Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3790 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 3790 conjugacy classes of subgroups — too many to draw. Only its 271 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 | C24×C3×C3⋊D3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#89049 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C3×#64162 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11723727 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #11723723 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10595527 | — | 3 | 1 | no | maximal |
| 7 | D3×#953 | — | 3 | 2 | no | maximal |
| 8 | C24×C33 | C22 | 1 | 1 | yes | characteristic, complemented |
| 9 | C23×C3×C3⋊D3 | — | 2 | 12 | no | — |
| 10 | C23×C3×C3⋊D3 | C22 | 1 | 3 | yes | — |
| 11 | C23×C3×C3⋊D3 | C22 | 1 | 3 | yes | complemented |
| 12 | C22×#1113 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C2×C3×#638 | C22 | 1 | 6 | yes | complemented |
| 14 | #89049 | — | 2 | 12 | no | — |
| 15 | C2×#6295 | C22 | 1 | 6 | yes | complemented |
| 16 | C2×#6294 | C22 | 1 | 3 | yes | complemented |
| 17 | C3×#3757 | C22 | 1 | 6 | yes | complemented |
| 18 | #88814 | C22 | 1 | 6 | yes | complemented |
| 19 | C24×C3⋊D3 | D3 | 1 | 1 | yes | characteristic, complemented |
| 20 | C24×C3×D3 | — | 3 | 2 | no | — |
| 21 | C24×C3×D3 | — | 6 | 1 | no | — |
| 22 | C2×#3811 | — | 3 | 3 | no | — |
| 23 | C2×D3×#67 | — | 3 | 6 | no | — |
| 24 | #64162 | D3 | 1 | 2 | yes | complemented |
| 25 | C3×#953 | — | 3 | 2 | no | — |
| 26 | C3×#953 | — | 3 | 2 | no | — |
| 27 | C3×#953 | — | 6 | 2 | no | — |
| 28 | #63981 | — | 3 | 6 | no | — |
| 29 | #63977 | — | 3 | 6 | no | — |
| 30 | #63976 | — | 3 | 6 | no | — |
| 31 | #63974 | — | 3 | 3 | no | — |
| 32 | D3×#217 | — | 3 | 6 | no | — |
| 33 | C23×C33 | — | 2 | 6 | no | — |
| 34 | C23×C33 | C23 | 1 | 3 | yes | — |
| 35 | C22×C3×C3⋊D3 | — | 2 | 32 | no | — |
| 36 | C22×C3×C3⋊D3 | — | 2 | 6 | no | — |
| 37 | C22×C3×C3⋊D3 | — | 2 | 12 | no | — |
| 38 | C22×C3×C3⋊D3 | — | 2 | 12 | no | — |
| 39 | C22×C3×C3⋊D3 | D4 | 1 | 12 | yes | complemented |
| 40 | C22×C3×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 41 | C22×C3×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 42 | C22×C3×C3⋊D3 | C23 | 1 | 2 | yes | complemented |
| 43 | C2×#1113 | — | 2 | 6 | no | — |
| 44 | C3×#638 | — | 2 | 12 | no | — |
| 45 | C2×C3×C3⋊Dic3 | C23 | 1 | 6 | yes | complemented |
| 46 | #6295 | — | 2 | 12 | no | — |
| 47 | #6294 | — | 2 | 6 | no | — |
| 48 | C2×#953 | — | 9 | 1 | no | — |
