Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2306 conjugacy classes of subgroups.
The subgroup lattice has 536 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10596694 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10596692 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10596647 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10596521 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #10596515 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #10596505 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×#64227 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #10596501 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #10596500 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #41×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 11 | C3×#1010 | — | 2 | 1 | no | — |
| 12 | C3×#1009 | — | 2 | 1 | no | — |
| 13 | #64320 | C22 | 1 | 2 | yes | complemented |
| 14 | #64319 | — | 2 | 1 | no | — |
| 15 | D32×Q8 | — | 2 | 1 | no | — |
| 16 | #64316 | C22 | 1 | 2 | yes | complemented |
| 17 | #64313 | C22 | 1 | 6 | yes | complemented |
| 18 | #64312 | — | 2 | 3 | no | — |
| 19 | D32×D4 | — | 2 | 3 | no | — |
| 20 | #64309 | C22 | 1 | 6 | yes | complemented |
| 21 | #64307 | — | 2 | 3 | no | — |
| 22 | #64306 | C22 | 1 | 3 | yes | — |
| 23 | #64306 | C22 | 1 | 3 | yes | complemented |
| 24 | C2×#3802 | C22 | 1 | 3 | yes | — |
| 25 | C2×#3797 | C22 | 1 | 3 | yes | complemented |
| 26 | #64297 | — | 2 | 3 | no | — |
| 27 | #64289 | C22 | 1 | 2 | yes | complemented |
| 28 | #64287 | C22 | 1 | 6 | yes | complemented |
| 29 | #64283 | C22 | 1 | 3 | yes | complemented |
| 30 | C2×#3787 | C22 | 1 | 3 | yes | complemented |
| 31 | #64239 | C22 | 1 | 12 | yes | complemented |
| 32 | C2×#3775 | C22 | 1 | 12 | yes | complemented |
| 33 | #64237 | C22 | 1 | 12 | yes | complemented |
| 34 | #64236 | C22 | 1 | 12 | yes | complemented |
| 35 | #64228 | C22 | 1 | 3 | yes | complemented |
| 36 | #64227 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #64227 | C22 | 1 | 3 | yes | complemented |
| 38 | #64227 | C22 | 1 | 6 | yes | complemented |
| 39 | #64227 | C22 | 1 | 12 | yes | complemented |
| 40 | #64226 | C22 | 1 | 12 | yes | complemented |
| 41 | #64225 | C22 | 1 | 3 | yes | complemented |
| 42 | #64224 | C22 | 1 | 12 | yes | complemented |
| 43 | #64223 | C22 | 1 | 12 | yes | complemented |
| 44 | D3×2−1+4 | — | 6 | 1 | no | — |
| 45 | D3×H(5,𝔽2) | — | 6 | 1 | no | — |
| 46 | C22×D32 | — | 2 | 3 | no | — |
| 47 | C32×#41 | D4 | 1 | 1 | yes | characteristic |
| 48 | #3832 | C23 | 1 | 1 | yes | characteristic |
| 49 | Q8×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 50 | #3830 | C23 | 1 | 3 | yes | — |
| 51 | D4×C3⋊D3 | D4 | 1 | 3 | yes | — |
| 52 | #3828 | D4 | 1 | 3 | yes | — |
| 53 | C2×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 54 | C3×#239 | — | 2 | 2 | no | — |
| 55 | C3×D3×Q8 | — | 2 | 2 | no | — |
| 56 | C3×#237 | — | 2 | 6 | no | — |
