Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2034 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 2034 conjugacy classes of subgroups — too many to draw. Only its 189 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 | C3×A4×#41 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10596582 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | Q8×C3⋊S4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10596577 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | D4×C3⋊S4 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10596575 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×C4×C3⋊S4 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #41×S4 | — | 3 | 3 | no | maximal |
| 9 | #41×#67 | — | 3 | 1 | no | maximal |
| 10 | C22×C3⋊S4 | C22 | 1 | 3 | yes | — |
| 11 | #41×C3⋊D3 | — | 4 | 1 | no | maximal |
| 12 | C3×Q8×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C3×D4×A4 | C22 | 1 | 3 | yes | complemented |
| 14 | C2×C3×C4×A4 | C22 | 1 | 3 | yes | complemented |
| 15 | #64269 | C22 | 1 | 6 | yes | complemented |
| 16 | C2×C3⋊SL(2,ℤ/4) | C22 | 1 | 3 | yes | complemented |
| 17 | C4⋊(C3⋊S4) | C22 | 1 | 3 | yes | complemented |
| 18 | C4×C3⋊S4 | C22 | 1 | 1 | yes | characteristic |
| 19 | C4×C3⋊S4 | C22 | 1 | 3 | yes | — |
| 20 | C4×C3⋊S4 | C22 | 1 | 3 | yes | complemented |
| 21 | C4×C3⋊S4 | C22 | 1 | 3 | yes | complemented |
| 22 | #64259 | C22 | 1 | 3 | yes | complemented |
| 23 | C22×C3×#41 | D3 | 1 | 1 | yes | characteristic, complemented |
| 24 | C2×D3×#41 | — | 3 | 1 | no | — |
| 25 | A4×#41 | D3 | 1 | 3 | yes | complemented |
| 26 | #5919 | — | 3 | 3 | no | — |
| 27 | Q8×S4 | — | 3 | 3 | no | — |
| 28 | #5914 | — | 3 | 9 | no | — |
| 29 | D4×S4 | — | 3 | 9 | no | — |
| 30 | #5912 | — | 3 | 9 | no | — |
| 31 | C2×C4×S4 | — | 3 | 9 | no | — |
| 32 | #5834 | — | 3 | 1 | no | — |
| 33 | #5832 | — | 3 | 3 | no | — |
| 34 | #5831 | — | 3 | 1 | no | — |
| 35 | #5829 | — | 3 | 3 | no | — |
| 36 | #5828 | — | 3 | 3 | no | — |
| 37 | Dic3×#41 | — | 3 | 1 | no | — |
| 38 | #5824 | — | 3 | 3 | no | — |
| 39 | #5817 | — | 3 | 1 | no | — |
| 40 | Q8×#67 | — | 3 | 1 | no | — |
| 41 | #5806 | — | 3 | 3 | no | — |
| 42 | D4×#67 | — | 3 | 3 | no | — |
| 43 | #5791 | — | 3 | 3 | no | — |
| 44 | C2×C4×#67 | — | 3 | 3 | no | — |
| 45 | C22×C3×A4 | C23 | 1 | 3 | yes | — |
| 46 | C2×C3⋊S4 | — | 2 | 6 | no | — |
| 47 | C2×C3⋊S4 | C23 | 1 | 3 | yes | — |
| 48 | C2×C3⋊S4 | C23 | 1 | 1 | yes | characteristic |
| 49 | C32×#41 | — | 4 | 1 | no | — |
| 50 | #3832 | — | 4 | 1 | no | — |
| 51 | Q8×C3⋊D3 | — | 4 | 1 | no | — |
| 52 | #3830 | — | 4 | 3 | no | — |
| 53 | D4×C3⋊D3 | — | 4 | 3 | no | — |
| 54 | #3828 | — | 4 | 3 | no | — |
| 55 | C2×C4×C3⋊D3 | — | 4 | 3 | no | — |
| 56 | C3×C4×A4 | C23 | 1 | 3 | yes | — |
| 57 | C3×C4×A4 | C23 | 1 | 1 | yes | characteristic |
| 58 | C3⋊SL(2,ℤ/4) | C23 | 1 | 3 | yes | — |
| 59 | C3⋊SL(2,ℤ/4) | C23 | 1 | 1 | yes | characteristic |
| 60 | D4×#41 | — | 9 | 1 | no | Sylow |
| 61 | C22×S4 | — | 3 | 9 | no | — |
| 62 | C2×C3×#41 | — | 3 | 1 | no | — |
| 63 | C2×C3×#41 | — | 3 | 3 | no | — |
| 64 | C2×C3×#41 | — | 3 | 3 | no | — |
| 65 | C2×C3×#41 | — | 3 | 1 | no | — |
| 66 | C22×C3×Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 67 | C22×C3×D4 | C2×D3 | 1 | 3 | yes | complemented |
