Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
961 conjugacy classes of subgroups.
The subgroup lattice has 652 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#5752 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10595464 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10594703 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10592843 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#5143 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10591664 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10591020 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10590980 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10590929 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10590919 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #10590869 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #84011 | — | 3 | 1 | no | maximal |
| 13 | #80946 | — | 3 | 1 | no | maximal |
| 14 | C3×#1009 | C22 | 1 | 2 | yes | — |
| 15 | #64297 | C22 | 1 | 2 | yes | complemented |
| 16 | C32×#131 | C22 | 1 | 1 | yes | characteristic |
| 17 | #64159 | C22 | 1 | 1 | yes | characteristic |
| 18 | #64110 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C3×#951 | C22 | 1 | 2 | yes | — |
| 20 | C3×#908 | — | 2 | 2 | no | — |
| 21 | C3×#908 | C22 | 1 | 2 | yes | — |
| 22 | C2×C3×Dic12 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C3×#904 | — | 2 | 1 | no | — |
| 24 | C3×#904 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×C3×D24 | — | 2 | 1 | no | — |
| 26 | C2×C3×D24 | C22 | 1 | 1 | yes | characteristic |
| 27 | #63949 | — | 2 | 2 | no | — |
| 28 | #63943 | — | 2 | 2 | no | — |
| 29 | #63934 | — | 2 | 2 | no | — |
| 30 | D3×#214 | — | 2 | 2 | no | — |
| 31 | #63863 | C22 | 1 | 2 | yes | complemented |
| 32 | #63830 | C22 | 1 | 2 | yes | complemented |
| 33 | #63827 | C22 | 1 | 2 | yes | complemented |
| 34 | C2×#3715 | C22 | 1 | 2 | yes | complemented |
| 35 | #63815 | C22 | 1 | 2 | yes | complemented |
| 36 | #63811 | — | 2 | 2 | no | — |
| 37 | #63810 | — | 2 | 1 | no | — |
| 38 | #63802 | — | 2 | 1 | no | — |
| 39 | #63664 | C22 | 1 | 1 | yes | characteristic |
| 40 | #63652 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #63649 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | C8×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | C3×#824 | C22 | 1 | 2 | yes | complemented |
| 44 | C3×#819 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | #63568 | C22 | 1 | 2 | yes | complemented |
| 46 | #63558 | C22 | 1 | 2 | yes | complemented |
| 47 | C3×#576 | — | 3 | 1 | no | — |
| 48 | #5836 | — | 3 | 2 | no | — |
| 49 | #5778 | — | 3 | 2 | no | — |
| 50 | #5771 | — | 3 | 1 | no | — |
| 51 | #5766 | — | 3 | 1 | no | — |
| 52 | #5752 | D3 | 1 | 1 | yes | characteristic, complemented |
| 53 | C3×#473 | — | 3 | 1 | no | — |
| 54 | #5242 | — | 3 | 2 | no | — |
| 55 | #5202 | — | 3 | 2 | no | — |
| 56 | #5201 | — | 3 | 2 | no | — |
| 57 | #5200 | — | 3 | 2 | no | — |
| 58 | #5196 | — | 3 | 1 | no | — |
| 59 | #5191 | — | 3 | 1 | no | — |
| 60 | #5160 | — | 3 | 1 | no | — |
| 61 | #5155 | — | 3 | 1 | no | — |
| 62 | #5144 | — | 3 | 1 | no | — |
| 63 | #5144 | — | 3 | 1 | no | — |
| 64 | #5144 | — | 6 | 1 | no | — |
| 65 | #5143 | D3 | 1 | 1 | yes | characteristic, complemented |
| 66 | #4897 | — | 3 | 1 | no | — |
| 67 | #4895 | — | 3 | 1 | no | — |
| 68 | #4754 | — | 3 | 2 | no | — |
| 69 | #4753 | — | 3 | 2 | no | — |
| 70 | C32×#41 | C23 | 1 | 1 | yes | characteristic |
| 71 | #3828 | C23 | 1 | 1 | yes | characteristic |
| 72 | C3×#239 | — | 2 | 2 | no | — |
