Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
698 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 69 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 | #11722675 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #64160⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11721114 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11721069 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #63664⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11720328 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11720325 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10591688 | — | 3 | 1 | no | maximal |
| 9 | #10591664 | — | 3 | 1 | no | maximal |
| 10 | #41×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 11 | #88748 | — | 2 | 1 | no | — |
| 12 | D4×#272 | — | 2 | 2 | no | — |
| 13 | D4×#272 | — | 2 | 1 | no | — |
| 14 | #88740 | — | 2 | 1 | no | — |
| 15 | #88740 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C4⋊#272 | — | 2 | 1 | no | — |
| 17 | C2×C4⋊#272 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#634⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #3756⋊C3 | — | 2 | 1 | no | — |
| 20 | #3754⋊C3 | — | 2 | 1 | no | — |
| 21 | C4×(C3⋊Dic3)⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #3748⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #3748⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #88451 | — | 2 | 2 | no | — |
| 25 | #88439 | — | 2 | 1 | no | — |
| 26 | #88437 | — | 2 | 1 | no | — |
| 27 | C3×#1009 | — | 3 | 1 | no | — |
| 28 | C3×#1009 | — | 3 | 1 | no | — |
| 29 | C3×#1009 | — | 6 | 1 | no | — |
| 30 | #64160 | D3 | 1 | 1 | yes | characteristic, complemented |
| 31 | C3×#951 | — | 3 | 1 | no | — |
| 32 | #63863 | — | 3 | 1 | no | — |
| 33 | #63860 | — | 3 | 1 | no | — |
| 34 | #63831 | — | 3 | 1 | no | — |
| 35 | #63827 | — | 3 | 1 | no | — |
| 36 | #63664 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | C3×#837 | — | 3 | 1 | no | — |
| 38 | #63569 | — | 3 | 1 | no | — |
| 39 | #63568 | — | 3 | 1 | no | — |
| 40 | #63558 | — | 3 | 1 | no | — |
| 41 | #63558 | — | 3 | 1 | no | — |
| 42 | C22×#272 | — | 2 | 2 | no | — |
| 43 | C22×#272 | D4 | 1 | 2 | yes | — |
| 44 | Q8×H(3,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 45 | D4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 46 | D4×H(3,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 47 | C2×C4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 48 | C2×C4×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 49 | #6235 | — | 2 | 2 | no | — |
| 50 | #6235 | — | 2 | 1 | no | — |
| 51 | C4⋊#272 | — | 2 | 2 | no | — |
| 52 | C4⋊#272 | — | 2 | 1 | no | — |
| 53 | C4⋊#272 | — | 2 | 1 | no | — |
| 54 | C4⋊#272 | D4 | 1 | 1 | yes | characteristic |
| 55 | C4×#272 | — | 2 | 2 | no | — |
| 56 | C4×#272 | — | 2 | 1 | no | — |
| 57 | #6229 | D4 | 1 | 1 | yes | characteristic |