| 68 | C23×C3×C4 | C2×D3 | 1 | 3 | yes | complemented |
| 69 | C22×#67 | — | 3 | 3 | no | — |
| 70 | D3×#41 | — | 6 | 1 | no | — |
| 71 | D3×#41 | — | 6 | 3 | no | — |
| 72 | D3×#41 | — | 6 | 3 | no | — |
| 73 | D3×#41 | — | 6 | 1 | no | — |
| 74 | D3×#41 | — | 12 | 3 | no | — |
| 75 | C2×#239 | — | 3 | 1 | no | — |
| 76 | C2×D3×Q8 | — | 3 | 1 | no | — |
| 77 | C2×#237 | — | 3 | 3 | no | — |
| 78 | C2×D3×D4 | — | 3 | 3 | no | — |
| 79 | C2×#235 | — | 3 | 3 | no | — |
| 80 | C22×C4×D3 | — | 3 | 3 | no | — |
| 81 | Q8×A4 | C2×D3 | 1 | 3 | yes | complemented |
| 82 | D4×A4 | C2×D3 | 1 | 9 | yes | complemented |
| 83 | C2×C4×A4 | C2×D3 | 1 | 9 | yes | complemented |
| 84 | GL(2,ℤ/4) | — | 3 | 18 | no | — |
| 85 | C2×SL(2,ℤ/4) | — | 3 | 9 | no | — |
| 86 | C4⋊S4 | — | 3 | 9 | no | — |
| 87 | C4×S4 | — | 3 | 3 | no | — |
| 88 | C4×S4 | — | 3 | 9 | no | — |
| 89 | C4×S4 | — | 3 | 9 | no | — |
| 90 | C4×S4 | — | 3 | 9 | no | — |
| 91 | A4⋊Q8 | — | 3 | 9 | no | — |
| 92 | #953 | — | 3 | 6 | no | — |
| 93 | C2×#217 | — | 3 | 3 | no | — |
| 94 | #947 | — | 3 | 3 | no | — |
| 95 | #946 | — | 3 | 3 | no | — |
| 96 | #946 | — | 3 | 3 | no | — |
| 97 | Q8×Dic3 | — | 3 | 1 | no | — |
| 98 | Q8×Dic3 | — | 3 | 1 | no | — |
| 99 | #944 | — | 3 | 3 | no | — |
| 100 | #940 | — | 3 | 3 | no | — |
| 101 | #939 | — | 3 | 6 | no | — |
| 102 | #939 | — | 3 | 6 | no | — |
| 103 | #938 | — | 3 | 3 | no | — |
| 104 | #938 | — | 3 | 3 | no | — |
| 105 | #937 | — | 3 | 6 | no | — |
| 106 | #936 | — | 3 | 3 | no | — |
| 107 | #935 | — | 3 | 6 | no | — |
| 108 | D4×Dic3 | — | 3 | 3 | no | — |
| 109 | D4×Dic3 | — | 3 | 3 | no | — |
| 110 | #930 | — | 3 | 3 | no | — |
| 111 | #930 | — | 3 | 3 | no | — |
| 112 | #929 | — | 3 | 6 | no | — |
| 113 | C4×#67 | — | 3 | 3 | no | — |
| 114 | C4×#67 | — | 3 | 3 | no | — |
| 115 | C4×#67 | — | 3 | 3 | no | — |
| 116 | C4×#67 | — | 3 | 3 | no | — |
| 117 | C4×#67 | — | 3 | 6 | no | — |
| 118 | C4×#67 | — | 3 | 1 | no | — |
| 119 | C4×#67 | — | 3 | 3 | no | — |
| 120 | C4×#67 | — | 3 | 3 | no | — |
| 121 | C4×#67 | — | 3 | 3 | no | — |
| 122 | C2×(C2×D3)⋊C4 | — | 3 | 3 | no | — |
| 123 | #926 | — | 3 | 3 | no | — |
| 124 | #924 | — | 3 | 3 | no | — |
| 125 | #924 | — | 3 | 3 | no | — |
| 126 | C2×Dic3⋊C4 | — | 3 | 3 | no | — |
| 127 | C2×C4×Dic3 | — | 3 | 3 | no | — |
| 128 | C22×C3⋊D3 | — | 4 | 3 | no | — |
| 129 | C2×C3×A4 | — | 2 | 3 | no | — |
| 130 | C2×C3×A4 | C24 | 1 | 1 | yes | characteristic |
| 131 | C3⋊S4 | — | 2 | 3 | no | — |
| 132 | C3⋊S4 | #41 | 1 | 2 | yes | direct product factor |
| 133 | C32×Q8 | — | 4 | 1 | no | — |
| 134 | C32×D4 | — | 4 | 3 | no | — |
| 135 | C2×C32×C4 | — | 4 | 3 | no | — |
| 136 | #638 | — | 4 | 6 | no | — |
| 137 | C2×C3⋊Dic3 | — | 4 | 3 | no | — |
| 138 | C4⋊(C3⋊D3) | — | 4 | 3 | no | — |
| 139 | C4×C3⋊D3 | — | 4 | 1 | no | — |
| 140 | C4×C3⋊D3 | — | 4 | 3 | no | — |
| 141 | C4×C3⋊D3 | — | 4 | 3 | no | — |
| 142 | C4×C3⋊D3 | — | 4 | 3 | no | — |
| 143 | #634 | — | 4 | 3 | no | — |
| 144 | C22×#41 | — | 9 | 1 | no | — |
| 145 | C22×#41 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 146 | #550 | — | 9 | 1 | no | — |
| 147 | D4×Q8 | — | 9 | 1 | no | — |
| 148 | #548 | — | 9 | 1 | no | — |
| 149 | #548 | — | 9 | 1 | no | — |
| 150 | #547 | — | 9 | 3 | no | — |
| 151 | #546 | — | 9 | 3 | no | — |
| 152 | #546 | — | 9 | 3 | no | — |
