Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
869 conjugacy classes of subgroups.
The subgroup lattice has 560 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3⋊D3×#135 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10594684 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5194 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10591049 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10591043 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10591039 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10591035 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10591029 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10591025 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10590632 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C2×#63542 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | D3×#508 | — | 3 | 2 | no | maximal |
| 13 | #41×C3⋊D3 | — | 2 | 1 | no | — |
| 14 | #64306 | — | 2 | 1 | no | — |
| 15 | C32×#135 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | #64159 | — | 2 | 1 | no | — |
| 17 | #64128 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | Q16×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 19 | #64125 | — | 2 | 1 | no | — |
| 20 | SD16×C3⋊D3 | — | 2 | 1 | no | — |
| 21 | #64121 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | D8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 23 | #64113 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C2×C8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 25 | C3×#904 | C22 | 1 | 2 | yes | complemented |
| 26 | #63822 | — | 2 | 1 | no | — |
| 27 | #63810 | C22 | 1 | 2 | yes | complemented |
| 28 | #63809 | — | 2 | 1 | no | — |
| 29 | #63802 | C22 | 1 | 1 | yes | characteristic |
| 30 | #63797 | C22 | 1 | 1 | yes | characteristic |
| 31 | #63796 | — | 2 | 1 | no | — |
| 32 | C3×#829 | C22 | 1 | 2 | yes | complemented |
| 33 | C3×#828 | C22 | 1 | 2 | yes | complemented |
| 34 | C3×#827 | C22 | 1 | 2 | yes | complemented |
| 35 | C3×#826 | C22 | 1 | 2 | yes | complemented |
| 36 | C2×C3×C3⋊C16 | C22 | 1 | 2 | yes | complemented |
| 37 | #63551 | C22 | 1 | 2 | yes | complemented |
| 38 | #63549 | C22 | 1 | 2 | yes | complemented |
| 39 | #63548 | C22 | 1 | 2 | yes | complemented |
| 40 | #63546 | C22 | 1 | 2 | yes | complemented |
| 41 | #63542 | C22 | 1 | 1 | yes | characteristic |
| 42 | #63542 | C22 | 1 | 1 | yes | characteristic |
| 43 | #63542 | C22 | 1 | 2 | yes | complemented |
| 44 | D3×#135 | — | 3 | 2 | no | — |
| 45 | D3×#135 | — | 3 | 2 | no | — |
| 46 | D3×#135 | — | 6 | 1 | no | — |
| 47 | C3×#508 | — | 3 | 2 | no | — |
| 48 | #5194 | — | 3 | 2 | no | — |
| 49 | #5194 | D3 | 1 | 2 | yes | complemented |
| 50 | #4919 | — | 3 | 2 | no | — |
| 51 | D3×Q32 | — | 3 | 2 | no | — |
| 52 | #4916 | — | 3 | 2 | no | — |
| 53 | #4916 | — | 3 | 2 | no | — |
| 54 | D3×SD32 | — | 3 | 2 | no | — |
| 55 | D3×SD32 | — | 3 | 2 | no | — |
| 56 | #4912 | — | 3 | 2 | no | — |
| 57 | D3×D16 | — | 3 | 2 | no | — |
| 58 | #4904 | — | 3 | 2 | no | — |
| 59 | C2×D3×C16 | — | 3 | 2 | no | — |
