Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
4986 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 4986 conjugacy classes of subgroups — too many to draw. Only its 312 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×A4×C3⋊D3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C22×C3×D3×A4 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×D32×A4 | C2 | 1 | 12 | yes | maximal, direct product factor |
| 4 | C24×D32 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C23×D3×A4 | — | 3 | 2 | no | maximal |
| 6 | C22×C32×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 7 | C22×C3×D32 | — | 4 | 1 | no | maximal |
| 8 | C2×A4×C3⋊D3 | C22 | 1 | 6 | yes | complemented |
| 9 | C2×C3×D3×A4 | C22 | 1 | 12 | yes | complemented |
| 10 | D32×A4 | C22 | 1 | 16 | yes | direct product factor |
| 11 | C24×C3⋊D3 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 12 | C24×C3×D3 | C2×C3 | 1 | 2 | yes | complemented |
| 13 | C23×C3×A4 | — | 3 | 2 | no | — |
| 14 | C23×D32 | — | 3 | 1 | no | — |
| 15 | C23×D32 | — | 3 | 1 | no | — |
| 16 | C23×D32 | — | 3 | 2 | no | — |
| 17 | C23×D32 | — | 3 | 12 | no | — |
| 18 | C23×D32 | C2×C3 | 1 | 12 | yes | complemented |
| 19 | C22×D3×A4 | — | 2 | 2 | no | — |
| 20 | C22×D3×A4 | — | 3 | 2 | no | — |
| 21 | C22×D3×A4 | — | 3 | 24 | no | — |
| 22 | C22×D3×A4 | — | 6 | 1 | no | — |
| 23 | C22×D3×A4 | D3 | 1 | 2 | yes | direct product factor |
| 24 | C22×C3×C3⋊D3 | — | 4 | 1 | no | — |
| 25 | C22×C32×D3 | — | 4 | 2 | no | — |
| 26 | C2×C32×A4 | C23 | 1 | 3 | yes | complemented |
| 27 | C2×C3×D32 | — | 4 | 12 | no | — |
| 28 | A4×C3⋊D3 | C23 | 1 | 4 | yes | complemented |
| 29 | C3×D3×A4 | C23 | 1 | 8 | yes | complemented |
| 30 | C25×D3 | — | 3 | 2 | no | — |
| 31 | C24×A4 | — | 9 | 1 | no | — |
| 32 | C24×C32 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 33 | C23×C3⋊D3 | — | 3 | 1 | no | — |
| 34 | C23×C3⋊D3 | — | 3 | 1 | no | — |
| 35 | C23×C3⋊D3 | — | 3 | 6 | no | — |
| 36 | C23×C3⋊D3 | C22×C3 | 1 | 6 | yes | complemented |
| 37 | C23×C3×D3 | — | 3 | 2 | no | — |
| 38 | C23×C3×D3 | — | 3 | 2 | no | — |
| 39 | C23×C3×D3 | — | 3 | 12 | no | — |
| 40 | C23×C3×D3 | — | 12 | 2 | no | — |
| 41 | C23×C3×D3 | C22×C3 | 1 | 12 | yes | complemented |
| 42 | C22×C3×A4 | — | 2 | 2 | no | — |
| 43 | C22×C3×A4 | — | 2 | 1 | no | — |
| 44 | C22×C3×A4 | — | 3 | 12 | no | — |
| 45 | C22×C3×A4 | — | 4 | 1 | no | — |
| 46 | C22×C3×A4 | C2×D3 | 1 | 2 | yes | complemented |
| 47 | C22×D32 | — | 3 | 2 | no | — |
| 48 | C22×D32 | — | 3 | 12 | no | — |
| 49 | C22×D32 | — | 3 | 24 | no | — |
| 50 | C22×D32 | — | 3 | 32 | no | — |
| 51 | C22×D32 | — | 3 | 1 | no | — |
| 52 | C22×D32 | — | 3 | 2 | no | — |
| 53 | C22×D32 | — | 3 | 12 | no | — |
| 54 | C22×D32 | — | 3 | 12 | no | — |
