Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
555 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 555 conjugacy classes of subgroups — too many to draw. Only its 65 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 | #11722482 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #64117⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11721113 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11721071 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11720562 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #63651⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11720305 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10591022 | — | 3 | 1 | no | maximal |
| 9 | #10591019 | — | 3 | 1 | no | maximal |
| 10 | #88740 | C22 | 1 | 1 | yes | characteristic |
| 11 | #3828⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C4⋊((C3⋊D3)⋊C3) | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#634⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 14 | #88671 | — | 2 | 2 | no | — |
| 15 | #88652 | — | 2 | 1 | no | — |
| 16 | #88651 | — | 2 | 1 | no | — |
| 17 | #88649 | — | 2 | 1 | no | — |
| 18 | ((C3⋊D3)⋊C3)⋊Q8 | — | 2 | 1 | no | — |
| 19 | M16×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 20 | C4×#1084 | C22 | 1 | 1 | yes | characteristic |
| 21 | #3748⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 22 | #3745⋊C3 | — | 2 | 1 | no | — |
| 23 | #3744⋊C3 | — | 2 | 1 | no | — |
| 24 | #88450 | — | 2 | 2 | no | — |
| 25 | #88438 | — | 2 | 1 | no | — |
| 26 | #88436 | — | 2 | 1 | no | — |
| 27 | #64298 | — | 3 | 1 | no | — |
| 28 | #64297 | — | 3 | 1 | no | — |
| 29 | #64117 | D3 | 1 | 1 | yes | characteristic, complemented |
| 30 | C3×#908 | — | 3 | 1 | no | — |
| 31 | #63864 | — | 3 | 1 | no | — |
| 32 | #63860 | — | 3 | 1 | no | — |
| 33 | #63825 | — | 3 | 1 | no | — |
| 34 | #63823 | — | 3 | 1 | no | — |
| 35 | #63651 | D3 | 1 | 1 | yes | characteristic, complemented |
| 36 | C3×#825 | — | 3 | 1 | no | — |
| 37 | C3×#825 | — | 3 | 1 | no | — |
| 38 | C3×#825 | — | 6 | 1 | no | — |
| 39 | C3×#824 | — | 3 | 1 | no | — |
| 40 | #63570 | — | 3 | 1 | no | — |
| 41 | #63569 | — | 3 | 1 | no | — |
| 42 | C22×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 43 | C2×C4×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 44 | #6235 | — | 2 | 1 | no | — |
| 45 | C2×#1084 | — | 2 | 1 | no | — |
| 46 | C4⋊#272 | D4 | 1 | 1 | yes | characteristic |
| 47 | C4×#272 | — | 2 | 1 | no | — |
| 48 | #6229 | D4 | 1 | 1 | yes | characteristic |
| 49 | #638⋊C3 | — | 2 | 1 | no | — |
| 50 | C2×(C3⋊Dic3)⋊C3 | D4 | 1 | 2 | yes | — |
