Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
754 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11724614 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11723364 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#63860 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#63830 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11722046 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11722029 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C3×#63570 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10591525 | — | 3 | 1 | no | maximal |
| 9 | #10591019 | — | 3 | 1 | no | maximal |
| 10 | #10590400 | — | 3 | 1 | no | maximal |
| 11 | C3×#3828 | C22 | 1 | 1 | yes | characteristic |
| 12 | C3×#3828 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C3×#634 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C32×D12 | C22 | 1 | 1 | yes | characteristic |
| 15 | #89046 | — | 2 | 2 | no | — |
| 16 | #89041 | — | 2 | 1 | no | — |
| 17 | #89041 | — | 2 | 1 | no | — |
| 18 | #89040 | — | 2 | 1 | no | — |
| 19 | #89040 | — | 2 | 1 | no | — |
| 20 | #88855 | C22 | 1 | 1 | yes | characteristic |
| 21 | C32×C4×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 22 | C32×#208 | C22 | 1 | 1 | yes | characteristic |
| 23 | #88792 | — | 2 | 1 | no | — |
| 24 | #88789 | — | 2 | 1 | no | — |
| 25 | C3×(C2×D3)⋊Dic3 | — | 2 | 2 | no | — |
| 26 | C3×#3716 | — | 2 | 1 | no | — |
| 27 | C3×#3714 | — | 2 | 1 | no | — |
| 28 | #64298 | — | 3 | 1 | no | — |
| 29 | #64297 | — | 3 | 1 | no | — |
| 30 | #64297 | — | 3 | 1 | no | — |
| 31 | #64141 | — | 3 | 1 | no | — |
| 32 | C3×#936 | — | 3 | 1 | no | — |
| 33 | C3×#932 | — | 3 | 1 | no | — |
| 34 | C3×#908 | — | 3 | 1 | no | — |
| 35 | C3×#875 | — | 3 | 1 | no | — |
| 36 | #63860 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | #63830 | D3 | 1 | 1 | yes | characteristic, complemented |
| 38 | #63823 | — | 3 | 1 | no | — |
| 39 | #63823 | — | 3 | 1 | no | — |
| 40 | #63823 | — | 6 | 1 | no | — |
| 41 | #63651 | — | 3 | 1 | no | — |
| 42 | #63632 | — | 3 | 1 | no | — |
| 43 | C3×#825 | — | 3 | 1 | no | — |
| 44 | C3×#805 | — | 3 | 1 | no | — |
| 45 | #63570 | D3 | 1 | 1 | yes | characteristic, complemented |
| 46 | #63569 | — | 3 | 1 | no | — |
| 47 | #63569 | — | 3 | 1 | no | — |
| 48 | #63569 | — | 6 | 1 | no | — |
| 49 | #63560 | — | 3 | 1 | no | — |
| 50 | #63560 | — | 3 | 1 | no | — |
| 51 | #63560 | — | 6 | 1 | no | — |
| 52 | C22×C32×D3 | — | 2 | 1 | no | — |
| 53 | C2×C33×C4 | C23 | 1 | 1 | yes | characteristic |
| 54 | C3×#638 | — | 2 | 1 | no | — |
| 55 | C3×#638 | — | 2 | 1 | no | — |
| 56 | C2×C3×C3⋊Dic3 | D4 | 1 | 2 | yes | — |
| 57 | C3×C4⋊(C3⋊D3) | D4 | 1 | 1 | yes | characteristic |
| 58 | C3×C4⋊(C3⋊D3) | D4 | 1 | 1 | yes | characteristic |
| 59 | C3×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 60 | C3×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 61 | C3×#634 | — | 2 | 1 | no | — |
| 62 | C3×#634 | — | 2 | 1 | no | — |
| 63 | C3×#634 | D4 | 1 | 1 | yes | characteristic |
| 64 | C3×#634 | D4 | 1 | 1 | yes | characteristic |
| 65 | C2×C32×Dic3 | — | 2 | 1 | no | — |
| 66 | C32×D12 | — | 2 | 1 | no | — |
| 67 | C32×D12 | — | 2 | 1 | no | — |
| 68 | #6296 | — | 2 | 2 | no | — |
| 69 | #6295 | — | 2 | 2 | no | — |
| 70 | #6294 | — | 2 | 2 | no | — |
| 71 | #6294 | — | 2 | 2 | no | — |
| 72 | C3⋊(C3⋊(C3⋊C8)) | — | 2 | 1 | no | — |
| 73 | C32×C3⋊C8 | — | 2 | 1 | no | — |
| 74 | #5201 | — | 9 | 1 | no | — |
| 75 | #5062 | — | 9 | 1 | no | — |
| 76 | #4827 | — | 9 | 1 | no | — |
