Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
854 conjugacy classes of subgroups.
The subgroup lattice has 571 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10596228 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10594703 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×C3×#827 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#5147 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10591036 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10591035 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10591030 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10591029 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10590642 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10590632 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #10590624 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #82037 | — | 3 | 1 | no | maximal |
| 13 | #82024 | — | 3 | 1 | no | maximal |
| 14 | #64361 | — | 2 | 1 | no | — |
| 15 | #64297 | — | 2 | 1 | no | — |
| 16 | C2×C32×D8 | C22 | 1 | 1 | yes | characteristic |
| 17 | #64141 | — | 2 | 1 | no | — |
| 18 | #64121 | C22 | 1 | 2 | yes | — |
| 19 | #64120 | — | 2 | 2 | no | — |
| 20 | D8×C3⋊D3 | C22 | 1 | 2 | yes | — |
| 21 | #64113 | C22 | 1 | 1 | yes | characteristic |
| 22 | #64110 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C3×Dic12 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C3×#904 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #63827 | — | 2 | 1 | no | — |
| 26 | #63811 | — | 2 | 2 | no | — |
| 27 | #63810 | C22 | 1 | 2 | yes | complemented |
| 28 | #63802 | C22 | 1 | 2 | yes | complemented |
| 29 | C3×#827 | C22 | 1 | 2 | yes | complemented |
| 30 | C3×#827 | C22 | 1 | 2 | yes | complemented |
| 31 | C3×#827 | C22 | 1 | 2 | yes | complemented |
| 32 | C3×#826 | C22 | 1 | 2 | yes | complemented |
| 33 | C3×#812 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | C2×C3×C3⋊C16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #63551 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #63551 | C22 | 1 | 2 | yes | complemented |
| 37 | #63549 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #63549 | C22 | 1 | 2 | yes | complemented |
| 39 | #63548 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #63546 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #63544 | C22 | 1 | 2 | yes | complemented |
| 42 | #63542 | C22 | 1 | 2 | yes | complemented |
| 43 | #5771 | — | 3 | 1 | no | — |
| 44 | #5766 | — | 3 | 1 | no | — |
| 45 | #5757 | — | 3 | 1 | no | — |
| 46 | #5757 | — | 3 | 1 | no | — |
| 47 | #5757 | — | 6 | 1 | no | — |
| 48 | C3×#509 | — | 3 | 1 | no | — |
| 49 | C2×C3×SD32 | — | 3 | 1 | no | — |
| 50 | #5194 | — | 3 | 1 | no | — |
| 51 | #5179 | — | 3 | 1 | no | — |
| 52 | C2×#827 | D3 | 1 | 1 | yes | characteristic, complemented |
| 53 | #5147 | D3 | 1 | 1 | yes | characteristic, complemented |
| 54 | #4916 | — | 3 | 2 | no | — |
| 55 | #4915 | — | 3 | 2 | no | — |
| 56 | #4915 | — | 3 | 2 | no | — |
| 57 | #4914 | — | 3 | 2 | no | — |
| 58 | D3×SD32 | — | 3 | 2 | no | — |
| 59 | D3×SD32 | — | 3 | 2 | no | — |
| 60 | #4912 | — | 3 | 2 | no | — |
| 61 | #4911 | — | 3 | 2 | no | — |
