Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1086 conjugacy classes of subgroups.
The subgroup lattice has 679 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 | #10595102 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10594678 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#5160 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#5151 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10591523 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10591511 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10591406 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10590929 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10590923 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #10590917 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #81791 | — | 3 | 1 | no | maximal |
| 13 | #80941 | — | 3 | 1 | no | maximal |
| 14 | #64361 | C22 | 1 | 2 | yes | complemented |
| 15 | #64307 | C22 | 1 | 2 | yes | complemented |
| 16 | C2×C32×D8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #64141 | C22 | 1 | 2 | yes | complemented |
| 18 | #64121 | — | 2 | 1 | no | — |
| 19 | #64120 | — | 2 | 2 | no | — |
| 20 | D8×C3⋊D3 | — | 2 | 1 | no | — |
| 21 | #64113 | C22 | 1 | 1 | yes | characteristic |
| 22 | #64110 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C3×#940 | C22 | 1 | 2 | yes | complemented |
| 24 | C3×#932 | C22 | 1 | 2 | yes | complemented |
| 25 | C2×C3×#213 | C22 | 1 | 2 | yes | complemented |
| 26 | C2×C3×D24 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C3×#901 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #63937 | — | 2 | 2 | no | — |
| 29 | #63936 | — | 2 | 2 | no | — |
| 30 | #63927 | — | 2 | 2 | no | — |
| 31 | #63926 | — | 2 | 2 | no | — |
| 32 | #63830 | C22 | 1 | 2 | yes | complemented |
| 33 | #63830 | C22 | 1 | 2 | yes | complemented |
| 34 | #63829 | C22 | 1 | 1 | yes | characteristic |
| 35 | #63817 | C22 | 1 | 2 | yes | complemented |
| 36 | #63807 | — | 2 | 1 | no | — |
| 37 | #63795 | — | 2 | 2 | no | — |
| 38 | D3×D24 | — | 2 | 1 | no | — |
| 39 | C3×#833 | C22 | 1 | 2 | yes | complemented |
| 40 | C3×#819 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C3×C8×Dic3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #63577 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | #63570 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | #63570 | C22 | 1 | 2 | yes | complemented |
| 45 | #63569 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #63558 | C22 | 1 | 2 | yes | complemented |
| 47 | #5774 | — | 3 | 2 | no | — |
| 48 | #5757 | — | 3 | 1 | no | — |
| 49 | #5757 | — | 3 | 1 | no | — |
| 50 | #5757 | — | 3 | 2 | no | — |
| 51 | #5757 | — | 3 | 1 | no | — |
| 52 | #5757 | — | 6 | 1 | no | — |
| 53 | #5752 | — | 3 | 1 | no | — |
| 54 | C3×#493 | — | 3 | 1 | no | — |
| 55 | C3×#472 | — | 3 | 1 | no | — |
| 56 | #5198 | — | 3 | 2 | no | — |
| 57 | #5160 | — | 3 | 2 | no | — |
| 58 | #5160 | — | 3 | 1 | no | — |
| 59 | #5160 | D3 | 1 | 1 | yes | characteristic, complemented |
| 60 | #5151 | D3 | 1 | 1 | yes | characteristic, complemented |
| 61 | #5144 | — | 3 | 1 | no | — |
| 62 | #5077 | — | 3 | 2 | no | — |
| 63 | #5077 | — | 3 | 2 | no | — |
| 64 | #4897 | — | 3 | 1 | no | — |
| 65 | #4895 | — | 3 | 1 | no | — |
| 66 | #4749 | — | 3 | 2 | no | — |
| 67 | #4747 | — | 3 | 2 | no | — |
| 68 | #4700 | — | 3 | 1 | no | — |
| 69 | #4700 | — | 3 | 1 | no | — |
| 70 | C2×C32×D4 | C23 | 1 | 2 | yes | — |
| 71 | C2×#638 | — | 4 | 2 | no | — |
| 72 | #3830 | — | 2 | 2 | no | — |
| 73 | #3830 | — | 2 | 2 | no | — |
| 74 | D4×C3⋊D3 | — | 2 | 2 | no | — |
| 75 | D4×C3⋊D3 | — | 2 | 2 | no | — |
| 76 | #3828 | C23 | 1 | 2 | yes | — |
| 77 | #3828 | C23 | 1 | 1 | yes | characteristic |
| 78 | C2×C3×#67 | — | 4 | 2 | no | — |