| 77 | C2×C32×D4 | — | 3 | 1 | no | — |
| 78 | #3828 | C2×D3 | 1 | 1 | yes | characteristic |
| 79 | #3828 | C2×D3 | 1 | 1 | yes | characteristic |
| 80 | C2×#634 | C2×D3 | 1 | 1 | yes | characteristic |
| 81 | C3×#235 | — | 3 | 1 | no | — |
| 82 | C3×#235 | — | 3 | 1 | no | — |
| 83 | C3×#235 | — | 3 | 1 | no | — |
| 84 | C3×#235 | — | 3 | 1 | no | — |
| 85 | C3×#235 | — | 6 | 1 | no | — |
| 86 | C3×#235 | — | 6 | 1 | no | — |
| 87 | C2×C3×D12 | — | 2 | 1 | no | — |
| 88 | C2×C3×D12 | C2×D3 | 1 | 1 | yes | characteristic |
| 89 | C2×C3×D12 | C2×D3 | 1 | 1 | yes | characteristic |
| 90 | C2×C3×Dic6 | — | 3 | 1 | no | — |
| 91 | C2×C3×Dic6 | — | 3 | 1 | no | — |
| 92 | C2×C3×Dic6 | — | 6 | 1 | no | — |
| 93 | #3805 | — | 6 | 2 | no | — |
| 94 | #3804 | — | 6 | 2 | no | — |
| 95 | #3804 | — | 6 | 2 | no | — |
| 96 | #3799 | — | 6 | 1 | no | — |
| 97 | #3799 | — | 6 | 1 | no | — |
| 98 | #3797 | — | 6 | 1 | no | — |
| 99 | #3797 | — | 6 | 1 | no | — |
| 100 | #3796 | — | 6 | 1 | no | — |
| 101 | #3796 | — | 6 | 1 | no | — |
| 102 | #3795 | — | 6 | 1 | no | — |
| 103 | #3795 | — | 6 | 1 | no | — |
| 104 | D3×Dic6 | — | 6 | 1 | no | — |
| 105 | D3×Dic6 | — | 6 | 1 | no | — |
| 106 | D3×Dic6 | — | 6 | 1 | no | — |
| 107 | D3×Dic6 | — | 6 | 1 | no | — |
| 108 | C32×M16 | — | 3 | 1 | no | — |
| 109 | C32×C42 | — | 3 | 1 | no | — |
| 110 | #3754 | — | 6 | 1 | no | — |
| 111 | #3753 | — | 6 | 1 | no | — |
| 112 | #3748 | — | 3 | 1 | no | — |
| 113 | #3748 | — | 3 | 1 | no | — |
| 114 | #3748 | — | 3 | 1 | no | — |
| 115 | #3748 | — | 6 | 1 | no | — |
| 116 | #3748 | — | 6 | 1 | no | — |
| 117 | #3748 | — | 6 | 1 | no | — |
| 118 | #3748 | — | 12 | 1 | no | — |
| 119 | C3×#217 | — | 6 | 2 | no | — |
| 120 | C3×#214 | — | 6 | 1 | no | — |
| 121 | C3×#213 | — | 6 | 1 | no | — |
| 122 | C3×(C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 123 | C3×C4×Dic3 | — | 2 | 1 | no | — |
| 124 | C3×C4×Dic3 | C2×D3 | 1 | 1 | yes | characteristic |
| 125 | C3×C4×Dic3 | C2×D3 | 1 | 1 | yes | characteristic |
| 126 | C3×#208 | — | 2 | 1 | no | — |
| 127 | C3×#208 | C2×D3 | 1 | 1 | yes | characteristic |
| 128 | C3×#208 | C2×D3 | 1 | 1 | yes | characteristic |
| 129 | C3×D24 | — | 6 | 1 | no | — |
| 130 | C3×#204 | — | 6 | 1 | no | — |
| 131 | (C2×D3)⋊Dic3 | — | 2 | 2 | no | — |
| 132 | #3716 | — | 2 | 1 | no | — |
| 133 | #3715 | — | 6 | 1 | no | — |
| 134 | #3715 | — | 6 | 1 | no | — |
| 135 | #3715 | — | 6 | 2 | no | — |
| 136 | #3714 | — | 2 | 1 | no | — |
| 137 | #3713 | — | 6 | 1 | no | — |
| 138 | #3713 | — | 6 | 1 | no | — |
| 139 | #3713 | — | 6 | 2 | no | — |
| 140 | C22×C33 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 142 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 143 | C2×C32×D3 | — | 4 | 2 | no | — |
| 144 | C2×C32×D3 | — | 4 | 1 | no | — |
| 145 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 146 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 147 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 148 | C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 149 | C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 150 | C32×Dic3 | — | 4 | 1 | no | — |
| 151 | #1010 | — | 9 | 1 | no | — |
| 152 | #1010 | — | 9 | 1 | no | — |
| 153 | #1007 | — | 9 | 1 | no | — |
| 154 | C3×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 155 | C3×#124 | — | 9 | 1 | no | — |
| 156 | #949 | — | 9 | 1 | no | — |
| 157 | #936 | — | 3 | 1 | no | — |
| 158 | #932 | — | 3 | 1 | no | — |
| 159 | #932 | — | 9 | 1 | no | — |
| 160 | #932 | — | 9 | 1 | no | — |