| 153 | D42 | — | 9 | 3 | no | — |
| 154 | #532 | — | 9 | 3 | no | — |
| 155 | #525 | — | 9 | 3 | no | — |
| 156 | #525 | — | 9 | 3 | no | — |
| 157 | C4×#41 | — | 9 | 1 | no | — |
| 158 | C2×C4×D4 | — | 9 | 3 | no | — |
| 159 | C24×C3 | C22×D3 | 1 | 3 | yes | — |
| 160 | C23×D3 | — | 3 | 3 | no | — |
| 161 | C22×A4 | C22×D3 | 1 | 9 | yes | — |
| 162 | C2×S4 | — | 3 | 3 | no | — |
| 163 | C2×S4 | — | 3 | 9 | no | — |
| 164 | C2×S4 | — | 6 | 18 | no | — |
| 165 | C3×#41 | — | 3 | 1 | no | — |
| 166 | C3×#41 | — | 3 | 3 | no | — |
| 167 | C3×#41 | — | 3 | 3 | no | — |
| 168 | C3×#41 | — | 4 | 3 | no | — |
| 169 | C3×#41 | — | 6 | 1 | no | — |
| 170 | C3×#41 | — | 6 | 3 | no | — |
| 171 | C3×#41 | — | 6 | 3 | no | — |
| 172 | C3×#41 | S4 | 1 | 1 | yes | characteristic, complemented |
| 173 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 174 | C2×C3×Q8 | — | 3 | 3 | no | — |
| 175 | C2×C3×D4 | — | 3 | 3 | no | — |
| 176 | C2×C3×D4 | — | 3 | 6 | no | — |
| 177 | C2×C3×D4 | — | 3 | 3 | no | — |
| 178 | C22×C3×C4 | — | 3 | 3 | no | — |
| 179 | C22×C3×C4 | — | 3 | 3 | no | — |
| 180 | C22×C3×C4 | — | 3 | 3 | no | — |
| 181 | C22×C3×C4 | — | 3 | 3 | no | — |
| 182 | C22×C3×C4 | C22×D3 | 1 | 3 | yes | — |
| 183 | C22×C3×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 184 | C2×#67 | — | 3 | 1 | no | — |
| 185 | C2×#67 | — | 3 | 3 | no | — |
| 186 | C2×#67 | — | 3 | 3 | no | — |
| 187 | C2×#67 | — | 3 | 6 | no | — |
| 188 | C2×#67 | — | 3 | 3 | no | — |
| 189 | C2×#67 | — | 3 | 6 | no | — |
| 190 | C2×#67 | — | 6 | 6 | no | — |
| 191 | C2×#67 | — | 6 | 6 | no | — |
| 192 | C22×Dic3 | — | 3 | 3 | no | — |
| 193 | C22×Dic3 | — | 3 | 3 | no | — |
| 194 | C22×Dic3 | — | 3 | 3 | no | — |
| 195 | #239 | — | 6 | 3 | no | — |
| 196 | #239 | — | 6 | 1 | no | — |
| 197 | #239 | — | 12 | 3 | no | — |
| 198 | D3×Q8 | — | 6 | 3 | no | — |
| 199 | D3×Q8 | — | 6 | 1 | no | — |
| 200 | D3×Q8 | — | 12 | 3 | no | — |
| 201 | #237 | — | 6 | 6 | no | — |
| 202 | #237 | — | 6 | 3 | no | — |
| 203 | #237 | — | 6 | 3 | no | — |
| 204 | #237 | — | 12 | 9 | no | — |
| 205 | D3×D4 | — | 6 | 6 | no | — |
| 206 | D3×D4 | — | 6 | 3 | no | — |
| 207 | D3×D4 | — | 6 | 3 | no | — |
| 208 | D3×D4 | — | 12 | 9 | no | — |
| 209 | #235 | — | 6 | 3 | no | — |
| 210 | #235 | — | 6 | 3 | no | — |
| 211 | #235 | — | 6 | 3 | no | — |
| 212 | #235 | — | 6 | 3 | no | — |
| 213 | #235 | — | 12 | 9 | no | — |
| 214 | C2×D12 | — | 3 | 3 | no | — |
| 215 | C2×C4×D3 | — | 3 | 1 | no | — |
| 216 | C2×C4×D3 | — | 3 | 3 | no | — |
| 217 | C2×C4×D3 | — | 3 | 3 | no | — |
| 218 | C2×C4×D3 | — | 3 | 3 | no | — |
| 219 | C2×C4×D3 | — | 6 | 3 | no | — |
| 220 | C2×C4×D3 | — | 6 | 3 | no | — |
| 221 | C2×C4×D3 | — | 6 | 3 | no | — |
| 222 | C2×C4×D3 | — | 6 | 3 | no | — |
| 223 | C2×C4×D3 | — | 12 | 9 | no | — |
| 224 | C2×Dic6 | — | 3 | 3 | no | — |
| 225 | C4×A4 | C22×D3 | 1 | 9 | yes | — |
| 226 | C4×A4 | C22×D3 | 1 | 3 | yes | — |
| 227 | SL(2,ℤ/4) | — | 3 | 9 | no | — |
| 228 | SL(2,ℤ/4) | — | 3 | 3 | no | — |
| 229 | #217 | — | 3 | 6 | no | — |
| 230 | #217 | — | 3 | 6 | no | — |
| 231 | #217 | — | 3 | 3 | no | — |
| 232 | #217 | — | 3 | 3 | no | — |
| 233 | #217 | — | 3 | 3 | no | — |
| 234 | #217 | — | 3 | 1 | no | — |
| 235 | (C2×D3)⋊C4 | — | 3 | 1 | no | — |
| 236 | (C2×D3)⋊C4 | — | 3 | 3 | no | — |
