Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
759 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 759 conjugacy classes of subgroups — too many to draw. Only its 83 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 | #41×#272 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C4×#6199 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11721065 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #63664⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11720328 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | D3×#837 | — | 3 | 2 | no | maximal |
| 7 | #41×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 8 | #88748 | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | Q8×#272 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | #88744 | — | 2 | 1 | no | — |
| 11 | #88744 | C4 | 1 | 1 | yes | characteristic, complemented |
| 12 | D4×#272 | — | 2 | 1 | no | — |
| 13 | D4×#272 | C4 | 1 | 1 | yes | characteristic, complemented |
| 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×#6199 | — | 2 | 1 | no | — |
| 19 | C4×(C3⋊Dic3)⋊C3 | C22 | 1 | 2 | yes | complemented |
| 20 | #3748⋊C3 | C22 | 1 | 2 | yes | complemented |
| 21 | #88447 | — | 2 | 1 | no | — |
| 22 | #88435 | — | 2 | 1 | no | — |
| 23 | #88434 | — | 2 | 1 | no | — |
| 24 | C3×D3×#41 | — | 3 | 2 | no | — |
| 25 | C3×D3×#41 | — | 6 | 1 | no | — |
| 26 | C4×D3×Dic3 | — | 3 | 2 | no | — |
| 27 | D3×#208 | — | 3 | 2 | no | — |
| 28 | #63664 | D3 | 1 | 2 | yes | complemented |
| 29 | C3×#837 | — | 3 | 2 | no | — |
| 30 | #63569 | — | 3 | 2 | no | — |
| 31 | #63568 | — | 3 | 2 | no | — |
| 32 | C22×#272 | — | 2 | 1 | no | — |
| 33 | C22×#272 | D4 | 1 | 1 | yes | characteristic |
| 34 | Q8×H(3,𝔽3) | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 35 | D4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 36 | D4×H(3,𝔽3) | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 37 | C2×C4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 38 | C2×C4×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 39 | #6235 | — | 2 | 1 | no | — |
| 40 | #6235 | — | 2 | 1 | no | — |
| 41 | #6235 | — | 2 | 1 | no | — |
| 42 | C2×#1084 | — | 2 | 1 | no | — |
| 43 | C2×#1084 | D4 | 1 | 1 | yes | characteristic |
| 44 | C4⋊#272 | — | 2 | 1 | no | — |
| 45 | C4⋊#272 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 46 | C4×#272 | — | 2 | 1 | no | — |
| 47 | C4×#272 | — | 2 | 1 | no | — |
| 48 | C4×#272 | — | 2 | 1 | no | — |
| 49 | C4×#272 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | C4×#272 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C4×#272 | D4 | 1 | 1 | yes | characteristic |