| 73 | C3×D3×D4 | — | 2 | 2 | no | — |
| 74 | C3×D3×D4 | — | 4 | 2 | no | — |
| 75 | C3×#235 | — | 2 | 2 | no | — |
| 76 | C3×#235 | C23 | 1 | 2 | yes | — |
| 77 | C2×C3×D12 | — | 2 | 2 | no | — |
| 78 | C2×C3×D12 | C23 | 1 | 2 | yes | — |
| 79 | C2×C3×Dic6 | C23 | 1 | 2 | yes | — |
| 80 | #3804 | — | 4 | 2 | no | — |
| 81 | #3799 | — | 2 | 2 | no | — |
| 82 | #3797 | — | 2 | 2 | no | — |
| 83 | #3796 | — | 2 | 2 | no | — |
| 84 | D3×Dic6 | — | 2 | 2 | no | — |
| 85 | C32×M16 | — | 2 | 1 | no | — |
| 86 | C32×M16 | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×C32×C8 | — | 2 | 1 | no | — |
| 88 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 89 | #3756 | D4 | 1 | 1 | yes | characteristic |
| 90 | #3755 | D4 | 1 | 1 | yes | characteristic |
| 91 | #3754 | D4 | 1 | 1 | yes | characteristic |
| 92 | #3753 | D4 | 1 | 1 | yes | characteristic |
| 93 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 94 | #3748 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 96 | #3743 | — | 2 | 1 | no | — |
| 97 | C8×C3⋊D3 | — | 2 | 1 | no | — |
| 98 | C3×#216 | — | 2 | 2 | no | — |
| 99 | C3×#214 | — | 2 | 2 | no | — |
| 100 | C3×#208 | C23 | 1 | 2 | yes | — |
| 101 | C3×Dic12 | — | 2 | 1 | no | — |
| 102 | C3×Dic12 | — | 2 | 1 | no | — |
| 103 | C3×Dic12 | D4 | 1 | 1 | yes | characteristic |
| 104 | C3×D24 | — | 2 | 2 | no | — |
| 105 | C3×D24 | — | 2 | 1 | no | — |
| 106 | C3×D24 | — | 2 | 1 | no | — |
| 107 | C3×D24 | D4 | 1 | 1 | yes | characteristic |
| 108 | C3×#204 | — | 2 | 2 | no | — |
| 109 | C3×#204 | D4 | 1 | 2 | yes | — |
| 110 | (C2×D3)⋊Dic3 | — | 4 | 2 | no | — |
| 111 | #3718 | — | 2 | 2 | no | — |
| 112 | #3716 | — | 2 | 2 | no | — |
| 113 | #3715 | — | 2 | 2 | no | — |
| 114 | #3715 | — | 2 | 2 | no | — |
| 115 | #3715 | — | 2 | 2 | no | — |
| 116 | #3714 | — | 2 | 2 | no | — |
| 117 | #3711 | — | 2 | 2 | no | — |
| 118 | D3×C3⋊C8 | — | 2 | 2 | no | — |
| 119 | #3290 | — | 9 | 1 | no | Sylow |
| 120 | C3×H(5,𝔽2) | — | 3 | 2 | no | — |
| 121 | #1010 | — | 3 | 2 | no | — |
| 122 | #1009 | C2×D3 | 1 | 2 | yes | — |
| 123 | #1007 | — | 3 | 2 | no | — |
| 124 | C3×#137 | — | 3 | 2 | no | — |
| 125 | C3×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 126 | C3×AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 127 | C3×#135 | — | 3 | 1 | no | — |
| 128 | C3×#135 | — | 6 | 1 | no | — |
| 129 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 130 | C2×C3×D8 | — | 3 | 1 | no | — |
| 131 | C2×C3×D8 | — | 6 | 1 | no | — |
| 132 | C3×#131 | — | 2 | 1 | no | — |
| 133 | C3×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 134 | C3×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 135 | #951 | — | 3 | 2 | no | — |
| 136 | #951 | — | 6 | 2 | no | — |
| 137 | #951 | C2×D3 | 1 | 2 | yes | — |
| 138 | #950 | — | 3 | 1 | no | — |
| 139 | #950 | — | 3 | 1 | no | — |
| 140 | #950 | — | 6 | 1 | no | — |
| 141 | #950 | — | 6 | 2 | no | — |
| 142 | #948 | — | 3 | 2 | no | — |
| 143 | #947 | — | 3 | 2 | no | — |
| 144 | #942 | — | 3 | 2 | no | — |
| 145 | C2×#215 | — | 3 | 2 | no | — |
| 146 | #936 | — | 3 | 2 | no | — |
| 147 | C2×#214 | — | 3 | 2 | no | — |
| 148 | C2×#214 | — | 6 | 2 | no | — |
| 149 | #932 | — | 3 | 2 | no | — |
| 150 | #932 | — | 6 | 2 | no | — |
| 151 | #919 | — | 6 | 2 | no | — |
| 152 | #919 | — | 6 | 1 | no | — |
| 153 | #918 | — | 6 | 2 | no | — |
| 154 | #918 | — | 6 | 2 | no | — |
| 155 | D3×Q16 | — | 6 | 1 | no | — |
| 156 | D3×Q16 | — | 6 | 1 | no | — |
| 157 | #915 | — | 6 | 2 | no | — |
| 158 | #914 | — | 6 | 2 | no | — |