| 51 | C4⋊((C3⋊D3)⋊C3) | — | 2 | 1 | no | — |
| 52 | C4⋊((C3⋊D3)⋊C3) | — | 2 | 1 | no | — |
| 53 | C4⋊((C3⋊D3)⋊C3) | D4 | 1 | 1 | yes | characteristic |
| 54 | C4×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 55 | #634⋊C3 | — | 2 | 1 | no | — |
| 56 | #634⋊C3 | — | 2 | 1 | no | — |
| 57 | #634⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 58 | #6200 | — | 2 | 2 | no | — |
| 59 | #6199 | — | 2 | 2 | no | — |
| 60 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 2 | no | — |
| 61 | #6196 | — | 2 | 2 | no | — |
| 62 | C8×H(3,𝔽3) | — | 2 | 1 | no | — |
| 63 | (C3⋊(C3⋊C8))⋊C3 | — | 2 | 1 | no | — |
| 64 | #5201 | — | 9 | 1 | no | — |
| 65 | #4827 | — | 9 | 1 | no | — |
| 66 | #4753 | — | 9 | 1 | no | — |
| 67 | #3828 | C2×D3 | 1 | 1 | yes | characteristic |
| 68 | C2×C4⋊(C3⋊D3) | C2×D3 | 1 | 1 | yes | characteristic |
| 69 | C2×#634 | C2×D3 | 1 | 1 | yes | characteristic |
| 70 | C3×#235 | — | 3 | 1 | no | — |
| 71 | C3×#235 | — | 3 | 1 | no | — |
| 72 | C3×#235 | — | 3 | 1 | no | — |
| 73 | C3×#235 | — | 6 | 1 | no | — |
| 74 | C2×C3×D12 | — | 3 | 1 | no | — |
| 75 | C2×C3×Dic6 | — | 3 | 1 | no | — |
| 76 | #3805 | — | 6 | 2 | no | — |
| 77 | #3804 | — | 6 | 2 | no | — |
| 78 | #3799 | — | 6 | 1 | no | — |
| 79 | #3797 | — | 6 | 1 | no | — |
| 80 | #3796 | — | 6 | 1 | no | — |
| 81 | #3795 | — | 6 | 1 | no | — |
| 82 | #3795 | — | 6 | 1 | no | — |
| 83 | D3×Dic6 | — | 6 | 1 | no | — |
| 84 | D3×Dic6 | — | 6 | 1 | no | — |
| 85 | D3×Dic6 | — | 6 | 1 | no | — |
| 86 | C32×M16 | — | 2 | 1 | no | — |
| 87 | C32×M16 | C2×D3 | 1 | 1 | yes | characteristic |
| 88 | C32×M16 | C2×D3 | 1 | 1 | yes | characteristic |
| 89 | #3748 | C2×D3 | 1 | 1 | yes | characteristic |
| 90 | #3745 | — | 2 | 1 | no | — |
| 91 | #3744 | — | 2 | 1 | no | — |
| 92 | C3×C4×Dic3 | — | 3 | 1 | no | — |
| 93 | C3×C4×Dic3 | — | 3 | 1 | no | — |
| 94 | C3×C4×Dic3 | — | 6 | 1 | no | — |
| 95 | C3×#208 | — | 3 | 1 | no | — |
| 96 | C3×D24 | — | 6 | 1 | no | — |
| 97 | C3×#204 | — | 6 | 1 | no | — |
| 98 | #3722 | — | 6 | 2 | no | — |
| 99 | (C2×D3)⋊Dic3 | — | 6 | 2 | no | — |
| 100 | #3717 | — | 6 | 1 | no | — |
| 101 | #3715 | — | 6 | 1 | no | — |
| 102 | #3714 | — | 6 | 1 | no | — |
| 103 | #3713 | — | 6 | 1 | no | — |
| 104 | C22×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | C2×#272 | — | 2 | 1 | no | — |
| 106 | C2×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 107 | C2×(C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 108 | C2×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 109 | C4×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | C4×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | #1084 | — | 2 | 1 | no | — |