| 62 | #4909 | — | 3 | 1 | no | — |
| 63 | #4907 | — | 3 | 1 | no | — |
| 64 | #4904 | — | 3 | 1 | no | — |
| 65 | #4901 | — | 3 | 1 | no | — |
| 66 | C2×C32×D4 | — | 2 | 1 | no | — |
| 67 | C2×#638 | — | 4 | 2 | no | — |
| 68 | #3830 | — | 2 | 2 | no | — |
| 69 | #3830 | — | 4 | 1 | no | — |
| 70 | D4×C3⋊D3 | — | 2 | 2 | no | — |
| 71 | D4×C3⋊D3 | — | 4 | 1 | no | — |
| 72 | #3828 | — | 2 | 1 | no | — |
| 73 | #3828 | D4 | 1 | 1 | yes | characteristic |
| 74 | C3×#235 | — | 2 | 1 | no | — |
| 75 | C2×C3×Dic6 | — | 2 | 1 | no | — |
| 76 | #3804 | — | 4 | 2 | no | — |
| 77 | #3799 | — | 4 | 1 | no | — |
| 78 | #3797 | — | 2 | 2 | no | — |
| 79 | #3796 | — | 2 | 2 | no | — |
| 80 | D3×Dic6 | — | 4 | 1 | no | — |
| 81 | C32×D8 | — | 2 | 1 | no | — |
| 82 | C32×D8 | C23 | 1 | 2 | yes | — |
| 83 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 84 | #3754 | — | 2 | 2 | no | — |
| 85 | #3753 | — | 2 | 2 | no | — |
| 86 | #3748 | D4 | 1 | 1 | yes | characteristic |
| 87 | #3746 | C23 | 1 | 1 | yes | characteristic |
| 88 | #3745 | C23 | 1 | 1 | yes | characteristic |
| 89 | #3744 | — | 2 | 1 | no | — |
| 90 | #3743 | D4 | 1 | 2 | yes | — |
| 91 | C8×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 92 | C3×Dic12 | — | 2 | 1 | no | — |
| 93 | C3×Dic12 | C23 | 1 | 1 | yes | characteristic |
| 94 | C3×Dic12 | C23 | 1 | 2 | yes | — |
| 95 | C3×D24 | C23 | 1 | 1 | yes | characteristic |
| 96 | C3×#204 | — | 2 | 1 | no | — |
| 97 | #3718 | — | 2 | 2 | no | — |
| 98 | #3715 | — | 2 | 2 | no | — |
| 99 | C3×C3⋊C16 | C23 | 1 | 1 | yes | characteristic |
| 100 | C3×C3⋊C16 | C23 | 1 | 2 | yes | — |
| 101 | C3×C3⋊C16 | C23 | 1 | 1 | yes | characteristic |
| 102 | #3416 | — | 9 | 1 | no | Sylow |
| 103 | #1010 | — | 6 | 1 | no | — |
| 104 | #1007 | — | 6 | 1 | no | — |
| 105 | #1004 | — | 6 | 1 | no | — |
| 106 | #1004 | — | 6 | 1 | no | — |
| 107 | #1004 | — | 6 | 2 | no | — |
| 108 | C3×#135 | — | 3 | 1 | no | — |
| 109 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 110 | C2×C3×D8 | — | 2 | 1 | no | — |
| 111 | C2×C3×D8 | C2×D3 | 1 | 1 | yes | characteristic |
| 112 | C2×C3×D8 | C2×D3 | 1 | 1 | yes | characteristic |
| 113 | #951 | — | 6 | 1 | no | — |
| 114 | #942 | — | 6 | 1 | no | — |
| 115 | #932 | — | 6 | 1 | no | — |
| 116 | #932 | — | 6 | 1 | no | — |
| 117 | #932 | — | 6 | 2 | no | — |
| 118 | #919 | — | 3 | 2 | no | — |
| 119 | #918 | — | 6 | 2 | no | — |
| 120 | D3×Q16 | — | 3 | 2 | no | — |
| 121 | D3×Q16 | — | 3 | 2 | no | — |
| 122 | #915 | — | 6 | 2 | no | — |
| 123 | #912 | — | 3 | 2 | no | — |
| 124 | #912 | — | 3 | 2 | no | — |
| 125 | #912 | — | 3 | 2 | no | — |
| 126 | #912 | — | 6 | 2 | no | — |
| 127 | #911 | — | 6 | 2 | no | — |
| 128 | #911 | — | 6 | 2 | no | — |
| 129 | #911 | — | 6 | 4 | no | — |
| 130 | D3×D8 | — | 3 | 2 | no | — |
| 131 | D3×D8 | — | 3 | 2 | no | — |
| 132 | D3×D8 | — | 6 | 2 | no | — |
| 133 | C2×Dic12 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 134 | #904 | — | 3 | 1 | no | — |
| 135 | #904 | — | 3 | 1 | no | — |
| 136 | #904 | — | 6 | 1 | no | — |
| 137 | #904 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 138 | #901 | — | 3 | 1 | no | — |
