Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
930 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 133 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 | #11722517 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11722502 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11721802 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #64124⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11721236 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11721227 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11721197 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11721189 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11720853 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11720842 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11720833 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10594756 | — | 3 | 2 | no | maximal |
| 13 | #88748 | C22 | 1 | 1 | yes | characteristic |
| 14 | #88744 | C22 | 1 | 1 | yes | characteristic |
| 15 | Q8×(C3⋊D3)⋊C3 | C22 | 1 | 2 | yes | — |
| 16 | #3830⋊C3 | C22 | 1 | 2 | yes | — |
| 17 | #88672 | — | 2 | 1 | no | — |
| 18 | #88671 | — | 2 | 2 | no | — |
| 19 | C2×#6196 | — | 2 | 1 | no | — |
| 20 | #88652 | — | 2 | 2 | no | — |
| 21 | #88652 | C22 | 1 | 2 | yes | — |
| 22 | #88651 | — | 2 | 1 | no | — |
| 23 | #88651 | C22 | 1 | 1 | yes | characteristic |
| 24 | #88651 | C22 | 1 | 1 | yes | characteristic |
| 25 | #88650 | — | 2 | 1 | no | — |
| 26 | #88650 | C22 | 1 | 1 | yes | characteristic |
| 27 | ((C3⋊D3)⋊C3)⋊Q8 | C22 | 1 | 2 | yes | — |
| 28 | SD16×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 29 | #88550 | C22 | 1 | 1 | yes | characteristic |
| 30 | #88545 | C22 | 1 | 1 | yes | characteristic |
| 31 | #88528 | C22 | 1 | 1 | yes | characteristic |
| 32 | C8×#272 | C22 | 1 | 1 | yes | characteristic |
| 33 | #3756⋊C3 | C22 | 1 | 2 | yes | — |
| 34 | #3754⋊C3 | C22 | 1 | 2 | yes | — |
| 35 | #3743⋊C3 | C22 | 1 | 2 | yes | — |
| 36 | #3746⋊C3 | C22 | 1 | 2 | yes | — |
| 37 | #88439 | C22 | 1 | 2 | yes | — |
| 38 | #88437 | C22 | 1 | 2 | yes | — |
| 39 | #88435 | C22 | 1 | 1 | yes | characteristic |
| 40 | #88433 | C22 | 1 | 2 | yes | — |
| 41 | ((C3⋊D3)⋊C3)⋊C8 | C22 | 1 | 2 | yes | — |
| 42 | #64315 | — | 3 | 2 | no | — |
| 43 | #64309 | — | 3 | 2 | no | — |
| 44 | #64124 | D3 | 1 | 2 | yes | complemented |
| 45 | C3×#916 | — | 3 | 2 | no | — |
| 46 | C3×#916 | — | 6 | 1 | no | — |
| 47 | C3×#915 | — | 3 | 2 | no | — |
| 48 | #63944 | — | 3 | 2 | no | — |
| 49 | #63943 | — | 3 | 2 | no | — |
| 50 | D3×#216 | — | 3 | 2 | no | — |
| 51 | #63936 | — | 3 | 2 | no | — |
| 52 | #63933 | — | 3 | 2 | no | — |
| 53 | #63929 | — | 3 | 2 | no | — |
| 54 | #63811 | — | 3 | 2 | no | — |
| 55 | #63804 | — | 3 | 2 | no | — |
| 56 | #63800 | — | 3 | 2 | no | — |
| 57 | D3×Dic12 | — | 3 | 2 | no | — |
| 58 | Q8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 59 | D4×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 60 | #6235 | — | 2 | 1 | no | — |