| 57 | C3×D3×D4 | — | 2 | 6 | no | — |
| 58 | C3×#235 | — | 2 | 3 | no | — |
| 59 | C3×#235 | — | 2 | 3 | no | — |
| 60 | C2×C3×D12 | — | 2 | 3 | no | — |
| 61 | C2×C3×Dic6 | — | 2 | 3 | no | — |
| 62 | #3811 | — | 2 | 3 | no | — |
| 63 | #3811 | — | 2 | 3 | no | — |
| 64 | D3×#67 | — | 2 | 12 | no | — |
| 65 | C2×#627 | C23 | 1 | 6 | yes | complemented |
| 66 | C2×#625 | C23 | 1 | 6 | yes | — |
| 67 | C2×#624 | — | 2 | 3 | no | — |
| 68 | #3805 | C23 | 1 | 6 | yes | — |
| 69 | #3805 | C23 | 1 | 6 | yes | complemented |
| 70 | #3804 | — | 2 | 12 | no | — |
| 71 | #3802 | — | 2 | 3 | no | — |
| 72 | #3802 | — | 2 | 3 | no | — |
| 73 | #3802 | C23 | 1 | 3 | yes | — |
| 74 | #3802 | C23 | 1 | 6 | yes | — |
| 75 | #3802 | C23 | 1 | 1 | yes | characteristic |
| 76 | D3×D12 | — | 2 | 6 | no | — |
| 77 | C4×D32 | — | 2 | 3 | no | — |
| 78 | C4×D32 | — | 2 | 3 | no | — |
| 79 | #3799 | — | 2 | 6 | no | — |
| 80 | #3798 | C23 | 1 | 6 | yes | — |
| 81 | #3798 | C23 | 1 | 6 | yes | complemented |
| 82 | #3797 | — | 2 | 3 | no | — |
| 83 | #3797 | — | 2 | 3 | no | — |
| 84 | #3797 | C23 | 1 | 3 | yes | — |
| 85 | #3797 | C23 | 1 | 1 | yes | characteristic |
| 86 | #3797 | C23 | 1 | 6 | yes | complemented |
| 87 | #3796 | — | 2 | 3 | no | — |
| 88 | #3796 | — | 2 | 3 | no | — |
| 89 | #3795 | — | 2 | 6 | no | — |
| 90 | D3×Dic6 | — | 2 | 6 | no | — |
| 91 | #3792 | C23 | 1 | 6 | yes | complemented |
| 92 | C2×#622 | C23 | 1 | 6 | yes | complemented |
| 93 | #3788 | C23 | 1 | 6 | yes | complemented |
| 94 | #3787 | C23 | 1 | 1 | yes | characteristic |
| 95 | #3787 | C23 | 1 | 3 | yes | — |
| 96 | #3787 | C23 | 1 | 6 | yes | complemented |
| 97 | #3776 | C23 | 1 | 12 | yes | complemented |
| 98 | #3775 | C23 | 1 | 4 | yes | complemented |
| 99 | #3775 | C23 | 1 | 12 | yes | complemented |
| 100 | #3775 | C23 | 1 | 24 | yes | complemented |
| 101 | #3774 | C23 | 1 | 12 | yes | complemented |
| 102 | C2×#577 | — | 9 | 1 | no | maximal, Sylow |
| 103 | C3×2−1+4 | — | 6 | 1 | no | — |
| 104 | C3×H(5,𝔽2) | — | 6 | 1 | no | — |
| 105 | #1010 | — | 2 | 1 | no | — |
| 106 | #1010 | — | 6 | 6 | no | — |
| 107 | #1010 | — | 6 | 3 | no | — |
| 108 | #1009 | — | 2 | 1 | no | — |
| 109 | #1009 | — | 6 | 2 | no | — |
| 110 | #1009 | — | 6 | 3 | no | — |
| 111 | D3×#41 | — | 6 | 3 | no | — |
| 112 | D3×#41 | — | 6 | 3 | no | — |
| 113 | D3×#41 | — | 6 | 1 | no | — |
| 114 | D3×#41 | — | 6 | 1 | no | — |
| 115 | D3×#41 | — | 6 | 6 | no | — |
| 116 | D3×#41 | — | 6 | 2 | no | — |
| 117 | #1007 | — | 6 | 2 | no | — |
| 118 | #1007 | — | 6 | 3 | no | — |
| 119 | C2×D3×Q8 | — | 6 | 3 | no | — |
| 120 | C2×D3×Q8 | — | 6 | 2 | no | — |
| 121 | #1004 | — | 6 | 6 | no | — |
| 122 | #1004 | — | 6 | 3 | no | — |
| 123 | C2×D3×D4 | — | 6 | 3 | no | — |
| 124 | C2×D3×D4 | — | 6 | 6 | no | — |
| 125 | C22×C3⋊D3 | C2×D4 | 1 | 3 | yes | — |
| 126 | C22×C3×D3 | — | 2 | 6 | no | — |
| 127 | C2×D32 | — | 2 | 3 | no | — |