| 55 | C22×D32 | — | 3 | 12 | no | — |
| 56 | C22×D32 | — | 3 | 24 | no | — |
| 57 | C22×D32 | — | 3 | 48 | no | — |
| 58 | C22×D32 | A4 | 1 | 1 | yes | characteristic, direct product factor |
| 59 | C22×D32 | C22×C3 | 1 | 16 | yes | complemented |
| 60 | C2×D3×A4 | — | 2 | 12 | no | — |
| 61 | C2×D3×A4 | — | 3 | 12 | no | — |
| 62 | C2×D3×A4 | — | 3 | 32 | no | — |
| 63 | C2×D3×A4 | — | 6 | 6 | no | — |
| 64 | C2×D3×A4 | C2×D3 | 1 | 12 | yes | direct product factor |
| 65 | C22×C33 | — | 4 | 1 | no | — |
| 66 | C2×C3×C3⋊D3 | — | 4 | 6 | no | — |
| 67 | C2×C32×D3 | — | 4 | 12 | no | — |
| 68 | C32×A4 | C24 | 1 | 1 | yes | characteristic, complemented |
| 69 | C3×D32 | — | 4 | 16 | no | — |
| 70 | C25×C3 | — | 3 | 2 | no | — |
| 71 | C24×D3 | — | 3 | 2 | no | — |
| 72 | C24×D3 | — | 3 | 24 | no | — |
| 73 | C24×D3 | — | 6 | 1 | no | — |
| 74 | C24×D3 | — | 9 | 2 | no | — |
| 75 | C24×D3 | — | 9 | 2 | no | — |
| 76 | C24×D3 | — | 9 | 24 | no | — |
| 77 | C24×D3 | — | 9 | 2 | no | — |
| 78 | C24×D3 | — | 9 | 2 | no | — |
| 79 | C24×D3 | C3×D3 | 1 | 2 | yes | complemented |
| 80 | C23×A4 | — | 3 | 2 | no | — |
| 81 | C23×A4 | — | 6 | 2 | no | — |
| 82 | C23×A4 | — | 9 | 12 | no | — |
| 83 | C23×A4 | — | 9 | 1 | no | — |
| 84 | C23×C32 | — | 3 | 3 | no | — |
| 85 | C23×C32 | — | 3 | 1 | no | — |
| 86 | C23×C32 | — | 12 | 2 | no | — |
| 87 | C23×C32 | C23×C3 | 1 | 3 | yes | complemented |
| 88 | C22×C3⋊D3 | — | 3 | 6 | no | — |
| 89 | C22×C3⋊D3 | — | 3 | 8 | no | — |
| 90 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 91 | C22×C3⋊D3 | — | 3 | 6 | no | — |
| 92 | C22×C3⋊D3 | — | 3 | 6 | no | — |
| 93 | C22×C3⋊D3 | — | 3 | 6 | no | — |
| 94 | C22×C3⋊D3 | — | 3 | 12 | no | — |
| 95 | C22×C3⋊D3 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 96 | C22×C3⋊D3 | C23×C3 | 1 | 4 | yes | complemented |
| 97 | C22×C3×D3 | — | 3 | 12 | no | — |
| 98 | C22×C3×D3 | — | 3 | 16 | no | — |
| 99 | C22×C3×D3 | — | 3 | 2 | no | — |
| 100 | C22×C3×D3 | — | 3 | 12 | no | — |
| 101 | C22×C3×D3 | — | 3 | 12 | no | — |
| 102 | C22×C3×D3 | — | 3 | 12 | no | — |
| 103 | C22×C3×D3 | — | 3 | 24 | no | — |
| 104 | C22×C3×D3 | — | 4 | 2 | no | — |
| 105 | C22×C3×D3 | — | 8 | 2 | no | — |
| 106 | C22×C3×D3 | — | 12 | 24 | no | — |
| 107 | C22×C3×D3 | — | 12 | 2 | no | — |
| 108 | C22×C3×D3 | — | 24 | 1 | no | — |
| 109 | C22×C3×D3 | C2×A4 | 1 | 2 | yes | complemented |
| 110 | C22×C3×D3 | C23×C3 | 1 | 8 | yes | complemented |
| 111 | C2×C3×A4 | — | 2 | 6 | no | — |
| 112 | C2×C3×A4 | — | 2 | 3 | no | — |
| 113 | C2×C3×A4 | — | 3 | 8 | no | — |
| 114 | C2×C3×A4 | — | 4 | 3 | no | — |
| 115 | C2×C3×A4 | C22×D3 | 1 | 6 | yes | complemented |
| 116 | C2×D32 | — | 3 | 24 | no | — |
| 117 | C2×D32 | — | 3 | 48 | no | — |
