Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
11997 conjugacy classes of subgroups.
The subgroup lattice has 504 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10596758 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#5966 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10596695 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #10596694 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | D3×#1010 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #10596679 | C2 | 1 | 9 | yes | maximal, complemented |
| 7 | #10596678 | C2 | 1 | 18 | yes | maximal, complemented |
| 8 | C2×#64309 | C2 | 1 | 9 | yes | maximal, complemented |
| 9 | #87572 | — | 3 | 2 | no | maximal |
| 10 | C32×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #64367 | C22 | 1 | 6 | yes | complemented |
| 12 | #41×C3⋊D3 | C22 | 1 | 6 | yes | complemented |
| 13 | #64361 | C22 | 1 | 9 | yes | complemented |
| 14 | C2×#3830 | C22 | 1 | 9 | yes | complemented |
| 15 | C3×#1010 | C22 | 1 | 12 | yes | complemented |
| 16 | C3×D3×#41 | C22 | 1 | 12 | yes | complemented |
| 17 | C3×#1004 | C22 | 1 | 18 | yes | complemented |
| 18 | C2×C3×#237 | C22 | 1 | 18 | yes | complemented |
| 19 | #64330 | C22 | 1 | 36 | yes | complemented |
| 20 | C22×#627 | C22 | 1 | 6 | yes | complemented |
| 21 | C2×#3805 | C22 | 1 | 18 | yes | complemented |
| 22 | C2×#3804 | C22 | 1 | 36 | yes | complemented |
| 23 | #64320 | C22 | 1 | 2 | yes | complemented |
| 24 | D32×Q8 | C22 | 1 | 12 | yes | complemented |
| 25 | #64316 | C22 | 1 | 6 | yes | complemented |
| 26 | #64315 | C22 | 1 | 12 | yes | complemented |
| 27 | #64314 | C22 | 1 | 36 | yes | complemented |
| 28 | #64313 | C22 | 1 | 18 | yes | complemented |
| 29 | #64312 | C22 | 1 | 36 | yes | complemented |
| 30 | D3×#237 | C22 | 1 | 72 | yes | complemented |
| 31 | #64309 | C22 | 1 | 18 | yes | complemented |
| 32 | #64309 | C22 | 1 | 72 | yes | complemented |
| 33 | #64309 | C22 | 1 | 36 | yes | complemented |
| 34 | #64306 | C22 | 1 | 18 | yes | complemented |
| 35 | D3×#235 | C22 | 1 | 36 | yes | complemented |
| 36 | C2×#3798 | C22 | 1 | 9 | yes | complemented |
| 37 | C2×#3797 | C22 | 1 | 9 | yes | complemented |
| 38 | #64298 | C22 | 1 | 18 | yes | complemented |
| 39 | #64297 | C22 | 1 | 36 | yes | complemented |
| 40 | C2×D3×Dic6 | C22 | 1 | 18 | yes | complemented |
| 41 | C3×#585 | — | 3 | 2 | no | — |
| 42 | D3×2−1+4 | — | 3 | 12 | no | — |
| 43 | D3×2−1+4 | — | 3 | 12 | no | — |
| 44 | #5966 | — | 3 | 2 | no | — |
| 45 | #5966 | — | 3 | 18 | no | — |
| 46 | #5966 | — | 3 | 18 | no | — |
| 47 | #5966 | — | 6 | 1 | no | — |
| 48 | #5966 | D3 | 1 | 2 | yes | complemented |
| 49 | #5964 | — | 3 | 12 | no | — |
| 50 | #5964 | — | 3 | 18 | no | — |
| 51 | C2×#1010 | — | 3 | 12 | no | — |
| 52 | C2×#1010 | — | 3 | 18 | no | — |
| 53 | C32×#41 | C23 | 1 | 6 | yes | — |