| 49 | D3×#120 | — | 9 | 2 | no | — |
| 50 | C24×C32 | — | 2 | 1 | no | — |
| 51 | C24×C32 | — | 2 | 2 | no | — |
| 52 | C24×C32 | — | 4 | 1 | no | — |
| 53 | C24×C32 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 54 | C24×C32 | C2×D3 | 1 | 2 | yes | complemented |
| 55 | C23×C3⋊D3 | — | 2 | 12 | no | — |
| 56 | C23×C3⋊D3 | C2×D3 | 1 | 3 | yes | — |
| 57 | C23×C3⋊D3 | C2×D3 | 1 | 3 | yes | complemented |
| 58 | C23×C3×D3 | — | 3 | 6 | no | — |
| 59 | C23×C3×D3 | — | 3 | 6 | no | — |
| 60 | C23×C3×D3 | — | 6 | 24 | no | — |
| 61 | C23×C3×D3 | — | 6 | 3 | no | — |
| 62 | C23×C3×D3 | — | 6 | 3 | no | — |
| 63 | C23×C3×D3 | — | 6 | 24 | no | — |
| 64 | C22×D32 | — | 3 | 1 | no | — |
| 65 | C22×D32 | — | 3 | 2 | no | — |
| 66 | C2×#638 | C2×D3 | 1 | 6 | yes | complemented |
| 67 | C2×C3×#67 | — | 3 | 6 | no | — |
| 68 | C2×C3×#67 | — | 3 | 6 | no | — |
| 69 | C2×C3×#67 | — | 6 | 6 | no | — |
| 70 | #3811 | — | 6 | 12 | no | — |
| 71 | D3×#67 | — | 6 | 24 | no | — |
| 72 | C2×#626 | — | 3 | 6 | no | — |
| 73 | C2×#626 | — | 3 | 6 | no | — |
| 74 | C2×#625 | — | 3 | 6 | no | — |
| 75 | C2×#624 | — | 3 | 3 | no | — |
| 76 | C2×D3×Dic3 | — | 3 | 6 | no | — |
| 77 | #3757 | C2×D3 | 1 | 6 | yes | complemented |
| 78 | C3×#217 | — | 3 | 6 | no | — |
| 79 | C3×#217 | — | 3 | 6 | no | — |
| 80 | C3×#217 | — | 6 | 6 | no | — |
| 81 | #3722 | — | 3 | 6 | no | — |
| 82 | (C2×D3)⋊Dic3 | — | 3 | 12 | no | — |
| 83 | C22×C33 | — | 2 | 8 | no | — |
| 84 | C22×C33 | — | 2 | 6 | no | — |
| 85 | C22×C33 | C2×D4 | 1 | 6 | yes | complemented |
| 86 | C22×C33 | C24 | 1 | 1 | yes | characteristic |
| 87 | C2×C3×C3⋊D3 | — | 2 | 24 | no | — |
| 88 | C2×C3×C3⋊D3 | — | 2 | 6 | no | — |
| 89 | C2×C3×C3⋊D3 | — | 2 | 24 | no | — |
| 90 | C2×C3×C3⋊D3 | — | 2 | 6 | no | — |
| 91 | C2×C3×C3⋊D3 | C2×D4 | 1 | 6 | yes | — |
| 92 | C2×C3×C3⋊D3 | C2×D4 | 1 | 6 | yes | complemented |
| 93 | #1113 | — | 4 | 4 | no | — |
| 94 | C3×C3⋊Dic3 | — | 2 | 6 | no | — |
| 95 | C25×C3 | — | 9 | 1 | no | — |
| 96 | C24×D3 | — | 3 | 2 | no | — |
| 97 | C24×D3 | — | 6 | 1 | no | — |
| 98 | C22×#67 | — | 9 | 3 | no | — |
| 99 | C2×D3×D4 | — | 9 | 6 | no | — |
| 100 | C3×#120 | — | 9 | 2 | no | — |
| 101 | #953 | — | 3 | 2 | no | — |
| 102 | #953 | — | 3 | 2 | no | — |
| 103 | #953 | — | 6 | 2 | no | — |
| 104 | #953 | — | 9 | 6 | no | — |
| 105 | C2×#217 | — | 9 | 3 | no | — |
| 106 | #937 | — | 9 | 6 | no | — |
| 107 | #882 | — | 9 | 6 | no | — |
| 108 | D3×C22⋊C4 | — | 9 | 6 | no | — |
| 109 | C23×C32 | — | 2 | 6 | no | — |
