Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3253 conjugacy classes of subgroups.
The subgroup lattice has 572 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10596756 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#5964 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×C3×#948 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10595450 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #10595449 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10595448 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10595447 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10594795 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | C2×#63829 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | #87297 | — | 3 | 1 | no | maximal |
| 11 | #87163 | — | 3 | 1 | no | maximal |
| 12 | C2×C32×#41 | C22 | 1 | 1 | yes | characteristic |
| 13 | #64367 | C22 | 1 | 4 | yes | complemented |
| 14 | #64366 | C22 | 1 | 4 | yes | complemented |
| 15 | #41×C3⋊D3 | — | 2 | 4 | no | — |
| 16 | #64364 | — | 2 | 1 | no | — |
| 17 | #64361 | — | 2 | 3 | no | — |
| 18 | C2×#3828 | C22 | 1 | 6 | yes | complemented |
| 19 | C3×#1010 | C22 | 1 | 4 | yes | complemented |
| 20 | C3×#1009 | C22 | 1 | 4 | yes | complemented |
| 21 | C3×D3×#41 | — | 2 | 4 | no | — |
| 22 | C3×#1007 | — | 2 | 1 | no | — |
| 23 | C3×#1004 | — | 2 | 3 | no | — |
| 24 | C2×C3×#235 | C22 | 1 | 6 | yes | complemented |
| 25 | C3×#948 | C22 | 1 | 4 | yes | complemented |
| 26 | C3×#948 | C22 | 1 | 4 | yes | complemented |
| 27 | C2×C3×#208 | C22 | 1 | 3 | yes | complemented |
| 28 | C22×C3×C3⋊C8 | C22 | 1 | 3 | yes | complemented |
| 29 | C2×#3719 | C22 | 1 | 6 | yes | complemented |
| 30 | #63833 | C22 | 1 | 12 | yes | complemented |
| 31 | C2×#3717 | C22 | 1 | 6 | yes | complemented |
| 32 | #63831 | C22 | 1 | 12 | yes | complemented |
| 33 | #63830 | C22 | 1 | 12 | yes | complemented |
| 34 | #63829 | C22 | 1 | 12 | yes | complemented |
| 35 | #63829 | C22 | 1 | 12 | yes | complemented |
| 36 | #63829 | C22 | 1 | 4 | yes | complemented |
| 37 | #63829 | C22 | 1 | 12 | yes | complemented |
| 38 | C2×#3716 | C22 | 1 | 6 | yes | complemented |
| 39 | #63825 | C22 | 1 | 12 | yes | complemented |
| 40 | C2×#3714 | C22 | 1 | 6 | yes | complemented |
| 41 | C3×#585 | — | 3 | 1 | no | — |
| 42 | #5964 | — | 3 | 1 | no | — |
| 43 | #5964 | — | 3 | 1 | no | — |
| 44 | #5964 | — | 6 | 1 | no | — |
| 45 | #5964 | D3 | 1 | 1 | yes | characteristic, complemented |
| 46 | C2×C3×#131 | — | 3 | 1 | no | — |
| 47 | #5838 | — | 3 | 4 | no | — |
| 48 | #5837 | — | 3 | 4 | no | — |
| 49 | #5836 | — | 3 | 4 | no | — |
| 50 | #5835 | — | 3 | 4 | no | — |
| 51 | #5822 | — | 3 | 6 | no | — |
| 52 | C2×#950 | — | 3 | 6 | no | — |
| 53 | C2×#948 | D3 | 1 | 1 | yes | characteristic, complemented |
| 54 | #5753 | — | 3 | 4 | no | — |
| 55 | #5752 | — | 3 | 4 | no | — |
| 56 | #5751 | — | 3 | 4 | no | — |
| 57 | #5751 | — | 3 | 4 | no | — |
| 58 | #5748 | — | 3 | 6 | no | — |
| 59 | C2×#904 | — | 3 | 6 | no | — |
| 60 | C32×#41 | D4 | 1 | 4 | yes | — |
| 61 | C32×#41 | C23 | 1 | 4 | yes | — |
| 62 | C2×C32×Q8 | D4 | 1 | 1 | yes | characteristic |
| 63 | C2×C32×D4 | D4 | 1 | 3 | yes | — |