| 128 | C2×D32 | — | 2 | 1 | no | — |
| 129 | C2×D32 | — | 2 | 6 | no | — |
| 130 | C2×D32 | — | 8 | 6 | no | — |
| 131 | C32×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | C32×D4 | C2×D4 | 1 | 3 | yes | — |
| 133 | C2×C32×C4 | C2×D4 | 1 | 3 | yes | — |
| 134 | #638 | C2×D4 | 1 | 6 | yes | — |
| 135 | C2×C3⋊Dic3 | C24 | 1 | 3 | yes | — |
| 136 | C4⋊(C3⋊D3) | C2×D4 | 1 | 3 | yes | — |
| 137 | C4×C3⋊D3 | C2×D4 | 1 | 3 | yes | — |
| 138 | C4×C3⋊D3 | C2×D4 | 1 | 3 | yes | — |
| 139 | C4×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 140 | C4×C3⋊D3 | C24 | 1 | 3 | yes | — |
| 141 | #634 | C2×D4 | 1 | 3 | yes | — |
| 142 | C3×#67 | — | 2 | 6 | no | — |
| 143 | C3×#67 | — | 2 | 6 | no | — |
| 144 | C2×C3×Dic3 | — | 2 | 6 | no | — |
| 145 | C3×D12 | — | 2 | 6 | no | — |
| 146 | C3×D12 | — | 2 | 1 | no | — |
| 147 | C3×D12 | — | 2 | 3 | no | — |
| 148 | C3×C4×D3 | — | 2 | 6 | no | — |
| 149 | C3×C4×D3 | — | 2 | 6 | no | — |
| 150 | C3×Dic6 | — | 2 | 6 | no | — |
| 151 | C3×Dic6 | — | 2 | 1 | no | — |
| 152 | C3×Dic6 | — | 2 | 3 | no | — |
| 153 | #627 | — | 2 | 6 | no | — |
| 154 | #627 | C24 | 1 | 6 | yes | — |
| 155 | #627 | C24 | 1 | 2 | yes | — |
| 156 | #626 | — | 2 | 6 | no | — |
| 157 | #626 | — | 2 | 6 | no | — |
| 158 | #625 | — | 2 | 6 | no | — |
| 159 | #625 | C24 | 1 | 2 | yes | — |
| 160 | #625 | C24 | 1 | 6 | yes | — |
| 161 | #624 | — | 2 | 3 | no | — |
| 162 | #624 | — | 2 | 6 | no | — |
| 163 | #624 | — | 2 | 1 | no | — |
| 164 | D3×Dic3 | — | 2 | 6 | no | — |
| 165 | D3×Dic3 | — | 2 | 6 | no | — |
| 166 | #622 | C24 | 1 | 6 | yes | — |
| 167 | #622 | C24 | 1 | 2 | yes | — |
| 168 | C2×2−1+4 | — | 9 | 1 | no | — |
| 169 | C2×H(5,𝔽2) | — | 9 | 1 | no | — |
| 170 | #577 | — | 9 | 12 | no | — |
| 171 | #577 | — | 9 | 4 | no | — |
| 172 | C2×#137 | — | 9 | 3 | no | — |
| 173 | C2×AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 174 | C2×#135 | — | 9 | 3 | no | — |
| 175 | C22×SD16 | — | 9 | 3 | no | — |
| 176 | C2×#131 | — | 9 | 1 | no | — |
| 177 | C23×D3 | — | 6 | 6 | no | — |
| 178 | C3×#41 | — | 2 | 1 | no | — |
| 179 | C3×#41 | — | 2 | 1 | no | — |
| 180 | C3×#41 | — | 6 | 3 | no | — |
| 181 | C3×#41 | — | 6 | 3 | no | — |
| 182 | C3×#41 | — | 6 | 6 | no | — |
| 183 | C3×#41 | — | 6 | 2 | no | — |
| 184 | C2×C3×Q8 | — | 6 | 3 | no | — |
| 185 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 186 | C2×C3×D4 | — | 6 | 3 | no | — |
| 187 | C2×C3×D4 | — | 6 | 6 | no | — |
| 188 | C2×#67 | — | 6 | 6 | no | — |
| 189 | C2×#67 | — | 6 | 12 | no | — |
| 190 | #239 | — | 2 | 2 | no | — |
| 191 | #239 | — | 6 | 1 | no | — |
| 192 | #239 | — | 6 | 1 | no | — |
| 193 | #239 | — | 6 | 6 | no | — |
| 194 | #239 | — | 6 | 3 | no | — |
| 195 | #239 | — | 6 | 3 | no | — |
| 196 | D3×Q8 | — | 2 | 2 | no | — |
| 197 | D3×Q8 | — | 6 | 3 | no | — |
| 198 | D3×Q8 | — | 6 | 1 | no | — |
| 199 | D3×Q8 | — | 6 | 6 | no | — |
| 200 | D3×Q8 | — | 6 | 1 | no | — |
