Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3235 conjugacy classes of subgroups.
The subgroup lattice has 557 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#64320 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#64316 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C4×#3832 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#5576 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10595409 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10594634 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #10594633 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #10594529 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #10594009 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #10594007 | C2 | 1 | 6 | yes | maximal, complemented |
| 11 | #10593972 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #86715 | — | 3 | 2 | no | maximal |
| 13 | C2×#3832 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C3×#239 | C22 | 1 | 2 | yes | — |
| 15 | C2×C3×D3×Q8 | C22 | 1 | 2 | yes | complemented |
| 16 | #64320 | — | 2 | 8 | no | — |
| 17 | #64316 | — | 2 | 8 | no | — |
| 18 | C2×#3802 | C22 | 1 | 3 | yes | — |
| 19 | C2×D3×D12 | C22 | 1 | 6 | yes | — |
| 20 | C2×#3799 | C22 | 1 | 6 | yes | complemented |
| 21 | C2×#3798 | C22 | 1 | 3 | yes | — |
| 22 | C2×#3798 | C22 | 1 | 3 | yes | complemented |
| 23 | C2×#3797 | C22 | 1 | 3 | yes | complemented |
| 24 | C32×C4×Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | Q8×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #64102 | C22 | 1 | 3 | yes | complemented |
| 27 | #64101 | C22 | 1 | 3 | yes | complemented |
| 28 | C4×C4⋊(C3⋊D3) | C22 | 1 | 3 | yes | complemented |
| 29 | C42×C3⋊D3 | C22 | 1 | 3 | yes | complemented |
| 30 | C3×#897 | C22 | 1 | 6 | yes | complemented |
| 31 | C3×#895 | C22 | 1 | 6 | yes | complemented |
| 32 | C3×#875 | C22 | 1 | 6 | yes | complemented |
| 33 | C3×C4×D12 | C22 | 1 | 6 | yes | complemented |
| 34 | #63922 | C22 | 1 | 12 | yes | complemented |
| 35 | #63921 | C22 | 1 | 6 | yes | complemented |
| 36 | #63921 | C22 | 1 | 6 | yes | complemented |
| 37 | #63919 | C22 | 1 | 3 | yes | complemented |
| 38 | #63916 | C22 | 1 | 6 | yes | complemented |
| 39 | #63915 | C22 | 1 | 6 | yes | complemented |
| 40 | #63915 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #63915 | C22 | 1 | 3 | yes | complemented |
| 42 | #63914 | C22 | 1 | 3 | yes | complemented |
| 43 | #63912 | C22 | 1 | 6 | yes | complemented |
| 44 | #63908 | C22 | 1 | 6 | yes | complemented |
| 45 | C4×#625 | C22 | 1 | 6 | yes | complemented |
| 46 | #63863 | C22 | 1 | 6 | yes | complemented |
| 47 | #63856 | C22 | 1 | 6 | yes | complemented |
| 48 | #63854 | C22 | 1 | 12 | yes | complemented |
| 49 | C2×#1009 | — | 3 | 2 | no | — |
| 50 | C2×#1007 | — | 3 | 2 | no | — |
| 51 | C3×#548 | — | 3 | 2 | no | — |
| 52 | #5831 | — | 3 | 2 | no | — |
| 53 | #5817 | — | 3 | 2 | no | — |
| 54 | #5676 | — | 3 | 6 | no | — |
| 55 | D3×#124 | — | 3 | 6 | no | — |
| 56 | #5630 | — | 3 | 6 | no | — |
| 57 | #5628 | — | 3 | 6 | no | — |
| 58 | #5612 | — | 3 | 6 | no | — |
| 59 | #5607 | — | 3 | 6 | no | — |