| 61 | C2×#1084 | — | 2 | 1 | no | — |
| 62 | C4⋊#272 | — | 2 | 1 | no | — |
| 63 | C4⋊#272 | C23 | 1 | 1 | yes | characteristic |
| 64 | C4×#272 | — | 2 | 1 | no | — |
| 65 | C4×#272 | C23 | 1 | 1 | yes | characteristic |
| 66 | #6229 | C23 | 1 | 1 | yes | characteristic |
| 67 | #638⋊C3 | — | 2 | 2 | no | — |
| 68 | C2×(C3⋊Dic3)⋊C3 | — | 2 | 2 | no | — |
| 69 | C4×(C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 70 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 2 | yes | — |
| 71 | #634⋊C3 | — | 2 | 2 | no | — |
| 72 | #634⋊C3 | C23 | 1 | 2 | yes | — |
| 73 | #634⋊C3 | C23 | 1 | 2 | yes | — |
| 74 | #6200 | — | 2 | 2 | no | — |
| 75 | #6200 | D4 | 1 | 2 | yes | — |
| 76 | #6199 | — | 2 | 1 | no | — |
| 77 | #6199 | — | 2 | 1 | no | — |
| 78 | #6199 | — | 2 | 2 | no | — |
| 79 | #6198 | D4 | 1 | 1 | yes | characteristic |
| 80 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 2 | no | — |
| 81 | #6196 | — | 2 | 1 | no | — |
| 82 | #6196 | — | 2 | 1 | no | — |
| 83 | #6196 | — | 2 | 2 | no | — |
| 84 | #6196 | D4 | 1 | 1 | yes | characteristic |
| 85 | C8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 86 | #6180 | C23 | 1 | 1 | yes | characteristic |
| 87 | (C3⋊(C3⋊C8))⋊C3 | C23 | 1 | 2 | yes | — |
| 88 | #5779 | — | 9 | 2 | no | — |
| 89 | #5771 | — | 9 | 1 | no | — |
| 90 | Q8×C3⋊D3 | C2×D3 | 1 | 2 | yes | — |
| 91 | #3830 | C2×D3 | 1 | 2 | yes | — |
| 92 | C3×#239 | — | 3 | 2 | no | — |
| 93 | C3×#239 | — | 6 | 1 | no | — |
| 94 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 95 | C3×#237 | — | 3 | 2 | no | — |
| 96 | C3×#237 | — | 3 | 2 | no | — |
| 97 | C3×#237 | — | 6 | 1 | no | — |
| 98 | C2×#627 | — | 6 | 2 | no | — |
| 99 | #3805 | — | 6 | 2 | no | — |
| 100 | #3804 | — | 6 | 2 | no | — |
| 101 | #3804 | — | 6 | 2 | no | — |
| 102 | #3798 | — | 3 | 2 | no | — |
| 103 | #3798 | — | 6 | 2 | no | — |
| 104 | #3797 | — | 3 | 2 | no | — |
| 105 | #3796 | — | 3 | 2 | no | — |
| 106 | #3796 | — | 6 | 2 | no | — |
| 107 | #3795 | — | 3 | 2 | no | — |
| 108 | #3795 | — | 6 | 2 | no | — |
| 109 | D3×Dic6 | — | 3 | 2 | no | — |
| 110 | D3×Dic6 | — | 3 | 2 | no | — |
| 111 | D3×Dic6 | — | 3 | 2 | no | — |
| 112 | D3×Dic6 | — | 6 | 2 | no | — |
| 113 | C32×SD16 | — | 2 | 1 | no | — |
| 114 | C32×SD16 | C2×D3 | 1 | 2 | yes | — |
| 115 | #3756 | C2×D3 | 1 | 2 | yes | — |
| 116 | #3754 | C2×D3 | 1 | 2 | yes | — |
| 117 | #3746 | C2×D3 | 1 | 2 | yes | — |
| 118 | #3743 | C2×D3 | 1 | 2 | yes | — |
| 119 | C3×#216 | — | 3 | 2 | no | — |
| 120 | C3×#216 | — | 3 | 2 | no | — |
| 121 | C3×#216 | — | 6 | 1 | no | — |
| 122 | C3×#214 | — | 3 | 2 | no | — |
| 123 | C3×#213 | — | 3 | 2 | no | — |
| 124 | C3×#213 | — | 6 | 1 | no | — |
| 125 | C3×Dic12 | — | 3 | 2 | no | — |
| 126 | C3×#204 | — | 3 | 2 | no | — |
| 127 | C3×#204 | — | 6 | 1 | no | — |
| 128 | C3×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 129 | C3×D3×C8 | — | 3 | 2 | no | — |
| 130 | C3×D3×C8 | — | 6 | 1 | no | — |
| 131 | #3719 | — | 3 | 2 | no | — |