| 139 | #901 | — | 3 | 1 | no | — |
| 140 | #901 | — | 6 | 1 | no | — |
| 141 | C3×SD32 | — | 3 | 2 | no | — |
| 142 | C3×SD32 | — | 3 | 2 | no | — |
| 143 | C3×SD32 | — | 3 | 2 | no | — |
| 144 | C3×D16 | — | 3 | 2 | no | — |
| 145 | C3×M32 | — | 3 | 1 | no | — |
| 146 | C2×C3×C16 | — | 3 | 1 | no | — |
| 147 | #829 | — | 3 | 1 | no | — |
| 148 | #829 | — | 3 | 2 | no | — |
| 149 | #828 | — | 3 | 1 | no | — |
| 150 | #828 | — | 3 | 2 | no | — |
| 151 | #827 | — | 3 | 1 | no | — |
| 152 | #827 | C2×D3 | 1 | 2 | yes | complemented |
| 153 | #827 | C2×D3 | 1 | 2 | yes | complemented |
| 154 | #827 | C2×D3 | 1 | 2 | yes | complemented |
| 155 | #826 | — | 3 | 1 | no | — |
| 156 | #826 | C2×D3 | 1 | 2 | yes | complemented |
| 157 | #812 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 158 | C2×C3⋊C16 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 159 | Dic24 | — | 3 | 1 | no | — |
| 160 | Dic24 | — | 3 | 2 | no | — |
| 161 | #800 | — | 3 | 1 | no | — |
| 162 | #800 | — | 3 | 2 | no | — |
| 163 | #800 | — | 3 | 1 | no | — |
| 164 | D48 | — | 3 | 1 | no | — |
| 165 | #798 | — | 3 | 2 | no | — |
| 166 | #798 | — | 3 | 2 | no | — |
| 167 | D3×C16 | — | 3 | 2 | no | — |
| 168 | D3×C16 | — | 3 | 2 | no | — |
| 169 | C23×C32 | — | 4 | 1 | no | — |
| 170 | C22×C3⋊D3 | — | 4 | 2 | no | — |
| 171 | C32×D4 | — | 2 | 2 | no | — |
| 172 | C32×D4 | — | 4 | 1 | no | — |
| 173 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | #638 | — | 4 | 1 | no | — |
| 175 | #638 | — | 4 | 2 | no | — |
| 176 | #638 | — | 4 | 2 | no | — |
| 177 | #638 | D8 | 1 | 2 | yes | — |
| 178 | C2×C3⋊Dic3 | — | 4 | 2 | no | — |
| 179 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 180 | C4⋊(C3⋊D3) | D8 | 1 | 1 | yes | characteristic |
| 181 | C4×C3⋊D3 | — | 4 | 1 | no | — |
| 182 | C4×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 183 | #634 | — | 2 | 1 | no | — |
| 184 | #634 | D8 | 1 | 1 | yes | characteristic |
| 185 | C3×#67 | — | 4 | 1 | no | — |
| 186 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 187 | C3×D12 | — | 2 | 1 | no | — |
| 188 | C3×C4×D3 | — | 4 | 1 | no | — |
| 189 | C3×Dic6 | — | 2 | 2 | no | — |
| 190 | C3×Dic6 | — | 2 | 1 | no | — |
| 191 | C3×Dic6 | — | 4 | 1 | no | — |
| 192 | #627 | — | 4 | 2 | no | — |
| 193 | #626 | — | 4 | 2 | no | — |
| 194 | #624 | — | 4 | 2 | no | — |
| 195 | D3×Dic3 | — | 4 | 2 | no | — |
| 196 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 197 | C32×C8 | C24 | 1 | 1 | yes | characteristic |
| 198 | C3⋊(C3⋊C8) | C2×D4 | 1 | 2 | yes | — |
| 199 | #578 | — | 9 | 1 | no | — |
| 200 | #576 | — | 9 | 1 | no | — |
| 201 | #510 | — | 9 | 1 | no | — |
| 202 | #510 | — | 9 | 2 | no | — |
| 203 | #509 | — | 3 | 1 | no | — |
| 204 | #509 | — | 9 | 2 | no | — |
| 205 | #508 | — | 9 | 1 | no | — |
| 206 | #508 | — | 9 | 2 | no | — |
| 207 | C2×SD32 | — | 3 | 1 | no | — |
| 208 | C2×SD32 | — | 9 | 2 | no | — |
| 209 | #504 | — | 9 | 1 | no | — |
| 210 | C3×#41 | — | 6 | 1 | no | — |
| 211 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 212 | C2×C3×D4 | — | 2 | 2 | no | — |
| 213 | C2×C3×D4 | — | 2 | 1 | no | — |
| 214 | C2×C3×D4 | — | 2 | 1 | no | — |
