Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3019 conjugacy classes of subgroups.
The subgroup lattice has 610 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#64162 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×C3×#953 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×#63979 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10595505 | C2 | 1 | 16 | yes | maximal, direct product factor |
| 5 | C2×#63975 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#63971 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C2×#63970 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C2×#63969 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C2×#63958 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×#63956 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C2×#5595 | — | 3 | 2 | no | maximal |
| 12 | C25×C32 | C22 | 1 | 1 | yes | characteristic |
| 13 | C22×#638 | C22 | 1 | 2 | yes | — |
| 14 | C22×#638 | C22 | 1 | 1 | yes | characteristic |
| 15 | C22×C3×#67 | C22 | 1 | 2 | yes | — |
| 16 | C22×C3×#67 | C22 | 1 | 2 | yes | — |
| 17 | C22×C3×#67 | C22 | 1 | 2 | yes | — |
| 18 | C22×#626 | C22 | 1 | 2 | yes | complemented |
| 19 | C22×#625 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C22×#624 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C22×D3×Dic3 | C22 | 1 | 2 | yes | complemented |
| 22 | #64162 | C22 | 1 | 8 | yes | complemented |
| 23 | C2×#3757 | C22 | 1 | 2 | yes | — |
| 24 | C2×#3757 | C22 | 1 | 1 | yes | characteristic |
| 25 | C3×#953 | C22 | 1 | 16 | yes | complemented |
| 26 | C2×C3×#217 | C22 | 1 | 2 | yes | — |
| 27 | C2×C3×#217 | C22 | 1 | 2 | yes | — |
| 28 | C2×C3×#217 | C22 | 1 | 2 | yes | — |
| 29 | #63979 | C22 | 1 | 8 | yes | complemented |
| 30 | #63975 | C22 | 1 | 8 | yes | complemented |
| 31 | #63971 | C22 | 1 | 16 | yes | complemented |
| 32 | #63970 | C22 | 1 | 16 | yes | complemented |
| 33 | #63969 | C22 | 1 | 16 | yes | complemented |
| 34 | C2×#3724 | C22 | 1 | 2 | yes | complemented |
| 35 | C2×Dic3⋊Dic3 | C22 | 1 | 2 | yes | complemented |
| 36 | C2×Dic3⋊Dic3 | C22 | 1 | 2 | yes | complemented |
| 37 | C2×#3722 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C2×(C2×D3)⋊Dic3 | C22 | 1 | 2 | yes | complemented |
| 39 | #63958 | C22 | 1 | 16 | yes | complemented |
| 40 | #63956 | C22 | 1 | 16 | yes | complemented |
| 41 | C2×Dic32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | C2×C3×#120 | — | 3 | 2 | no | — |
| 43 | C2×#953 | — | 3 | 2 | no | — |
| 44 | C2×#953 | — | 6 | 1 | no | — |
| 45 | C2×#953 | D3 | 1 | 2 | yes | complemented |
| 46 | C2×#940 | — | 3 | 2 | no | — |
| 47 | C2×#939 | — | 3 | 2 | no | — |
| 48 | C2×#939 | — | 3 | 2 | no | — |
| 49 | C2×#938 | — | 3 | 2 | no | — |
| 50 | C2×#938 | — | 3 | 2 | no | — |
| 51 | C2×#935 | — | 3 | 2 | no | — |
| 52 | #5595 | — | 3 | 32 | no | — |
| 53 | C2×#884 | — | 3 | 2 | no | — |
| 54 | C2×#884 | — | 3 | 2 | no | — |
| 55 | C2×#883 | — | 3 | 2 | no | — |
| 56 | C2×#883 | — | 3 | 2 | no | — |
| 57 | C2×#879 | — | 3 | 2 | no | — |
| 58 | C2×#879 | — | 3 | 2 | no | — |
| 59 | C24×C32 | — | 4 | 4 | no | — |
| 60 | C24×C32 | — | 4 | 2 | no | — |
| 61 | C24×C32 | C23 | 1 | 2 | yes | — |
| 62 | C24×C32 | C23 | 1 | 1 | yes | characteristic |
| 63 | C24×C32 | C23 | 1 | 4 | yes | — |
| 64 | C23×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 65 | C23×C3×D3 | C23 | 1 | 2 | yes | — |
| 66 | C2×#638 | — | 4 | 4 | no | — |
| 67 | C2×#638 | — | 4 | 2 | no | — |