| 161 | #932 | — | 18 | 1 | no | — |
| 162 | #908 | — | 3 | 1 | no | — |
| 163 | #875 | — | 3 | 1 | no | — |
| 164 | C3×#104 | — | 9 | 1 | no | — |
| 165 | #837 | — | 9 | 1 | no | — |
| 166 | #836 | — | 9 | 1 | no | — |
| 167 | #825 | — | 3 | 1 | no | — |
| 168 | #824 | — | 9 | 1 | no | — |
| 169 | #824 | — | 9 | 1 | no | — |
| 170 | #824 | — | 18 | 1 | no | — |
| 171 | #805 | — | 3 | 1 | no | — |
| 172 | #805 | — | 9 | 1 | no | — |
| 173 | #805 | — | 9 | 1 | no | — |
| 174 | #805 | — | 18 | 1 | no | — |
| 175 | C23×C32 | — | 6 | 1 | no | — |
| 176 | C22×C3×D3 | — | 2 | 1 | no | — |
| 177 | C22×C3×D3 | — | 2 | 1 | no | — |
| 178 | C22×C3×D3 | — | 4 | 1 | no | — |
| 179 | C32×D4 | — | 6 | 1 | no | — |
| 180 | C32×D4 | — | 6 | 1 | no | — |
| 181 | C2×C32×C4 | — | 2 | 1 | no | — |
| 182 | C2×C32×C4 | — | 2 | 1 | no | — |
| 183 | C2×C32×C4 | — | 2 | 1 | no | — |
| 184 | C2×C32×C4 | — | 4 | 1 | no | — |
| 185 | C2×C32×C4 | — | 6 | 1 | no | — |
| 186 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 187 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 188 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 189 | #638 | — | 2 | 1 | no | — |
| 190 | #638 | — | 2 | 1 | no | — |
| 191 | C2×C3⋊Dic3 | #67 | 1 | 2 | yes | — |
| 192 | C4⋊(C3⋊D3) | D12 | 1 | 1 | yes | characteristic |
| 193 | C4⋊(C3⋊D3) | #67 | 1 | 1 | yes | characteristic |
| 194 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 195 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 196 | #634 | — | 2 | 1 | no | — |
| 197 | #634 | — | 2 | 1 | no | — |
| 198 | #634 | D12 | 1 | 1 | yes | characteristic |
| 199 | #634 | #67 | 1 | 1 | yes | characteristic |
| 200 | C3×#67 | — | 6 | 1 | no | — |
| 201 | C3×#67 | — | 6 | 1 | no | — |
| 202 | C3×#67 | — | 6 | 1 | no | — |
| 203 | C3×#67 | — | 6 | 1 | no | — |
| 204 | C3×#67 | — | 12 | 1 | no | — |
| 205 | C3×#67 | — | 12 | 1 | no | — |
| 206 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 207 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 208 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 209 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 210 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 211 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 212 | C3×D12 | — | 2 | 2 | no | — |
| 213 | C3×D12 | — | 2 | 1 | no | — |
| 214 | C3×D12 | — | 2 | 1 | no | — |
| 215 | C3×D12 | — | 2 | 1 | no | — |
| 216 | C3×D12 | — | 2 | 1 | no | — |
| 217 | C3×D12 | — | 3 | 1 | no | — |
| 218 | C3×D12 | — | 3 | 1 | no | — |
| 219 | C3×D12 | — | 3 | 1 | no | — |
| 220 | C3×D12 | — | 3 | 1 | no | — |
| 221 | C3×D12 | — | 4 | 1 | no | — |
| 222 | C3×D12 | — | 6 | 1 | no | — |
| 223 | C3×D12 | — | 6 | 1 | no | — |
| 224 | C3×C4×D3 | — | 6 | 1 | no | — |
| 225 | C3×C4×D3 | — | 6 | 1 | no | — |
| 226 | C3×C4×D3 | — | 6 | 1 | no | — |
| 227 | C3×C4×D3 | — | 6 | 1 | no | — |
| 228 | C3×C4×D3 | — | 12 | 1 | no | — |
| 229 | C3×C4×D3 | — | 12 | 1 | no | — |
| 230 | C3×Dic6 | — | 3 | 1 | no | — |
| 231 | C3×Dic6 | — | 3 | 1 | no | — |
| 232 | C3×Dic6 | — | 3 | 1 | no | — |
| 233 | C3×Dic6 | — | 3 | 1 | no | — |
| 234 | C3×Dic6 | — | 6 | 1 | no | — |
| 235 | C3×Dic6 | — | 6 | 1 | no | — |
| 236 | C3×Dic6 | — | 6 | 1 | no | — |
| 237 | C3×Dic6 | — | 6 | 1 | no | — |
| 238 | C3×Dic6 | — | 6 | 1 | no | — |
| 239 | C3×Dic6 | — | 6 | 1 | no | — |
| 240 | C3×Dic6 | — | 12 | 1 | no | — |
| 241 | C3×Dic6 | — | 12 | 1 | no | — |
| 242 | #627 | — | 6 | 2 | no | — |
| 243 | #627 | — | 6 | 2 | no | — |
| 244 | #627 | — | 6 | 2 | no | — |
| 245 | #626 | — | 6 | 2 | no | — |