| 201 | D3×Q8 | — | 6 | 1 | no | — |
| 202 | D3×Q8 | — | 6 | 6 | no | — |
| 203 | D3×Q8 | — | 6 | 6 | no | — |
| 204 | D3×Q8 | — | 6 | 6 | no | — |
| 205 | #237 | — | 2 | 6 | no | — |
| 206 | #237 | — | 6 | 6 | no | — |
| 207 | #237 | — | 6 | 6 | no | — |
| 208 | #237 | — | 6 | 3 | no | — |
| 209 | #237 | — | 6 | 3 | no | — |
| 210 | #237 | — | 6 | 3 | no | — |
| 211 | #237 | — | 6 | 3 | no | — |
| 212 | #237 | — | 6 | 6 | no | — |
| 213 | #237 | — | 6 | 12 | no | — |
| 214 | D3×D4 | — | 2 | 6 | no | — |
| 215 | D3×D4 | — | 6 | 3 | no | — |
| 216 | D3×D4 | — | 6 | 6 | no | — |
| 217 | D3×D4 | — | 6 | 1 | no | — |
| 218 | D3×D4 | — | 6 | 3 | no | — |
| 219 | D3×D4 | — | 6 | 3 | no | — |
| 220 | D3×D4 | — | 6 | 6 | no | — |
| 221 | D3×D4 | — | 6 | 6 | no | — |
| 222 | D3×D4 | — | 6 | 6 | no | — |
| 223 | D3×D4 | — | 6 | 6 | no | — |
| 224 | D3×D4 | — | 6 | 6 | no | — |
| 225 | D3×D4 | — | 6 | 12 | no | — |
| 226 | #235 | — | 2 | 3 | no | — |
| 227 | #235 | — | 2 | 3 | no | — |
| 228 | #235 | — | 6 | 6 | no | — |
| 229 | #235 | — | 6 | 6 | no | — |
| 230 | #235 | — | 6 | 3 | no | — |
| 231 | #235 | — | 6 | 3 | no | — |
| 232 | #235 | — | 6 | 6 | no | — |
| 233 | #235 | — | 6 | 6 | no | — |
| 234 | #235 | — | 6 | 12 | no | — |
| 235 | C2×D12 | — | 2 | 3 | no | — |
| 236 | C2×D12 | — | 6 | 6 | no | — |
| 237 | C2×C4×D3 | — | 6 | 3 | no | — |
| 238 | C2×C4×D3 | — | 6 | 3 | no | — |
| 239 | C2×C4×D3 | — | 6 | 6 | no | — |
| 240 | C2×C4×D3 | — | 6 | 6 | no | — |
| 241 | C2×C4×D3 | — | 6 | 6 | no | — |
| 242 | C2×Dic6 | — | 2 | 3 | no | — |
| 243 | C2×Dic6 | — | 6 | 6 | no | — |
| 244 | C2×Dic6 | — | 6 | 6 | no | — |
| 245 | C22×C32 | C22×D4 | 1 | 3 | yes | — |
| 246 | C2×C3⋊D3 | — | 2 | 6 | no | — |
| 247 | C2×C3⋊D3 | C22×D4 | 1 | 3 | yes | — |
| 248 | C2×C3⋊D3 | C22×D4 | 1 | 1 | yes | characteristic |
| 249 | C2×C3×D3 | — | 2 | 2 | no | — |
| 250 | C2×C3×D3 | — | 2 | 6 | no | — |
| 251 | C2×C3×D3 | — | 8 | 6 | no | — |
| 252 | D32 | — | 4 | 2 | no | — |
| 253 | D32 | — | 4 | 6 | no | — |
| 254 | D32 | — | 8 | 6 | no | — |
| 255 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 256 | C32×C4 | C22×D4 | 1 | 3 | yes | — |
| 257 | C3⋊Dic3 | C22×D4 | 1 | 3 | yes | — |
| 258 | C3⋊Dic3 | C25 | 1 | 1 | yes | characteristic |
| 259 | C3×Dic3 | — | 2 | 2 | no | — |
| 260 | C3×Dic3 | — | 2 | 6 | no | — |
| 261 | 2−1+4 | — | 6 | 1 | no | — |
| 262 | 2−1+4 | — | 9 | 2 | no | — |
| 263 | 2−1+4 | — | 9 | 6 | no | — |
| 264 | 2−1+4 | — | 18 | 3 | no | — |
| 265 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 266 | H(5,𝔽2) | — | 9 | 6 | no | — |
| 267 | H(5,𝔽2) | — | 9 | 2 | no | — |
| 268 | H(5,𝔽2) | — | 18 | 3 | no | — |
| 269 | C2×#41 | — | 9 | 1 | no | — |
| 270 | C2×#41 | — | 9 | 3 | no | — |
| 271 | C2×#41 | — | 9 | 3 | no | — |
| 272 | C2×#41 | — | 18 | 3 | no | — |
| 273 | C2×#41 | — | 18 | 1 | no | — |
| 274 | C22×Q8 | — | 9 | 3 | no | — |
| 275 | C22×Q8 | — | 18 | 1 | no | — |