| 60 | C32×#41 | — | 2 | 1 | no | — |
| 61 | #3832 | — | 2 | 1 | no | — |
| 62 | Q8×C3⋊D3 | — | 2 | 1 | no | — |
| 63 | #3830 | — | 2 | 1 | no | — |
| 64 | #3830 | — | 4 | 1 | no | — |
| 65 | D4×C3⋊D3 | — | 2 | 1 | no | — |
| 66 | D4×C3⋊D3 | — | 4 | 1 | no | — |
| 67 | #3828 | — | 2 | 1 | no | — |
| 68 | #3828 | — | 4 | 1 | no | — |
| 69 | C2×C4×C3⋊D3 | — | 4 | 1 | no | — |
| 70 | C2×C4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 71 | C3×#235 | — | 2 | 2 | no | — |
| 72 | #3811 | — | 4 | 1 | no | — |
| 73 | #3805 | — | 4 | 1 | no | — |
| 74 | #3802 | — | 2 | 1 | no | — |
| 75 | C4×D32 | — | 4 | 1 | no | — |
| 76 | #3798 | — | 4 | 1 | no | — |
| 77 | #3797 | — | 2 | 1 | no | — |
| 78 | #3796 | — | 2 | 2 | no | — |
| 79 | C32×Q16 | C23 | 1 | 1 | yes | characteristic |
| 80 | C32×SD16 | — | 2 | 1 | no | — |
| 81 | C32×D8 | C23 | 1 | 1 | yes | characteristic |
| 82 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 83 | #3756 | — | 2 | 1 | no | — |
| 84 | #3755 | — | 2 | 1 | no | — |
| 85 | #3754 | — | 2 | 1 | no | — |
| 86 | #3753 | — | 2 | 1 | no | — |
| 87 | C2×C3⋊(C3⋊C8) | D4 | 1 | 1 | yes | characteristic |
| 88 | #3746 | C23 | 1 | 1 | yes | characteristic |
| 89 | #3745 | C23 | 1 | 1 | yes | characteristic |
| 90 | #3744 | — | 2 | 1 | no | — |
| 91 | C8×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 92 | C8×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 93 | C8×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 94 | C8×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 95 | C3×Dic12 | C23 | 1 | 2 | yes | — |
| 96 | C3×D24 | C23 | 1 | 2 | yes | — |
| 97 | C3×#204 | — | 2 | 2 | no | — |
| 98 | #3718 | — | 2 | 1 | no | — |
| 99 | #3715 | — | 2 | 2 | no | — |
| 100 | #3713 | — | 2 | 1 | no | — |
| 101 | C3×C3⋊C16 | C23 | 1 | 2 | yes | — |
| 102 | C3×C3⋊C16 | C23 | 1 | 2 | yes | — |
| 103 | C2×#508 | — | 9 | 1 | no | Sylow |
| 104 | D3×#41 | — | 6 | 2 | no | — |
| 105 | D3×#41 | — | 6 | 2 | no | — |
| 106 | D3×#41 | — | 6 | 2 | no | — |
| 107 | C3×#135 | — | 2 | 1 | no | — |
| 108 | C3×#135 | — | 3 | 2 | no | — |
| 109 | C3×#135 | C2×D3 | 1 | 2 | yes | complemented |
| 110 | #950 | — | 6 | 2 | no | — |
| 111 | #950 | — | 6 | 2 | no | — |
| 112 | #950 | — | 6 | 2 | no | — |
| 113 | #919 | — | 3 | 2 | no | — |
| 114 | #919 | — | 3 | 2 | no | — |
| 115 | #919 | — | 6 | 1 | no | — |
| 116 | D3×Q16 | — | 3 | 2 | no | — |
| 117 | D3×Q16 | — | 3 | 2 | no | — |
| 118 | D3×Q16 | — | 6 | 1 | no | — |
| 119 | #916 | — | 6 | 2 | no | — |
| 120 | #916 | — | 6 | 2 | no | — |
| 121 | #916 | — | 6 | 2 | no | — |
| 122 | D3×SD16 | — | 6 | 2 | no | — |
| 123 | D3×SD16 | — | 6 | 2 | no | — |
| 124 | D3×SD16 | — | 6 | 2 | no | — |
| 125 | #912 | — | 3 | 2 | no | — |
| 126 | #912 | — | 3 | 2 | no | — |
| 127 | #912 | — | 6 | 1 | no | — |
| 128 | D3×D8 | — | 3 | 2 | no | — |
| 129 | D3×D8 | — | 3 | 2 | no | — |
| 130 | D3×D8 | — | 6 | 1 | no | — |
| 131 | #904 | — | 3 | 2 | no | — |
| 132 | #904 | — | 6 | 1 | no | — |
| 133 | #904 | C2×D3 | 1 | 2 | yes | complemented |