| 54 | C2×C32×D4 | C23 | 1 | 9 | yes | — |
| 55 | C2×#638 | C23 | 1 | 18 | yes | — |
| 56 | C22×C3⋊Dic3 | C23 | 1 | 6 | yes | — |
| 57 | #3832 | C23 | 1 | 2 | yes | — |
| 58 | Q8×C3⋊D3 | C23 | 1 | 6 | yes | — |
| 59 | #3830 | C23 | 1 | 18 | yes | — |
| 60 | #3830 | C23 | 1 | 36 | yes | — |
| 61 | D4×C3⋊D3 | C23 | 1 | 18 | yes | — |
| 62 | #3828 | C23 | 1 | 18 | yes | — |
| 63 | C2×C4×C3⋊D3 | C23 | 1 | 9 | yes | — |
| 64 | C2×#634 | C23 | 1 | 9 | yes | — |
| 65 | C2×C3×#67 | C23 | 1 | 36 | yes | — |
| 66 | C22×C3×Dic3 | C23 | 1 | 12 | yes | — |
| 67 | C3×#239 | C23 | 1 | 4 | yes | — |
| 68 | C3×D3×Q8 | C23 | 1 | 12 | yes | — |
| 69 | C3×#237 | C23 | 1 | 36 | yes | — |
| 70 | C3×#237 | C23 | 1 | 72 | yes | — |
| 71 | C3×D3×D4 | C23 | 1 | 36 | yes | — |
| 72 | C3×#235 | C23 | 1 | 36 | yes | — |
| 73 | C2×C3×C4×D3 | C23 | 1 | 18 | yes | — |
| 74 | C2×C3×Dic6 | C23 | 1 | 18 | yes | — |
| 75 | #3811 | C23 | 1 | 36 | yes | — |
| 76 | D3×#67 | C23 | 1 | 72 | yes | — |
| 77 | C2×#627 | C23 | 1 | 36 | yes | — |
| 78 | C2×#627 | C23 | 1 | 18 | yes | — |
| 79 | C2×#627 | C23 | 1 | 9 | yes | — |
| 80 | C2×#626 | C23 | 1 | 18 | yes | — |
| 81 | C2×#625 | C23 | 1 | 9 | yes | — |
| 82 | C2×#624 | C23 | 1 | 18 | yes | — |
| 83 | #3805 | C23 | 1 | 72 | yes | — |
| 84 | #3805 | C23 | 1 | 36 | yes | — |
| 85 | #3804 | C23 | 1 | 144 | yes | — |
| 86 | #3804 | C23 | 1 | 72 | yes | — |
| 87 | C2×D3×Dic3 | C23 | 1 | 36 | yes | — |
| 88 | #3802 | C23 | 1 | 6 | yes | — |
| 89 | D3×D12 | C23 | 1 | 12 | yes | — |
| 90 | C4×D32 | C23 | 1 | 36 | yes | — |
| 91 | #3799 | C23 | 1 | 36 | yes | — |
| 92 | #3798 | C23 | 1 | 6 | yes | — |
| 93 | #3798 | C23 | 1 | 36 | yes | — |
| 94 | #3798 | C23 | 1 | 18 | yes | — |
| 95 | #3797 | C23 | 1 | 36 | yes | — |
| 96 | #3797 | C23 | 1 | 18 | yes | — |
| 97 | #3796 | C23 | 1 | 36 | yes | — |
| 98 | #3795 | C23 | 1 | 36 | yes | — |
| 99 | D3×Dic6 | C23 | 1 | 36 | yes | — |
| 100 | D3×Dic6 | C23 | 1 | 72 | yes | — |
| 101 | 2−1+6 | — | 9 | 1 | no | Sylow |
| 102 | C3×2−1+4 | — | 3 | 12 | no | — |
| 103 | C3×H(5,𝔽2) | — | 2 | 1 | no | — |
| 104 | C3×H(5,𝔽2) | — | 3 | 18 | no | — |
| 105 | C3×H(5,𝔽2) | C2×D3 | 1 | 2 | yes | complemented |
| 106 | C2×C3×#41 | — | 3 | 12 | no | — |
| 107 | C2×C3×#41 | — | 3 | 18 | no | — |
| 108 | #1010 | — | 3 | 12 | no | — |
| 109 | #1010 | — | 3 | 12 | no | — |
| 110 | #1010 | — | 3 | 72 | no | — |
| 111 | #1010 | — | 3 | 36 | no | — |
| 112 | #1010 | — | 3 | 72 | no | — |
| 113 | #1010 | — | 3 | 72 | no | — |
| 114 | #1010 | — | 3 | 36 | no | — |
| 115 | #1010 | — | 3 | 36 | no | — |
| 116 | #1010 | — | 6 | 6 | no | — |
| 117 | #1010 | C2×D3 | 1 | 12 | yes | complemented |
| 118 | #1009 | — | 3 | 4 | no | — |
| 119 | #1009 | — | 3 | 36 | no | — |
| 120 | D3×#41 | — | 3 | 12 | no | — |
| 121 | D3×#41 | — | 3 | 72 | no | — |
| 122 | D3×#41 | — | 3 | 72 | no | — |