| 64 | C22×C32×C4 | C23 | 1 | 3 | yes | — |
| 65 | C2×#638 | — | 2 | 6 | no | — |
| 66 | #3832 | — | 2 | 4 | no | — |
| 67 | Q8×C3⋊D3 | — | 2 | 4 | no | — |
| 68 | #3830 | — | 2 | 12 | no | — |
| 69 | D4×C3⋊D3 | — | 2 | 12 | no | — |
| 70 | #3828 | — | 2 | 6 | no | — |
| 71 | #3828 | — | 2 | 6 | no | — |
| 72 | #3828 | C23 | 1 | 4 | yes | — |
| 73 | #3828 | C23 | 1 | 12 | yes | — |
| 74 | C2×C4⋊(C3⋊D3) | C23 | 1 | 6 | yes | — |
| 75 | C2×C4×C3⋊D3 | — | 2 | 6 | no | — |
| 76 | C2×#634 | C23 | 1 | 6 | yes | — |
| 77 | C2×C3×#67 | — | 2 | 6 | no | — |
| 78 | C3×#239 | — | 2 | 4 | no | — |
| 79 | C3×D3×Q8 | — | 2 | 4 | no | — |
| 80 | C3×#237 | — | 2 | 12 | no | — |
| 81 | C3×D3×D4 | — | 2 | 12 | no | — |
| 82 | C3×#235 | — | 2 | 6 | no | — |
| 83 | C3×#235 | — | 2 | 6 | no | — |
| 84 | C3×#235 | C23 | 1 | 12 | yes | — |
| 85 | C3×#235 | C23 | 1 | 4 | yes | — |
| 86 | C2×C3×D12 | C23 | 1 | 6 | yes | — |
| 87 | C2×C3×C4×D3 | — | 2 | 6 | no | — |
| 88 | C2×C3×Dic6 | C23 | 1 | 6 | yes | — |
| 89 | C3×#208 | C23 | 1 | 12 | yes | — |
| 90 | C2×C3×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 91 | C2×C3×C3⋊C8 | C23 | 1 | 3 | yes | — |
| 92 | C2×C3×C3⋊C8 | C23 | 1 | 6 | yes | — |
| 93 | C2×C3×C3⋊C8 | C23 | 1 | 6 | yes | — |
| 94 | #3719 | C23 | 1 | 4 | yes | — |
| 95 | #3719 | C23 | 1 | 12 | yes | — |
| 96 | #3717 | C23 | 1 | 12 | yes | — |
| 97 | #3717 | C23 | 1 | 4 | yes | — |
| 98 | #3716 | C23 | 1 | 4 | yes | — |
| 99 | #3716 | C23 | 1 | 12 | yes | — |
| 100 | #3714 | C23 | 1 | 4 | yes | — |
| 101 | #3714 | C23 | 1 | 12 | yes | — |
| 102 | #3584 | — | 9 | 1 | no | Sylow |
| 103 | C3×2−1+4 | — | 3 | 4 | no | — |
| 104 | C3×2−1+4 | — | 6 | 1 | no | — |
| 105 | C3×H(5,𝔽2) | — | 3 | 4 | no | — |
| 106 | C3×H(5,𝔽2) | — | 6 | 3 | no | — |
| 107 | C2×C3×#41 | — | 2 | 1 | no | — |
| 108 | C2×C3×#41 | — | 3 | 6 | no | — |
| 109 | C2×C3×#41 | — | 6 | 4 | no | — |
| 110 | C2×C3×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 111 | C2×C3×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 112 | #1010 | — | 3 | 4 | no | — |
| 113 | #1010 | — | 3 | 4 | no | — |
| 114 | #1010 | — | 6 | 4 | no | — |
| 115 | #1010 | C2×D3 | 1 | 4 | yes | complemented |
| 116 | #1009 | — | 3 | 4 | no | — |
| 117 | #1009 | — | 3 | 4 | no | — |
| 118 | #1009 | — | 6 | 4 | no | — |
| 119 | #1009 | C2×D3 | 1 | 4 | yes | complemented |
| 120 | D3×#41 | — | 2 | 4 | no | — |
| 121 | D3×#41 | — | 6 | 8 | no | — |
| 122 | D3×#41 | — | 6 | 4 | no | — |
| 123 | D3×#41 | — | 6 | 4 | no | — |
| 124 | #1007 | — | 2 | 1 | no | — |
| 125 | #1007 | — | 6 | 2 | no | — |
| 126 | #1007 | — | 6 | 1 | no | — |
| 127 | #1007 | — | 6 | 1 | no | — |
| 128 | #1004 | — | 2 | 3 | no | — |
| 129 | #1004 | — | 6 | 6 | no | — |
| 130 | #1004 | — | 6 | 3 | no | — |
| 131 | #1004 | — | 6 | 3 | no | — |
| 132 | C2×#235 | — | 3 | 6 | no | — |
| 133 | C2×#235 | — | 3 | 6 | no | — |
| 134 | C2×#235 | — | 6 | 6 | no | — |
| 135 | C2×#235 | C2×D3 | 1 | 6 | yes | complemented |
| 136 | C3×#131 | — | 3 | 4 | no | — |
| 137 | C3×#131 | — | 3 | 4 | no | — |
| 138 | C2×C3×M16 | — | 3 | 3 | no | — |
| 139 | C22×C3×C8 | — | 3 | 3 | no | — |
| 140 | #951 | — | 3 | 12 | no | — |
| 141 | #950 | — | 3 | 4 | no | — |
| 142 | #950 | — | 3 | 12 | no | — |