| 112 | #1084 | — | 4 | 1 | no | — |
| 113 | (C3⋊Dic3)⋊C3 | — | 2 | 1 | no | — |
| 114 | (C3⋊Dic3)⋊C3 | — | 2 | 2 | no | — |
| 115 | #1010 | — | 9 | 1 | no | — |
| 116 | #1010 | — | 9 | 1 | no | — |
| 117 | #1007 | — | 9 | 1 | no | — |
| 118 | C3×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 119 | #949 | — | 9 | 1 | no | — |
| 120 | #947 | — | 9 | 1 | no | — |
| 121 | #936 | — | 9 | 1 | no | — |
| 122 | #932 | — | 9 | 1 | no | — |
| 123 | #908 | — | 3 | 1 | no | — |
| 124 | #908 | — | 9 | 1 | no | — |
| 125 | #908 | — | 9 | 1 | no | — |
| 126 | #875 | — | 9 | 1 | no | — |
| 127 | C3×#104 | — | 9 | 1 | no | — |
| 128 | C3×#101 | — | 9 | 1 | no | — |
| 129 | #837 | — | 9 | 1 | no | — |
| 130 | #825 | — | 3 | 1 | no | — |
| 131 | #825 | — | 3 | 1 | no | — |
| 132 | #825 | — | 6 | 1 | no | — |
| 133 | #825 | — | 9 | 1 | no | — |
| 134 | #824 | — | 3 | 1 | no | — |
| 135 | #824 | — | 9 | 1 | no | — |
| 136 | #805 | — | 9 | 1 | no | — |
| 137 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 138 | C22×C3×D3 | — | 6 | 1 | no | — |
| 139 | C2×C32×C4 | — | 2 | 1 | no | — |
| 140 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 141 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 142 | #638 | — | 2 | 1 | no | — |
| 143 | C2×C3⋊Dic3 | D12 | 1 | 2 | yes | — |
| 144 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 145 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 146 | C4⋊(C3⋊D3) | #67 | 1 | 1 | yes | characteristic |
| 147 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 148 | #634 | — | 2 | 1 | no | — |
| 149 | #634 | — | 2 | 1 | no | — |
| 150 | #634 | #67 | 1 | 1 | yes | characteristic |
| 151 | C3×#67 | — | 6 | 1 | no | — |
| 152 | C3×#67 | — | 6 | 1 | no | — |
| 153 | C3×#67 | — | 6 | 1 | no | — |
| 154 | C3×#67 | — | 12 | 1 | no | — |
| 155 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 156 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 157 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 158 | C2×C3×Dic3 | — | 12 | 1 | no | — |
| 159 | C3×D12 | — | 3 | 1 | no | — |
| 160 | C3×D12 | — | 3 | 1 | no | — |
| 161 | C3×D12 | — | 3 | 1 | no | — |
| 162 | C3×D12 | — | 6 | 1 | no | — |
| 163 | C3×D12 | — | 6 | 1 | no | — |
| 164 | C3×D12 | — | 6 | 1 | no | — |
| 165 | C3×C4×D3 | — | 6 | 1 | no | — |
| 166 | C3×C4×D3 | — | 6 | 1 | no | — |
| 167 | C3×C4×D3 | — | 6 | 1 | no | — |
| 168 | C3×C4×D3 | — | 12 | 1 | no | — |
| 169 | C3×Dic6 | — | 3 | 1 | no | — |
| 170 | C3×Dic6 | — | 3 | 1 | no | — |
| 171 | C3×Dic6 | — | 3 | 1 | no | — |
| 172 | C3×Dic6 | — | 6 | 1 | no | — |
| 173 | C3×Dic6 | — | 6 | 1 | no | — |
