Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3130 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 3130 conjugacy classes of subgroups — too many to draw. Only its 166 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×C3⋊S4 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×#89101 | C2 | 1 | 12 | yes | maximal, direct product factor |
| 4 | C22×D3×S4 | — | 3 | 2 | no | maximal |
| 5 | C22×#3811 | — | 3 | 1 | no | maximal |
| 6 | C22×C32×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 7 | C22×#1113 | — | 4 | 1 | no | maximal |
| 8 | C2×A4×C3⋊D3 | C22 | 1 | 6 | yes | complemented |
| 9 | C2×C3×C3⋊S4 | C22 | 1 | 12 | yes | complemented |
| 10 | #89101 | C22 | 1 | 16 | yes | direct product factor |
| 11 | C24×C3⋊D3 | D3 | 1 | 1 | yes | characteristic, complemented |
| 12 | C23×D32 | — | 3 | 1 | no | — |
| 13 | C22×D3×A4 | — | 3 | 2 | no | — |
| 14 | C22×D3×A4 | — | 6 | 1 | no | — |
| 15 | C22×C3⋊S4 | D3 | 1 | 2 | yes | complemented |
| 16 | C22×C3×S4 | — | 3 | 2 | no | — |
| 17 | C22×C3×S4 | — | 6 | 2 | no | — |
| 18 | C2×D3×S4 | — | 3 | 24 | no | — |
| 19 | C22×C3×#67 | — | 3 | 2 | no | — |
| 20 | C2×#3811 | — | 3 | 12 | no | — |
| 21 | C2×#3811 | — | 3 | 12 | no | — |
| 22 | C22×#626 | — | 3 | 2 | no | — |
| 23 | C22×#624 | — | 3 | 1 | no | — |
| 24 | C22×C3×C3⋊D3 | — | 4 | 2 | no | — |
| 25 | C22×C3×C3⋊D3 | — | 4 | 1 | no | — |
| 26 | C2×C32×A4 | C23 | 1 | 3 | yes | complemented |
| 27 | C2×#1113 | — | 4 | 12 | no | — |
| 28 | A4×C3⋊D3 | C23 | 1 | 4 | yes | complemented |
| 29 | C3×C3⋊S4 | C23 | 1 | 8 | yes | complemented |
| 30 | C23×S4 | — | 9 | 1 | no | — |
| 31 | C22×D3×D4 | — | 9 | 2 | no | — |
| 32 | C24×C32 | C2×D3 | 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 | C2×D3 | 1 | 6 | yes | complemented |
| 37 | C23×C3×D3 | — | 3 | 2 | no | — |
| 38 | C22×C3×A4 | — | 2 | 2 | no | — |
| 39 | C22×C3×A4 | — | 2 | 1 | no | — |
| 40 | C22×C3×A4 | — | 4 | 1 | no | — |
| 41 | C22×C3×A4 | C2×D3 | 1 | 2 | yes | complemented |
| 42 | C22×D32 | — | 3 | 12 | no | — |
| 43 | C22×D32 | — | 6 | 1 | no | — |
| 44 | C22×D32 | — | 6 | 6 | no | — |
| 45 | C22×D32 | — | 6 | 1 | no | — |
| 46 | C22×D32 | — | 12 | 2 | no | — |
| 47 | C2×D3×A4 | — | 3 | 12 | no | — |
| 48 | C2×D3×A4 | — | 6 | 6 | no | — |
| 49 | C2×C3⋊S4 | C2×D3 | 1 | 12 | yes | complemented |
| 50 | C2×C3×S4 | — | 3 | 12 | no | — |
| 51 | C2×C3×S4 | — | 6 | 12 | no | — |
| 52 | D3×S4 | — | 3 | 32 | no | — |
| 53 | C2×C3×#67 | — | 3 | 12 | no | — |
| 54 | C2×C3×#67 | — | 3 | 12 | no | — |
| 55 | C22×C3×Dic3 | — | 3 | 2 | no | — |
| 56 | #3811 | — | 3 | 48 | no | — |