| 58 | C2×(C3⋊Dic3)⋊C3 | — | 2 | 1 | no | — |
| 59 | C2×(C3⋊Dic3)⋊C3 | — | 2 | 1 | no | — |
| 60 | #634⋊C3 | — | 2 | 1 | no | — |
| 61 | #634⋊C3 | — | 2 | 1 | no | — |
| 62 | (C3⋊(C3⋊C8))⋊C3 | — | 2 | 1 | no | — |
| 63 | (C3⋊(C3⋊C8))⋊C3 | — | 2 | 1 | no | — |
| 64 | #5242 | — | 9 | 1 | no | — |
| 65 | #5202 | — | 9 | 1 | no | — |
| 66 | #4825 | — | 9 | 1 | no | — |
| 67 | C32×#41 | — | 2 | 1 | no | — |
| 68 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 69 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 70 | C2×#634 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 71 | C3×#239 | — | 6 | 2 | no | — |
| 72 | C3×#239 | — | 6 | 1 | no | — |
| 73 | C3×#239 | — | 6 | 1 | no | — |
| 74 | C3×D3×D4 | — | 6 | 2 | no | — |
| 75 | C3×D3×D4 | — | 6 | 2 | no | — |
| 76 | C3×D3×D4 | — | 6 | 4 | no | — |
| 77 | C3×D3×D4 | — | 6 | 2 | no | — |
| 78 | C3×D3×D4 | — | 6 | 1 | no | — |
| 79 | C3×D3×D4 | — | 6 | 1 | no | — |
| 80 | C3×#235 | — | 3 | 1 | no | — |
| 81 | C3×#235 | — | 3 | 1 | no | — |
| 82 | C3×#235 | — | 6 | 1 | no | — |
| 83 | C3×#235 | — | 6 | 1 | no | — |
| 84 | C3×#235 | — | 6 | 1 | no | — |
| 85 | C3×#235 | — | 6 | 2 | no | — |
| 86 | C2×C3×D12 | — | 3 | 1 | no | — |
| 87 | C2×C3×D12 | — | 3 | 1 | no | — |
| 88 | C2×C3×D12 | — | 6 | 1 | no | — |
| 89 | C2×C3×D12 | — | 6 | 1 | no | — |
| 90 | C2×C3×D12 | — | 6 | 1 | no | — |
| 91 | C2×C3×D12 | — | 6 | 2 | no | — |
| 92 | C2×C3×Dic6 | — | 3 | 1 | no | — |
| 93 | #3756 | — | 2 | 1 | no | — |
| 94 | #3754 | — | 2 | 1 | no | — |
| 95 | C4×C3⋊Dic3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 96 | #3748 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 97 | #3748 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 98 | C3×#216 | — | 6 | 1 | no | — |
| 99 | C3×#214 | — | 6 | 1 | no | — |
| 100 | C3×C4×Dic3 | — | 3 | 1 | no | — |
| 101 | C3×#208 | — | 3 | 1 | no | — |
| 102 | C3×#208 | — | 3 | 1 | no | — |
| 103 | (C2×D3)⋊Dic3 | — | 6 | 2 | no | — |
| 104 | (C2×D3)⋊Dic3 | — | 6 | 2 | no | — |
| 105 | #3719 | — | 6 | 1 | no | — |
| 106 | #3718 | — | 6 | 1 | no | — |
| 107 | #3716 | — | 6 | 1 | no | — |
| 108 | #3715 | — | 6 | 1 | no | — |
| 109 | C22×H(3,𝔽3) | — | 2 | 1 | no | — |
| 110 | C22×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | C2×#272 | — | 2 | 2 | no | — |
| 112 | C2×#272 | — | 2 | 1 | no | — |
| 113 | C2×#272 | — | 4 | 2 | no | — |
| 114 | C2×#272 | — | 8 | 2 | no | — |
| 115 | C4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 116 | C4×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 117 | C4×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | #1084 | — | 2 | 1 | no | — |
| 119 | (C3⋊Dic3)⋊C3 | — | 4 | 1 | no | — |
| 120 | (C3⋊Dic3)⋊C3 | — | 4 | 1 | no | — |
| 121 | C3×H(5,𝔽2) | — | 9 | 1 | no | — |
| 122 | #1009 | — | 3 | 1 | no | — |
| 123 | #1009 | — | 3 | 1 | no | — |
| 124 | #1009 | — | 6 | 1 | no | — |