| 134 | C2×D3×C8 | — | 3 | 2 | no | — |
| 135 | C2×D3×C8 | — | 6 | 1 | no | — |
| 136 | C3×Q32 | — | 3 | 2 | no | — |
| 137 | C3×SD32 | — | 3 | 2 | no | — |
| 138 | C3×SD32 | — | 3 | 2 | no | — |
| 139 | C3×D16 | — | 3 | 2 | no | — |
| 140 | C2×C3×C16 | — | 3 | 2 | no | — |
| 141 | #829 | — | 3 | 2 | no | — |
| 142 | #829 | C2×D3 | 1 | 2 | yes | complemented |
| 143 | #828 | — | 3 | 2 | no | — |
| 144 | #828 | C2×D3 | 1 | 2 | yes | complemented |
| 145 | #827 | — | 3 | 2 | no | — |
| 146 | #827 | C2×D3 | 1 | 2 | yes | complemented |
| 147 | #826 | — | 3 | 2 | no | — |
| 148 | #826 | C2×D3 | 1 | 2 | yes | complemented |
| 149 | C2×C3⋊C16 | C2×D3 | 1 | 2 | yes | complemented |
| 150 | Dic24 | — | 3 | 2 | no | — |
| 151 | #800 | — | 3 | 2 | no | — |
| 152 | #800 | — | 3 | 2 | no | — |
| 153 | D48 | — | 3 | 2 | no | — |
| 154 | D3×C16 | — | 3 | 2 | no | — |
| 155 | D3×C16 | — | 3 | 2 | no | — |
| 156 | D3×C16 | — | 3 | 2 | no | — |
| 157 | D3×C16 | — | 3 | 2 | no | — |
| 158 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 159 | C22×C3⋊D3 | D8 | 1 | 1 | yes | characteristic |
| 160 | C2×D32 | — | 4 | 1 | no | — |
| 161 | C32×Q8 | — | 2 | 1 | no | — |
| 162 | C32×D4 | — | 2 | 1 | no | — |
| 163 | C32×D4 | — | 4 | 1 | no | — |
| 164 | C2×C32×C4 | — | 4 | 1 | no | — |
| 165 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 166 | #638 | — | 4 | 1 | no | — |
| 167 | #638 | — | 4 | 1 | no | — |
| 168 | #638 | — | 4 | 1 | no | — |
| 169 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 170 | C2×C3⋊Dic3 | D8 | 1 | 1 | yes | characteristic |
| 171 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 172 | C4⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 173 | C4×C3⋊D3 | — | 4 | 1 | no | — |
| 174 | C4×C3⋊D3 | — | 4 | 1 | no | — |
| 175 | C4×C3⋊D3 | — | 4 | 1 | no | — |
| 176 | C4×C3⋊D3 | D8 | 1 | 1 | yes | characteristic |
| 177 | C4×C3⋊D3 | D8 | 1 | 1 | yes | characteristic |
| 178 | C4×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | C4×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | #634 | — | 2 | 1 | no | — |
| 181 | #634 | — | 4 | 1 | no | — |
| 182 | C3×#67 | — | 4 | 2 | no | — |
| 183 | C3×D12 | — | 2 | 2 | no | — |
| 184 | C3×C4×D3 | — | 4 | 2 | no | — |
| 185 | C3×Dic6 | — | 2 | 2 | no | — |
| 186 | #627 | — | 4 | 1 | no | — |
| 187 | #626 | — | 4 | 2 | no | — |
| 188 | #625 | — | 4 | 1 | no | — |
| 189 | #624 | — | 4 | 1 | no | — |
| 190 | D3×Dic3 | — | 4 | 2 | no | — |
| 191 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C32×C8 | C24 | 1 | 1 | yes | characteristic |
| 193 | C3⋊(C3⋊C8) | C2×D4 | 1 | 1 | yes | characteristic |
| 194 | C3⋊(C3⋊C8) | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | C2×#135 | — | 9 | 1 | no | — |
| 196 | C2×#135 | — | 9 | 1 | no | — |
| 197 | #508 | — | 3 | 2 | no | — |
| 198 | #508 | — | 9 | 2 | no | — |
| 199 | #508 | — | 9 | 2 | no | — |
| 200 | #508 | — | 9 | 2 | no | — |
| 201 | C2×Q32 | — | 9 | 1 | no | — |
| 202 | C2×SD32 | — | 9 | 1 | no | — |
| 203 | C2×SD32 | — | 9 | 1 | no | — |
| 204 | C2×D16 | — | 9 | 1 | no | — |
| 205 | C22×C16 | — | 9 | 1 | no | — |