| 159 | D3×SD16 | — | 6 | 2 | no | — |
| 160 | #912 | — | 6 | 1 | no | — |
| 161 | #908 | — | 2 | 2 | no | — |
| 162 | #908 | — | 3 | 2 | no | — |
| 163 | #908 | C2×D3 | 1 | 2 | yes | — |
| 164 | #907 | — | 3 | 2 | no | — |
| 165 | C2×Dic12 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 166 | #904 | — | 2 | 1 | no | — |
| 167 | #904 | C2×D3 | 1 | 1 | yes | characteristic |
| 168 | C2×D24 | — | 2 | 1 | no | — |
| 169 | C2×D24 | C2×D3 | 1 | 1 | yes | characteristic |
| 170 | #901 | — | 3 | 1 | no | — |
| 171 | #901 | — | 3 | 1 | no | — |
| 172 | #901 | — | 6 | 1 | no | — |
| 173 | C3×#108 | — | 3 | 1 | no | — |
| 174 | C3×#101 | — | 3 | 2 | no | — |
| 175 | #837 | — | 3 | 1 | no | — |
| 176 | #837 | — | 3 | 1 | no | — |
| 177 | #837 | — | 3 | 2 | no | — |
| 178 | #837 | — | 6 | 1 | no | — |
| 179 | #833 | — | 3 | 2 | no | — |
| 180 | #825 | — | 3 | 2 | no | — |
| 181 | #825 | — | 3 | 1 | no | — |
| 182 | #825 | — | 3 | 1 | no | — |
| 183 | #825 | — | 6 | 1 | no | — |
| 184 | #824 | C2×D3 | 1 | 2 | yes | complemented |
| 185 | #823 | — | 3 | 2 | no | — |
| 186 | #822 | — | 3 | 1 | no | — |
| 187 | #822 | — | 3 | 1 | no | — |
| 188 | #822 | — | 6 | 1 | no | — |
| 189 | #819 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 190 | C8×Dic3 | — | 3 | 1 | no | — |
| 191 | C8×Dic3 | — | 3 | 1 | no | — |
| 192 | C8×Dic3 | — | 6 | 1 | no | — |
| 193 | C22×C3×D3 | — | 2 | 2 | no | — |
| 194 | C22×C3×D3 | — | 4 | 2 | no | — |
| 195 | C32×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 196 | C32×D4 | — | 2 | 1 | no | — |
| 197 | C32×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 198 | C2×C32×C4 | — | 2 | 1 | no | — |
| 199 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 200 | #638 | — | 2 | 1 | no | — |
| 201 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 202 | C4⋊(C3⋊D3) | C2×D4 | 1 | 1 | yes | characteristic |
| 203 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 204 | #634 | C2×D4 | 1 | 1 | yes | characteristic |
| 205 | C3×#67 | — | 2 | 2 | no | — |
| 206 | C3×#67 | — | 4 | 2 | no | — |
| 207 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 208 | C3×D12 | — | 2 | 2 | no | — |
| 209 | C3×D12 | — | 2 | 2 | no | — |
| 210 | C3×D12 | — | 4 | 2 | no | — |
| 211 | C3×D12 | C2×D4 | 1 | 2 | yes | — |
| 212 | C3×C4×D3 | — | 2 | 2 | no | — |
| 213 | C3×C4×D3 | — | 4 | 2 | no | — |
| 214 | C3×Dic6 | — | 2 | 2 | no | — |
| 215 | C3×Dic6 | — | 2 | 2 | no | — |
| 216 | C3×Dic6 | C2×D4 | 1 | 2 | yes | — |
| 217 | #627 | — | 4 | 2 | no | — |
| 218 | #626 | — | 4 | 2 | no | — |
| 219 | #624 | — | 4 | 2 | no | — |
| 220 | D3×Dic3 | — | 4 | 2 | no | — |
| 221 | C32×C8 | — | 2 | 1 | no | — |
| 222 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 223 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 224 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 225 | C3⋊(C3⋊C8) | C2×D4 | 1 | 1 | yes | characteristic |
| 226 | C3⋊(C3⋊C8) | C2×D4 | 1 | 1 | yes | characteristic |
| 227 | C3×C3⋊C8 | — | 2 | 2 | no | — |
| 228 | #578 | — | 9 | 1 | no | — |
| 229 | #577 | — | 9 | 2 | no | — |
| 230 | #576 | — | 3 | 1 | no | — |
| 231 | #495 | — | 9 | 1 | no | — |
| 232 | #473 | — | 3 | 1 | no | — |
| 233 | #472 | — | 9 | 1 | no | — |
| 234 | #471 | — | 9 | 2 | no | — |
| 235 | #455 | — | 9 | 2 | no | — |
| 236 | #454 | — | 9 | 2 | no | — |
| 237 | #443 | — | 9 | 1 | no | — |
| 238 | #443 | — | 9 | 1 | no | — |
| 239 | C3×#41 | — | 2 | 1 | no | — |
| 240 | C3×#41 | — | 3 | 2 | no | — |
| 241 | C3×#41 | — | 6 | 2 | no | — |
| 242 | C3×#41 | — | 6 | 2 | no | — |