| 125 | C3×#137 | — | 9 | 1 | no | — |
| 126 | #951 | — | 3 | 1 | no | — |
| 127 | #951 | — | 9 | 1 | no | — |
| 128 | #951 | — | 9 | 1 | no | — |
| 129 | #947 | — | 9 | 1 | no | — |
| 130 | #942 | — | 9 | 1 | no | — |
| 131 | #936 | — | 9 | 1 | no | — |
| 132 | #909 | — | 9 | 1 | no | — |
| 133 | #875 | — | 9 | 1 | no | — |
| 134 | C3×#104 | — | 9 | 1 | no | — |
| 135 | #837 | — | 3 | 1 | no | — |
| 136 | #837 | — | 9 | 1 | no | — |
| 137 | #837 | — | 9 | 1 | no | — |
| 138 | #833 | — | 9 | 1 | no | — |
| 139 | #825 | — | 9 | 1 | no | — |
| 140 | #823 | — | 9 | 1 | no | — |
| 141 | #823 | — | 9 | 1 | no | — |
| 142 | #805 | — | 9 | 1 | no | — |
| 143 | C22×C3×D3 | — | 3 | 2 | no | — |
| 144 | C22×C3×D3 | — | 3 | 2 | no | — |
| 145 | C22×C3×D3 | — | 6 | 2 | no | — |
| 146 | C22×C3×D3 | — | 6 | 4 | no | — |
| 147 | C22×C3×D3 | — | 6 | 2 | no | — |
| 148 | C22×C3×D3 | — | 6 | 2 | no | — |
| 149 | C32×Q8 | — | 2 | 1 | no | — |
| 150 | C32×Q8 | D12 | 1 | 1 | yes | characteristic |
| 151 | C32×Q8 | #67 | 1 | 1 | yes | characteristic |
| 152 | C32×D4 | — | 2 | 2 | no | — |
| 153 | C32×D4 | — | 2 | 1 | no | — |
| 154 | C32×D4 | — | 2 | 1 | no | — |
| 155 | C32×D4 | — | 2 | 1 | no | — |
| 156 | C32×D4 | D12 | 1 | 1 | yes | characteristic |
| 157 | C32×D4 | #67 | 1 | 1 | yes | characteristic |
| 158 | C2×C32×C4 | — | 2 | 2 | no | — |
| 159 | C2×C32×C4 | — | 2 | 1 | no | — |
| 160 | C2×C32×C4 | — | 2 | 1 | no | — |
| 161 | C2×C32×C4 | — | 2 | 1 | no | — |
| 162 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 163 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 164 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 165 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 166 | #634 | — | 2 | 1 | no | — |
| 167 | #634 | — | 2 | 1 | no | — |
| 168 | C3×#67 | — | 6 | 4 | no | — |
| 169 | C3×#67 | — | 6 | 2 | no | — |
| 170 | C3×#67 | — | 6 | 2 | no | — |
| 171 | C3×#67 | — | 6 | 2 | no | — |
| 172 | C3×#67 | — | 6 | 1 | no | — |
| 173 | C3×#67 | — | 6 | 1 | no | — |
| 174 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 175 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 176 | C3×D12 | — | 3 | 1 | no | — |
| 177 | C3×D12 | — | 3 | 1 | no | — |
| 178 | C3×D12 | — | 6 | 1 | no | — |
| 179 | C3×D12 | — | 6 | 2 | no | — |
| 180 | C3×D12 | — | 6 | 4 | no | — |
| 181 | C3×D12 | — | 6 | 2 | no | — |
| 182 | C3×D12 | — | 6 | 2 | no | — |
| 183 | C3×D12 | — | 6 | 2 | no | — |
| 184 | C3×D12 | — | 6 | 1 | no | — |
| 185 | C3×D12 | — | 6 | 1 | no | — |
| 186 | C3×D12 | — | 6 | 1 | no | — |
| 187 | C3×D12 | — | 6 | 1 | no | — |
| 188 | C3×C4×D3 | — | 6 | 4 | no | — |
| 189 | C3×C4×D3 | — | 6 | 2 | no | — |
| 190 | C3×C4×D3 | — | 6 | 2 | no | — |
| 191 | C3×C4×D3 | — | 6 | 2 | no | — |
| 192 | C3×C4×D3 | — | 6 | 1 | no | — |
| 193 | C3×C4×D3 | — | 6 | 1 | no | — |
| 194 | C3×Dic6 | — | 3 | 1 | no | — |
| 195 | C3×Dic6 | — | 3 | 1 | no | — |