| 206 | C3×#41 | — | 2 | 2 | no | — |
| 207 | C3×#41 | — | 2 | 2 | no | — |
| 208 | C3×#41 | — | 6 | 2 | no | — |
| 209 | #239 | — | 6 | 2 | no | — |
| 210 | #239 | — | 6 | 2 | no | — |
| 211 | #239 | — | 6 | 2 | no | — |
| 212 | D3×Q8 | — | 6 | 2 | no | — |
| 213 | D3×Q8 | — | 6 | 2 | no | — |
| 214 | D3×Q8 | — | 6 | 2 | no | — |
| 215 | #237 | — | 6 | 2 | no | — |
| 216 | #237 | — | 6 | 2 | no | — |
| 217 | #237 | — | 6 | 2 | no | — |
| 218 | #237 | — | 12 | 2 | no | — |
| 219 | #237 | — | 12 | 2 | no | — |
| 220 | #237 | — | 12 | 2 | no | — |
| 221 | D3×D4 | — | 6 | 2 | no | — |
| 222 | D3×D4 | — | 6 | 2 | no | — |
| 223 | D3×D4 | — | 6 | 2 | no | — |
| 224 | D3×D4 | — | 12 | 2 | no | — |
| 225 | D3×D4 | — | 12 | 2 | no | — |
| 226 | D3×D4 | — | 12 | 2 | no | — |
| 227 | #235 | — | 2 | 2 | no | — |
| 228 | #235 | — | 6 | 2 | no | — |
| 229 | #235 | — | 6 | 2 | no | — |
| 230 | #235 | — | 12 | 2 | no | — |
| 231 | #235 | — | 12 | 2 | no | — |
| 232 | #235 | — | 12 | 2 | no | — |
| 233 | C2×C4×D3 | — | 3 | 2 | no | — |
| 234 | C2×C4×D3 | — | 6 | 1 | no | — |
| 235 | C2×C4×D3 | — | 12 | 2 | no | — |
| 236 | C2×C4×D3 | — | 12 | 2 | no | — |
| 237 | C2×C4×D3 | — | 12 | 2 | no | — |
| 238 | C3×Q16 | — | 2 | 1 | no | — |
| 239 | C3×Q16 | — | 3 | 2 | no | — |
| 240 | C3×Q16 | C22×D3 | 1 | 2 | yes | — |
| 241 | C3×SD16 | — | 2 | 2 | no | — |
| 242 | C3×SD16 | — | 2 | 2 | no | — |
| 243 | C3×SD16 | — | 6 | 2 | no | — |
| 244 | C3×D8 | — | 2 | 1 | no | — |
| 245 | C3×D8 | — | 3 | 2 | no | — |
| 246 | C3×D8 | C22×D3 | 1 | 2 | yes | — |
| 247 | C2×C3×C8 | — | 2 | 1 | no | — |
| 248 | C2×C3×C8 | C22×D3 | 1 | 2 | yes | — |
| 249 | #216 | — | 6 | 2 | no | — |
| 250 | #216 | — | 6 | 2 | no | — |
| 251 | #216 | — | 6 | 2 | no | — |
| 252 | #215 | — | 6 | 2 | no | — |
| 253 | #215 | — | 6 | 2 | no | — |
| 254 | #215 | — | 6 | 2 | no | — |
| 255 | #214 | — | 6 | 2 | no | — |
| 256 | #214 | — | 6 | 2 | no | — |
| 257 | #214 | — | 6 | 2 | no | — |
| 258 | #213 | — | 6 | 2 | no | — |
| 259 | #213 | — | 6 | 2 | no | — |
| 260 | #213 | — | 6 | 2 | no | — |
| 261 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 262 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 263 | Dic12 | — | 3 | 2 | no | — |
| 264 | Dic12 | — | 6 | 1 | no | — |
| 265 | Dic12 | C22×D3 | 1 | 2 | yes | — |
| 266 | D24 | — | 3 | 2 | no | — |
| 267 | D24 | — | 6 | 1 | no | — |
| 268 | D24 | C22×D3 | 1 | 2 | yes | — |
| 269 | #204 | — | 2 | 2 | no | — |
| 270 | #204 | — | 6 | 2 | no | — |
| 271 | #204 | — | 6 | 2 | no | — |
| 272 | D3×C8 | — | 3 | 2 | no | — |
| 273 | D3×C8 | — | 3 | 2 | no | — |
| 274 | D3×C8 | — | 3 | 2 | no | — |
| 275 | D3×C8 | — | 3 | 2 | no | — |
| 276 | D3×C8 | — | 6 | 1 | no | — |
| 277 | D3×C8 | — | 6 | 1 | no | — |
| 278 | D3×C8 | — | 6 | 1 | no | — |
| 279 | D3×C8 | — | 6 | 1 | no | — |
| 280 | C3×C16 | — | 3 | 2 | no | — |
| 281 | C3×C16 | — | 3 | 2 | no | — |
| 282 | C3⋊C16 | C22×D3 | 1 | 2 | yes | — |
| 283 | C3⋊C16 | C22×D3 | 1 | 2 | yes | — |
| 284 | C22×C32 | — | 4 | 1 | no | — |