| 52 | C4×#272 | D4 | 1 | 1 | yes | characteristic |
| 53 | #6229 | — | 2 | 1 | no | — |
| 54 | #6229 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 55 | C2×(C3⋊Dic3)⋊C3 | — | 2 | 2 | no | — |
| 56 | #6199 | — | 2 | 4 | no | — |
| 57 | (C3⋊(C3⋊C8))⋊C3 | — | 2 | 2 | no | — |
| 58 | C2×#837 | — | 9 | 1 | no | — |
| 59 | D3×#104 | — | 9 | 2 | no | — |
| 60 | C32×#41 | — | 2 | 1 | no | — |
| 61 | C32×#41 | C2×D3 | 1 | 2 | yes | — |
| 62 | C3×#239 | — | 3 | 2 | no | — |
| 63 | C3×#239 | — | 6 | 1 | no | — |
| 64 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 65 | C3×D3×Q8 | — | 6 | 1 | no | — |
| 66 | C3×#237 | — | 3 | 2 | no | — |
| 67 | C3×#237 | — | 6 | 2 | no | — |
| 68 | C3×#237 | — | 6 | 1 | no | — |
| 69 | C3×#237 | — | 6 | 2 | no | — |
| 70 | C3×D3×D4 | — | 3 | 2 | no | — |
| 71 | C3×D3×D4 | — | 6 | 2 | no | — |
| 72 | C3×D3×D4 | — | 6 | 1 | no | — |
| 73 | C3×D3×D4 | — | 6 | 2 | no | — |
| 74 | C3×#235 | — | 3 | 2 | no | — |
| 75 | C3×#235 | — | 6 | 2 | no | — |
| 76 | C3×#235 | — | 6 | 1 | no | — |
| 77 | C3×#235 | — | 6 | 2 | no | — |
| 78 | C2×C3×C4×D3 | — | 3 | 2 | no | — |
| 79 | C2×C3×C4×D3 | — | 6 | 2 | no | — |
| 80 | C2×C3×C4×D3 | — | 6 | 1 | no | — |
| 81 | C2×C3×C4×D3 | — | 6 | 2 | no | — |
| 82 | C2×D3×Dic3 | — | 6 | 2 | no | — |
| 83 | C4×C3⋊Dic3 | C2×D3 | 1 | 2 | yes | complemented |
| 84 | #3748 | C2×D3 | 1 | 2 | yes | complemented |
| 85 | C3×C4×Dic3 | — | 3 | 2 | no | — |
| 86 | C3×#208 | — | 3 | 2 | no | — |
| 87 | Dic32 | — | 6 | 2 | no | — |
| 88 | #3711 | — | 6 | 2 | no | — |
| 89 | D3×C3⋊C8 | — | 6 | 2 | no | — |
| 90 | C22×H(3,𝔽3) | — | 2 | 1 | no | — |
| 91 | C22×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 92 | C2×#272 | — | 2 | 2 | no | — |
| 93 | C2×#272 | — | 2 | 1 | no | — |
| 94 | C2×#272 | — | 4 | 2 | no | — |
| 95 | C2×#272 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 96 | C2×#272 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 97 | C4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 98 | C4×H(3,𝔽3) | C22×C4 | 1 | 1 | yes | characteristic |
| 99 | C4×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 100 | #1084 | — | 2 | 1 | no | — |
| 101 | #1084 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 102 | #1084 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 103 | (C3⋊Dic3)⋊C3 | — | 2 | 4 | no | — |
| 104 | C2×C3×#41 | — | 9 | 1 | no | — |
| 105 | D3×#41 | — | 3 | 2 | no | — |
| 106 | D3×#41 | — | 6 | 1 | no | — |
| 107 | C2×C4×Dic3 | — | 9 | 1 | no | — |
| 108 | C2×#208 | — | 9 | 1 | no | — |