| 143 | #950 | — | 3 | 12 | no | — |
| 144 | #950 | — | 3 | 12 | no | — |
| 145 | #949 | — | 3 | 12 | no | — |
| 146 | #948 | C2×D3 | 1 | 4 | yes | complemented |
| 147 | #948 | C2×D3 | 1 | 4 | yes | complemented |
| 148 | C2×#216 | — | 3 | 6 | no | — |
| 149 | #942 | — | 3 | 12 | no | — |
| 150 | C2×#215 | — | 3 | 6 | no | — |
| 151 | C2×#214 | — | 3 | 6 | no | — |
| 152 | #932 | — | 3 | 12 | no | — |
| 153 | C2×#213 | — | 3 | 6 | no | — |
| 154 | C2×#208 | C2×D3 | 1 | 3 | yes | complemented |
| 155 | C22×C3⋊C8 | C2×D3 | 1 | 3 | yes | complemented |
| 156 | #909 | — | 3 | 12 | no | — |
| 157 | #909 | — | 3 | 12 | no | — |
| 158 | #908 | — | 3 | 12 | no | — |
| 159 | #908 | — | 3 | 12 | no | — |
| 160 | C2×Dic12 | — | 3 | 6 | no | — |
| 161 | #904 | — | 3 | 4 | no | — |
| 162 | #904 | — | 3 | 12 | no | — |
| 163 | #904 | — | 3 | 12 | no | — |
| 164 | #904 | — | 3 | 12 | no | — |
| 165 | C2×D24 | — | 3 | 6 | no | — |
| 166 | C2×#204 | — | 3 | 6 | no | — |
| 167 | C2×#204 | — | 3 | 6 | no | — |
| 168 | C23×C32 | C2×D4 | 1 | 3 | yes | — |
| 169 | C22×C3⋊D3 | — | 2 | 6 | no | — |
| 170 | C22×C3×D3 | — | 2 | 6 | no | — |
| 171 | C32×Q8 | C2×D4 | 1 | 4 | yes | — |
| 172 | C32×D4 | C2×D4 | 1 | 12 | yes | — |
| 173 | C2×C32×C4 | C2×D4 | 1 | 6 | yes | — |
| 174 | C2×C32×C4 | C2×D4 | 1 | 3 | yes | — |
| 175 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 176 | C2×C32×C4 | C24 | 1 | 6 | yes | — |
| 177 | #638 | — | 2 | 4 | no | — |
| 178 | #638 | — | 2 | 12 | no | — |
| 179 | C2×C3⋊Dic3 | — | 2 | 6 | no | — |
| 180 | C4⋊(C3⋊D3) | — | 2 | 6 | no | — |
| 181 | C4⋊(C3⋊D3) | C24 | 1 | 4 | yes | — |
| 182 | C4×C3⋊D3 | — | 2 | 4 | no | — |
| 183 | C4×C3⋊D3 | — | 2 | 12 | no | — |
| 184 | #634 | — | 2 | 6 | no | — |
| 185 | #634 | C24 | 1 | 4 | yes | — |
| 186 | C3×#67 | — | 2 | 4 | no | — |
| 187 | C3×#67 | — | 2 | 12 | no | — |
| 188 | C2×C3×Dic3 | — | 2 | 6 | no | — |
| 189 | C3×D12 | — | 2 | 6 | no | — |
| 190 | C3×D12 | C24 | 1 | 4 | yes | — |
| 191 | C3×C4×D3 | — | 2 | 4 | no | — |
| 192 | C3×C4×D3 | — | 2 | 12 | no | — |
| 193 | C3×Dic6 | — | 2 | 6 | no | — |
| 194 | C3×Dic6 | C24 | 1 | 4 | yes | — |
| 195 | C3×C3⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 196 | C3×C3⋊C8 | C24 | 1 | 6 | yes | — |
| 197 | C3×C3⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 198 | #585 | — | 3 | 1 | no | — |
| 199 | #585 | — | 9 | 1 | no | — |
| 200 | #578 | — | 9 | 4 | no | — |
| 201 | #577 | — | 9 | 4 | no | — |
| 202 | #577 | — | 9 | 4 | no | — |
| 203 | #576 | — | 9 | 4 | no | — |
| 204 | #575 | — | 9 | 6 | no | — |
| 205 | C2×#135 | — | 9 | 6 | no | — |
| 206 | C2×#131 | — | 3 | 1 | no | — |
| 207 | C3×#41 | — | 2 | 4 | no | — |
| 208 | C3×#41 | — | 2 | 4 | no | — |
| 209 | C3×#41 | — | 3 | 12 | no | — |
| 210 | C3×#41 | — | 3 | 4 | no | — |
| 211 | C3×#41 | — | 6 | 4 | no | — |
| 212 | C3×#41 | — | 6 | 12 | no | — |
| 213 | C3×#41 | — | 6 | 6 | no | — |
| 214 | C3×#41 | — | 6 | 6 | no | — |
| 215 | C3×#41 | D12 | 1 | 4 | yes | — |
| 216 | C3×#41 | #67 | 1 | 4 | yes | — |
| 217 | C3×#41 | C22×D3 | 1 | 4 | yes | — |
| 218 | C3×#41 | C22×D3 | 1 | 4 | yes | — |
| 219 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 220 | C2×C3×Q8 | — | 3 | 6 | no | — |