| 196 | C3×Dic6 | — | 6 | 1 | no | — |
| 197 | C3×Dic6 | — | 6 | 1 | no | — |
| 198 | C3×Dic6 | — | 6 | 1 | no | — |
| 199 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 200 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 201 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 202 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 203 | #455 | — | 27 | 1 | no | Sylow |
| 204 | C2×H(3,𝔽3) | — | 2 | 1 | no | — |
| 205 | C2×H(3,𝔽3) | — | 4 | 1 | no | — |
| 206 | C2×H(3,𝔽3) | #120 | 1 | 1 | yes | characteristic |
| 207 | #272 | — | 4 | 2 | no | — |
| 208 | #272 | — | 4 | 1 | no | — |
| 209 | C3×#41 | — | 3 | 1 | no | — |
| 210 | C3×#41 | — | 3 | 1 | no | — |
| 211 | C3×#41 | — | 6 | 1 | no | — |
| 212 | C3×#41 | — | 9 | 1 | no | — |
| 213 | C3×#41 | — | 18 | 1 | no | — |
| 214 | C3×#41 | — | 18 | 1 | no | — |
| 215 | C3×#41 | D32 | 1 | 1 | yes | characteristic |
| 216 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 217 | C2×C3×D4 | — | 9 | 1 | no | — |
| 218 | C2×C3×D4 | — | 18 | 1 | no | — |
| 219 | C2×C3×D4 | — | 18 | 2 | no | — |
| 220 | C2×C3×D4 | — | 18 | 1 | no | — |
| 221 | #239 | — | 6 | 1 | no | — |
| 222 | #239 | — | 6 | 1 | no | — |
| 223 | #239 | — | 6 | 2 | no | — |
| 224 | D3×D4 | — | 6 | 1 | no | — |
| 225 | D3×D4 | — | 6 | 1 | no | — |
| 226 | D3×D4 | — | 6 | 2 | no | — |
| 227 | D3×D4 | — | 6 | 2 | no | — |
| 228 | D3×D4 | — | 6 | 4 | no | — |
| 229 | D3×D4 | — | 6 | 2 | no | — |
| 230 | #235 | — | 3 | 1 | no | — |
| 231 | #235 | — | 3 | 1 | no | — |
| 232 | #235 | — | 6 | 1 | no | — |
| 233 | #235 | — | 6 | 1 | no | — |
| 234 | #235 | — | 6 | 1 | no | — |
| 235 | #235 | — | 6 | 2 | no | — |
| 236 | C2×D12 | — | 3 | 1 | no | — |
| 237 | C2×D12 | — | 3 | 1 | no | — |
| 238 | C2×D12 | — | 6 | 1 | no | — |
| 239 | C2×D12 | — | 6 | 1 | no | — |
| 240 | C2×D12 | — | 6 | 1 | no | — |
| 241 | C2×D12 | — | 6 | 2 | no | — |
| 242 | C2×Dic6 | — | 3 | 1 | no | — |
| 243 | C2×Dic6 | — | 9 | 1 | no | — |
| 244 | C3×Q16 | — | 18 | 1 | no | — |
| 245 | C3×SD16 | — | 18 | 1 | no | — |
| 246 | C3×M16 | — | 9 | 1 | no | — |
| 247 | C3×M16 | — | 9 | 1 | no | — |
| 248 | C3×C42 | — | 9 | 1 | no | — |
| 249 | #217 | — | 18 | 2 | no | — |
| 250 | #216 | — | 6 | 1 | no | — |
| 251 | #216 | — | 18 | 1 | no | — |
| 252 | #216 | — | 18 | 1 | no | — |
| 253 | #216 | — | 18 | 1 | no | — |
| 254 | #215 | — | 18 | 1 | no | — |
| 255 | #214 | — | 6 | 1 | no | — |
| 256 | #214 | — | 18 | 1 | no | — |
| 257 | #214 | — | 18 | 1 | no | — |
| 258 | (C2×D3)⋊C4 | — | 18 | 2 | no | — |
| 259 | (C2×D3)⋊C4 | — | 18 | 2 | no | — |
| 260 | C4×Dic3 | — | 3 | 1 | no | — |
| 261 | C4×Dic3 | — | 9 | 1 | no | — |
| 262 | #208 | — | 3 | 1 | no | — |
| 263 | #208 | — | 3 | 1 | no | — |
| 264 | #208 | — | 9 | 1 | no | — |
| 265 | #208 | — | 9 | 1 | no | — |
| 266 | Dic12 | — | 18 | 1 | no | — |
| 267 | #204 | — | 18 | 1 | no | — |