| 110 | C23×C32 | — | 2 | 12 | no | — |
| 111 | C23×C32 | — | 2 | 12 | no | — |
| 112 | C23×C32 | — | 2 | 3 | no | — |
| 113 | C23×C32 | — | 2 | 6 | no | — |
| 114 | C23×C32 | — | 4 | 3 | no | — |
| 115 | C23×C32 | — | 4 | 12 | no | — |
| 116 | C23×C32 | — | 4 | 12 | no | — |
| 117 | C23×C32 | C22×D3 | 1 | 6 | yes | — |
| 118 | C23×C32 | C22×D3 | 1 | 3 | yes | — |
| 119 | C22×C3⋊D3 | — | 2 | 32 | no | — |
| 120 | C22×C3⋊D3 | — | 2 | 6 | no | — |
| 121 | C22×C3⋊D3 | — | 2 | 12 | no | — |
| 122 | C22×C3⋊D3 | — | 2 | 12 | no | — |
| 123 | C22×C3⋊D3 | #67 | 1 | 12 | yes | complemented |
| 124 | C22×C3⋊D3 | C22×D3 | 1 | 3 | yes | — |
| 125 | C22×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 126 | C22×C3⋊D3 | C22×D3 | 1 | 2 | yes | complemented |
| 127 | C22×C3×D3 | — | 3 | 2 | no | — |
| 128 | C22×C3×D3 | — | 3 | 24 | no | — |
| 129 | C22×C3×D3 | — | 3 | 6 | no | — |
| 130 | C22×C3×D3 | — | 3 | 2 | no | — |
| 131 | C22×C3×D3 | — | 3 | 2 | no | — |
| 132 | C22×C3×D3 | — | 6 | 12 | no | — |
| 133 | C22×C3×D3 | — | 6 | 1 | no | — |
| 134 | C22×C3×D3 | — | 6 | 3 | no | — |
| 135 | C22×C3×D3 | — | 6 | 2 | no | — |
| 136 | C22×C3×D3 | — | 6 | 24 | no | — |
| 137 | C22×C3×D3 | — | 6 | 24 | no | — |
| 138 | C22×C3×D3 | — | 6 | 24 | no | — |
| 139 | C22×C3×D3 | — | 6 | 24 | no | — |
| 140 | C22×C3×D3 | — | 6 | 64 | no | — |
| 141 | C22×C3×D3 | — | 6 | 64 | no | — |
| 142 | C22×C3×D3 | — | 6 | 12 | no | — |
| 143 | C22×C3×D3 | — | 6 | 12 | no | — |
| 144 | C2×D32 | — | 6 | 12 | no | — |
| 145 | C2×D32 | — | 6 | 6 | no | — |
| 146 | #638 | — | 2 | 12 | no | — |
| 147 | C2×C3⋊Dic3 | C22×D3 | 1 | 6 | yes | complemented |
| 148 | C3×#67 | — | 6 | 12 | no | — |
| 149 | C3×#67 | — | 6 | 12 | no | — |
| 150 | C3×#67 | — | 12 | 12 | no | — |
| 151 | C2×C3×Dic3 | — | 3 | 6 | no | — |
| 152 | C2×C3×Dic3 | — | 3 | 6 | no | — |
| 153 | C2×C3×Dic3 | — | 6 | 6 | no | — |
| 154 | #626 | — | 6 | 12 | no | — |
| 155 | #626 | — | 6 | 12 | no | — |
| 156 | #625 | — | 6 | 12 | no | — |
| 157 | #624 | — | 6 | 6 | no | — |
| 158 | D3×Dic3 | — | 6 | 12 | no | — |
| 159 | C2×#120 | — | 27 | 1 | no | Sylow |
| 160 | C2×C33 | — | 2 | 6 | no | — |
| 161 | C2×C33 | C22×D4 | 1 | 3 | yes | — |
| 162 | C3×C3⋊D3 | — | 2 | 6 | no | — |
| 163 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 164 | C3×C3⋊D3 | #120 | 1 | 4 | yes | complemented |
| 165 | C24×C3 | — | 2 | 1 | no | — |
| 166 | C24×C3 | — | 2 | 2 | no | — |
| 167 | C24×C3 | — | 4 | 1 | no | — |
| 168 | C24×C3 | — | 9 | 3 | no | — |
| 169 | C24×C3 | — | 9 | 3 | no | — |