| 57 | #3811 | — | 3 | 16 | no | — |
| 58 | C2×#626 | — | 3 | 24 | no | — |
| 59 | C2×#624 | — | 3 | 12 | no | — |
| 60 | C22×C33 | — | 4 | 1 | no | — |
| 61 | C2×C3×C3⋊D3 | — | 4 | 12 | no | — |
| 62 | C2×C3×C3⋊D3 | — | 4 | 6 | no | — |
| 63 | C32×A4 | C24 | 1 | 1 | yes | characteristic, complemented |
| 64 | #1113 | — | 4 | 16 | no | — |
| 65 | C24×D3 | — | 3 | 2 | no | — |
| 66 | C24×D3 | — | 6 | 1 | no | — |
| 67 | C24×D3 | — | 9 | 2 | no | — |
| 68 | C23×A4 | — | 9 | 1 | no | — |
| 69 | C22×S4 | — | 3 | 2 | no | — |
| 70 | C22×S4 | — | 6 | 2 | no | — |
| 71 | C22×S4 | — | 9 | 12 | no | — |
| 72 | C22×C3×D4 | — | 9 | 2 | no | — |
| 73 | C22×#67 | — | 3 | 2 | no | — |
| 74 | C22×#67 | — | 9 | 2 | no | — |
| 75 | C2×D3×D4 | — | 9 | 24 | no | — |
| 76 | C2×D3×D4 | — | 9 | 24 | no | — |
| 77 | C22×D12 | — | 9 | 2 | no | — |
| 78 | C22×C4×D3 | — | 9 | 2 | no | — |
| 79 | C23×C32 | — | 3 | 1 | no | — |
| 80 | C23×C32 | — | 3 | 3 | no | — |
| 81 | C23×C32 | C22×D3 | 1 | 3 | yes | complemented |
| 82 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 83 | C22×C3⋊D3 | — | 3 | 6 | no | — |
| 84 | C22×C3⋊D3 | — | 3 | 6 | no | — |
| 85 | C22×C3⋊D3 | — | 3 | 6 | no | — |
| 86 | C22×C3⋊D3 | — | 3 | 12 | no | — |
| 87 | C22×C3⋊D3 | — | 4 | 2 | no | — |
| 88 | C22×C3⋊D3 | — | 6 | 4 | no | — |
| 89 | C22×C3⋊D3 | — | 6 | 3 | no | — |
| 90 | C22×C3⋊D3 | S4 | 1 | 1 | yes | characteristic, complemented |
| 91 | C22×C3⋊D3 | C22×D3 | 1 | 4 | yes | complemented |
| 92 | C22×C3×D3 | — | 3 | 12 | no | — |
| 93 | C22×C3×D3 | — | 6 | 6 | no | — |
| 94 | C22×C3×D3 | — | 6 | 2 | no | — |
| 95 | C22×C3×D3 | — | 12 | 2 | no | — |
| 96 | C22×C3×D3 | — | 12 | 2 | no | — |
| 97 | C22×C3×D3 | — | 24 | 1 | no | — |
| 98 | C22×C3×D3 | — | 24 | 2 | no | — |
| 99 | C2×C3×A4 | — | 2 | 6 | no | — |
| 100 | C2×C3×A4 | — | 2 | 3 | no | — |
| 101 | C2×C3×A4 | — | 4 | 3 | no | — |
| 102 | C2×C3×A4 | C22×D3 | 1 | 6 | yes | complemented |
| 103 | C2×D32 | — | 3 | 16 | no | — |
| 104 | C2×D32 | — | 6 | 12 | no | — |
| 105 | C2×D32 | — | 6 | 24 | no | — |
| 106 | C2×D32 | — | 6 | 12 | no | — |
| 107 | C2×D32 | — | 12 | 24 | no | — |
| 108 | D3×A4 | — | 3 | 8 | no | — |
| 109 | D3×A4 | — | 6 | 4 | no | — |
| 110 | C3⋊S4 | C22×D3 | 1 | 8 | yes | complemented |
| 111 | C3×S4 | — | 3 | 8 | no | — |
| 112 | C3×S4 | — | 6 | 8 | no | — |
| 113 | C3×#67 | — | 3 | 24 | no | — |
| 114 | C3×#67 | — | 3 | 8 | no | — |
| 115 | C2×C3×Dic3 | — | 3 | 12 | no | — |
| 116 | #626 | — | 3 | 32 | no | — |
| 117 | #624 | — | 3 | 16 | no | — |
| 118 | C23×D4 | — | 27 | 1 | no | Sylow |
| 119 | C2×C33 | — | 4 | 3 | no | — |