| 268 | C22×C32 | — | 2 | 2 | no | — |
| 269 | C22×C32 | — | 2 | 1 | no | — |
| 270 | C22×C32 | — | 2 | 1 | no | — |
| 271 | C22×C32 | — | 2 | 1 | no | — |
| 272 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 273 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 274 | C2×C3×D3 | — | 6 | 2 | no | — |
| 275 | C2×C3×D3 | — | 6 | 4 | no | — |
| 276 | C2×C3×D3 | — | 6 | 1 | no | — |
| 277 | C2×C3×D3 | — | 6 | 2 | no | — |
| 278 | C2×C3×D3 | — | 6 | 1 | no | — |
| 279 | C2×C3×D3 | — | 6 | 2 | no | — |
| 280 | C2×C3×D3 | — | 12 | 2 | no | — |
| 281 | C2×C3×D3 | — | 12 | 2 | no | — |
| 282 | C2×C3×D3 | — | 24 | 2 | no | — |
| 283 | C2×C3×D3 | — | 24 | 4 | no | — |
| 284 | C2×C3×D3 | — | 24 | 2 | no | — |
| 285 | C2×C3×D3 | — | 24 | 2 | no | — |
| 286 | C32×C4 | — | 2 | 2 | no | — |
| 287 | C32×C4 | — | 2 | 1 | no | — |
| 288 | C32×C4 | — | 2 | 1 | no | — |
| 289 | C32×C4 | — | 2 | 1 | no | — |
| 290 | C32×C4 | — | 2 | 1 | no | — |
| 291 | C32×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 292 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 293 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 294 | C32×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 295 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 296 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 297 | C3×Dic3 | — | 6 | 2 | no | — |
| 298 | C3×Dic3 | — | 6 | 1 | no | — |
| 299 | C3×Dic3 | — | 6 | 1 | no | — |
| 300 | C3×Dic3 | — | 12 | 1 | no | — |
| 301 | C3×Dic3 | — | 12 | 1 | no | — |
| 302 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 303 | #137 | — | 9 | 1 | no | — |
| 304 | #137 | — | 27 | 1 | no | — |
| 305 | #124 | — | 27 | 1 | no | — |
| 306 | #104 | — | 9 | 1 | no | — |
| 307 | #104 | — | 27 | 1 | no | — |
| 308 | #100 | — | 27 | 1 | no | — |
| 309 | H(3,𝔽3) | #455 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 310 | C23×C3 | — | 9 | 2 | no | — |
| 311 | C23×C3 | — | 18 | 2 | no | — |
| 312 | C22×D3 | — | 3 | 2 | no | — |
| 313 | C22×D3 | — | 3 | 2 | no | — |
| 314 | C22×D3 | — | 6 | 2 | no | — |
| 315 | C22×D3 | — | 6 | 2 | no | — |
| 316 | C22×D3 | — | 6 | 2 | no | — |
| 317 | C22×D3 | — | 6 | 4 | no | — |
| 318 | C3×Q8 | — | 3 | 1 | no | — |
| 319 | C3×Q8 | — | 3 | 1 | no | — |
| 320 | C3×Q8 | — | 6 | 1 | no | — |
| 321 | C3×Q8 | — | 9 | 1 | no | — |
| 322 | C3×Q8 | — | 18 | 1 | no | — |
| 323 | C3×Q8 | — | 18 | 1 | no | — |
| 324 | C3×Q8 | #626 | 1 | 1 | yes | characteristic |
| 325 | C3×D4 | — | 2 | 1 | no | — |
| 326 | C3×D4 | — | 3 | 1 | no | — |
| 327 | C3×D4 | — | 3 | 1 | no | — |
| 328 | C3×D4 | — | 6 | 1 | no | — |
| 329 | C3×D4 | — | 6 | 1 | no | — |
| 330 | C3×D4 | — | 6 | 2 | no | — |
| 331 | C3×D4 | — | 6 | 1 | no | — |
| 332 | C3×D4 | — | 9 | 1 | no | — |
| 333 | C3×D4 | — | 18 | 2 | no | — |
| 334 | C3×D4 | — | 18 | 2 | no | — |
| 335 | C3×D4 | — | 18 | 1 | no | — |
| 336 | C3×D4 | — | 18 | 1 | no | — |