| 170 | C24×C3 | — | 18 | 12 | no | — |
| 171 | C24×C3 | D32 | 1 | 1 | yes | characteristic, complemented |
| 172 | C24×C3 | D32 | 1 | 2 | yes | complemented |
| 173 | C23×D3 | — | 3 | 6 | no | — |
| 174 | C23×D3 | — | 3 | 6 | no | — |
| 175 | C23×D3 | — | 6 | 3 | no | — |
| 176 | C23×D3 | — | 6 | 3 | no | — |
| 177 | C23×D3 | — | 6 | 24 | no | — |
| 178 | C23×D3 | — | 6 | 24 | no | — |
| 179 | C23×D3 | — | 9 | 2 | no | — |
| 180 | C23×D3 | — | 9 | 1 | no | — |
| 181 | C2×C3×D4 | — | 9 | 6 | no | — |
| 182 | C2×#67 | — | 3 | 6 | no | — |
| 183 | C2×#67 | — | 3 | 6 | no | — |
| 184 | C2×#67 | — | 6 | 6 | no | — |
| 185 | C2×#67 | — | 9 | 6 | no | — |
| 186 | C2×#67 | — | 9 | 6 | no | — |
| 187 | C2×#67 | — | 18 | 12 | no | — |
| 188 | C22×Dic3 | — | 9 | 3 | no | — |
| 189 | D3×D4 | — | 18 | 24 | no | — |
| 190 | C2×D12 | — | 9 | 6 | no | — |
| 191 | C2×C4×D3 | — | 9 | 6 | no | — |
| 192 | C3×C22⋊C4 | — | 9 | 6 | no | — |
| 193 | #217 | — | 3 | 6 | no | — |
| 194 | #217 | — | 3 | 6 | no | — |
| 195 | #217 | — | 6 | 6 | no | — |
| 196 | #217 | — | 9 | 6 | no | — |
| 197 | (C2×D3)⋊C4 | — | 9 | 12 | no | — |
| 198 | C22×C32 | — | 2 | 8 | no | — |
| 199 | C22×C32 | — | 2 | 6 | no | — |
| 200 | C22×C32 | — | 2 | 16 | no | — |
| 201 | C22×C32 | — | 2 | 16 | no | — |
| 202 | C22×C32 | — | 2 | 12 | no | — |
| 203 | C22×C32 | — | 2 | 12 | no | — |
| 204 | C22×C32 | — | 2 | 2 | no | — |
| 205 | C22×C32 | — | 2 | 1 | no | — |
| 206 | C22×C32 | — | 2 | 12 | no | — |
| 207 | C22×C32 | — | 2 | 6 | no | — |
| 208 | C22×C32 | — | 4 | 6 | no | — |
| 209 | C22×C32 | — | 4 | 1 | no | — |
| 210 | C22×C32 | — | 4 | 12 | no | — |
| 211 | C22×C32 | — | 4 | 12 | no | — |
| 212 | C22×C32 | — | 4 | 16 | no | — |
| 213 | C22×C32 | — | 4 | 16 | no | — |
| 214 | C22×C32 | D3×D4 | 1 | 12 | yes | complemented |
| 215 | C22×C32 | C2×#67 | 1 | 6 | yes | complemented |
| 216 | C22×C32 | C23×D3 | 1 | 2 | yes | — |
| 217 | C22×C32 | C23×D3 | 1 | 1 | yes | characteristic |
| 218 | C2×C3⋊D3 | — | 2 | 24 | no | — |
| 219 | C2×C3⋊D3 | — | 2 | 6 | no | — |
| 220 | C2×C3⋊D3 | — | 2 | 24 | no | — |
| 221 | C2×C3⋊D3 | — | 2 | 6 | no | — |
| 222 | C2×C3⋊D3 | C2×#67 | 1 | 6 | yes | — |
| 223 | C2×C3⋊D3 | C2×#67 | 1 | 6 | yes | complemented |
| 224 | C2×C3×D3 | — | 3 | 12 | no | — |
| 225 | C2×C3×D3 | — | 3 | 12 | no | — |
| 226 | C2×C3×D3 | — | 6 | 6 | no | — |
| 227 | C2×C3×D3 | — | 6 | 6 | no | — |
| 228 | C2×C3×D3 | — | 6 | 48 | no | — |
| 229 | C2×C3×D3 | — | 6 | 48 | no | — |
| 230 | C2×C3×D3 | — | 6 | 48 | no | — |