| 285 | C22×C32 | C2×D8 | 1 | 1 | yes | characteristic |
| 286 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 287 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 288 | C2×C3⋊D3 | — | 8 | 2 | no | — |
| 289 | C2×C3⋊D3 | C2×D8 | 1 | 1 | yes | characteristic |
| 290 | C2×C3⋊D3 | C2×D8 | 1 | 1 | yes | characteristic |
| 291 | C2×C3×D3 | — | 4 | 2 | no | — |
| 292 | D32 | — | 8 | 2 | no | — |
| 293 | C32×C4 | — | 4 | 1 | no | — |
| 294 | C32×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 295 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 296 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 297 | C3⋊Dic3 | C2×D8 | 1 | 1 | yes | characteristic |
| 298 | C3⋊Dic3 | C2×D8 | 1 | 1 | yes | characteristic |
| 299 | C3×Dic3 | — | 4 | 2 | no | — |
| 300 | C2×#41 | — | 18 | 1 | no | — |
| 301 | C2×#41 | — | 18 | 1 | no | — |
| 302 | #135 | — | 3 | 2 | no | — |
| 303 | #135 | — | 9 | 2 | no | — |
| 304 | #135 | — | 9 | 1 | no | — |
| 305 | #135 | — | 9 | 1 | no | — |
| 306 | #135 | — | 9 | 1 | no | — |
| 307 | #135 | — | 18 | 1 | no | — |
| 308 | #135 | — | 18 | 1 | no | — |
| 309 | #135 | — | 18 | 1 | no | — |
| 310 | #135 | — | 18 | 1 | no | — |
| 311 | #135 | D32 | 1 | 1 | yes | characteristic, complemented |
| 312 | C2×Q16 | — | 9 | 1 | no | — |
| 313 | C2×Q16 | — | 9 | 1 | no | — |
| 314 | C2×SD16 | — | 18 | 1 | no | — |
| 315 | C2×SD16 | — | 18 | 1 | no | — |
| 316 | C2×D8 | — | 9 | 1 | no | — |
| 317 | C2×D8 | — | 9 | 1 | no | — |
| 318 | C22×C8 | — | 9 | 1 | no | — |
| 319 | Q32 | — | 3 | 2 | no | — |
| 320 | Q32 | — | 9 | 2 | no | — |
| 321 | SD32 | — | 3 | 2 | no | — |
| 322 | SD32 | — | 3 | 2 | no | — |
| 323 | SD32 | — | 9 | 2 | no | — |
| 324 | SD32 | — | 9 | 2 | no | — |
| 325 | D16 | — | 3 | 2 | no | — |
| 326 | D16 | — | 9 | 2 | no | — |
| 327 | C2×C16 | — | 3 | 2 | no | — |
| 328 | C2×C16 | — | 9 | 1 | no | — |
| 329 | C2×C16 | — | 9 | 1 | no | — |
| 330 | C2×C16 | — | 9 | 2 | no | — |
| 331 | C22×D3 | — | 3 | 2 | no | — |
| 332 | C22×D3 | — | 6 | 1 | no | — |
| 333 | C22×D3 | — | 12 | 2 | no | — |
| 334 | C22×D3 | — | 12 | 2 | no | — |
| 335 | C22×D3 | — | 12 | 2 | no | — |
| 336 | C3×Q8 | — | 2 | 2 | no | — |
| 337 | C3×Q8 | — | 2 | 2 | no | — |
| 338 | C3×Q8 | — | 6 | 2 | no | — |
| 339 | C3×D4 | — | 2 | 2 | no | — |
| 340 | C3×D4 | — | 2 | 2 | no | — |
| 341 | C3×D4 | — | 4 | 2 | no | — |
| 342 | C3×D4 | — | 4 | 2 | no | — |
| 343 | C3×D4 | — | 6 | 2 | no | — |
| 344 | C3×D4 | — | 12 | 2 | no | — |
| 345 | C2×C3×C4 | — | 2 | 1 | no | — |
| 346 | C2×C3×C4 | — | 4 | 2 | no | — |
| 347 | C2×C3×C4 | — | 4 | 2 | no | — |
| 348 | C2×C3×C4 | — | 12 | 2 | no | — |
| 349 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 350 | #67 | — | 4 | 2 | no | — |
| 351 | #67 | — | 12 | 2 | no | — |
| 352 | #67 | — | 12 | 2 | no | — |
| 353 | #67 | — | 12 | 2 | no | — |
| 354 | #67 | — | 12 | 2 | no | — |
| 355 | #67 | — | 12 | 2 | no | — |
| 356 | #67 | — | 12 | 2 | no | — |
| 357 | #67 | — | 12 | 2 | no | — |
| 358 | #67 | — | 12 | 2 | no | — |
| 359 | C2×Dic3 | — | 3 | 2 | no | — |
| 360 | C2×Dic3 | — | 6 | 1 | no | — |