| 237 | (C2×D3)⋊C4 | — | 3 | 3 | no | — |
| 238 | (C2×D3)⋊C4 | — | 3 | 3 | no | — |
| 239 | (C2×D3)⋊C4 | — | 3 | 6 | no | — |
| 240 | C4⋊Dic3 | — | 3 | 3 | no | — |
| 241 | C4⋊Dic3 | — | 3 | 3 | no | — |
| 242 | Dic3⋊C4 | — | 3 | 1 | no | — |
| 243 | Dic3⋊C4 | — | 3 | 3 | no | — |
| 244 | Dic3⋊C4 | — | 3 | 3 | no | — |
| 245 | Dic3⋊C4 | — | 3 | 3 | no | — |
| 246 | Dic3⋊C4 | — | 3 | 6 | no | — |
| 247 | C4×Dic3 | — | 3 | 1 | no | — |
| 248 | C4×Dic3 | — | 3 | 3 | no | — |
| 249 | C4×Dic3 | — | 3 | 3 | no | — |
| 250 | C4×Dic3 | — | 3 | 3 | no | — |
| 251 | C22×C32 | — | 4 | 3 | no | — |
| 252 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 253 | C2×C3⋊D3 | — | 4 | 3 | no | — |
| 254 | C2×C3⋊D3 | — | 8 | 6 | no | — |
| 255 | C3×A4 | C2×#41 | 1 | 1 | yes | characteristic, complemented |
| 256 | C32×C4 | — | 4 | 3 | no | — |
| 257 | C32×C4 | — | 4 | 1 | no | — |
| 258 | C3⋊Dic3 | — | 4 | 3 | no | — |
| 259 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 260 | C2×#41 | — | 3 | 1 | no | — |
| 261 | C2×#41 | — | 3 | 3 | no | — |
| 262 | C2×#41 | — | 3 | 3 | no | — |
| 263 | C2×#41 | — | 3 | 1 | no | — |
| 264 | C2×#41 | — | 9 | 3 | no | — |
| 265 | C2×#41 | — | 9 | 3 | no | — |
| 266 | C2×#41 | — | 9 | 1 | no | — |
| 267 | C2×#41 | — | 18 | 1 | no | — |
| 268 | C2×#41 | — | 18 | 3 | no | — |
| 269 | C2×#41 | — | 18 | 3 | no | — |
| 270 | C2×#41 | — | 18 | 1 | no | — |
| 271 | C22×Q8 | — | 9 | 1 | no | — |
| 272 | C22×Q8 | C2×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 273 | C22×D4 | — | 9 | 3 | no | — |
| 274 | C22×D4 | — | 9 | 3 | no | — |
| 275 | C22×D4 | C2×C3⋊D3 | 1 | 3 | yes | complemented |
| 276 | C23×C4 | — | 9 | 3 | no | — |
| 277 | C23×C4 | C2×C3⋊D3 | 1 | 3 | yes | complemented |
| 278 | C4⋊Q8 | — | 9 | 3 | no | — |
| 279 | #127 | — | 9 | 3 | no | — |
| 280 | #124 | — | 9 | 3 | no | — |
| 281 | #124 | — | 9 | 3 | no | — |
| 282 | #123 | — | 9 | 6 | no | — |
| 283 | #123 | — | 9 | 6 | no | — |
| 284 | C22⋊Q8 | — | 9 | 3 | no | — |
| 285 | C22⋊Q8 | — | 9 | 3 | no | — |
| 286 | C22⋊Q8 | — | 9 | 3 | no | — |
| 287 | C22⋊Q8 | — | 9 | 3 | no | — |
| 288 | #121 | — | 9 | 3 | no | — |
| 289 | #121 | — | 9 | 3 | no | — |
| 290 | #121 | — | 9 | 3 | no | — |
| 291 | #121 | — | 9 | 6 | no | — |
| 292 | #121 | — | 9 | 6 | no | — |
| 293 | #121 | — | 9 | 3 | no | — |
| 294 | #120 | — | 9 | 6 | no | — |
| 295 | #120 | — | 9 | 6 | no | — |
| 296 | C4×Q8 | — | 9 | 1 | no | — |
| 297 | C4×Q8 | — | 9 | 1 | no | — |
| 298 | C4×D4 | — | 9 | 3 | no | — |
| 299 | C4×D4 | — | 9 | 3 | no | — |
| 300 | C4×D4 | — | 9 | 3 | no | — |
| 301 | C4×D4 | — | 9 | 3 | no | — |
| 302 | C4×D4 | — | 9 | 6 | no | — |
| 303 | C4×D4 | — | 9 | 3 | no | — |
| 304 | C4×D4 | — | 9 | 3 | no | — |
| 305 | C4×D4 | — | 9 | 1 | no | — |
| 306 | C4×D4 | — | 9 | 3 | no | — |
| 307 | C4×D4 | — | 9 | 3 | no | — |
| 308 | C4×D4 | — | 9 | 3 | no | — |
| 309 | #117 | — | 9 | 3 | no | — |
| 310 | C2×C4⋊C4 | — | 9 | 3 | no | — |
| 311 | C2×C22⋊C4 | — | 9 | 3 | no | — |
| 312 | C2×C22⋊C4 | — | 9 | 3 | no | — |
| 313 | C2×C42 | — | 9 | 3 | no | — |
| 314 | C23×C3 | — | 2 | 3 | no | — |
| 315 | C23×C3 | — | 3 | 3 | no | — |
| 316 | C23×C3 | — | 3 | 3 | no | — |
| 317 | C23×C3 | — | 6 | 3 | no | — |
| 318 | C23×C3 | C23×D3 | 1 | 1 | yes | characteristic |