| 221 | C2×C3×Q8 | — | 6 | 4 | no | — |
| 222 | C2×C3×Q8 | D12 | 1 | 1 | yes | characteristic |
| 223 | C2×C3×Q8 | #67 | 1 | 1 | yes | characteristic |
| 224 | C2×C3×D4 | — | 2 | 3 | no | — |
| 225 | C2×C3×D4 | — | 3 | 6 | no | — |
| 226 | C2×C3×D4 | — | 6 | 6 | no | — |
| 227 | C2×C3×D4 | — | 6 | 12 | no | — |
| 228 | C2×C3×D4 | D12 | 1 | 3 | yes | — |
| 229 | C2×C3×D4 | #67 | 1 | 3 | yes | — |
| 230 | C22×C3×C4 | — | 2 | 3 | no | — |
| 231 | C22×C3×C4 | — | 6 | 6 | no | — |
| 232 | C22×C3×C4 | C22×D3 | 1 | 3 | yes | — |
| 233 | C22×C3×C4 | C22×D3 | 1 | 3 | yes | — |
| 234 | C2×#67 | — | 2 | 6 | no | — |
| 235 | C2×#67 | — | 6 | 12 | no | — |
| 236 | C2×#67 | — | 6 | 6 | no | — |
| 237 | C2×#67 | — | 6 | 6 | no | — |
| 238 | #239 | — | 2 | 4 | no | — |
| 239 | #239 | — | 6 | 8 | no | — |
| 240 | #239 | — | 6 | 4 | no | — |
| 241 | #239 | — | 6 | 4 | no | — |
| 242 | D3×Q8 | — | 2 | 4 | no | — |
| 243 | D3×Q8 | — | 6 | 8 | no | — |
| 244 | D3×Q8 | — | 6 | 4 | no | — |
| 245 | D3×Q8 | — | 6 | 4 | no | — |
| 246 | #237 | — | 2 | 12 | no | — |
| 247 | #237 | — | 6 | 24 | no | — |
| 248 | #237 | — | 6 | 12 | no | — |
| 249 | #237 | — | 6 | 12 | no | — |
| 250 | D3×D4 | — | 2 | 12 | no | — |
| 251 | D3×D4 | — | 6 | 24 | no | — |
| 252 | D3×D4 | — | 6 | 12 | no | — |
| 253 | D3×D4 | — | 6 | 12 | no | — |
| 254 | #235 | — | 2 | 6 | no | — |
| 255 | #235 | — | 2 | 6 | no | — |
| 256 | #235 | — | 3 | 4 | no | — |
| 257 | #235 | — | 3 | 12 | no | — |
| 258 | #235 | — | 3 | 12 | no | — |
| 259 | #235 | — | 3 | 4 | no | — |
| 260 | #235 | — | 6 | 4 | no | — |
| 261 | #235 | — | 6 | 12 | no | — |
| 262 | #235 | — | 6 | 12 | no | — |
| 263 | #235 | — | 6 | 12 | no | — |
| 264 | #235 | — | 6 | 6 | no | — |
| 265 | #235 | — | 6 | 6 | no | — |
| 266 | #235 | — | 6 | 6 | no | — |
| 267 | #235 | — | 6 | 6 | no | — |
| 268 | #235 | C22×D3 | 1 | 4 | yes | — |
| 269 | #235 | C22×D3 | 1 | 12 | yes | — |
| 270 | C2×D12 | — | 3 | 6 | no | — |
| 271 | C2×D12 | — | 3 | 6 | no | — |
| 272 | C2×D12 | — | 6 | 6 | no | — |
| 273 | C2×D12 | C22×D3 | 1 | 6 | yes | — |
| 274 | C2×C4×D3 | — | 2 | 6 | no | — |
| 275 | C2×C4×D3 | — | 6 | 12 | no | — |
| 276 | C2×C4×D3 | — | 6 | 6 | no | — |
| 277 | C2×C4×D3 | — | 6 | 6 | no | — |
| 278 | C2×Dic6 | — | 3 | 6 | no | — |
| 279 | C2×Dic6 | — | 3 | 6 | no | — |
| 280 | C2×Dic6 | — | 6 | 6 | no | — |
| 281 | C2×Dic6 | C22×D3 | 1 | 6 | yes | — |
| 282 | C3×M16 | — | 3 | 12 | no | — |
| 283 | C2×C3×C8 | — | 3 | 6 | no | — |
| 284 | C2×C3×C8 | — | 3 | 6 | no | — |
| 285 | C2×C3×C8 | — | 3 | 1 | no | — |
| 286 | C2×C3×C8 | — | 3 | 3 | no | — |
| 287 | #216 | — | 3 | 12 | no | — |
| 288 | #216 | — | 3 | 4 | no | — |
| 289 | #215 | — | 3 | 4 | no | — |
| 290 | #215 | — | 3 | 12 | no | — |
| 291 | #214 | — | 3 | 12 | no | — |
| 292 | #214 | — | 3 | 4 | no | — |
| 293 | #213 | — | 3 | 4 | no | — |
| 294 | #213 | — | 3 | 12 | no | — |
| 295 | #208 | C22×D3 | 1 | 12 | yes | — |
| 296 | C2×C3⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 297 | C2×C3⋊C8 | C22×D3 | 1 | 3 | yes | — |
| 298 | C2×C3⋊C8 | C22×D3 | 1 | 6 | yes | — |
| 299 | C2×C3⋊C8 | C22×D3 | 1 | 6 | yes | — |
| 300 | Dic12 | — | 3 | 4 | no | — |