| 123 | D3×#41 | — | 3 | 36 | no | — |
| 124 | D3×#41 | — | 3 | 36 | no | — |
| 125 | D3×#41 | — | 6 | 6 | no | — |
| 126 | D3×#41 | C2×D3 | 1 | 12 | yes | complemented |
| 127 | #1007 | — | 3 | 12 | no | — |
| 128 | #1007 | — | 3 | 12 | no | — |
| 129 | #1007 | — | 3 | 36 | no | — |
| 130 | C2×D3×Q8 | — | 3 | 24 | no | — |
| 131 | C2×D3×Q8 | — | 3 | 18 | no | — |
| 132 | C2×D3×Q8 | — | 3 | 18 | no | — |
| 133 | #1004 | — | 3 | 18 | no | — |
| 134 | #1004 | — | 3 | 72 | no | — |
| 135 | #1004 | — | 3 | 36 | no | — |
| 136 | #1004 | — | 3 | 36 | no | — |
| 137 | #1004 | — | 6 | 9 | no | — |
| 138 | #1004 | C2×D3 | 1 | 18 | yes | complemented |
| 139 | C2×#237 | — | 3 | 18 | no | — |
| 140 | C2×#237 | — | 3 | 36 | no | — |
| 141 | C2×#237 | — | 3 | 36 | no | — |
| 142 | C2×#237 | — | 3 | 72 | no | — |
| 143 | C2×#237 | — | 6 | 9 | no | — |
| 144 | C2×#237 | C2×D3 | 1 | 18 | yes | complemented |
| 145 | C2×#235 | — | 3 | 36 | no | — |
| 146 | C2×#235 | — | 3 | 36 | no | — |
| 147 | C2×#235 | — | 3 | 18 | no | — |
| 148 | C22×Dic6 | — | 3 | 12 | no | — |
| 149 | C22×Dic6 | — | 3 | 18 | no | — |
| 150 | C23×C32 | C24 | 1 | 6 | yes | — |
| 151 | C22×C3⋊D3 | C24 | 1 | 9 | yes | — |
| 152 | C22×C3×D3 | C24 | 1 | 18 | yes | — |
| 153 | C2×D32 | C24 | 1 | 12 | yes | — |
| 154 | C32×Q8 | C24 | 1 | 2 | yes | — |
| 155 | C32×D4 | C24 | 1 | 18 | yes | — |
| 156 | C2×C32×C4 | C24 | 1 | 9 | yes | — |
| 157 | #638 | C24 | 1 | 36 | yes | — |
| 158 | C2×C3⋊Dic3 | C24 | 1 | 18 | yes | — |
| 159 | C2×C3⋊Dic3 | C24 | 1 | 9 | yes | — |
| 160 | C4⋊(C3⋊D3) | C24 | 1 | 6 | yes | — |
| 161 | C4×C3⋊D3 | C24 | 1 | 18 | yes | — |
| 162 | C4×C3⋊D3 | C24 | 1 | 6 | yes | — |
| 163 | #634 | C24 | 1 | 18 | yes | — |
| 164 | C3×#67 | C24 | 1 | 72 | yes | — |
| 165 | C2×C3×Dic3 | C24 | 1 | 36 | yes | — |
| 166 | C2×C3×Dic3 | C24 | 1 | 18 | yes | — |
| 167 | C3×D12 | C24 | 1 | 12 | yes | — |
| 168 | C3×C4×D3 | C24 | 1 | 12 | yes | — |
| 169 | C3×C4×D3 | C24 | 1 | 36 | yes | — |
| 170 | C3×Dic6 | C24 | 1 | 36 | yes | — |
| 171 | #627 | C24 | 1 | 36 | yes | — |
| 172 | #627 | C24 | 1 | 18 | yes | — |
| 173 | #627 | C24 | 1 | 9 | yes | — |
| 174 | #627 | C24 | 1 | 1 | yes | characteristic |
| 175 | #626 | C24 | 1 | 36 | yes | — |
| 176 | #626 | C24 | 1 | 12 | yes | — |
| 177 | #625 | C24 | 1 | 18 | yes | — |
| 178 | #625 | C24 | 1 | 6 | yes | — |
| 179 | #624 | C24 | 1 | 36 | yes | — |
| 180 | D3×Dic3 | C24 | 1 | 72 | yes | — |
| 181 | #585 | — | 3 | 2 | no | — |
| 182 | #585 | — | 9 | 6 | no | — |
| 183 | #585 | — | 9 | 18 | no | — |
| 184 | #585 | — | 9 | 9 | no | — |
| 185 | #585 | — | 9 | 1 | no | — |
| 186 | C2×2−1+4 | — | 9 | 9 | no | — |
| 187 | C2×2−1+4 | — | 9 | 12 | no | — |
| 188 | C2×2−1+4 | — | 9 | 6 | no | — |
| 189 | C3×#41 | — | 2 | 6 | no | — |
| 190 | C3×#41 | — | 3 | 4 | no | — |