| 79 | C3×#235 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×C3×D12 | C23 | 1 | 2 | yes | — |
| 81 | D3×#67 | — | 4 | 2 | no | — |
| 82 | #3802 | — | 2 | 2 | no | — |
| 83 | D3×D12 | — | 2 | 2 | no | — |
| 84 | #3796 | — | 2 | 2 | no | — |
| 85 | #3795 | — | 2 | 2 | no | — |
| 86 | C32×D8 | — | 2 | 1 | no | — |
| 87 | C32×D8 | — | 2 | 1 | no | — |
| 88 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 89 | #3754 | — | 2 | 2 | no | — |
| 90 | #3753 | — | 2 | 2 | no | — |
| 91 | #3748 | C23 | 1 | 1 | yes | characteristic |
| 92 | #3746 | D4 | 1 | 1 | yes | characteristic, complemented |
| 93 | #3745 | D4 | 1 | 1 | yes | characteristic, complemented |
| 94 | #3744 | D4 | 1 | 2 | yes | complemented |
| 95 | #3743 | — | 2 | 1 | no | — |
| 96 | C8×C3⋊D3 | — | 2 | 1 | no | — |
| 97 | C3×#214 | — | 2 | 2 | no | — |
| 98 | C3×#213 | — | 2 | 2 | no | — |
| 99 | C3×#213 | — | 2 | 2 | no | — |
| 100 | C3×#213 | — | 2 | 2 | no | — |
| 101 | C3×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 102 | C3×#208 | C23 | 1 | 1 | yes | characteristic |
| 103 | C3×#208 | C23 | 1 | 2 | yes | — |
| 104 | C2×C3×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 105 | C3×D24 | — | 2 | 1 | no | — |
| 106 | C3×D24 | — | 2 | 1 | no | — |
| 107 | C3×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 108 | C3×D3×C8 | — | 2 | 1 | no | — |
| 109 | #3719 | D4 | 1 | 1 | yes | characteristic, complemented |
| 110 | #3717 | D4 | 1 | 1 | yes | characteristic, complemented |
| 111 | #3716 | — | 2 | 2 | no | — |
| 112 | #3716 | — | 2 | 2 | no | — |
| 113 | #3716 | D4 | 1 | 1 | yes | characteristic, complemented |
| 114 | #3714 | — | 2 | 2 | no | — |
| 115 | #3714 | — | 2 | 2 | no | — |
| 116 | #3714 | D4 | 1 | 1 | yes | characteristic, complemented |
| 117 | #3712 | — | 2 | 2 | no | — |
| 118 | #3710 | — | 2 | 2 | no | — |
| 119 | #3292 | — | 9 | 1 | no | Sylow |
| 120 | #1009 | — | 3 | 2 | no | — |
| 121 | #1004 | — | 3 | 2 | no | — |
| 122 | #1004 | — | 3 | 2 | no | — |
| 123 | #1004 | — | 3 | 2 | no | — |
| 124 | #1004 | — | 6 | 2 | no | — |
| 125 | C3×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 126 | C2×C3×D8 | — | 2 | 1 | no | — |
| 127 | C2×C3×D8 | — | 3 | 2 | no | — |
| 128 | C2×C3×D8 | — | 3 | 1 | no | — |
| 129 | C2×C3×D8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 130 | C2×C3×D8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 131 | C3×#131 | — | 3 | 1 | no | — |
| 132 | C3×#127 | — | 3 | 2 | no | — |
| 133 | #950 | — | 3 | 1 | no | — |
| 134 | #940 | C2×D3 | 1 | 2 | yes | complemented |
| 135 | #932 | — | 3 | 2 | no | — |
| 136 | #932 | — | 3 | 2 | no | — |
| 137 | #932 | — | 3 | 2 | no | — |
| 138 | #932 | — | 3 | 2 | no | — |
| 139 | #932 | — | 6 | 2 | no | — |
| 140 | #932 | C2×D3 | 1 | 2 | yes | complemented |
| 141 | C2×#213 | C2×D3 | 1 | 2 | yes | complemented |
| 142 | #916 | — | 6 | 2 | no | — |
| 143 | #914 | — | 6 | 2 | no | — |
| 144 | #912 | — | 6 | 1 | no | — |
| 145 | #912 | — | 6 | 2 | no | — |
| 146 | #912 | — | 6 | 1 | no | — |
| 147 | #912 | — | 6 | 1 | no | — |
| 148 | #912 | — | 6 | 2 | no | — |
| 149 | #911 | — | 6 | 2 | no | — |
| 150 | #911 | — | 6 | 2 | no | — |
| 151 | #911 | — | 6 | 2 | no | — |
| 152 | #911 | — | 6 | 2 | no | — |
| 153 | #911 | — | 6 | 2 | no | — |
| 154 | #911 | — | 6 | 2 | no | — |
| 155 | #911 | — | 6 | 4 | no | — |
| 156 | D3×D8 | — | 6 | 1 | no | — |
| 157 | D3×D8 | — | 6 | 2 | no | — |
| 158 | D3×D8 | — | 6 | 1 | no | — |
| 159 | D3×D8 | — | 6 | 1 | no | — |
| 160 | D3×D8 | — | 6 | 2 | no | — |
| 161 | D3×D8 | — | 6 | 2 | no | — |
| 162 | #908 | — | 3 | 2 | no | — |
| 163 | #908 | — | 3 | 2 | no | — |
| 164 | #908 | — | 6 | 2 | no | — |
| 165 | #907 | — | 3 | 2 | no | — |
| 166 | #904 | — | 3 | 1 | no | — |
| 167 | #904 | — | 3 | 1 | no | — |