| 174 | C3×Dic6 | — | 6 | 1 | no | — |
| 175 | #627 | — | 6 | 2 | no | — |
| 176 | #627 | — | 6 | 2 | no | — |
| 177 | #626 | — | 6 | 2 | no | — |
| 178 | #625 | — | 6 | 2 | no | — |
| 179 | #624 | — | 6 | 2 | no | — |
| 180 | D3×Dic3 | — | 6 | 2 | no | — |
| 181 | D3×Dic3 | — | 6 | 2 | no | — |
| 182 | D3×Dic3 | — | 6 | 2 | no | — |
| 183 | C32×C8 | — | 2 | 1 | no | — |
| 184 | C32×C8 | — | 2 | 1 | no | — |
| 185 | C32×C8 | — | 4 | 1 | no | — |
| 186 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 187 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 188 | #454 | — | 27 | 1 | no | Sylow |
| 189 | C2×H(3,𝔽3) | — | 2 | 1 | no | — |
| 190 | C2×H(3,𝔽3) | #120 | 1 | 1 | yes | characteristic |
| 191 | #272 | — | 4 | 1 | no | — |
| 192 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 193 | (C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 194 | C3×#41 | — | 9 | 1 | no | — |
| 195 | C3×#41 | — | 9 | 1 | no | — |
| 196 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 197 | C2×C3×D4 | — | 9 | 1 | no | — |
| 198 | #239 | — | 18 | 1 | no | — |
| 199 | #239 | — | 18 | 1 | no | — |
| 200 | D3×Q8 | — | 18 | 1 | no | — |
| 201 | D3×Q8 | — | 18 | 1 | no | — |
| 202 | D3×Q8 | — | 18 | 1 | no | — |
| 203 | D3×Q8 | — | 18 | 1 | no | — |
| 204 | #237 | — | 18 | 1 | no | — |
| 205 | #237 | — | 18 | 1 | no | — |
| 206 | #237 | — | 18 | 2 | no | — |
| 207 | #237 | — | 18 | 2 | no | — |
| 208 | #235 | — | 3 | 1 | no | — |
| 209 | #235 | — | 3 | 1 | no | — |
| 210 | #235 | — | 3 | 1 | no | — |
| 211 | #235 | — | 6 | 1 | no | — |
| 212 | #235 | — | 9 | 1 | no | — |
| 213 | #235 | — | 18 | 1 | no | — |
| 214 | #235 | — | 18 | 1 | no | — |
| 215 | #235 | — | 18 | 2 | no | — |
| 216 | C2×D12 | — | 3 | 1 | no | — |
| 217 | C2×D12 | — | 9 | 1 | no | — |
| 218 | C2×Dic6 | — | 3 | 1 | no | — |
| 219 | C2×Dic6 | — | 9 | 1 | no | — |
| 220 | C2×Dic6 | — | 18 | 1 | no | — |
| 221 | C2×Dic6 | — | 18 | 1 | no | — |
| 222 | C3×SD16 | — | 18 | 1 | no | — |
| 223 | C3×D8 | — | 18 | 1 | no | — |
| 224 | C3×M16 | — | 3 | 1 | no | — |
| 225 | C3×M16 | — | 3 | 1 | no | — |
| 226 | C3×M16 | — | 6 | 1 | no | — |
| 227 | C3×M16 | — | 9 | 1 | no | — |
| 228 | C3×M16 | D32 | 1 | 1 | yes | characteristic |
| 229 | C3×C42 | — | 9 | 1 | no | — |
| 230 | #217 | — | 18 | 2 | no | — |
| 231 | #215 | — | 18 | 1 | no | — |
| 232 | #214 | — | 18 | 1 | no | — |
| 233 | #213 | — | 18 | 1 | no | — |
| 234 | #213 | — | 18 | 1 | no | — |
| 235 | (C2×D3)⋊C4 | — | 18 | 2 | no | — |
| 236 | (C2×D3)⋊C4 | — | 18 | 2 | no | — |
| 237 | C4×Dic3 | — | 3 | 1 | no | — |
| 238 | C4×Dic3 | — | 3 | 1 | no | — |