| 60 | #5576 | D3 | 1 | 2 | yes | complemented |
| 61 | C4×#239 | — | 3 | 2 | no | — |
| 62 | C4×#239 | — | 6 | 1 | no | — |
| 63 | #5550 | — | 3 | 6 | no | — |
| 64 | #5548 | — | 3 | 6 | no | — |
| 65 | C22×D32 | C23 | 1 | 6 | yes | — |
| 66 | C2×C32×Q8 | C23 | 1 | 1 | yes | characteristic |
| 67 | #3832 | D4 | 1 | 8 | yes | complemented |
| 68 | C2×C4⋊(C3⋊D3) | C23 | 1 | 3 | yes | — |
| 69 | C2×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 70 | C2×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 71 | C2×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 72 | C3×#239 | — | 2 | 8 | no | — |
| 73 | C3×D3×Q8 | — | 2 | 8 | no | — |
| 74 | C2×C3×D12 | C23 | 1 | 6 | yes | — |
| 75 | C2×C3×D12 | C23 | 1 | 6 | yes | — |
| 76 | C2×C3×C4×D3 | C23 | 1 | 6 | yes | — |
| 77 | C2×C3×C4×D3 | C23 | 1 | 6 | yes | — |
| 78 | C2×C3×Dic6 | C23 | 1 | 6 | yes | — |
| 79 | C2×#627 | C23 | 1 | 3 | yes | — |
| 80 | C2×#627 | C23 | 1 | 1 | yes | characteristic |
| 81 | C2×#626 | C23 | 1 | 6 | yes | — |
| 82 | C2×#626 | C23 | 1 | 6 | yes | — |
| 83 | C2×#625 | C23 | 1 | 3 | yes | — |
| 84 | C2×#625 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×#625 | C23 | 1 | 6 | yes | — |
| 86 | C2×#624 | C23 | 1 | 6 | yes | — |
| 87 | #3802 | — | 2 | 12 | no | — |
| 88 | D3×D12 | — | 2 | 24 | no | — |
| 89 | #3799 | — | 2 | 24 | no | — |
| 90 | #3798 | — | 2 | 12 | no | — |
| 91 | #3798 | — | 2 | 12 | no | — |
| 92 | #3797 | — | 2 | 12 | no | — |
| 93 | C32×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 94 | C32×C42 | C23 | 1 | 3 | yes | — |
| 95 | #3752 | C23 | 1 | 6 | yes | — |
| 96 | C4⋊(C3⋊Dic3) | C23 | 1 | 3 | yes | — |
| 97 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 98 | C4×C3⋊Dic3 | C23 | 1 | 3 | yes | — |
| 99 | C4×C3⋊Dic3 | C23 | 1 | 3 | yes | — |
| 100 | C3×(C2×D3)⋊C4 | C23 | 1 | 12 | yes | — |
| 101 | C3×(C2×D3)⋊C4 | C23 | 1 | 2 | yes | — |
| 102 | C3×(C2×D3)⋊C4 | C23 | 1 | 6 | yes | — |
| 103 | C3×C4⋊Dic3 | C23 | 1 | 6 | yes | — |
| 104 | #3724 | C23 | 1 | 6 | yes | — |
| 105 | (C2×D3)⋊Dic3 | C23 | 1 | 12 | yes | — |
| 106 | (C2×D3)⋊Dic3 | C23 | 1 | 6 | yes | — |
| 107 | (C2×D3)⋊Dic3 | C23 | 1 | 2 | yes | — |
| 108 | #3500 | — | 9 | 1 | no | Sylow |
| 109 | C2×C3×#41 | — | 3 | 2 | no | — |
| 110 | C22×C3×Q8 | — | 3 | 2 | no | — |
| 111 | #1009 | — | 6 | 16 | no | — |
| 112 | #1007 | — | 6 | 16 | no | — |
| 113 | C2×#239 | — | 3 | 2 | no | — |
| 114 | C2×#239 | — | 3 | 6 | no | — |
| 115 | C2×#239 | — | 6 | 1 | no | — |
| 116 | C2×#239 | C2×D3 | 1 | 2 | yes | — |
| 117 | C2×D3×Q8 | — | 3 | 6 | no | — |
| 118 | C2×D3×Q8 | C2×D3 | 1 | 2 | yes | complemented |
| 119 | C2×D3×D4 | — | 3 | 6 | no | — |
| 120 | C2×D3×D4 | — | 3 | 6 | no | — |
| 121 | C2×#235 | — | 3 | 6 | no | — |
| 122 | C2×#235 | — | 3 | 6 | no | — |
| 123 | C2×#235 | — | 3 | 6 | no | — |
| 124 | C22×D12 | — | 3 | 6 | no | — |
| 125 | C3×#124 | — | 3 | 6 | no | — |
| 126 | C3×C22⋊Q8 | — | 3 | 6 | no | — |
| 127 | C3×#121 | — | 3 | 6 | no | — |
| 128 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 129 | C3×C4×Q8 | C2×D3 | 1 | 2 | yes | complemented |
| 130 | C3×C4×D4 | — | 3 | 6 | no | — |
| 131 | #947 | — | 3 | 6 | no | — |