| 319 | C22×D3 | — | 3 | 1 | no | — |
| 320 | C22×D3 | — | 3 | 3 | no | — |
| 321 | C22×D3 | — | 6 | 6 | no | — |
| 322 | C22×D3 | — | 6 | 3 | no | — |
| 323 | C22×D3 | — | 6 | 3 | no | — |
| 324 | C22×D3 | — | 12 | 9 | no | — |
| 325 | C22×D3 | — | 12 | 3 | no | — |
| 326 | C2×A4 | — | 2 | 9 | no | — |
| 327 | C2×A4 | C23×D3 | 1 | 3 | yes | — |
| 328 | S4 | — | 3 | 6 | no | — |
| 329 | S4 | — | 6 | 9 | no | — |
| 330 | C3×Q8 | — | 3 | 3 | no | — |
| 331 | C3×Q8 | — | 4 | 3 | no | — |
| 332 | C3×Q8 | — | 6 | 1 | no | — |
| 333 | C3×Q8 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 334 | C3×D4 | — | 3 | 6 | no | — |
| 335 | C3×D4 | — | 3 | 3 | no | — |
| 336 | C3×D4 | — | 4 | 9 | no | — |
| 337 | C3×D4 | — | 6 | 3 | no | — |
| 338 | C3×D4 | C2×S4 | 1 | 3 | yes | complemented |
| 339 | C2×C3×C4 | — | 3 | 3 | no | — |
| 340 | C2×C3×C4 | — | 3 | 1 | no | — |
| 341 | C2×C3×C4 | — | 3 | 3 | no | — |
| 342 | C2×C3×C4 | — | 3 | 3 | no | — |
| 343 | C2×C3×C4 | — | 3 | 3 | no | — |
| 344 | C2×C3×C4 | — | 3 | 1 | no | — |
| 345 | C2×C3×C4 | — | 3 | 3 | no | — |
| 346 | C2×C3×C4 | — | 4 | 9 | no | — |
| 347 | C2×C3×C4 | — | 6 | 3 | no | — |
| 348 | C2×C3×C4 | C2×S4 | 1 | 3 | yes | complemented |
| 349 | #67 | — | 3 | 2 | no | — |
| 350 | #67 | — | 3 | 2 | no | — |
| 351 | #67 | — | 6 | 6 | no | — |
| 352 | #67 | — | 6 | 6 | no | — |
| 353 | #67 | — | 6 | 6 | no | — |
| 354 | #67 | — | 6 | 3 | no | — |
| 355 | #67 | — | 6 | 3 | no | — |
| 356 | #67 | — | 6 | 6 | no | — |
| 357 | #67 | — | 12 | 18 | no | — |
| 358 | #67 | — | 12 | 6 | no | — |
| 359 | C2×Dic3 | — | 3 | 1 | no | — |
| 360 | C2×Dic3 | — | 3 | 1 | no | — |
| 361 | C2×Dic3 | — | 3 | 3 | no | — |
| 362 | C2×Dic3 | — | 3 | 3 | no | — |
| 363 | C2×Dic3 | — | 3 | 3 | no | — |
| 364 | C2×Dic3 | — | 3 | 1 | no | — |
| 365 | C2×Dic3 | — | 6 | 6 | no | — |
| 366 | C2×Dic3 | — | 6 | 3 | no | — |
| 367 | C2×Dic3 | — | 6 | 3 | no | — |
| 368 | C2×Dic3 | — | 12 | 9 | no | — |
| 369 | C2×Dic3 | — | 12 | 3 | no | — |
| 370 | D12 | — | 6 | 3 | no | — |
| 371 | D12 | — | 6 | 3 | no | — |
| 372 | D12 | — | 12 | 9 | no | — |
| 373 | C4×D3 | — | 6 | 1 | no | — |
| 374 | C4×D3 | — | 6 | 3 | no | — |
| 375 | C4×D3 | — | 6 | 3 | no | — |
| 376 | C4×D3 | — | 6 | 3 | no | — |
| 377 | C4×D3 | — | 6 | 1 | no | — |
| 378 | C4×D3 | — | 6 | 3 | no | — |
| 379 | C4×D3 | — | 6 | 3 | no | — |
| 380 | C4×D3 | — | 6 | 3 | no | — |
| 381 | C4×D3 | — | 12 | 3 | no | — |
| 382 | C4×D3 | — | 12 | 9 | no | — |
| 383 | C4×D3 | — | 12 | 9 | no | — |
| 384 | C4×D3 | — | 12 | 9 | no | — |
| 385 | Dic6 | — | 6 | 3 | no | — |
| 386 | Dic6 | — | 6 | 3 | no | — |
| 387 | Dic6 | — | 12 | 9 | no | — |
| 388 | C2×C32 | — | 4 | 1 | no | — |
| 389 | C2×C32 | — | 8 | 3 | no | — |
| 390 | C3⋊D3 | — | 4 | 2 | no | — |
| 391 | C3⋊D3 | — | 8 | 3 | no | — |
| 392 | C24 | — | 9 | 3 | no | — |
| 393 | C24 | C22×C3⋊D3 | 1 | 3 | yes | — |
| 394 | #41 | — | 3 | 1 | no | — |
| 395 | #41 | — | 3 | 3 | no | — |
| 396 | #41 | — | 3 | 3 | no | — |
| 397 | #41 | — | 6 | 1 | no | — |
| 398 | #41 | — | 6 | 3 | no | — |
| 399 | #41 | — | 6 | 3 | no | — |
| 400 | #41 | — | 18 | 3 | no | — |
| 401 | #41 | — | 18 | 3 | no | — |
| 402 | #41 | — | 18 | 3 | no | — |
| 403 | #41 | — | 18 | 6 | no | — |
| 404 | #41 | — | 18 | 3 | no | — |
| 405 | #41 | — | 18 | 3 | no | — |