| 118 | C2×D32 | — | 3 | 96 | no | — |
| 119 | C2×D32 | — | 3 | 12 | no | — |
| 120 | C2×D32 | — | 3 | 24 | no | — |
| 121 | C2×D32 | — | 3 | 48 | no | — |
| 122 | C2×D32 | — | 3 | 16 | no | — |
| 123 | C2×D32 | — | 3 | 16 | no | — |
| 124 | C2×D32 | — | 3 | 32 | no | — |
| 125 | C2×D32 | C2×A4 | 1 | 12 | yes | direct product factor |
| 126 | D3×A4 | — | 2 | 8 | no | — |
| 127 | D3×A4 | — | 3 | 8 | no | — |
| 128 | D3×A4 | — | 6 | 4 | no | — |
| 129 | D3×A4 | C22×D3 | 1 | 8 | yes | direct product factor |
| 130 | C26 | — | 9 | 1 | no | Sylow |
| 131 | C2×C33 | — | 4 | 3 | no | — |
| 132 | C3×C3⋊D3 | — | 4 | 4 | no | — |
| 133 | C32×D3 | — | 4 | 8 | no | — |
| 134 | C24×C3 | — | 2 | 1 | no | — |
| 135 | C24×C3 | — | 3 | 12 | no | — |
| 136 | C24×C3 | — | 9 | 2 | no | — |
| 137 | C24×C3 | — | 9 | 12 | no | — |
| 138 | C24×C3 | — | 9 | 2 | no | — |
| 139 | C24×C3 | — | 36 | 1 | no | — |
| 140 | C24×C3 | C2×C3×D3 | 1 | 2 | yes | complemented |
| 141 | C23×D3 | — | 3 | 2 | no | — |
| 142 | C23×D3 | — | 3 | 2 | no | — |
| 143 | C23×D3 | — | 3 | 2 | no | — |
| 144 | C23×D3 | — | 3 | 12 | no | — |
| 145 | C23×D3 | — | 3 | 12 | no | — |
| 146 | C23×D3 | — | 3 | 32 | no | — |
| 147 | C23×D3 | — | 6 | 6 | no | — |
| 148 | C23×D3 | — | 9 | 24 | no | — |
| 149 | C23×D3 | — | 9 | 2 | no | — |
| 150 | C23×D3 | — | 9 | 24 | no | — |
| 151 | C23×D3 | — | 9 | 2 | no | — |
| 152 | C23×D3 | — | 9 | 2 | no | — |
| 153 | C23×D3 | — | 9 | 64 | no | — |
| 154 | C23×D3 | — | 9 | 24 | no | — |
| 155 | C23×D3 | — | 9 | 24 | no | — |
| 156 | C23×D3 | — | 9 | 4 | no | — |
| 157 | C23×D3 | — | 9 | 24 | no | — |
| 158 | C23×D3 | — | 9 | 24 | no | — |
| 159 | C23×D3 | — | 9 | 96 | no | — |
| 160 | C23×D3 | — | 9 | 24 | no | — |
| 161 | C23×D3 | — | 9 | 24 | no | — |
| 162 | C23×D3 | — | 9 | 2 | no | — |
| 163 | C23×D3 | — | 9 | 12 | no | — |
| 164 | C23×D3 | — | 9 | 2 | no | — |
| 165 | C23×D3 | — | 18 | 1 | no | — |
| 166 | C23×D3 | — | 18 | 6 | no | — |
| 167 | C23×D3 | — | 18 | 1 | no | — |
| 168 | C23×D3 | C2×C3×D3 | 1 | 12 | yes | complemented |
| 169 | C22×A4 | — | 2 | 2 | no | — |
| 170 | C22×A4 | — | 3 | 12 | no | — |
| 171 | C22×A4 | — | 4 | 1 | no | — |
| 172 | C22×A4 | — | 6 | 12 | no | — |
| 173 | C22×A4 | — | 9 | 16 | no | — |
| 174 | C22×A4 | — | 9 | 6 | no | — |
| 175 | C22×A4 | D32 | 1 | 1 | yes | characteristic, direct product factor |
| 176 | C22×C32 | — | 3 | 3 | no | — |
| 177 | C22×C32 | — | 3 | 2 | no | — |
| 178 | C22×C32 | — | 3 | 3 | no | — |
| 179 | C22×C32 | — | 3 | 3 | no | — |
| 180 | C22×C32 | — | 4 | 2 | no | — |
| 181 | C22×C32 | — | 8 | 1 | no | — |
| 182 | C22×C32 | — | 8 | 2 | no | — |
| 183 | C22×C32 | — | 12 | 12 | no | — |
| 184 | C22×C32 | — | 16 | 1 | no | — |
| 185 | C22×C32 | C22×A4 | 1 | 1 | yes | characteristic, complemented |