| 109 | D3×M16 | — | 9 | 2 | no | — |
| 110 | C42×D3 | — | 9 | 2 | no | — |
| 111 | C3×#104 | — | 9 | 2 | no | — |
| 112 | #837 | — | 3 | 2 | no | — |
| 113 | #837 | — | 9 | 2 | no | — |
| 114 | #837 | — | 9 | 2 | no | — |
| 115 | #825 | — | 9 | 2 | no | — |
| 116 | #805 | — | 9 | 2 | no | — |
| 117 | C22×C3×D3 | — | 3 | 2 | no | — |
| 118 | C22×C3×D3 | — | 6 | 1 | no | — |
| 119 | C22×C3×D3 | — | 6 | 2 | no | — |
| 120 | C22×C3×D3 | — | 6 | 2 | no | — |
| 121 | C32×Q8 | — | 2 | 1 | no | — |
| 122 | C32×Q8 | C4×D3 | 1 | 2 | yes | complemented |
| 123 | C32×D4 | — | 2 | 2 | no | — |
| 124 | C32×D4 | — | 2 | 2 | no | — |
| 125 | C32×D4 | — | 2 | 1 | no | — |
| 126 | C32×D4 | C4×D3 | 1 | 2 | yes | complemented |
| 127 | C2×C32×C4 | — | 2 | 2 | no | — |
| 128 | C2×C32×C4 | — | 2 | 2 | no | — |
| 129 | C2×C32×C4 | — | 2 | 1 | no | — |
| 130 | C2×C32×C4 | C22×D3 | 1 | 2 | yes | — |
| 131 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 132 | C3×#67 | — | 6 | 2 | no | — |
| 133 | C3×#67 | — | 6 | 2 | no | — |
| 134 | C3×#67 | — | 6 | 2 | no | — |
| 135 | C3×#67 | — | 6 | 2 | no | — |
| 136 | C3×#67 | — | 6 | 2 | no | — |
| 137 | C3×#67 | — | 6 | 2 | no | — |
| 138 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 139 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 140 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 141 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 142 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 143 | C3×D12 | — | 3 | 2 | no | — |
| 144 | C3×D12 | — | 6 | 1 | no | — |
| 145 | C3×D12 | — | 6 | 2 | no | — |
| 146 | C3×D12 | — | 6 | 2 | no | — |
| 147 | C3×C4×D3 | — | 3 | 2 | no | — |
| 148 | C3×C4×D3 | — | 3 | 2 | no | — |
| 149 | C3×C4×D3 | — | 3 | 2 | no | — |
| 150 | C3×C4×D3 | — | 3 | 2 | no | — |
| 151 | C3×C4×D3 | — | 6 | 1 | no | — |
| 152 | C3×C4×D3 | — | 6 | 1 | no | — |
| 153 | C3×C4×D3 | — | 6 | 1 | no | — |
| 154 | C3×C4×D3 | — | 6 | 1 | no | — |
| 155 | C3×C4×D3 | — | 6 | 2 | no | — |
| 156 | C3×C4×D3 | — | 6 | 2 | no | — |
| 157 | C3×C4×D3 | — | 6 | 2 | no | — |
| 158 | C3×C4×D3 | — | 6 | 2 | no | — |
| 159 | C3×C4×D3 | — | 6 | 2 | no | — |
| 160 | C3×C4×D3 | — | 6 | 2 | no | — |
| 161 | C3×Dic6 | — | 3 | 2 | no | — |
| 162 | C3×Dic6 | — | 6 | 1 | no | — |
| 163 | C3×Dic6 | — | 6 | 2 | no | — |
| 164 | C3×Dic6 | — | 6 | 2 | no | — |
| 165 | D3×Dic3 | — | 6 | 8 | no | — |
| 166 | C3⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 167 | C3×C3⋊C8 | — | 6 | 2 | no | — |
| 168 | C2×#104 | — | 27 | 1 | no | Sylow |
| 169 | C2×H(3,𝔽3) | — | 2 | 1 | no | — |