| 406 | #41 | — | 18 | 1 | no | — |
| 407 | #41 | — | 18 | 3 | no | — |
| 408 | #41 | — | 18 | 3 | no | — |
| 409 | #41 | C3⋊S4 | 1 | 1 | yes | characteristic, direct product factor |
| 410 | C2×Q8 | — | 3 | 1 | no | — |
| 411 | C2×Q8 | — | 3 | 3 | no | — |
| 412 | C2×Q8 | — | 9 | 3 | no | — |
| 413 | C2×Q8 | — | 18 | 3 | no | — |
| 414 | C2×Q8 | — | 18 | 1 | no | — |
| 415 | C2×D4 | — | 3 | 3 | no | — |
| 416 | C2×D4 | — | 3 | 6 | no | — |
| 417 | C2×D4 | — | 3 | 3 | no | — |
| 418 | C2×D4 | — | 9 | 3 | no | — |
| 419 | C2×D4 | — | 9 | 1 | no | — |
| 420 | C2×D4 | — | 9 | 3 | no | — |
| 421 | C2×D4 | — | 9 | 3 | no | — |
| 422 | C2×D4 | — | 9 | 6 | no | — |
| 423 | C2×D4 | — | 9 | 3 | no | — |
| 424 | C2×D4 | — | 9 | 6 | no | — |
| 425 | C2×D4 | — | 18 | 6 | no | — |
| 426 | C2×D4 | — | 18 | 3 | no | — |
| 427 | C2×D4 | — | 18 | 6 | no | — |
| 428 | C2×D4 | — | 18 | 6 | no | — |
| 429 | C2×D4 | — | 18 | 3 | no | — |
| 430 | C22×C4 | — | 3 | 3 | no | — |
| 431 | C22×C4 | — | 3 | 3 | no | — |
| 432 | C22×C4 | — | 3 | 3 | no | — |
| 433 | C22×C4 | — | 3 | 3 | no | — |
| 434 | C22×C4 | — | 9 | 1 | no | — |
| 435 | C22×C4 | — | 9 | 3 | no | — |
| 436 | C22×C4 | — | 9 | 3 | no | — |
| 437 | C22×C4 | — | 9 | 3 | no | — |
| 438 | C22×C4 | — | 9 | 3 | no | — |
| 439 | C22×C4 | — | 9 | 3 | no | — |
| 440 | C22×C4 | — | 9 | 3 | no | — |
| 441 | C22×C4 | — | 18 | 3 | no | — |
| 442 | C22×C4 | — | 18 | 3 | no | — |
| 443 | C22×C4 | — | 18 | 3 | no | — |
| 444 | C22×C4 | — | 18 | 3 | no | — |
| 445 | C22×C4 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 446 | C22×C4 | C22×C3⋊D3 | 1 | 3 | yes | — |
| 447 | C4⋊C4 | — | 9 | 1 | no | — |
| 448 | C4⋊C4 | — | 9 | 3 | no | — |
| 449 | C4⋊C4 | — | 9 | 3 | no | — |
| 450 | C4⋊C4 | — | 9 | 3 | no | — |
| 451 | C4⋊C4 | — | 9 | 3 | no | — |
| 452 | C4⋊C4 | — | 9 | 3 | no | — |
| 453 | C4⋊C4 | — | 9 | 6 | no | — |
| 454 | C22⋊C4 | — | 9 | 1 | no | — |
| 455 | C22⋊C4 | — | 9 | 3 | no | — |
| 456 | C22⋊C4 | — | 9 | 3 | no | — |
| 457 | C22⋊C4 | — | 9 | 3 | no | — |
| 458 | C22⋊C4 | — | 9 | 6 | no | — |
| 459 | C22⋊C4 | — | 9 | 3 | no | — |
| 460 | C22⋊C4 | — | 9 | 3 | no | — |
| 461 | C22⋊C4 | — | 9 | 6 | no | — |
| 462 | C22⋊C4 | — | 9 | 6 | no | — |
| 463 | C22⋊C4 | — | 9 | 1 | no | — |
| 464 | C22⋊C4 | — | 9 | 3 | no | — |
| 465 | C42 | — | 9 | 1 | no | — |
| 466 | C42 | — | 9 | 3 | no | — |
| 467 | C42 | — | 9 | 3 | no | — |
| 468 | C42 | — | 9 | 3 | no | — |
| 469 | C22×C3 | — | 3 | 1 | no | — |
| 470 | C22×C3 | — | 3 | 1 | no | — |
| 471 | C22×C3 | — | 3 | 3 | no | — |
| 472 | C22×C3 | — | 4 | 9 | no | — |
| 473 | C22×C3 | — | 6 | 3 | no | — |
| 474 | C22×C3 | — | 6 | 3 | no | — |
| 475 | C22×C3 | — | 6 | 3 | no | — |
| 476 | C22×C3 | — | 6 | 3 | no | — |
| 477 | C22×C3 | D3×#41 | 1 | 1 | yes | characteristic, complemented |
| 478 | C22×C3 | C22×S4 | 1 | 3 | yes | — |
| 479 | C2×D3 | — | 3 | 2 | no | — |
| 480 | C2×D3 | — | 6 | 1 | no | — |
| 481 | C2×D3 | — | 6 | 1 | no | — |
| 482 | C2×D3 | — | 6 | 3 | no | — |
| 483 | C2×D3 | — | 6 | 3 | no | — |
| 484 | C2×D3 | — | 6 | 3 | no | — |
| 485 | C2×D3 | — | 12 | 3 | no | — |
| 486 | C2×D3 | — | 12 | 9 | no | — |
| 487 | C2×D3 | — | 12 | 6 | no | — |
| 488 | C2×D3 | — | 12 | 6 | no | — |
| 489 | C2×D3 | — | 24 | 18 | no | — |
| 490 | A4 | D3×#41 | 1 | 3 | yes | complemented |