| 276 | C22×D4 | — | 9 | 3 | no | — |
| 277 | C22×D4 | — | 18 | 3 | no | — |
| 278 | #137 | — | 9 | 12 | no | — |
| 279 | #137 | — | 9 | 12 | no | — |
| 280 | AGL(1,ℤ/8) | — | 9 | 12 | no | — |
| 281 | AGL(1,ℤ/8) | — | 9 | 12 | no | — |
| 282 | #135 | — | 9 | 12 | no | — |
| 283 | #135 | — | 9 | 12 | no | — |
| 284 | C2×Q16 | — | 9 | 3 | no | — |
| 285 | C2×SD16 | — | 9 | 3 | no | — |
| 286 | C2×SD16 | — | 9 | 6 | no | — |
| 287 | C2×SD16 | — | 9 | 12 | no | — |
| 288 | C2×SD16 | — | 9 | 12 | no | — |
| 289 | C2×SD16 | — | 9 | 1 | no | — |
| 290 | C2×D8 | — | 9 | 3 | no | — |
| 291 | #131 | — | 9 | 6 | no | — |
| 292 | #131 | — | 9 | 2 | no | — |
| 293 | C2×M16 | — | 9 | 3 | no | — |
| 294 | C22×C8 | — | 9 | 3 | no | — |
| 295 | C23×C3 | — | 6 | 6 | no | — |
| 296 | C22×D3 | — | 2 | 6 | no | — |
| 297 | C22×D3 | — | 6 | 3 | no | — |
| 298 | C22×D3 | — | 6 | 3 | no | — |
| 299 | C22×D3 | — | 6 | 2 | no | — |
| 300 | C22×D3 | — | 6 | 6 | no | — |
| 301 | C22×D3 | — | 6 | 12 | no | — |
| 302 | C22×D3 | — | 24 | 12 | no | — |
| 303 | C3×Q8 | — | 2 | 1 | no | — |
| 304 | C3×Q8 | — | 2 | 1 | no | — |
| 305 | C3×Q8 | — | 6 | 3 | no | — |
| 306 | C3×Q8 | — | 6 | 6 | no | — |
| 307 | C3×Q8 | — | 6 | 1 | no | — |
| 308 | C3×D4 | — | 2 | 3 | no | — |
| 309 | C3×D4 | — | 2 | 3 | no | — |
| 310 | C3×D4 | — | 6 | 3 | no | — |
| 311 | C3×D4 | — | 6 | 6 | no | — |
| 312 | C3×D4 | — | 6 | 1 | no | — |
| 313 | C3×D4 | — | 6 | 6 | no | — |
| 314 | C3×D4 | — | 6 | 6 | no | — |
| 315 | C2×C3×C4 | — | 2 | 3 | no | — |
| 316 | C2×C3×C4 | — | 2 | 3 | no | — |
| 317 | C2×C3×C4 | — | 6 | 6 | no | — |
| 318 | C2×C3×C4 | — | 6 | 6 | no | — |
| 319 | C2×C3×C4 | — | 6 | 6 | no | — |
| 320 | #67 | — | 2 | 6 | no | — |
| 321 | #67 | — | 2 | 6 | no | — |
| 322 | #67 | — | 6 | 2 | no | — |
| 323 | #67 | — | 6 | 6 | no | — |
| 324 | #67 | — | 6 | 6 | no | — |
| 325 | #67 | — | 6 | 6 | no | — |
| 326 | #67 | — | 6 | 6 | no | — |
| 327 | #67 | — | 6 | 6 | no | — |
| 328 | #67 | — | 6 | 12 | no | — |
| 329 | C2×Dic3 | — | 2 | 6 | no | — |
| 330 | C2×Dic3 | — | 6 | 3 | no | — |
| 331 | C2×Dic3 | — | 6 | 3 | no | — |
| 332 | C2×Dic3 | — | 6 | 6 | no | — |
| 333 | C2×Dic3 | — | 6 | 6 | no | — |
| 334 | D12 | — | 2 | 3 | no | — |
| 335 | D12 | — | 2 | 6 | no | — |
| 336 | D12 | — | 2 | 1 | no | — |
| 337 | D12 | — | 6 | 3 | no | — |
| 338 | D12 | — | 6 | 3 | no | — |
| 339 | D12 | — | 6 | 6 | no | — |
| 340 | D12 | — | 6 | 6 | no | — |
| 341 | C4×D3 | — | 2 | 6 | no | — |
| 342 | C4×D3 | — | 2 | 6 | no | — |
| 343 | C4×D3 | — | 6 | 3 | no | — |
| 344 | C4×D3 | — | 6 | 3 | no | — |
| 345 | C4×D3 | — | 6 | 3 | no | — |
| 346 | C4×D3 | — | 6 | 3 | no | — |
| 347 | C4×D3 | — | 6 | 1 | no | — |
| 348 | C4×D3 | — | 6 | 1 | no | — |
| 349 | C4×D3 | — | 6 | 3 | no | — |
| 350 | C4×D3 | — | 6 | 3 | no | — |
| 351 | C4×D3 | — | 6 | 2 | no | — |
| 352 | C4×D3 | — | 6 | 6 | no | — |
| 353 | C4×D3 | — | 6 | 12 | no | — |
| 354 | C4×D3 | — | 6 | 6 | no | — |