| 215 | C2×#67 | — | 12 | 2 | no | — |
| 216 | C2×#67 | — | 12 | 2 | no | — |
| 217 | C2×#67 | — | 12 | 4 | no | — |
| 218 | #239 | — | 6 | 2 | no | — |
| 219 | #239 | — | 12 | 1 | no | — |
| 220 | D3×Q8 | — | 6 | 2 | no | — |
| 221 | D3×Q8 | — | 6 | 2 | no | — |
| 222 | D3×Q8 | — | 12 | 1 | no | — |
| 223 | #237 | — | 6 | 2 | no | — |
| 224 | #237 | — | 6 | 2 | no | — |
| 225 | #237 | — | 6 | 2 | no | — |
| 226 | #237 | — | 6 | 4 | no | — |
| 227 | #237 | — | 12 | 1 | no | — |
| 228 | #237 | — | 12 | 1 | no | — |
| 229 | #237 | — | 12 | 2 | no | — |
| 230 | #237 | — | 12 | 2 | no | — |
| 231 | D3×D4 | — | 6 | 2 | no | — |
| 232 | D3×D4 | — | 6 | 2 | no | — |
| 233 | D3×D4 | — | 6 | 4 | no | — |
| 234 | D3×D4 | — | 12 | 1 | no | — |
| 235 | D3×D4 | — | 12 | 1 | no | — |
| 236 | D3×D4 | — | 12 | 2 | no | — |
| 237 | #235 | — | 2 | 1 | no | — |
| 238 | #235 | — | 3 | 1 | no | — |
| 239 | #235 | — | 3 | 1 | no | — |
| 240 | #235 | — | 6 | 1 | no | — |
| 241 | #235 | — | 6 | 2 | no | — |
| 242 | #235 | — | 6 | 1 | no | — |
| 243 | #235 | — | 6 | 1 | no | — |
| 244 | #235 | — | 12 | 1 | no | — |
| 245 | #235 | — | 12 | 2 | no | — |
| 246 | C2×Dic6 | — | 2 | 1 | no | — |
| 247 | C2×Dic6 | — | 12 | 1 | no | — |
| 248 | C3×Q16 | — | 3 | 1 | no | — |
| 249 | C3×Q16 | — | 3 | 2 | no | — |
| 250 | C3×Q16 | — | 6 | 1 | no | — |
| 251 | C3×SD16 | — | 6 | 1 | no | — |
| 252 | C3×D8 | — | 2 | 2 | no | — |
| 253 | C3×D8 | — | 2 | 1 | no | — |
| 254 | C3×D8 | — | 2 | 1 | no | — |
| 255 | C3×D8 | — | 2 | 2 | no | — |
| 256 | C3×D8 | — | 3 | 1 | no | — |
| 257 | C3×D8 | C22×D3 | 1 | 2 | yes | — |
| 258 | C3×D8 | C22×D3 | 1 | 2 | yes | — |
| 259 | C2×C3×C8 | — | 2 | 1 | no | — |
| 260 | C2×C3×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 261 | C2×C3×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 262 | #216 | — | 6 | 2 | no | — |
| 263 | #216 | — | 6 | 2 | no | — |
| 264 | #215 | — | 6 | 2 | no | — |
| 265 | #214 | — | 6 | 2 | no | — |
| 266 | #214 | — | 6 | 2 | no | — |
| 267 | #214 | — | 6 | 2 | no | — |
| 268 | #214 | — | 6 | 4 | no | — |
| 269 | #213 | — | 6 | 2 | no | — |
| 270 | #213 | — | 6 | 2 | no | — |
| 271 | #213 | — | 6 | 4 | no | — |
| 272 | #208 | — | 3 | 1 | no | — |
| 273 | #208 | — | 3 | 1 | no | — |
| 274 | #208 | — | 6 | 1 | no | — |
| 275 | Dic12 | — | 2 | 1 | no | — |
| 276 | Dic12 | — | 3 | 1 | no | — |
| 277 | Dic12 | — | 3 | 1 | no | — |
| 278 | Dic12 | — | 6 | 1 | no | — |
| 279 | Dic12 | C22×D3 | 1 | 1 | yes | characteristic |
| 280 | Dic12 | C22×D3 | 1 | 2 | yes | — |
| 281 | D24 | — | 3 | 1 | no | — |
| 282 | D24 | — | 3 | 1 | no | — |
| 283 | D24 | — | 6 | 1 | no | — |
| 284 | D24 | C22×D3 | 1 | 1 | yes | characteristic |
| 285 | #204 | — | 2 | 1 | no | — |
| 286 | #204 | — | 6 | 2 | no | — |
| 287 | #204 | — | 6 | 1 | no | — |
| 288 | #204 | — | 6 | 1 | no | — |
| 289 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 290 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 291 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 292 | D3×C8 | — | 3 | 2 | no | — |
| 293 | D3×C8 | — | 3 | 2 | no | — |
| 294 | D3×C8 | — | 6 | 2 | no | — |