| 168 | #904 | — | 3 | 1 | no | — |
| 169 | #904 | — | 6 | 1 | no | — |
| 170 | #904 | — | 6 | 1 | no | — |
| 171 | C2×D24 | — | 6 | 1 | no | — |
| 172 | C2×D24 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 173 | #901 | — | 3 | 1 | no | — |
| 174 | #901 | — | 3 | 1 | no | — |
| 175 | #901 | — | 3 | 2 | no | — |
| 176 | #901 | — | 6 | 1 | no | — |
| 177 | #901 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 178 | C3×#108 | — | 3 | 1 | no | — |
| 179 | C3×#100 | — | 3 | 2 | no | — |
| 180 | C3×C4×C8 | — | 3 | 1 | no | — |
| 181 | #837 | — | 3 | 1 | no | — |
| 182 | #833 | — | 3 | 2 | no | — |
| 183 | #833 | C2×D3 | 1 | 2 | yes | complemented |
| 184 | #825 | — | 3 | 1 | no | — |
| 185 | #825 | — | 3 | 2 | no | — |
| 186 | #823 | — | 3 | 2 | no | — |
| 187 | #822 | — | 3 | 1 | no | — |
| 188 | #819 | — | 3 | 1 | no | — |
| 189 | #819 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 190 | C8×Dic3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 191 | #805 | — | 3 | 1 | no | — |
| 192 | #805 | — | 3 | 1 | no | — |
| 193 | #805 | — | 3 | 2 | no | — |
| 194 | C23×C32 | — | 2 | 2 | no | — |
| 195 | C22×C3⋊D3 | — | 4 | 2 | no | — |
| 196 | C22×C3×D3 | — | 2 | 2 | no | — |
| 197 | C2×D32 | — | 4 | 2 | no | — |
| 198 | C32×D4 | — | 2 | 2 | no | — |
| 199 | C32×D4 | — | 2 | 2 | no | — |
| 200 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 201 | #638 | — | 2 | 1 | no | — |
| 202 | #638 | — | 2 | 2 | no | — |
| 203 | #638 | — | 4 | 2 | no | — |
| 204 | #638 | — | 4 | 2 | no | — |
| 205 | C2×C3⋊Dic3 | — | 4 | 2 | no | — |
| 206 | C4⋊(C3⋊D3) | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | C4⋊(C3⋊D3) | C2×D4 | 1 | 2 | yes | — |
| 208 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 209 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 210 | #634 | C2×D4 | 1 | 1 | yes | characteristic |
| 211 | #634 | C2×D4 | 1 | 2 | yes | — |
| 212 | C3×#67 | — | 2 | 1 | no | — |
| 213 | C3×#67 | — | 8 | 4 | no | — |
| 214 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 215 | C3×D12 | — | 2 | 2 | no | — |
| 216 | C3×D12 | — | 2 | 2 | no | — |
| 217 | C3×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 218 | C3×C4×D3 | — | 2 | 1 | no | — |
| 219 | C3×Dic6 | C2×D4 | 1 | 1 | yes | characteristic |
| 220 | #626 | — | 4 | 2 | no | — |
| 221 | #625 | — | 4 | 2 | no | — |
| 222 | D3×Dic3 | — | 4 | 2 | no | — |
| 223 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 224 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 225 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 226 | C3×C3⋊C8 | — | 2 | 2 | no | — |
| 227 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 228 | C3×C3⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 229 | C3×C3⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 230 | #576 | — | 9 | 1 | no | — |
| 231 | #576 | — | 9 | 2 | no | — |
| 232 | #576 | — | 9 | 1 | no | — |
| 233 | #493 | — | 3 | 1 | no | — |
| 234 | #472 | — | 3 | 1 | no | — |
| 235 | #472 | — | 9 | 2 | no | — |
| 236 | #472 | — | 9 | 1 | no | — |
| 237 | #453 | — | 9 | 2 | no | — |
| 238 | #453 | — | 9 | 2 | no | — |
| 239 | #443 | — | 9 | 1 | no | — |
| 240 | #443 | — | 9 | 1 | no | — |
| 241 | C3×#41 | — | 3 | 1 | no | — |
| 242 | C2×C3×D4 | — | 2 | 2 | no | — |
| 243 | C2×C3×D4 | — | 3 | 2 | no | — |
| 244 | C2×C3×D4 | — | 12 | 2 | no | — |
| 245 | C2×C3×D4 | C22×D3 | 1 | 2 | yes | — |
| 246 | C2×C3×D4 | C22×D3 | 1 | 2 | yes | — |
| 247 | C2×#67 | — | 4 | 2 | no | — |
| 248 | C2×#67 | — | 12 | 2 | no | — |
| 249 | C2×#67 | — | 12 | 2 | no | — |
| 250 | C2×#67 | — | 12 | 2 | no | — |
| 251 | C2×#67 | — | 12 | 4 | no | — |
| 252 | #239 | — | 6 | 2 | no | — |
| 253 | #237 | — | 6 | 2 | no | — |
| 254 | #237 | — | 6 | 2 | no | — |
| 255 | #237 | — | 6 | 2 | no | — |
| 256 | #237 | — | 6 | 2 | no | — |