| 186 | C22×C32 | C24×C3 | 1 | 1 | yes | characteristic, complemented |
| 187 | C2×C3⋊D3 | — | 3 | 12 | no | — |
| 188 | C2×C3⋊D3 | — | 3 | 6 | no | — |
| 189 | C2×C3⋊D3 | — | 3 | 12 | no | — |
| 190 | C2×C3⋊D3 | — | 3 | 4 | no | — |
| 191 | C2×C3⋊D3 | — | 3 | 4 | no | — |
| 192 | C2×C3⋊D3 | C22×A4 | 1 | 6 | yes | complemented |
| 193 | C2×C3×D3 | — | 3 | 24 | no | — |
| 194 | C2×C3×D3 | — | 3 | 12 | no | — |
| 195 | C2×C3×D3 | — | 3 | 24 | no | — |
| 196 | C2×C3×D3 | — | 3 | 8 | no | — |
| 197 | C2×C3×D3 | — | 3 | 8 | no | — |
| 198 | C2×C3×D3 | — | 4 | 12 | no | — |
| 199 | C2×C3×D3 | — | 8 | 12 | no | — |
| 200 | C2×C3×D3 | — | 12 | 32 | no | — |
| 201 | C2×C3×D3 | — | 12 | 12 | no | — |
| 202 | C2×C3×D3 | — | 24 | 6 | no | — |
| 203 | C2×C3×D3 | C22×A4 | 1 | 12 | yes | complemented |
| 204 | C3×A4 | — | 2 | 2 | no | — |
| 205 | C3×A4 | — | 2 | 1 | no | — |
| 206 | C3×A4 | — | 4 | 1 | no | — |
| 207 | C3×A4 | C23×D3 | 1 | 2 | yes | complemented |
| 208 | D32 | — | 3 | 32 | no | — |
| 209 | D32 | — | 3 | 16 | no | — |
| 210 | D32 | — | 3 | 32 | no | — |
| 211 | D32 | C22×A4 | 1 | 16 | yes | direct product factor |
| 212 | C25 | — | 3 | 2 | no | — |
| 213 | C25 | — | 9 | 12 | no | — |
| 214 | C25 | — | 9 | 1 | no | — |
| 215 | C25 | — | 27 | 1 | no | — |
| 216 | C25 | — | 27 | 2 | no | — |
| 217 | C25 | — | 27 | 1 | no | — |
| 218 | C25 | — | 27 | 12 | no | — |
| 219 | C33 | — | 4 | 1 | no | Sylow |
| 220 | C23×C3 | — | 2 | 3 | no | — |
| 221 | C23×C3 | — | 3 | 6 | no | — |
| 222 | C23×C3 | — | 3 | 2 | no | — |
| 223 | C23×C3 | — | 3 | 2 | no | — |
| 224 | C23×C3 | — | 3 | 8 | no | — |
| 225 | C23×C3 | — | 6 | 1 | no | — |
| 226 | C23×C3 | — | 6 | 3 | no | — |
| 227 | C23×C3 | — | 9 | 12 | no | — |
| 228 | C23×C3 | — | 9 | 12 | no | — |
| 229 | C23×C3 | — | 9 | 24 | no | — |
| 230 | C23×C3 | — | 9 | 12 | no | — |
| 231 | C23×C3 | — | 9 | 16 | no | — |
| 232 | C23×C3 | — | 9 | 12 | no | — |
| 233 | C23×C3 | — | 9 | 2 | no | — |
| 234 | C23×C3 | — | 12 | 2 | no | — |
| 235 | C23×C3 | — | 24 | 2 | no | — |
| 236 | C23×C3 | — | 36 | 1 | no | — |
| 237 | C23×C3 | — | 36 | 12 | no | — |
| 238 | C23×C3 | C22×C3×D3 | 1 | 6 | yes | complemented |
| 239 | C22×D3 | — | 3 | 12 | no | — |
| 240 | C22×D3 | — | 3 | 16 | no | — |
| 241 | C22×D3 | — | 3 | 2 | no | — |
| 242 | C22×D3 | — | 3 | 2 | no | — |
| 243 | C22×D3 | — | 3 | 24 | no | — |
| 244 | C22×D3 | — | 3 | 12 | no | — |
| 245 | C22×D3 | — | 3 | 12 | no | — |
| 246 | C22×D3 | — | 3 | 12 | no | — |
| 247 | C22×D3 | — | 3 | 24 | no | — |
| 248 | C22×D3 | — | 3 | 8 | no | — |
| 249 | C22×D3 | — | 6 | 1 | no | — |
| 250 | C22×D3 | — | 6 | 4 | no | — |
| 251 | C22×D3 | — | 9 | 32 | no | — |
| 252 | C22×D3 | — | 9 | 24 | no | — |