| 355 | C4×D3 | — | 6 | 6 | no | — |
| 356 | Dic6 | — | 2 | 3 | no | — |
| 357 | Dic6 | — | 2 | 6 | no | — |
| 358 | Dic6 | — | 2 | 1 | no | — |
| 359 | Dic6 | — | 6 | 6 | no | — |
| 360 | Dic6 | — | 6 | 2 | no | — |
| 361 | Dic6 | — | 6 | 3 | no | — |
| 362 | Dic6 | — | 6 | 3 | no | — |
| 363 | Dic6 | — | 6 | 12 | no | — |
| 364 | C2×C32 | — | 2 | 3 | no | — |
| 365 | C2×C32 | C23×D4 | 1 | 1 | yes | characteristic |
| 366 | C3⋊D3 | — | 2 | 3 | no | — |
| 367 | C3⋊D3 | #577 | 1 | 2 | yes | complemented |
| 368 | C3×D3 | — | 4 | 6 | no | — |
| 369 | C3×D3 | — | 4 | 2 | no | — |
| 370 | C24 | — | 18 | 3 | no | — |
| 371 | #41 | — | 6 | 2 | no | — |
| 372 | #41 | — | 6 | 6 | no | — |
| 373 | #41 | — | 6 | 3 | no | — |
| 374 | #41 | — | 6 | 3 | no | — |
| 375 | #41 | — | 9 | 6 | no | — |
| 376 | #41 | — | 9 | 6 | no | — |
| 377 | #41 | — | 9 | 1 | no | — |
| 378 | #41 | — | 9 | 3 | no | — |
| 379 | #41 | — | 9 | 3 | no | — |
| 380 | #41 | — | 9 | 6 | no | — |
| 381 | #41 | — | 9 | 6 | no | — |
| 382 | #41 | — | 18 | 12 | no | — |
| 383 | #41 | — | 18 | 6 | no | — |
| 384 | #41 | — | 18 | 6 | no | — |
| 385 | #41 | — | 18 | 3 | no | — |
| 386 | #41 | — | 18 | 3 | no | — |
| 387 | #41 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 388 | C2×Q8 | — | 6 | 2 | no | — |
| 389 | C2×Q8 | — | 6 | 3 | no | — |
| 390 | C2×Q8 | — | 9 | 6 | no | — |
| 391 | C2×Q8 | — | 9 | 1 | no | — |
| 392 | C2×Q8 | — | 9 | 3 | no | — |
| 393 | C2×Q8 | — | 9 | 6 | no | — |
| 394 | C2×Q8 | — | 9 | 1 | no | — |
| 395 | C2×Q8 | — | 18 | 6 | no | — |
| 396 | C2×Q8 | — | 18 | 3 | no | — |
| 397 | C2×Q8 | — | 18 | 3 | no | — |
| 398 | C2×D4 | — | 6 | 6 | no | — |
| 399 | C2×D4 | — | 6 | 3 | no | — |
| 400 | C2×D4 | — | 9 | 1 | no | — |
| 401 | C2×D4 | — | 9 | 3 | no | — |
| 402 | C2×D4 | — | 9 | 6 | no | — |
| 403 | C2×D4 | — | 9 | 3 | no | — |
| 404 | C2×D4 | — | 9 | 6 | no | — |
| 405 | C2×D4 | — | 18 | 6 | no | — |
| 406 | C2×D4 | — | 18 | 3 | no | — |
| 407 | C2×D4 | — | 18 | 3 | no | — |
| 408 | C2×D4 | — | 18 | 3 | no | — |
| 409 | C2×D4 | — | 18 | 3 | no | — |
| 410 | C2×D4 | — | 18 | 12 | no | — |
| 411 | C22×C4 | — | 9 | 3 | no | — |
| 412 | C22×C4 | — | 18 | 3 | no | — |
| 413 | C22×C4 | — | 18 | 3 | no | — |
| 414 | C22×C4 | — | 18 | 3 | no | — |
| 415 | Q16 | — | 9 | 12 | no | — |
| 416 | SD16 | — | 9 | 12 | no | — |
| 417 | SD16 | — | 9 | 24 | no | — |
| 418 | SD16 | — | 9 | 4 | no | — |
| 419 | D8 | — | 9 | 12 | no | — |
| 420 | M16 | — | 9 | 6 | no | — |
| 421 | M16 | — | 9 | 6 | no | — |
| 422 | C2×C8 | — | 9 | 1 | no | — |
| 423 | C2×C8 | — | 9 | 3 | no | — |
| 424 | C2×C8 | — | 9 | 6 | no | — |
| 425 | C2×C8 | — | 9 | 6 | no | — |
| 426 | C22×C3 | — | 2 | 3 | no | — |
| 427 | C22×C3 | — | 2 | 3 | no | — |
| 428 | C22×C3 | — | 6 | 2 | no | — |
| 429 | C22×C3 | — | 6 | 6 | no | — |
| 430 | C22×C3 | — | 24 | 6 | no | — |
| 431 | C2×D3 | — | 2 | 2 | no | — |
| 432 | C2×D3 | — | 2 | 6 | no | — |