| 132 | #3719 | — | 3 | 2 | no | — |
| 133 | #3719 | — | 3 | 2 | no | — |
| 134 | #3718 | — | 3 | 2 | no | — |
| 135 | #3716 | — | 3 | 2 | no | — |
| 136 | #3715 | — | 3 | 2 | no | — |
| 137 | #3711 | — | 3 | 2 | no | — |
| 138 | #3710 | — | 3 | 2 | no | — |
| 139 | D3×C3⋊C8 | — | 3 | 2 | no | — |
| 140 | C22×H(3,𝔽3) | — | 2 | 1 | no | — |
| 141 | C2×#272 | — | 2 | 1 | no | — |
| 142 | C2×#272 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C2×(C3⋊D3)⋊C3 | C2×D4 | 1 | 2 | yes | — |
| 144 | C4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 145 | C4×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 146 | #1084 | — | 2 | 1 | no | — |
| 147 | #1084 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | (C3⋊Dic3)⋊C3 | — | 2 | 2 | no | — |
| 149 | (C3⋊Dic3)⋊C3 | — | 2 | 2 | no | — |
| 150 | (C3⋊Dic3)⋊C3 | C2×D4 | 1 | 2 | yes | — |
| 151 | #1010 | — | 9 | 1 | no | — |
| 152 | #1010 | — | 9 | 2 | no | — |
| 153 | #1010 | — | 9 | 1 | no | — |
| 154 | #1007 | — | 9 | 2 | no | — |
| 155 | C3×#137 | — | 9 | 2 | no | — |
| 156 | C3×#135 | — | 9 | 1 | no | — |
| 157 | #951 | — | 9 | 1 | no | — |
| 158 | #951 | — | 9 | 1 | no | — |
| 159 | #950 | — | 9 | 2 | no | — |
| 160 | C2×#216 | — | 9 | 2 | no | — |
| 161 | #918 | — | 9 | 2 | no | — |
| 162 | #918 | — | 9 | 2 | no | — |
| 163 | D3×Q16 | — | 9 | 2 | no | — |
| 164 | D3×Q16 | — | 9 | 2 | no | — |
| 165 | D3×Q16 | — | 9 | 2 | no | — |
| 166 | #916 | — | 3 | 2 | no | — |
| 167 | #916 | — | 6 | 1 | no | — |
| 168 | #916 | — | 9 | 2 | no | — |
| 169 | #915 | — | 3 | 2 | no | — |
| 170 | #915 | — | 9 | 2 | no | — |
| 171 | #915 | — | 9 | 2 | no | — |
| 172 | #915 | — | 9 | 2 | no | — |
| 173 | #912 | — | 9 | 2 | no | — |
| 174 | #909 | — | 9 | 2 | no | — |
| 175 | #907 | — | 9 | 2 | no | — |
| 176 | C2×Dic12 | — | 9 | 1 | no | — |
| 177 | #901 | — | 9 | 1 | no | — |
| 178 | C32×Q8 | — | 2 | 1 | no | — |
| 179 | C32×Q8 | C22×D3 | 1 | 2 | yes | — |
| 180 | C32×D4 | — | 2 | 1 | no | — |
| 181 | C32×D4 | C22×D3 | 1 | 2 | yes | — |
| 182 | #638 | — | 2 | 2 | no | — |
| 183 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 184 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 185 | C4×C3⋊D3 | C22×D3 | 1 | 2 | yes | — |
| 186 | #634 | — | 2 | 2 | no | — |
| 187 | #634 | C22×D3 | 1 | 2 | yes | — |
| 188 | #634 | C22×D3 | 1 | 2 | yes | — |
| 189 | C3×#67 | — | 6 | 2 | no | — |
| 190 | C3×#67 | — | 6 | 2 | no | — |
| 191 | C3×#67 | — | 12 | 1 | no | — |
| 192 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 193 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 194 | C2×C3×Dic3 | — | 12 | 1 | no | — |
| 195 | C3×D12 | — | 3 | 2 | no | — |
| 196 | C3×D12 | — | 6 | 1 | no | — |
| 197 | C3×D12 | — | 6 | 2 | no | — |
| 198 | C3×D12 | — | 12 | 1 | no | — |
| 199 | C3×C4×D3 | — | 3 | 2 | no | — |
| 200 | C3×C4×D3 | — | 3 | 2 | no | — |
| 201 | C3×C4×D3 | — | 6 | 1 | no | — |
| 202 | C3×C4×D3 | — | 6 | 2 | no | — |
| 203 | C3×C4×D3 | — | 6 | 2 | no | — |
| 204 | C3×C4×D3 | — | 12 | 1 | no | — |