| 253 | C22×D3 | — | 9 | 96 | no | — |
| 254 | C22×D3 | — | 9 | 24 | no | — |
| 255 | C22×D3 | — | 9 | 12 | no | — |
| 256 | C22×D3 | — | 9 | 12 | no | — |
| 257 | C22×D3 | — | 9 | 96 | no | — |
| 258 | C22×D3 | — | 9 | 96 | no | — |
| 259 | C22×D3 | — | 9 | 48 | no | — |
| 260 | C22×D3 | — | 9 | 96 | no | — |
| 261 | C22×D3 | — | 9 | 32 | no | — |
| 262 | C22×D3 | — | 9 | 32 | no | — |
| 263 | C22×D3 | — | 9 | 32 | no | — |
| 264 | C22×D3 | — | 9 | 16 | no | — |
| 265 | C22×D3 | — | 9 | 12 | no | — |
| 266 | C22×D3 | — | 9 | 2 | no | — |
| 267 | C22×D3 | — | 9 | 24 | no | — |
| 268 | C22×D3 | — | 9 | 24 | no | — |
| 269 | C22×D3 | — | 9 | 12 | no | — |
| 270 | C22×D3 | — | 18 | 6 | no | — |
| 271 | C22×D3 | — | 18 | 6 | no | — |
| 272 | C22×D3 | — | 18 | 1 | no | — |
| 273 | C22×D3 | — | 18 | 8 | no | — |
| 274 | C22×D3 | — | 18 | 6 | no | — |
| 275 | C22×D3 | — | 18 | 12 | no | — |
| 276 | C22×D3 | — | 18 | 6 | no | — |
| 277 | C22×D3 | D3×A4 | 1 | 2 | yes | direct product factor |
| 278 | C22×D3 | C22×C3×D3 | 1 | 8 | yes | complemented |
| 279 | C2×A4 | — | 2 | 6 | no | — |
| 280 | C2×A4 | — | 3 | 8 | no | — |
| 281 | C2×A4 | — | 4 | 3 | no | — |
| 282 | C2×A4 | — | 6 | 8 | no | — |
| 283 | C2×A4 | — | 9 | 4 | no | — |
| 284 | C2×A4 | C2×D32 | 1 | 3 | yes | direct product factor |
| 285 | C2×C32 | — | 3 | 3 | no | — |
| 286 | C2×C32 | — | 3 | 1 | no | — |
| 287 | C2×C32 | — | 4 | 6 | no | — |
| 288 | C2×C32 | — | 8 | 3 | no | — |
| 289 | C2×C32 | — | 8 | 6 | no | — |
| 290 | C2×C32 | — | 12 | 8 | no | — |
| 291 | C2×C32 | — | 16 | 3 | no | — |
| 292 | C2×C32 | C23×A4 | 1 | 3 | yes | complemented |
| 293 | C3⋊D3 | — | 3 | 4 | no | — |
| 294 | C3⋊D3 | C23×A4 | 1 | 4 | yes | complemented |
| 295 | C3×D3 | — | 3 | 8 | no | — |
| 296 | C3×D3 | — | 4 | 8 | no | — |
| 297 | C3×D3 | — | 8 | 8 | no | — |
| 298 | C3×D3 | — | 12 | 8 | no | — |
| 299 | C3×D3 | — | 24 | 4 | no | — |
| 300 | C3×D3 | C23×A4 | 1 | 8 | yes | complemented |
| 301 | C24 | — | 3 | 12 | no | — |
| 302 | C24 | — | 9 | 2 | no | — |
| 303 | C24 | — | 9 | 1 | no | — |
| 304 | C24 | — | 9 | 16 | no | — |
| 305 | C24 | — | 9 | 12 | no | — |
| 306 | C24 | — | 9 | 2 | no | — |
| 307 | C24 | — | 9 | 6 | no | — |
| 308 | C24 | — | 27 | 1 | no | — |
| 309 | C24 | — | 27 | 2 | no | — |
| 310 | C24 | — | 27 | 6 | no | — |
| 311 | C24 | — | 27 | 1 | no | — |
| 312 | C24 | — | 27 | 12 | no | — |
| 313 | C24 | — | 27 | 12 | no | — |
| 314 | C24 | — | 27 | 1 | no | — |
| 315 | C24 | — | 27 | 24 | no | — |
| 316 | C24 | — | 27 | 12 | no | — |
| 317 | C24 | — | 27 | 48 | no | — |
| 318 | C24 | — | 27 | 24 | no | — |
| 319 | C24 | — | 27 | 12 | no | — |
| 320 | C24 | — | 27 | 32 | no | — |
| 321 | C24 | — | 27 | 2 | no | — |
| 322 | C24 | C3×D32 | 1 | 1 | yes | characteristic, complemented |