| 239 | C4×Dic3 | — | 6 | 1 | no | — |
| 240 | #208 | — | 3 | 1 | no | — |
| 241 | #208 | — | 9 | 1 | no | — |
| 242 | D24 | — | 6 | 1 | no | — |
| 243 | D24 | — | 18 | 1 | no | — |
| 244 | D24 | — | 18 | 1 | no | — |
| 245 | #204 | — | 6 | 1 | no | — |
| 246 | #204 | — | 18 | 1 | no | — |
| 247 | #204 | — | 18 | 1 | no | — |
| 248 | C22×C32 | — | 2 | 1 | no | — |
| 249 | C22×C32 | C2×D12 | 1 | 1 | yes | characteristic |
| 250 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 251 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 252 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 253 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 254 | C2×C3×D3 | — | 6 | 1 | no | — |
| 255 | C2×C3×D3 | — | 6 | 1 | no | — |
| 256 | C2×C3×D3 | — | 6 | 1 | no | — |
| 257 | C2×C3×D3 | — | 12 | 1 | no | — |
| 258 | C2×C3×D3 | — | 12 | 2 | no | — |
| 259 | C2×C3×D3 | — | 12 | 1 | no | — |
| 260 | C32×C4 | — | 2 | 1 | no | — |
| 261 | C32×C4 | — | 2 | 1 | no | — |
| 262 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 263 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 264 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 265 | C32×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 266 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 267 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 268 | C3×Dic3 | — | 6 | 1 | no | — |
| 269 | C3×Dic3 | — | 6 | 1 | no | — |
| 270 | C3×Dic3 | — | 6 | 2 | no | — |
| 271 | C3×Dic3 | — | 6 | 1 | no | — |
| 272 | C3×Dic3 | — | 12 | 1 | no | — |
| 273 | C3×Dic3 | — | 12 | 1 | no | — |
| 274 | C3×Dic3 | — | 12 | 1 | no | — |
| 275 | C3×Dic3 | — | 12 | 2 | no | — |
| 276 | 2−1+4 | — | 27 | 1 | no | — |
| 277 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 278 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 279 | #124 | — | 27 | 1 | no | — |
| 280 | #104 | — | 9 | 1 | no | — |
| 281 | #104 | — | 27 | 1 | no | — |
| 282 | #101 | — | 9 | 1 | no | — |
| 283 | H(3,𝔽3) | #454 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 284 | C23×C3 | — | 18 | 1 | no | — |
| 285 | C22×D3 | — | 6 | 1 | no | — |
| 286 | C22×D3 | — | 18 | 1 | no | — |
| 287 | C3×Q8 | — | 9 | 1 | no | — |
| 288 | C3×Q8 | — | 9 | 1 | no | — |
| 289 | C3×Q8 | — | 18 | 1 | no | — |
| 290 | C3×Q8 | — | 18 | 1 | no | — |
| 291 | C3×D4 | — | 9 | 1 | no | — |
| 292 | C3×D4 | — | 9 | 1 | no | — |
| 293 | C3×D4 | — | 18 | 1 | no | — |
| 294 | C3×D4 | — | 18 | 1 | no | — |
| 295 | C3×D4 | — | 18 | 1 | no | — |
| 296 | C3×D4 | — | 18 | 1 | no | — |
| 297 | C2×C3×C4 | — | 3 | 1 | no | — |
| 298 | C2×C3×C4 | — | 3 | 1 | no | — |
| 299 | C2×C3×C4 | — | 6 | 1 | no | — |