| 337 | C3×D4 | — | 18 | 1 | no | — |
| 338 | C3×D4 | #626 | 1 | 1 | yes | characteristic |
| 339 | C2×C3×C4 | — | 2 | 1 | no | — |
| 340 | C2×C3×C4 | — | 3 | 1 | no | — |
| 341 | C2×C3×C4 | — | 3 | 1 | no | — |
| 342 | C2×C3×C4 | — | 6 | 1 | no | — |
| 343 | C2×C3×C4 | — | 6 | 1 | no | — |
| 344 | C2×C3×C4 | — | 6 | 2 | no | — |
| 345 | C2×C3×C4 | — | 6 | 1 | no | — |
| 346 | C2×C3×C4 | — | 18 | 2 | no | — |
| 347 | C2×C3×C4 | — | 18 | 1 | no | — |
| 348 | C2×C3×C4 | — | 18 | 1 | no | — |
| 349 | C2×C3×C4 | — | 18 | 1 | no | — |
| 350 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 351 | #67 | — | 6 | 1 | no | — |
| 352 | #67 | — | 6 | 1 | no | — |
| 353 | #67 | — | 6 | 2 | no | — |
| 354 | #67 | — | 6 | 2 | no | — |
| 355 | #67 | — | 6 | 4 | no | — |
| 356 | #67 | — | 6 | 2 | no | — |
| 357 | C2×Dic3 | — | 6 | 1 | no | — |
| 358 | C2×Dic3 | — | 6 | 1 | no | — |
| 359 | C2×Dic3 | — | 18 | 1 | no | — |
| 360 | C2×Dic3 | — | 18 | 1 | no | — |
| 361 | D12 | — | 3 | 1 | no | — |
| 362 | D12 | — | 3 | 1 | no | — |
| 363 | D12 | — | 6 | 1 | no | — |
| 364 | D12 | — | 6 | 1 | no | — |
| 365 | D12 | — | 6 | 1 | no | — |
| 366 | D12 | — | 6 | 1 | no | — |
| 367 | D12 | — | 6 | 1 | no | — |
| 368 | D12 | — | 6 | 2 | no | — |
| 369 | D12 | — | 6 | 2 | no | — |
| 370 | D12 | — | 6 | 2 | no | — |
| 371 | D12 | — | 6 | 4 | no | — |
| 372 | D12 | — | 6 | 2 | no | — |
| 373 | C4×D3 | — | 6 | 1 | no | — |
| 374 | C4×D3 | — | 6 | 1 | no | — |
| 375 | C4×D3 | — | 6 | 2 | no | — |
| 376 | C4×D3 | — | 6 | 2 | no | — |
| 377 | C4×D3 | — | 6 | 4 | no | — |
| 378 | C4×D3 | — | 6 | 2 | no | — |
| 379 | Dic6 | — | 3 | 1 | no | — |
| 380 | Dic6 | — | 3 | 1 | no | — |
| 381 | Dic6 | — | 6 | 1 | no | — |
| 382 | Dic6 | — | 6 | 1 | no | — |
| 383 | Dic6 | — | 6 | 1 | no | — |
| 384 | Dic6 | — | 18 | 1 | no | — |
| 385 | Dic6 | — | 18 | 1 | no | — |
| 386 | C3×C8 | — | 18 | 1 | no | — |
| 387 | C3×C8 | — | 18 | 1 | no | — |
| 388 | C3⋊C8 | — | 6 | 1 | no | — |
| 389 | C3⋊C8 | — | 6 | 1 | no | — |
| 390 | C3⋊C8 | — | 18 | 1 | no | — |
| 391 | C3⋊C8 | — | 18 | 1 | no | — |
| 392 | C2×C32 | — | 2 | 1 | no | — |
| 393 | C2×C32 | — | 2 | 1 | no | — |
| 394 | C2×C32 | — | 2 | 1 | no | — |
| 395 | C2×C32 | — | 4 | 1 | no | — |
| 396 | C2×C32 | — | 4 | 2 | no | — |
| 397 | C2×C32 | — | 4 | 1 | no | — |
| 398 | C2×C32 | — | 4 | 1 | no | — |
| 399 | C2×C32 | #882 | 1 | 1 | yes | characteristic |
| 400 | C2×C32 | #937 | 1 | 1 | yes | characteristic |
| 401 | C3×D3 | — | 12 | 4 | no | — |
| 402 | C3×D3 | — | 12 | 2 | no | — |
| 403 | C3×D3 | — | 12 | 2 | no | — |
| 404 | C3×D3 | — | 12 | 1 | no | — |
| 405 | C3×D3 | — | 12 | 2 | no | — |
| 406 | C3×D3 | — | 12 | 1 | no | — |
| 407 | #41 | — | 9 | 1 | no | — |
| 408 | #41 | — | 18 | 1 | no | — |
| 409 | #41 | — | 18 | 1 | no | — |
| 410 | #41 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 411 | C2×Q8 | — | 9 | 1 | no | — |