| 361 | C2×Dic3 | — | 12 | 2 | no | — |
| 362 | C2×Dic3 | — | 12 | 2 | no | — |
| 363 | C2×Dic3 | — | 12 | 2 | no | — |
| 364 | D12 | — | 2 | 2 | no | — |
| 365 | D12 | — | 6 | 2 | no | — |
| 366 | D12 | — | 6 | 2 | no | — |
| 367 | D12 | — | 12 | 2 | no | — |
| 368 | D12 | — | 12 | 2 | no | — |
| 369 | D12 | — | 12 | 2 | no | — |
| 370 | C4×D3 | — | 3 | 2 | no | — |
| 371 | C4×D3 | — | 3 | 2 | no | — |
| 372 | C4×D3 | — | 3 | 2 | no | — |
| 373 | C4×D3 | — | 3 | 2 | no | — |
| 374 | C4×D3 | — | 4 | 2 | no | — |
| 375 | C4×D3 | — | 6 | 1 | no | — |
| 376 | C4×D3 | — | 6 | 1 | no | — |
| 377 | C4×D3 | — | 6 | 1 | no | — |
| 378 | C4×D3 | — | 6 | 1 | no | — |
| 379 | C4×D3 | — | 12 | 2 | no | — |
| 380 | C4×D3 | — | 12 | 2 | no | — |
| 381 | C4×D3 | — | 12 | 2 | no | — |
| 382 | C4×D3 | — | 12 | 2 | no | — |
| 383 | C4×D3 | — | 12 | 2 | no | — |
| 384 | C4×D3 | — | 12 | 2 | no | — |
| 385 | C4×D3 | — | 12 | 2 | no | — |
| 386 | C4×D3 | — | 12 | 2 | no | — |
| 387 | Dic6 | — | 2 | 2 | no | — |
| 388 | Dic6 | — | 6 | 2 | no | — |
| 389 | Dic6 | — | 6 | 2 | no | — |
| 390 | Dic6 | — | 12 | 2 | no | — |
| 391 | Dic6 | — | 12 | 2 | no | — |
| 392 | Dic6 | — | 12 | 2 | no | — |
| 393 | C3×C8 | — | 2 | 1 | no | — |
| 394 | C3×C8 | — | 2 | 1 | no | — |
| 395 | C3×C8 | D3×D4 | 1 | 2 | yes | — |
| 396 | C3×C8 | C23×D3 | 1 | 2 | yes | — |
| 397 | C3⋊C8 | — | 3 | 2 | no | — |
| 398 | C3⋊C8 | — | 3 | 2 | no | — |
| 399 | C3⋊C8 | — | 6 | 1 | no | — |
| 400 | C3⋊C8 | — | 6 | 1 | no | — |
| 401 | C2×C32 | — | 2 | 1 | no | — |
| 402 | C2×C32 | — | 8 | 1 | no | — |
| 403 | C2×C32 | C22×D8 | 1 | 1 | yes | characteristic |
| 404 | C3⋊D3 | — | 2 | 1 | no | — |
| 405 | C3⋊D3 | — | 8 | 1 | no | — |
| 406 | C3⋊D3 | #508 | 1 | 2 | yes | complemented |
| 407 | C3×D3 | — | 8 | 2 | no | — |
| 408 | #41 | — | 2 | 1 | no | — |
| 409 | #41 | — | 6 | 2 | no | — |
| 410 | #41 | — | 18 | 1 | no | — |
| 411 | #41 | — | 18 | 2 | no | — |
| 412 | #41 | — | 18 | 1 | no | — |
| 413 | #41 | — | 18 | 1 | no | — |
| 414 | #41 | — | 36 | 1 | no | — |
| 415 | #41 | — | 36 | 1 | no | — |
| 416 | #41 | — | 36 | 1 | no | — |
| 417 | #41 | — | 36 | 1 | no | — |
| 418 | C2×Q8 | — | 18 | 1 | no | — |
| 419 | C2×Q8 | — | 18 | 1 | no | — |
| 420 | C2×D4 | — | 18 | 1 | no | — |
| 421 | C2×D4 | — | 18 | 1 | no | — |
| 422 | C2×D4 | — | 36 | 1 | no | — |
| 423 | C2×D4 | — | 36 | 1 | no | — |
| 424 | C22×C4 | — | 9 | 1 | no | — |
| 425 | C22×C4 | — | 36 | 1 | no | — |
| 426 | C22×C4 | — | 36 | 1 | no | — |
| 427 | Q16 | — | 3 | 2 | no | — |
| 428 | Q16 | — | 9 | 1 | no | — |
| 429 | Q16 | — | 18 | 1 | no | — |
| 430 | Q16 | — | 18 | 1 | no | — |
| 431 | Q16 | C2×D32 | 1 | 1 | yes | characteristic |
| 432 | SD16 | — | 2 | 1 | no | — |
| 433 | SD16 | — | 6 | 2 | no | — |
| 434 | SD16 | — | 18 | 1 | no | — |
| 435 | SD16 | — | 18 | 2 | no | — |
| 436 | SD16 | — | 18 | 1 | no | — |
| 437 | SD16 | — | 18 | 1 | no | — |
| 438 | D8 | — | 3 | 2 | no | — |
| 439 | D8 | — | 9 | 1 | no | — |
| 440 | D8 | — | 18 | 1 | no | — |
| 441 | D8 | — | 18 | 1 | no | — |