| 257 | #237 | — | 6 | 2 | no | — |
| 258 | #237 | — | 6 | 4 | no | — |
| 259 | #237 | — | 6 | 2 | no | — |
| 260 | #237 | — | 12 | 2 | no | — |
| 261 | D3×D4 | — | 6 | 2 | no | — |
| 262 | D3×D4 | — | 6 | 2 | no | — |
| 263 | D3×D4 | — | 6 | 2 | no | — |
| 264 | D3×D4 | — | 6 | 2 | no | — |
| 265 | D3×D4 | — | 6 | 2 | no | — |
| 266 | D3×D4 | — | 6 | 2 | no | — |
| 267 | D3×D4 | — | 6 | 4 | no | — |
| 268 | D3×D4 | — | 6 | 2 | no | — |
| 269 | D3×D4 | — | 12 | 2 | no | — |
| 270 | D3×D4 | — | 12 | 2 | no | — |
| 271 | #235 | — | 3 | 1 | no | — |
| 272 | #235 | — | 3 | 2 | no | — |
| 273 | #235 | — | 3 | 1 | no | — |
| 274 | #235 | — | 3 | 2 | no | — |
| 275 | #235 | — | 6 | 1 | no | — |
| 276 | #235 | — | 6 | 2 | no | — |
| 277 | #235 | — | 6 | 2 | no | — |
| 278 | #235 | C22×D3 | 1 | 1 | yes | characteristic |
| 279 | C2×D12 | — | 6 | 2 | no | — |
| 280 | C2×D12 | C22×D3 | 1 | 2 | yes | — |
| 281 | C3×SD16 | — | 6 | 2 | no | — |
| 282 | C3×D8 | — | 2 | 2 | no | — |
| 283 | C3×D8 | — | 2 | 2 | no | — |
| 284 | C3×D8 | — | 2 | 1 | no | — |
| 285 | C3×D8 | — | 2 | 1 | no | — |
| 286 | C3×D8 | — | 2 | 1 | no | — |
| 287 | C3×D8 | — | 2 | 1 | no | — |
| 288 | C3×D8 | — | 6 | 2 | no | — |
| 289 | C3×D8 | — | 6 | 2 | no | — |
| 290 | C3×D8 | — | 6 | 2 | no | — |
| 291 | C3×D8 | — | 6 | 1 | no | — |
| 292 | C3×D8 | — | 6 | 1 | no | — |
| 293 | C3×M16 | — | 3 | 1 | no | — |
| 294 | C3×M16 | — | 3 | 2 | no | — |
| 295 | C3×M16 | — | 6 | 1 | no | — |
| 296 | C2×C3×C8 | — | 2 | 1 | no | — |
| 297 | C2×C3×C8 | — | 3 | 1 | no | — |
| 298 | C2×C3×C8 | — | 6 | 1 | no | — |
| 299 | C2×C3×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 300 | C2×C3×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 301 | C3×C42 | — | 3 | 1 | no | — |
| 302 | #216 | — | 3 | 1 | no | — |
| 303 | #215 | — | 3 | 1 | no | — |
| 304 | #214 | — | 2 | 2 | no | — |
| 305 | #214 | — | 3 | 1 | no | — |
| 306 | #214 | — | 6 | 2 | no | — |
| 307 | #214 | — | 6 | 2 | no | — |
| 308 | #214 | — | 6 | 2 | no | — |
| 309 | #214 | — | 6 | 2 | no | — |
| 310 | #214 | — | 6 | 4 | no | — |
| 311 | #213 | — | 2 | 2 | no | — |
| 312 | #213 | — | 2 | 2 | no | — |
| 313 | #213 | — | 2 | 2 | no | — |
| 314 | #213 | — | 3 | 1 | no | — |
| 315 | #213 | — | 6 | 2 | no | — |
| 316 | #213 | — | 6 | 2 | no | — |
| 317 | #213 | — | 6 | 2 | no | — |
| 318 | #213 | — | 6 | 2 | no | — |
| 319 | #213 | — | 6 | 4 | no | — |
| 320 | C4×Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 321 | #208 | — | 3 | 1 | no | — |
| 322 | #208 | — | 3 | 1 | no | — |
| 323 | #208 | — | 6 | 1 | no | — |
| 324 | #208 | C22×D3 | 1 | 1 | yes | characteristic |
| 325 | #208 | C22×D3 | 1 | 2 | yes | — |
| 326 | C2×C3⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 327 | Dic12 | — | 3 | 1 | no | — |
| 328 | Dic12 | — | 3 | 1 | no | — |
| 329 | Dic12 | — | 3 | 1 | no | — |
| 330 | Dic12 | — | 6 | 1 | no | — |
| 331 | D24 | — | 2 | 1 | no | — |
| 332 | D24 | — | 2 | 1 | no | — |
| 333 | D24 | — | 3 | 1 | no | — |
| 334 | D24 | — | 3 | 1 | no | — |
| 335 | D24 | — | 3 | 1 | no | — |
| 336 | D24 | — | 6 | 1 | no | — |
| 337 | D24 | — | 6 | 2 | no | — |
| 338 | D24 | — | 6 | 2 | no | — |
| 339 | #204 | — | 3 | 1 | no | — |
| 340 | #204 | — | 3 | 1 | no | — |
| 341 | #204 | — | 3 | 2 | no | — |
| 342 | #204 | — | 3 | 2 | no | — |
| 343 | #204 | — | 6 | 2 | no | — |
| 344 | #204 | — | 6 | 2 | no | — |
| 345 | #204 | — | 6 | 2 | no | — |
| 346 | ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 347 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 348 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 349 | ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 350 | ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 351 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 352 | D3×C8 | — | 2 | 1 | no | — |