| 295 | C3×C16 | — | 3 | 1 | no | — |
| 296 | C3×C16 | — | 3 | 2 | no | — |
| 297 | C3×C16 | — | 3 | 1 | no | — |
| 298 | C3⋊C16 | C22×D3 | 1 | 1 | yes | characteristic |
| 299 | C3⋊C16 | C22×D3 | 1 | 2 | yes | — |
| 300 | C3⋊C16 | C22×D3 | 1 | 1 | yes | characteristic |
| 301 | C22×C32 | — | 4 | 2 | no | — |
| 302 | C22×C32 | — | 16 | 1 | no | — |
| 303 | C22×C32 | C2×D8 | 1 | 1 | yes | characteristic |
| 304 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 305 | C2×C3⋊D3 | — | 16 | 2 | no | — |
| 306 | C2×C3⋊D3 | C2×D8 | 1 | 2 | yes | — |
| 307 | C2×C3×D3 | — | 4 | 1 | no | — |
| 308 | C32×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 309 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 310 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 311 | C3⋊Dic3 | C2×D8 | 1 | 2 | yes | — |
| 312 | C3×Dic3 | — | 4 | 2 | no | — |
| 313 | C3×Dic3 | — | 4 | 1 | no | — |
| 314 | 2−1+4 | — | 18 | 1 | no | — |
| 315 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 316 | #137 | — | 18 | 2 | no | — |
| 317 | #137 | — | 18 | 1 | no | — |
| 318 | AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 319 | AGL(1,ℤ/8) | — | 18 | 1 | no | — |
| 320 | #135 | — | 3 | 1 | no | — |
| 321 | #135 | — | 9 | 2 | no | — |
| 322 | #135 | — | 9 | 2 | no | — |
| 323 | #135 | — | 9 | 1 | no | — |
| 324 | C2×Q16 | — | 3 | 1 | no | — |
| 325 | C2×Q16 | — | 9 | 2 | no | — |
| 326 | C2×D8 | — | 9 | 2 | no | — |
| 327 | C2×D8 | D32 | 1 | 1 | yes | characteristic |
| 328 | #131 | — | 9 | 1 | no | — |
| 329 | Q32 | — | 9 | 1 | no | — |
| 330 | Q32 | — | 9 | 2 | no | — |
| 331 | SD32 | — | 3 | 2 | no | — |
| 332 | SD32 | — | 3 | 2 | no | — |
| 333 | SD32 | — | 3 | 2 | no | — |
| 334 | SD32 | — | 9 | 1 | no | — |
| 335 | SD32 | — | 9 | 1 | no | — |
| 336 | SD32 | — | 9 | 2 | no | — |
| 337 | D16 | — | 3 | 2 | no | — |
| 338 | D16 | — | 9 | 1 | no | — |
| 339 | M32 | — | 3 | 1 | no | — |
| 340 | M32 | — | 9 | 2 | no | — |
| 341 | C2×C16 | — | 3 | 1 | no | — |
| 342 | C2×C16 | — | 9 | 2 | no | — |
| 343 | C23×C3 | — | 4 | 2 | no | — |
| 344 | C23×C3 | — | 4 | 1 | no | — |
| 345 | C23×C3 | — | 4 | 1 | no | — |
| 346 | C22×D3 | — | 12 | 2 | no | — |
| 347 | C22×D3 | — | 12 | 2 | no | — |
| 348 | C22×D3 | — | 12 | 4 | no | — |
| 349 | C3×Q8 | — | 6 | 2 | no | — |
| 350 | C3×Q8 | — | 6 | 1 | no | — |
| 351 | C3×Q8 | — | 12 | 1 | no | — |
| 352 | C3×D4 | — | 2 | 4 | no | — |
| 353 | C3×D4 | — | 2 | 2 | no | — |
| 354 | C3×D4 | — | 2 | 2 | no | — |
| 355 | C3×D4 | — | 4 | 2 | no | — |
| 356 | C3×D4 | — | 4 | 1 | no | — |
| 357 | C3×D4 | — | 4 | 1 | no | — |
| 358 | C3×D4 | — | 6 | 1 | no | — |
| 359 | C3×D4 | — | 12 | 1 | no | — |
| 360 | C2×C3×C4 | — | 2 | 1 | no | — |
| 361 | C2×C3×C4 | — | 12 | 1 | no | — |
| 362 | C2×C3×C4 | — | 12 | 1 | no | — |
| 363 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 364 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 365 | #67 | — | 3 | 2 | no | — |
| 366 | #67 | — | 3 | 2 | no | — |
| 367 | #67 | — | 4 | 1 | no | — |
| 368 | #67 | — | 6 | 2 | no | — |
| 369 | #67 | — | 12 | 2 | no | — |
| 370 | #67 | — | 12 | 2 | no | — |
| 371 | #67 | — | 12 | 2 | no | — |
| 372 | #67 | — | 12 | 4 | no | — |