| 300 | C2×C3×C4 | — | 9 | 2 | no | — |
| 301 | C2×C3×C4 | — | 18 | 1 | no | — |
| 302 | C2×C3×C4 | — | 18 | 1 | no | — |
| 303 | C2×C3×C4 | — | 18 | 1 | no | — |
| 304 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 305 | #67 | — | 6 | 1 | no | — |
| 306 | #67 | — | 6 | 1 | no | — |
| 307 | #67 | — | 6 | 1 | no | — |
| 308 | #67 | — | 12 | 1 | no | — |
| 309 | #67 | — | 18 | 1 | no | — |
| 310 | #67 | — | 18 | 2 | no | — |
| 311 | #67 | — | 18 | 2 | no | — |
| 312 | C2×Dic3 | — | 3 | 2 | no | — |
| 313 | C2×Dic3 | — | 6 | 1 | no | — |
| 314 | C2×Dic3 | — | 6 | 1 | no | — |
| 315 | C2×Dic3 | — | 9 | 2 | no | — |
| 316 | C2×Dic3 | — | 12 | 1 | no | — |
| 317 | C2×Dic3 | — | 18 | 2 | no | — |
| 318 | C2×Dic3 | — | 18 | 2 | no | — |
| 319 | D12 | — | 3 | 1 | no | — |
| 320 | D12 | — | 3 | 1 | no | — |
| 321 | D12 | — | 3 | 1 | no | — |
| 322 | D12 | — | 6 | 1 | no | — |
| 323 | D12 | — | 6 | 1 | no | — |
| 324 | D12 | — | 6 | 1 | no | — |
| 325 | D12 | — | 9 | 1 | no | — |
| 326 | D12 | — | 18 | 1 | no | — |
| 327 | D12 | — | 18 | 1 | no | — |
| 328 | D12 | — | 18 | 2 | no | — |
| 329 | C4×D3 | — | 6 | 1 | no | — |
| 330 | C4×D3 | — | 6 | 1 | no | — |
| 331 | C4×D3 | — | 6 | 1 | no | — |
| 332 | C4×D3 | — | 12 | 1 | no | — |
| 333 | C4×D3 | — | 18 | 1 | no | — |
| 334 | C4×D3 | — | 18 | 2 | no | — |
| 335 | C4×D3 | — | 18 | 2 | no | — |
| 336 | C4×D3 | — | 18 | 2 | no | — |
| 337 | C4×D3 | — | 18 | 2 | no | — |
| 338 | Dic6 | — | 3 | 1 | no | — |
| 339 | Dic6 | — | 3 | 1 | no | — |
| 340 | Dic6 | — | 3 | 1 | no | — |
| 341 | Dic6 | — | 6 | 1 | no | — |
| 342 | Dic6 | — | 6 | 1 | no | — |
| 343 | Dic6 | — | 6 | 1 | no | — |
| 344 | Dic6 | — | 9 | 1 | no | — |
| 345 | Dic6 | — | 18 | 1 | no | — |
| 346 | Dic6 | — | 18 | 1 | no | — |
| 347 | Dic6 | — | 18 | 2 | no | — |
| 348 | Dic6 | — | 18 | 2 | no | — |
| 349 | Dic6 | — | 18 | 2 | no | — |
| 350 | C3×C8 | — | 2 | 1 | no | — |
| 351 | C3×C8 | — | 6 | 1 | no | — |
| 352 | C3×C8 | — | 6 | 1 | no | — |
| 353 | C3×C8 | — | 12 | 1 | no | — |
| 354 | C3×C8 | — | 18 | 1 | no | — |
| 355 | C3⋊C8 | — | 6 | 1 | no | — |
| 356 | C3⋊C8 | — | 18 | 1 | no | — |
| 357 | C2×C32 | — | 2 | 1 | no | — |
| 358 | C2×C32 | — | 2 | 1 | no | — |
| 359 | C2×C32 | — | 2 | 1 | no | — |
| 360 | C2×C32 | — | 4 | 1 | no | — |
| 361 | C2×C32 | #882 | 1 | 1 | yes | characteristic |
| 362 | C2×C32 | #937 | 1 | 1 | yes | characteristic |
| 363 | C3⋊D3 | — | 4 | 1 | no | — |
| 364 | C3⋊D3 | — | 8 | 1 | no | — |
| 365 | C3×D3 | — | 12 | 1 | no | — |
| 366 | C3×D3 | — | 12 | 1 | no | — |
| 367 | C3×D3 | — | 12 | 1 | no | — |
| 368 | C3×D3 | — | 24 | 1 | no | — |