| 442 | D8 | C2×D32 | 1 | 1 | yes | characteristic |
| 443 | C2×C8 | — | 9 | 1 | no | — |
| 444 | C2×C8 | — | 9 | 1 | no | — |
| 445 | C2×C8 | — | 9 | 1 | no | — |
| 446 | C2×C8 | — | 9 | 1 | no | — |
| 447 | C2×C8 | — | 9 | 1 | no | — |
| 448 | C2×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 449 | C16 | — | 3 | 2 | no | — |
| 450 | C16 | — | 3 | 2 | no | — |
| 451 | C22×C3 | — | 2 | 1 | no | — |
| 452 | C22×C3 | — | 4 | 2 | no | — |
| 453 | C22×C3 | — | 4 | 2 | no | — |
| 454 | C22×C3 | — | 12 | 2 | no | — |
| 455 | C22×C3 | D3×D8 | 1 | 2 | yes | — |
| 456 | C2×D3 | — | 3 | 2 | no | — |
| 457 | C2×D3 | — | 3 | 2 | no | — |
| 458 | C2×D3 | — | 4 | 2 | no | — |
| 459 | C2×D3 | — | 6 | 1 | no | — |
| 460 | C2×D3 | — | 6 | 1 | no | — |
| 461 | C2×D3 | — | 6 | 4 | no | — |
| 462 | C2×D3 | — | 12 | 2 | no | — |
| 463 | C2×D3 | — | 12 | 2 | no | — |
| 464 | C2×D3 | — | 12 | 2 | no | — |
| 465 | C2×D3 | — | 24 | 4 | no | — |
| 466 | C2×D3 | — | 24 | 4 | no | — |
| 467 | C2×D3 | — | 24 | 4 | no | — |
| 468 | C3×C4 | — | 2 | 1 | no | — |
| 469 | C3×C4 | — | 2 | 1 | no | — |
| 470 | C3×C4 | — | 4 | 2 | no | — |
| 471 | C3×C4 | — | 4 | 2 | no | — |
| 472 | C3×C4 | — | 12 | 2 | no | — |
| 473 | C3×C4 | D3×D8 | 1 | 2 | yes | — |
| 474 | C3×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 475 | Dic3 | — | 3 | 2 | no | — |
| 476 | Dic3 | — | 3 | 2 | no | — |
| 477 | Dic3 | — | 4 | 2 | no | — |
| 478 | Dic3 | — | 6 | 1 | no | — |
| 479 | Dic3 | — | 6 | 1 | no | — |
| 480 | Dic3 | — | 12 | 2 | no | — |
| 481 | Dic3 | — | 12 | 2 | no | — |
| 482 | C32 | C2×#508 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 483 | C23 | — | 9 | 1 | no | — |
| 484 | C23 | — | 36 | 1 | no | — |
| 485 | C23 | — | 36 | 1 | no | — |
| 486 | Q8 | — | 2 | 1 | no | — |
| 487 | Q8 | — | 6 | 2 | no | — |
| 488 | Q8 | — | 18 | 1 | no | — |
| 489 | Q8 | — | 36 | 1 | no | — |
| 490 | Q8 | — | 36 | 1 | no | — |
| 491 | D4 | — | 2 | 1 | no | — |
| 492 | D4 | — | 4 | 1 | no | — |
| 493 | D4 | — | 6 | 2 | no | — |
| 494 | D4 | — | 12 | 2 | no | — |
| 495 | D4 | — | 18 | 1 | no | — |
| 496 | D4 | — | 36 | 1 | no | — |
| 497 | D4 | — | 36 | 1 | no | — |
| 498 | D4 | — | 36 | 1 | no | — |
| 499 | D4 | — | 36 | 2 | no | — |
| 500 | D4 | — | 36 | 1 | no | — |
| 501 | D4 | — | 36 | 1 | no | — |
| 502 | C2×C4 | — | 4 | 1 | no | — |
| 503 | C2×C4 | — | 9 | 1 | no | — |
| 504 | C2×C4 | — | 9 | 1 | no | — |
| 505 | C2×C4 | — | 9 | 1 | no | — |
| 506 | C2×C4 | — | 9 | 1 | no | — |
| 507 | C2×C4 | — | 9 | 1 | no | — |
| 508 | C2×C4 | — | 12 | 2 | no | — |
| 509 | C2×C4 | — | 36 | 1 | no | — |
| 510 | C2×C4 | — | 36 | 1 | no | — |
| 511 | C2×C4 | — | 36 | 2 | no | — |
| 512 | C2×C4 | — | 36 | 1 | no | — |
| 513 | C2×C4 | — | 36 | 1 | no | — |
| 514 | C2×C4 | — | 36 | 1 | no | — |
| 515 | C2×C4 | #3811 | 1 | 1 | yes | characteristic |
| 516 | C8 | — | 9 | 1 | no | — |
| 517 | C8 | — | 9 | 1 | no | — |
| 518 | C8 | #3811 | 1 | 1 | yes | characteristic |
| 519 | C8 | C22×D32 | 1 | 1 | yes | characteristic |
| 520 | C2×C3 | — | 2 | 2 | no | — |