| 301 | Dic12 | — | 3 | 12 | no | — |
| 302 | D24 | — | 3 | 4 | no | — |
| 303 | D24 | — | 3 | 12 | no | — |
| 304 | #204 | — | 3 | 4 | no | — |
| 305 | #204 | — | 3 | 12 | no | — |
| 306 | #204 | — | 3 | 4 | no | — |
| 307 | #204 | — | 3 | 12 | no | — |
| 308 | C22×C32 | — | 4 | 3 | no | — |
| 309 | C22×C32 | C22×D4 | 1 | 6 | yes | — |
| 310 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 311 | C2×C3⋊D3 | — | 2 | 4 | no | — |
| 312 | C2×C3⋊D3 | — | 8 | 6 | no | — |
| 313 | C2×C3×D3 | — | 2 | 4 | no | — |
| 314 | C2×C3×D3 | — | 8 | 6 | no | — |
| 315 | C32×C4 | C22×D4 | 1 | 6 | yes | — |
| 316 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 317 | C32×C4 | C25 | 1 | 1 | yes | characteristic |
| 318 | C3⋊Dic3 | — | 2 | 4 | no | — |
| 319 | C3×Dic3 | — | 2 | 4 | no | — |
| 320 | 2−1+4 | — | 3 | 4 | no | — |
| 321 | 2−1+4 | — | 6 | 1 | no | — |
| 322 | 2−1+4 | — | 9 | 4 | no | — |
| 323 | 2−1+4 | — | 18 | 1 | no | — |
| 324 | H(5,𝔽2) | — | 3 | 4 | no | — |
| 325 | H(5,𝔽2) | — | 6 | 3 | no | — |
| 326 | H(5,𝔽2) | — | 9 | 4 | no | — |
| 327 | H(5,𝔽2) | — | 18 | 3 | no | — |
| 328 | C2×#41 | — | 3 | 6 | no | — |
| 329 | C2×#41 | — | 6 | 4 | no | — |
| 330 | C2×#41 | — | 9 | 6 | no | — |
| 331 | C2×#41 | — | 18 | 4 | no | — |
| 332 | C2×#41 | D32 | 1 | 1 | yes | characteristic |
| 333 | #137 | — | 9 | 12 | no | — |
| 334 | #137 | — | 9 | 12 | no | — |
| 335 | AGL(1,ℤ/8) | — | 9 | 12 | no | — |
| 336 | AGL(1,ℤ/8) | — | 9 | 12 | no | — |
| 337 | #135 | — | 9 | 4 | no | — |
| 338 | #135 | — | 9 | 12 | no | — |
| 339 | #135 | — | 9 | 12 | no | — |
| 340 | #135 | — | 9 | 12 | no | — |
| 341 | C2×Q16 | — | 9 | 6 | no | — |
| 342 | C2×SD16 | — | 9 | 6 | no | — |
| 343 | C2×SD16 | — | 9 | 6 | no | — |
| 344 | C2×D8 | — | 9 | 6 | no | — |
| 345 | #131 | — | 3 | 4 | no | — |
| 346 | #131 | — | 3 | 4 | no | — |
| 347 | C2×M16 | — | 3 | 3 | no | — |
| 348 | C22×C8 | — | 3 | 3 | no | — |
| 349 | C23×C3 | — | 2 | 3 | no | — |
| 350 | C23×C3 | — | 6 | 6 | no | — |
| 351 | C23×C3 | C2×D12 | 1 | 3 | yes | — |
| 352 | C23×C3 | C2×#67 | 1 | 3 | yes | — |
| 353 | C22×D3 | — | 2 | 6 | no | — |
| 354 | C22×D3 | — | 6 | 12 | no | — |
| 355 | C22×D3 | — | 6 | 6 | no | — |
| 356 | C22×D3 | — | 6 | 6 | no | — |
| 357 | C3×Q8 | — | 2 | 4 | no | — |
| 358 | C3×Q8 | — | 3 | 4 | no | — |
| 359 | C3×Q8 | — | 6 | 6 | no | — |
| 360 | C3×Q8 | C2×D12 | 1 | 4 | yes | — |
| 361 | C3×Q8 | C2×#67 | 1 | 4 | yes | — |
| 362 | C3×D4 | — | 2 | 12 | no | — |
| 363 | C3×D4 | — | 3 | 4 | no | — |
| 364 | C3×D4 | — | 6 | 12 | no | — |
| 365 | C3×D4 | — | 6 | 4 | no | — |
| 366 | C3×D4 | — | 6 | 6 | no | — |
| 367 | C3×D4 | C2×D12 | 1 | 12 | yes | — |
| 368 | C3×D4 | C2×#67 | 1 | 12 | yes | — |
| 369 | C2×C3×C4 | — | 2 | 6 | no | — |
| 370 | C2×C3×C4 | — | 2 | 1 | no | — |
| 371 | C2×C3×C4 | — | 2 | 6 | no | — |
| 372 | C2×C3×C4 | — | 2 | 3 | no | — |
| 373 | C2×C3×C4 | — | 6 | 6 | no | — |
| 374 | C2×C3×C4 | — | 6 | 4 | no | — |
| 375 | C2×C3×C4 | — | 6 | 12 | no | — |
| 376 | C2×C3×C4 | C2×D12 | 1 | 6 | yes | — |
| 377 | C2×C3×C4 | C2×D12 | 1 | 3 | yes | — |
| 378 | C2×C3×C4 | C2×#67 | 1 | 6 | yes | — |
| 379 | C2×C3×C4 | C2×#67 | 1 | 3 | yes | — |
| 380 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 381 | C2×C3×C4 | C23×D3 | 1 | 6 | yes | — |