| 132 | #946 | — | 3 | 6 | no | — |
| 133 | Q8×Dic3 | — | 3 | 2 | no | — |
| 134 | Q8×Dic3 | — | 6 | 1 | no | — |
| 135 | #940 | — | 3 | 6 | no | — |
| 136 | #938 | — | 3 | 6 | no | — |
| 137 | #938 | — | 3 | 6 | no | — |
| 138 | #937 | — | 3 | 12 | no | — |
| 139 | #936 | — | 3 | 6 | no | — |
| 140 | #930 | — | 3 | 6 | no | — |
| 141 | C4×#67 | — | 3 | 6 | no | — |
| 142 | C4×#67 | — | 3 | 6 | no | — |
| 143 | #924 | — | 3 | 6 | no | — |
| 144 | #897 | C2×D3 | 1 | 6 | yes | complemented |
| 145 | #895 | — | 3 | 6 | no | — |
| 146 | #895 | C2×D3 | 1 | 6 | yes | complemented |
| 147 | #894 | — | 3 | 12 | no | — |
| 148 | #893 | — | 3 | 6 | no | — |
| 149 | #893 | — | 6 | 3 | no | — |
| 150 | #892 | — | 3 | 6 | no | — |
| 151 | #892 | — | 6 | 3 | no | — |
| 152 | #888 | — | 3 | 6 | no | — |
| 153 | #885 | — | 3 | 6 | no | — |
| 154 | #885 | — | 3 | 12 | no | — |
| 155 | #885 | — | 3 | 2 | no | — |
| 156 | #884 | — | 3 | 6 | no | — |
| 157 | #884 | — | 3 | 6 | no | — |
| 158 | #883 | — | 3 | 12 | no | — |
| 159 | #882 | — | 3 | 12 | no | — |
| 160 | D3×C22⋊C4 | — | 3 | 12 | no | — |
| 161 | D3×C22⋊C4 | — | 3 | 12 | no | — |
| 162 | #875 | C2×D3 | 1 | 6 | yes | complemented |
| 163 | C4×D12 | — | 3 | 6 | no | — |
| 164 | C4×D12 | — | 6 | 3 | no | — |
| 165 | C4×D12 | C2×D3 | 1 | 6 | yes | complemented |
| 166 | C42×D3 | — | 3 | 6 | no | — |
| 167 | C42×D3 | — | 6 | 3 | no | — |
| 168 | C22×C3⋊D3 | C24 | 1 | 3 | yes | — |
| 169 | C22×C3×D3 | C24 | 1 | 6 | yes | — |
| 170 | C22×C3×D3 | C24 | 1 | 2 | yes | — |
| 171 | C2×D32 | — | 2 | 12 | no | — |
| 172 | C2×D32 | — | 4 | 6 | no | — |
| 173 | C2×D32 | — | 4 | 6 | no | — |
| 174 | C32×Q8 | C2×D4 | 1 | 4 | yes | — |
| 175 | C2×C32×C4 | C24 | 1 | 3 | yes | — |
| 176 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 177 | C2×C32×C4 | C24 | 1 | 3 | yes | — |
| 178 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 179 | C2×C3⋊Dic3 | C24 | 1 | 3 | yes | — |
| 180 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 181 | C4⋊(C3⋊D3) | C2×D4 | 1 | 12 | yes | — |
| 182 | C4×C3⋊D3 | — | 4 | 3 | no | — |
| 183 | C4×C3⋊D3 | — | 4 | 3 | no | — |
| 184 | C4×C3⋊D3 | C2×D4 | 1 | 12 | yes | — |
| 185 | C2×C3×Dic3 | C24 | 1 | 6 | yes | — |
| 186 | C2×C3×Dic3 | C24 | 1 | 2 | yes | — |
| 187 | C3×D12 | — | 2 | 12 | no | — |
| 188 | C3×D12 | — | 4 | 6 | no | — |
| 189 | C3×C4×D3 | — | 2 | 12 | no | — |
| 190 | C3×C4×D3 | — | 2 | 12 | no | — |
| 191 | C3×Dic6 | — | 2 | 12 | no | — |
| 192 | #627 | — | 2 | 6 | no | — |
| 193 | #627 | — | 2 | 2 | no | — |
| 194 | #626 | — | 2 | 12 | no | — |
| 195 | #626 | — | 2 | 12 | no | — |
| 196 | #625 | — | 2 | 2 | no | — |
| 197 | #625 | — | 2 | 6 | no | — |
| 198 | #625 | — | 4 | 6 | no | — |
| 199 | #624 | — | 2 | 12 | no | — |
| 200 | C2×2−1+4 | — | 9 | 1 | no | — |
| 201 | C2×H(5,𝔽2) | — | 9 | 1 | no | — |
| 202 | #548 | — | 3 | 2 | no | — |
| 203 | #548 | — | 9 | 2 | no | — |
| 204 | #546 | — | 9 | 6 | no | — |
| 205 | #546 | — | 9 | 6 | no | — |
| 206 | #536 | — | 9 | 3 | no | — |
| 207 | #535 | — | 9 | 3 | no | — |
| 208 | #532 | — | 9 | 3 | no | — |
| 209 | C2×#124 | — | 9 | 3 | no | — |
| 210 | C4×#41 | — | 9 | 1 | no | — |