| 170 | C2×H(3,𝔽3) | — | 4 | 1 | no | — |
| 171 | C2×H(3,𝔽3) | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 172 | #272 | — | 2 | 1 | no | — |
| 173 | #272 | — | 4 | 1 | no | — |
| 174 | #272 | #104 | 1 | 2 | yes | complemented |
| 175 | C3×#41 | — | 3 | 2 | no | — |
| 176 | C3×#41 | — | 6 | 1 | no | — |
| 177 | C3×#41 | — | 9 | 1 | no | — |
| 178 | C3×#41 | — | 9 | 1 | no | — |
| 179 | C3×#41 | — | 9 | 1 | no | — |
| 180 | C3×#41 | — | 18 | 1 | no | — |
| 181 | C3×#41 | — | 18 | 1 | no | — |
| 182 | C3×#41 | D32 | 1 | 1 | yes | characteristic |
| 183 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 184 | C2×C3×D4 | — | 9 | 1 | no | — |
| 185 | C2×C3×D4 | — | 18 | 1 | no | — |
| 186 | C22×C3×C4 | — | 9 | 1 | no | — |
| 187 | C22×C3×C4 | — | 18 | 1 | no | — |
| 188 | C22×Dic3 | — | 18 | 1 | no | — |
| 189 | #239 | — | 3 | 2 | no | — |
| 190 | #239 | — | 6 | 1 | no | — |
| 191 | D3×Q8 | — | 3 | 2 | no | — |
| 192 | D3×Q8 | — | 6 | 1 | no | — |
| 193 | #237 | — | 3 | 2 | no | — |
| 194 | #237 | — | 6 | 1 | no | — |
| 195 | #237 | — | 6 | 2 | no | — |
| 196 | #237 | — | 6 | 2 | no | — |
| 197 | D3×D4 | — | 3 | 2 | no | — |
| 198 | D3×D4 | — | 6 | 1 | no | — |
| 199 | D3×D4 | — | 6 | 2 | no | — |
| 200 | D3×D4 | — | 6 | 2 | no | — |
| 201 | #235 | — | 3 | 2 | no | — |
| 202 | #235 | — | 6 | 1 | no | — |
| 203 | #235 | — | 6 | 2 | no | — |
| 204 | #235 | — | 6 | 2 | no | — |
| 205 | C2×C4×D3 | — | 3 | 2 | no | — |
| 206 | C2×C4×D3 | — | 6 | 1 | no | — |
| 207 | C2×C4×D3 | — | 6 | 2 | no | — |
| 208 | C2×C4×D3 | — | 6 | 2 | no | — |
| 209 | C2×C4×D3 | — | 18 | 2 | no | — |
| 210 | C3×M16 | — | 9 | 2 | no | — |
| 211 | C3×C42 | — | 9 | 2 | no | — |
| 212 | C4×Dic3 | — | 3 | 2 | no | — |
| 213 | C4×Dic3 | — | 9 | 2 | no | — |
| 214 | C4×Dic3 | — | 18 | 2 | no | — |
| 215 | C4×Dic3 | — | 18 | 1 | no | — |
| 216 | #208 | — | 3 | 2 | no | — |
| 217 | #208 | — | 9 | 2 | no | — |
| 218 | #208 | — | 18 | 1 | no | — |
| 219 | C2×C3⋊C8 | — | 18 | 1 | no | — |
| 220 | ΓL(1,𝔽25) | — | 18 | 2 | no | — |
| 221 | D3×C8 | — | 18 | 2 | no | — |
| 222 | C22×C32 | — | 2 | 2 | no | — |
| 223 | C22×C32 | — | 2 | 2 | no | — |
| 224 | C22×C32 | — | 2 | 1 | no | — |
| 225 | C22×C32 | D3×D4 | 1 | 2 | yes | — |
| 226 | C2×C3×D3 | — | 3 | 2 | no | — |
| 227 | C2×C3×D3 | — | 3 | 2 | no | — |
| 228 | C2×C3×D3 | — | 6 | 1 | no | — |
| 229 | C2×C3×D3 | — | 6 | 1 | no | — |
| 230 | C2×C3×D3 | — | 6 | 4 | no | — |
| 231 | C2×C3×D3 | — | 6 | 2 | no | — |
| 232 | C2×C3×D3 | — | 6 | 2 | no | — |
| 233 | C2×C3×D3 | — | 12 | 2 | no | — |