| 68 | C2×#638 | C23 | 1 | 8 | yes | — |
| 69 | C2×#638 | C23 | 1 | 4 | yes | — |
| 70 | C22×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 71 | C22×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 72 | C2×C3×#67 | — | 4 | 4 | no | — |
| 73 | C2×C3×#67 | — | 4 | 4 | no | — |
| 74 | C2×C3×#67 | — | 4 | 4 | no | — |
| 75 | C2×C3×#67 | C23 | 1 | 8 | yes | — |
| 76 | C2×C3×#67 | C23 | 1 | 8 | yes | — |
| 77 | C2×C3×#67 | C23 | 1 | 8 | yes | — |
| 78 | C22×C3×Dic3 | C23 | 1 | 2 | yes | — |
| 79 | C22×C3×Dic3 | C23 | 1 | 2 | yes | — |
| 80 | C22×C3×Dic3 | C23 | 1 | 2 | yes | — |
| 81 | C2×#626 | — | 4 | 4 | no | — |
| 82 | C2×#626 | C23 | 1 | 8 | yes | complemented |
| 83 | C2×#625 | — | 4 | 2 | no | — |
| 84 | C2×#625 | C23 | 1 | 4 | yes | complemented |
| 85 | C2×#624 | — | 4 | 2 | no | — |
| 86 | C2×#624 | C23 | 1 | 4 | yes | complemented |
| 87 | C2×D3×Dic3 | — | 4 | 4 | no | — |
| 88 | C2×D3×Dic3 | C23 | 1 | 8 | yes | complemented |
| 89 | #3757 | C23 | 1 | 8 | yes | — |
| 90 | #3757 | C23 | 1 | 4 | yes | — |
| 91 | C3×#217 | C23 | 1 | 8 | yes | — |
| 92 | C3×#217 | C23 | 1 | 8 | yes | — |
| 93 | C3×#217 | C23 | 1 | 8 | yes | — |
| 94 | #3724 | C23 | 1 | 8 | yes | complemented |
| 95 | Dic3⋊Dic3 | C23 | 1 | 8 | yes | complemented |
| 96 | Dic3⋊Dic3 | C23 | 1 | 8 | yes | complemented |
| 97 | #3722 | C23 | 1 | 4 | yes | complemented |
| 98 | (C2×D3)⋊Dic3 | C23 | 1 | 8 | yes | complemented |
| 99 | Dic32 | C23 | 1 | 4 | yes | complemented |
| 100 | C2×#560 | — | 9 | 1 | no | Sylow |
| 101 | C25×C3 | — | 2 | 1 | no | — |
| 102 | C25×C3 | C2×D3 | 1 | 2 | yes | — |
| 103 | C22×C3×D4 | — | 3 | 2 | no | — |
| 104 | C22×C3×D4 | — | 3 | 2 | no | — |
| 105 | C22×C3×D4 | — | 3 | 2 | no | — |
| 106 | C22×#67 | — | 3 | 2 | no | — |
| 107 | C22×#67 | — | 3 | 2 | no | — |
| 108 | C22×#67 | — | 3 | 2 | no | — |
| 109 | C22×#67 | — | 3 | 2 | no | — |
| 110 | C22×#67 | — | 3 | 2 | no | — |
| 111 | C22×#67 | — | 6 | 2 | no | — |
| 112 | C22×#67 | — | 6 | 1 | no | — |
| 113 | C22×#67 | C2×D3 | 1 | 2 | yes | — |
| 114 | C22×#67 | C2×D3 | 1 | 2 | yes | — |
| 115 | C22×#67 | C2×D3 | 1 | 2 | yes | — |
| 116 | C23×Dic3 | — | 3 | 2 | no | — |
| 117 | C22×D12 | — | 3 | 2 | no | — |
| 118 | C22×C4×D3 | — | 3 | 2 | no | — |
| 119 | C22×C4×D3 | — | 3 | 2 | no | — |
| 120 | C3×#120 | — | 3 | 16 | no | — |
| 121 | C2×C3×C22⋊C4 | — | 3 | 2 | no | — |
| 122 | C2×C3×C22⋊C4 | — | 3 | 2 | no | — |
| 123 | C2×C3×C22⋊C4 | — | 3 | 2 | no | — |
| 124 | #953 | — | 3 | 16 | no | — |
| 125 | #953 | — | 6 | 8 | no | — |
| 126 | #953 | C2×D3 | 1 | 16 | yes | complemented |
| 127 | C2×#217 | — | 3 | 2 | no | — |
| 128 | C2×#217 | — | 3 | 2 | no | — |
| 129 | C2×#217 | — | 3 | 2 | no | — |
| 130 | C2×#217 | — | 3 | 2 | no | — |
| 131 | C2×#217 | — | 6 | 2 | no | — |
| 132 | C2×#217 | — | 6 | 1 | no | — |
| 133 | C2×#217 | C2×D3 | 1 | 2 | yes | — |
| 134 | C2×#217 | C2×D3 | 1 | 2 | yes | — |
| 135 | C2×#217 | C2×D3 | 1 | 2 | yes | — |
| 136 | #940 | — | 3 | 16 | no | — |
| 137 | #939 | — | 3 | 16 | no | — |
| 138 | #939 | — | 3 | 16 | no | — |
| 139 | #938 | — | 3 | 16 | no | — |
| 140 | #938 | — | 3 | 16 | no | — |
| 141 | #935 | — | 3 | 16 | no | — |
| 142 | C2×(C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 143 | C2×(C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 144 | C2×C4⋊Dic3 | — | 3 | 2 | no | — |
| 145 | C2×C4⋊Dic3 | — | 3 | 2 | no | — |
| 146 | C2×Dic3⋊C4 | — | 3 | 2 | no | — |