| 243 | C3×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 244 | C3×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 245 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 246 | C2×C3×D4 | — | 3 | 2 | no | — |
| 247 | C2×C3×D4 | — | 6 | 2 | no | — |
| 248 | C2×C3×D4 | — | 6 | 2 | no | — |
| 249 | C2×C3×D4 | — | 12 | 2 | no | — |
| 250 | #239 | — | 2 | 2 | no | — |
| 251 | #239 | — | 6 | 2 | no | — |
| 252 | #239 | — | 6 | 2 | no | — |
| 253 | D3×Q8 | — | 6 | 2 | no | — |
| 254 | D3×Q8 | — | 6 | 2 | no | — |
| 255 | D3×Q8 | — | 6 | 2 | no | — |
| 256 | #237 | — | 6 | 2 | no | — |
| 257 | #237 | — | 12 | 2 | no | — |
| 258 | D3×D4 | — | 2 | 2 | no | — |
| 259 | D3×D4 | — | 4 | 2 | no | — |
| 260 | #235 | — | 2 | 2 | no | — |
| 261 | #235 | — | 3 | 1 | no | — |
| 262 | #235 | — | 3 | 1 | no | — |
| 263 | #235 | — | 6 | 1 | no | — |
| 264 | #235 | — | 6 | 2 | no | — |
| 265 | #235 | — | 12 | 2 | no | — |
| 266 | #235 | C22×D3 | 1 | 2 | yes | — |
| 267 | C2×D12 | — | 2 | 2 | no | — |
| 268 | C2×D12 | C22×D3 | 1 | 2 | yes | — |
| 269 | C2×Dic6 | — | 6 | 2 | no | — |
| 270 | C2×Dic6 | C22×D3 | 1 | 2 | yes | — |
| 271 | C3×Q16 | — | 3 | 1 | no | — |
| 272 | C3×Q16 | — | 6 | 2 | no | — |
| 273 | C3×Q16 | — | 6 | 1 | no | — |
| 274 | C3×Q16 | — | 6 | 1 | no | — |
| 275 | C3×SD16 | — | 3 | 2 | no | — |
| 276 | C3×SD16 | — | 6 | 2 | no | — |
| 277 | C3×SD16 | — | 6 | 2 | no | — |
| 278 | C3×D8 | — | 3 | 1 | no | — |
| 279 | C3×D8 | — | 6 | 2 | no | — |
| 280 | C3×D8 | — | 6 | 1 | no | — |
| 281 | C3×D8 | — | 6 | 1 | no | — |
| 282 | C3×M16 | — | 2 | 1 | no | — |
| 283 | C3×M16 | — | 2 | 1 | no | — |
| 284 | C3×M16 | — | 2 | 1 | no | — |
| 285 | C3×M16 | — | 3 | 2 | no | — |
| 286 | C3×M16 | — | 4 | 1 | no | — |
| 287 | C3×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 288 | C3×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 289 | C2×C3×C8 | — | 2 | 1 | no | — |
| 290 | C2×C3×C8 | — | 2 | 1 | no | — |
| 291 | C2×C3×C8 | — | 2 | 1 | no | — |
| 292 | C2×C3×C8 | — | 4 | 1 | no | — |
| 293 | C2×C3×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 294 | C2×C3×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 295 | #217 | — | 12 | 2 | no | — |
| 296 | #216 | — | 2 | 2 | no | — |
| 297 | #216 | — | 3 | 1 | no | — |
| 298 | #216 | — | 3 | 1 | no | — |
| 299 | #216 | — | 6 | 1 | no | — |
| 300 | #216 | — | 6 | 2 | no | — |
| 301 | #216 | — | 6 | 2 | no | — |
| 302 | #215 | — | 3 | 1 | no | — |
| 303 | #215 | — | 3 | 1 | no | — |
| 304 | #215 | — | 6 | 1 | no | — |
| 305 | #215 | — | 6 | 2 | no | — |
| 306 | #215 | — | 6 | 2 | no | — |
| 307 | #215 | — | 6 | 2 | no | — |
| 308 | #214 | — | 2 | 2 | no | — |
| 309 | #214 | — | 3 | 1 | no | — |
| 310 | #214 | — | 3 | 1 | no | — |
| 311 | #214 | — | 6 | 1 | no | — |
| 312 | #214 | — | 6 | 2 | no | — |
| 313 | #214 | — | 6 | 2 | no | — |
| 314 | #214 | — | 6 | 2 | no | — |
| 315 | #214 | — | 6 | 2 | no | — |
| 316 | #213 | — | 3 | 1 | no | — |
| 317 | #213 | — | 3 | 1 | no | — |
| 318 | #213 | — | 6 | 1 | no | — |
| 319 | #213 | — | 6 | 2 | no | — |
| 320 | (C2×D3)⋊C4 | — | 12 | 2 | no | — |
| 321 | C4×Dic3 | — | 3 | 1 | no | — |
| 322 | C4×Dic3 | — | 3 | 1 | no | — |
| 323 | C4×Dic3 | — | 6 | 1 | no | — |
| 324 | #208 | — | 3 | 1 | no | — |
| 325 | #208 | — | 3 | 1 | no | — |
| 326 | #208 | — | 6 | 1 | no | — |
| 327 | #208 | — | 6 | 2 | no | — |
| 328 | #208 | C22×D3 | 1 | 2 | yes | — |
| 329 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 330 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 331 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 332 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 333 | Dic12 | — | 2 | 1 | no | — |