| 353 | D3×C8 | — | 6 | 2 | no | — |
| 354 | D3×C8 | — | 6 | 2 | no | — |
| 355 | D3×C8 | — | 6 | 1 | no | — |
| 356 | D3×C8 | — | 6 | 1 | no | — |
| 357 | D3×C8 | — | 6 | 2 | no | — |
| 358 | C22×C32 | — | 4 | 2 | no | — |
| 359 | C22×C32 | — | 8 | 2 | no | — |
| 360 | C22×C32 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 361 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 362 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 363 | C2×C3⋊D3 | — | 16 | 2 | no | — |
| 364 | C2×C3×D3 | — | 2 | 1 | no | — |
| 365 | C2×C3×D3 | — | 4 | 2 | no | — |
| 366 | C2×C3×D3 | — | 8 | 2 | no | — |
| 367 | D32 | — | 16 | 2 | no | — |
| 368 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 369 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 370 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 371 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 372 | C3×Dic3 | — | 2 | 2 | no | — |
| 373 | C3×Dic3 | — | 2 | 1 | no | — |
| 374 | H(5,𝔽2) | — | 9 | 2 | no | — |
| 375 | H(5,𝔽2) | — | 9 | 2 | no | — |
| 376 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 377 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 378 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 379 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 380 | AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 381 | AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 382 | AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 383 | AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 384 | #135 | — | 9 | 1 | no | — |
| 385 | #135 | — | 9 | 1 | no | — |
| 386 | #135 | — | 18 | 1 | no | — |
| 387 | #135 | — | 18 | 1 | no | — |
| 388 | #135 | — | 18 | 2 | no | — |
| 389 | C2×D8 | — | 3 | 2 | no | — |
| 390 | C2×D8 | — | 3 | 1 | no | — |
| 391 | C2×D8 | — | 18 | 1 | no | — |
| 392 | C2×D8 | — | 18 | 1 | no | — |
| 393 | C2×D8 | — | 18 | 2 | no | — |
| 394 | C2×D8 | D32 | 1 | 1 | yes | characteristic, complemented |
| 395 | #131 | — | 3 | 1 | no | — |
| 396 | #131 | — | 9 | 2 | no | — |
| 397 | #131 | — | 9 | 1 | no | — |
| 398 | #127 | — | 3 | 2 | no | — |
| 399 | #108 | — | 3 | 1 | no | — |
| 400 | #108 | — | 9 | 1 | no | — |
| 401 | #104 | — | 9 | 1 | no | — |
| 402 | #104 | — | 9 | 2 | no | — |
| 403 | #104 | — | 9 | 1 | no | — |
| 404 | #100 | — | 3 | 2 | no | — |
| 405 | #100 | — | 9 | 2 | no | — |
| 406 | C4×C8 | — | 3 | 1 | no | — |
| 407 | C23×C3 | — | 2 | 2 | no | — |
| 408 | C23×C3 | — | 2 | 2 | no | — |
| 409 | C23×C3 | — | 4 | 2 | no | — |
| 410 | C23×C3 | — | 6 | 2 | no | — |
| 411 | C22×D3 | — | 2 | 2 | no | — |
| 412 | C22×D3 | — | 12 | 2 | no | — |
| 413 | C22×D3 | — | 12 | 2 | no | — |
| 414 | C22×D3 | — | 12 | 2 | no | — |
| 415 | C22×D3 | — | 12 | 2 | no | — |
| 416 | C22×D3 | — | 12 | 4 | no | — |
| 417 | C3×Q8 | — | 3 | 1 | no | — |
| 418 | C3×D4 | — | 2 | 4 | no | — |
| 419 | C3×D4 | — | 2 | 2 | no | — |
| 420 | C3×D4 | — | 2 | 2 | no | — |
| 421 | C3×D4 | — | 2 | 2 | no | — |
| 422 | C3×D4 | — | 2 | 2 | no | — |
| 423 | C3×D4 | — | 3 | 1 | no | — |
| 424 | C3×D4 | — | 4 | 2 | no | — |
| 425 | C3×D4 | — | 6 | 1 | no | — |
| 426 | C3×D4 | — | 6 | 2 | no | — |
| 427 | C3×D4 | — | 6 | 2 | no | — |
| 428 | C3×D4 | — | 24 | 4 | no | — |
| 429 | C2×C3×C4 | — | 2 | 1 | no | — |
| 430 | C2×C3×C4 | — | 6 | 1 | no | — |
| 431 | C2×C3×C4 | — | 6 | 1 | no | — |
| 432 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 433 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 434 | #67 | — | 2 | 1 | no | — |
| 435 | #67 | — | 6 | 2 | no | — |
| 436 | #67 | — | 6 | 2 | no | — |
| 437 | #67 | — | 6 | 1 | no | — |
| 438 | #67 | — | 6 | 1 | no | — |
| 439 | #67 | — | 6 | 2 | no | — |
| 440 | #67 | — | 8 | 4 | no | — |
| 441 | #67 | — | 12 | 2 | no | — |
| 442 | #67 | — | 12 | 2 | no | — |
