Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1354 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 1354 conjugacy classes of subgroups — too many to draw. Only its 196 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 | C2×#89040 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#89014 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×#88800 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C2×C3×#3716 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×C3×#3712 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11722895 | C2 | 1 | 8 | yes | maximal, direct product factor |
| 7 | C2×#63931 | — | 3 | 1 | no | maximal |
| 8 | C2×#63800 | — | 3 | 2 | no | maximal |
| 9 | C2×#6308 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×C3×C4×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C3×#634 | C22 | 1 | 2 | yes | — |
| 12 | C2×C32×D12 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#6296 | — | 2 | 1 | no | — |
| 14 | C2×#6294 | — | 2 | 1 | no | — |
| 15 | #89040 | — | 2 | 2 | no | — |
| 16 | #89040 | C22 | 1 | 4 | yes | complemented |
| 17 | C2×#6290 | — | 2 | 1 | no | — |
| 18 | C2×D3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 19 | #89014 | — | 2 | 2 | no | — |
| 20 | #89014 | C22 | 1 | 4 | yes | — |
| 21 | C2×C32×C3⋊C8 | C22 | 1 | 2 | yes | — |
| 22 | #88800 | C22 | 1 | 8 | yes | complemented |
| 23 | C3×#3716 | C22 | 1 | 8 | yes | complemented |
| 24 | C3×#3712 | C22 | 1 | 4 | yes | complemented |
| 25 | C2×#3830 | — | 3 | 1 | no | — |
| 26 | C2×#3797 | — | 3 | 1 | no | — |
| 27 | C2×#3795 | — | 3 | 2 | no | — |
| 28 | C2×#3795 | — | 6 | 1 | no | — |
| 29 | C2×D3×Dic6 | — | 3 | 2 | no | — |
| 30 | C2×#3746 | — | 3 | 2 | no | — |
| 31 | C2×C3×#214 | — | 3 | 2 | no | — |
| 32 | C2×C3×#204 | — | 3 | 2 | no | — |
| 33 | C2×C3×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 34 | #63931 | — | 3 | 8 | no | — |
| 35 | C2×#3719 | — | 3 | 2 | no | — |
| 36 | C2×#3719 | — | 3 | 2 | no | — |
| 37 | C2×#3719 | — | 6 | 2 | no | — |
| 38 | C2×#3716 | D3 | 1 | 2 | yes | complemented |
| 39 | C2×#3712 | D3 | 1 | 1 | yes | characteristic, complemented |
| 40 | #63800 | — | 3 | 16 | no | — |
| 41 | C22×C3×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 42 | C22×C32×D3 | — | 2 | 1 | no | — |
| 43 | C2×C33×C4 | C23 | 1 | 1 | yes | characteristic |
| 44 | C2×C3⋊(C3⋊Dic3) | — | 2 | 1 | no | — |
| 45 | #6308 | — | 2 | 1 | no | — |
| 46 | #6308 | C23 | 1 | 2 | yes | — |
| 47 | C2×C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 48 | C2×C3×C3⋊Dic3 | D4 | 1 | 1 | yes | characteristic |
| 49 | C3×C4×C3⋊D3 | D4 | 1 | 2 | yes | — |
| 50 | C3×C4×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 51 | C3×#634 | — | 2 | 2 | no | — |
| 52 | C3×#634 | C23 | 1 | 4 | yes | — |
| 53 | C32×D12 | — | 2 | 1 | no | — |
| 54 | C32×D12 | C23 | 1 | 2 | yes | — |
| 55 | #6296 | — | 2 | 4 | no | — |