| 191 | C3×#41 | — | 3 | 72 | no | — |
| 192 | C3×#41 | — | 3 | 36 | no | — |
| 193 | C3×#41 | — | 3 | 36 | no | — |
| 194 | C3×#41 | C22×D3 | 1 | 12 | yes | — |
| 195 | C2×C3×Q8 | — | 3 | 12 | no | — |
| 196 | C2×C3×Q8 | — | 3 | 18 | no | — |
| 197 | C2×C3×D4 | — | 2 | 9 | no | — |
| 198 | C2×C3×D4 | — | 3 | 36 | no | — |
| 199 | C2×C3×D4 | — | 3 | 36 | no | — |
| 200 | C2×C3×D4 | C22×D3 | 1 | 18 | yes | — |
| 201 | C22×C3×C4 | — | 3 | 12 | no | — |
| 202 | C22×C3×C4 | — | 3 | 18 | no | — |
| 203 | C2×#67 | — | 3 | 36 | no | — |
| 204 | C2×#67 | — | 3 | 18 | no | — |
| 205 | C2×#67 | — | 3 | 72 | no | — |
| 206 | C2×#67 | — | 3 | 18 | no | — |
| 207 | C2×#67 | — | 6 | 18 | no | — |
| 208 | C2×#67 | C22×D3 | 1 | 36 | yes | — |
| 209 | C22×Dic3 | — | 3 | 12 | no | — |
| 210 | C22×Dic3 | — | 3 | 36 | no | — |
| 211 | C22×Dic3 | — | 6 | 6 | no | — |
| 212 | C22×Dic3 | C22×D3 | 1 | 12 | yes | — |
| 213 | #239 | — | 3 | 4 | no | — |
| 214 | #239 | — | 3 | 36 | no | — |
| 215 | #239 | — | 3 | 36 | no | — |
| 216 | #239 | — | 6 | 2 | no | — |
| 217 | #239 | C22×D3 | 1 | 4 | yes | — |
| 218 | D3×Q8 | — | 3 | 12 | no | — |
| 219 | D3×Q8 | — | 3 | 72 | no | — |
| 220 | D3×Q8 | — | 3 | 36 | no | — |
| 221 | D3×Q8 | — | 3 | 72 | no | — |
| 222 | D3×Q8 | — | 3 | 36 | no | — |
| 223 | D3×Q8 | — | 6 | 6 | no | — |
| 224 | D3×Q8 | C22×D3 | 1 | 12 | yes | — |
| 225 | #237 | — | 3 | 36 | no | — |
| 226 | #237 | — | 3 | 72 | no | — |
| 227 | #237 | — | 3 | 144 | no | — |
| 228 | #237 | — | 3 | 72 | no | — |
| 229 | #237 | — | 3 | 72 | no | — |
| 230 | #237 | — | 3 | 144 | no | — |
| 231 | #237 | — | 3 | 36 | no | — |
| 232 | #237 | — | 3 | 36 | no | — |
| 233 | #237 | — | 6 | 18 | no | — |
| 234 | #237 | — | 6 | 36 | no | — |
| 235 | #237 | C22×D3 | 1 | 72 | yes | — |
| 236 | #237 | C22×D3 | 1 | 36 | yes | — |
| 237 | D3×D4 | — | 3 | 72 | no | — |
| 238 | D3×D4 | — | 3 | 36 | no | — |
| 239 | D3×D4 | — | 3 | 72 | no | — |
| 240 | D3×D4 | — | 3 | 12 | no | — |
| 241 | D3×D4 | — | 3 | 12 | no | — |
| 242 | D3×D4 | — | 6 | 18 | no | — |
| 243 | D3×D4 | C22×D3 | 1 | 36 | yes | — |
| 244 | #235 | — | 3 | 36 | no | — |
| 245 | #235 | — | 3 | 72 | no | — |
| 246 | #235 | — | 3 | 144 | no | — |
| 247 | #235 | — | 3 | 36 | no | — |
| 248 | #235 | — | 3 | 36 | no | — |
| 249 | #235 | — | 3 | 12 | no | — |
| 250 | #235 | — | 3 | 36 | no | — |
| 251 | #235 | — | 3 | 36 | no | — |
| 252 | #235 | — | 3 | 36 | no | — |
| 253 | #235 | — | 6 | 18 | no | — |
| 254 | #235 | C22×D3 | 1 | 36 | yes | — |
| 255 | C2×D12 | — | 3 | 18 | no | — |
| 256 | C2×D12 | — | 3 | 12 | no | — |
| 257 | C2×C4×D3 | — | 3 | 36 | no | — |
| 258 | C2×C4×D3 | — | 3 | 18 | no | — |
| 259 | C2×C4×D3 | — | 3 | 36 | no | — |
| 260 | C2×C4×D3 | — | 3 | 72 | no | — |
| 261 | C2×C4×D3 | — | 6 | 9 | no | — |
| 262 | C2×C4×D3 | C22×D3 | 1 | 18 | yes | — |
| 263 | C2×Dic6 | — | 3 | 18 | no | — |