| 382 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 383 | C2×C3×C4 | C23×D3 | 1 | 6 | yes | — |
| 384 | #67 | — | 2 | 4 | no | — |
| 385 | #67 | — | 2 | 12 | no | — |
| 386 | #67 | — | 6 | 8 | no | — |
| 387 | #67 | — | 6 | 24 | no | — |
| 388 | #67 | — | 6 | 4 | no | — |
| 389 | #67 | — | 6 | 12 | no | — |
| 390 | #67 | — | 6 | 4 | no | — |
| 391 | #67 | — | 6 | 12 | no | — |
| 392 | C2×Dic3 | — | 2 | 6 | no | — |
| 393 | C2×Dic3 | — | 6 | 12 | no | — |
| 394 | C2×Dic3 | — | 6 | 6 | no | — |
| 395 | C2×Dic3 | — | 6 | 6 | no | — |
| 396 | D12 | — | 2 | 6 | no | — |
| 397 | D12 | — | 3 | 4 | no | — |
| 398 | D12 | — | 3 | 4 | no | — |
| 399 | D12 | — | 6 | 4 | no | — |
| 400 | D12 | — | 6 | 12 | no | — |
| 401 | D12 | — | 6 | 6 | no | — |
| 402 | D12 | — | 6 | 6 | no | — |
| 403 | D12 | C23×D3 | 1 | 4 | yes | — |
| 404 | C4×D3 | — | 2 | 4 | no | — |
| 405 | C4×D3 | — | 2 | 12 | no | — |
| 406 | C4×D3 | — | 6 | 8 | no | — |
| 407 | C4×D3 | — | 6 | 24 | no | — |
| 408 | C4×D3 | — | 6 | 4 | no | — |
| 409 | C4×D3 | — | 6 | 12 | no | — |
| 410 | C4×D3 | — | 6 | 4 | no | — |
| 411 | C4×D3 | — | 6 | 12 | no | — |
| 412 | Dic6 | — | 2 | 6 | no | — |
| 413 | Dic6 | — | 3 | 4 | no | — |
| 414 | Dic6 | — | 3 | 4 | no | — |
| 415 | Dic6 | — | 6 | 4 | no | — |
| 416 | Dic6 | — | 6 | 12 | no | — |
| 417 | Dic6 | — | 6 | 6 | no | — |
| 418 | Dic6 | — | 6 | 6 | no | — |
| 419 | Dic6 | C23×D3 | 1 | 4 | yes | — |
| 420 | C3×C8 | — | 3 | 1 | no | — |
| 421 | C3×C8 | — | 3 | 6 | no | — |
| 422 | C3×C8 | — | 3 | 1 | no | — |
| 423 | C3⋊C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 424 | C3⋊C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 425 | C3⋊C8 | C23×D3 | 1 | 6 | yes | — |
| 426 | C2×C32 | — | 2 | 6 | no | — |
| 427 | C2×C32 | — | 2 | 1 | no | — |
| 428 | C2×C32 | C23×D4 | 1 | 1 | yes | characteristic |
| 429 | C3⋊D3 | — | 4 | 4 | no | — |
| 430 | C3×D3 | — | 4 | 4 | no | — |
| 431 | #41 | — | 3 | 4 | no | — |
| 432 | #41 | — | 3 | 12 | no | — |
| 433 | #41 | — | 6 | 4 | no | — |
| 434 | #41 | — | 6 | 12 | no | — |
| 435 | #41 | — | 6 | 6 | no | — |
| 436 | #41 | — | 6 | 6 | no | — |
| 437 | #41 | — | 9 | 4 | no | — |
| 438 | #41 | — | 9 | 12 | no | — |
| 439 | #41 | — | 18 | 4 | no | — |
| 440 | #41 | — | 18 | 12 | no | — |
| 441 | #41 | — | 18 | 6 | no | — |
| 442 | #41 | — | 18 | 6 | no | — |
| 443 | #41 | #626 | 1 | 4 | yes | — |
| 444 | #41 | C2×D32 | 1 | 4 | yes | — |
| 445 | C2×Q8 | — | 3 | 6 | no | — |
| 446 | C2×Q8 | — | 6 | 4 | no | — |
| 447 | C2×Q8 | — | 9 | 6 | no | — |
| 448 | C2×Q8 | — | 18 | 4 | no | — |
| 449 | C2×Q8 | #626 | 1 | 1 | yes | characteristic |
| 450 | C2×D4 | — | 3 | 6 | no | — |
| 451 | C2×D4 | — | 6 | 6 | no | — |
| 452 | C2×D4 | — | 6 | 12 | no | — |
| 453 | C2×D4 | — | 9 | 6 | no | — |
| 454 | C2×D4 | — | 18 | 6 | no | — |
| 455 | C2×D4 | — | 18 | 12 | no | — |
| 456 | C2×D4 | #626 | 1 | 3 | yes | — |
| 457 | C22×C4 | — | 6 | 6 | no | — |
| 458 | C22×C4 | — | 18 | 6 | no | — |
| 459 | C22×C4 | C2×D32 | 1 | 3 | yes | — |
| 460 | Q16 | — | 9 | 4 | no | — |
| 461 | Q16 | — | 9 | 12 | no | — |
| 462 | SD16 | — | 9 | 4 | no | — |
| 463 | SD16 | — | 9 | 12 | no | — |