| 211 | C23×D3 | — | 3 | 12 | no | — |
| 212 | C3×#41 | — | 6 | 8 | no | — |
| 213 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 214 | C2×C3×Q8 | — | 3 | 6 | no | — |
| 215 | C2×C3×Q8 | — | 6 | 8 | no | — |
| 216 | C2×C3×Q8 | C22×D3 | 1 | 2 | yes | — |
| 217 | C2×C3×D4 | — | 3 | 6 | no | — |
| 218 | C2×C3×D4 | — | 3 | 6 | no | — |
| 219 | C22×C3×C4 | — | 3 | 6 | no | — |
| 220 | C22×C3×C4 | — | 3 | 6 | no | — |
| 221 | C2×#67 | — | 3 | 6 | no | — |
| 222 | C2×#67 | — | 3 | 2 | no | — |
| 223 | C2×#67 | — | 3 | 6 | no | — |
| 224 | C2×#67 | — | 3 | 6 | no | — |
| 225 | C2×#67 | — | 3 | 6 | no | — |
| 226 | C2×#67 | — | 3 | 6 | no | — |
| 227 | #239 | — | 2 | 8 | no | — |
| 228 | #239 | — | 3 | 16 | no | — |
| 229 | #239 | — | 6 | 8 | no | — |
| 230 | #239 | — | 6 | 24 | no | — |
| 231 | D3×Q8 | — | 2 | 8 | no | — |
| 232 | D3×Q8 | — | 6 | 24 | no | — |
| 233 | D3×D4 | — | 6 | 24 | no | — |
| 234 | D3×D4 | — | 6 | 24 | no | — |
| 235 | #235 | — | 6 | 24 | no | — |
| 236 | #235 | — | 6 | 24 | no | — |
| 237 | #235 | — | 6 | 24 | no | — |
| 238 | C2×D12 | — | 3 | 6 | no | — |
| 239 | C2×D12 | — | 3 | 6 | no | — |
| 240 | C2×D12 | — | 3 | 6 | no | — |
| 241 | C2×D12 | — | 6 | 3 | no | — |
| 242 | C2×D12 | — | 6 | 24 | no | — |
| 243 | C2×D12 | C22×D3 | 1 | 6 | yes | — |
| 244 | C2×D12 | C22×D3 | 1 | 6 | yes | — |
| 245 | C2×C4×D3 | — | 3 | 6 | no | — |
| 246 | C2×C4×D3 | — | 3 | 12 | no | — |
| 247 | C2×C4×D3 | — | 3 | 6 | no | — |
| 248 | C2×C4×D3 | — | 3 | 6 | no | — |
| 249 | C2×C4×D3 | — | 6 | 3 | no | — |
| 250 | C2×C4×D3 | — | 6 | 3 | no | — |
| 251 | C2×C4×D3 | — | 6 | 3 | no | — |
| 252 | C2×C4×D3 | C22×D3 | 1 | 6 | yes | — |
| 253 | C2×C4×D3 | C22×D3 | 1 | 6 | yes | — |
| 254 | C2×Dic6 | — | 3 | 6 | no | — |
| 255 | C2×Dic6 | — | 3 | 2 | no | — |
| 256 | C2×Dic6 | C22×D3 | 1 | 6 | yes | — |
| 257 | C3×C4⋊C4 | — | 2 | 3 | no | — |
| 258 | C3×C4⋊C4 | — | 3 | 6 | no | — |
| 259 | C3×C4⋊C4 | C22×D3 | 1 | 6 | yes | — |
| 260 | C3×C22⋊C4 | — | 3 | 6 | no | — |
| 261 | C3×C22⋊C4 | — | 3 | 12 | no | — |
| 262 | C3×C22⋊C4 | — | 3 | 2 | no | — |
| 263 | C3×C42 | — | 2 | 3 | no | — |
| 264 | C3×C42 | C22×D3 | 1 | 6 | yes | — |
| 265 | #217 | — | 3 | 6 | no | — |
| 266 | #217 | — | 3 | 12 | no | — |
| 267 | #217 | — | 3 | 2 | no | — |
| 268 | (C2×D3)⋊C4 | — | 3 | 6 | no | — |
| 269 | (C2×D3)⋊C4 | — | 3 | 12 | no | — |
| 270 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 271 | (C2×D3)⋊C4 | — | 3 | 12 | no | — |
| 272 | (C2×D3)⋊C4 | — | 6 | 6 | no | — |
| 273 | (C2×D3)⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 274 | (C2×D3)⋊C4 | C22×D3 | 1 | 6 | yes | — |
| 275 | (C2×D3)⋊C4 | C22×D3 | 1 | 12 | yes | — |
| 276 | C4⋊Dic3 | — | 3 | 6 | no | — |
| 277 | C4⋊Dic3 | — | 6 | 3 | no | — |
| 278 | C4⋊Dic3 | C22×D3 | 1 | 6 | yes | — |
| 279 | Dic3⋊C4 | — | 3 | 6 | no | — |
| 280 | Dic3⋊C4 | — | 3 | 6 | no | — |
| 281 | C4×Dic3 | — | 3 | 2 | no | — |
| 282 | C4×Dic3 | — | 3 | 6 | no | — |
| 283 | C4×Dic3 | — | 3 | 6 | no | — |
| 284 | C4×Dic3 | — | 6 | 1 | no | — |
| 285 | C4×Dic3 | — | 6 | 3 | no | — |
| 286 | C4×Dic3 | — | 6 | 3 | no | — |