| 373 | #67 | — | 12 | 2 | no | — |
| 374 | #67 | — | 12 | 2 | no | — |
| 375 | #67 | — | 12 | 4 | no | — |
| 376 | #67 | — | 12 | 2 | no | — |
| 377 | #67 | — | 12 | 1 | no | — |
| 378 | #67 | — | 12 | 1 | no | — |
| 379 | C2×Dic3 | — | 4 | 1 | no | — |
| 380 | C2×Dic3 | — | 12 | 2 | no | — |
| 381 | C2×Dic3 | — | 12 | 2 | no | — |
| 382 | C2×Dic3 | — | 12 | 2 | no | — |
| 383 | C2×Dic3 | — | 12 | 4 | no | — |
| 384 | D12 | — | 2 | 1 | no | — |
| 385 | D12 | — | 3 | 1 | no | — |
| 386 | D12 | — | 3 | 1 | no | — |
| 387 | D12 | — | 6 | 1 | no | — |
| 388 | D12 | — | 6 | 2 | no | — |
| 389 | D12 | — | 6 | 1 | no | — |
| 390 | D12 | — | 6 | 1 | no | — |
| 391 | D12 | — | 12 | 2 | no | — |
| 392 | C4×D3 | — | 3 | 2 | no | — |
| 393 | C4×D3 | — | 3 | 2 | no | — |
| 394 | C4×D3 | — | 4 | 1 | no | — |
| 395 | C4×D3 | — | 6 | 2 | no | — |
| 396 | C4×D3 | — | 12 | 2 | no | — |
| 397 | C4×D3 | — | 12 | 2 | no | — |
| 398 | C4×D3 | — | 12 | 2 | no | — |
| 399 | C4×D3 | — | 12 | 2 | no | — |
| 400 | C4×D3 | — | 12 | 1 | no | — |
| 401 | C4×D3 | — | 12 | 1 | no | — |
| 402 | Dic6 | — | 2 | 1 | no | — |
| 403 | Dic6 | — | 2 | 2 | no | — |
| 404 | Dic6 | — | 3 | 1 | no | — |
| 405 | Dic6 | — | 3 | 1 | no | — |
| 406 | Dic6 | — | 4 | 1 | no | — |
| 407 | Dic6 | — | 6 | 1 | no | — |
| 408 | Dic6 | — | 6 | 2 | no | — |
| 409 | Dic6 | — | 6 | 1 | no | — |
| 410 | Dic6 | — | 6 | 1 | no | — |
| 411 | Dic6 | — | 12 | 2 | no | — |
| 412 | Dic6 | — | 12 | 2 | no | — |
| 413 | C3×C8 | — | 2 | 1 | no | — |
| 414 | C3×C8 | — | 2 | 1 | no | — |
| 415 | C3×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 416 | C3×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 417 | C3×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 418 | C3×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 419 | C3⋊C8 | — | 3 | 2 | no | — |
| 420 | C3⋊C8 | — | 3 | 2 | no | — |
| 421 | C3⋊C8 | — | 6 | 2 | no | — |
| 422 | C2×C32 | — | 2 | 1 | no | — |
| 423 | C2×C32 | — | 8 | 2 | no | — |
| 424 | C2×C32 | C22×D8 | 1 | 1 | yes | characteristic |
| 425 | C3⋊D3 | — | 2 | 2 | no | — |
| 426 | C3⋊D3 | — | 8 | 1 | no | — |
| 427 | C3×D3 | — | 8 | 1 | no | — |
| 428 | #41 | — | 6 | 1 | no | — |
| 429 | #41 | — | 9 | 1 | no | — |
| 430 | #41 | — | 18 | 2 | no | — |
| 431 | #41 | — | 18 | 2 | no | — |
| 432 | #41 | — | 18 | 1 | no | — |
| 433 | #41 | — | 36 | 2 | no | — |
| 434 | #41 | — | 36 | 1 | no | — |
| 435 | #41 | — | 36 | 1 | no | — |
| 436 | C2×Q8 | — | 6 | 1 | no | — |
| 437 | C2×Q8 | — | 18 | 2 | no | — |
| 438 | C2×Q8 | — | 36 | 1 | no | — |
| 439 | C2×D4 | — | 2 | 1 | no | — |
| 440 | C2×D4 | — | 18 | 2 | no | — |
| 441 | C2×D4 | — | 36 | 1 | no | — |
| 442 | C2×D4 | — | 36 | 2 | no | — |
| 443 | Q16 | — | 3 | 2 | no | — |
| 444 | Q16 | — | 3 | 1 | no | — |
| 445 | Q16 | — | 6 | 1 | no | — |
| 446 | Q16 | — | 9 | 1 | no | — |
| 447 | Q16 | — | 18 | 2 | no | — |
| 448 | SD16 | — | 6 | 1 | no | — |
| 449 | SD16 | — | 18 | 2 | no | — |
| 450 | SD16 | — | 18 | 2 | no | — |
| 451 | SD16 | — | 18 | 1 | no | — |
| 452 | D8 | — | 2 | 1 | no | — |
| 453 | D8 | — | 3 | 1 | no | — |
| 454 | D8 | — | 9 | 1 | no | — |
| 455 | D8 | — | 18 | 2 | no | — |