| 147 | C2×Dic3⋊C4 | — | 3 | 2 | no | — |
| 148 | C2×Dic3⋊C4 | — | 3 | 2 | no | — |
| 149 | C2×Dic3⋊C4 | — | 3 | 2 | no | — |
| 150 | C2×C4×Dic3 | — | 3 | 2 | no | — |
| 151 | #884 | — | 3 | 16 | no | — |
| 152 | #884 | — | 3 | 16 | no | — |
| 153 | #883 | — | 3 | 16 | no | — |
| 154 | #883 | — | 3 | 16 | no | — |
| 155 | #879 | — | 3 | 16 | no | — |
| 156 | #879 | — | 3 | 16 | no | — |
| 157 | C23×C32 | — | 2 | 4 | no | — |
| 158 | C23×C32 | — | 2 | 2 | no | — |
| 159 | C23×C32 | — | 2 | 4 | no | — |
| 160 | C23×C32 | — | 2 | 4 | no | — |
| 161 | C23×C32 | — | 2 | 4 | no | — |
| 162 | C23×C32 | — | 4 | 8 | no | — |
| 163 | C23×C32 | — | 4 | 4 | no | — |
| 164 | C23×C32 | — | 4 | 16 | no | — |
| 165 | C23×C32 | C24 | 1 | 4 | yes | — |
| 166 | C23×C32 | C24 | 1 | 2 | yes | — |
| 167 | C23×C32 | C24 | 1 | 1 | yes | characteristic |
| 168 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 169 | C22×C3⋊D3 | — | 2 | 4 | no | — |
| 170 | C22×C3⋊D3 | C24 | 1 | 2 | yes | — |
| 171 | C22×C3×D3 | — | 2 | 4 | no | — |
| 172 | C22×C3×D3 | — | 2 | 4 | no | — |
| 173 | C22×C3×D3 | — | 2 | 4 | no | — |
| 174 | C22×C3×D3 | C24 | 1 | 4 | yes | — |
| 175 | #638 | — | 4 | 8 | no | — |
| 176 | #638 | — | 4 | 4 | no | — |
| 177 | C2×C3⋊Dic3 | — | 2 | 4 | no | — |
| 178 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 179 | C2×C3⋊Dic3 | C24 | 1 | 2 | yes | — |
| 180 | C2×C3⋊Dic3 | C24 | 1 | 4 | yes | — |
| 181 | C3×#67 | — | 4 | 8 | no | — |
| 182 | C3×#67 | — | 4 | 8 | no | — |
| 183 | C3×#67 | — | 4 | 8 | no | — |
| 184 | C2×C3×Dic3 | — | 2 | 4 | no | — |
| 185 | C2×C3×Dic3 | — | 2 | 4 | no | — |
| 186 | C2×C3×Dic3 | — | 2 | 4 | no | — |
| 187 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 188 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 189 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 190 | #626 | — | 4 | 8 | no | — |
| 191 | #625 | — | 4 | 4 | no | — |
| 192 | #624 | — | 4 | 4 | no | — |
| 193 | D3×Dic3 | — | 4 | 8 | no | — |
| 194 | #560 | — | 9 | 16 | no | — |
| 195 | C2×#127 | — | 9 | 1 | no | — |
| 196 | C2×#126 | — | 9 | 2 | no | — |
| 197 | C2×#123 | — | 9 | 1 | no | — |
| 198 | C2×#123 | — | 9 | 2 | no | — |
| 199 | C2×#121 | — | 9 | 2 | no | — |
| 200 | C2×#121 | — | 9 | 2 | no | — |
| 201 | C2×#121 | — | 9 | 2 | no | — |
| 202 | C2×#120 | — | 3 | 2 | no | — |
| 203 | C2×#120 | — | 9 | 1 | no | — |
| 204 | C24×C3 | — | 2 | 2 | no | — |
| 205 | C24×C3 | — | 2 | 1 | no | — |
| 206 | C24×C3 | — | 2 | 4 | no | — |
| 207 | C24×C3 | — | 3 | 2 | no | — |
| 208 | C24×C3 | — | 4 | 4 | no | — |
| 209 | C24×C3 | — | 4 | 4 | no | — |
| 210 | C24×C3 | — | 4 | 4 | no | — |
| 211 | C24×C3 | — | 4 | 4 | no | — |
| 212 | C24×C3 | — | 4 | 8 | no | — |
| 213 | C24×C3 | C22×D3 | 1 | 2 | yes | — |
| 214 | C24×C3 | C22×D3 | 1 | 2 | yes | — |
| 215 | C24×C3 | C22×D3 | 1 | 2 | yes | — |
| 216 | C24×C3 | C22×D3 | 1 | 8 | yes | — |
| 217 | C23×D3 | — | 3 | 2 | no | — |
| 218 | C23×D3 | — | 6 | 1 | no | — |
| 219 | C23×D3 | C22×D3 | 1 | 2 | yes | — |
| 220 | C2×C3×D4 | — | 3 | 8 | no | — |
| 221 | C2×C3×D4 | — | 3 | 8 | no | — |
| 222 | C2×C3×D4 | — | 3 | 8 | no | — |
| 223 | C2×C3×D4 | — | 12 | 4 | no | — |
| 224 | C2×C3×D4 | — | 12 | 4 | no | — |
| 225 | C2×C3×D4 | — | 12 | 4 | no | — |
| 226 | C22×C3×C4 | — | 3 | 2 | no | — |
| 227 | C22×C3×C4 | — | 3 | 2 | no | — |
| 228 | C22×C3×C4 | — | 3 | 2 | no | — |
| 229 | C2×#67 | — | 3 | 8 | no | — |