| 264 | C2×Dic6 | — | 3 | 18 | no | — |
| 265 | C2×Dic6 | — | 3 | 36 | no | — |
| 266 | C2×Dic6 | — | 3 | 36 | no | — |
| 267 | C2×Dic6 | — | 3 | 36 | no | — |
| 268 | C2×Dic6 | — | 3 | 36 | no | — |
| 269 | C2×Dic6 | — | 3 | 72 | no | — |
| 270 | C2×Dic6 | — | 6 | 9 | no | — |
| 271 | C2×Dic6 | C22×D3 | 1 | 18 | yes | — |
| 272 | C22×C32 | — | 4 | 6 | no | — |
| 273 | C22×C32 | C25 | 1 | 9 | yes | — |
| 274 | C2×C3⋊D3 | — | 4 | 9 | no | — |
| 275 | C2×C3⋊D3 | C25 | 1 | 6 | yes | — |
| 276 | C2×C3×D3 | — | 4 | 18 | no | — |
| 277 | C2×C3×D3 | C25 | 1 | 12 | yes | — |
| 278 | D32 | — | 4 | 12 | no | — |
| 279 | C32×C4 | C25 | 1 | 6 | yes | — |
| 280 | C3⋊Dic3 | C25 | 1 | 9 | yes | — |
| 281 | C3⋊Dic3 | C25 | 1 | 1 | yes | characteristic |
| 282 | C3×Dic3 | C25 | 1 | 18 | yes | — |
| 283 | C3×Dic3 | C25 | 1 | 2 | yes | — |
| 284 | 2−1+4 | — | 3 | 12 | no | — |
| 285 | 2−1+4 | — | 9 | 6 | no | — |
| 286 | 2−1+4 | — | 9 | 12 | no | — |
| 287 | 2−1+4 | — | 9 | 36 | no | — |
| 288 | 2−1+4 | — | 9 | 18 | no | — |
| 289 | 2−1+4 | — | 9 | 72 | no | — |
| 290 | 2−1+4 | — | 9 | 36 | no | — |
| 291 | 2−1+4 | — | 9 | 18 | no | — |
| 292 | 2−1+4 | — | 9 | 6 | no | — |
| 293 | H(5,𝔽2) | — | 3 | 18 | no | — |
| 294 | H(5,𝔽2) | — | 9 | 36 | no | — |
| 295 | H(5,𝔽2) | — | 9 | 18 | no | — |
| 296 | H(5,𝔽2) | — | 9 | 36 | no | — |
| 297 | H(5,𝔽2) | — | 9 | 2 | no | — |
| 298 | H(5,𝔽2) | — | 9 | 9 | no | — |
| 299 | H(5,𝔽2) | D32 | 1 | 1 | yes | characteristic, complemented |
| 300 | C2×#41 | — | 3 | 12 | no | — |
| 301 | C2×#41 | — | 3 | 18 | no | — |
| 302 | C2×#41 | — | 9 | 9 | no | — |
| 303 | C2×#41 | — | 9 | 36 | no | — |
| 304 | C2×#41 | — | 9 | 36 | no | — |
| 305 | C2×#41 | — | 9 | 18 | no | — |
| 306 | C2×#41 | — | 9 | 72 | no | — |
| 307 | C2×#41 | — | 9 | 36 | no | — |
| 308 | C2×#41 | — | 9 | 18 | no | — |
| 309 | C2×#41 | — | 9 | 6 | no | — |
| 310 | C2×#41 | — | 9 | 9 | no | — |
| 311 | C22×Q8 | — | 9 | 6 | no | — |
| 312 | C22×Q8 | — | 9 | 18 | no | — |
| 313 | C22×Q8 | — | 9 | 12 | no | — |
| 314 | C22×Q8 | — | 9 | 9 | no | — |
| 315 | C23×C3 | — | 2 | 6 | no | — |
| 316 | C23×C3 | — | 3 | 18 | no | — |
| 317 | C23×C3 | C23×D3 | 1 | 12 | yes | — |
| 318 | C22×D3 | — | 3 | 18 | no | — |
| 319 | C22×D3 | — | 3 | 24 | no | — |
| 320 | C22×D3 | — | 6 | 9 | no | — |
| 321 | C22×D3 | C23×D3 | 1 | 18 | yes | — |
| 322 | C3×Q8 | — | 2 | 2 | no | — |
| 323 | C3×Q8 | — | 3 | 36 | no | — |
| 324 | C3×Q8 | C23×D3 | 1 | 4 | yes | — |
| 325 | C3×D4 | — | 2 | 18 | no | — |
| 326 | C3×D4 | — | 3 | 72 | no | — |
| 327 | C3×D4 | — | 3 | 12 | no | — |
| 328 | C3×D4 | C23×D3 | 1 | 36 | yes | — |
| 329 | C2×C3×C4 | — | 2 | 9 | no | — |
| 330 | C2×C3×C4 | — | 3 | 18 | no | — |
| 331 | C2×C3×C4 | — | 3 | 36 | no | — |
| 332 | C2×C3×C4 | — | 3 | 12 | no | — |
| 333 | C2×C3×C4 | — | 3 | 36 | no | — |