| 369 | C3×D3 | — | 24 | 1 | no | — |
| 370 | #41 | — | 9 | 1 | no | — |
| 371 | #41 | — | 9 | 1 | no | — |
| 372 | #41 | — | 54 | 2 | no | — |
| 373 | #41 | — | 54 | 1 | no | — |
| 374 | #41 | — | 54 | 1 | no | — |
| 375 | C2×Q8 | — | 9 | 1 | no | — |
| 376 | C2×Q8 | — | 54 | 1 | no | — |
| 377 | C2×Q8 | — | 54 | 1 | no | — |
| 378 | C2×D4 | — | 9 | 1 | no | — |
| 379 | SD16 | — | 18 | 1 | no | — |
| 380 | SD16 | — | 54 | 1 | no | — |
| 381 | D8 | — | 18 | 1 | no | — |
| 382 | D8 | — | 54 | 1 | no | — |
| 383 | M16 | — | 9 | 1 | no | — |
| 384 | M16 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 385 | C22⋊C4 | — | 54 | 2 | no | — |
| 386 | C42 | — | 9 | 1 | no | — |
| 387 | C22×C3 | — | 3 | 1 | no | — |
| 388 | C22×C3 | — | 3 | 1 | no | — |
| 389 | C22×C3 | — | 6 | 1 | no | — |
| 390 | C22×C3 | — | 18 | 1 | no | — |
| 391 | C22×C3 | — | 18 | 1 | no | — |
| 392 | C22×C3 | — | 36 | 1 | no | — |
| 393 | C22×C3 | — | 36 | 2 | no | — |
| 394 | C22×C3 | D3×D12 | 1 | 1 | yes | characteristic |
| 395 | C2×D3 | — | 6 | 1 | no | — |
| 396 | C2×D3 | — | 6 | 1 | no | — |
| 397 | C2×D3 | — | 6 | 1 | no | — |
| 398 | C2×D3 | — | 12 | 1 | no | — |
| 399 | C2×D3 | — | 12 | 2 | no | — |
| 400 | C2×D3 | — | 12 | 1 | no | — |
| 401 | C2×D3 | — | 18 | 1 | no | — |
| 402 | C2×D3 | — | 36 | 1 | no | — |
| 403 | C2×D3 | — | 36 | 2 | no | — |
| 404 | C3×C4 | — | 3 | 1 | no | — |
| 405 | C3×C4 | — | 3 | 1 | no | — |
| 406 | C3×C4 | — | 3 | 1 | no | — |
| 407 | C3×C4 | — | 3 | 1 | no | — |
| 408 | C3×C4 | — | 6 | 1 | no | — |
| 409 | C3×C4 | — | 6 | 1 | no | — |
| 410 | C3×C4 | — | 18 | 1 | no | — |
| 411 | C3×C4 | — | 18 | 2 | no | — |
| 412 | C3×C4 | — | 18 | 1 | no | — |
| 413 | C3×C4 | — | 36 | 1 | no | — |
| 414 | C3×C4 | #3802 | 1 | 1 | yes | characteristic |
| 415 | C3×C4 | D3×#67 | 1 | 1 | yes | characteristic |
| 416 | Dic3 | — | 6 | 1 | no | — |
| 417 | Dic3 | — | 6 | 1 | no | — |
| 418 | Dic3 | — | 6 | 1 | no | — |
| 419 | Dic3 | — | 6 | 2 | no | — |
| 420 | Dic3 | — | 12 | 1 | no | — |
| 421 | Dic3 | — | 12 | 1 | no | — |
| 422 | Dic3 | — | 12 | 1 | no | — |
| 423 | Dic3 | — | 12 | 2 | no | — |
| 424 | Dic3 | — | 18 | 1 | no | — |
| 425 | Dic3 | — | 18 | 2 | no | — |
| 426 | C32 | — | 2 | 1 | no | — |
| 427 | C32 | #4753 | 1 | 1 | yes | characteristic, complemented |
| 428 | C32 | #5201 | 1 | 1 | yes | characteristic, complemented |
| 429 | C23 | — | 18 | 1 | no | — |
| 430 | Q8 | — | 9 | 1 | no | — |
| 431 | Q8 | — | 9 | 1 | no | — |
| 432 | Q8 | — | 18 | 1 | no | — |
| 433 | Q8 | — | 18 | 1 | no | — |
| 434 | Q8 | — | 54 | 2 | no | — |
| 435 | D4 | — | 9 | 1 | no | — |
| 436 | D4 | — | 9 | 1 | no | — |