| 56 | #6294 | — | 2 | 4 | no | — |
| 57 | #6290 | — | 2 | 4 | no | — |
| 58 | D3×C3⋊Dic3 | — | 2 | 4 | no | — |
| 59 | C32×C3⋊C8 | C23 | 1 | 4 | yes | — |
| 60 | C2×#915 | — | 9 | 2 | no | — |
| 61 | C2×#909 | — | 9 | 1 | no | — |
| 62 | C2×C32×D4 | — | 3 | 1 | no | — |
| 63 | C2×#638 | — | 6 | 1 | no | — |
| 64 | C22×C3⋊Dic3 | — | 6 | 1 | no | — |
| 65 | #3830 | — | 3 | 4 | no | — |
| 66 | #3830 | — | 6 | 2 | no | — |
| 67 | C2×C4×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 68 | C2×#634 | — | 3 | 2 | no | — |
| 69 | C2×#634 | — | 3 | 1 | no | — |
| 70 | C2×#634 | — | 6 | 1 | no | — |
| 71 | C2×#634 | — | 6 | 2 | no | — |
| 72 | C2×#634 | — | 12 | 1 | no | — |
| 73 | C2×#634 | C2×D3 | 1 | 2 | yes | — |
| 74 | C2×C3×D12 | — | 2 | 1 | no | — |
| 75 | C2×C3×D12 | C2×D3 | 1 | 2 | yes | — |
| 76 | C2×C3×C4×D3 | — | 3 | 2 | no | — |
| 77 | C2×C3×C4×D3 | — | 6 | 1 | no | — |
| 78 | C2×C3×Dic6 | — | 3 | 2 | no | — |
| 79 | C2×C3×Dic6 | — | 3 | 2 | no | — |
| 80 | C2×C3×Dic6 | — | 6 | 2 | no | — |
| 81 | C2×#627 | — | 6 | 2 | no | — |
| 82 | C2×#627 | — | 6 | 1 | no | — |
| 83 | C2×#625 | — | 6 | 2 | no | — |
| 84 | C2×#625 | — | 6 | 2 | no | — |
| 85 | C2×#624 | — | 6 | 1 | no | — |
| 86 | C2×D3×Dic3 | — | 6 | 2 | no | — |
| 87 | C2×D3×Dic3 | — | 6 | 2 | no | — |
| 88 | C2×D3×Dic3 | — | 6 | 2 | no | — |
| 89 | #3797 | — | 3 | 4 | no | — |
| 90 | #3797 | — | 6 | 2 | no | — |
| 91 | #3795 | — | 3 | 8 | no | — |
| 92 | #3795 | — | 6 | 4 | no | — |
| 93 | #3795 | — | 6 | 4 | no | — |
| 94 | #3795 | — | 6 | 4 | no | — |
| 95 | D3×Dic6 | — | 3 | 8 | no | — |
| 96 | D3×Dic6 | — | 6 | 4 | no | — |
| 97 | C2×C32×C8 | — | 3 | 2 | no | — |
| 98 | #3746 | — | 3 | 8 | no | — |
| 99 | C3×#214 | — | 3 | 8 | no | — |
| 100 | C2×C3×C3⋊C8 | — | 2 | 2 | no | — |
| 101 | C2×C3×C3⋊C8 | C2×D3 | 1 | 2 | yes | — |
| 102 | C2×C3×C3⋊C8 | C2×D3 | 1 | 2 | yes | — |
| 103 | C3×#204 | — | 3 | 8 | no | — |
| 104 | C3×ΓL(1,𝔽25) | — | 3 | 8 | no | — |
| 105 | #3719 | — | 3 | 8 | no | — |
| 106 | #3719 | — | 3 | 8 | no | — |
| 107 | #3719 | — | 6 | 8 | no | — |
| 108 | #3716 | C2×D3 | 1 | 8 | yes | complemented |
| 109 | #3712 | C2×D3 | 1 | 4 | yes | complemented |
| 110 | C22×C33 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 112 | C2×C3×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 113 | C2×C32×D3 | — | 2 | 2 | no | — |
| 114 | C2×C32×D3 | — | 4 | 2 | no | — |
| 115 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C33×C4 | C24 | 1 | 1 | yes | characteristic |
| 117 | C3⋊(C3⋊Dic3) | — | 2 | 2 | no | — |
| 118 | C3×C3⋊Dic3 | — | 2 | 4 | no | — |
| 119 | C3×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 120 | C2×D3×Q8 | — | 9 | 2 | no | — |
| 121 | C2×#237 | — | 9 | 2 | no | — |
| 122 | C2×#237 | — | 18 | 1 | no | — |
| 123 | C2×#235 | — | 9 | 1 | no | — |
| 124 | C22×Dic6 | — | 9 | 1 | no | — |
| 125 | C2×C3×SD16 | — | 9 | 2 | no | — |