| 287 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 288 | C2×C3⋊D3 | — | 2 | 3 | no | — |
| 289 | C2×C3⋊D3 | — | 2 | 3 | no | — |
| 290 | C2×C3⋊D3 | C22×D4 | 1 | 6 | yes | — |
| 291 | C2×C3×D3 | — | 2 | 2 | no | — |
| 292 | C2×C3×D3 | — | 2 | 6 | no | — |
| 293 | C2×C3×D3 | — | 2 | 2 | no | — |
| 294 | C2×C3×D3 | — | 2 | 6 | no | — |
| 295 | C2×C3×D3 | — | 2 | 2 | no | — |
| 296 | C2×C3×D3 | — | 2 | 6 | no | — |
| 297 | D32 | — | 8 | 12 | no | — |
| 298 | C32×C4 | — | 2 | 1 | no | — |
| 299 | C32×C4 | — | 2 | 3 | no | — |
| 300 | C32×C4 | C22×D4 | 1 | 6 | yes | — |
| 301 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 302 | C3⋊Dic3 | — | 2 | 3 | no | — |
| 303 | C3⋊Dic3 | C22×D4 | 1 | 2 | yes | — |
| 304 | C3×Dic3 | — | 2 | 6 | no | — |
| 305 | C3×Dic3 | — | 2 | 2 | no | — |
| 306 | 2−1+4 | — | 18 | 8 | no | — |
| 307 | H(5,𝔽2) | — | 18 | 8 | no | — |
| 308 | C2×#41 | — | 3 | 2 | no | — |
| 309 | C2×#41 | — | 9 | 3 | no | — |
| 310 | C2×#41 | — | 9 | 3 | no | — |
| 311 | C2×#41 | — | 9 | 6 | no | — |
| 312 | C2×#41 | — | 9 | 1 | no | — |
| 313 | C22×Q8 | — | 3 | 2 | no | — |
| 314 | C22×Q8 | — | 9 | 3 | no | — |
| 315 | C22×D4 | — | 9 | 6 | no | — |
| 316 | C22×D4 | — | 9 | 3 | no | — |
| 317 | C4⋊Q8 | — | 9 | 3 | no | — |
| 318 | #127 | — | 9 | 3 | no | — |
| 319 | #124 | — | 3 | 6 | no | — |
| 320 | #124 | — | 9 | 3 | no | — |
| 321 | #124 | — | 9 | 6 | no | — |
| 322 | #124 | — | 9 | 1 | no | — |
| 323 | #124 | — | 9 | 6 | no | — |
| 324 | #123 | — | 9 | 12 | no | — |
| 325 | C22⋊Q8 | — | 3 | 6 | no | — |
| 326 | C22⋊Q8 | — | 9 | 6 | no | — |
| 327 | #121 | — | 3 | 6 | no | — |
| 328 | #121 | — | 9 | 6 | no | — |
| 329 | #121 | — | 9 | 6 | no | — |
| 330 | #121 | — | 9 | 6 | no | — |
| 331 | #120 | — | 9 | 12 | no | — |
| 332 | C4×Q8 | — | 9 | 1 | no | — |
| 333 | C4×Q8 | D32 | 1 | 1 | yes | characteristic, complemented |
| 334 | C4×D4 | — | 3 | 6 | no | — |
| 335 | C4×D4 | — | 9 | 6 | no | — |
| 336 | C4×D4 | — | 9 | 3 | no | — |
| 337 | C4×D4 | — | 9 | 3 | no | — |
| 338 | #117 | — | 9 | 3 | no | — |
| 339 | C2×C22⋊C4 | — | 9 | 6 | no | — |
| 340 | C2×C22⋊C4 | — | 9 | 6 | no | — |
| 341 | C2×C42 | — | 9 | 3 | no | — |
| 342 | C23×C3 | — | 3 | 6 | no | — |
| 343 | C23×C3 | — | 3 | 2 | no | — |
| 344 | C22×D3 | — | 3 | 6 | no | — |
| 345 | C22×D3 | — | 6 | 3 | no | — |
| 346 | C22×D3 | — | 6 | 24 | no | — |
| 347 | C22×D3 | — | 12 | 12 | no | — |
| 348 | C22×D3 | — | 12 | 12 | no | — |
| 349 | C22×D3 | C23×D3 | 1 | 6 | yes | — |
| 350 | C22×D3 | C23×D3 | 1 | 2 | yes | — |
| 351 | C3×Q8 | — | 2 | 4 | no | — |
| 352 | C3×Q8 | — | 6 | 12 | no | — |
| 353 | C3×Q8 | D3×D4 | 1 | 8 | yes | — |
| 354 | C3×D4 | — | 6 | 12 | no | — |
| 355 | C3×D4 | — | 12 | 6 | no | — |
| 356 | C2×C3×C4 | — | 2 | 3 | no | — |
| 357 | C2×C3×C4 | — | 2 | 1 | no | — |
| 358 | C2×C3×C4 | — | 2 | 3 | no | — |
| 359 | C2×C3×C4 | — | 3 | 2 | no | — |
| 360 | C2×C3×C4 | — | 3 | 6 | no | — |
| 361 | C2×C3×C4 | — | 6 | 12 | no | — |
| 362 | C2×C3×C4 | — | 6 | 12 | no | — |
| 363 | C2×C3×C4 | C23×D3 | 1 | 6 | yes | — |
| 364 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 365 | C2×C3×C4 | C23×D3 | 1 | 6 | yes | — |