| 231 | C2×C3×D3 | — | 6 | 48 | no | — |
| 232 | C2×C3×D3 | — | 6 | 12 | no | — |
| 233 | C2×C3×D3 | — | 6 | 12 | no | — |
| 234 | C2×C3×D3 | — | 6 | 6 | no | — |
| 235 | C2×C3×D3 | — | 6 | 6 | no | — |
| 236 | C2×C3×D3 | — | 12 | 6 | no | — |
| 237 | D32 | — | 12 | 8 | no | — |
| 238 | D32 | — | 12 | 4 | no | — |
| 239 | C3⋊Dic3 | — | 2 | 6 | no | — |
| 240 | C3×Dic3 | — | 6 | 6 | no | — |
| 241 | C3×Dic3 | — | 6 | 6 | no | — |
| 242 | C3×Dic3 | — | 12 | 6 | no | — |
| 243 | C25 | — | 9 | 1 | no | — |
| 244 | C22×D4 | — | 27 | 3 | no | — |
| 245 | #120 | — | 9 | 2 | no | — |
| 246 | #120 | — | 27 | 6 | no | — |
| 247 | C2×C22⋊C4 | — | 27 | 3 | no | — |
| 248 | C33 | C2×#120 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 249 | C23×C3 | — | 2 | 12 | no | — |
| 250 | C23×C3 | — | 2 | 12 | no | — |
| 251 | C23×C3 | — | 2 | 6 | no | — |
| 252 | C23×C3 | — | 2 | 3 | no | — |
| 253 | C23×C3 | — | 2 | 6 | no | — |
| 254 | C23×C3 | — | 4 | 12 | no | — |
| 255 | C23×C3 | — | 4 | 12 | no | — |
| 256 | C23×C3 | — | 4 | 3 | no | — |
| 257 | C23×C3 | — | 9 | 1 | no | — |
| 258 | C23×C3 | — | 9 | 3 | no | — |
| 259 | C23×C3 | — | 9 | 12 | no | — |
| 260 | C23×C3 | — | 9 | 2 | no | — |
| 261 | C23×C3 | — | 18 | 12 | no | — |
| 262 | C23×C3 | — | 18 | 12 | no | — |
| 263 | C23×C3 | — | 18 | 32 | no | — |
| 264 | C23×C3 | — | 18 | 6 | no | — |
| 265 | C23×C3 | C2×D32 | 1 | 6 | yes | — |
| 266 | C23×C3 | C2×D32 | 1 | 3 | yes | — |
| 267 | C22×D3 | — | 3 | 2 | no | — |
| 268 | C22×D3 | — | 3 | 6 | no | — |
| 269 | C22×D3 | — | 3 | 24 | no | — |
| 270 | C22×D3 | — | 3 | 2 | no | — |
| 271 | C22×D3 | — | 3 | 2 | no | — |
| 272 | C22×D3 | — | 6 | 12 | no | — |
| 273 | C22×D3 | — | 6 | 1 | no | — |
| 274 | C22×D3 | — | 6 | 3 | no | — |
| 275 | C22×D3 | — | 6 | 2 | no | — |
| 276 | C22×D3 | — | 6 | 24 | no | — |
| 277 | C22×D3 | — | 6 | 24 | no | — |
| 278 | C22×D3 | — | 6 | 24 | no | — |
| 279 | C22×D3 | — | 6 | 24 | no | — |
| 280 | C22×D3 | — | 6 | 64 | no | — |
| 281 | C22×D3 | — | 6 | 64 | no | — |
| 282 | C22×D3 | — | 6 | 12 | no | — |
| 283 | C22×D3 | — | 6 | 12 | no | — |
| 284 | C22×D3 | — | 18 | 12 | no | — |
| 285 | C22×D3 | — | 18 | 6 | no | — |
| 286 | C3×D4 | — | 18 | 12 | no | — |
| 287 | C2×C3×C4 | — | 9 | 6 | no | — |
| 288 | #67 | — | 6 | 12 | no | — |
| 289 | #67 | — | 6 | 12 | no | — |
| 290 | #67 | — | 12 | 12 | no | — |
| 291 | #67 | — | 18 | 12 | no | — |
| 292 | #67 | — | 18 | 12 | no | — |
| 293 | C2×Dic3 | — | 3 | 6 | no | — |
| 294 | C2×Dic3 | — | 3 | 6 | no | — |