| 443 | #67 | — | 12 | 2 | no | — |
| 444 | #67 | — | 12 | 2 | no | — |
| 445 | #67 | — | 12 | 2 | no | — |
| 446 | #67 | — | 12 | 2 | no | — |
| 447 | #67 | — | 12 | 2 | no | — |
| 448 | #67 | — | 12 | 2 | no | — |
| 449 | #67 | — | 12 | 4 | no | — |
| 450 | #67 | — | 12 | 4 | no | — |
| 451 | C2×Dic3 | — | 2 | 1 | no | — |
| 452 | C2×Dic3 | — | 12 | 2 | no | — |
| 453 | C2×Dic3 | — | 12 | 2 | no | — |
| 454 | C2×Dic3 | — | 12 | 2 | no | — |
| 455 | C2×Dic3 | — | 12 | 4 | no | — |
| 456 | D12 | — | 2 | 2 | no | — |
| 457 | D12 | — | 2 | 2 | no | — |
| 458 | D12 | — | 3 | 2 | no | — |
| 459 | D12 | — | 3 | 1 | no | — |
| 460 | D12 | — | 3 | 2 | no | — |
| 461 | D12 | — | 3 | 1 | no | — |
| 462 | D12 | — | 6 | 1 | no | — |
| 463 | D12 | — | 6 | 2 | no | — |
| 464 | D12 | — | 12 | 2 | no | — |
| 465 | D12 | D3×D4 | 1 | 1 | yes | characteristic |
| 466 | C4×D3 | — | 2 | 1 | no | — |
| 467 | C4×D3 | — | 6 | 2 | no | — |
| 468 | C4×D3 | — | 6 | 2 | no | — |
| 469 | C4×D3 | — | 6 | 1 | no | — |
| 470 | C4×D3 | — | 6 | 1 | no | — |
| 471 | C4×D3 | — | 6 | 2 | no | — |
| 472 | C4×D3 | — | 12 | 2 | no | — |
| 473 | C4×D3 | — | 12 | 2 | no | — |
| 474 | Dic6 | — | 3 | 2 | no | — |
| 475 | Dic6 | — | 3 | 1 | no | — |
| 476 | Dic6 | — | 3 | 2 | no | — |
| 477 | Dic6 | — | 3 | 1 | no | — |
| 478 | Dic6 | — | 6 | 1 | no | — |
| 479 | Dic6 | — | 6 | 2 | no | — |
| 480 | Dic6 | D3×D4 | 1 | 1 | yes | characteristic |
| 481 | C3×C8 | — | 2 | 1 | no | — |
| 482 | C3×C8 | — | 2 | 1 | no | — |
| 483 | C3×C8 | — | 3 | 1 | no | — |
| 484 | C3×C8 | — | 3 | 1 | no | — |
| 485 | C3×C8 | — | 6 | 2 | no | — |
| 486 | C3×C8 | — | 6 | 1 | no | — |
| 487 | C3×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 488 | C3×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 489 | C3×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 490 | C3×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 491 | C3⋊C8 | — | 2 | 1 | no | — |
| 492 | C3⋊C8 | — | 2 | 2 | no | — |
| 493 | C3⋊C8 | — | 6 | 2 | no | — |
| 494 | C3⋊C8 | — | 6 | 1 | no | — |
| 495 | C3⋊C8 | — | 6 | 1 | no | — |
| 496 | C3⋊C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 497 | C3⋊C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 498 | C2×C32 | — | 2 | 1 | no | — |
| 499 | C2×C32 | — | 8 | 2 | no | — |
| 500 | C2×C32 | D42 | 1 | 1 | yes | characteristic |
| 501 | C3⋊D3 | — | 4 | 1 | no | — |
| 502 | C3⋊D3 | — | 4 | 2 | no | — |
| 503 | C3×D3 | — | 4 | 1 | no | — |
| 504 | C3×D3 | — | 8 | 2 | no | — |
| 505 | #41 | — | 3 | 1 | no | — |
| 506 | #41 | — | 9 | 2 | no | — |
| 507 | #41 | — | 9 | 1 | no | — |
| 508 | #41 | — | 18 | 2 | no | — |
| 509 | #41 | — | 18 | 2 | no | — |
| 510 | #41 | — | 18 | 2 | no | — |
| 511 | #41 | — | 18 | 2 | no | — |
| 512 | C2×D4 | — | 3 | 2 | no | — |
| 513 | C2×D4 | — | 12 | 2 | no | — |
| 514 | C2×D4 | — | 18 | 2 | no | — |
| 515 | C2×D4 | — | 18 | 2 | no | — |
| 516 | C2×D4 | — | 18 | 2 | no | — |
| 517 | C2×D4 | — | 18 | 2 | no | — |
| 518 | C2×D4 | — | 36 | 2 | no | — |
| 519 | C2×D4 | — | 36 | 2 | no | — |
| 520 | C2×D4 | C2×D32 | 1 | 2 | yes | — |
| 521 | Q16 | — | 9 | 1 | no | — |
| 522 | Q16 | — | 9 | 1 | no | — |
| 523 | SD16 | — | 6 | 2 | no | — |
| 524 | SD16 | — | 9 | 1 | no | — |
| 525 | SD16 | — | 9 | 1 | no | — |
| 526 | SD16 | — | 9 | 2 | no | — |
| 527 | SD16 | — | 18 | 2 | no | — |
| 528 | SD16 | — | 18 | 2 | no | — |
| 529 | SD16 | — | 18 | 2 | no | — |
| 530 | D8 | — | 2 | 1 | no | — |
| 531 | D8 | — | 2 | 1 | no | — |
| 532 | D8 | — | 6 | 2 | no | — |
| 533 | D8 | — | 6 | 2 | no | — |
| 534 | D8 | — | 6 | 2 | no | — |
| 535 | D8 | — | 6 | 1 | no | — |
| 536 | D8 | — | 6 | 1 | no | — |
| 537 | D8 | — | 9 | 1 | no | — |
| 538 | D8 | — | 9 | 1 | no | — |
| 539 | D8 | — | 18 | 2 | no | — |
| 540 | D8 | — | 18 | 2 | no | — |