| 366 | #67 | — | 6 | 12 | no | — |
| 367 | #67 | — | 6 | 12 | no | — |
| 368 | #67 | — | 6 | 4 | no | — |
| 369 | #67 | — | 6 | 12 | no | — |
| 370 | #67 | — | 12 | 6 | no | — |
| 371 | #67 | — | 12 | 6 | no | — |
| 372 | C2×Dic3 | — | 3 | 2 | no | — |
| 373 | C2×Dic3 | — | 3 | 2 | no | — |
| 374 | C2×Dic3 | — | 3 | 6 | no | — |
| 375 | C2×Dic3 | — | 6 | 1 | no | — |
| 376 | C2×Dic3 | — | 6 | 1 | no | — |
| 377 | C2×Dic3 | — | 6 | 3 | no | — |
| 378 | C2×Dic3 | C23×D3 | 1 | 2 | yes | — |
| 379 | C2×Dic3 | C23×D3 | 1 | 6 | yes | — |
| 380 | D12 | — | 2 | 12 | no | — |
| 381 | D12 | — | 3 | 24 | no | — |
| 382 | D12 | — | 4 | 6 | no | — |
| 383 | D12 | — | 6 | 12 | no | — |
| 384 | D12 | — | 6 | 12 | no | — |
| 385 | D12 | — | 6 | 12 | no | — |
| 386 | C4×D3 | — | 2 | 12 | no | — |
| 387 | C4×D3 | — | 2 | 12 | no | — |
| 388 | C4×D3 | — | 3 | 24 | no | — |
| 389 | C4×D3 | — | 6 | 12 | no | — |
| 390 | C4×D3 | — | 6 | 24 | no | — |
| 391 | C4×D3 | — | 12 | 6 | no | — |
| 392 | C4×D3 | — | 12 | 6 | no | — |
| 393 | C4×D3 | — | 12 | 6 | no | — |
| 394 | C4×D3 | — | 12 | 6 | no | — |
| 395 | Dic6 | — | 2 | 12 | no | — |
| 396 | Dic6 | — | 6 | 4 | no | — |
| 397 | Dic6 | — | 6 | 12 | no | — |
| 398 | C2×C32 | C23×D4 | 1 | 1 | yes | characteristic |
| 399 | C2×C32 | #585 | 1 | 1 | yes | characteristic |
| 400 | C2×C32 | #585 | 1 | 1 | yes | characteristic |
| 401 | C3⋊D3 | — | 2 | 6 | no | — |
| 402 | C3×D3 | — | 4 | 6 | no | — |
| 403 | C3×D3 | — | 4 | 2 | no | — |
| 404 | C24 | — | 9 | 6 | no | — |
| 405 | #41 | — | 6 | 8 | no | — |
| 406 | #41 | — | 9 | 8 | no | — |
| 407 | #41 | — | 18 | 12 | no | — |
| 408 | #41 | — | 18 | 12 | no | — |
| 409 | #41 | — | 18 | 24 | no | — |
| 410 | C2×Q8 | — | 3 | 6 | no | — |
| 411 | C2×Q8 | — | 6 | 8 | no | — |
| 412 | C2×Q8 | — | 9 | 3 | no | — |
| 413 | C2×Q8 | — | 9 | 1 | no | — |
| 414 | C2×Q8 | — | 18 | 12 | no | — |
| 415 | C2×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 416 | C2×D4 | — | 3 | 6 | no | — |
| 417 | C2×D4 | — | 3 | 6 | no | — |
| 418 | C2×D4 | — | 9 | 6 | no | — |
| 419 | C2×D4 | — | 9 | 6 | no | — |
| 420 | C2×D4 | — | 9 | 3 | no | — |
| 421 | C2×D4 | — | 9 | 1 | no | — |
| 422 | C2×D4 | — | 9 | 6 | no | — |
| 423 | C2×D4 | — | 9 | 3 | no | — |
| 424 | C2×D4 | — | 18 | 24 | no | — |
| 425 | C2×D4 | — | 18 | 12 | no | — |
| 426 | C22×C4 | — | 3 | 6 | no | — |
| 427 | C22×C4 | — | 3 | 6 | no | — |
| 428 | C22×C4 | — | 9 | 6 | no | — |
| 429 | C22×C4 | — | 9 | 3 | no | — |
| 430 | C22×C4 | — | 9 | 3 | no | — |
| 431 | C22×C4 | — | 9 | 3 | no | — |
| 432 | C4⋊C4 | — | 3 | 6 | no | — |
| 433 | C4⋊C4 | — | 9 | 6 | no | — |
| 434 | C4⋊C4 | — | 9 | 3 | no | — |
| 435 | C4⋊C4 | C2×D32 | 1 | 3 | yes | — |
| 436 | C22⋊C4 | — | 3 | 6 | no | — |
| 437 | C22⋊C4 | — | 3 | 12 | no | — |
| 438 | C22⋊C4 | — | 3 | 2 | no | — |
| 439 | C22⋊C4 | — | 9 | 6 | no | — |
| 440 | C22⋊C4 | — | 9 | 12 | no | — |
| 441 | C22⋊C4 | — | 9 | 2 | no | — |
| 442 | C22⋊C4 | — | 9 | 6 | no | — |
| 443 | C42 | — | 9 | 1 | no | — |
| 444 | C42 | — | 9 | 3 | no | — |
| 445 | C42 | — | 9 | 3 | no | — |
| 446 | C42 | C2×D32 | 1 | 3 | yes | — |
| 447 | C22×C3 | — | 2 | 1 | no | — |