| 120 | C3×C3⋊D3 | — | 4 | 8 | no | — |
| 121 | C3×C3⋊D3 | — | 4 | 4 | no | — |
| 122 | C24×C3 | — | 2 | 1 | no | — |
| 123 | C24×C3 | — | 9 | 2 | no | — |
| 124 | C24×C3 | D32 | 1 | 2 | yes | complemented |
| 125 | C23×D3 | — | 3 | 2 | no | — |
| 126 | C23×D3 | — | 3 | 12 | no | — |
| 127 | C23×D3 | — | 6 | 6 | no | — |
| 128 | C23×D3 | — | 9 | 2 | no | — |
| 129 | C23×D3 | — | 9 | 24 | no | — |
| 130 | C23×D3 | — | 9 | 2 | no | — |
| 131 | C23×D3 | — | 9 | 12 | no | — |
| 132 | C23×D3 | — | 18 | 1 | no | — |
| 133 | C23×D3 | — | 18 | 6 | no | — |
| 134 | C23×D3 | — | 18 | 1 | no | — |
| 135 | C23×D3 | — | 18 | 2 | no | — |
| 136 | C23×D3 | — | 18 | 12 | no | — |
| 137 | C23×D3 | — | 18 | 2 | no | — |
| 138 | C23×D3 | — | 36 | 1 | no | — |
| 139 | C22×A4 | — | 2 | 2 | no | — |
| 140 | C22×A4 | — | 4 | 1 | no | — |
| 141 | C22×A4 | — | 9 | 6 | no | — |
| 142 | C22×A4 | D32 | 1 | 1 | yes | characteristic, complemented |
| 143 | C2×S4 | — | 3 | 12 | no | — |
| 144 | C2×S4 | — | 6 | 12 | no | — |
| 145 | C2×S4 | — | 9 | 16 | no | — |
| 146 | C2×C3×D4 | — | 9 | 12 | no | — |
| 147 | C2×C3×D4 | — | 9 | 12 | no | — |
| 148 | C22×C3×C4 | — | 9 | 2 | no | — |
| 149 | C2×#67 | — | 3 | 12 | no | — |
| 150 | C2×#67 | — | 3 | 12 | no | — |
| 151 | C2×#67 | — | 9 | 24 | no | — |
| 152 | C22×Dic3 | — | 3 | 2 | no | — |
| 153 | D3×D4 | — | 9 | 32 | no | — |
| 154 | D3×D4 | — | 9 | 96 | no | — |
| 155 | C2×D12 | — | 9 | 24 | no | — |
| 156 | C2×C4×D3 | — | 9 | 24 | no | — |
| 157 | C22×C32 | — | 3 | 3 | no | — |
| 158 | C22×C32 | — | 3 | 3 | no | — |
| 159 | C22×C32 | — | 3 | 3 | no | — |
| 160 | C22×C32 | — | 4 | 2 | no | — |
| 161 | C22×C32 | — | 6 | 1 | no | — |
| 162 | C22×C32 | — | 8 | 1 | no | — |
| 163 | C22×C32 | — | 8 | 2 | no | — |
| 164 | C22×C32 | — | 16 | 1 | no | — |
| 165 | C22×C32 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 166 | C22×C32 | C23×D3 | 1 | 1 | yes | characteristic, complemented |
| 167 | C2×C3⋊D3 | — | 3 | 6 | no | — |
| 168 | C2×C3⋊D3 | — | 3 | 4 | no | — |
| 169 | C2×C3⋊D3 | — | 3 | 12 | no | — |
| 170 | C2×C3⋊D3 | — | 3 | 4 | no | — |
| 171 | C2×C3⋊D3 | — | 4 | 12 | no | — |
| 172 | C2×C3⋊D3 | — | 6 | 6 | no | — |
| 173 | C2×C3⋊D3 | C2×S4 | 1 | 6 | yes | complemented |
| 174 | C2×C3×D3 | — | 3 | 8 | no | — |
| 175 | C2×C3×D3 | — | 6 | 12 | no | — |
| 176 | C2×C3×D3 | — | 6 | 12 | no | — |
| 177 | C2×C3×D3 | — | 12 | 12 | no | — |
| 178 | C2×C3×D3 | — | 12 | 12 | no | — |
| 179 | C2×C3×D3 | — | 24 | 6 | no | — |
| 180 | C2×C3×D3 | — | 24 | 12 | no | — |
| 181 | C3×A4 | — | 2 | 2 | no | — |
| 182 | C3×A4 | — | 2 | 1 | no | — |
| 183 | C3×A4 | — | 4 | 1 | no | — |