| 334 | C2×C3×C4 | C23×D3 | 1 | 18 | yes | — |
| 335 | #67 | — | 3 | 72 | no | — |
| 336 | #67 | — | 3 | 36 | no | — |
| 337 | #67 | — | 3 | 12 | no | — |
| 338 | #67 | — | 3 | 12 | no | — |
| 339 | #67 | — | 3 | 36 | no | — |
| 340 | #67 | — | 6 | 36 | no | — |
| 341 | #67 | C23×D3 | 1 | 72 | yes | — |
| 342 | C2×Dic3 | — | 3 | 36 | no | — |
| 343 | C2×Dic3 | — | 3 | 18 | no | — |
| 344 | C2×Dic3 | — | 3 | 72 | no | — |
| 345 | C2×Dic3 | — | 6 | 18 | no | — |
| 346 | C2×Dic3 | — | 6 | 9 | no | — |
| 347 | C2×Dic3 | C23×D3 | 1 | 18 | yes | — |
| 348 | C2×Dic3 | C23×D3 | 1 | 36 | yes | — |
| 349 | D12 | — | 3 | 12 | no | — |
| 350 | D12 | — | 3 | 36 | no | — |
| 351 | D12 | — | 3 | 12 | no | — |
| 352 | D12 | — | 6 | 6 | no | — |
| 353 | D12 | C23×D3 | 1 | 12 | yes | — |
| 354 | C4×D3 | — | 3 | 72 | no | — |
| 355 | C4×D3 | — | 3 | 36 | no | — |
| 356 | C4×D3 | — | 3 | 12 | no | — |
| 357 | C4×D3 | — | 3 | 72 | no | — |
| 358 | C4×D3 | — | 6 | 6 | no | — |
| 359 | C4×D3 | — | 6 | 18 | no | — |
| 360 | C4×D3 | C23×D3 | 1 | 36 | yes | — |
| 361 | C4×D3 | C23×D3 | 1 | 12 | yes | — |
| 362 | Dic6 | — | 3 | 36 | no | — |
| 363 | Dic6 | — | 3 | 2 | no | — |
| 364 | Dic6 | — | 3 | 18 | no | — |
| 365 | Dic6 | — | 3 | 18 | no | — |
| 366 | Dic6 | — | 3 | 72 | no | — |
| 367 | Dic6 | — | 3 | 18 | no | — |
| 368 | Dic6 | — | 6 | 18 | no | — |
| 369 | Dic6 | C23×D3 | 1 | 36 | yes | — |
| 370 | C2×C32 | — | 2 | 9 | no | — |
| 371 | C2×C32 | C26 | 1 | 1 | yes | characteristic |
| 372 | C3⋊D3 | — | 2 | 6 | no | — |
| 373 | C3×D3 | — | 2 | 12 | no | — |
| 374 | #41 | — | 3 | 4 | no | — |
| 375 | #41 | — | 3 | 36 | no | — |
| 376 | #41 | — | 3 | 72 | no | — |
| 377 | #41 | — | 3 | 36 | no | — |
| 378 | #41 | — | 9 | 6 | no | — |
| 379 | #41 | — | 9 | 36 | no | — |
| 380 | #41 | — | 9 | 18 | no | — |
| 381 | #41 | — | 9 | 72 | no | — |
| 382 | #41 | — | 9 | 144 | no | — |
| 383 | #41 | — | 9 | 36 | no | — |
| 384 | #41 | — | 9 | 36 | no | — |
| 385 | #41 | — | 9 | 36 | no | — |
| 386 | #41 | — | 9 | 72 | no | — |
| 387 | #41 | — | 9 | 36 | no | — |
| 388 | #41 | — | 9 | 2 | no | — |
| 389 | #41 | — | 9 | 36 | no | — |
| 390 | #41 | — | 9 | 18 | no | — |
| 391 | #41 | — | 9 | 18 | no | — |
| 392 | #41 | C2×D32 | 1 | 6 | yes | — |
| 393 | C2×Q8 | — | 3 | 12 | no | — |
| 394 | C2×Q8 | — | 3 | 18 | no | — |
| 395 | C2×Q8 | — | 9 | 9 | no | — |
| 396 | C2×Q8 | — | 9 | 36 | no | — |
| 397 | C2×Q8 | — | 9 | 18 | no | — |
| 398 | C2×Q8 | — | 9 | 36 | no | — |
| 399 | C2×Q8 | — | 9 | 72 | no | — |
| 400 | C2×Q8 | — | 9 | 18 | no | — |
| 401 | C2×Q8 | — | 9 | 36 | no | — |
| 402 | C2×Q8 | — | 9 | 6 | no | — |
| 403 | C2×Q8 | — | 9 | 9 | no | — |
| 404 | C2×D4 | — | 3 | 36 | no | — |
| 405 | C2×D4 | — | 3 | 36 | no | — |
| 406 | C2×D4 | — | 9 | 12 | no | — |
| 407 | C2×D4 | — | 9 | 18 | no | — |
| 408 | C2×D4 | — | 9 | 36 | no | — |