| 334 | Dic12 | — | 2 | 1 | no | — |
| 335 | Dic12 | #67 | 1 | 1 | yes | characteristic |
| 336 | D24 | — | 2 | 2 | no | — |
| 337 | D24 | — | 2 | 1 | no | — |
| 338 | D24 | — | 2 | 1 | no | — |
| 339 | D24 | — | 6 | 2 | no | — |
| 340 | D24 | #67 | 1 | 1 | yes | characteristic |
| 341 | #204 | — | 2 | 2 | no | — |
| 342 | #204 | — | 6 | 2 | no | — |
| 343 | #204 | #67 | 1 | 2 | yes | — |
| 344 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 345 | ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 346 | ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 347 | ΓL(1,𝔽25) | — | 12 | 1 | no | — |
| 348 | D3×C8 | — | 6 | 2 | no | — |
| 349 | D3×C8 | — | 6 | 1 | no | — |
| 350 | D3×C8 | — | 6 | 1 | no | — |
| 351 | D3×C8 | — | 12 | 1 | no | — |
| 352 | C22×C32 | — | 2 | 1 | no | — |
| 353 | C22×C32 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 354 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 355 | C2×C3×D3 | — | 2 | 2 | no | — |
| 356 | C2×C3×D3 | — | 4 | 2 | no | — |
| 357 | C2×C3×D3 | — | 8 | 2 | no | — |
| 358 | C2×C3×D3 | — | 16 | 2 | no | — |
| 359 | C32×C4 | — | 2 | 1 | no | — |
| 360 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 361 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 362 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 363 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 364 | C3×Dic3 | — | 2 | 2 | no | — |
| 365 | C3×Dic3 | — | 4 | 2 | no | — |
| 366 | 2−1+4 | — | 9 | 2 | no | — |
| 367 | H(5,𝔽2) | — | 3 | 2 | no | — |
| 368 | #137 | — | 3 | 2 | no | — |
| 369 | #137 | — | 9 | 2 | no | — |
| 370 | #137 | — | 18 | 2 | no | — |
| 371 | #137 | — | 18 | 2 | no | — |
| 372 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 373 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 374 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 375 | AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 376 | #135 | — | 3 | 1 | no | — |
| 377 | #135 | — | 6 | 1 | no | — |
| 378 | #135 | — | 9 | 1 | no | — |
| 379 | #135 | — | 18 | 1 | no | — |
| 380 | #135 | — | 18 | 2 | no | — |
| 381 | C2×Q16 | — | 3 | 1 | no | — |
| 382 | C2×Q16 | — | 18 | 1 | no | — |
| 383 | C2×SD16 | — | 9 | 2 | no | — |
| 384 | C2×SD16 | — | 18 | 2 | no | — |
| 385 | C2×D8 | — | 3 | 1 | no | — |
| 386 | C2×D8 | — | 6 | 1 | no | — |
| 387 | #131 | — | 9 | 2 | no | — |
| 388 | #131 | — | 9 | 1 | no | — |
| 389 | #131 | D32 | 1 | 1 | yes | characteristic |
| 390 | #124 | — | 9 | 2 | no | — |
| 391 | #108 | — | 3 | 1 | no | — |
| 392 | #108 | — | 9 | 1 | no | — |
| 393 | #104 | — | 9 | 2 | no | — |
| 394 | #104 | — | 9 | 1 | no | — |
| 395 | #104 | — | 9 | 1 | no | — |
| 396 | #101 | — | 3 | 2 | no | — |
| 397 | #100 | — | 9 | 2 | no | — |
| 398 | C4×C8 | — | 9 | 1 | no | — |
| 399 | C23×C3 | — | 6 | 2 | no | — |
| 400 | C23×C3 | — | 12 | 2 | no | — |
| 401 | C22×D3 | — | 2 | 2 | no | — |
| 402 | C22×D3 | — | 4 | 2 | no | — |
| 403 | C3×Q8 | — | 2 | 1 | no | — |
| 404 | C3×Q8 | — | 3 | 2 | no | — |
| 405 | C3×Q8 | — | 6 | 2 | no | — |
| 406 | C3×Q8 | — | 6 | 2 | no | — |
| 407 | C3×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 408 | C3×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 409 | C3×D4 | — | 2 | 1 | no | — |
| 410 | C3×D4 | — | 2 | 1 | no | — |
| 411 | C3×D4 | — | 2 | 1 | no | — |
| 412 | C3×D4 | — | 3 | 2 | no | — |
| 413 | C3×D4 | — | 4 | 1 | no | — |
| 414 | C3×D4 | — | 6 | 2 | no | — |
| 415 | C3×D4 | — | 6 | 2 | no | — |
| 416 | C3×D4 | — | 6 | 2 | no | — |