| 491 | C3×C4 | — | 3 | 3 | no | — |
| 492 | C3×C4 | — | 3 | 1 | no | — |
| 493 | C3×C4 | — | 4 | 9 | no | — |
| 494 | C3×C4 | — | 4 | 3 | no | — |
| 495 | C3×C4 | C22×S4 | 1 | 3 | yes | — |
| 496 | C3×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 497 | Dic3 | — | 3 | 2 | no | — |
| 498 | Dic3 | — | 6 | 3 | no | — |
| 499 | Dic3 | — | 6 | 1 | no | — |
| 500 | Dic3 | — | 6 | 3 | no | — |
| 501 | Dic3 | — | 6 | 3 | no | — |
| 502 | Dic3 | — | 6 | 1 | no | — |
| 503 | Dic3 | — | 12 | 9 | no | — |
| 504 | Dic3 | — | 12 | 3 | no | — |
| 505 | C32 | — | 4 | 1 | no | Sylow |
| 506 | C23 | — | 2 | 3 | no | — |
| 507 | C23 | — | 3 | 3 | no | — |
| 508 | C23 | — | 3 | 3 | no | — |
| 509 | C23 | — | 6 | 3 | no | — |
| 510 | C23 | — | 9 | 1 | no | — |
| 511 | C23 | — | 9 | 3 | no | — |
| 512 | C23 | — | 18 | 3 | no | — |
| 513 | C23 | — | 18 | 6 | no | — |
| 514 | C23 | — | 18 | 3 | no | — |
| 515 | C23 | — | 36 | 3 | no | — |
| 516 | C23 | C23×C3⋊D3 | 1 | 1 | yes | characteristic |
| 517 | Q8 | — | 3 | 3 | no | — |
| 518 | Q8 | — | 6 | 1 | no | — |
| 519 | Q8 | — | 18 | 3 | no | — |
| 520 | Q8 | — | 18 | 3 | no | — |
| 521 | Q8 | C2×C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 522 | D4 | — | 3 | 6 | no | — |
| 523 | D4 | — | 3 | 3 | no | — |
| 524 | D4 | — | 6 | 3 | no | — |
| 525 | D4 | — | 9 | 2 | no | — |
| 526 | D4 | — | 9 | 2 | no | — |
| 527 | D4 | — | 18 | 3 | no | — |
| 528 | D4 | — | 18 | 6 | no | — |
| 529 | D4 | — | 18 | 6 | no | — |
| 530 | D4 | — | 18 | 3 | no | — |
| 531 | D4 | — | 18 | 6 | no | — |
| 532 | D4 | — | 18 | 3 | no | — |
| 533 | D4 | — | 18 | 6 | no | — |
| 534 | D4 | — | 18 | 3 | no | — |
| 535 | D4 | — | 36 | 6 | no | — |
| 536 | D4 | C2×C3⋊S4 | 1 | 3 | yes | complemented |
| 537 | C2×C4 | — | 3 | 3 | no | — |
| 538 | C2×C4 | — | 3 | 3 | no | — |
| 539 | C2×C4 | — | 3 | 3 | no | — |
| 540 | C2×C4 | — | 3 | 1 | no | — |
| 541 | C2×C4 | — | 3 | 3 | no | — |
| 542 | C2×C4 | — | 3 | 1 | no | — |
| 543 | C2×C4 | — | 3 | 3 | no | — |
| 544 | C2×C4 | — | 6 | 3 | no | — |
| 545 | C2×C4 | — | 9 | 1 | no | — |
| 546 | C2×C4 | — | 9 | 1 | no | — |
| 547 | C2×C4 | — | 9 | 3 | no | — |
| 548 | C2×C4 | — | 9 | 3 | no | — |
| 549 | C2×C4 | — | 9 | 1 | no | — |
| 550 | C2×C4 | — | 9 | 3 | no | — |
| 551 | C2×C4 | — | 18 | 1 | no | — |
| 552 | C2×C4 | — | 18 | 3 | no | — |
| 553 | C2×C4 | — | 18 | 3 | no | — |
| 554 | C2×C4 | — | 18 | 3 | no | — |
| 555 | C2×C4 | — | 18 | 6 | no | — |
| 556 | C2×C4 | — | 18 | 3 | no | — |
| 557 | C2×C4 | — | 18 | 3 | no | — |
| 558 | C2×C4 | — | 18 | 3 | no | — |
| 559 | C2×C4 | — | 18 | 3 | no | — |
| 560 | C2×C4 | — | 18 | 1 | no | — |
| 561 | C2×C4 | — | 18 | 3 | no | — |
| 562 | C2×C4 | — | 36 | 3 | no | — |
| 563 | C2×C4 | C2×C3⋊S4 | 1 | 3 | yes | complemented |
| 564 | C2×C3 | — | 2 | 3 | no | — |
| 565 | C2×C3 | — | 3 | 1 | no | — |
| 566 | C2×C3 | — | 3 | 1 | no | — |
| 567 | C2×C3 | — | 4 | 3 | no | — |
| 568 | C2×C3 | — | 6 | 3 | no | — |
| 569 | C2×C3 | — | 8 | 9 | no | — |
| 570 | C2×C3 | C23×S4 | 1 | 1 | yes | characteristic |
| 571 | D3 | — | 6 | 2 | no | — |
| 572 | D3 | — | 12 | 6 | no | — |
| 573 | D3 | — | 12 | 3 | no | — |
| 574 | D3 | — | 24 | 9 | no | — |
| 575 | C22 | — | 3 | 1 | no | — |
| 576 | C22 | — | 3 | 1 | no | — |
| 577 | C22 | — | 3 | 3 | no | — |
| 578 | C22 | — | 6 | 3 | no | — |