| 456 | D8 | C2×D32 | 1 | 2 | yes | — |
| 457 | M16 | — | 9 | 1 | no | — |
| 458 | M16 | — | 9 | 2 | no | — |
| 459 | C2×C8 | — | 9 | 2 | no | — |
| 460 | C2×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 461 | C16 | — | 3 | 1 | no | — |
| 462 | C16 | — | 3 | 1 | no | — |
| 463 | C16 | — | 3 | 2 | no | — |
| 464 | C22×C3 | — | 2 | 1 | no | — |
| 465 | C22×C3 | — | 4 | 4 | no | — |
| 466 | C22×C3 | — | 4 | 2 | no | — |
| 467 | C22×C3 | — | 4 | 2 | no | — |
| 468 | C22×C3 | — | 12 | 1 | no | — |
| 469 | C22×C3 | — | 16 | 1 | no | — |
| 470 | C22×C3 | — | 16 | 1 | no | — |
| 471 | C22×C3 | — | 16 | 2 | no | — |
| 472 | C22×C3 | D3×D8 | 1 | 1 | yes | characteristic |
| 473 | C22×C3 | D3×D8 | 1 | 1 | yes | characteristic |
| 474 | C2×D3 | — | 3 | 2 | no | — |
| 475 | C2×D3 | — | 3 | 2 | no | — |
| 476 | C2×D3 | — | 4 | 1 | no | — |
| 477 | C2×D3 | — | 6 | 2 | no | — |
| 478 | C2×D3 | — | 12 | 2 | no | — |
| 479 | C2×D3 | — | 12 | 1 | no | — |
| 480 | C2×D3 | — | 12 | 1 | no | — |
| 481 | C2×D3 | — | 48 | 2 | no | — |
| 482 | C2×D3 | — | 48 | 2 | no | — |
| 483 | C2×D3 | — | 48 | 4 | no | — |
| 484 | C3×C4 | — | 2 | 1 | no | — |
| 485 | C3×C4 | — | 2 | 1 | no | — |
| 486 | C3×C4 | — | 12 | 1 | no | — |
| 487 | C3×C4 | — | 12 | 2 | no | — |
| 488 | C3×C4 | D3×D8 | 1 | 1 | yes | characteristic |
| 489 | C3×C4 | D3×D8 | 1 | 1 | yes | characteristic |
| 490 | C3×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 491 | C3×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 492 | Dic3 | — | 3 | 2 | no | — |
| 493 | Dic3 | — | 3 | 2 | no | — |
| 494 | Dic3 | — | 4 | 2 | no | — |
| 495 | Dic3 | — | 4 | 1 | no | — |
| 496 | Dic3 | — | 6 | 2 | no | — |
| 497 | Dic3 | — | 12 | 2 | no | — |
| 498 | Dic3 | — | 12 | 1 | no | — |
| 499 | Dic3 | — | 12 | 1 | no | — |
| 500 | C32 | #3416 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 501 | C23 | — | 4 | 1 | no | — |
| 502 | C23 | — | 36 | 2 | no | — |
| 503 | Q8 | — | 6 | 1 | no | — |
| 504 | Q8 | — | 6 | 2 | no | — |
| 505 | Q8 | — | 9 | 1 | no | — |
| 506 | Q8 | — | 12 | 1 | no | — |
| 507 | Q8 | — | 18 | 1 | no | — |
| 508 | Q8 | — | 36 | 2 | no | — |
| 509 | D4 | — | 2 | 2 | no | — |
| 510 | D4 | — | 4 | 1 | no | — |
| 511 | D4 | — | 6 | 1 | no | — |
| 512 | D4 | — | 9 | 2 | no | — |
| 513 | D4 | — | 9 | 1 | no | — |
| 514 | D4 | — | 12 | 1 | no | — |
| 515 | D4 | — | 18 | 1 | no | — |
| 516 | D4 | — | 36 | 2 | no | — |
| 517 | D4 | — | 36 | 2 | no | — |
| 518 | D4 | — | 36 | 2 | no | — |
| 519 | D4 | — | 36 | 1 | no | — |
| 520 | C2×C4 | — | 9 | 2 | no | — |
| 521 | C2×C4 | — | 12 | 1 | no | — |
| 522 | C2×C4 | — | 12 | 1 | no | — |
| 523 | C2×C4 | — | 36 | 2 | no | — |
| 524 | C2×C4 | — | 36 | 2 | no | — |
| 525 | C2×C4 | — | 36 | 2 | no | — |
| 526 | C2×C4 | — | 36 | 1 | no | — |
| 527 | C2×C4 | #3811 | 1 | 1 | yes | characteristic |
| 528 | C8 | — | 9 | 2 | no | — |
| 529 | C8 | #3811 | 1 | 1 | yes | characteristic |
| 530 | C8 | C22×D32 | 1 | 1 | yes | characteristic |
| 531 | C2×C3 | — | 2 | 1 | no | — |
| 532 | C2×C3 | — | 2 | 1 | no | — |
| 533 | C2×C3 | — | 2 | 1 | no | — |
| 534 | C2×C3 | — | 4 | 1 | no | — |