| 417 | C3×D4 | — | 12 | 2 | no | — |
| 418 | C3×D4 | — | 12 | 2 | no | — |
| 419 | C3×D4 | D3×D4 | 1 | 1 | yes | characteristic |
| 420 | C3×D4 | D3×D4 | 1 | 1 | yes | characteristic |
| 421 | C2×C3×C4 | — | 2 | 1 | no | — |
| 422 | C2×C3×C4 | — | 2 | 1 | no | — |
| 423 | C2×C3×C4 | — | 2 | 1 | no | — |
| 424 | C2×C3×C4 | — | 4 | 1 | no | — |
| 425 | C2×C3×C4 | — | 6 | 2 | no | — |
| 426 | C2×C3×C4 | — | 6 | 2 | no | — |
| 427 | C2×C3×C4 | — | 12 | 2 | no | — |
| 428 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 429 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 430 | #67 | — | 2 | 2 | no | — |
| 431 | #67 | — | 4 | 2 | no | — |
| 432 | #67 | — | 6 | 1 | no | — |
| 433 | #67 | — | 6 | 1 | no | — |
| 434 | #67 | — | 12 | 1 | no | — |
| 435 | #67 | — | 12 | 2 | no | — |
| 436 | C2×Dic3 | — | 2 | 2 | no | — |
| 437 | C2×Dic3 | — | 6 | 1 | no | — |
| 438 | C2×Dic3 | — | 6 | 1 | no | — |
| 439 | C2×Dic3 | — | 12 | 1 | no | — |
| 440 | C2×Dic3 | — | 12 | 2 | no | — |
| 441 | D12 | — | 2 | 2 | no | — |
| 442 | D12 | — | 2 | 2 | no | — |
| 443 | D12 | — | 3 | 1 | no | — |
| 444 | D12 | — | 3 | 1 | no | — |
| 445 | D12 | — | 4 | 2 | no | — |
| 446 | D12 | — | 6 | 1 | no | — |
| 447 | D12 | — | 12 | 2 | no | — |
| 448 | D12 | C2×#67 | 1 | 2 | yes | — |
| 449 | C4×D3 | — | 2 | 2 | no | — |
| 450 | C4×D3 | — | 4 | 2 | no | — |
| 451 | C4×D3 | — | 6 | 1 | no | — |
| 452 | C4×D3 | — | 6 | 1 | no | — |
| 453 | C4×D3 | — | 12 | 1 | no | — |
| 454 | C4×D3 | — | 12 | 2 | no | — |
| 455 | C4×D3 | — | 12 | 2 | no | — |
| 456 | C4×D3 | — | 12 | 2 | no | — |
| 457 | Dic6 | — | 2 | 2 | no | — |
| 458 | Dic6 | — | 2 | 2 | no | — |
| 459 | Dic6 | — | 3 | 1 | no | — |
| 460 | Dic6 | — | 3 | 1 | no | — |
| 461 | Dic6 | — | 6 | 1 | no | — |
| 462 | Dic6 | — | 12 | 2 | no | — |
| 463 | Dic6 | — | 12 | 2 | no | — |
| 464 | Dic6 | C2×#67 | 1 | 2 | yes | — |
| 465 | C3×C8 | — | 2 | 1 | no | — |
| 466 | C3×C8 | — | 2 | 1 | no | — |
| 467 | C3×C8 | — | 2 | 1 | no | — |
| 468 | C3×C8 | — | 2 | 1 | no | — |
| 469 | C3×C8 | — | 4 | 1 | no | — |
| 470 | C3×C8 | — | 6 | 2 | no | — |
| 471 | C3×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 472 | C3×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 473 | C3×C8 | C2×#67 | 1 | 1 | yes | characteristic |
| 474 | C3×C8 | C2×#67 | 1 | 1 | yes | characteristic |
| 475 | C3⋊C8 | — | 2 | 2 | no | — |
| 476 | C3⋊C8 | — | 3 | 1 | no | — |
| 477 | C3⋊C8 | — | 3 | 1 | no | — |
| 478 | C3⋊C8 | — | 3 | 1 | no | — |
| 479 | C3⋊C8 | — | 3 | 1 | no | — |
| 480 | C3⋊C8 | — | 6 | 1 | no | — |
| 481 | C3⋊C8 | — | 6 | 1 | no | — |
| 482 | C3⋊C8 | — | 6 | 1 | no | — |
| 483 | C3⋊C8 | — | 6 | 1 | no | — |
| 484 | C3⋊C8 | — | 12 | 1 | no | — |
| 485 | C2×C32 | — | 2 | 1 | no | — |
| 486 | C2×C32 | — | 4 | 1 | no | — |
| 487 | C2×C32 | D42 | 1 | 1 | yes | characteristic |
| 488 | C3⋊D3 | — | 4 | 1 | no | — |
| 489 | C3×D3 | — | 4 | 2 | no | — |
| 490 | C3×D3 | — | 8 | 2 | no | — |
| 491 | #41 | — | 3 | 2 | no | — |
| 492 | #41 | — | 6 | 2 | no | — |
| 493 | #41 | — | 6 | 2 | no | — |
| 494 | #41 | — | 9 | 1 | no | — |
| 495 | #41 | — | 18 | 2 | no | — |
| 496 | #41 | — | 18 | 2 | no | — |
| 497 | #41 | — | 36 | 2 | no | — |
| 498 | #41 | C2×D32 | 1 | 1 | yes | characteristic |
| 499 | C2×Q8 | — | 3 | 2 | no | — |
| 500 | C2×Q8 | — | 18 | 2 | no | — |
| 501 | C2×Q8 | — | 18 | 2 | no | — |
| 502 | C2×D4 | — | 3 | 2 | no | — |
| 503 | C2×D4 | — | 6 | 2 | no | — |
| 504 | C2×D4 | — | 6 | 2 | no | — |
| 505 | C2×D4 | — | 12 | 2 | no | — |
| 506 | Q16 | — | 3 | 1 | no | — |