| 295 | C2×Dic3 | — | 6 | 6 | no | — |
| 296 | C2×Dic3 | — | 18 | 6 | no | — |
| 297 | D12 | — | 18 | 12 | no | — |
| 298 | C4×D3 | — | 18 | 12 | no | — |
| 299 | C2×C32 | — | 2 | 6 | no | — |
| 300 | C2×C32 | — | 2 | 12 | no | — |
| 301 | C2×C32 | — | 2 | 12 | no | — |
| 302 | C2×C32 | — | 2 | 6 | no | — |
| 303 | C2×C32 | — | 2 | 3 | no | — |
| 304 | C2×C32 | — | 4 | 3 | no | — |
| 305 | C2×C32 | — | 4 | 12 | no | — |
| 306 | C2×C32 | — | 4 | 12 | no | — |
| 307 | C2×C32 | C2×D3×D4 | 1 | 6 | yes | — |
| 308 | C2×C32 | C22×#67 | 1 | 3 | yes | — |
| 309 | C3⋊D3 | — | 2 | 6 | no | — |
| 310 | C3⋊D3 | — | 4 | 2 | no | — |
| 311 | C3⋊D3 | #953 | 1 | 4 | yes | complemented |
| 312 | C3×D3 | — | 3 | 8 | no | — |
| 313 | C3×D3 | — | 6 | 4 | no | — |
| 314 | C3×D3 | — | 6 | 12 | no | — |
| 315 | C3×D3 | — | 6 | 12 | no | — |
| 316 | C3×D3 | — | 12 | 2 | no | — |
| 317 | C3×D3 | — | 12 | 2 | no | — |
| 318 | C3×D3 | — | 24 | 2 | no | — |
| 319 | C24 | — | 9 | 3 | no | — |
| 320 | C24 | — | 9 | 3 | no | — |
| 321 | C24 | — | 18 | 12 | no | — |
| 322 | C24 | — | 27 | 1 | no | — |
| 323 | C24 | #1113 | 1 | 1 | yes | characteristic, complemented |
| 324 | C2×D4 | — | 9 | 6 | no | — |
| 325 | C2×D4 | — | 27 | 6 | no | — |
| 326 | C2×D4 | — | 54 | 12 | no | — |
| 327 | C22×C4 | — | 27 | 3 | no | — |
| 328 | C22⋊C4 | — | 9 | 6 | no | — |
| 329 | C22⋊C4 | — | 27 | 6 | no | — |
| 330 | C22×C3 | — | 2 | 16 | no | — |
| 331 | C22×C3 | — | 2 | 16 | no | — |
| 332 | C22×C3 | — | 2 | 12 | no | — |
| 333 | C22×C3 | — | 2 | 8 | no | — |
| 334 | C22×C3 | — | 2 | 12 | no | — |
| 335 | C22×C3 | — | 2 | 6 | no | — |
| 336 | C22×C3 | — | 2 | 2 | no | — |
| 337 | C22×C3 | — | 2 | 1 | no | — |
| 338 | C22×C3 | — | 2 | 6 | no | — |
| 339 | C22×C3 | — | 2 | 12 | no | — |
| 340 | C22×C3 | — | 4 | 12 | no | — |
| 341 | C22×C3 | — | 4 | 16 | no | — |
| 342 | C22×C3 | — | 4 | 16 | no | — |
| 343 | C22×C3 | — | 4 | 12 | no | — |
| 344 | C22×C3 | — | 4 | 1 | no | — |
| 345 | C22×C3 | — | 4 | 6 | no | — |
| 346 | C22×C3 | — | 9 | 6 | no | — |
| 347 | C22×C3 | — | 9 | 6 | no | — |
| 348 | C22×C3 | — | 18 | 24 | no | — |
| 349 | C22×C3 | — | 18 | 24 | no | — |
| 350 | C22×C3 | — | 18 | 6 | no | — |
| 351 | C22×C3 | — | 18 | 6 | no | — |
| 352 | C22×C3 | D3×#67 | 1 | 12 | yes | complemented |
| 353 | C22×C3 | #3811 | 1 | 6 | yes | complemented |
| 354 | C22×C3 | C22×D32 | 1 | 2 | yes | — |
| 355 | C22×C3 | C22×D32 | 1 | 1 | yes | characteristic |
| 356 | C2×D3 | — | 3 | 12 | no | — |
| 357 | C2×D3 | — | 3 | 12 | no | — |
| 358 | C2×D3 | — | 6 | 6 | no | — |