| 448 | C22×C3 | — | 6 | 2 | no | — |
| 449 | C22×C3 | — | 6 | 6 | no | — |
| 450 | C22×C3 | — | 6 | 2 | no | — |
| 451 | C22×C3 | — | 6 | 6 | no | — |
| 452 | C22×C3 | — | 6 | 2 | no | — |
| 453 | C22×C3 | — | 6 | 6 | no | — |
| 454 | C22×C3 | C24×D3 | 1 | 2 | yes | — |
| 455 | C2×D3 | — | 2 | 2 | no | — |
| 456 | C2×D3 | — | 2 | 6 | no | — |
| 457 | C2×D3 | — | 2 | 2 | no | — |
| 458 | C2×D3 | — | 2 | 6 | no | — |
| 459 | C2×D3 | — | 2 | 2 | no | — |
| 460 | C2×D3 | — | 2 | 6 | no | — |
| 461 | C2×D3 | — | 3 | 12 | no | — |
| 462 | C2×D3 | — | 6 | 6 | no | — |
| 463 | C2×D3 | — | 6 | 6 | no | — |
| 464 | C2×D3 | — | 6 | 6 | no | — |
| 465 | C2×D3 | — | 12 | 3 | no | — |
| 466 | C2×D3 | — | 12 | 3 | no | — |
| 467 | C2×D3 | — | 24 | 24 | no | — |
| 468 | C3×C4 | — | 2 | 2 | no | — |
| 469 | C3×C4 | — | 2 | 6 | no | — |
| 470 | C3×C4 | — | 2 | 2 | no | — |
| 471 | C3×C4 | — | 2 | 6 | no | — |
| 472 | C3×C4 | — | 4 | 3 | no | — |
| 473 | C3×C4 | — | 6 | 6 | no | — |
| 474 | C3×C4 | — | 6 | 2 | no | — |
| 475 | C3×C4 | C2×D3×D4 | 1 | 12 | yes | — |
| 476 | Dic3 | — | 2 | 6 | no | — |
| 477 | Dic3 | — | 2 | 2 | no | — |
| 478 | Dic3 | — | 3 | 4 | no | — |
| 479 | Dic3 | — | 6 | 2 | no | — |
| 480 | Dic3 | — | 6 | 2 | no | — |
| 481 | Dic3 | — | 6 | 2 | no | — |
| 482 | Dic3 | — | 6 | 6 | no | — |
| 483 | Dic3 | — | 12 | 3 | no | — |
| 484 | C32 | #3500 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 485 | C23 | — | 3 | 6 | no | — |
| 486 | C23 | — | 3 | 2 | no | — |
| 487 | C23 | — | 9 | 3 | no | — |
| 488 | C23 | — | 18 | 12 | no | — |
| 489 | C23 | — | 36 | 6 | no | — |
| 490 | C23 | — | 36 | 6 | no | — |
| 491 | Q8 | — | 6 | 12 | no | — |
| 492 | Q8 | — | 18 | 6 | no | — |
| 493 | Q8 | — | 18 | 2 | no | — |
| 494 | Q8 | #3802 | 1 | 4 | yes | — |
| 495 | D4 | — | 6 | 12 | no | — |
| 496 | D4 | — | 9 | 12 | no | — |
| 497 | D4 | — | 12 | 6 | no | — |
| 498 | D4 | — | 18 | 12 | no | — |
| 499 | D4 | — | 18 | 12 | no | — |
| 500 | D4 | — | 18 | 6 | no | — |
| 501 | D4 | — | 18 | 2 | no | — |
| 502 | D4 | — | 36 | 6 | no | — |
| 503 | C2×C4 | — | 3 | 6 | no | — |
| 504 | C2×C4 | — | 3 | 2 | no | — |
| 505 | C2×C4 | — | 6 | 12 | no | — |
| 506 | C2×C4 | — | 6 | 12 | no | — |
| 507 | C2×C4 | — | 9 | 1 | no | — |
| 508 | C2×C4 | — | 9 | 12 | no | — |
| 509 | C2×C4 | — | 9 | 1 | no | — |
| 510 | C2×C4 | — | 9 | 3 | no | — |
| 511 | C2×C4 | — | 18 | 12 | no | — |
| 512 | C2×C4 | — | 36 | 3 | no | — |
| 513 | C2×C4 | — | 36 | 3 | no | — |
| 514 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 515 | C2×C4 | C22×D32 | 1 | 3 | yes | — |
| 516 | C2×C4 | C22×D32 | 1 | 3 | yes | — |
| 517 | C2×C3 | — | 2 | 1 | no | — |
| 518 | C2×C3 | — | 2 | 1 | no | — |
| 519 | C2×C3 | — | 2 | 1 | no | — |
| 520 | C2×C3 | — | 12 | 6 | no | — |
| 521 | C2×C3 | — | 12 | 2 | no | — |
| 522 | C2×C3 | C22×D3×D4 | 1 | 2 | yes | — |
| 523 | C2×C3 | #5964 | 1 | 2 | yes | — |
| 524 | C2×C3 | #5968 | 1 | 2 | yes | — |
| 525 | D3 | — | 4 | 6 | no | — |
| 526 | D3 | — | 4 | 2 | no | — |
| 527 | D3 | — | 6 | 12 | no | — |
| 528 | D3 | — | 12 | 6 | no | — |
| 529 | C22 | — | 6 | 2 | no | — |
| 530 | C22 | — | 6 | 6 | no | — |