| 535 | C2×C3 | — | 8 | 4 | no | — |
| 536 | C2×C3 | — | 8 | 2 | no | — |
| 537 | C2×C3 | — | 8 | 2 | no | — |
| 538 | C2×C3 | — | 24 | 1 | no | — |
| 539 | C2×C3 | C2×D3×D8 | 1 | 1 | yes | characteristic |
| 540 | C2×C3 | C2×D3×D8 | 1 | 1 | yes | characteristic |
| 541 | D3 | — | 6 | 2 | no | — |
| 542 | D3 | — | 6 | 2 | no | — |
| 543 | D3 | — | 8 | 1 | no | — |
| 544 | D3 | — | 12 | 2 | no | — |
| 545 | D3 | — | 24 | 2 | no | — |
| 546 | D3 | — | 24 | 1 | no | — |
| 547 | D3 | — | 24 | 1 | no | — |
| 548 | C22 | — | 4 | 2 | no | — |
| 549 | C22 | — | 9 | 2 | no | — |
| 550 | C22 | — | 12 | 1 | no | — |
| 551 | C22 | — | 16 | 1 | no | — |
| 552 | C22 | — | 36 | 1 | no | — |
| 553 | C22 | — | 144 | 2 | no | — |
| 554 | C22 | #63926 | 1 | 1 | yes | characteristic |
| 555 | C4 | — | 9 | 2 | no | — |
| 556 | C4 | — | 12 | 1 | no | — |
| 557 | C4 | — | 12 | 2 | no | — |
| 558 | C4 | — | 36 | 1 | no | — |
| 559 | C4 | #63926 | 1 | 1 | yes | characteristic |
| 560 | C4 | C2×#3811 | 1 | 1 | yes | characteristic |
| 561 | C3 | — | 2 | 1 | no | — |
| 562 | C3 | #82024 | 1 | 1 | yes | characteristic, complemented |
| 563 | C3 | #82037 | 1 | 1 | yes | characteristic, complemented |
| 564 | C2 | — | 2 | 1 | no | — |
| 565 | C2 | — | 8 | 2 | no | — |
| 566 | C2 | — | 18 | 2 | no | — |
| 567 | C2 | — | 24 | 1 | no | — |
| 568 | C2 | — | 72 | 1 | no | — |
| 569 | C2 | C2×#63926 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596228 | C2 | semidirect |
| 2. #10594703 | C2 | semidirect |
| 3. C2×C3×#827 | C2 | semidirect |
| 4. C3×#5147 | C2 | semidirect |
| 5. #10591036 | C2 | semidirect |
| 6. #10591035 | C2 | semidirect |
| 7. #10591030 | C2 | semidirect |
| 8. #10591029 | C2 | semidirect |
| 9. #10590642 | C2 | semidirect |
| 10. #10590632 | C2 | semidirect |
| 11. #10590624 | C2 | semidirect |
| 23. C2×C3×Dic12 | C22 | semidirect |
| 24. C3×#904 | C22 | semidirect |
| 27. #63810 | C22 | semidirect |
| 28. #63802 | C22 | semidirect |
| 29. C3×#827 | C22 | semidirect |
| 30. C3×#827 | C22 | semidirect |
| 31. C3×#827 | C22 | semidirect |
| 32. C3×#826 | C22 | semidirect |
| 33. C3×#812 | C22 | semidirect |
| 34. C2×C3×C3⋊C16 | C22 | semidirect |
| 35. #63551 | C22 | semidirect |
| 36. #63551 | C22 | semidirect |
| 37. #63549 | C22 | semidirect |
| 38. #63549 | C22 | semidirect |
| 39. #63548 | C22 | semidirect |
| 40. #63546 | C22 | semidirect |
| 41. #63544 | C22 | semidirect |
| 42. #63542 | C22 | semidirect |
| 52. C2×#827 | D3 | semidirect |
| 53. #5147 | D3 | semidirect |
| 133. C2×Dic12 | C2×D3 | semidirect |
| 137. #904 | C2×D3 | semidirect |
| 152. #827 | C2×D3 | semidirect |
| 153. #827 | C2×D3 | semidirect |
| 154. #827 | C2×D3 | semidirect |
| 156. #826 | C2×D3 | semidirect |
| 157. #812 | C2×D3 | semidirect |
| 158. C2×C3⋊C16 | C2×D3 | semidirect |
| 500. C32 | #3416 | semidirect |
| 562. C3 | #82024 | semidirect |
| 563. C3 | #82037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596228 | 2 |
| #10594703 | 2 |
| C2×C3×#827 | 2 |
| C3×#5147 | 2 |
| #10591036 | 2 |
| #10591035 | 2 |
| #10591030 | 2 |
| #10591029 | 2 |
| #10590642 | 2 |
| #10590632 | 2 |
| #10590624 | 2 |
| #82037 | 3 |
| #82024 | 3 |