| 205 | C3×Dic6 | — | 3 | 2 | no | — |
| 206 | C3×Dic6 | — | 3 | 2 | no | — |
| 207 | C3×Dic6 | — | 3 | 2 | no | — |
| 208 | C3×Dic6 | — | 6 | 1 | no | — |
| 209 | C3×Dic6 | — | 6 | 2 | no | — |
| 210 | #627 | — | 3 | 2 | no | — |
| 211 | #627 | — | 6 | 2 | no | — |
| 212 | #627 | — | 6 | 2 | no | — |
| 213 | #627 | — | 6 | 2 | no | — |
| 214 | #627 | — | 6 | 2 | no | — |
| 215 | #626 | — | 3 | 2 | no | — |
| 216 | #626 | — | 3 | 2 | no | — |
| 217 | #626 | — | 6 | 2 | no | — |
| 218 | #625 | — | 3 | 2 | no | — |
| 219 | #625 | — | 6 | 2 | no | — |
| 220 | #624 | — | 6 | 2 | no | — |
| 221 | D3×Dic3 | — | 6 | 2 | no | — |
| 222 | D3×Dic3 | — | 6 | 2 | no | — |
| 223 | D3×Dic3 | — | 6 | 2 | no | — |
| 224 | D3×Dic3 | — | 6 | 2 | no | — |
| 225 | D3×Dic3 | — | 6 | 2 | no | — |
| 226 | C32×C8 | — | 2 | 1 | no | — |
| 227 | C32×C8 | C22×D3 | 1 | 2 | yes | — |
| 228 | C3⋊(C3⋊C8) | C22×D3 | 1 | 2 | yes | — |
| 229 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 230 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 231 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 232 | #578 | — | 27 | 1 | no | Sylow |
| 233 | C2×H(3,𝔽3) | — | 4 | 1 | no | — |
| 234 | C2×H(3,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 235 | #272 | — | 2 | 1 | no | — |
| 236 | #272 | — | 4 | 1 | no | — |
| 237 | (C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 238 | C3×#41 | — | 9 | 2 | no | — |
| 239 | C3×#41 | — | 9 | 1 | no | — |
| 240 | C3×#41 | — | 9 | 1 | no | — |
| 241 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 242 | #239 | — | 3 | 2 | no | — |
| 243 | #239 | — | 6 | 1 | no | — |
| 244 | #239 | — | 9 | 2 | no | — |
| 245 | #239 | — | 18 | 2 | no | — |
| 246 | D3×Q8 | — | 3 | 2 | no | — |
| 247 | D3×Q8 | — | 9 | 2 | no | — |
| 248 | D3×Q8 | — | 9 | 2 | no | — |
| 249 | D3×Q8 | — | 9 | 2 | no | — |
| 250 | D3×Q8 | — | 9 | 2 | no | — |
| 251 | D3×Q8 | — | 9 | 2 | no | — |
| 252 | D3×Q8 | — | 18 | 2 | no | — |
| 253 | #237 | — | 3 | 2 | no | — |
| 254 | #237 | — | 3 | 2 | no | — |
| 255 | #237 | — | 6 | 1 | no | — |
| 256 | #237 | — | 9 | 2 | no | — |
| 257 | #237 | — | 9 | 2 | no | — |
| 258 | #237 | — | 18 | 2 | no | — |
| 259 | #237 | — | 18 | 2 | no | — |
| 260 | #237 | — | 18 | 2 | no | — |
| 261 | #237 | — | 18 | 2 | no | — |
| 262 | #235 | — | 9 | 1 | no | — |
| 263 | #235 | — | 9 | 2 | no | — |
| 264 | #235 | — | 9 | 2 | no | — |
| 265 | #235 | — | 18 | 1 | no | — |
| 266 | #235 | — | 18 | 2 | no | — |
| 267 | #235 | — | 18 | 2 | no | — |
| 268 | #235 | — | 18 | 1 | no | — |
| 269 | #235 | — | 18 | 2 | no | — |
| 270 | C2×Dic6 | — | 9 | 1 | no | — |
| 271 | C2×Dic6 | — | 9 | 1 | no | — |
| 272 | C2×Dic6 | — | 9 | 2 | no | — |
| 273 | C2×Dic6 | — | 18 | 1 | no | — |
| 274 | C2×Dic6 | — | 18 | 1 | no | — |
| 275 | C2×Dic6 | — | 18 | 2 | no | — |
| 276 | C3×Q16 | — | 9 | 2 | no | — |
| 277 | C3×Q16 | — | 9 | 2 | no | — |
| 278 | C3×Q16 | — | 9 | 1 | no | — |
| 279 | C3×SD16 | — | 3 | 2 | no | — |
| 280 | C3×SD16 | — | 6 | 1 | no | — |