| 230 | C2×#67 | — | 3 | 8 | no | — |
| 231 | C2×#67 | — | 3 | 8 | no | — |
| 232 | C2×#67 | — | 3 | 8 | no | — |
| 233 | C2×#67 | — | 3 | 8 | no | — |
| 234 | C2×#67 | — | 4 | 4 | no | — |
| 235 | C2×#67 | — | 4 | 4 | no | — |
| 236 | C2×#67 | — | 4 | 4 | no | — |
| 237 | C2×#67 | — | 6 | 8 | no | — |
| 238 | C2×#67 | — | 6 | 4 | no | — |
| 239 | C2×#67 | — | 12 | 4 | no | — |
| 240 | C2×#67 | — | 12 | 4 | no | — |
| 241 | C2×#67 | — | 12 | 4 | no | — |
| 242 | C2×#67 | — | 12 | 4 | no | — |
| 243 | C2×#67 | — | 12 | 4 | no | — |
| 244 | C2×#67 | — | 12 | 8 | no | — |
| 245 | C2×#67 | — | 12 | 4 | no | — |
| 246 | C2×#67 | C22×D3 | 1 | 8 | yes | — |
| 247 | C2×#67 | C22×D3 | 1 | 8 | yes | — |
| 248 | C2×#67 | C22×D3 | 1 | 8 | yes | — |
| 249 | C22×Dic3 | — | 3 | 2 | no | — |
| 250 | C22×Dic3 | — | 3 | 2 | no | — |
| 251 | C22×Dic3 | — | 3 | 2 | no | — |
| 252 | C22×Dic3 | — | 3 | 8 | no | — |
| 253 | C22×Dic3 | — | 6 | 1 | no | — |
| 254 | C22×Dic3 | — | 6 | 2 | no | — |
| 255 | C22×Dic3 | — | 12 | 4 | no | — |
| 256 | C22×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 257 | C22×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 258 | C22×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 259 | C2×D12 | — | 3 | 8 | no | — |
| 260 | C2×D12 | — | 12 | 4 | no | — |
| 261 | C2×C4×D3 | — | 3 | 8 | no | — |
| 262 | C2×C4×D3 | — | 3 | 8 | no | — |
| 263 | C2×C4×D3 | — | 12 | 4 | no | — |
| 264 | C2×C4×D3 | — | 12 | 4 | no | — |
| 265 | C3×C22⋊C4 | — | 3 | 8 | no | — |
| 266 | C3×C22⋊C4 | — | 3 | 8 | no | — |
| 267 | C3×C22⋊C4 | — | 3 | 8 | no | — |
| 268 | #217 | — | 3 | 8 | no | — |
| 269 | #217 | — | 3 | 8 | no | — |
| 270 | #217 | — | 3 | 8 | no | — |
| 271 | #217 | — | 3 | 8 | no | — |
| 272 | #217 | — | 6 | 8 | no | — |
| 273 | #217 | — | 6 | 4 | no | — |
| 274 | #217 | C22×D3 | 1 | 8 | yes | — |
| 275 | #217 | C22×D3 | 1 | 8 | yes | — |
| 276 | #217 | C22×D3 | 1 | 8 | yes | — |
| 277 | (C2×D3)⋊C4 | — | 3 | 8 | no | — |
| 278 | (C2×D3)⋊C4 | — | 3 | 8 | no | — |
| 279 | C4⋊Dic3 | — | 3 | 8 | no | — |
| 280 | C4⋊Dic3 | — | 3 | 8 | no | — |
| 281 | Dic3⋊C4 | — | 3 | 8 | no | — |
| 282 | Dic3⋊C4 | — | 3 | 8 | no | — |
| 283 | Dic3⋊C4 | — | 3 | 8 | no | — |
| 284 | Dic3⋊C4 | — | 3 | 8 | no | — |
| 285 | C4×Dic3 | — | 3 | 8 | no | — |
| 286 | C22×C32 | — | 2 | 4 | no | — |
| 287 | C22×C32 | — | 2 | 2 | no | — |
| 288 | C22×C32 | — | 2 | 4 | no | — |
| 289 | C22×C32 | — | 2 | 4 | no | — |
| 290 | C22×C32 | — | 2 | 4 | no | — |
| 291 | C22×C32 | — | 4 | 16 | no | — |
| 292 | C22×C32 | — | 4 | 8 | no | — |
| 293 | C22×C32 | — | 4 | 4 | no | — |
| 294 | C22×C32 | H(5,𝔽2) | 1 | 4 | yes | — |
| 295 | C22×C32 | H(5,𝔽2) | 1 | 2 | yes | — |
| 296 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 297 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 298 | C2×C3⋊D3 | — | 2 | 4 | no | — |
| 299 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 300 | C2×C3×D3 | — | 2 | 4 | no | — |
| 301 | C2×C3×D3 | — | 2 | 4 | no | — |
| 302 | C2×C3×D3 | — | 2 | 4 | no | — |
| 303 | C2×C3×D3 | — | 4 | 8 | no | — |
| 304 | C3⋊Dic3 | — | 2 | 4 | no | — |
| 305 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 306 | C3×Dic3 | — | 2 | 4 | no | — |
| 307 | C3×Dic3 | — | 2 | 4 | no | — |
| 308 | C3×Dic3 | — | 2 | 4 | no | — |
| 309 | C25 | D32 | 1 | 1 | yes | characteristic |
| 310 | C22×D4 | — | 3 | 2 | no | — |
| 311 | C22×D4 | — | 3 | 2 | no | — |
| 312 | C22×D4 | — | 3 | 2 | no | — |