| 234 | C2×C3×D3 | — | 12 | 4 | no | — |
| 235 | C2×C3×D3 | — | 12 | 4 | no | — |
| 236 | C32×C4 | — | 2 | 2 | no | — |
| 237 | C32×C4 | — | 2 | 2 | no | — |
| 238 | C32×C4 | — | 2 | 1 | no | — |
| 239 | C32×C4 | — | 2 | 1 | no | — |
| 240 | C32×C4 | C2×C4×D3 | 1 | 2 | yes | — |
| 241 | C32×C4 | D3×D4 | 1 | 2 | yes | — |
| 242 | C3⋊Dic3 | — | 2 | 4 | no | — |
| 243 | C3×Dic3 | — | 3 | 2 | no | — |
| 244 | C3×Dic3 | — | 3 | 2 | no | — |
| 245 | C3×Dic3 | — | 6 | 1 | no | — |
| 246 | C3×Dic3 | — | 6 | 1 | no | — |
| 247 | C3×Dic3 | — | 6 | 4 | no | — |
| 248 | C3×Dic3 | — | 6 | 2 | no | — |
| 249 | C3×Dic3 | — | 6 | 2 | no | — |
| 250 | C2×#41 | — | 9 | 1 | no | — |
| 251 | C2×M16 | — | 27 | 1 | no | — |
| 252 | C2×C42 | — | 27 | 1 | no | — |
| 253 | #104 | — | 9 | 2 | no | — |
| 254 | #104 | — | 27 | 2 | no | — |
| 255 | H(3,𝔽3) | C2×#104 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 256 | C23×C3 | — | 9 | 1 | no | — |
| 257 | C23×C3 | — | 18 | 1 | no | — |
| 258 | C22×D3 | — | 3 | 2 | no | — |
| 259 | C22×D3 | — | 6 | 1 | no | — |
| 260 | C22×D3 | — | 6 | 2 | no | — |
| 261 | C22×D3 | — | 6 | 2 | no | — |
| 262 | C3×Q8 | — | 3 | 2 | no | — |
| 263 | C3×Q8 | — | 6 | 1 | no | — |
| 264 | C3×Q8 | — | 9 | 1 | no | — |
| 265 | C3×Q8 | — | 18 | 1 | no | — |
| 266 | C3×Q8 | #624 | 1 | 1 | yes | characteristic |
| 267 | C3×D4 | — | 2 | 1 | no | — |
| 268 | C3×D4 | — | 3 | 2 | no | — |
| 269 | C3×D4 | — | 6 | 2 | no | — |
| 270 | C3×D4 | — | 6 | 2 | no | — |
| 271 | C3×D4 | — | 6 | 1 | no | — |
| 272 | C3×D4 | — | 9 | 1 | no | — |
| 273 | C3×D4 | — | 18 | 1 | no | — |
| 274 | C3×D4 | — | 18 | 1 | no | — |
| 275 | C3×D4 | — | 18 | 1 | no | — |
| 276 | C3×D4 | — | 18 | 1 | no | — |
| 277 | C3×D4 | #624 | 1 | 1 | yes | characteristic |
| 278 | C2×C3×C4 | — | 2 | 1 | no | — |
| 279 | C2×C3×C4 | — | 3 | 2 | no | — |
| 280 | C2×C3×C4 | — | 6 | 2 | no | — |
| 281 | C2×C3×C4 | — | 6 | 2 | no | — |
| 282 | C2×C3×C4 | — | 6 | 1 | no | — |
| 283 | C2×C3×C4 | — | 9 | 1 | no | — |
| 284 | C2×C3×C4 | — | 9 | 1 | no | — |
| 285 | C2×C3×C4 | — | 9 | 1 | no | — |
| 286 | C2×C3×C4 | — | 9 | 1 | no | — |
| 287 | C2×C3×C4 | — | 9 | 1 | no | — |
| 288 | C2×C3×C4 | — | 18 | 1 | no | — |
| 289 | C2×C3×C4 | — | 18 | 1 | no | — |
| 290 | C2×C3×C4 | — | 18 | 1 | no | — |
| 291 | C2×C3×C4 | — | 18 | 2 | no | — |
| 292 | C2×C3×C4 | — | 18 | 1 | no | — |
| 293 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 294 | #67 | — | 6 | 2 | no | — |
| 295 | #67 | — | 6 | 2 | no | — |
| 296 | #67 | — | 6 | 2 | no | — |
| 297 | #67 | — | 6 | 2 | no | — |
| 298 | #67 | — | 6 | 2 | no | — |