| 541 | D8 | — | 18 | 2 | no | — |
| 542 | M16 | — | 3 | 1 | no | — |
| 543 | M16 | — | 3 | 2 | no | — |
| 544 | M16 | — | 6 | 1 | no | — |
| 545 | M16 | — | 9 | 1 | no | — |
| 546 | M16 | — | 18 | 2 | no | — |
| 547 | M16 | — | 18 | 1 | no | — |
| 548 | C2×C8 | — | 3 | 1 | no | — |
| 549 | C2×C8 | — | 6 | 1 | no | — |
| 550 | C2×C8 | — | 18 | 2 | no | — |
| 551 | C2×C8 | — | 18 | 1 | no | — |
| 552 | C2×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 553 | C42 | — | 3 | 1 | no | — |
| 554 | C22×C3 | — | 2 | 1 | no | — |
| 555 | C22×C3 | — | 4 | 4 | no | — |
| 556 | C22×C3 | — | 4 | 2 | no | — |
| 557 | C22×C3 | — | 4 | 2 | no | — |
| 558 | C22×C3 | — | 6 | 1 | no | — |
| 559 | C22×C3 | — | 8 | 2 | no | — |
| 560 | C22×C3 | — | 8 | 2 | no | — |
| 561 | C22×C3 | — | 12 | 2 | no | — |
| 562 | C22×C3 | — | 16 | 2 | no | — |
| 563 | C22×C3 | — | 24 | 2 | no | — |
| 564 | C22×C3 | #1004 | 1 | 1 | yes | characteristic |
| 565 | C22×C3 | #1009 | 1 | 1 | yes | characteristic |
| 566 | C2×D3 | — | 2 | 1 | no | — |
| 567 | C2×D3 | — | 4 | 2 | no | — |
| 568 | C2×D3 | — | 6 | 2 | no | — |
| 569 | C2×D3 | — | 6 | 2 | no | — |
| 570 | C2×D3 | — | 6 | 1 | no | — |
| 571 | C2×D3 | — | 6 | 1 | no | — |
| 572 | C2×D3 | — | 6 | 2 | no | — |
| 573 | C2×D3 | — | 8 | 2 | no | — |
| 574 | C2×D3 | — | 12 | 2 | no | — |
| 575 | C2×D3 | — | 48 | 2 | no | — |
| 576 | C2×D3 | — | 48 | 2 | no | — |
| 577 | C2×D3 | — | 48 | 2 | no | — |
| 578 | C2×D3 | — | 48 | 2 | no | — |
| 579 | C2×D3 | — | 48 | 4 | no | — |
| 580 | C3×C4 | — | 2 | 1 | no | — |
| 581 | C3×C4 | — | 2 | 1 | no | — |
| 582 | C3×C4 | — | 6 | 2 | no | — |
| 583 | C3×C4 | — | 6 | 1 | no | — |
| 584 | C3×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 585 | C3×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 586 | C3×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 587 | C3×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 588 | Dic3 | — | 2 | 2 | no | — |
| 589 | Dic3 | — | 2 | 1 | no | — |
| 590 | Dic3 | — | 6 | 2 | no | — |
| 591 | Dic3 | — | 6 | 2 | no | — |
| 592 | Dic3 | — | 6 | 1 | no | — |
| 593 | Dic3 | — | 6 | 1 | no | — |
| 594 | Dic3 | — | 6 | 2 | no | — |
| 595 | Dic3 | — | 12 | 2 | no | — |
| 596 | C32 | #3292 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 597 | C23 | — | 2 | 2 | no | — |
| 598 | C23 | — | 6 | 2 | no | — |
| 599 | C23 | — | 36 | 2 | no | — |
| 600 | C23 | — | 36 | 2 | no | — |
| 601 | Q8 | — | 3 | 1 | no | — |
| 602 | Q8 | — | 9 | 1 | no | — |
| 603 | Q8 | — | 9 | 2 | no | — |
| 604 | D4 | — | 2 | 2 | no | — |
| 605 | D4 | — | 2 | 2 | no | — |
| 606 | D4 | — | 3 | 1 | no | — |
| 607 | D4 | — | 6 | 1 | no | — |
| 608 | D4 | — | 6 | 2 | no | — |
| 609 | D4 | — | 6 | 2 | no | — |
| 610 | D4 | — | 9 | 1 | no | — |
| 611 | D4 | — | 9 | 2 | no | — |
| 612 | D4 | — | 18 | 1 | no | — |
| 613 | D4 | — | 18 | 2 | no | — |
| 614 | D4 | — | 24 | 4 | no | — |
| 615 | D4 | — | 36 | 2 | no | — |
| 616 | D4 | — | 36 | 2 | no | — |
| 617 | D4 | — | 36 | 2 | no | — |
| 618 | D4 | — | 36 | 2 | no | — |
| 619 | C2×C4 | — | 6 | 1 | no | — |
| 620 | C2×C4 | — | 6 | 1 | no | — |
| 621 | C2×C4 | — | 18 | 2 | no | — |
| 622 | C2×C4 | — | 18 | 1 | no | — |
| 623 | C2×C4 | — | 36 | 2 | no | — |
| 624 | C2×C4 | — | 36 | 2 | no | — |
| 625 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 626 | C8 | — | 3 | 1 | no | — |
| 627 | C8 | — | 3 | 1 | no | — |
| 628 | C8 | — | 6 | 2 | no | — |
| 629 | C8 | — | 6 | 1 | no | — |
| 630 | C8 | — | 18 | 1 | no | — |
| 631 | C8 | #3811 | 1 | 1 | yes | characteristic |
| 632 | C8 | #3811 | 1 | 1 | yes | characteristic |
| 633 | C2×C3 | — | 2 | 1 | no | — |
| 634 | C2×C3 | — | 2 | 1 | no | — |
| 635 | C2×C3 | — | 2 | 1 | no | — |
| 636 | C2×C3 | — | 4 | 1 | no | — |
| 637 | C2×C3 | — | 8 | 4 | no | — |