| 433 | C2×D3 | — | 6 | 1 | no | — |
| 434 | C2×D3 | — | 6 | 1 | no | — |
| 435 | C2×D3 | — | 6 | 3 | no | — |
| 436 | C2×D3 | — | 6 | 3 | no | — |
| 437 | C2×D3 | — | 8 | 6 | no | — |
| 438 | C2×D3 | — | 12 | 6 | no | — |
| 439 | C2×D3 | — | 12 | 6 | no | — |
| 440 | C2×D3 | — | 12 | 12 | no | — |
| 441 | C2×D3 | — | 12 | 4 | no | — |
| 442 | C2×D3 | — | 24 | 12 | no | — |
| 443 | C3×C4 | — | 2 | 1 | no | — |
| 444 | C3×C4 | — | 2 | 3 | no | — |
| 445 | C3×C4 | — | 2 | 1 | no | — |
| 446 | C3×C4 | — | 2 | 3 | no | — |
| 447 | C3×C4 | — | 6 | 6 | no | — |
| 448 | C3×C4 | — | 6 | 2 | no | — |
| 449 | Dic3 | — | 2 | 6 | no | — |
| 450 | Dic3 | — | 2 | 2 | no | — |
| 451 | Dic3 | — | 6 | 3 | no | — |
| 452 | Dic3 | — | 6 | 1 | no | — |
| 453 | Dic3 | — | 6 | 3 | no | — |
| 454 | Dic3 | — | 6 | 1 | no | — |
| 455 | C32 | C2×#577 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 456 | C23 | — | 6 | 6 | no | — |
| 457 | C23 | — | 9 | 3 | no | — |
| 458 | C23 | — | 18 | 1 | no | — |
| 459 | C23 | — | 18 | 3 | no | — |
| 460 | C23 | — | 18 | 6 | no | — |
| 461 | C23 | — | 72 | 6 | no | — |
| 462 | Q8 | — | 6 | 6 | no | — |
| 463 | Q8 | — | 6 | 3 | no | — |
| 464 | Q8 | — | 6 | 1 | no | — |
| 465 | Q8 | — | 9 | 6 | no | — |
| 466 | Q8 | — | 9 | 2 | no | — |
| 467 | Q8 | — | 9 | 3 | no | — |
| 468 | Q8 | — | 18 | 6 | no | — |
| 469 | Q8 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 470 | D4 | — | 6 | 6 | no | — |
| 471 | D4 | — | 6 | 6 | no | — |
| 472 | D4 | — | 6 | 6 | no | — |
| 473 | D4 | — | 6 | 3 | no | — |
| 474 | D4 | — | 6 | 1 | no | — |
| 475 | D4 | — | 9 | 2 | no | — |
| 476 | D4 | — | 9 | 6 | no | — |
| 477 | D4 | — | 9 | 6 | no | — |
| 478 | D4 | — | 9 | 3 | no | — |
| 479 | D4 | — | 18 | 6 | no | — |
| 480 | D4 | — | 18 | 6 | no | — |
| 481 | D4 | — | 18 | 6 | no | — |
| 482 | D4 | C2×GO+(4,𝔽2) | 1 | 3 | yes | — |
| 483 | C2×C4 | — | 6 | 6 | no | — |
| 484 | C2×C4 | — | 6 | 6 | no | — |
| 485 | C2×C4 | — | 6 | 6 | no | — |
| 486 | C2×C4 | — | 9 | 3 | no | — |
| 487 | C2×C4 | — | 9 | 1 | no | — |
| 488 | C2×C4 | — | 9 | 3 | no | — |
| 489 | C2×C4 | — | 9 | 3 | no | — |
| 490 | C2×C4 | — | 9 | 3 | no | — |
| 491 | C2×C4 | — | 18 | 1 | no | — |
| 492 | C2×C4 | — | 18 | 3 | no | — |
| 493 | C2×C4 | — | 18 | 6 | no | — |
| 494 | C2×C4 | — | 18 | 6 | no | — |
| 495 | C2×C4 | — | 18 | 6 | no | — |
| 496 | C2×C4 | C2×GO+(4,𝔽2) | 1 | 3 | yes | — |
| 497 | C8 | — | 9 | 2 | no | — |
| 498 | C8 | — | 9 | 6 | no | — |
| 499 | C2×C3 | — | 2 | 1 | no | — |
| 500 | C2×C3 | — | 2 | 1 | no | — |
| 501 | C2×C3 | — | 4 | 3 | no | — |
| 502 | C2×C3 | — | 4 | 3 | no | — |
| 503 | C2×C3 | — | 12 | 6 | no | — |
| 504 | C2×C3 | — | 12 | 2 | no | — |
| 505 | D3 | — | 4 | 6 | no | — |
| 506 | D3 | — | 4 | 2 | no | — |
| 507 | D3 | — | 6 | 2 | no | — |
| 508 | D3 | — | 6 | 2 | no | — |
| 509 | D3 | — | 12 | 3 | no | — |
| 510 | D3 | — | 12 | 3 | no | — |
| 511 | C22 | — | 6 | 2 | no | — |