| 184 | C3×A4 | C23×D3 | 1 | 2 | yes | complemented |
| 185 | D32 | — | 6 | 16 | no | — |
| 186 | D32 | — | 6 | 16 | no | — |
| 187 | D32 | — | 12 | 32 | no | — |
| 188 | C3×Dic3 | — | 3 | 8 | no | — |
| 189 | C25 | — | 9 | 1 | no | — |
| 190 | C25 | — | 27 | 1 | no | — |
| 191 | C22×D4 | — | 9 | 2 | no | — |
| 192 | C22×D4 | — | 27 | 2 | no | — |
| 193 | C22×D4 | — | 27 | 12 | no | — |
| 194 | C22×D4 | — | 27 | 12 | no | — |
| 195 | C23×C4 | — | 27 | 1 | no | — |
| 196 | C33 | — | 4 | 1 | no | Sylow |
| 197 | C23×C3 | — | 2 | 3 | no | — |
| 198 | C23×C3 | — | 3 | 2 | no | — |
| 199 | C23×C3 | — | 3 | 6 | no | — |
| 200 | C23×C3 | — | 6 | 1 | no | — |
| 201 | C23×C3 | — | 6 | 3 | no | — |
| 202 | C23×C3 | — | 9 | 12 | no | — |
| 203 | C23×C3 | — | 18 | 6 | no | — |
| 204 | C23×C3 | — | 18 | 2 | no | — |
| 205 | C23×C3 | — | 36 | 1 | no | — |
| 206 | C23×C3 | C2×D32 | 1 | 6 | yes | complemented |
| 207 | C22×D3 | — | 3 | 2 | no | — |
| 208 | C22×D3 | — | 3 | 12 | no | — |
| 209 | C22×D3 | — | 3 | 8 | no | — |
| 210 | C22×D3 | — | 6 | 1 | no | — |
| 211 | C22×D3 | — | 6 | 4 | no | — |
| 212 | C22×D3 | — | 6 | 6 | no | — |
| 213 | C22×D3 | — | 6 | 2 | no | — |
| 214 | C22×D3 | — | 9 | 12 | no | — |
| 215 | C22×D3 | — | 9 | 12 | no | — |
| 216 | C22×D3 | — | 9 | 32 | no | — |
| 217 | C22×D3 | — | 9 | 2 | no | — |
| 218 | C22×D3 | — | 9 | 12 | no | — |
| 219 | C22×D3 | — | 9 | 24 | no | — |
| 220 | C22×D3 | — | 12 | 2 | no | — |
| 221 | C22×D3 | — | 18 | 6 | no | — |
| 222 | C22×D3 | — | 18 | 6 | no | — |
| 223 | C22×D3 | — | 18 | 1 | no | — |
| 224 | C22×D3 | — | 18 | 12 | no | — |
| 225 | C22×D3 | — | 18 | 6 | no | — |
| 226 | C22×D3 | — | 18 | 24 | no | — |
| 227 | C22×D3 | — | 18 | 48 | no | — |
| 228 | C22×D3 | — | 18 | 24 | no | — |
| 229 | C22×D3 | — | 18 | 8 | no | — |
| 230 | C22×D3 | — | 18 | 6 | no | — |
| 231 | C22×D3 | — | 18 | 6 | no | — |
| 232 | C22×D3 | — | 18 | 8 | no | — |
| 233 | C22×D3 | — | 24 | 2 | no | — |
| 234 | C22×D3 | — | 36 | 12 | no | — |
| 235 | C2×A4 | — | 2 | 6 | no | — |
| 236 | C2×A4 | — | 4 | 3 | no | — |
| 237 | C2×A4 | — | 9 | 4 | no | — |
| 238 | C2×A4 | C2×D32 | 1 | 3 | yes | complemented |
| 239 | S4 | — | 3 | 8 | no | — |
| 240 | S4 | — | 6 | 8 | no | — |
| 241 | C3×D4 | — | 9 | 24 | no | — |
| 242 | C3×D4 | — | 9 | 8 | no | — |
| 243 | C2×C3×C4 | — | 9 | 12 | no | — |
| 244 | #67 | — | 3 | 24 | no | — |
| 245 | #67 | — | 3 | 8 | no | — |
| 246 | #67 | — | 9 | 32 | no | — |
| 247 | C2×Dic3 | — | 3 | 12 | no | — |
| 248 | D12 | — | 9 | 32 | no | — |
| 249 | C4×D3 | — | 9 | 32 | no | — |
| 250 | C2×C32 | — | 3 | 1 | no | — |