| 638 | C2×C3 | — | 8 | 2 | no | — |
| 639 | C2×C3 | — | 8 | 2 | no | — |
| 640 | C2×C3 | — | 12 | 1 | no | — |
| 641 | C2×C3 | — | 24 | 2 | no | — |
| 642 | C2×C3 | #5609 | 1 | 1 | yes | characteristic |
| 643 | C2×C3 | #5717 | 1 | 1 | yes | characteristic |
| 644 | D3 | — | 4 | 1 | no | — |
| 645 | D3 | — | 8 | 2 | no | — |
| 646 | D3 | — | 12 | 2 | no | — |
| 647 | D3 | — | 12 | 1 | no | — |
| 648 | D3 | — | 12 | 2 | no | — |
| 649 | D3 | — | 12 | 1 | no | — |
| 650 | D3 | — | 12 | 2 | no | — |
| 651 | D3 | — | 24 | 2 | no | — |
| 652 | C22 | — | 4 | 2 | no | — |
| 653 | C22 | — | 6 | 1 | no | — |
| 654 | C22 | — | 8 | 2 | no | — |
| 655 | C22 | — | 12 | 2 | no | — |
| 656 | C22 | — | 18 | 1 | no | — |
| 657 | C22 | — | 18 | 2 | no | — |
| 658 | C22 | — | 24 | 2 | no | — |
| 659 | C22 | — | 144 | 2 | no | — |
| 660 | C22 | — | 144 | 2 | no | — |
| 661 | C22 | #64314 | 1 | 1 | yes | characteristic |
| 662 | C4 | — | 6 | 2 | no | — |
| 663 | C4 | — | 6 | 1 | no | — |
| 664 | C4 | — | 18 | 1 | no | — |
| 665 | C4 | — | 18 | 2 | no | — |
| 666 | C4 | D32×D4 | 1 | 1 | yes | characteristic |
| 667 | C4 | C2×#3811 | 1 | 1 | yes | characteristic |
| 668 | C3 | — | 2 | 1 | no | — |
| 669 | C3 | #80941 | 1 | 1 | yes | characteristic, complemented |
| 670 | C3 | #81791 | 1 | 1 | yes | characteristic, complemented |
| 671 | C2 | — | 2 | 1 | no | — |
| 672 | C2 | — | 8 | 2 | no | — |
| 673 | C2 | — | 12 | 1 | no | — |
| 674 | C2 | — | 24 | 2 | no | — |
| 675 | C2 | — | 36 | 1 | no | — |
| 676 | C2 | — | 36 | 2 | no | — |
| 677 | C2 | #10595297 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596228 | C2 | semidirect |
| 2. #10595102 | C2 | semidirect |
| 3. #10594678 | C2 | semidirect |
| 4. C3×#5160 | C2 | semidirect |
| 5. C3×#5151 | C2 | semidirect |
| 6. #10591523 | C2 | semidirect |
| 7. #10591511 | C2 | semidirect |
| 8. #10591406 | C2 | semidirect |
| 9. #10590929 | C2 | semidirect |
| 10. #10590923 | C2 | semidirect |
| 11. #10590917 | C2 | semidirect |
| 14. #64361 | C22 | semidirect |
| 15. #64307 | C22 | semidirect |
| 16. C2×C32×D8 | C22 | semidirect |
| 17. #64141 | C22 | semidirect |
| 22. #64110 | C22 | semidirect |
| 23. C3×#940 | C22 | semidirect |
| 24. C3×#932 | C22 | semidirect |
| 25. C2×C3×#213 | C22 | semidirect |
| 26. C2×C3×D24 | C22 | semidirect |
| 27. C3×#901 | C22 | semidirect |
| 32. #63830 | C22 | semidirect |
| 33. #63830 | C22 | semidirect |
| 35. #63817 | C22 | semidirect |
| 39. C3×#833 | C22 | semidirect |
| 40. C3×#819 | C22 | semidirect |
| 41. C3×C8×Dic3 | C22 | semidirect |
| 42. #63577 | C22 | semidirect |
| 43. #63570 | C22 | semidirect |
| 44. #63570 | C22 | semidirect |
| 45. #63569 | C22 | semidirect |
| 46. #63558 | C22 | semidirect |
| 59. #5160 | D3 | semidirect |
| 60. #5151 | D3 | semidirect |
| 92. #3746 | D4 | semidirect |
| 93. #3745 | D4 | semidirect |
| 94. #3744 | D4 | semidirect |
| 109. #3719 | D4 | semidirect |
| 110. #3717 | D4 | semidirect |
| 113. #3716 | D4 | semidirect |
| 116. #3714 | D4 | semidirect |
| 129. C2×C3×D8 | C2×D3 | semidirect |
| 130. C2×C3×D8 | C2×D3 | semidirect |
| 134. #940 | C2×D3 | semidirect |
| 140. #932 | C2×D3 | semidirect |
| 141. C2×#213 | C2×D3 | semidirect |
| 172. C2×D24 | C2×D3 | semidirect |
| 177. #901 | C2×D3 | semidirect |
| 183. #833 | C2×D3 | semidirect |
| 189. #819 | C2×D3 | semidirect |
| 190. C8×Dic3 | C2×D3 | semidirect |
| 394. C2×D8 | D32 | semidirect |
| 596. C32 | #3292 | semidirect |
| 669. C3 | #80941 | semidirect |
| 670. C3 | #81791 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596228 | 2 |
| #10595102 | 2 |
| #10594678 | 2 |
| C3×#5160 | 2 |
| C3×#5151 | 2 |
| #10591523 | 2 |
| #10591511 | 2 |
| #10591406 | 2 |
| #10590929 | 2 |
| #10590923 | 2 |
| #10590917 | 2 |
| #81791 | 3 |
| #80941 | 3 |