| 126 | C2×C3×M16 | — | 9 | 1 | no | — |
| 127 | C2×#216 | — | 9 | 2 | no | — |
| 128 | C2×#214 | — | 3 | 2 | no | — |
| 129 | #915 | — | 9 | 16 | no | — |
| 130 | #909 | — | 9 | 8 | no | — |
| 131 | C2×Dic12 | — | 9 | 2 | no | — |
| 132 | C2×Dic12 | — | 9 | 2 | no | — |
| 133 | C2×Dic12 | — | 18 | 2 | no | — |
| 134 | C2×#204 | — | 3 | 2 | no | — |
| 135 | C2×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 136 | C23×C32 | — | 6 | 1 | no | — |
| 137 | C22×C3⋊D3 | D12 | 1 | 1 | yes | characteristic |
| 138 | C22×C3×D3 | — | 2 | 2 | no | — |
| 139 | C22×C3×D3 | — | 2 | 2 | no | — |
| 140 | C22×C3×D3 | — | 3 | 2 | no | — |
| 141 | C22×C3×D3 | — | 6 | 1 | no | — |
| 142 | C32×D4 | — | 3 | 2 | no | — |
| 143 | C32×D4 | — | 6 | 1 | no | — |
| 144 | C2×C32×C4 | — | 2 | 2 | no | — |
| 145 | C2×C32×C4 | — | 2 | 1 | no | — |
| 146 | C2×C32×C4 | — | 4 | 1 | no | — |
| 147 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 148 | C2×C32×C4 | C22×D3 | 1 | 2 | yes | — |
| 149 | #638 | — | 6 | 4 | no | — |
| 150 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 151 | C2×C3⋊Dic3 | — | 6 | 1 | no | — |
| 152 | C2×C3⋊Dic3 | — | 6 | 4 | no | — |
| 153 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 154 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 155 | C2×C3⋊Dic3 | — | 12 | 2 | no | — |
| 156 | C2×C3⋊Dic3 | — | 12 | 2 | no | — |
| 157 | C2×C3⋊Dic3 | D12 | 1 | 1 | yes | characteristic |
| 158 | C4×C3⋊D3 | D12 | 1 | 2 | yes | — |
| 159 | C4×C3⋊D3 | C22×D3 | 1 | 2 | yes | — |
| 160 | #634 | — | 2 | 2 | no | — |
| 161 | #634 | — | 3 | 2 | no | — |
| 162 | #634 | — | 3 | 4 | no | — |
| 163 | #634 | — | 6 | 2 | no | — |
| 164 | #634 | — | 6 | 4 | no | — |
| 165 | #634 | — | 6 | 1 | no | — |
| 166 | #634 | — | 6 | 2 | no | — |
| 167 | #634 | — | 6 | 2 | no | — |
| 168 | #634 | — | 12 | 2 | no | — |
| 169 | #634 | — | 12 | 2 | no | — |
| 170 | #634 | — | 12 | 2 | no | — |
| 171 | #634 | C22×D3 | 1 | 4 | yes | — |
| 172 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 173 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 174 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 175 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 176 | C2×C3×Dic3 | — | 12 | 2 | no | — |
| 177 | C3×D12 | — | 2 | 2 | no | — |
| 178 | C3×D12 | — | 2 | 2 | no | — |
| 179 | C3×D12 | — | 2 | 2 | no | — |
| 180 | C3×D12 | C22×D3 | 1 | 4 | yes | — |
| 181 | C3×C4×D3 | — | 3 | 4 | no | — |
| 182 | C3×C4×D3 | — | 3 | 4 | no | — |
| 183 | C3×C4×D3 | — | 6 | 2 | no | — |
| 184 | C3×C4×D3 | — | 6 | 2 | no | — |
| 185 | C3×Dic6 | — | 3 | 4 | no | — |
| 186 | C3×Dic6 | — | 3 | 4 | no | — |
| 187 | C3×Dic6 | — | 6 | 4 | no | — |
| 188 | C3×Dic6 | — | 6 | 2 | no | — |
| 189 | C3×Dic6 | — | 6 | 2 | no | — |
| 190 | C3×Dic6 | — | 12 | 2 | no | — |
| 191 | #627 | — | 6 | 8 | no | — |
| 192 | #627 | — | 6 | 4 | no | — |
| 193 | #625 | — | 6 | 8 | no | — |
| 194 | #625 | — | 6 | 8 | no | — |