| 251 | C2×C32 | — | 3 | 3 | no | — |
| 252 | C2×C32 | — | 4 | 6 | no | — |
| 253 | C2×C32 | — | 8 | 3 | no | — |
| 254 | C2×C32 | — | 8 | 6 | no | — |
| 255 | C2×C32 | — | 16 | 3 | no | — |
| 256 | C2×C32 | C22×S4 | 1 | 3 | yes | complemented |
| 257 | C3⋊D3 | — | 3 | 4 | no | — |
| 258 | C3⋊D3 | — | 4 | 8 | no | — |
| 259 | C3⋊D3 | C22×S4 | 1 | 4 | yes | complemented |
| 260 | C3×D3 | — | 6 | 8 | no | — |
| 261 | C3×D3 | — | 12 | 8 | no | — |
| 262 | C3×D3 | — | 12 | 8 | no | — |
| 263 | C3×D3 | — | 24 | 4 | no | — |
| 264 | C3×D3 | — | 24 | 8 | no | — |
| 265 | C24 | — | 9 | 2 | no | — |
| 266 | C24 | — | 9 | 6 | no | — |
| 267 | C24 | — | 27 | 1 | no | — |
| 268 | C24 | — | 27 | 1 | no | — |
| 269 | C24 | — | 27 | 6 | no | — |
| 270 | C24 | — | 27 | 12 | no | — |
| 271 | C24 | — | 54 | 1 | no | — |
| 272 | C24 | — | 54 | 6 | no | — |
| 273 | C24 | — | 54 | 1 | no | — |
| 274 | C24 | #1113 | 1 | 1 | yes | characteristic, complemented |
| 275 | C2×D4 | — | 9 | 12 | no | — |
| 276 | C2×D4 | — | 9 | 12 | no | — |
| 277 | C2×D4 | — | 27 | 24 | no | — |
| 278 | C2×D4 | — | 27 | 16 | no | — |
| 279 | C2×D4 | — | 27 | 48 | no | — |
| 280 | C22×C4 | — | 9 | 2 | no | — |
| 281 | C22×C4 | — | 27 | 12 | no | — |
| 282 | C22×C3 | — | 2 | 1 | no | — |
| 283 | C22×C3 | — | 2 | 1 | no | — |
| 284 | C22×C3 | — | 3 | 6 | no | — |
| 285 | C22×C3 | — | 3 | 6 | no | — |
| 286 | C22×C3 | — | 3 | 6 | no | — |
| 287 | C22×C3 | — | 4 | 1 | no | — |
| 288 | C22×C3 | — | 6 | 3 | no | — |
| 289 | C22×C3 | — | 6 | 3 | no | — |
| 290 | C22×C3 | — | 6 | 3 | no | — |
| 291 | C22×C3 | — | 6 | 2 | no | — |
| 292 | C22×C3 | — | 6 | 2 | no | — |
| 293 | C22×C3 | — | 8 | 2 | no | — |
| 294 | C22×C3 | — | 9 | 8 | no | — |
| 295 | C22×C3 | — | 16 | 1 | no | — |
| 296 | C22×C3 | — | 18 | 12 | no | — |
| 297 | C22×C3 | — | 18 | 12 | no | — |
| 298 | C22×C3 | — | 36 | 6 | no | — |
| 299 | C22×C3 | D3×S4 | 1 | 2 | yes | complemented |
| 300 | C22×C3 | C22×D32 | 1 | 2 | yes | complemented |
| 301 | C2×D3 | — | 3 | 12 | no | — |
| 302 | C2×D3 | — | 3 | 8 | no | — |
| 303 | C2×D3 | — | 6 | 6 | no | — |
| 304 | C2×D3 | — | 6 | 12 | no | — |
| 305 | C2×D3 | — | 6 | 12 | no | — |
| 306 | C2×D3 | — | 9 | 8 | no | — |
| 307 | C2×D3 | — | 9 | 24 | no | — |
| 308 | C2×D3 | — | 9 | 12 | no | — |
| 309 | C2×D3 | — | 9 | 8 | no | — |
| 310 | C2×D3 | — | 12 | 12 | no | — |
| 311 | C2×D3 | — | 18 | 4 | no | — |
| 312 | C2×D3 | — | 18 | 12 | no | — |
| 313 | C2×D3 | — | 18 | 6 | no | — |
| 314 | C2×D3 | — | 18 | 4 | no | — |
| 315 | C2×D3 | — | 18 | 32 | no | — |
| 316 | C2×D3 | — | 18 | 32 | no | — |