| 507 | Q16 | — | 6 | 2 | no | — |
| 508 | Q16 | — | 6 | 1 | no | — |
| 509 | Q16 | — | 6 | 1 | no | — |
| 510 | Q16 | — | 9 | 1 | no | — |
| 511 | Q16 | — | 18 | 2 | no | — |
| 512 | SD16 | — | 3 | 2 | no | — |
| 513 | SD16 | — | 6 | 2 | no | — |
| 514 | SD16 | — | 6 | 2 | no | — |
| 515 | SD16 | — | 9 | 1 | no | — |
| 516 | SD16 | — | 9 | 1 | no | — |
| 517 | SD16 | — | 18 | 2 | no | — |
| 518 | SD16 | — | 18 | 2 | no | — |
| 519 | SD16 | — | 18 | 2 | no | — |
| 520 | SD16 | — | 18 | 2 | no | — |
| 521 | D8 | — | 3 | 1 | no | — |
| 522 | D8 | — | 6 | 2 | no | — |
| 523 | D8 | — | 6 | 1 | no | — |
| 524 | D8 | — | 6 | 1 | no | — |
| 525 | D8 | — | 9 | 1 | no | — |
| 526 | D8 | — | 18 | 2 | no | — |
| 527 | M16 | — | 2 | 1 | no | — |
| 528 | M16 | — | 3 | 2 | no | — |
| 529 | M16 | — | 9 | 1 | no | — |
| 530 | M16 | — | 18 | 2 | no | — |
| 531 | M16 | — | 18 | 1 | no | — |
| 532 | M16 | C2×D32 | 1 | 1 | yes | characteristic |
| 533 | C2×C8 | — | 2 | 1 | no | — |
| 534 | C2×C8 | — | 9 | 1 | no | — |
| 535 | C2×C8 | — | 18 | 2 | no | — |
| 536 | C2×C8 | — | 18 | 1 | no | — |
| 537 | C2×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 538 | C22⋊C4 | — | 36 | 2 | no | — |
| 539 | C42 | — | 9 | 1 | no | — |
| 540 | C22×C3 | — | 2 | 1 | no | — |
| 541 | C22×C3 | — | 2 | 1 | no | — |
| 542 | C22×C3 | — | 2 | 1 | no | — |
| 543 | C22×C3 | — | 4 | 1 | no | — |
| 544 | C22×C3 | — | 6 | 2 | no | — |
| 545 | C22×C3 | — | 12 | 2 | no | — |
| 546 | C22×C3 | — | 24 | 2 | no | — |
| 547 | C22×C3 | — | 48 | 2 | no | — |
| 548 | C22×C3 | #1004 | 1 | 1 | yes | characteristic |
| 549 | C22×C3 | #1009 | 1 | 1 | yes | characteristic |
| 550 | C2×D3 | — | 2 | 2 | no | — |
| 551 | C2×D3 | — | 4 | 2 | no | — |
| 552 | C2×D3 | — | 6 | 1 | no | — |
| 553 | C2×D3 | — | 6 | 1 | no | — |
| 554 | C2×D3 | — | 8 | 2 | no | — |
| 555 | C2×D3 | — | 12 | 1 | no | — |
| 556 | C2×D3 | — | 16 | 2 | no | — |
| 557 | C3×C4 | — | 2 | 1 | no | — |
| 558 | C3×C4 | — | 2 | 1 | no | — |
| 559 | C3×C4 | — | 2 | 1 | no | — |
| 560 | C3×C4 | — | 2 | 1 | no | — |
| 561 | C3×C4 | — | 4 | 1 | no | — |
| 562 | C3×C4 | — | 6 | 2 | no | — |
| 563 | C3×C4 | — | 12 | 2 | no | — |
| 564 | C3×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 565 | C3×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 566 | C3×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 567 | C3×C4 | C22×#67 | 1 | 1 | yes | characteristic |
| 568 | Dic3 | — | 2 | 2 | no | — |
| 569 | Dic3 | — | 4 | 2 | no | — |
| 570 | Dic3 | — | 6 | 1 | no | — |
| 571 | Dic3 | — | 6 | 1 | no | — |
| 572 | Dic3 | — | 12 | 1 | no | — |
| 573 | Dic3 | — | 12 | 1 | no | — |
| 574 | Dic3 | — | 12 | 1 | no | — |
| 575 | Dic3 | — | 12 | 2 | no | — |
| 576 | C32 | #3290 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 577 | C23 | — | 6 | 2 | no | — |
| 578 | C23 | — | 12 | 2 | no | — |
| 579 | Q8 | — | 3 | 2 | no | — |
| 580 | Q8 | — | 6 | 2 | no | — |
| 581 | Q8 | — | 6 | 2 | no | — |
| 582 | Q8 | — | 9 | 1 | no | — |
| 583 | Q8 | — | 36 | 2 | no | — |
| 584 | Q8 | #3802 | 1 | 1 | yes | characteristic |
| 585 | D4 | — | 2 | 1 | no | — |
| 586 | D4 | — | 3 | 2 | no | — |
| 587 | D4 | — | 6 | 2 | no | — |
| 588 | D4 | — | 6 | 2 | no | — |
| 589 | D4 | — | 6 | 2 | no | — |
| 590 | D4 | — | 9 | 1 | no | — |
| 591 | D4 | — | 12 | 2 | no | — |
| 592 | D4 | — | 12 | 2 | no | — |
| 593 | D4 | — | 18 | 1 | no | — |
| 594 | D4 | — | 36 | 2 | no | — |
| 595 | D4 | #3802 | 1 | 1 | yes | characteristic |
| 596 | C2×C4 | — | 2 | 1 | no | — |
| 597 | C2×C4 | — | 6 | 2 | no | — |
| 598 | C2×C4 | — | 6 | 2 | no | — |