| 313 | C22×D4 | — | 9 | 2 | no | — |
| 314 | C22×D4 | — | 9 | 1 | no | — |
| 315 | C22×D4 | — | 9 | 2 | no | — |
| 316 | C22×D4 | — | 9 | 1 | no | — |
| 317 | C23×C4 | — | 9 | 1 | no | — |
| 318 | C23×C4 | — | 9 | 2 | no | — |
| 319 | #127 | — | 9 | 8 | no | — |
| 320 | #126 | — | 9 | 16 | no | — |
| 321 | #123 | — | 9 | 8 | no | — |
| 322 | #123 | — | 9 | 16 | no | — |
| 323 | #121 | — | 9 | 16 | no | — |
| 324 | #121 | — | 9 | 16 | no | — |
| 325 | #121 | — | 9 | 16 | no | — |
| 326 | #120 | — | 3 | 16 | no | — |
| 327 | #120 | — | 9 | 8 | no | — |
| 328 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 329 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 330 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 331 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 332 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 333 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 334 | C2×C22⋊C4 | — | 9 | 1 | no | — |
| 335 | C2×C22⋊C4 | — | 9 | 2 | no | — |
| 336 | C2×C22⋊C4 | — | 9 | 2 | no | — |
| 337 | C2×C22⋊C4 | — | 9 | 1 | no | — |
| 338 | C2×C42 | — | 9 | 1 | no | — |
| 339 | C23×C3 | — | 2 | 4 | no | — |
| 340 | C23×C3 | — | 2 | 8 | no | — |
| 341 | C23×C3 | — | 2 | 4 | no | — |
| 342 | C23×C3 | — | 2 | 4 | no | — |
| 343 | C23×C3 | — | 2 | 4 | no | — |
| 344 | C23×C3 | — | 2 | 4 | no | — |
| 345 | C23×C3 | — | 2 | 4 | no | — |
| 346 | C23×C3 | — | 2 | 4 | no | — |
| 347 | C23×C3 | — | 2 | 4 | no | — |
| 348 | C23×C3 | — | 2 | 4 | no | — |
| 349 | C23×C3 | — | 2 | 4 | no | — |
| 350 | C23×C3 | — | 2 | 4 | no | — |
| 351 | C23×C3 | — | 2 | 2 | no | — |
| 352 | C23×C3 | — | 2 | 1 | no | — |
| 353 | C23×C3 | — | 3 | 4 | no | — |
| 354 | C23×C3 | — | 4 | 4 | no | — |
| 355 | C23×C3 | — | 4 | 4 | no | — |
| 356 | C23×C3 | — | 4 | 4 | no | — |
| 357 | C23×C3 | — | 4 | 8 | no | — |
| 358 | C23×C3 | — | 4 | 8 | no | — |
| 359 | C23×C3 | — | 4 | 8 | no | — |
| 360 | C23×C3 | — | 4 | 8 | no | — |
| 361 | C23×C3 | — | 4 | 16 | no | — |
| 362 | C23×C3 | — | 4 | 32 | no | — |
| 363 | C23×C3 | — | 4 | 32 | no | — |
| 364 | C23×C3 | — | 6 | 4 | no | — |
| 365 | C23×C3 | — | 6 | 4 | no | — |
| 366 | C23×C3 | — | 6 | 4 | no | — |
| 367 | C23×C3 | C23×D3 | 1 | 4 | yes | — |
| 368 | C23×C3 | C23×D3 | 1 | 4 | yes | — |
| 369 | C23×C3 | C23×D3 | 1 | 4 | yes | — |
| 370 | C23×C3 | C23×D3 | 1 | 2 | yes | — |
| 371 | C22×D3 | — | 2 | 4 | no | — |
| 372 | C22×D3 | — | 2 | 4 | no | — |
| 373 | C22×D3 | — | 2 | 4 | no | — |
| 374 | C22×D3 | — | 3 | 4 | no | — |
| 375 | C22×D3 | — | 6 | 2 | no | — |
| 376 | C22×D3 | — | 6 | 4 | no | — |
| 377 | C22×D3 | — | 6 | 4 | no | — |
| 378 | C22×D3 | — | 6 | 4 | no | — |
| 379 | C22×D3 | — | 12 | 2 | no | — |
| 380 | C22×D3 | — | 12 | 4 | no | — |
| 381 | C22×D3 | C23×D3 | 1 | 4 | yes | — |
| 382 | C3×D4 | — | 12 | 8 | no | — |
| 383 | C3×D4 | — | 12 | 8 | no | — |
| 384 | C3×D4 | — | 12 | 8 | no | — |
| 385 | C2×C3×C4 | — | 3 | 4 | no | — |
| 386 | C2×C3×C4 | — | 3 | 4 | no | — |
| 387 | C2×C3×C4 | — | 3 | 4 | no | — |
| 388 | C2×C3×C4 | — | 6 | 4 | no | — |
| 389 | C2×C3×C4 | — | 6 | 4 | no | — |
| 390 | C2×C3×C4 | — | 6 | 4 | no | — |
| 391 | #67 | — | 4 | 8 | no | — |
| 392 | #67 | — | 4 | 8 | no | — |
| 393 | #67 | — | 4 | 8 | no | — |
| 394 | #67 | — | 12 | 8 | no | — |
| 395 | #67 | — | 12 | 8 | no | — |
| 396 | #67 | — | 12 | 8 | no | — |
| 397 | #67 | — | 12 | 8 | no | — |
| 398 | #67 | — | 12 | 8 | no | — |
| 399 | #67 | — | 12 | 16 | no | — |