| 437 | D4 | — | 18 | 1 | no | — |
| 438 | D4 | — | 18 | 1 | no | — |
| 439 | D4 | — | 18 | 1 | no | — |
| 440 | D4 | — | 18 | 1 | no | — |
| 441 | D4 | — | 54 | 2 | no | — |
| 442 | C2×C4 | — | 9 | 2 | no | — |
| 443 | C2×C4 | — | 18 | 1 | no | — |
| 444 | C2×C4 | — | 18 | 1 | no | — |
| 445 | C2×C4 | — | 18 | 1 | no | — |
| 446 | C2×C4 | — | 54 | 2 | no | — |
| 447 | C2×C4 | — | 54 | 2 | no | — |
| 448 | C2×C4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 449 | C8 | — | 2 | 1 | no | — |
| 450 | C8 | — | 18 | 1 | no | — |
| 451 | C2×C3 | — | 2 | 1 | no | — |
| 452 | C2×C3 | — | 3 | 1 | no | — |
| 453 | C2×C3 | — | 3 | 1 | no | — |
| 454 | C2×C3 | — | 6 | 1 | no | — |
| 455 | C2×C3 | — | 6 | 1 | no | — |
| 456 | C2×C3 | — | 6 | 1 | no | — |
| 457 | C2×C3 | — | 12 | 1 | no | — |
| 458 | C2×C3 | — | 36 | 1 | no | — |
| 459 | C2×C3 | — | 36 | 1 | no | — |
| 460 | C2×C3 | — | 72 | 1 | no | — |
| 461 | C2×C3 | #63922 | 1 | 1 | yes | characteristic |
| 462 | D3 | — | 12 | 1 | no | — |
| 463 | D3 | — | 12 | 1 | no | — |
| 464 | D3 | — | 12 | 1 | no | — |
| 465 | D3 | — | 24 | 1 | no | — |
| 466 | D3 | — | 24 | 1 | no | — |
| 467 | D3 | — | 36 | 1 | no | — |
| 468 | D3 | — | 72 | 1 | no | — |
| 469 | C22 | — | 18 | 1 | no | — |
| 470 | C22 | — | 18 | 1 | no | — |
| 471 | C22 | — | 36 | 2 | no | — |
| 472 | C22 | — | 36 | 1 | no | — |
| 473 | C22 | #88654 | 1 | 1 | yes | characteristic |
| 474 | C4 | — | 18 | 2 | no | — |
| 475 | C4 | — | 18 | 1 | no | — |
| 476 | C4 | — | 18 | 1 | no | — |
| 477 | C4 | — | 36 | 1 | no | — |
| 478 | C4 | #88655 | 1 | 1 | yes | characteristic |
| 479 | C4 | #88676 | 1 | 1 | yes | characteristic |
| 480 | C3 | — | 3 | 1 | no | — |
| 481 | C3 | — | 3 | 1 | no | — |
| 482 | C3 | — | 6 | 1 | no | — |
| 483 | C3 | #10591020 | 1 | 1 | yes | characteristic |
| 484 | C2 | — | 2 | 1 | no | — |
| 485 | C2 | — | 36 | 1 | no | — |
| 486 | C2 | — | 36 | 1 | no | — |
| 487 | C2 | — | 72 | 1 | no | — |
| 488 | C2 | #11721162 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722482 | C2 | semidirect |
| 2. #64117⋊C3 | C2 | semidirect |
| 3. #11721113 | C2 | semidirect |
| 4. #11721071 | C2 | semidirect |
| 5. #11720562 | C2 | semidirect |
| 6. #63651⋊C3 | C2 | semidirect |
| 7. #11720305 | C2 | semidirect |
| 29. #64117 | D3 | semidirect |
| 35. #63651 | D3 | semidirect |
| 283. H(3,𝔽3) | #454 | semidirect |
| 427. C32 | #4753 | semidirect |
| 428. C32 | #5201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722482 | 2 |
| #64117⋊C3 | 2 |
| #11721113 | 2 |
| #11721071 | 2 |
| #11720562 | 2 |
| #63651⋊C3 | 2 |
| #11720305 | 2 |
| #10591022 | 3 |
| #10591019 | 3 |