| 281 | C3×SD16 | — | 9 | 2 | no | — |
| 282 | C3×SD16 | — | 9 | 1 | no | — |
| 283 | C3×SD16 | D32 | 1 | 1 | yes | characteristic |
| 284 | C3×D8 | — | 9 | 1 | no | — |
| 285 | C3×M16 | — | 9 | 2 | no | — |
| 286 | C2×C3×C8 | — | 9 | 1 | no | — |
| 287 | #216 | — | 3 | 2 | no | — |
| 288 | #216 | — | 3 | 2 | no | — |
| 289 | #216 | — | 6 | 1 | no | — |
| 290 | #216 | — | 9 | 2 | no | — |
| 291 | #216 | — | 9 | 2 | no | — |
| 292 | #216 | — | 9 | 2 | no | — |
| 293 | #216 | — | 9 | 2 | no | — |
| 294 | #216 | — | 9 | 2 | no | — |
| 295 | #215 | — | 9 | 2 | no | — |
| 296 | #214 | — | 3 | 2 | no | — |
| 297 | #214 | — | 9 | 2 | no | — |
| 298 | #214 | — | 9 | 2 | no | — |
| 299 | #213 | — | 3 | 2 | no | — |
| 300 | #213 | — | 6 | 1 | no | — |
| 301 | #208 | — | 9 | 1 | no | — |
| 302 | C2×C3⋊C8 | — | 9 | 2 | no | — |
| 303 | Dic12 | — | 3 | 2 | no | — |
| 304 | Dic12 | — | 9 | 2 | no | — |
| 305 | Dic12 | — | 9 | 2 | no | — |
| 306 | Dic12 | — | 9 | 2 | no | — |
| 307 | #204 | — | 3 | 2 | no | — |
| 308 | #204 | — | 6 | 1 | no | — |
| 309 | #204 | — | 9 | 2 | no | — |
| 310 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 311 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 312 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 313 | D3×C8 | — | 3 | 2 | no | — |
| 314 | D3×C8 | — | 6 | 1 | no | — |
| 315 | D3×C8 | — | 9 | 2 | no | — |
| 316 | D3×C8 | — | 9 | 2 | no | — |
| 317 | C22×C32 | — | 2 | 2 | no | — |
| 318 | C22×C32 | — | 4 | 1 | no | — |
| 319 | C2×C3⋊D3 | D3×D4 | 1 | 2 | yes | — |
| 320 | C2×C3×D3 | — | 3 | 2 | no | — |
| 321 | C2×C3×D3 | — | 3 | 2 | no | — |
| 322 | C2×C3×D3 | — | 6 | 1 | no | — |
| 323 | C2×C3×D3 | — | 6 | 2 | no | — |
| 324 | C2×C3×D3 | — | 12 | 1 | no | — |
| 325 | C32×C4 | — | 2 | 2 | no | — |
| 326 | C32×C4 | — | 2 | 1 | no | — |
| 327 | C32×C4 | — | 4 | 1 | no | — |
| 328 | C32×C4 | C23×D3 | 1 | 2 | yes | — |
| 329 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 330 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 331 | C3⋊Dic3 | D3×D4 | 1 | 2 | yes | — |
| 332 | C3×Dic3 | — | 3 | 2 | no | — |
| 333 | C3×Dic3 | — | 3 | 2 | no | — |
| 334 | C3×Dic3 | — | 6 | 1 | no | — |
| 335 | C3×Dic3 | — | 6 | 2 | no | — |
| 336 | C3×Dic3 | — | 6 | 2 | no | — |
| 337 | C3×Dic3 | — | 6 | 2 | no | — |
| 338 | C3×Dic3 | — | 12 | 1 | no | — |
| 339 | 2−1+4 | — | 27 | 1 | no | — |
| 340 | 2−1+4 | — | 27 | 1 | no | — |
| 341 | #137 | — | 9 | 2 | no | — |
| 342 | #137 | — | 27 | 2 | no | — |
| 343 | #137 | — | 27 | 1 | no | — |
| 344 | #137 | — | 27 | 1 | no | — |
| 345 | #135 | — | 9 | 1 | no | — |
| 346 | #135 | — | 27 | 2 | no | — |
| 347 | C2×Q16 | — | 27 | 1 | no | — |
| 348 | C2×Q16 | — | 27 | 2 | no | — |
| 349 | #131 | — | 27 | 1 | no | — |
| 350 | H(3,𝔽3) | #578 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 351 | C3×Q8 | — | 3 | 2 | no | — |
| 352 | C3×Q8 | — | 6 | 1 | no | — |
| 353 | C3×Q8 | — | 9 | 2 | no | — |
| 354 | C3×Q8 | — | 9 | 2 | no | — |
| 355 | C3×Q8 | — | 9 | 1 | no | — |