| 579 | C22 | — | 6 | 3 | no | — |
| 580 | C22 | — | 6 | 3 | no | — |
| 581 | C22 | — | 6 | 3 | no | — |
| 582 | C22 | — | 9 | 2 | no | — |
| 583 | C22 | — | 18 | 1 | no | — |
| 584 | C22 | — | 18 | 3 | no | — |
| 585 | C22 | — | 18 | 3 | no | — |
| 586 | C22 | — | 18 | 1 | no | — |
| 587 | C22 | — | 18 | 3 | no | — |
| 588 | C22 | — | 36 | 6 | no | — |
| 589 | C22 | — | 36 | 6 | no | — |
| 590 | C22 | #41×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 591 | C22 | C22×C3⋊S4 | 1 | 3 | yes | — |
| 592 | C4 | — | 3 | 1 | no | — |
| 593 | C4 | — | 3 | 3 | no | — |
| 594 | C4 | — | 9 | 2 | no | — |
| 595 | C4 | — | 18 | 3 | no | — |
| 596 | C4 | — | 18 | 1 | no | — |
| 597 | C4 | — | 18 | 3 | no | — |
| 598 | C4 | — | 18 | 1 | no | — |
| 599 | C4 | — | 18 | 3 | no | — |
| 600 | C4 | C22×C3⋊S4 | 1 | 3 | yes | — |
| 601 | C4 | C22×C3⋊S4 | 1 | 1 | yes | characteristic |
| 602 | C3 | — | 4 | 3 | no | — |
| 603 | C3 | #41×S4 | 1 | 1 | yes | characteristic, complemented |
| 604 | C2 | — | 2 | 3 | no | — |
| 605 | C2 | — | 3 | 1 | no | — |
| 606 | C2 | — | 3 | 1 | no | — |
| 607 | C2 | — | 6 | 3 | no | — |
| 608 | C2 | — | 18 | 2 | no | — |
| 609 | C2 | — | 36 | 3 | no | — |
| 610 | C2 | C23×C3⋊S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×C3⋊S4 |
| commutator, cosocle | C2×C3×A4 | C24 |
| Frattini | C2 | C23×C3⋊S4 |
| Fitting | C22×C3×#41 | D3 |
| socle | C23×C3 | C23×D3 |
| hypercenter | #41 | C3⋊S4 |
| hypocenter | C3×A4 | C2×#41 |
| LCS | G ▷ C2×C3×A4 ▷ C3×A4 | |
| UCS | C1 ◁ C4 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×A4×#41 | C2 | semidirect |
| 2. #10596582 | C2 | semidirect |
| 3. Q8×C3⋊S4 | C2 | semidirect |
| 4. #10596577 | C2 | semidirect |
| 5. D4×C3⋊S4 | C2 | semidirect |
| 6. #10596575 | C2 | semidirect |
| 7. C2×C4×C3⋊S4 | C2 | semidirect |
| 12. C3×Q8×A4 | C22 | semidirect |
| 13. C3×D4×A4 | C22 | semidirect |
| 14. C2×C3×C4×A4 | C22 | semidirect |
| 15. #64269 | C22 | semidirect |
| 16. C2×C3⋊SL(2,ℤ/4) | C22 | semidirect |
| 17. C4⋊(C3⋊S4) | C22 | semidirect |
| 20. C4×C3⋊S4 | C22 | semidirect |
| 21. C4×C3⋊S4 | C22 | semidirect |
| 22. #64259 | C22 | semidirect |
| 23. C22×C3×#41 | D3 | semidirect |
| 25. A4×#41 | D3 | semidirect |
| 66. C22×C3×Q8 | C2×D3 | semidirect |
| 67. C22×C3×D4 | C2×D3 | semidirect |
| 68. C23×C3×C4 | C2×D3 | semidirect |
| 81. Q8×A4 | C2×D3 | semidirect |
| 82. D4×A4 | C2×D3 | semidirect |
| 83. C2×C4×A4 | C2×D3 | semidirect |
| 132. C3⋊S4 | #41 | direct (N × H) |
| 145. C22×#41 | C3⋊D3 | semidirect |
| 172. C3×#41 | S4 | semidirect |
| 255. C3×A4 | C2×#41 | semidirect |
| 272. C22×Q8 | C2×C3⋊D3 | semidirect |
| 275. C22×D4 | C2×C3⋊D3 | semidirect |
| 277. C23×C4 | C2×C3⋊D3 | semidirect |
| 333. C3×Q8 | C2×S4 | semidirect |
| 338. C3×D4 | C2×S4 | semidirect |
| 348. C2×C3×C4 | C2×S4 | semidirect |
| 409. #41 | C3⋊S4 | direct (N × H) |
| 477. C22×C3 | D3×#41 | semidirect |
| 490. A4 | D3×#41 | semidirect |
| 521. Q8 | C2×C3⋊S4 | semidirect |
| 536. D4 | C2×C3⋊S4 | semidirect |
| 563. C2×C4 | C2×C3⋊S4 | semidirect |
| 590. C22 | #41×C3⋊D3 | semidirect |
| 603. C3 | #41×S4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4×#41 | 2 |
| #10596582 | 2 |
| Q8×C3⋊S4 | 2 |
| #10596577 | 2 |
| D4×C3⋊S4 | 2 |
| #10596575 | 2 |
| C2×C4×C3⋊S4 | 2 |
| #41×S4 | 3 |
| #41×#67 | 3 |
| #41×C3⋊D3 | 4 |