| 464 | SD16 | — | 9 | 4 | no | — |
| 465 | SD16 | — | 9 | 12 | no | — |
| 466 | D8 | — | 9 | 4 | no | — |
| 467 | D8 | — | 9 | 12 | no | — |
| 468 | M16 | — | 3 | 12 | no | — |
| 469 | C2×C8 | — | 3 | 1 | no | — |
| 470 | C2×C8 | — | 3 | 3 | no | — |
| 471 | C2×C8 | — | 3 | 6 | no | — |
| 472 | C2×C8 | — | 3 | 6 | no | — |
| 473 | C22×C3 | — | 2 | 6 | no | — |
| 474 | C22×C3 | — | 2 | 1 | no | — |
| 475 | C22×C3 | — | 4 | 3 | no | — |
| 476 | C22×C3 | — | 4 | 3 | no | — |
| 477 | C22×C3 | — | 6 | 4 | no | — |
| 478 | C22×C3 | — | 8 | 3 | no | — |
| 479 | C22×C3 | — | 24 | 6 | no | — |
| 480 | C22×C3 | C22×D12 | 1 | 6 | yes | — |
| 481 | C22×C3 | C22×D12 | 1 | 1 | yes | characteristic |
| 482 | C22×C3 | C22×#67 | 1 | 6 | yes | — |
| 483 | C22×C3 | C22×#67 | 1 | 1 | yes | characteristic |
| 484 | C2×D3 | — | 2 | 4 | no | — |
| 485 | C2×D3 | — | 6 | 8 | no | — |
| 486 | C2×D3 | — | 6 | 4 | no | — |
| 487 | C2×D3 | — | 6 | 4 | no | — |
| 488 | C2×D3 | — | 8 | 6 | no | — |
| 489 | C2×D3 | — | 24 | 6 | no | — |
| 490 | C2×D3 | — | 24 | 6 | no | — |
| 491 | C2×D3 | — | 24 | 12 | no | — |
| 492 | C3×C4 | — | 2 | 6 | no | — |
| 493 | C3×C4 | — | 2 | 1 | no | — |
| 494 | C3×C4 | — | 2 | 1 | no | — |
| 495 | C3×C4 | — | 6 | 4 | no | — |
| 496 | C3×C4 | C22×D12 | 1 | 6 | yes | — |
| 497 | C3×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 498 | C3×C4 | C22×#67 | 1 | 6 | yes | — |
| 499 | C3×C4 | C22×#67 | 1 | 1 | yes | characteristic |
| 500 | C3×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 501 | C3×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 502 | Dic3 | — | 2 | 4 | no | — |
| 503 | Dic3 | — | 6 | 8 | no | — |
| 504 | Dic3 | — | 6 | 4 | no | — |
| 505 | Dic3 | — | 6 | 4 | no | — |
| 506 | C32 | #3584 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 507 | C23 | — | 6 | 6 | no | — |
| 508 | C23 | — | 18 | 6 | no | — |
| 509 | C23 | C2×#626 | 1 | 3 | yes | — |
| 510 | Q8 | — | 3 | 4 | no | — |
| 511 | Q8 | — | 6 | 6 | no | — |
| 512 | Q8 | — | 9 | 4 | no | — |
| 513 | Q8 | — | 18 | 6 | no | — |
| 514 | Q8 | C2×#626 | 1 | 4 | yes | — |
| 515 | D4 | — | 3 | 4 | no | — |
| 516 | D4 | — | 6 | 12 | no | — |
| 517 | D4 | — | 6 | 4 | no | — |
| 518 | D4 | — | 6 | 6 | no | — |
| 519 | D4 | — | 9 | 4 | no | — |
| 520 | D4 | — | 18 | 12 | no | — |
| 521 | D4 | — | 18 | 4 | no | — |
| 522 | D4 | — | 18 | 6 | no | — |
| 523 | D4 | C2×#626 | 1 | 12 | yes | — |
| 524 | C2×C4 | — | 6 | 6 | no | — |
| 525 | C2×C4 | — | 6 | 12 | no | — |
| 526 | C2×C4 | — | 6 | 4 | no | — |
| 527 | C2×C4 | — | 18 | 6 | no | — |
| 528 | C2×C4 | — | 18 | 12 | no | — |
| 529 | C2×C4 | — | 18 | 4 | no | — |
| 530 | C2×C4 | C2×#626 | 1 | 3 | yes | — |
| 531 | C2×C4 | C2×#626 | 1 | 6 | yes | — |
| 532 | C2×C4 | C22×D32 | 1 | 6 | yes | — |
| 533 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 534 | C8 | — | 3 | 1 | no | — |
| 535 | C8 | — | 3 | 1 | no | — |
| 536 | C8 | — | 3 | 6 | no | — |
| 537 | C2×C3 | — | 2 | 6 | no | — |
| 538 | C2×C3 | — | 2 | 1 | no | — |
| 539 | C2×C3 | — | 2 | 6 | no | — |
| 540 | C2×C3 | — | 2 | 1 | no | — |
| 541 | C2×C3 | — | 2 | 1 | no | — |
| 542 | C2×C3 | — | 4 | 6 | no | — |
| 543 | C2×C3 | — | 4 | 1 | no | — |