| 356 | C3×Q8 | — | 18 | 2 | no | — |
| 357 | C3×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 358 | C3×D4 | — | 3 | 2 | no | — |
| 359 | C3×D4 | — | 6 | 1 | no | — |
| 360 | C3×D4 | — | 9 | 1 | no | — |
| 361 | C3×D4 | — | 18 | 1 | no | — |
| 362 | C3×D4 | — | 18 | 1 | no | — |
| 363 | C3×D4 | — | 18 | 2 | no | — |
| 364 | C3×D4 | C2×D32 | 1 | 1 | yes | characteristic |
| 365 | C2×C3×C4 | — | 9 | 2 | no | — |
| 366 | C2×C3×C4 | — | 9 | 1 | no | — |
| 367 | C2×C3×C4 | — | 18 | 1 | no | — |
| 368 | C2×C3×C4 | — | 18 | 2 | no | — |
| 369 | C2×C3×C4 | — | 18 | 1 | no | — |
| 370 | C2×C3×C4 | — | 18 | 2 | no | — |
| 371 | #67 | — | 6 | 2 | no | — |
| 372 | #67 | — | 6 | 2 | no | — |
| 373 | #67 | — | 9 | 2 | no | — |
| 374 | #67 | — | 9 | 2 | no | — |
| 375 | #67 | — | 9 | 2 | no | — |
| 376 | #67 | — | 12 | 1 | no | — |
| 377 | #67 | — | 18 | 2 | no | — |
| 378 | #67 | — | 18 | 2 | no | — |
| 379 | #67 | — | 18 | 2 | no | — |
| 380 | C2×Dic3 | — | 6 | 2 | no | — |
| 381 | C2×Dic3 | — | 6 | 2 | no | — |
| 382 | C2×Dic3 | — | 12 | 1 | no | — |
| 383 | C2×Dic3 | — | 18 | 2 | no | — |
| 384 | C2×Dic3 | — | 18 | 2 | no | — |
| 385 | C2×Dic3 | — | 18 | 1 | no | — |
| 386 | C2×Dic3 | — | 18 | 1 | no | — |
| 387 | C2×Dic3 | — | 18 | 2 | no | — |
| 388 | D12 | — | 3 | 2 | no | — |
| 389 | D12 | — | 6 | 1 | no | — |
| 390 | D12 | — | 6 | 2 | no | — |
| 391 | D12 | — | 9 | 1 | no | — |
| 392 | D12 | — | 9 | 2 | no | — |
| 393 | D12 | — | 12 | 1 | no | — |
| 394 | D12 | — | 18 | 2 | no | — |
| 395 | C4×D3 | — | 3 | 2 | no | — |
| 396 | C4×D3 | — | 3 | 2 | no | — |
| 397 | C4×D3 | — | 6 | 1 | no | — |
| 398 | C4×D3 | — | 6 | 2 | no | — |
| 399 | C4×D3 | — | 6 | 2 | no | — |
| 400 | C4×D3 | — | 9 | 2 | no | — |
| 401 | C4×D3 | — | 12 | 1 | no | — |
| 402 | C4×D3 | — | 18 | 2 | no | — |
| 403 | C4×D3 | — | 18 | 2 | no | — |
| 404 | C4×D3 | — | 18 | 2 | no | — |
| 405 | C4×D3 | — | 18 | 2 | no | — |
| 406 | C4×D3 | — | 18 | 2 | no | — |
| 407 | C4×D3 | — | 18 | 2 | no | — |
| 408 | C4×D3 | — | 18 | 2 | no | — |
| 409 | Dic6 | — | 3 | 2 | no | — |
| 410 | Dic6 | — | 3 | 2 | no | — |
| 411 | Dic6 | — | 3 | 2 | no | — |
| 412 | Dic6 | — | 6 | 1 | no | — |
| 413 | Dic6 | — | 6 | 2 | no | — |
| 414 | Dic6 | — | 9 | 2 | no | — |
| 415 | Dic6 | — | 9 | 2 | no | — |
| 416 | Dic6 | — | 9 | 1 | no | — |
| 417 | Dic6 | — | 9 | 2 | no | — |
| 418 | Dic6 | — | 18 | 2 | no | — |
| 419 | Dic6 | — | 18 | 2 | no | — |
| 420 | Dic6 | — | 18 | 2 | no | — |
| 421 | Dic6 | — | 18 | 2 | no | — |
| 422 | Dic6 | — | 18 | 1 | no | — |
| 423 | Dic6 | — | 18 | 1 | no | — |
| 424 | Dic6 | — | 18 | 2 | no | — |
| 425 | Dic6 | — | 18 | 2 | no | — |
| 426 | C3×C8 | — | 3 | 2 | no | — |
| 427 | C3×C8 | — | 6 | 1 | no | — |
| 428 | C3×C8 | — | 9 | 2 | no | — |
| 429 | C3×C8 | — | 9 | 1 | no | — |
| 430 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 431 | C3⋊C8 | — | 3 | 2 | no | — |
| 432 | C3⋊C8 | — | 3 | 2 | no | — |
| 433 | C3⋊C8 | — | 6 | 1 | no | — |
| 434 | C3⋊C8 | — | 9 | 2 | no | — |