| 412 | C2×D4 | — | 9 | 1 | no | — |
| 413 | C2×D4 | — | 18 | 1 | no | — |
| 414 | C2×D4 | — | 18 | 2 | no | — |
| 415 | C2×D4 | — | 18 | 1 | no | — |
| 416 | Q16 | — | 18 | 1 | no | — |
| 417 | Q16 | — | 54 | 1 | no | — |
| 418 | SD16 | — | 18 | 1 | no | — |
| 419 | SD16 | — | 54 | 1 | no | — |
| 420 | M16 | — | 9 | 1 | no | — |
| 421 | M16 | — | 9 | 1 | no | — |
| 422 | C22⋊C4 | — | 54 | 2 | no | — |
| 423 | C42 | — | 9 | 1 | no | — |
| 424 | C22×C3 | — | 2 | 1 | no | — |
| 425 | C22×C3 | — | 3 | 1 | no | — |
| 426 | C22×C3 | — | 3 | 1 | no | — |
| 427 | C22×C3 | — | 6 | 1 | no | — |
| 428 | C22×C3 | — | 6 | 1 | no | — |
| 429 | C22×C3 | — | 6 | 2 | no | — |
| 430 | C22×C3 | — | 6 | 1 | no | — |
| 431 | C22×C3 | — | 18 | 1 | no | — |
| 432 | C22×C3 | — | 18 | 2 | no | — |
| 433 | C22×C3 | — | 36 | 2 | no | — |
| 434 | C22×C3 | — | 72 | 2 | no | — |
| 435 | C22×C3 | #3811 | 1 | 1 | yes | characteristic |
| 436 | C2×D3 | — | 6 | 1 | no | — |
| 437 | C2×D3 | — | 6 | 1 | no | — |
| 438 | C2×D3 | — | 6 | 2 | no | — |
| 439 | C2×D3 | — | 6 | 2 | no | — |
| 440 | C2×D3 | — | 6 | 2 | no | — |
| 441 | C2×D3 | — | 6 | 4 | no | — |
| 442 | C2×D3 | — | 12 | 2 | no | — |
| 443 | C2×D3 | — | 12 | 2 | no | — |
| 444 | C2×D3 | — | 24 | 2 | no | — |
| 445 | C2×D3 | — | 24 | 2 | no | — |
| 446 | C2×D3 | — | 24 | 2 | no | — |
| 447 | C2×D3 | — | 24 | 4 | no | — |
| 448 | C3×C4 | — | 2 | 1 | no | — |
| 449 | C3×C4 | — | 3 | 1 | no | — |
| 450 | C3×C4 | — | 3 | 1 | no | — |
| 451 | C3×C4 | — | 3 | 1 | no | — |
| 452 | C3×C4 | — | 3 | 1 | no | — |
| 453 | C3×C4 | — | 6 | 1 | no | — |
| 454 | C3×C4 | — | 6 | 1 | no | — |
| 455 | C3×C4 | — | 6 | 2 | no | — |
| 456 | C3×C4 | — | 6 | 1 | no | — |
| 457 | C3×C4 | — | 6 | 1 | no | — |
| 458 | C3×C4 | — | 18 | 1 | no | — |
| 459 | C3×C4 | — | 36 | 1 | no | — |
| 460 | C3×C4 | — | 36 | 1 | no | — |
| 461 | C3×C4 | C2×#626 | 1 | 1 | yes | characteristic |
| 462 | C3×C4 | #3811 | 1 | 1 | yes | characteristic |
| 463 | Dic3 | — | 6 | 1 | no | — |
| 464 | Dic3 | — | 6 | 1 | no | — |
| 465 | Dic3 | — | 6 | 2 | no | — |
| 466 | Dic3 | — | 12 | 1 | no | — |
| 467 | Dic3 | — | 12 | 1 | no | — |
| 468 | Dic3 | — | 36 | 1 | no | — |
| 469 | Dic3 | — | 36 | 1 | no | — |
| 470 | C32 | — | 2 | 1 | no | — |
| 471 | C32 | #4825 | 1 | 1 | yes | characteristic, complemented |
| 472 | C32 | #5202 | 1 | 1 | yes | characteristic, complemented |
| 473 | C23 | — | 9 | 2 | no | — |
| 474 | C23 | — | 18 | 2 | no | — |
| 475 | Q8 | — | 9 | 1 | no | — |
| 476 | Q8 | — | 18 | 1 | no | — |
| 477 | Q8 | — | 18 | 1 | no | — |
| 478 | Q8 | #6200 | 1 | 1 | yes | characteristic |
| 479 | D4 | — | 2 | 1 | no | — |
| 480 | D4 | — | 9 | 1 | no | — |
| 481 | D4 | — | 18 | 2 | no | — |
| 482 | D4 | — | 18 | 2 | no | — |
| 483 | D4 | — | 18 | 1 | no | — |
| 484 | D4 | — | 18 | 1 | no | — |