| 299 | #67 | — | 6 | 2 | no | — |
| 300 | C2×Dic3 | — | 3 | 2 | no | — |
| 301 | C2×Dic3 | — | 6 | 1 | no | — |
| 302 | C2×Dic3 | — | 6 | 2 | no | — |
| 303 | C2×Dic3 | — | 6 | 2 | no | — |
| 304 | C2×Dic3 | — | 6 | 2 | no | — |
| 305 | C2×Dic3 | — | 18 | 2 | no | — |
| 306 | C2×Dic3 | — | 18 | 4 | no | — |
| 307 | D12 | — | 3 | 2 | no | — |
| 308 | D12 | — | 6 | 1 | no | — |
| 309 | D12 | — | 6 | 2 | no | — |
| 310 | D12 | — | 6 | 2 | no | — |
| 311 | C4×D3 | — | 3 | 2 | no | — |
| 312 | C4×D3 | — | 3 | 2 | no | — |
| 313 | C4×D3 | — | 3 | 2 | no | — |
| 314 | C4×D3 | — | 3 | 2 | no | — |
| 315 | C4×D3 | — | 6 | 1 | no | — |
| 316 | C4×D3 | — | 6 | 1 | no | — |
| 317 | C4×D3 | — | 6 | 1 | no | — |
| 318 | C4×D3 | — | 6 | 1 | no | — |
| 319 | C4×D3 | — | 6 | 2 | no | — |
| 320 | C4×D3 | — | 6 | 2 | no | — |
| 321 | C4×D3 | — | 6 | 2 | no | — |
| 322 | C4×D3 | — | 6 | 2 | no | — |
| 323 | C4×D3 | — | 6 | 2 | no | — |
| 324 | C4×D3 | — | 6 | 2 | no | — |
| 325 | C4×D3 | — | 18 | 8 | no | — |
| 326 | Dic6 | — | 3 | 2 | no | — |
| 327 | Dic6 | — | 6 | 1 | no | — |
| 328 | Dic6 | — | 6 | 2 | no | — |
| 329 | Dic6 | — | 6 | 2 | no | — |
| 330 | C3×C8 | — | 18 | 2 | no | — |
| 331 | C3⋊C8 | — | 6 | 2 | no | — |
| 332 | C3⋊C8 | — | 18 | 2 | no | — |
| 333 | C2×C32 | — | 2 | 2 | no | — |
| 334 | C2×C32 | — | 2 | 1 | no | — |
| 335 | C2×C32 | — | 4 | 1 | no | — |
| 336 | C2×C32 | — | 4 | 2 | no | — |
| 337 | C2×C32 | — | 4 | 2 | no | — |
| 338 | C2×C32 | D3×C22⋊C4 | 1 | 2 | yes | — |
| 339 | C3×D3 | — | 3 | 4 | no | — |
| 340 | C3×D3 | — | 6 | 2 | no | — |
| 341 | C3×D3 | — | 6 | 2 | no | — |
| 342 | C3×D3 | — | 12 | 1 | no | — |
| 343 | C3×D3 | — | 12 | 2 | no | — |
| 344 | C3×D3 | — | 12 | 2 | no | — |
| 345 | #41 | — | 9 | 1 | no | — |
| 346 | #41 | — | 9 | 1 | no | — |
| 347 | #41 | — | 9 | 1 | no | — |
| 348 | #41 | — | 18 | 1 | no | — |
| 349 | #41 | — | 18 | 1 | no | — |
| 350 | #41 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 351 | C2×Q8 | — | 9 | 1 | no | — |
| 352 | C2×D4 | — | 9 | 1 | no | — |
| 353 | C2×D4 | — | 18 | 1 | no | — |
| 354 | C22×C4 | — | 9 | 1 | no | — |
| 355 | C22×C4 | — | 18 | 1 | no | — |
| 356 | C22×C4 | — | 54 | 1 | no | — |
| 357 | M16 | — | 9 | 2 | no | — |
| 358 | M16 | — | 54 | 1 | no | — |
| 359 | C2×C8 | — | 54 | 1 | no | — |
| 360 | C42 | — | 9 | 2 | no | — |
| 361 | C42 | — | 54 | 1 | no | — |
| 362 | C22×C3 | — | 2 | 1 | no | — |
| 363 | C22×C3 | — | 3 | 2 | no | — |
| 364 | C22×C3 | — | 6 | 2 | no | — |
| 365 | C22×C3 | — | 6 | 2 | no | — |
| 366 | C22×C3 | — | 6 | 1 | no | — |