| 246 | #626 | — | 6 | 2 | no | — |
| 247 | #625 | — | 6 | 2 | no | — |
| 248 | #624 | — | 6 | 2 | no | — |
| 249 | #624 | — | 6 | 2 | no | — |
| 250 | D3×Dic3 | — | 6 | 2 | no | — |
| 251 | D3×Dic3 | — | 6 | 2 | no | — |
| 252 | D3×Dic3 | — | 6 | 2 | no | — |
| 253 | D3×Dic3 | — | 6 | 2 | no | — |
| 254 | C32×C8 | — | 6 | 1 | no | — |
| 255 | C3⋊(C3⋊C8) | — | 6 | 1 | no | — |
| 256 | C3⋊(C3⋊C8) | — | 6 | 2 | no | — |
| 257 | C3⋊(C3⋊C8) | — | 6 | 1 | no | — |
| 258 | C3⋊(C3⋊C8) | — | 6 | 1 | no | — |
| 259 | C3⋊(C3⋊C8) | — | 12 | 1 | no | — |
| 260 | C3⋊(C3⋊C8) | — | 12 | 1 | no | — |
| 261 | C3⋊(C3⋊C8) | — | 12 | 2 | no | — |
| 262 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 263 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 264 | C3×C3⋊C8 | — | 4 | 1 | no | — |
| 265 | #454 | — | 27 | 1 | no | Sylow |
| 266 | C2×C33 | — | 2 | 1 | no | — |
| 267 | C2×C33 | #120 | 1 | 1 | yes | characteristic |
| 268 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 269 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 270 | C32×D3 | — | 8 | 1 | no | — |
| 271 | C3×#41 | — | 9 | 1 | no | — |
| 272 | C3×#41 | — | 9 | 1 | no | — |
| 273 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 274 | C2×C3×D4 | — | 3 | 1 | no | — |
| 275 | C2×C3×D4 | — | 3 | 1 | no | — |
| 276 | C2×C3×D4 | — | 6 | 1 | no | — |
| 277 | #239 | — | 18 | 1 | no | — |
| 278 | #239 | — | 18 | 1 | no | — |
| 279 | D3×Q8 | — | 18 | 1 | no | — |
| 280 | D3×Q8 | — | 18 | 1 | no | — |
| 281 | D3×Q8 | — | 18 | 1 | no | — |
| 282 | D3×Q8 | — | 18 | 1 | no | — |
| 283 | #237 | — | 18 | 1 | no | — |
| 284 | #237 | — | 18 | 1 | no | — |
| 285 | #237 | — | 18 | 2 | no | — |
| 286 | #237 | — | 18 | 2 | no | — |
| 287 | #235 | — | 3 | 1 | no | — |
| 288 | #235 | — | 3 | 1 | no | — |
| 289 | #235 | — | 3 | 1 | no | — |
| 290 | #235 | — | 3 | 1 | no | — |
| 291 | #235 | — | 6 | 1 | no | — |
| 292 | #235 | — | 6 | 1 | no | — |
| 293 | #235 | — | 18 | 1 | no | — |
| 294 | #235 | — | 18 | 1 | no | — |
| 295 | #235 | — | 18 | 2 | no | — |
| 296 | C2×D12 | D32 | 1 | 1 | yes | characteristic |
| 297 | C2×Dic6 | — | 3 | 1 | no | — |
| 298 | C2×Dic6 | — | 3 | 1 | no | — |
| 299 | C2×Dic6 | — | 6 | 1 | no | — |
| 300 | C2×Dic6 | — | 18 | 1 | no | — |
| 301 | C2×Dic6 | — | 18 | 1 | no | — |
| 302 | C3×SD16 | — | 18 | 1 | no | — |
| 303 | C3×D8 | — | 18 | 1 | no | — |
| 304 | C3×M16 | — | 3 | 1 | no | — |
| 305 | C3×M16 | — | 3 | 1 | no | — |
| 306 | C3×M16 | — | 6 | 1 | no | — |
| 307 | C3×C22⋊C4 | — | 18 | 2 | no | — |
| 308 | C3×C42 | — | 3 | 1 | no | — |
| 309 | C3×C42 | — | 3 | 1 | no | — |
| 310 | C3×C42 | — | 6 | 1 | no | — |
| 311 | #217 | — | 6 | 2 | no | — |
| 312 | #215 | — | 18 | 1 | no | — |
| 313 | #214 | — | 6 | 1 | no | — |
| 314 | #214 | — | 18 | 1 | no | — |
| 315 | #214 | — | 18 | 1 | no | — |
| 316 | #214 | — | 18 | 2 | no | — |
| 317 | #213 | — | 6 | 1 | no | — |
| 318 | #213 | — | 18 | 1 | no | — |
| 319 | #213 | — | 18 | 1 | no | — |
| 320 | #213 | — | 18 | 1 | no | — |
| 321 | #213 | — | 18 | 2 | no | — |
| 322 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 323 | C4×Dic3 | D32 | 1 | 1 | yes | characteristic |
| 324 | #208 | — | 9 | 1 | no | — |
| 325 | #208 | — | 9 | 1 | no | — |
| 326 | #208 | — | 9 | 1 | no | — |
| 327 | #208 | — | 18 | 1 | no | — |
| 328 | #208 | — | 18 | 1 | no | — |
| 329 | #208 | — | 18 | 1 | no | — |
| 330 | #208 | — | 36 | 1 | no | — |
| 331 | #208 | D32 | 1 | 1 | yes | characteristic |
| 332 | D24 | — | 6 | 1 | no | — |
| 333 | #204 | — | 6 | 1 | no | — |