| 531 | C22 | — | 6 | 2 | no | — |
| 532 | C22 | — | 6 | 6 | no | — |
| 533 | C22 | — | 6 | 2 | no | — |
| 534 | C22 | — | 6 | 6 | no | — |
| 535 | C22 | — | 9 | 6 | no | — |
| 536 | C22 | — | 18 | 3 | no | — |
| 537 | C22 | — | 18 | 3 | no | — |
| 538 | C22 | — | 72 | 12 | no | — |
| 539 | C22 | C23×D32 | 1 | 1 | yes | characteristic |
| 540 | C4 | — | 2 | 1 | no | — |
| 541 | C4 | — | 2 | 3 | no | — |
| 542 | C4 | — | 6 | 2 | no | — |
| 543 | C4 | — | 6 | 6 | no | — |
| 544 | C4 | — | 9 | 2 | no | — |
| 545 | C4 | — | 18 | 3 | no | — |
| 546 | C4 | — | 18 | 1 | no | — |
| 547 | C4 | C2×#3802 | 1 | 6 | yes | — |
| 548 | C3 | — | 2 | 1 | no | — |
| 549 | C3 | #86715 | 1 | 2 | yes | complemented |
| 550 | C2 | — | 12 | 6 | no | — |
| 551 | C2 | — | 12 | 2 | no | — |
| 552 | C2 | — | 18 | 6 | no | — |
| 553 | C2 | C22×#3802 | 1 | 1 | yes | characteristic |
| 554 | C2 | #10596689 | 1 | 1 | yes | characteristic |
| 555 | C2 | #10596695 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×C4×Q8 | C22 |
| hypercenter | C4×Q8 | D32 |
| hypocenter | C32 | #3500 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#64320 | C2 | semidirect |
| 2. C2×#64316 | C2 | semidirect |
| 3. C4×#3832 | C2 | semidirect |
| 4. C3×#5576 | C2 | semidirect |
| 5. #10595409 | C2 | semidirect |
| 6. #10594634 | C2 | semidirect |
| 7. #10594633 | C2 | semidirect |
| 8. #10594529 | C2 | semidirect |
| 9. #10594009 | C2 | semidirect |
| 10. #10594007 | C2 | semidirect |
| 11. #10593972 | C2 | semidirect |
| 15. C2×C3×D3×Q8 | C22 | semidirect |
| 20. C2×#3799 | C22 | semidirect |
| 22. C2×#3798 | C22 | semidirect |
| 23. C2×#3797 | C22 | semidirect |
| 24. C32×C4×Q8 | C22 | semidirect |
| 25. Q8×C3⋊Dic3 | C22 | semidirect |
| 26. #64102 | C22 | semidirect |
| 27. #64101 | C22 | semidirect |
| 28. C4×C4⋊(C3⋊D3) | C22 | semidirect |
| 29. C42×C3⋊D3 | C22 | semidirect |
| 30. C3×#897 | C22 | semidirect |
| 31. C3×#895 | C22 | semidirect |
| 32. C3×#875 | C22 | semidirect |
| 33. C3×C4×D12 | C22 | semidirect |
| 34. #63922 | C22 | semidirect |
| 35. #63921 | C22 | semidirect |
| 36. #63921 | C22 | semidirect |
| 37. #63919 | C22 | semidirect |
| 38. #63916 | C22 | semidirect |
| 39. #63915 | C22 | semidirect |
| 40. #63915 | C22 | semidirect |
| 41. #63915 | C22 | semidirect |
| 42. #63914 | C22 | semidirect |
| 43. #63912 | C22 | semidirect |
| 44. #63908 | C22 | semidirect |
| 45. C4×#625 | C22 | semidirect |
| 46. #63863 | C22 | semidirect |
| 47. #63856 | C22 | semidirect |
| 48. #63854 | C22 | semidirect |
| 60. #5576 | D3 | semidirect |
| 67. #3832 | D4 | semidirect |
| 118. C2×D3×Q8 | C2×D3 | semidirect |
| 129. C3×C4×Q8 | C2×D3 | semidirect |
| 144. #897 | C2×D3 | semidirect |
| 146. #895 | C2×D3 | semidirect |
| 162. #875 | C2×D3 | semidirect |
| 165. C4×D12 | C2×D3 | semidirect |
| 333. C4×Q8 | D32 | semidirect |
| 484. C32 | #3500 | semidirect |
| 549. C3 | #86715 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64320 | 2 |
| C2×#64316 | 2 |
| C4×#3832 | 2 |
| C3×#5576 | 2 |
| #10595409 | 2 |
| #10594634 | 2 |
| #10594633 | 2 |
| #10594529 | 2 |
| #10594009 | 2 |
| #10594007 | 2 |
| #10593972 | 2 |
| #86715 | 3 |