3 | no | — |
| 328 | C2×C4 | — | 12 | 3 | no | — |
| 329 | C2×C4 | — | 12 | 3 | no | — |
| 330 | C2×C3 | #2401 | 1 | 1 | yes | characteristic |
| 331 | C2×C3 | #2559 | 1 | 3 | yes | — |
| 332 | C2×C3 | #2560 | 1 | 3 | yes | — |
| 333 | C2×C3 | #2576 | 1 | 3 | yes | — |
| 334 | C2×C3 | #2594 | 1 | 3 | yes | — |
| 335 | C2×C3 | #2643 | 1 | 1 | yes | characteristic |
| 336 | C2×C3 | #2860 | 1 | 1 | yes | characteristic |
| 337 | D3 | — | 8 | 2 | no | — |
| 338 | C22 | — | 12 | 2 | no | — |
| 339 | C22 | — | 12 | 6 | no | — |
| 340 | C22 | — | 12 | 6 | no | — |
| 341 | C22 | — | 24 | 3 | no | — |
| 342 | C22 | — | 24 | 1 | no | — |
| 343 | C22 | — | 24 | 1 | no | — |
| 344 | C22 | — | 24 | 3 | no | — |
| 345 | C22 | #5702 | 1 | 3 | yes | — |
| 346 | C22 | D3×#126 | 1 | 1 | yes | characteristic |
| 347 | C22 | #5704 | 1 | 3 | yes | — |
| 348 | C22 | #5705 | 1 | 3 | yes | — |
| 349 | C22 | #5706 | 1 | 3 | yes | — |
| 350 | C22 | #5706 | 1 | 3 | yes | — |
| 351 | C22 | #5706 | 1 | 3 | yes | — |
| 352 | C22 | #5707 | 1 | 3 | yes | — |
| 353 | C22 | #5709 | 1 | 3 | yes | — |
| 354 | C22 | #5709 | 1 | 3 | yes | — |
| 355 | C22 | #5829 | 1 | 3 | yes | — |
| 356 | C22 | #5831 | 1 | 1 | yes | characteristic |
| 357 | C22 | #5832 | 1 | 3 | yes | — |
| 358 | C4 | — | 4 | 6 | no | — |
| 359 | C4 | — | 6 | 4 | no | — |
| 360 | C4 | — | 8 | 1 | no | — |
| 361 | C4 | — | 8 | 3 | no | — |
| 362 | C4 | — | 12 | 6 | no | — |
| 363 | C4 | — | 12 | 6 | no | — |
| 364 | C3 | #15171 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 365 | C2 | — | 24 | 2 | no | — |
| 366 | C2 | #78409 | 1 | 1 | yes | characteristic |
| 367 | C2 | #78414 | 1 | 3 | yes | — |
| 368 | C2 | #78415 | 1 | 3 | yes | — |
| 369 | C2 | #78432 | 1 | 1 | yes | characteristic |
| 370 | C2 | #83104 | 1 | 1 | yes | characteristic |
| 371 | C2 | #83109 | 1 | 3 | yes | — |
| 372 | C2 | #83110 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D3 |
| commutator, socle, cosocle | C24×C3 | C24 |
| Fitting | C2×C3×#401 | C2 |
| prime radical | C24×D3 | C23 |
| hypercenter | C2×#401 | D3 |
| hypocenter | C3 | #15171 |
| LCS | G ▷ C24×C3 ▷ C3 | |
| UCS | C1 ◁ C24 ◁ C2×#401 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×#401 | C2 | semidirect |
| 4. #69414 | C2 | semidirect |
| 6. #69405 | C2 | semidirect |
| 7. Dic3×#95 | C2 | semidirect |
| 24. C2×#401 | D3 | semidirect |
| 364. C3 | #15171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#401 | 2 |
| C2×#4676 | 2 |
| #69429 | 2 |
| #69414 | 2 |
| #69408 | 2 |
| #69405 | 2 |
| Dic3×#95 | 2 |
| #15171 | 3 |