| 367 | C22×C3 | — | 9 | 1 | no | — |
| 368 | C22×C3 | — | 9 | 1 | no | — |
| 369 | C22×C3 | — | 18 | 2 | no | — |
| 370 | C22×C3 | — | 18 | 1 | no | — |
| 371 | C22×C3 | — | 36 | 2 | no | — |
| 372 | C22×C3 | #3811 | 1 | 1 | yes | characteristic |
| 373 | C2×D3 | — | 3 | 2 | no | — |
| 374 | C2×D3 | — | 3 | 2 | no | — |
| 375 | C2×D3 | — | 6 | 1 | no | — |
| 376 | C2×D3 | — | 6 | 1 | no | — |
| 377 | C2×D3 | — | 6 | 4 | no | — |
| 378 | C2×D3 | — | 6 | 2 | no | — |
| 379 | C2×D3 | — | 6 | 2 | no | — |
| 380 | C2×D3 | — | 12 | 2 | no | — |
| 381 | C2×D3 | — | 12 | 4 | no | — |
| 382 | C2×D3 | — | 12 | 4 | no | — |
| 383 | C3×C4 | — | 2 | 1 | no | — |
| 384 | C3×C4 | — | 3 | 2 | no | — |
| 385 | C3×C4 | — | 3 | 2 | no | — |
| 386 | C3×C4 | — | 6 | 2 | no | — |
| 387 | C3×C4 | — | 6 | 2 | no | — |
| 388 | C3×C4 | — | 6 | 1 | no | — |
| 389 | C3×C4 | — | 6 | 1 | no | — |
| 390 | C3×C4 | — | 9 | 1 | no | — |
| 391 | C3×C4 | — | 9 | 1 | no | — |
| 392 | C3×C4 | — | 18 | 4 | no | — |
| 393 | C3×C4 | — | 18 | 1 | no | — |
| 394 | C3×C4 | C2×#624 | 1 | 1 | yes | characteristic |
| 395 | C3×C4 | #3811 | 1 | 1 | yes | characteristic |
| 396 | Dic3 | — | 3 | 2 | no | — |
| 397 | Dic3 | — | 3 | 2 | no | — |
| 398 | Dic3 | — | 6 | 1 | no | — |
| 399 | Dic3 | — | 6 | 1 | no | — |
| 400 | Dic3 | — | 6 | 4 | no | — |
| 401 | Dic3 | — | 6 | 2 | no | — |
| 402 | Dic3 | — | 6 | 2 | no | — |
| 403 | Dic3 | — | 18 | 4 | no | — |
| 404 | C32 | — | 2 | 1 | no | — |
| 405 | C32 | D3×#104 | 1 | 2 | yes | complemented |
| 406 | C23 | — | 9 | 1 | no | — |
| 407 | C23 | — | 18 | 1 | no | — |
| 408 | Q8 | — | 9 | 1 | no | — |
| 409 | Q8 | — | 18 | 1 | no | — |
| 410 | Q8 | #6199 | 1 | 1 | yes | characteristic, complemented |
| 411 | D4 | — | 2 | 1 | no | — |
| 412 | D4 | — | 9 | 1 | no | — |
| 413 | D4 | — | 18 | 1 | no | — |
| 414 | D4 | — | 18 | 1 | no | — |
| 415 | D4 | — | 18 | 1 | no | — |
| 416 | D4 | — | 18 | 1 | no | — |
| 417 | D4 | #6199 | 1 | 1 | yes | characteristic, complemented |
| 418 | C2×C4 | — | 2 | 1 | no | — |
| 419 | C2×C4 | — | 9 | 1 | no | — |
| 420 | C2×C4 | — | 9 | 1 | no | — |
| 421 | C2×C4 | — | 9 | 1 | no | — |
| 422 | C2×C4 | — | 9 | 1 | no | — |
| 423 | C2×C4 | — | 9 | 1 | no | — |
| 424 | C2×C4 | — | 18 | 1 | no | — |
| 425 | C2×C4 | — | 18 | 1 | no | — |
| 426 | C2×C4 | — | 18 | 1 | no | — |
| 427 | C2×C4 | — | 18 | 2 | no | — |
| 428 | C2×C4 | — | 18 | 1 | no | — |
| 429 | C2×C4 | — | 54 | 4 | no | — |
| 430 | C2×C4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 431 | C8 | — | 18 | 2 | no | — |