| 334 | C22×C32 | — | 2 | 1 | no | — |
| 335 | C22×C32 | — | 2 | 1 | no | — |
| 336 | C22×C32 | — | 2 | 1 | no | — |
| 337 | C22×C32 | — | 4 | 1 | no | — |
| 338 | C22×C32 | — | 12 | 1 | no | — |
| 339 | C22×C32 | — | 12 | 2 | no | — |
| 340 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 341 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 342 | C22×C32 | C2×#67 | 1 | 1 | yes | characteristic |
| 343 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 344 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 345 | C2×C3×D3 | — | 4 | 2 | no | — |
| 346 | C2×C3×D3 | — | 4 | 2 | no | — |
| 347 | C2×C3×D3 | — | 4 | 2 | no | — |
| 348 | C2×C3×D3 | — | 4 | 1 | no | — |
| 349 | C2×C3×D3 | — | 4 | 1 | no | — |
| 350 | C2×C3×D3 | — | 6 | 1 | no | — |
| 351 | C2×C3×D3 | — | 6 | 1 | no | — |
| 352 | C2×C3×D3 | — | 6 | 1 | no | — |
| 353 | C2×C3×D3 | — | 6 | 1 | no | — |
| 354 | C2×C3×D3 | — | 8 | 2 | no | — |
| 355 | C2×C3×D3 | — | 12 | 1 | no | — |
| 356 | C2×C3×D3 | — | 12 | 1 | no | — |
| 357 | C32×C4 | — | 2 | 1 | no | — |
| 358 | C32×C4 | — | 2 | 1 | no | — |
| 359 | C32×C4 | — | 2 | 1 | no | — |
| 360 | C32×C4 | — | 2 | 1 | no | — |
| 361 | C32×C4 | — | 2 | 1 | no | — |
| 362 | C32×C4 | — | 2 | 1 | no | — |
| 363 | C32×C4 | — | 4 | 1 | no | — |
| 364 | C32×C4 | — | 4 | 1 | no | — |
| 365 | C32×C4 | — | 12 | 1 | no | — |
| 366 | C32×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 367 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 368 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 369 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 370 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 371 | C32×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 372 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 373 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 374 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 375 | C3×Dic3 | — | 4 | 1 | no | — |
| 376 | C3×Dic3 | — | 4 | 1 | no | — |
| 377 | C3×Dic3 | — | 4 | 2 | no | — |
| 378 | C3×Dic3 | — | 6 | 2 | no | — |
| 379 | C3×Dic3 | — | 6 | 1 | no | — |
| 380 | C3×Dic3 | — | 6 | 1 | no | — |
| 381 | C3×Dic3 | — | 6 | 1 | no | — |
| 382 | C3×Dic3 | — | 6 | 2 | no | — |
| 383 | C3×Dic3 | — | 6 | 1 | no | — |
| 384 | C3×Dic3 | — | 12 | 1 | no | — |
| 385 | C3×Dic3 | — | 12 | 1 | no | — |
| 386 | C3×Dic3 | — | 12 | 2 | no | — |
| 387 | 2−1+4 | — | 27 | 1 | no | — |
| 388 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 389 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 390 | #124 | — | 9 | 1 | no | — |
| 391 | #104 | — | 9 | 1 | no | — |
| 392 | #104 | — | 27 | 1 | no | — |
| 393 | #101 | — | 27 | 1 | no | — |
| 394 | C33 | #454 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 395 | C23×C3 | — | 6 | 1 | no | — |
| 396 | C23×C3 | — | 6 | 1 | no | — |
| 397 | C23×C3 | — | 12 | 1 | no | — |
| 398 | C22×D3 | — | 2 | 1 | no | — |
| 399 | C3×Q8 | — | 9 | 1 | no | — |
| 400 | C3×Q8 | — | 9 | 1 | no | — |
| 401 | C3×Q8 | — | 18 | 1 | no | — |
| 402 | C3×Q8 | — | 18 | 1 | no | — |
| 403 | C3×D4 | — | 6 | 2 | no | — |
| 404 | C3×D4 | — | 6 | 1 | no | — |
| 405 | C3×D4 | — | 6 | 1 | no | — |
| 406 | C3×D4 | — | 6 | 1 | no | — |
| 407 | C3×D4 | — | 6 | 1 | no | — |
| 408 | C3×D4 | — | 9 | 1 | no | — |
| 409 | C3×D4 | — | 9 | 1 | no | — |
| 410 | C3×D4 | — | 12 | 1 | no | — |
| 411 | C3×D4 | — | 18 | 1 | no | — |
| 412 | C3×D4 | — | 18 | 1 | no | — |
| 413 | C2×C3×C4 | — | 2 | 1 | no | — |
| 414 | C2×C3×C4 | — | 2 | 1 | no | — |
| 415 | C2×C3×C4 | — | 2 | 1 | no | — |