| 323 | C22×C3 | — | 2 | 1 | no | — |
| 324 | C22×C3 | — | 2 | 1 | no | — |
| 325 | C22×C3 | — | 3 | 6 | no | — |
| 326 | C22×C3 | — | 3 | 4 | no | — |
| 327 | C22×C3 | — | 3 | 6 | no | — |
| 328 | C22×C3 | — | 3 | 6 | no | — |
| 329 | C22×C3 | — | 3 | 12 | no | — |
| 330 | C22×C3 | — | 4 | 1 | no | — |
| 331 | C22×C3 | — | 6 | 3 | no | — |
| 332 | C22×C3 | — | 6 | 3 | no | — |
| 333 | C22×C3 | — | 6 | 3 | no | — |
| 334 | C22×C3 | — | 6 | 2 | no | — |
| 335 | C22×C3 | — | 8 | 2 | no | — |
| 336 | C22×C3 | — | 9 | 8 | no | — |
| 337 | C22×C3 | — | 9 | 24 | no | — |
| 338 | C22×C3 | — | 9 | 8 | no | — |
| 339 | C22×C3 | — | 9 | 24 | no | — |
| 340 | C22×C3 | — | 9 | 12 | no | — |
| 341 | C22×C3 | — | 12 | 12 | no | — |
| 342 | C22×C3 | — | 16 | 1 | no | — |
| 343 | C22×C3 | — | 24 | 12 | no | — |
| 344 | C22×C3 | — | 36 | 6 | no | — |
| 345 | C22×C3 | — | 36 | 16 | no | — |
| 346 | C22×C3 | C2×D3×A4 | 1 | 2 | yes | complemented |
| 347 | C22×C3 | C23×C3×D3 | 1 | 2 | yes | complemented |
| 348 | C2×D3 | — | 3 | 24 | no | — |
| 349 | C2×D3 | — | 3 | 12 | no | — |
| 350 | C2×D3 | — | 3 | 12 | no | — |
| 351 | C2×D3 | — | 3 | 8 | no | — |
| 352 | C2×D3 | — | 3 | 24 | no | — |
| 353 | C2×D3 | — | 3 | 32 | no | — |
| 354 | C2×D3 | — | 3 | 8 | no | — |
| 355 | C2×D3 | — | 6 | 6 | no | — |
| 356 | C2×D3 | — | 9 | 32 | no | — |
| 357 | C2×D3 | — | 9 | 8 | no | — |
| 358 | C2×D3 | — | 9 | 32 | no | — |
| 359 | C2×D3 | — | 9 | 24 | no | — |
| 360 | C2×D3 | — | 9 | 64 | no | — |
| 361 | C2×D3 | — | 9 | 24 | no | — |
| 362 | C2×D3 | — | 9 | 12 | no | — |
| 363 | C2×D3 | — | 9 | 32 | no | — |
| 364 | C2×D3 | — | 9 | 8 | no | — |
| 365 | C2×D3 | — | 18 | 4 | no | — |
| 366 | C2×D3 | — | 18 | 12 | no | — |
| 367 | C2×D3 | — | 18 | 6 | no | — |
| 368 | C2×D3 | — | 18 | 12 | no | — |
| 369 | C2×D3 | — | 18 | 4 | no | — |
| 370 | C2×D3 | C2×D3×A4 | 1 | 12 | yes | direct product factor |
| 371 | A4 | — | 2 | 2 | no | — |
| 372 | A4 | — | 4 | 1 | no | — |
| 373 | A4 | C22×D32 | 1 | 1 | yes | characteristic, direct product factor |
| 374 | C32 | — | 4 | 2 | no | — |
| 375 | C32 | — | 8 | 1 | no | — |
| 376 | C32 | — | 8 | 2 | no | — |
| 377 | C32 | — | 16 | 1 | no | — |
| 378 | C32 | C24×A4 | 1 | 1 | yes | characteristic, complemented |
| 379 | C23 | — | 3 | 3 | no | — |
| 380 | C23 | — | 3 | 1 | no | — |
| 381 | C23 | — | 3 | 2 | no | — |
| 382 | C23 | — | 3 | 8 | no | — |
| 383 | C23 | — | 9 | 12 | no | — |
| 384 | C23 | — | 9 | 12 | no | — |
| 385 | C23 | — | 9 | 12 | no | — |
| 386 | C23 | — | 9 | 24 | no | — |
| 387 | C23 | — | 9 | 12 | no | — |
| 388 | C23 | — | 9 | 16 | no | — |
| 389 | C23 | — | 9 | 12 | no | — |
| 390 | C23 | — | 9 | 2 | no | — |
| 391 | C23 | — | 9 | 1 | no | — |