| 400 | #67 | — | 12 | 8 | no | — |
| 401 | C2×Dic3 | — | 2 | 4 | no | — |
| 402 | C2×Dic3 | — | 2 | 4 | no | — |
| 403 | C2×Dic3 | — | 2 | 4 | no | — |
| 404 | C2×Dic3 | — | 3 | 4 | no | — |
| 405 | C2×Dic3 | — | 3 | 4 | no | — |
| 406 | C2×Dic3 | — | 3 | 4 | no | — |
| 407 | C2×Dic3 | — | 6 | 2 | no | — |
| 408 | C2×Dic3 | — | 6 | 4 | no | — |
| 409 | C2×Dic3 | — | 6 | 4 | no | — |
| 410 | C2×Dic3 | — | 6 | 4 | no | — |
| 411 | C2×Dic3 | — | 6 | 4 | no | — |
| 412 | C2×Dic3 | — | 12 | 4 | no | — |
| 413 | C2×Dic3 | — | 12 | 2 | no | — |
| 414 | C2×Dic3 | — | 12 | 8 | no | — |
| 415 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 416 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 417 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 418 | D12 | — | 12 | 8 | no | — |
| 419 | C4×D3 | — | 12 | 8 | no | — |
| 420 | C4×D3 | — | 12 | 8 | no | — |
| 421 | C2×C32 | — | 4 | 4 | no | — |
| 422 | C2×C32 | — | 4 | 2 | no | — |
| 423 | C2×C32 | #560 | 1 | 4 | yes | complemented |
| 424 | C2×C32 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 425 | C2×C32 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 426 | C3⋊D3 | — | 4 | 2 | no | — |
| 427 | C3×D3 | — | 4 | 4 | no | — |
| 428 | C24 | — | 3 | 2 | no | — |
| 429 | C24 | — | 4 | 2 | no | — |
| 430 | C24 | — | 4 | 4 | no | — |
| 431 | C24 | — | 9 | 1 | no | — |
| 432 | C24 | C2×D32 | 1 | 2 | yes | — |
| 433 | C24 | C2×D32 | 1 | 1 | yes | characteristic |
| 434 | C24 | C2×D32 | 1 | 4 | yes | — |
| 435 | C2×D4 | — | 3 | 8 | no | — |
| 436 | C2×D4 | — | 3 | 8 | no | — |
| 437 | C2×D4 | — | 3 | 8 | no | — |
| 438 | C2×D4 | — | 9 | 8 | no | — |
| 439 | C2×D4 | — | 9 | 4 | no | — |
| 440 | C2×D4 | — | 9 | 8 | no | — |
| 441 | C2×D4 | — | 9 | 4 | no | — |
| 442 | C2×D4 | — | 12 | 4 | no | — |
| 443 | C2×D4 | — | 12 | 4 | no | — |
| 444 | C2×D4 | — | 12 | 4 | no | — |
| 445 | C2×D4 | — | 36 | 4 | no | — |
| 446 | C2×D4 | — | 36 | 4 | no | — |
| 447 | C2×D4 | — | 36 | 2 | no | — |
| 448 | C2×D4 | — | 36 | 2 | no | — |
| 449 | C22×C4 | — | 3 | 2 | no | — |
| 450 | C22×C4 | — | 3 | 2 | no | — |
| 451 | C22×C4 | — | 3 | 2 | no | — |
| 452 | C22×C4 | — | 9 | 4 | no | — |
| 453 | C22×C4 | — | 9 | 8 | no | — |
| 454 | C22×C4 | — | 9 | 1 | no | — |
| 455 | C22×C4 | — | 9 | 2 | no | — |
| 456 | C22×C4 | — | 36 | 2 | no | — |
| 457 | C22×C4 | — | 36 | 4 | no | — |
| 458 | C4⋊C4 | — | 9 | 8 | no | — |
| 459 | C4⋊C4 | — | 9 | 8 | no | — |
| 460 | C4⋊C4 | — | 9 | 8 | no | — |
| 461 | C22⋊C4 | — | 3 | 8 | no | — |
| 462 | C22⋊C4 | — | 3 | 8 | no | — |
| 463 | C22⋊C4 | — | 3 | 8 | no | — |
| 464 | C22⋊C4 | — | 9 | 4 | no | — |
| 465 | C22⋊C4 | — | 9 | 8 | no | — |
| 466 | C22⋊C4 | — | 9 | 8 | no | — |
| 467 | C22⋊C4 | — | 9 | 4 | no | — |
| 468 | C42 | — | 9 | 4 | no | — |
| 469 | C22×C3 | — | 2 | 4 | no | — |
| 470 | C22×C3 | — | 2 | 8 | no | — |
| 471 | C22×C3 | — | 2 | 4 | no | — |
| 472 | C22×C3 | — | 2 | 4 | no | — |
| 473 | C22×C3 | — | 2 | 4 | no | — |
| 474 | C22×C3 | — | 2 | 4 | no | — |
| 475 | C22×C3 | — | 2 | 4 | no | — |
| 476 | C22×C3 | — | 2 | 4 | no | — |
| 477 | C22×C3 | — | 2 | 4 | no | — |
| 478 | C22×C3 | — | 2 | 4 | no | — |
| 479 | C22×C3 | — | 2 | 4 | no | — |
| 480 | C22×C3 | — | 2 | 2 | no | — |
| 481 | C22×C3 | — | 2 | 4 | no | — |
| 482 | C22×C3 | — | 2 | 1 | no | — |
| 483 | C22×C3 | — | 4 | 4 | no | — |
| 484 | C22×C3 | — | 4 | 4 | no | — |
| 485 | C22×C3 | — | 4 | 4 | no | — |
| 486 | C22×C3 | — | 4 | 16 | no | — |