| 599 | C2×C4 | — | 12 | 2 | no | — |
| 600 | C2×C4 | — | 18 | 1 | no | — |
| 601 | C2×C4 | — | 18 | 1 | no | — |
| 602 | C2×C4 | — | 36 | 2 | no | — |
| 603 | C2×C4 | — | 36 | 2 | no | — |
| 604 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 605 | C8 | — | 2 | 1 | no | — |
| 606 | C8 | — | 6 | 2 | no | — |
| 607 | C8 | — | 9 | 1 | no | — |
| 608 | C8 | — | 9 | 1 | no | — |
| 609 | C8 | — | 18 | 1 | no | — |
| 610 | C8 | D3×#67 | 1 | 1 | yes | characteristic |
| 611 | C8 | D3×#67 | 1 | 1 | yes | characteristic |
| 612 | C2×C3 | — | 2 | 1 | no | — |
| 613 | C2×C3 | — | 2 | 1 | no | — |
| 614 | C2×C3 | — | 2 | 1 | no | — |
| 615 | C2×C3 | — | 4 | 1 | no | — |
| 616 | C2×C3 | — | 4 | 1 | no | — |
| 617 | C2×C3 | — | 4 | 1 | no | — |
| 618 | C2×C3 | — | 8 | 1 | no | — |
| 619 | C2×C3 | — | 12 | 2 | no | — |
| 620 | C2×C3 | — | 24 | 2 | no | — |
| 621 | C2×C3 | #5609 | 1 | 1 | yes | characteristic |
| 622 | C2×C3 | D4×#67 | 1 | 1 | yes | characteristic |
| 623 | D3 | — | 4 | 2 | no | — |
| 624 | D3 | — | 8 | 2 | no | — |
| 625 | D3 | — | 12 | 1 | no | — |
| 626 | D3 | — | 12 | 1 | no | — |
| 627 | D3 | — | 24 | 1 | no | — |
| 628 | C22 | — | 2 | 1 | no | — |
| 629 | C22 | — | 6 | 2 | no | — |
| 630 | C22 | — | 12 | 2 | no | — |
| 631 | C22 | — | 18 | 1 | no | — |
| 632 | C22 | — | 24 | 2 | no | — |
| 633 | C22 | — | 48 | 2 | no | — |
| 634 | C22 | #64307 | 1 | 1 | yes | characteristic |
| 635 | C4 | — | 2 | 1 | no | — |
| 636 | C4 | — | 6 | 2 | no | — |
| 637 | C4 | — | 12 | 2 | no | — |
| 638 | C4 | — | 18 | 1 | no | — |
| 639 | C4 | — | 36 | 1 | no | — |
| 640 | C4 | C2×#3802 | 1 | 1 | yes | characteristic |
| 641 | C4 | C2×D3×#67 | 1 | 1 | yes | characteristic |
| 642 | C3 | — | 2 | 1 | no | — |
| 643 | C3 | #80946 | 1 | 1 | yes | characteristic, complemented |
| 644 | C3 | #84011 | 1 | 1 | yes | characteristic, complemented |
| 645 | C2 | — | 2 | 1 | no | — |
| 646 | C2 | — | 4 | 1 | no | — |
| 647 | C2 | — | 12 | 2 | no | — |
| 648 | C2 | — | 24 | 2 | no | — |
| 649 | C2 | — | 36 | 1 | no | — |
| 650 | C2 | #10595069 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#5752 | C2 | semidirect |
| 2. #10595464 | C2 | semidirect |
| 3. #10594703 | C2 | semidirect |
| 4. #10592843 | C2 | semidirect |
| 5. C3×#5143 | C2 | semidirect |
| 6. #10591664 | C2 | semidirect |
| 7. #10591020 | C2 | semidirect |
| 8. #10590980 | C2 | semidirect |
| 9. #10590929 | C2 | semidirect |
| 10. #10590919 | C2 | semidirect |
| 11. #10590869 | C2 | semidirect |
| 15. #64297 | C22 | semidirect |
| 18. #64110 | C22 | semidirect |
| 22. C2×C3×Dic12 | C22 | semidirect |
| 31. #63863 | C22 | semidirect |
| 32. #63830 | C22 | semidirect |
| 33. #63827 | C22 | semidirect |
| 34. C2×#3715 | C22 | semidirect |
| 35. #63815 | C22 | semidirect |
| 40. #63652 | C22 | semidirect |
| 41. #63649 | C22 | semidirect |
| 42. C8×C3⋊Dic3 | C22 | semidirect |
| 43. C3×#824 | C22 | semidirect |
| 44. C3×#819 | C22 | semidirect |
| 45. #63568 | C22 | semidirect |
| 46. #63558 | C22 | semidirect |
| 52. #5752 | D3 | semidirect |
| 65. #5143 | D3 | semidirect |
| 165. C2×Dic12 | C2×D3 | semidirect |
| 184. #824 | C2×D3 | semidirect |
| 189. #819 | C2×D3 | semidirect |
| 576. C32 | #3290 | semidirect |
| 643. C3 | #80946 | semidirect |
| 644. C3 | #84011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5752 | 2 |
| #10595464 | 2 |
| #10594703 | 2 |
| #10592843 | 2 |
| C3×#5143 | 2 |
| #10591664 | 2 |
| #10591020 | 2 |
| #10590980 | 2 |
| #10590929 | 2 |
| #10590919 | 2 |
| #10590869 | 2 |
| #84011 | 3 |
| #80946 | 3 |