| 544 | C2×C3 | — | 12 | 4 | no | — |
| 545 | C2×C3 | C23×D12 | 1 | 1 | yes | characteristic |
| 546 | C2×C3 | C23×#67 | 1 | 1 | yes | characteristic |
| 547 | D3 | — | 4 | 4 | no | — |
| 548 | D3 | — | 12 | 8 | no | — |
| 549 | D3 | — | 12 | 4 | no | — |
| 550 | D3 | — | 12 | 4 | no | — |
| 551 | C22 | — | 4 | 3 | no | — |
| 552 | C22 | — | 6 | 4 | no | — |
| 553 | C22 | — | 18 | 4 | no | — |
| 554 | C22 | — | 24 | 6 | no | — |
| 555 | C22 | — | 72 | 6 | no | — |
| 556 | C22 | C22×#626 | 1 | 6 | yes | — |
| 557 | C22 | C22×#626 | 1 | 1 | yes | characteristic |
| 558 | C4 | — | 6 | 4 | no | — |
| 559 | C4 | — | 18 | 4 | no | — |
| 560 | C4 | C22×#626 | 1 | 6 | yes | — |
| 561 | C4 | C22×#626 | 1 | 1 | yes | characteristic |
| 562 | C4 | C23×D32 | 1 | 1 | yes | characteristic |
| 563 | C3 | — | 2 | 1 | no | — |
| 564 | C3 | #87163 | 1 | 1 | yes | characteristic, complemented |
| 565 | C3 | #87297 | 1 | 1 | yes | characteristic, complemented |
| 566 | C2 | — | 2 | 1 | no | — |
| 567 | C2 | — | 2 | 6 | no | — |
| 568 | C2 | — | 12 | 4 | no | — |
| 569 | C2 | — | 36 | 4 | no | — |
| 570 | C2 | C23×#626 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×#626 |
| commutator, cosocle | C32×C4 | C25 |
| Frattini | C4 | C23×D32 |
| Fitting | C2×C32×#41 | C22 |
| socle | C2×C32 | C23×D4 |
| hypercenter | C2×#41 | D32 |
| hypocenter | C32 | #3584 |
| LCS | G ▷ C32×C4 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C4 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596756 | C2 | semidirect |
| 2. C3×#5964 | C2 | semidirect |
| 3. C2×C3×#948 | C2 | semidirect |
| 4. #10595450 | C2 | semidirect |
| 5. #10595449 | C2 | semidirect |
| 6. #10595448 | C2 | semidirect |
| 7. #10595447 | C2 | semidirect |
| 8. #10594795 | C2 | semidirect |
| 9. C2×#63829 | C2 | semidirect |
| 13. #64367 | C22 | semidirect |
| 14. #64366 | C22 | semidirect |
| 18. C2×#3828 | C22 | semidirect |
| 19. C3×#1010 | C22 | semidirect |
| 20. C3×#1009 | C22 | semidirect |
| 24. C2×C3×#235 | C22 | semidirect |
| 25. C3×#948 | C22 | semidirect |
| 26. C3×#948 | C22 | semidirect |
| 27. C2×C3×#208 | C22 | semidirect |
| 28. C22×C3×C3⋊C8 | C22 | semidirect |
| 29. C2×#3719 | C22 | semidirect |
| 30. #63833 | C22 | semidirect |
| 31. C2×#3717 | C22 | semidirect |
| 32. #63831 | C22 | semidirect |
| 33. #63830 | C22 | semidirect |
| 34. #63829 | C22 | semidirect |
| 35. #63829 | C22 | semidirect |
| 36. #63829 | C22 | semidirect |
| 37. #63829 | C22 | semidirect |
| 38. C2×#3716 | C22 | semidirect |
| 39. #63825 | C22 | semidirect |
| 40. C2×#3714 | C22 | semidirect |
| 45. #5964 | D3 | semidirect |
| 53. C2×#948 | D3 | semidirect |
| 115. #1010 | C2×D3 | semidirect |
| 119. #1009 | C2×D3 | semidirect |
| 135. C2×#235 | C2×D3 | semidirect |
| 146. #948 | C2×D3 | semidirect |
| 147. #948 | C2×D3 | semidirect |
| 154. C2×#208 | C2×D3 | semidirect |
| 155. C22×C3⋊C8 | C2×D3 | semidirect |
| 506. C32 | #3584 | semidirect |
| 564. C3 | #87163 | semidirect |
| 565. C3 | #87297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596756 | 2 |
| C3×#5964 | 2 |
| C2×C3×#948 | 2 |
| #10595450 | 2 |
| #10595449 | 2 |
| #10595448 | 2 |
| #10595447 | 2 |
| #10594795 | 2 |
| C2×#63829 | 2 |
| #87297 | 3 |
| #87163 | 3 |