| 512 | C22 | — | 6 | 6 | no | — |
| 513 | C22 | — | 9 | 1 | no | — |
| 514 | C22 | — | 9 | 3 | no | — |
| 515 | C22 | — | 18 | 6 | no | — |
| 516 | C22 | — | 24 | 6 | no | — |
| 517 | C22 | — | 36 | 6 | no | — |
| 518 | C22 | — | 36 | 2 | no | — |
| 519 | C22 | — | 72 | 6 | no | — |
| 520 | C22 | C22×GO+(4,𝔽2) | 1 | 3 | yes | — |
| 521 | C4 | — | 6 | 2 | no | — |
| 522 | C4 | — | 6 | 6 | no | — |
| 523 | C4 | — | 9 | 1 | no | — |
| 524 | C4 | — | 9 | 3 | no | — |
| 525 | C4 | C22×GO+(4,𝔽2) | 1 | 3 | yes | — |
| 526 | C4 | C22×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 527 | C3 | — | 2 | 1 | no | — |
| 528 | C3 | — | 2 | 1 | no | — |
| 529 | C2 | — | 2 | 3 | no | — |
| 530 | C2 | — | 9 | 2 | no | — |
| 531 | C2 | — | 12 | 6 | no | — |
| 532 | C2 | — | 12 | 2 | no | — |
| 533 | C2 | — | 18 | 3 | no | — |
| 534 | C2 | C23×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×GO+(4,𝔽2) |
| commutator, cosocle | C3⋊Dic3 | C25 |
| Fitting | C32×#41 | D4 |
| socle | C2×C32 | C23×D4 |
| hypercenter | #41 | GO+(4,𝔽2) |
| hypocenter | C32 | C2×#577 |
| LCS | G ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596694 | C2 | semidirect |
| 2. #10596692 | C2 | semidirect |
| 3. #10596647 | C2 | semidirect |
| 4. #10596521 | C2 | semidirect |
| 5. #10596515 | C2 | semidirect |
| 6. #10596505 | C2 | semidirect |
| 7. C2×#64227 | C2 | semidirect |
| 8. #10596501 | C2 | semidirect |
| 9. #10596500 | C2 | semidirect |
| 13. #64320 | C22 | semidirect |
| 16. #64316 | C22 | semidirect |
| 17. #64313 | C22 | semidirect |
| 20. #64309 | C22 | semidirect |
| 23. #64306 | C22 | semidirect |
| 25. C2×#3797 | C22 | semidirect |
| 27. #64289 | C22 | semidirect |
| 28. #64287 | C22 | semidirect |
| 29. #64283 | C22 | semidirect |
| 30. C2×#3787 | C22 | semidirect |
| 31. #64239 | C22 | semidirect |
| 32. C2×#3775 | C22 | semidirect |
| 33. #64237 | C22 | semidirect |
| 34. #64236 | C22 | semidirect |
| 35. #64228 | C22 | semidirect |
| 36. #64227 | C22 | semidirect |
| 37. #64227 | C22 | semidirect |
| 38. #64227 | C22 | semidirect |
| 39. #64227 | C22 | semidirect |
| 40. #64226 | C22 | semidirect |
| 41. #64225 | C22 | semidirect |
| 42. #64224 | C22 | semidirect |
| 43. #64223 | C22 | semidirect |
| 65. C2×#627 | C23 | semidirect |
| 69. #3805 | C23 | semidirect |
| 81. #3798 | C23 | semidirect |
| 86. #3797 | C23 | semidirect |
| 91. #3792 | C23 | semidirect |
| 92. C2×#622 | C23 | semidirect |
| 93. #3788 | C23 | semidirect |
| 96. #3787 | C23 | semidirect |
| 97. #3776 | C23 | semidirect |
| 98. #3775 | C23 | semidirect |
| 99. #3775 | C23 | semidirect |
| 100. #3775 | C23 | semidirect |
| 101. #3774 | C23 | semidirect |
| 367. C3⋊D3 | #577 | semidirect |
| 455. C32 | C2×#577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596694 | 2 |
| #10596692 | 2 |
| #10596647 | 2 |
| #10596521 | 2 |
| #10596515 | 2 |
| #10596505 | 2 |
| C2×#64227 | 2 |
| #10596501 | 2 |
| #10596500 | 2 |
| C2×#577 | 9 |