| 521 | C2×C3 | — | 2 | 1 | no | — |
| 522 | C2×C3 | — | 4 | 1 | no | — |
| 523 | C2×C3 | — | 8 | 2 | no | — |
| 524 | C2×C3 | — | 8 | 2 | no | — |
| 525 | C2×C3 | — | 24 | 2 | no | — |
| 526 | C2×C3 | C2×D3×D8 | 1 | 2 | yes | — |
| 527 | D3 | — | 3 | 4 | no | — |
| 528 | D3 | — | 6 | 2 | no | — |
| 529 | D3 | — | 6 | 2 | no | — |
| 530 | D3 | — | 8 | 2 | no | — |
| 531 | D3 | — | 12 | 1 | no | — |
| 532 | D3 | — | 24 | 2 | no | — |
| 533 | D3 | — | 24 | 2 | no | — |
| 534 | C22 | — | 4 | 1 | no | — |
| 535 | C22 | — | 9 | 1 | no | — |
| 536 | C22 | — | 9 | 1 | no | — |
| 537 | C22 | — | 12 | 2 | no | — |
| 538 | C22 | — | 18 | 2 | no | — |
| 539 | C22 | — | 36 | 1 | no | — |
| 540 | C22 | — | 72 | 2 | no | — |
| 541 | C22 | — | 72 | 2 | no | — |
| 542 | C22 | #63926 | 1 | 1 | yes | characteristic |
| 543 | C4 | — | 4 | 1 | no | — |
| 544 | C4 | — | 9 | 1 | no | — |
| 545 | C4 | — | 9 | 1 | no | — |
| 546 | C4 | — | 12 | 2 | no | — |
| 547 | C4 | — | 36 | 1 | no | — |
| 548 | C4 | #63926 | 1 | 1 | yes | characteristic |
| 549 | C4 | C2×#3811 | 1 | 1 | yes | characteristic |
| 550 | C3 | — | 2 | 1 | no | — |
| 551 | C3 | D3×#508 | 1 | 2 | yes | complemented |
| 552 | C2 | — | 2 | 1 | no | — |
| 553 | C2 | — | 8 | 1 | no | — |
| 554 | C2 | — | 9 | 2 | no | — |
| 555 | C2 | — | 18 | 1 | no | — |
| 556 | C2 | — | 24 | 2 | no | — |
| 557 | C2 | — | 72 | 1 | no | — |
| 558 | C2 | C2×#63926 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊D3×#135 | C2 | semidirect |
| 2. #10594684 | C2 | semidirect |
| 3. C3×#5194 | C2 | semidirect |
| 4. #10591049 | C2 | semidirect |
| 5. #10591043 | C2 | semidirect |
| 6. #10591039 | C2 | semidirect |
| 7. #10591035 | C2 | semidirect |
| 8. #10591029 | C2 | semidirect |
| 9. #10591025 | C2 | semidirect |
| 10. #10590632 | C2 | semidirect |
| 11. C2×#63542 | C2 | semidirect |
| 15. C32×#135 | C22 | semidirect |
| 17. #64128 | C22 | semidirect |
| 21. #64121 | C22 | semidirect |
| 23. #64113 | C22 | semidirect |
| 25. C3×#904 | C22 | semidirect |
| 27. #63810 | C22 | semidirect |
| 32. C3×#829 | C22 | semidirect |
| 33. C3×#828 | C22 | semidirect |
| 34. C3×#827 | C22 | semidirect |
| 35. C3×#826 | C22 | semidirect |
| 36. C2×C3×C3⋊C16 | C22 | semidirect |
| 37. #63551 | C22 | semidirect |
| 38. #63549 | C22 | semidirect |
| 39. #63548 | C22 | semidirect |
| 40. #63546 | C22 | semidirect |
| 43. #63542 | C22 | semidirect |
| 49. #5194 | D3 | semidirect |
| 109. C3×#135 | C2×D3 | semidirect |
| 133. #904 | C2×D3 | semidirect |
| 142. #829 | C2×D3 | semidirect |
| 144. #828 | C2×D3 | semidirect |
| 146. #827 | C2×D3 | semidirect |
| 148. #826 | C2×D3 | semidirect |
| 149. C2×C3⋊C16 | C2×D3 | semidirect |
| 311. #135 | D32 | semidirect |
| 406. C3⋊D3 | #508 | semidirect |
| 482. C32 | C2×#508 | semidirect |
| 551. C3 | D3×#508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×#135 | 2 |
| #10594684 | 2 |
| C3×#5194 | 2 |
| #10591049 | 2 |
| #10591043 | 2 |
| #10591039 | 2 |
| #10591035 | 2 |
| #10591029 | 2 |
| #10591025 | 2 |
| #10590632 | 2 |
| C2×#63542 | 2 |
| D3×#508 | 3 |