| 409 | C2×D4 | — | 9 | 6 | no | — |
| 410 | C2×D4 | — | 9 | 72 | no | — |
| 411 | C2×D4 | — | 9 | 9 | no | — |
| 412 | C2×D4 | — | 9 | 18 | no | — |
| 413 | C2×D4 | — | 9 | 18 | no | — |
| 414 | C2×D4 | C2×D32 | 1 | 9 | yes | — |
| 415 | C22×C4 | — | 3 | 12 | no | — |
| 416 | C22×C4 | — | 3 | 18 | no | — |
| 417 | C22×C4 | — | 9 | 18 | no | — |
| 418 | C22×C4 | — | 9 | 36 | no | — |
| 419 | C22×C4 | — | 9 | 36 | no | — |
| 420 | C22×C4 | — | 9 | 6 | no | — |
| 421 | C22×C4 | — | 9 | 9 | no | — |
| 422 | C22×C3 | — | 2 | 9 | no | — |
| 423 | C22×C3 | — | 3 | 12 | no | — |
| 424 | C22×C3 | — | 4 | 12 | no | — |
| 425 | C22×C3 | — | 8 | 6 | no | — |
| 426 | C22×C3 | — | 12 | 18 | no | — |
| 427 | C22×C3 | C24×D3 | 1 | 18 | yes | — |
| 428 | C2×D3 | — | 3 | 12 | no | — |
| 429 | C2×D3 | — | 4 | 18 | no | — |
| 430 | C2×D3 | — | 6 | 6 | no | — |
| 431 | C2×D3 | — | 12 | 24 | no | — |
| 432 | C2×D3 | — | 12 | 18 | no | — |
| 433 | C2×D3 | — | 24 | 9 | no | — |
| 434 | C2×D3 | C24×D3 | 1 | 12 | yes | — |
| 435 | C3×C4 | — | 2 | 6 | no | — |
| 436 | C3×C4 | — | 3 | 2 | no | — |
| 437 | C3×C4 | — | 3 | 18 | no | — |
| 438 | C3×C4 | C24×D3 | 1 | 12 | yes | — |
| 439 | Dic3 | — | 3 | 18 | no | — |
| 440 | Dic3 | — | 3 | 2 | no | — |
| 441 | Dic3 | — | 6 | 9 | no | — |
| 442 | Dic3 | — | 6 | 1 | no | — |
| 443 | Dic3 | C24×D3 | 1 | 2 | yes | — |
| 444 | Dic3 | C24×D3 | 1 | 18 | yes | — |
| 445 | C32 | 2−1+6 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 446 | C23 | — | 3 | 18 | no | — |
| 447 | C23 | — | 9 | 12 | no | — |
| 448 | C23 | — | 9 | 9 | no | — |
| 449 | C23 | C22×D32 | 1 | 6 | yes | — |
| 450 | Q8 | — | 3 | 36 | no | — |
| 451 | Q8 | — | 9 | 1 | no | — |
| 452 | Q8 | — | 9 | 18 | no | — |
| 453 | Q8 | — | 9 | 9 | no | — |
| 454 | Q8 | — | 9 | 36 | no | — |
| 455 | Q8 | — | 9 | 18 | no | — |
| 456 | Q8 | C22×D32 | 1 | 2 | yes | — |
| 457 | D4 | — | 3 | 72 | no | — |
| 458 | D4 | — | 3 | 12 | no | — |
| 459 | D4 | — | 9 | 12 | no | — |
| 460 | D4 | — | 9 | 36 | no | — |
| 461 | D4 | — | 9 | 6 | no | — |
| 462 | D4 | — | 9 | 18 | no | — |
| 463 | D4 | — | 9 | 36 | no | — |
| 464 | D4 | — | 9 | 6 | no | — |
| 465 | D4 | C22×D32 | 1 | 18 | yes | — |
| 466 | C2×C4 | — | 3 | 18 | no | — |
| 467 | C2×C4 | — | 3 | 36 | no | — |
| 468 | C2×C4 | — | 3 | 12 | no | — |
| 469 | C2×C4 | — | 3 | 36 | no | — |
| 470 | C2×C4 | — | 9 | 36 | no | — |
| 471 | C2×C4 | — | 9 | 72 | no | — |
| 472 | C2×C4 | — | 9 | 18 | no | — |
| 473 | C2×C4 | — | 9 | 9 | no | — |
| 474 | C2×C4 | — | 9 | 18 | no | — |
| 475 | C2×C4 | — | 9 | 6 | no | — |
| 476 | C2×C4 | C22×D32 | 1 | 9 | yes | — |
| 477 | C2×C3 | — | 2 | 18 | no | — |
| 478 | C2×C3 | — | 2 | 1 | no | — |
| 479 | C2×C3 | — | 4 | 9 | no | — |
| 480 | C2×C3 | — | 6 | 12 | no | — |
| 481 | C2×C3 | C25×D3 | 1 | 2 | yes | — |
| 482 | D3 | — | 2 | 12 | no | — |