| 416 | C2×C3×C4 | — | 4 | 1 | no | — |
| 417 | C2×C3×C4 | — | 6 | 1 | no | — |
| 418 | C2×C3×C4 | — | 6 | 1 | no | — |
| 419 | C2×C3×C4 | — | 9 | 2 | no | — |
| 420 | C2×C3×C4 | — | 12 | 1 | no | — |
| 421 | C2×C3×C4 | — | 18 | 1 | no | — |
| 422 | C2×C3×C4 | — | 18 | 1 | no | — |
| 423 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 424 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 425 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 426 | #67 | — | 6 | 1 | no | — |
| 427 | #67 | — | 6 | 1 | no | — |
| 428 | #67 | — | 6 | 1 | no | — |
| 429 | #67 | — | 6 | 1 | no | — |
| 430 | #67 | — | 12 | 1 | no | — |
| 431 | #67 | — | 12 | 1 | no | — |
| 432 | #67 | — | 18 | 2 | no | — |
| 433 | #67 | — | 18 | 2 | no | — |
| 434 | C2×Dic3 | — | 2 | 1 | no | — |
| 435 | C2×Dic3 | — | 3 | 2 | no | — |
| 436 | C2×Dic3 | — | 3 | 2 | no | — |
| 437 | C2×Dic3 | — | 6 | 2 | no | — |
| 438 | C2×Dic3 | — | 18 | 2 | no | — |
| 439 | C2×Dic3 | — | 18 | 2 | no | — |
| 440 | D12 | — | 2 | 1 | no | — |
| 441 | D12 | — | 2 | 1 | no | — |
| 442 | D12 | — | 3 | 1 | no | — |
| 443 | D12 | — | 3 | 1 | no | — |
| 444 | D12 | — | 3 | 1 | no | — |
| 445 | D12 | — | 3 | 1 | no | — |
| 446 | D12 | — | 6 | 1 | no | — |
| 447 | D12 | — | 6 | 1 | no | — |
| 448 | D12 | — | 18 | 2 | no | — |
| 449 | C4×D3 | — | 6 | 1 | no | — |
| 450 | C4×D3 | — | 6 | 1 | no | — |
| 451 | C4×D3 | — | 6 | 1 | no | — |
| 452 | C4×D3 | — | 6 | 1 | no | — |
| 453 | C4×D3 | — | 12 | 1 | no | — |
| 454 | C4×D3 | — | 12 | 1 | no | — |
| 455 | C4×D3 | — | 18 | 2 | no | — |
| 456 | C4×D3 | — | 18 | 2 | no | — |
| 457 | C4×D3 | — | 18 | 2 | no | — |
| 458 | C4×D3 | — | 18 | 2 | no | — |
| 459 | Dic6 | — | 3 | 1 | no | — |
| 460 | Dic6 | — | 3 | 1 | no | — |
| 461 | Dic6 | — | 3 | 1 | no | — |
| 462 | Dic6 | — | 3 | 1 | no | — |
| 463 | Dic6 | — | 6 | 1 | no | — |
| 464 | Dic6 | — | 6 | 1 | no | — |
| 465 | Dic6 | — | 6 | 1 | no | — |
| 466 | Dic6 | — | 6 | 1 | no | — |
| 467 | Dic6 | — | 6 | 1 | no | — |
| 468 | Dic6 | — | 6 | 1 | no | — |
| 469 | Dic6 | — | 12 | 1 | no | — |
| 470 | Dic6 | — | 12 | 1 | no | — |
| 471 | Dic6 | — | 18 | 2 | no | — |
| 472 | Dic6 | — | 18 | 2 | no | — |
| 473 | Dic6 | — | 18 | 2 | no | — |
| 474 | C3×C8 | — | 6 | 1 | no | — |
| 475 | C3×C8 | — | 6 | 1 | no | — |
| 476 | C3×C8 | — | 12 | 1 | no | — |
| 477 | C3⋊C8 | — | 2 | 1 | no | — |
| 478 | C3⋊C8 | — | 18 | 2 | no | — |
| 479 | C3⋊C8 | — | 18 | 1 | no | — |
| 480 | C3⋊C8 | — | 18 | 1 | no | — |
| 481 | C3⋊C8 | — | 18 | 1 | no | — |
| 482 | C3⋊C8 | — | 36 | 1 | no | — |
| 483 | C3⋊C8 | — | 36 | 1 | no | — |
| 484 | C3⋊C8 | — | 36 | 2 | no | — |
| 485 | C2×C32 | — | 2 | 1 | no | — |
| 486 | C2×C32 | — | 2 | 1 | no | — |
| 487 | C2×C32 | — | 2 | 1 | no | — |
| 488 | C2×C32 | — | 2 | 1 | no | — |
| 489 | C2×C32 | — | 2 | 1 | no | — |
| 490 | C2×C32 | — | 2 | 1 | no | — |
| 491 | C2×C32 | — | 4 | 1 | no | — |
| 492 | C2×C32 | — | 4 | 1 | no | — |
| 493 | C2×C32 | — | 4 | 1 | no | — |
| 494 | C2×C32 | — | 4 | 1 | no | — |
| 495 | C2×C32 | — | 8 | 1 | no | — |
| 496 | C2×C32 | — | 24 | 1 | no | — |
| 497 | C2×C32 | #882 | 1 | 1 | yes | characteristic |
| 498 | C2×C32 | #937 | 1 | 1 | yes | characteristic |
| 499 | C2×C32 | #937 | 1 | 1 | yes | characteristic |
| 500 | C3⋊D3 | — | 4 | 1 | no | — |
| 501 | C3⋊D3 | — | 4 | 1 | no | — |
| 502 | C3×D3 | — | 8 | 2 | no | — |
| 503 | C3×D3 | — | 8 | 1 | no | — |
| 504 | C3×D3 | — | 8 | 1 | no | — |
| 505 | C3×D3 | — | 12 | 1 | no | — |
| 506 | C3×D3 | — | 12 | 1 | no | — |
| 507 | C3×D3 | — | 12 | 1 | no | — |