| 487 | C22×C3 | — | 4 | 8 | no | — |
| 488 | C22×C3 | — | 4 | 32 | no | — |
| 489 | C22×C3 | — | 4 | 32 | no | — |
| 490 | C22×C3 | — | 4 | 8 | no | — |
| 491 | C22×C3 | — | 4 | 8 | no | — |
| 492 | C22×C3 | — | 4 | 8 | no | — |
| 493 | C22×C3 | — | 6 | 4 | no | — |
| 494 | C22×C3 | — | 6 | 4 | no | — |
| 495 | C22×C3 | — | 6 | 4 | no | — |
| 496 | C22×C3 | — | 12 | 8 | no | — |
| 497 | C22×C3 | #1004 | 1 | 4 | yes | — |
| 498 | C22×C3 | #1004 | 1 | 4 | yes | — |
| 499 | C22×C3 | #1004 | 1 | 4 | yes | — |
| 500 | C22×C3 | C24×D3 | 1 | 2 | yes | — |
| 501 | C2×D3 | — | 2 | 4 | no | — |
| 502 | C2×D3 | — | 2 | 4 | no | — |
| 503 | C2×D3 | — | 2 | 4 | no | — |
| 504 | C2×D3 | — | 4 | 8 | no | — |
| 505 | C2×D3 | — | 6 | 4 | no | — |
| 506 | C2×D3 | — | 6 | 4 | no | — |
| 507 | C2×D3 | — | 6 | 4 | no | — |
| 508 | C2×D3 | — | 12 | 2 | no | — |
| 509 | C2×D3 | — | 12 | 4 | no | — |
| 510 | C2×D3 | — | 12 | 8 | no | — |
| 511 | C2×D3 | — | 24 | 4 | no | — |
| 512 | C3×C4 | — | 6 | 4 | no | — |
| 513 | C3×C4 | — | 6 | 4 | no | — |
| 514 | C3×C4 | — | 6 | 4 | no | — |
| 515 | Dic3 | — | 2 | 4 | no | — |
| 516 | Dic3 | — | 2 | 4 | no | — |
| 517 | Dic3 | — | 2 | 4 | no | — |
| 518 | Dic3 | — | 6 | 4 | no | — |
| 519 | Dic3 | — | 6 | 4 | no | — |
| 520 | Dic3 | — | 6 | 4 | no | — |
| 521 | Dic3 | — | 12 | 4 | no | — |
| 522 | Dic3 | — | 12 | 2 | no | — |
| 523 | C32 | C2×#560 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 524 | C23 | — | 2 | 4 | no | — |
| 525 | C23 | — | 2 | 4 | no | — |
| 526 | C23 | — | 2 | 4 | no | — |
| 527 | C23 | — | 2 | 2 | no | — |
| 528 | C23 | — | 2 | 4 | no | — |
| 529 | C23 | — | 3 | 4 | no | — |
| 530 | C23 | — | 4 | 4 | no | — |
| 531 | C23 | — | 4 | 8 | no | — |
| 532 | C23 | — | 4 | 16 | no | — |
| 533 | C23 | — | 6 | 4 | no | — |
| 534 | C23 | — | 6 | 4 | no | — |
| 535 | C23 | — | 6 | 4 | no | — |
| 536 | C23 | — | 9 | 2 | no | — |
| 537 | C23 | — | 18 | 2 | no | — |
| 538 | C23 | — | 18 | 4 | no | — |
| 539 | C23 | C22×D32 | 1 | 4 | yes | — |
| 540 | C23 | C22×D32 | 1 | 2 | yes | — |
| 541 | C23 | C22×D32 | 1 | 1 | yes | characteristic |
| 542 | D4 | — | 12 | 8 | no | — |
| 543 | D4 | — | 12 | 8 | no | — |
| 544 | D4 | — | 12 | 8 | no | — |
| 545 | D4 | — | 36 | 8 | no | — |
| 546 | D4 | — | 36 | 8 | no | — |
| 547 | D4 | — | 36 | 4 | no | — |
| 548 | D4 | — | 36 | 4 | no | — |
| 549 | C2×C4 | — | 3 | 4 | no | — |
| 550 | C2×C4 | — | 3 | 4 | no | — |
| 551 | C2×C4 | — | 3 | 4 | no | — |
| 552 | C2×C4 | — | 6 | 4 | no | — |
| 553 | C2×C4 | — | 6 | 4 | no | — |
| 554 | C2×C4 | — | 6 | 4 | no | — |
| 555 | C2×C4 | — | 9 | 2 | no | — |
| 556 | C2×C4 | — | 9 | 4 | no | — |
| 557 | C2×C4 | — | 18 | 4 | no | — |
| 558 | C2×C4 | — | 18 | 2 | no | — |
| 559 | C2×C4 | — | 36 | 4 | no | — |
| 560 | C2×C4 | — | 36 | 8 | no | — |
| 561 | C2×C3 | — | 2 | 1 | no | — |
| 562 | C2×C3 | — | 2 | 2 | no | — |
| 563 | C2×C3 | — | 2 | 4 | no | — |
| 564 | C2×C3 | — | 4 | 8 | no | — |
| 565 | C2×C3 | — | 4 | 4 | no | — |
| 566 | C2×C3 | — | 4 | 4 | no | — |
| 567 | C2×C3 | — | 4 | 4 | no | — |
| 568 | C2×C3 | — | 4 | 4 | no | — |
| 569 | C2×C3 | — | 12 | 4 | no | — |
| 570 | C2×C3 | #5595 | 1 | 8 | yes | complemented |
| 571 | C2×C3 | C2×#1004 | 1 | 2 | yes | — |
| 572 | C2×C3 | C2×#1004 | 1 | 2 | yes | — |
| 573 | C2×C3 | C2×#1004 | 1 | 2 | yes | — |
| 574 | D3 | — | 4 | 4 | no | — |
| 575 | D3 | — | 12 | 4 | no | — |
| 576 | D3 | — | 24 | 2 | no | — |