| 317 | C2×D3 | — | 18 | 12 | no | — |
| 318 | C2×D3 | — | 18 | 12 | no | — |
| 319 | C2×D3 | — | 24 | 12 | no | — |
| 320 | C2×D3 | — | 36 | 16 | no | — |
| 321 | A4 | — | 2 | 2 | no | — |
| 322 | A4 | — | 4 | 1 | no | — |
| 323 | A4 | C22×D32 | 1 | 1 | yes | characteristic, complemented |
| 324 | C3×C4 | — | 9 | 8 | no | — |
| 325 | Dic3 | — | 3 | 8 | no | — |
| 326 | C32 | — | 4 | 2 | no | — |
| 327 | C32 | — | 8 | 1 | no | — |
| 328 | C32 | — | 8 | 2 | no | — |
| 329 | C32 | — | 16 | 1 | no | — |
| 330 | C32 | C23×S4 | 1 | 1 | yes | characteristic, complemented |
| 331 | C23 | — | 3 | 1 | no | — |
| 332 | C23 | — | 3 | 3 | no | — |
| 333 | C23 | — | 9 | 12 | no | — |
| 334 | C23 | — | 9 | 1 | no | — |
| 335 | C23 | — | 9 | 4 | no | — |
| 336 | C23 | — | 18 | 6 | no | — |
| 337 | C23 | — | 18 | 2 | no | — |
| 338 | C23 | — | 27 | 6 | no | — |
| 339 | C23 | — | 27 | 6 | no | — |
| 340 | C23 | — | 27 | 12 | no | — |
| 341 | C23 | — | 27 | 6 | no | — |
| 342 | C23 | — | 27 | 16 | no | — |
| 343 | C23 | — | 27 | 1 | no | — |
| 344 | C23 | — | 54 | 3 | no | — |
| 345 | C23 | — | 54 | 4 | no | — |
| 346 | C23 | — | 54 | 12 | no | — |
| 347 | C23 | — | 54 | 24 | no | — |
| 348 | C23 | — | 54 | 12 | no | — |
| 349 | C23 | C2×#1113 | 1 | 3 | yes | complemented |
| 350 | D4 | — | 9 | 24 | no | — |
| 351 | D4 | — | 9 | 8 | no | — |
| 352 | D4 | — | 27 | 32 | no | — |
| 353 | C2×C4 | — | 9 | 12 | no | — |
| 354 | C2×C4 | — | 27 | 16 | no | — |
| 355 | C2×C3 | — | 2 | 3 | no | — |
| 356 | C2×C3 | — | 3 | 2 | no | — |
| 357 | C2×C3 | — | 3 | 6 | no | — |
| 358 | C2×C3 | — | 4 | 3 | no | — |
| 359 | C2×C3 | — | 6 | 1 | no | — |
| 360 | C2×C3 | — | 6 | 3 | no | — |
| 361 | C2×C3 | — | 8 | 6 | no | — |
| 362 | C2×C3 | — | 16 | 3 | no | — |
| 363 | C2×C3 | — | 18 | 8 | no | — |
| 364 | C2×C3 | — | 36 | 4 | no | — |
| 365 | C2×C3 | C2×D3×S4 | 1 | 6 | yes | complemented |
| 366 | D3 | — | 3 | 8 | no | — |
| 367 | D3 | — | 6 | 4 | no | — |
| 368 | D3 | — | 6 | 8 | no | — |
| 369 | D3 | — | 9 | 8 | no | — |
| 370 | D3 | — | 12 | 8 | no | — |
| 371 | D3 | — | 18 | 4 | no | — |
| 372 | D3 | — | 24 | 8 | no | — |
| 373 | C22 | — | 3 | 3 | no | — |
| 374 | C22 | — | 3 | 3 | no | — |
| 375 | C22 | — | 3 | 3 | no | — |
| 376 | C22 | — | 6 | 1 | no | — |
| 377 | C22 | — | 9 | 8 | no | — |
| 378 | C22 | — | 9 | 6 | no | — |
| 379 | C22 | — | 18 | 12 | no | — |
| 380 | C22 | — | 18 | 12 | no | — |
| 381 | C22 | — | 27 | 4 | no | — |
| 382 | C22 | — | 27 | 12 | no | — |
| 383 | C22 | — | 27 | 4 | no | — |
| 384 | C22 | — | 27 | 6 | no | — |
| 385 | C22 | — | 54 | 6 | no | — |