| 508 | C3×D3 | — | 12 | 1 | no | — |
| 509 | C3×D3 | — | 24 | 1 | no | — |
| 510 | C3×D3 | — | 24 | 1 | no | — |
| 511 | #41 | — | 9 | 1 | no | — |
| 512 | #41 | — | 9 | 1 | no | — |
| 513 | #41 | — | 54 | 2 | no | — |
| 514 | #41 | — | 54 | 1 | no | — |
| 515 | #41 | — | 54 | 1 | no | — |
| 516 | C2×Q8 | — | 9 | 1 | no | — |
| 517 | C2×Q8 | — | 54 | 1 | no | — |
| 518 | C2×Q8 | — | 54 | 1 | no | — |
| 519 | C2×D4 | — | 3 | 1 | no | — |
| 520 | SD16 | — | 18 | 1 | no | — |
| 521 | SD16 | — | 54 | 1 | no | — |
| 522 | D8 | — | 18 | 1 | no | — |
| 523 | D8 | — | 54 | 1 | no | — |
| 524 | M16 | — | 3 | 1 | no | — |
| 525 | M16 | — | 27 | 1 | no | — |
| 526 | C22⋊C4 | — | 18 | 2 | no | — |
| 527 | C42 | — | 3 | 1 | no | — |
| 528 | C22×C3 | — | 2 | 1 | no | — |
| 529 | C22×C3 | — | 2 | 1 | no | — |
| 530 | C22×C3 | — | 2 | 1 | no | — |
| 531 | C22×C3 | — | 4 | 1 | no | — |
| 532 | C22×C3 | — | 12 | 2 | no | — |
| 533 | C22×C3 | — | 12 | 2 | no | — |
| 534 | C22×C3 | — | 12 | 2 | no | — |
| 535 | C22×C3 | — | 12 | 1 | no | — |
| 536 | C22×C3 | — | 12 | 1 | no | — |
| 537 | C22×C3 | — | 18 | 1 | no | — |
| 538 | C22×C3 | — | 18 | 1 | no | — |
| 539 | C22×C3 | — | 24 | 2 | no | — |
| 540 | C22×C3 | #3802 | 1 | 1 | yes | characteristic |
| 541 | C22×C3 | D3×#67 | 1 | 1 | yes | characteristic |
| 542 | C22×C3 | D3×#67 | 1 | 1 | yes | characteristic |
| 543 | C2×D3 | — | 4 | 2 | no | — |
| 544 | C2×D3 | — | 4 | 1 | no | — |
| 545 | C2×D3 | — | 6 | 1 | no | — |
| 546 | C2×D3 | — | 6 | 1 | no | — |
| 547 | C2×D3 | — | 6 | 1 | no | — |
| 548 | C2×D3 | — | 6 | 1 | no | — |
| 549 | C2×D3 | — | 12 | 1 | no | — |
| 550 | C2×D3 | — | 12 | 1 | no | — |
| 551 | C3×C4 | — | 2 | 1 | no | — |
| 552 | C3×C4 | — | 2 | 1 | no | — |
| 553 | C3×C4 | — | 2 | 1 | no | — |
| 554 | C3×C4 | — | 2 | 1 | no | — |
| 555 | C3×C4 | — | 2 | 1 | no | — |
| 556 | C3×C4 | — | 2 | 1 | no | — |
| 557 | C3×C4 | — | 4 | 1 | no | — |
| 558 | C3×C4 | — | 4 | 1 | no | — |
| 559 | C3×C4 | — | 12 | 1 | no | — |
| 560 | C3×C4 | — | 12 | 1 | no | — |
| 561 | C3×C4 | — | 12 | 2 | no | — |
| 562 | C3×C4 | — | 18 | 1 | no | — |
| 563 | C3×C4 | — | 18 | 2 | no | — |
| 564 | C3×C4 | — | 18 | 1 | no | — |
| 565 | C3×C4 | D3×D12 | 1 | 1 | yes | characteristic |
| 566 | C3×C4 | D3×D12 | 1 | 1 | yes | characteristic |
| 567 | C3×C4 | #3802 | 1 | 1 | yes | characteristic |
| 568 | C3×C4 | D3×#67 | 1 | 1 | yes | characteristic |
| 569 | C3×C4 | D3×#67 | 1 | 1 | yes | characteristic |
| 570 | C3×C4 | #3811 | 1 | 1 | yes | characteristic |
| 571 | Dic3 | — | 4 | 1 | no | — |
| 572 | Dic3 | — | 6 | 1 | no | — |
| 573 | Dic3 | — | 6 | 1 | no | — |
| 574 | Dic3 | — | 6 | 1 | no | — |
| 575 | Dic3 | — | 6 | 2 | no | — |
| 576 | Dic3 | — | 6 | 1 | no | — |
| 577 | Dic3 | — | 6 | 2 | no | — |
| 578 | Dic3 | — | 12 | 1 | no | — |
| 579 | Dic3 | — | 12 | 1 | no | — |
| 580 | Dic3 | — | 12 | 2 | no | — |
| 581 | C32 | — | 2 | 1 | no | — |
| 582 | C32 | — | 2 | 1 | no | — |
| 583 | C32 | — | 2 | 1 | no | — |
| 584 | C32 | — | 4 | 1 | no | — |
| 585 | C32 | #4827 | 1 | 1 | yes | characteristic, complemented |
| 586 | C32 | #5062 | 1 | 1 | yes | characteristic, complemented |
| 587 | C32 | #5201 | 1 | 1 | yes | characteristic, complemented |
| 588 | C23 | — | 6 | 1 | no | — |
| 589 | Q8 | — | 9 | 1 | no | — |
| 590 | Q8 | — | 9 | 1 | no | — |
| 591 | Q8 | — | 18 | 1 | no | — |
| 592 | Q8 | — | 18 | 1 | no | — |
| 593 | Q8 | — | 54 | 2 | no | — |
| 594 | D4 | — | 6 | 1 | no | — |
| 595 | D4 | — | 6 | 1 | no | — |
| 596 | D4 | — | 9 | 1 | no | — |