| 359 | C2×D3 | — | 6 | 6 | no | — |
| 360 | C2×D3 | — | 6 | 48 | no | — |
| 361 | C2×D3 | — | 6 | 48 | no | — |
| 362 | C2×D3 | — | 6 | 48 | no | — |
| 363 | C2×D3 | — | 6 | 48 | no | — |
| 364 | C2×D3 | — | 6 | 12 | no | — |
| 365 | C2×D3 | — | 6 | 12 | no | — |
| 366 | C2×D3 | — | 6 | 6 | no | — |
| 367 | C2×D3 | — | 6 | 6 | no | — |
| 368 | C2×D3 | — | 12 | 6 | no | — |
| 369 | C2×D3 | — | 36 | 8 | no | — |
| 370 | C2×D3 | — | 36 | 4 | no | — |
| 371 | C3×C4 | — | 18 | 6 | no | — |
| 372 | Dic3 | — | 6 | 6 | no | — |
| 373 | Dic3 | — | 6 | 6 | no | — |
| 374 | Dic3 | — | 12 | 6 | no | — |
| 375 | C32 | — | 2 | 2 | no | — |
| 376 | C32 | — | 2 | 1 | no | — |
| 377 | C32 | — | 4 | 1 | no | — |
| 378 | C32 | D3×#120 | 1 | 2 | yes | complemented |
| 379 | C32 | C2×#953 | 1 | 1 | yes | characteristic, complemented |
| 380 | C23 | — | 2 | 6 | no | — |
| 381 | C23 | — | 9 | 1 | no | — |
| 382 | C23 | — | 9 | 3 | no | — |
| 383 | C23 | — | 9 | 12 | no | — |
| 384 | C23 | — | 9 | 2 | no | — |
| 385 | C23 | — | 18 | 12 | no | — |
| 386 | C23 | — | 18 | 12 | no | — |
| 387 | C23 | — | 18 | 32 | no | — |
| 388 | C23 | — | 18 | 6 | no | — |
| 389 | C23 | — | 54 | 6 | no | — |
| 390 | C23 | C2×#1113 | 1 | 3 | yes | — |
| 391 | D4 | — | 18 | 12 | no | — |
| 392 | D4 | — | 54 | 12 | no | — |
| 393 | C2×C4 | — | 9 | 6 | no | — |
| 394 | C2×C4 | — | 54 | 6 | no | — |
| 395 | C2×C3 | — | 2 | 12 | no | — |
| 396 | C2×C3 | — | 2 | 12 | no | — |
| 397 | C2×C3 | — | 2 | 6 | no | — |
| 398 | C2×C3 | — | 2 | 6 | no | — |
| 399 | C2×C3 | — | 2 | 3 | no | — |
| 400 | C2×C3 | — | 4 | 12 | no | — |
| 401 | C2×C3 | — | 4 | 12 | no | — |
| 402 | C2×C3 | — | 4 | 3 | no | — |
| 403 | C2×C3 | — | 9 | 4 | no | — |
| 404 | C2×C3 | — | 18 | 6 | no | — |
| 405 | C2×C3 | — | 36 | 2 | no | — |
| 406 | C2×C3 | C2×D3×#67 | 1 | 6 | yes | — |
| 407 | C2×C3 | C2×#3811 | 1 | 3 | yes | — |
| 408 | D3 | — | 3 | 8 | no | — |
| 409 | D3 | — | 6 | 4 | no | — |
| 410 | D3 | — | 6 | 12 | no | — |
| 411 | D3 | — | 6 | 12 | no | — |
| 412 | D3 | — | 12 | 2 | no | — |
| 413 | D3 | — | 12 | 2 | no | — |
| 414 | D3 | — | 24 | 2 | no | — |
| 415 | C22 | — | 2 | 8 | no | — |
| 416 | C22 | — | 2 | 6 | no | — |
| 417 | C22 | — | 9 | 6 | no | — |
| 418 | C22 | — | 9 | 6 | no | — |
| 419 | C22 | — | 18 | 24 | no | — |
| 420 | C22 | — | 18 | 24 | no | — |
| 421 | C22 | — | 18 | 6 | no | — |
| 422 | C22 | — | 18 | 6 | no | — |
| 423 | C22 | — | 108 | 4 | no | — |
| 424 | C22 | #89049 | 1 | 6 | yes | complemented |