| 386 | C22 | — | 54 | 16 | no | — |
| 387 | C22 | — | 54 | 16 | no | — |
| 388 | C22 | #89101 | 1 | 1 | yes | characteristic, direct product factor |
| 389 | C22 | C22×#1113 | 1 | 1 | yes | characteristic, complemented |
| 390 | C4 | — | 9 | 8 | no | — |
| 391 | C3 | — | 2 | 1 | no | — |
| 392 | C3 | — | 4 | 1 | no | — |
| 393 | C3 | — | 8 | 2 | no | — |
| 394 | C3 | — | 16 | 1 | no | — |
| 395 | C3 | C22×D3×S4 | 1 | 2 | yes | complemented |
| 396 | C2 | — | 3 | 1 | no | — |
| 397 | C2 | — | 3 | 3 | no | — |
| 398 | C2 | — | 9 | 4 | no | — |
| 399 | C2 | — | 18 | 8 | no | — |
| 400 | C2 | — | 27 | 4 | no | — |
| 401 | C2 | C2×#89101 | 1 | 3 | yes | direct product factor |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #89101 |
| commutator, cosocle, hypocenter | C32×A4 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C24×C32 | C2×D3 |
| LCS | G ▷ C32×A4 | |
| 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×C3⋊S4 | C2 | semidirect |
| 3. C2×#89101 | C2 | direct (N × H) |
| 6. C22×C32×A4 | C22 | semidirect |
| 8. C2×A4×C3⋊D3 | C22 | semidirect |
| 9. C2×C3×C3⋊S4 | C22 | semidirect |
| 10. #89101 | C22 | direct (N × H) |
| 11. C24×C3⋊D3 | D3 | semidirect |
| 15. C22×C3⋊S4 | D3 | semidirect |
| 26. C2×C32×A4 | C23 | semidirect |
| 28. A4×C3⋊D3 | C23 | semidirect |
| 29. C3×C3⋊S4 | C23 | semidirect |
| 32. C24×C32 | C2×D3 | semidirect |
| 36. C23×C3⋊D3 | C2×D3 | semidirect |
| 41. C22×C3×A4 | C2×D3 | semidirect |
| 49. C2×C3⋊S4 | C2×D3 | semidirect |
| 63. C32×A4 | C24 | semidirect |
| 81. C23×C32 | C22×D3 | semidirect |
| 90. C22×C3⋊D3 | S4 | semidirect |
| 91. C22×C3⋊D3 | C22×D3 | semidirect |
| 102. C2×C3×A4 | C22×D3 | semidirect |
| 110. C3⋊S4 | C22×D3 | semidirect |
| 124. C24×C3 | D32 | semidirect |
| 142. C22×A4 | D32 | semidirect |
| 165. C22×C32 | C2×S4 | semidirect |
| 166. C22×C32 | C23×D3 | semidirect |
| 173. C2×C3⋊D3 | C2×S4 | semidirect |
| 184. C3×A4 | C23×D3 | semidirect |
| 206. C23×C3 | C2×D32 | semidirect |
| 238. C2×A4 | C2×D32 | semidirect |
| 256. C2×C32 | C22×S4 | semidirect |
| 259. C3⋊D3 | C22×S4 | semidirect |
| 274. C24 | #1113 | semidirect |
| 299. C22×C3 | D3×S4 | semidirect |
| 300. C22×C3 | C22×D32 | semidirect |
| 323. A4 | C22×D32 | semidirect |
| 330. C32 | C23×S4 | semidirect |
| 349. C23 | C2×#1113 | semidirect |
| 365. C2×C3 | C2×D3×S4 | semidirect |
| 388. C22 | #89101 | direct (N × H) |
| 389. C22 | C22×#1113 | semidirect |
| 395. C3 | C22×D3×S4 | semidirect |
| 401. C2 | C2×#89101 | 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×C3⋊S4 | 2 |
| C2×#89101 | 2 |
| C22×D3×S4 | 3 |
| C22×#3811 | 3 |
| C22×#1113 | 4 |