| 435 | C2×C32 | — | 2 | 1 | no | — |
| 436 | C2×C32 | — | 4 | 2 | no | — |
| 437 | C2×C32 | — | 8 | 1 | no | — |
| 438 | C2×C32 | C2×D3×D4 | 1 | 2 | yes | — |
| 439 | C3⋊D3 | — | 2 | 2 | no | — |
| 440 | C3×D3 | — | 6 | 2 | no | — |
| 441 | C3×D3 | — | 6 | 2 | no | — |
| 442 | C3×D3 | — | 12 | 1 | no | — |
| 443 | C3×D3 | — | 12 | 2 | no | — |
| 444 | C3×D3 | — | 24 | 1 | no | — |
| 445 | #41 | — | 9 | 1 | no | — |
| 446 | #41 | — | 9 | 1 | no | — |
| 447 | #41 | — | 9 | 2 | no | — |
| 448 | #41 | — | 27 | 1 | no | — |
| 449 | #41 | — | 27 | 2 | no | — |
| 450 | #41 | — | 54 | 1 | no | — |
| 451 | #41 | — | 54 | 1 | no | — |
| 452 | #41 | — | 54 | 2 | no | — |
| 453 | #41 | — | 54 | 2 | no | — |
| 454 | C2×Q8 | — | 9 | 2 | no | — |
| 455 | C2×Q8 | — | 27 | 1 | no | — |
| 456 | C2×Q8 | — | 27 | 1 | no | — |
| 457 | C2×Q8 | — | 27 | 2 | no | — |
| 458 | C2×Q8 | — | 54 | 1 | no | — |
| 459 | C2×Q8 | — | 54 | 1 | no | — |
| 460 | Q16 | — | 9 | 1 | no | — |
| 461 | Q16 | — | 9 | 2 | no | — |
| 462 | Q16 | — | 9 | 2 | no | — |
| 463 | Q16 | — | 27 | 2 | no | — |
| 464 | Q16 | — | 27 | 2 | no | — |
| 465 | SD16 | — | 9 | 2 | no | — |
| 466 | SD16 | — | 9 | 1 | no | — |
| 467 | SD16 | — | 27 | 2 | no | — |
| 468 | SD16 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 469 | D8 | — | 9 | 1 | no | — |
| 470 | M16 | — | 9 | 2 | no | — |
| 471 | M16 | — | 27 | 1 | no | — |
| 472 | C2×C8 | — | 9 | 1 | no | — |
| 473 | C2×C8 | — | 27 | 2 | no | — |
| 474 | C22×C3 | — | 2 | 1 | no | — |
| 475 | C22×C3 | — | 6 | 2 | no | — |
| 476 | C22×C3 | — | 9 | 2 | no | — |
| 477 | C22×C3 | — | 9 | 1 | no | — |
| 478 | C22×C3 | — | 12 | 1 | no | — |
| 479 | C22×C3 | — | 18 | 1 | no | — |
| 480 | C2×D3 | — | 3 | 2 | no | — |
| 481 | C2×D3 | — | 3 | 2 | no | — |
| 482 | C2×D3 | — | 6 | 1 | no | — |
| 483 | C2×D3 | — | 6 | 2 | no | — |
| 484 | C2×D3 | — | 9 | 2 | no | — |
| 485 | C2×D3 | — | 12 | 1 | no | — |
| 486 | C3×C4 | — | 2 | 1 | no | — |
| 487 | C3×C4 | — | 3 | 2 | no | — |
| 488 | C3×C4 | — | 6 | 2 | no | — |
| 489 | C3×C4 | — | 6 | 1 | no | — |
| 490 | C3×C4 | — | 9 | 2 | no | — |
| 491 | C3×C4 | — | 9 | 1 | no | — |
| 492 | C3×C4 | — | 12 | 1 | no | — |
| 493 | C3×C4 | — | 18 | 2 | no | — |
| 494 | C3×C4 | — | 18 | 2 | no | — |
| 495 | C3×C4 | — | 18 | 1 | no | — |
| 496 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 497 | Dic3 | — | 3 | 2 | no | — |
| 498 | Dic3 | — | 3 | 2 | no | — |
| 499 | Dic3 | — | 6 | 1 | no | — |
| 500 | Dic3 | — | 6 | 2 | no | — |
| 501 | Dic3 | — | 6 | 2 | no | — |
| 502 | Dic3 | — | 6 | 2 | no | — |
| 503 | Dic3 | — | 9 | 2 | no | — |
| 504 | Dic3 | — | 12 | 1 | no | — |
| 505 | Dic3 | — | 18 | 2 | no | — |
| 506 | Dic3 | — | 18 | 2 | no | — |
| 507 | C32 | — | 2 | 1 | no | — |
| 508 | C32 | #5779 | 1 | 2 | yes | complemented |
| 509 | Q8 | — | 9 | 2 | no | — |
| 510 | Q8 | — | 9 | 1 | no | — |
| 511 | Q8 | — | 9 | 2 | no | — |
| 512 | Q8 | — | 18 | 2 | no | — |
| 513 | Q8 | — | 27 | 1 | no | — |