| 597 | D4 | — | 9 | 1 | no | — |
| 598 | D4 | — | 18 | 1 | no | — |
| 599 | D4 | — | 18 | 1 | no | — |
| 600 | D4 | — | 54 | 2 | no | — |
| 601 | C2×C4 | — | 6 | 1 | no | — |
| 602 | C2×C4 | — | 9 | 2 | no | — |
| 603 | C2×C4 | — | 18 | 1 | no | — |
| 604 | C2×C4 | — | 18 | 1 | no | — |
| 605 | C2×C4 | — | 54 | 2 | no | — |
| 606 | C2×C4 | — | 54 | 2 | no | — |
| 607 | C2×C4 | D33 | 1 | 1 | yes | characteristic |
| 608 | C8 | — | 6 | 1 | no | — |
| 609 | C8 | — | 54 | 1 | no | — |
| 610 | C2×C3 | — | 2 | 1 | no | — |
| 611 | C2×C3 | — | 2 | 1 | no | — |
| 612 | C2×C3 | — | 2 | 1 | no | — |
| 613 | C2×C3 | — | 2 | 1 | no | — |
| 614 | C2×C3 | — | 2 | 1 | no | — |
| 615 | C2×C3 | — | 2 | 1 | no | — |
| 616 | C2×C3 | — | 4 | 1 | no | — |
| 617 | C2×C3 | — | 4 | 1 | no | — |
| 618 | C2×C3 | — | 4 | 1 | no | — |
| 619 | C2×C3 | — | 4 | 1 | no | — |
| 620 | C2×C3 | — | 8 | 1 | no | — |
| 621 | C2×C3 | — | 24 | 2 | no | — |
| 622 | C2×C3 | — | 24 | 1 | no | — |
| 623 | C2×C3 | — | 24 | 1 | no | — |
| 624 | C2×C3 | — | 36 | 1 | no | — |
| 625 | C2×C3 | — | 36 | 1 | no | — |
| 626 | C2×C3 | #63922 | 1 | 1 | yes | characteristic |
| 627 | C2×C3 | #63922 | 1 | 1 | yes | characteristic |
| 628 | C2×C3 | #63983 | 1 | 1 | yes | characteristic |
| 629 | D3 | — | 8 | 1 | no | — |
| 630 | D3 | — | 12 | 1 | no | — |
| 631 | D3 | — | 12 | 1 | no | — |
| 632 | D3 | — | 12 | 1 | no | — |
| 633 | D3 | — | 12 | 1 | no | — |
| 634 | D3 | — | 24 | 1 | no | — |
| 635 | D3 | — | 24 | 1 | no | — |
| 636 | C22 | — | 12 | 2 | no | — |
| 637 | C22 | — | 12 | 1 | no | — |
| 638 | C22 | — | 18 | 1 | no | — |
| 639 | C22 | — | 18 | 1 | no | — |
| 640 | C22 | #88953 | 1 | 1 | yes | characteristic |
| 641 | C4 | — | 12 | 1 | no | — |
| 642 | C4 | — | 18 | 2 | no | — |
| 643 | C4 | — | 18 | 1 | no | — |
| 644 | C4 | — | 18 | 1 | no | — |
| 645 | C4 | #88953 | 1 | 1 | yes | characteristic |
| 646 | C4 | #88955 | 1 | 1 | yes | characteristic |
| 647 | C3 | — | 2 | 1 | no | — |
| 648 | C3 | — | 2 | 1 | no | — |
| 649 | C3 | — | 2 | 1 | no | — |
| 650 | C3 | — | 4 | 1 | no | — |
| 651 | C3 | #10590400 | 1 | 1 | yes | characteristic, complemented |
| 652 | C3 | #10591019 | 1 | 1 | yes | characteristic, complemented |
| 653 | C3 | #10591525 | 1 | 1 | yes | characteristic, complemented |
| 654 | C2 | — | 2 | 1 | no | — |
| 655 | C2 | — | 24 | 1 | no | — |
| 656 | C2 | — | 36 | 1 | no | — |
| 657 | C2 | — | 36 | 1 | no | — |
| 658 | C2 | #11722951 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11722951 |
| commutator, Fitting, cosocle | C2×C33×C4 | C23 |
| Frattini, hypercenter | C2×C4 | D33 |
| socle | C2×C33 | #120 |
| hypocenter | C33 | #454 |
| LCS | G ▷ C2×C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11724614 | C2 | semidirect |
| 2. #11723364 | C2 | semidirect |
| 3. C3×#63860 | C2 | semidirect |
| 4. C3×#63830 | C2 | semidirect |
| 5. #11722046 | C2 | semidirect |
| 6. #11722029 | C2 | semidirect |
| 7. C3×#63570 | C2 | semidirect |
| 36. #63860 | D3 | semidirect |
| 37. #63830 | D3 | semidirect |
| 45. #63570 | D3 | semidirect |
| 394. C33 | #454 | semidirect |
| 585. C32 | #4827 | semidirect |
| 586. C32 | #5062 | semidirect |
| 587. C32 | #5201 | semidirect |
| 651. C3 | #10590400 | semidirect |
| 652. C3 | #10591019 | semidirect |
| 653. C3 | #10591525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724614 | 2 |
| #11723364 | 2 |
| C3×#63860 | 2 |
| C3×#63830 | 2 |
| #11722046 | 2 |
| #11722029 | 2 |
| C3×#63570 | 2 |
| #10591525 | 3 |
| #10591019 | 3 |
| #10590400 | 3 |