| 483 | D3 | — | 6 | 12 | no | — |
| 484 | D3 | — | 12 | 6 | no | — |
| 485 | C22 | — | 3 | 12 | no | — |
| 486 | C22 | — | 4 | 6 | no | — |
| 487 | C22 | — | 9 | 6 | no | — |
| 488 | C22 | — | 12 | 18 | no | — |
| 489 | C22 | — | 36 | 9 | no | — |
| 490 | C22 | — | 36 | 12 | no | — |
| 491 | C22 | C23×D32 | 1 | 9 | yes | — |
| 492 | C4 | — | 3 | 2 | no | — |
| 493 | C4 | — | 3 | 18 | no | — |
| 494 | C4 | — | 9 | 9 | no | — |
| 495 | C4 | — | 9 | 1 | no | — |
| 496 | C4 | C23×D32 | 1 | 6 | yes | — |
| 497 | C3 | — | 2 | 1 | no | — |
| 498 | C3 | #87572 | 1 | 2 | yes | complemented |
| 499 | C2 | — | 2 | 9 | no | — |
| 500 | C2 | — | 6 | 12 | no | — |
| 501 | C2 | — | 18 | 6 | no | — |
| 502 | C2 | C24×D32 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D32 |
| commutator, socle, cosocle | C2×C32 | C26 |
| Fitting | C32×H(5,𝔽2) | C22 |
| hypercenter | H(5,𝔽2) | D32 |
| hypocenter | C32 | 2−1+6 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596758 | C2 | semidirect |
| 2. C3×#5966 | C2 | semidirect |
| 3. #10596695 | C2 | semidirect |
| 4. #10596694 | C2 | semidirect |
| 5. D3×#1010 | C2 | semidirect |
| 6. #10596679 | C2 | semidirect |
| 7. #10596678 | C2 | semidirect |
| 8. C2×#64309 | C2 | semidirect |
| 10. C32×H(5,𝔽2) | C22 | semidirect |
| 11. #64367 | C22 | semidirect |
| 12. #41×C3⋊D3 | C22 | semidirect |
| 13. #64361 | C22 | semidirect |
| 14. C2×#3830 | C22 | semidirect |
| 15. C3×#1010 | C22 | semidirect |
| 16. C3×D3×#41 | C22 | semidirect |
| 17. C3×#1004 | C22 | semidirect |
| 18. C2×C3×#237 | C22 | semidirect |
| 19. #64330 | C22 | semidirect |
| 20. C22×#627 | C22 | semidirect |
| 21. C2×#3805 | C22 | semidirect |
| 22. C2×#3804 | C22 | semidirect |
| 23. #64320 | C22 | semidirect |
| 24. D32×Q8 | C22 | semidirect |
| 25. #64316 | C22 | semidirect |
| 26. #64315 | C22 | semidirect |
| 27. #64314 | C22 | semidirect |
| 28. #64313 | C22 | semidirect |
| 29. #64312 | C22 | semidirect |
| 30. D3×#237 | C22 | semidirect |
| 31. #64309 | C22 | semidirect |
| 32. #64309 | C22 | semidirect |
| 33. #64309 | C22 | semidirect |
| 34. #64306 | C22 | semidirect |
| 35. D3×#235 | C22 | semidirect |
| 36. C2×#3798 | C22 | semidirect |
| 37. C2×#3797 | C22 | semidirect |
| 38. #64298 | C22 | semidirect |
| 39. #64297 | C22 | semidirect |
| 40. C2×D3×Dic6 | C22 | semidirect |
| 48. #5966 | D3 | semidirect |
| 105. C3×H(5,𝔽2) | C2×D3 | semidirect |
| 117. #1010 | C2×D3 | semidirect |
| 126. D3×#41 | C2×D3 | semidirect |
| 138. #1004 | C2×D3 | semidirect |
| 144. C2×#237 | C2×D3 | semidirect |
| 299. H(5,𝔽2) | D32 | semidirect |
| 445. C32 | 2−1+6 | semidirect |
| 498. C3 | #87572 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596758 | 2 |
| C3×#5966 | 2 |
| #10596695 | 2 |
| #10596694 | 2 |
| D3×#1010 | 2 |
| #10596679 | 2 |
| #10596678 | 2 |
| C2×#64309 | 2 |
| #87572 | 3 |