| 514 | Q8 | — | 54 | 1 | no | — |
| 515 | Q8 | — | 54 | 1 | no | — |
| 516 | Q8 | — | 54 | 2 | no | — |
| 517 | Q8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 518 | D4 | — | 9 | 1 | no | — |
| 519 | D4 | — | 18 | 1 | no | — |
| 520 | D4 | — | 18 | 1 | no | — |
| 521 | D4 | — | 18 | 2 | no | — |
| 522 | D4 | — | 27 | 1 | no | — |
| 523 | D4 | — | 27 | 2 | no | — |
| 524 | D4 | — | 54 | 2 | no | — |
| 525 | D4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 526 | C2×C4 | — | 9 | 1 | no | — |
| 527 | C2×C4 | — | 9 | 2 | no | — |
| 528 | C2×C4 | — | 18 | 1 | no | — |
| 529 | C2×C4 | — | 18 | 2 | no | — |
| 530 | C2×C4 | — | 18 | 1 | no | — |
| 531 | C2×C4 | — | 18 | 2 | no | — |
| 532 | C2×C4 | — | 54 | 2 | no | — |
| 533 | C2×C4 | — | 54 | 2 | no | — |
| 534 | C2×C4 | — | 54 | 1 | no | — |
| 535 | C2×C4 | — | 54 | 1 | no | — |
| 536 | C8 | — | 9 | 1 | no | — |
| 537 | C8 | — | 9 | 2 | no | — |
| 538 | C8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 539 | C2×C3 | — | 3 | 2 | no | — |
| 540 | C2×C3 | — | 4 | 1 | no | — |
| 541 | C2×C3 | — | 6 | 1 | no | — |
| 542 | C2×C3 | — | 12 | 2 | no | — |
| 543 | C2×C3 | — | 18 | 2 | no | — |
| 544 | C2×C3 | — | 18 | 1 | no | — |
| 545 | C2×C3 | — | 24 | 1 | no | — |
| 546 | C2×C3 | — | 36 | 1 | no | — |
| 547 | C2×C3 | D32×D4 | 1 | 1 | yes | characteristic |
| 548 | D3 | — | 6 | 2 | no | — |
| 549 | D3 | — | 6 | 2 | no | — |
| 550 | D3 | — | 12 | 1 | no | — |
| 551 | D3 | — | 12 | 2 | no | — |
| 552 | D3 | — | 18 | 2 | no | — |
| 553 | D3 | — | 24 | 1 | no | — |
| 554 | C22 | — | 2 | 1 | no | — |
| 555 | C22 | — | 9 | 2 | no | — |
| 556 | C22 | — | 9 | 1 | no | — |
| 557 | C22 | — | 18 | 1 | no | — |
| 558 | C4 | — | 2 | 1 | no | — |
| 559 | C4 | — | 9 | 1 | no | — |
| 560 | C4 | — | 9 | 2 | no | — |
| 561 | C4 | — | 18 | 1 | no | — |
| 562 | C4 | — | 18 | 2 | no | — |
| 563 | C4 | — | 18 | 2 | no | — |
| 564 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 565 | C3 | — | 3 | 2 | no | — |
| 566 | C3 | — | 6 | 1 | no | — |
| 567 | C3 | #10594752 | 1 | 1 | yes | characteristic |
| 568 | C2 | — | 4 | 1 | no | — |
| 569 | C2 | — | 18 | 1 | no | — |
| 570 | C2 | — | 18 | 2 | no | — |
| 571 | C2 | — | 36 | 1 | no | — |
| 572 | C2 | D4×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722517 | C2 | semidirect |
| 2. #11722502 | C2 | semidirect |
| 3. #11721802 | C2 | semidirect |
| 4. #64124⋊C3 | C2 | semidirect |
| 5. #11721236 | C2 | semidirect |
| 6. #11721227 | C2 | semidirect |
| 7. #11721197 | C2 | semidirect |
| 8. #11721189 | C2 | semidirect |
| 9. #11720853 | C2 | semidirect |
| 10. #11720842 | C2 | semidirect |
| 11. #11720833 | C2 | semidirect |
| 44. #64124 | D3 | semidirect |
| 350. H(3,𝔽3) | #578 | semidirect |
| 508. C32 | #5779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722517 | 2 |
| #11722502 | 2 |
| #11721802 | 2 |
| #64124⋊C3 | 2 |
| #11721236 | 2 |
| #11721227 | 2 |
| #11721197 | 2 |
| #11721189 | 2 |
| #11720853 | 2 |
| #11720842 | 2 |
| #11720833 | 2 |
| #10594756 | 3 |