| 195 | #624 | — | 6 | 4 | no | — |
| 196 | D3×Dic3 | — | 6 | 8 | no | — |
| 197 | D3×Dic3 | — | 6 | 8 | no | — |
| 198 | D3×Dic3 | — | 6 | 8 | no | — |
| 199 | C32×C8 | — | 3 | 4 | no | — |
| 200 | C3×C3⋊C8 | — | 2 | 4 | no | — |
| 201 | C3×C3⋊C8 | C22×D3 | 1 | 4 | yes | — |
| 202 | C3×C3⋊C8 | C22×D3 | 1 | 4 | yes | — |
| 203 | C2×#137 | — | 27 | 1 | no | Sylow |
| 204 | C2×C33 | #137 | 1 | 2 | yes | complemented |
| 205 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 206 | C3×C3⋊D3 | — | 2 | 2 | no | — |
| 207 | C32×D3 | — | 4 | 2 | no | — |
| 208 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 209 | C2×C3×D4 | — | 3 | 2 | no | — |
| 210 | C2×C3×D4 | — | 6 | 1 | no | — |
| 211 | C22×C3×C4 | — | 9 | 1 | no | — |
| 212 | C2×#67 | — | 18 | 1 | no | — |
| 213 | C2×#67 | — | 18 | 2 | no | — |
| 214 | C2×#67 | — | 18 | 2 | no | — |
| 215 | C22×Dic3 | — | 18 | 2 | no | — |
| 216 | C22×Dic3 | — | 18 | 1 | no | — |
| 217 | C22×Dic3 | — | 18 | 2 | no | — |
| 218 | D3×Q8 | — | 9 | 8 | no | — |
| 219 | D3×Q8 | — | 18 | 4 | no | — |
| 220 | #237 | — | 9 | 8 | no | — |
| 221 | #237 | — | 18 | 4 | no | — |
| 222 | #237 | — | 18 | 4 | no | — |
| 223 | #237 | — | 18 | 4 | no | — |
| 224 | #235 | — | 9 | 4 | no | — |
| 225 | #235 | — | 18 | 2 | no | — |
| 226 | C2×D12 | D32 | 1 | 1 | yes | characteristic |
| 227 | C2×C4×D3 | — | 3 | 2 | no | — |
| 228 | C2×C4×D3 | — | 6 | 1 | no | — |
| 229 | C2×C4×D3 | — | 18 | 2 | no | — |
| 230 | C2×C4×D3 | — | 18 | 1 | no | — |
| 231 | C2×Dic6 | — | 3 | 2 | no | — |
| 232 | C2×Dic6 | — | 3 | 2 | no | — |
| 233 | C2×Dic6 | — | 6 | 2 | no | — |
| 234 | C2×Dic6 | — | 9 | 4 | no | — |
| 235 | C2×Dic6 | — | 9 | 1 | no | — |
| 236 | C2×Dic6 | — | 9 | 2 | no | — |
| 237 | C2×Dic6 | — | 18 | 1 | no | — |
| 238 | C2×Dic6 | — | 18 | 2 | no | — |
| 239 | C2×Dic6 | — | 18 | 2 | no | — |
| 240 | C2×Dic6 | — | 18 | 2 | no | — |
| 241 | C2×Dic6 | — | 18 | 1 | no | — |
| 242 | C2×Dic6 | — | 36 | 1 | no | — |
| 243 | C3×SD16 | — | 9 | 8 | no | — |
| 244 | C3×M16 | — | 9 | 4 | no | — |
| 245 | C2×C3×C8 | — | 3 | 2 | no | — |
| 246 | C2×C3×C8 | — | 3 | 2 | no | — |
| 247 | C2×C3×C8 | — | 6 | 2 | no | — |
| 248 | #216 | — | 9 | 8 | no | — |
| 249 | #214 | — | 3 | 8 | no | — |
| 250 | C2×C3⋊C8 | D32 | 1 | 2 | yes | — |
| 251 | Dic12 | — | 9 | 8 | no | — |
| 252 | Dic12 | — | 9 | 8 | no | — |
| 253 | Dic12 | — | 18 | 8 | no | — |
| 254 | #204 | — | 3 | 8 | no | — |
| 255 | ΓL(1,𝔽25) | — | 3 | 8 | no | — |
| 256 | C22×C32 | — | 2 | 2 | no | — |
| 257 | C22×C32 | — | 2 | 1 | no | — |
| 258 | C22×C32 | — | 4 | 1 | no | — |
| 259 | C22×C32 | — | 6 | 2 | no | — |
| 260 | C22×C32 | — | 12 | 2 | no | — |
| 261 | C22×C32 | C2×D12 | 1 | 1 | yes | characteristic |
| 262 | C22×C32 | D3×D4 | 1 | 2 | yes | — |
| 263 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 264 | C2×C3⋊D3 | C2×D12 | 1 | 2 | yes | — |