| 432 | C2×C3 | — | 2 | 1 | no | — |
| 433 | C2×C3 | — | 3 | 2 | no | — |
| 434 | C2×C3 | — | 4 | 1 | no | — |
| 435 | C2×C3 | — | 6 | 2 | no | — |
| 436 | C2×C3 | — | 6 | 1 | no | — |
| 437 | C2×C3 | — | 9 | 2 | no | — |
| 438 | C2×C3 | — | 12 | 1 | no | — |
| 439 | C2×C3 | — | 12 | 2 | no | — |
| 440 | C2×C3 | — | 12 | 2 | no | — |
| 441 | C2×C3 | — | 18 | 1 | no | — |
| 442 | C2×C3 | — | 36 | 1 | no | — |
| 443 | C2×C3 | #63974 | 1 | 1 | yes | characteristic |
| 444 | D3 | — | 3 | 4 | no | — |
| 445 | D3 | — | 6 | 2 | no | — |
| 446 | D3 | — | 6 | 2 | no | — |
| 447 | D3 | — | 12 | 1 | no | — |
| 448 | D3 | — | 12 | 2 | no | — |
| 449 | D3 | — | 12 | 2 | no | — |
| 450 | C22 | — | 2 | 1 | no | — |
| 451 | C22 | — | 9 | 1 | no | — |
| 452 | C22 | — | 9 | 1 | no | — |
| 453 | C22 | — | 18 | 2 | no | — |
| 454 | C22 | — | 18 | 1 | no | — |
| 455 | C22 | — | 36 | 2 | no | — |
| 456 | C22 | #88677 | 1 | 1 | yes | characteristic |
| 457 | C4 | — | 2 | 1 | no | — |
| 458 | C4 | — | 9 | 1 | no | — |
| 459 | C4 | — | 9 | 1 | no | — |
| 460 | C4 | — | 18 | 4 | no | — |
| 461 | C4 | — | 18 | 1 | no | — |
| 462 | C4 | C2×#6199 | 1 | 1 | yes | characteristic |
| 463 | C4 | #88677 | 1 | 1 | yes | characteristic |
| 464 | C3 | — | 3 | 2 | no | — |
| 465 | C3 | — | 6 | 1 | no | — |
| 466 | C3 | #10591671 | 1 | 1 | yes | characteristic |
| 467 | C2 | — | 2 | 1 | no | — |
| 468 | C2 | — | 4 | 1 | no | — |
| 469 | C2 | — | 9 | 2 | no | — |
| 470 | C2 | — | 18 | 1 | no | — |
| 471 | C2 | — | 36 | 1 | no | — |
| 472 | C2 | #11721320 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#6199 | C2 | semidirect |
| 3. #11721065 | C2 | semidirect |
| 4. #63664⋊C3 | C2 | semidirect |
| 5. #11720328 | C2 | semidirect |
| 8. #88748 | C4 | semidirect |
| 9. Q8×#272 | C4 | semidirect |
| 11. #88744 | C4 | semidirect |
| 13. D4×#272 | C4 | semidirect |
| 19. C4×(C3⋊Dic3)⋊C3 | C22 | semidirect |
| 20. #3748⋊C3 | C22 | semidirect |
| 28. #63664 | D3 | semidirect |
| 34. Q8×H(3,𝔽3) | C2×C4 | semidirect |
| 36. D4×H(3,𝔽3) | C2×C4 | semidirect |
| 45. C4⋊#272 | C2×C4 | semidirect |
| 54. #6229 | C2×C4 | semidirect |
| 83. C4×C3⋊Dic3 | C2×D3 | semidirect |
| 84. #3748 | C2×D3 | semidirect |
| 122. C32×Q8 | C4×D3 | semidirect |
| 126. C32×D4 | C4×D3 | semidirect |
| 174. #272 | #104 | semidirect |
| 255. H(3,𝔽3) | C2×#104 | semidirect |
| 405. C32 | D3×#104 | semidirect |
| 410. Q8 | #6199 | semidirect |
| 417. D4 | #6199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#272 | 2 |
| C4×#6199 | 2 |
| #11721065 | 2 |
| #63664⋊C3 | 2 |
| #11720328 | 2 |
| D3×#837 | 3 |