| 485 | D4 | — | 18 | 1 | no | — |
| 486 | D4 | #6200 | 1 | 1 | yes | characteristic |
| 487 | C2×C4 | — | 2 | 1 | no | — |
| 488 | C2×C4 | — | 18 | 2 | no | — |
| 489 | C2×C4 | — | 18 | 1 | no | — |
| 490 | C2×C4 | — | 18 | 1 | no | — |
| 491 | C2×C4 | — | 18 | 1 | no | — |
| 492 | C2×C4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 493 | C8 | — | 18 | 1 | no | — |
| 494 | C8 | — | 18 | 1 | no | — |
| 495 | C2×C3 | — | 2 | 1 | no | — |
| 496 | C2×C3 | — | 3 | 1 | no | — |
| 497 | C2×C3 | — | 3 | 1 | no | — |
| 498 | C2×C3 | — | 4 | 1 | no | — |
| 499 | C2×C3 | — | 6 | 1 | no | — |
| 500 | C2×C3 | — | 6 | 1 | no | — |
| 501 | C2×C3 | — | 6 | 1 | no | — |
| 502 | C2×C3 | — | 12 | 1 | no | — |
| 503 | C2×C3 | — | 12 | 1 | no | — |
| 504 | C2×C3 | — | 12 | 1 | no | — |
| 505 | C2×C3 | — | 12 | 2 | no | — |
| 506 | C2×C3 | — | 36 | 2 | no | — |
| 507 | C2×C3 | — | 36 | 1 | no | — |
| 508 | C2×C3 | #63981 | 1 | 1 | yes | characteristic |
| 509 | D3 | — | 12 | 2 | no | — |
| 510 | D3 | — | 12 | 2 | no | — |
| 511 | D3 | — | 12 | 1 | no | — |
| 512 | D3 | — | 12 | 1 | no | — |
| 513 | D3 | — | 12 | 4 | no | — |
| 514 | D3 | — | 12 | 2 | no | — |
| 515 | C22 | — | 2 | 1 | no | — |
| 516 | C22 | — | 18 | 1 | no | — |
| 517 | C22 | — | 18 | 2 | no | — |
| 518 | C22 | — | 36 | 2 | no | — |
| 519 | C22 | — | 72 | 2 | no | — |
| 520 | C22 | #88677 | 1 | 1 | yes | characteristic |
| 521 | C4 | — | 2 | 1 | no | — |
| 522 | C4 | — | 18 | 1 | no | — |
| 523 | C4 | — | 36 | 1 | no | — |
| 524 | C4 | — | 36 | 1 | no | — |
| 525 | C4 | C2×#6200 | 1 | 1 | yes | characteristic |
| 526 | C4 | #88677 | 1 | 1 | yes | characteristic |
| 527 | C3 | — | 3 | 1 | no | — |
| 528 | C3 | — | 3 | 1 | no | — |
| 529 | C3 | — | 6 | 1 | no | — |
| 530 | C3 | #10591690 | 1 | 1 | yes | characteristic |
| 531 | C2 | — | 2 | 1 | no | — |
| 532 | C2 | — | 4 | 1 | no | — |
| 533 | C2 | — | 36 | 2 | no | — |
| 534 | C2 | — | 36 | 1 | no | — |
| 535 | C2 | #11721323 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #64160⋊C3 | C2 | semidirect |
| 3. #11721114 | C2 | semidirect |
| 4. #11721069 | C2 | semidirect |
| 5. #63664⋊C3 | C2 | semidirect |
| 6. #11720328 | C2 | semidirect |
| 7. #11720325 | C2 | semidirect |
| 18. C2×#634⋊C3 | C22 | semidirect |
| 21. C4×(C3⋊Dic3)⋊C3 | C22 | semidirect |
| 22. #3748⋊C3 | C22 | semidirect |
| 23. #3748⋊C3 | C22 | semidirect |
| 30. #64160 | D3 | semidirect |
| 36. #63664 | D3 | semidirect |
| 70. C2×#634 | C2×D3 | semidirect |
| 95. C4×C3⋊Dic3 | C2×D3 | semidirect |
| 96. #3748 | C2×D3 | semidirect |
| 97. #3748 | C2×D3 | semidirect |
| 309. H(3,𝔽3) | #455 | semidirect |
| 471. C32 | #4825 | semidirect |
| 472. C32 | #5202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722675 | 2 |
| #64160⋊C3 | 2 |
| #11721114 | 2 |
| #11721069 | 2 |
| #63664⋊C3 | 2 |
| #11720328 | 2 |
| #11720325 | 2 |
| #10591688 | 3 |
| #10591664 | 3 |