| 392 | C23 | — | 9 | 4 | no | — |
| 393 | C23 | — | 27 | 6 | no | — |
| 394 | C23 | — | 27 | 24 | no | — |
| 395 | C23 | — | 27 | 6 | no | — |
| 396 | C23 | — | 27 | 12 | no | — |
| 397 | C23 | — | 27 | 6 | no | — |
| 398 | C23 | — | 27 | 8 | no | — |
| 399 | C23 | — | 27 | 6 | no | — |
| 400 | C23 | — | 27 | 16 | no | — |
| 401 | C23 | — | 27 | 48 | no | — |
| 402 | C23 | — | 27 | 12 | no | — |
| 403 | C23 | — | 27 | 32 | no | — |
| 404 | C23 | — | 27 | 16 | no | — |
| 405 | C23 | — | 27 | 96 | no | — |
| 406 | C23 | — | 27 | 48 | no | — |
| 407 | C23 | — | 27 | 24 | no | — |
| 408 | C23 | — | 27 | 1 | no | — |
| 409 | C23 | C2×C3×D32 | 1 | 3 | yes | complemented |
| 410 | C2×C3 | — | 2 | 3 | no | — |
| 411 | C2×C3 | — | 3 | 2 | no | — |
| 412 | C2×C3 | — | 3 | 6 | no | — |
| 413 | C2×C3 | — | 3 | 8 | no | — |
| 414 | C2×C3 | — | 4 | 3 | no | — |
| 415 | C2×C3 | — | 6 | 1 | no | — |
| 416 | C2×C3 | — | 6 | 3 | no | — |
| 417 | C2×C3 | — | 8 | 6 | no | — |
| 418 | C2×C3 | — | 9 | 8 | no | — |
| 419 | C2×C3 | — | 12 | 8 | no | — |
| 420 | C2×C3 | — | 16 | 3 | no | — |
| 421 | C2×C3 | — | 24 | 8 | no | — |
| 422 | C2×C3 | — | 36 | 4 | no | — |
| 423 | C2×C3 | C22×D3×A4 | 1 | 6 | yes | complemented |
| 424 | D3 | — | 3 | 8 | no | — |
| 425 | D3 | — | 3 | 8 | no | — |
| 426 | D3 | — | 6 | 4 | no | — |
| 427 | D3 | — | 9 | 8 | no | — |
| 428 | D3 | — | 18 | 4 | no | — |
| 429 | D3 | C22×D3×A4 | 1 | 8 | yes | direct product factor |
| 430 | C22 | — | 3 | 3 | no | — |
| 431 | C22 | — | 3 | 2 | no | — |
| 432 | C22 | — | 3 | 3 | no | — |
| 433 | C22 | — | 3 | 3 | no | — |
| 434 | C22 | — | 3 | 12 | no | — |
| 435 | C22 | — | 9 | 8 | no | — |
| 436 | C22 | — | 9 | 24 | no | — |
| 437 | C22 | — | 9 | 16 | no | — |
| 438 | C22 | — | 9 | 8 | no | — |
| 439 | C22 | — | 9 | 24 | no | — |
| 440 | C22 | — | 9 | 12 | no | — |
| 441 | C22 | — | 9 | 6 | no | — |
| 442 | C22 | — | 27 | 4 | no | — |
| 443 | C22 | — | 27 | 32 | no | — |
| 444 | C22 | — | 27 | 12 | no | — |
| 445 | C22 | — | 27 | 4 | no | — |
| 446 | C22 | — | 27 | 12 | no | — |
| 447 | C22 | — | 27 | 16 | no | — |
| 448 | C22 | — | 27 | 32 | no | — |
| 449 | C22 | — | 27 | 6 | no | — |
| 450 | C22 | D32×A4 | 1 | 1 | yes | characteristic, direct product factor |
| 451 | C22 | C22×C3×D32 | 1 | 1 | yes | characteristic, complemented |
| 452 | C3 | — | 2 | 1 | no | — |
| 453 | C3 | — | 4 | 1 | no | — |
| 454 | C3 | — | 8 | 2 | no | — |
| 455 | C3 | — | 16 | 1 | no | — |
| 456 | C3 | C23×D3×A4 | 1 | 2 | yes | complemented |
| 457 | C2 | — | 3 | 1 | no | — |
| 458 | C2 | — | 3 | 3 | no | — |
| 459 | C2 | — | 3 | 8 | no | — |
| 460 | C2 | — | 9 | 8 | no | — |
| 461 | C2 | — | 9 | 4 | no | — |
| 462 | C2 | — | 27 | 4 | no | — |