| 577 | C22 | — | 2 | 4 | no | — |
| 578 | C22 | — | 2 | 4 | no | — |
| 579 | C22 | — | 2 | 4 | no | — |
| 580 | C22 | — | 2 | 2 | no | — |
| 581 | C22 | — | 2 | 4 | no | — |
| 582 | C22 | — | 4 | 16 | no | — |
| 583 | C22 | — | 4 | 8 | no | — |
| 584 | C22 | — | 4 | 4 | no | — |
| 585 | C22 | — | 6 | 4 | no | — |
| 586 | C22 | — | 6 | 4 | no | — |
| 587 | C22 | — | 6 | 4 | no | — |
| 588 | C22 | — | 12 | 8 | no | — |
| 589 | C22 | — | 18 | 2 | no | — |
| 590 | C22 | — | 18 | 4 | no | — |
| 591 | C22 | — | 36 | 4 | no | — |
| 592 | C22 | #64330 | 1 | 2 | yes | — |
| 593 | C22 | #64330 | 1 | 4 | yes | — |
| 594 | C22 | C23×D32 | 1 | 1 | yes | characteristic |
| 595 | C4 | — | 6 | 4 | no | — |
| 596 | C4 | — | 6 | 4 | no | — |
| 597 | C4 | — | 6 | 4 | no | — |
| 598 | C4 | — | 18 | 4 | no | — |
| 599 | C4 | — | 18 | 2 | no | — |
| 600 | C3 | — | 2 | 1 | no | — |
| 601 | C3 | C2×#5595 | 1 | 2 | yes | complemented |
| 602 | C2 | — | 4 | 4 | no | — |
| 603 | C2 | — | 4 | 2 | no | — |
| 604 | C2 | — | 12 | 4 | no | — |
| 605 | C2 | — | 36 | 2 | no | — |
| 606 | C2 | #10595505 | 1 | 4 | yes | direct product factor |
| 607 | C2 | C2×#64330 | 1 | 1 | yes | characteristic |
| 608 | C2 | C2×#64330 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D32 |
| commutator, cosocle | C22×C32 | C25 |
| Frattini | C22 | C23×D32 |
| Fitting | C25×C32 | C22 |
| socle | C23×C32 | C24 |
| hypercenter | C25 | D32 |
| hypocenter | C32 | C2×#560 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C25 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#64162 | C2 | semidirect |
| 2. C2×C3×#953 | C2 | semidirect |
| 3. C2×#63979 | C2 | semidirect |
| 4. #10595505 | C2 | direct (N × H) |
| 5. C2×#63975 | C2 | semidirect |
| 6. C2×#63971 | C2 | semidirect |
| 7. C2×#63970 | C2 | semidirect |
| 8. C2×#63969 | C2 | semidirect |
| 9. C2×#63958 | C2 | semidirect |
| 10. C2×#63956 | C2 | semidirect |
| 18. C22×#626 | C22 | semidirect |
| 19. C22×#625 | C22 | semidirect |
| 20. C22×#624 | C22 | semidirect |
| 21. C22×D3×Dic3 | C22 | semidirect |
| 22. #64162 | C22 | semidirect |
| 25. C3×#953 | C22 | semidirect |
| 29. #63979 | C22 | semidirect |
| 30. #63975 | C22 | semidirect |
| 31. #63971 | C22 | semidirect |
| 32. #63970 | C22 | semidirect |
| 33. #63969 | C22 | semidirect |
| 34. C2×#3724 | C22 | semidirect |
| 35. C2×Dic3⋊Dic3 | C22 | semidirect |
| 36. C2×Dic3⋊Dic3 | C22 | semidirect |
| 37. C2×#3722 | C22 | semidirect |
| 38. C2×(C2×D3)⋊Dic3 | C22 | semidirect |
| 39. #63958 | C22 | semidirect |
| 40. #63956 | C22 | semidirect |
| 41. C2×Dic32 | C22 | semidirect |
| 45. C2×#953 | D3 | semidirect |
| 82. C2×#626 | C23 | semidirect |
| 84. C2×#625 | C23 | semidirect |
| 86. C2×#624 | C23 | semidirect |
| 88. C2×D3×Dic3 | C23 | semidirect |
| 94. #3724 | C23 | semidirect |
| 95. Dic3⋊Dic3 | C23 | semidirect |
| 96. Dic3⋊Dic3 | C23 | semidirect |
| 97. #3722 | C23 | semidirect |
| 98. (C2×D3)⋊Dic3 | C23 | semidirect |
| 99. Dic32 | C23 | semidirect |
| 126. #953 | C2×D3 | semidirect |
| 423. C2×C32 | #560 | semidirect |
| 523. C32 | C2×#560 | semidirect |
| 570. C2×C3 | #5595 | semidirect |
| 601. C3 | C2×#5595 | semidirect |
| 606. C2 | #10595505 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64162 | 2 |
| C2×C3×#953 | 2 |
| C2×#63979 | 2 |
| #10595505 | 2 |
| C2×#63975 | 2 |
| C2×#63971 | 2 |
| C2×#63970 | 2 |
| C2×#63969 | 2 |
| C2×#63958 | 2 |
| C2×#63956 | 2 |
| C2×#5595 | 3 |