| 425 | C22 | C22×#1113 | 1 | 1 | yes | characteristic |
| 426 | C4 | — | 18 | 6 | no | — |
| 427 | C3 | — | 2 | 1 | no | — |
| 428 | C3 | — | 2 | 2 | no | — |
| 429 | C3 | — | 4 | 1 | no | — |
| 430 | C3 | D3×#953 | 1 | 2 | yes | complemented |
| 431 | C3 | #10595527 | 1 | 1 | yes | characteristic, complemented |
| 432 | C2 | — | 2 | 6 | no | — |
| 433 | C2 | — | 9 | 4 | no | — |
| 434 | C2 | — | 18 | 6 | no | — |
| 435 | C2 | — | 36 | 2 | no | — |
| 436 | C2 | C2×#89049 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#1113 |
| commutator, socle, cosocle | C22×C33 | C24 |
| Fitting | C24×C33 | C22 |
| hypercenter | C24 | #1113 |
| hypocenter | C33 | C2×#120 |
| LCS | G ▷ C22×C33 ▷ C33 | |
| UCS | C1 ◁ C22 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×C3×C3⋊D3 | C2 | semidirect |
| 2. C2×#89049 | C2 | semidirect |
| 3. C3×#64162 | C2 | semidirect |
| 4. #11723727 | C2 | semidirect |
| 5. #11723723 | C2 | semidirect |
| 8. C24×C33 | C22 | semidirect |
| 11. C23×C3×C3⋊D3 | C22 | semidirect |
| 12. C22×#1113 | C22 | semidirect |
| 13. C2×C3×#638 | C22 | semidirect |
| 15. C2×#6295 | C22 | semidirect |
| 16. C2×#6294 | C22 | semidirect |
| 17. C3×#3757 | C22 | semidirect |
| 18. #88814 | C22 | semidirect |
| 19. C24×C3⋊D3 | D3 | semidirect |
| 24. #64162 | D3 | semidirect |
| 39. C22×C3×C3⋊D3 | D4 | semidirect |
| 42. C22×C3×C3⋊D3 | C23 | semidirect |
| 45. C2×C3×C3⋊Dic3 | C23 | semidirect |
| 53. C24×C32 | C2×D3 | semidirect |
| 54. C24×C32 | C2×D3 | semidirect |
| 57. C23×C3⋊D3 | C2×D3 | semidirect |
| 66. C2×#638 | C2×D3 | semidirect |
| 77. #3757 | C2×D3 | semidirect |
| 85. C22×C33 | C2×D4 | semidirect |
| 92. C2×C3×C3⋊D3 | C2×D4 | semidirect |
| 123. C22×C3⋊D3 | #67 | semidirect |
| 126. C22×C3⋊D3 | C22×D3 | semidirect |
| 147. C2×C3⋊Dic3 | C22×D3 | semidirect |
| 164. C3×C3⋊D3 | #120 | semidirect |
| 171. C24×C3 | D32 | semidirect |
| 172. C24×C3 | D32 | semidirect |
| 214. C22×C32 | D3×D4 | semidirect |
| 215. C22×C32 | C2×#67 | semidirect |
| 223. C2×C3⋊D3 | C2×#67 | semidirect |
| 248. C33 | C2×#120 | semidirect |
| 311. C3⋊D3 | #953 | semidirect |
| 323. C24 | #1113 | semidirect |
| 352. C22×C3 | D3×#67 | semidirect |
| 353. C22×C3 | #3811 | semidirect |
| 378. C32 | D3×#120 | semidirect |
| 379. C32 | C2×#953 | semidirect |
| 424. C22 | #89049 | semidirect |
| 430. C3 | D3×#953 | semidirect |
| 431. C3 | #10595527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×C3⋊D3 | 2 |
| C2×#89049 | 2 |
| C3×#64162 | 2 |
| #11723727 | 2 |
| #11723723 | 2 |
| #10595527 | 3 |
| D3×#953 | 3 |