| 463 | C2 | C2×D32×A4 | 1 | 3 | yes | direct product factor |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D32×A4 |
| commutator, cosocle, hypocenter | C22×C32 | C24×C3 |
| Frattini | C1 | G |
| Fitting, socle | C24×C32 | C22×C3 |
| LCS | G ▷ C22×C32 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×A4×C3⋊D3 | C2 | semidirect |
| 2. C22×C3×D3×A4 | C2 | semidirect |
| 3. C2×D32×A4 | C2 | direct (N × H) |
| 4. C24×D32 | C3 | semidirect |
| 6. C22×C32×A4 | C22 | semidirect |
| 8. C2×A4×C3⋊D3 | C22 | semidirect |
| 9. C2×C3×D3×A4 | C22 | semidirect |
| 10. D32×A4 | C22 | direct (N × H) |
| 11. C24×C3⋊D3 | C2×C3 | semidirect |
| 12. C24×C3×D3 | C2×C3 | semidirect |
| 18. C23×D32 | C2×C3 | semidirect |
| 23. C22×D3×A4 | D3 | direct (N × H) |
| 26. C2×C32×A4 | C23 | semidirect |
| 28. A4×C3⋊D3 | C23 | semidirect |
| 29. C3×D3×A4 | C23 | semidirect |
| 32. C24×C32 | C22×C3 | semidirect |
| 36. C23×C3⋊D3 | C22×C3 | semidirect |
| 41. C23×C3×D3 | C22×C3 | semidirect |
| 46. C22×C3×A4 | C2×D3 | semidirect |
| 58. C22×D32 | A4 | direct (N × H) |
| 59. C22×D32 | C22×C3 | semidirect |
| 64. C2×D3×A4 | C2×D3 | direct (N × H) |
| 68. C32×A4 | C24 | semidirect |
| 79. C24×D3 | C3×D3 | semidirect |
| 87. C23×C32 | C23×C3 | semidirect |
| 95. C22×C3⋊D3 | C2×A4 | semidirect |
| 96. C22×C3⋊D3 | C23×C3 | semidirect |
| 109. C22×C3×D3 | C2×A4 | semidirect |
| 110. C22×C3×D3 | C23×C3 | semidirect |
| 115. C2×C3×A4 | C22×D3 | semidirect |
| 125. C2×D32 | C2×A4 | direct (N × H) |
| 129. D3×A4 | C22×D3 | direct (N × H) |
| 140. C24×C3 | C2×C3×D3 | semidirect |
| 168. C23×D3 | C2×C3×D3 | semidirect |
| 175. C22×A4 | D32 | direct (N × H) |
| 185. C22×C32 | C22×A4 | semidirect |
| 186. C22×C32 | C24×C3 | semidirect |
| 192. C2×C3⋊D3 | C22×A4 | semidirect |
| 203. C2×C3×D3 | C22×A4 | semidirect |
| 207. C3×A4 | C23×D3 | semidirect |
| 211. D32 | C22×A4 | direct (N × H) |
| 238. C23×C3 | C22×C3×D3 | semidirect |
| 277. C22×D3 | D3×A4 | direct (N × H) |
| 278. C22×D3 | C22×C3×D3 | semidirect |
| 284. C2×A4 | C2×D32 | direct (N × H) |
| 292. C2×C32 | C23×A4 | semidirect |
| 294. C3⋊D3 | C23×A4 | semidirect |
| 300. C3×D3 | C23×A4 | semidirect |
| 322. C24 | C3×D32 | semidirect |
| 346. C22×C3 | C2×D3×A4 | semidirect |
| 347. C22×C3 | C23×C3×D3 | semidirect |
| 370. C2×D3 | C2×D3×A4 | direct (N × H) |
| 373. A4 | C22×D32 | direct (N × H) |
| 378. C32 | C24×A4 | semidirect |
| 409. C23 | C2×C3×D32 | semidirect |
| 423. C2×C3 | C22×D3×A4 | semidirect |
| 429. D3 | C22×D3×A4 | direct (N × H) |
| 450. C22 | D32×A4 | direct (N × H) |
| 451. C22 | C22×C3×D32 | semidirect |
| 456. C3 | C23×D3×A4 | semidirect |
| 463. C2 | C2×D32×A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×A4×C3⋊D3 | 2 |
| C22×C3×D3×A4 | 2 |
| C2×D32×A4 | 2 |
| C24×D32 | 3 |
| C23×D3×A4 | 3 |
| C22×C3×D32 | 4 |