| 265 | C2×C3×D3 | — | 2 | 4 | no | — |
| 266 | C2×C3×D3 | — | 2 | 4 | no | — |
| 267 | C2×C3×D3 | — | 3 | 4 | no | — |
| 268 | C2×C3×D3 | — | 4 | 4 | no | — |
| 269 | C2×C3×D3 | — | 4 | 4 | no | — |
| 270 | C2×C3×D3 | — | 6 | 2 | no | — |
| 271 | C2×C3×D3 | — | 6 | 4 | no | — |
| 272 | C2×C3×D3 | — | 12 | 2 | no | — |
| 273 | C32×C4 | — | 2 | 2 | no | — |
| 274 | C32×C4 | — | 2 | 1 | no | — |
| 275 | C32×C4 | — | 2 | 2 | no | — |
| 276 | C32×C4 | — | 2 | 1 | no | — |
| 277 | C32×C4 | — | 4 | 1 | no | — |
| 278 | C32×C4 | — | 4 | 1 | no | — |
| 279 | C32×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 280 | C32×C4 | D3×D4 | 1 | 2 | yes | — |
| 281 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 282 | C32×C4 | C23×D3 | 1 | 2 | yes | — |
| 283 | C3⋊Dic3 | — | 2 | 4 | no | — |
| 284 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 285 | C3⋊Dic3 | — | 6 | 4 | no | — |
| 286 | C3⋊Dic3 | — | 6 | 4 | no | — |
| 287 | C3⋊Dic3 | — | 12 | 4 | no | — |
| 288 | C3⋊Dic3 | — | 12 | 4 | no | — |
| 289 | C3⋊Dic3 | C2×D12 | 1 | 2 | yes | — |
| 290 | C3×Dic3 | — | 3 | 4 | no | — |
| 291 | C3×Dic3 | — | 6 | 2 | no | — |
| 292 | C3×Dic3 | — | 6 | 4 | no | — |
| 293 | C3×Dic3 | — | 6 | 4 | no | — |
| 294 | C3×Dic3 | — | 12 | 4 | no | — |
| 295 | C2×#41 | — | 27 | 1 | no | — |
| 296 | C22×Q8 | — | 27 | 1 | no | — |
| 297 | #137 | — | 27 | 8 | no | — |
| 298 | C2×Q16 | — | 27 | 2 | no | — |
| 299 | C2×SD16 | — | 9 | 2 | no | — |
| 300 | C2×M16 | — | 9 | 1 | no | — |
| 301 | C33 | C2×#137 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 302 | C23×C3 | — | 6 | 2 | no | — |
| 303 | C23×C3 | — | 6 | 2 | no | — |
| 304 | C23×C3 | — | 9 | 1 | no | — |
| 305 | C22×D3 | — | 2 | 1 | no | — |
| 306 | C22×D3 | — | 3 | 2 | no | — |
| 307 | C22×D3 | — | 6 | 1 | no | — |
| 308 | C3×Q8 | — | 9 | 4 | no | — |
| 309 | C3×Q8 | — | 18 | 2 | no | — |
| 310 | C3×D4 | — | 3 | 4 | no | — |
| 311 | C3×D4 | — | 6 | 2 | no | — |
| 312 | C3×D4 | — | 6 | 2 | no | — |
| 313 | C3×D4 | — | 6 | 2 | no | — |
| 314 | C2×C3×C4 | — | 2 | 2 | no | — |
| 315 | C2×C3×C4 | — | 2 | 1 | no | — |
| 316 | C2×C3×C4 | — | 4 | 1 | no | — |
| 317 | C2×C3×C4 | — | 9 | 1 | no | — |
| 318 | C2×C3×C4 | — | 9 | 2 | no | — |
| 319 | C2×C3×C4 | — | 9 | 2 | no | — |
| 320 | C2×C3×C4 | — | 18 | 2 | no | — |
| 321 | C2×C3×C4 | C2×D32 | 1 | 2 | yes | — |
| 322 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 323 | #67 | — | 18 | 4 | no | — |
| 324 | #67 | — | 18 | 8 | no | — |
| 325 | #67 | — | 18 | 8 | no | — |
| 326 | C2×Dic3 | — | 3 | 2 | no | — |
| 327 | C2×Dic3 | — | 6 | 1 | no | — |
| 328 | C2×Dic3 | — | 6 | 2 | no | — |
| 329 | C2×Dic3 | — | 6 | 2 | no | — |
| 330 | C2×Dic3 | — | 12 | 2 | no | — |
| 331 | C2×Dic3 | — | 18 | 8 | no | — |
| 332 | C2×Dic3 | — | 18 | 4 | no | — |
| 333 | C2×Dic3 | — | 18 | 8 | no | — |
| 334 | C2×Dic3 | — | 18 | 2 | no | — |
| 335 | C2×Dic3 | — | 18 | 2 | no | — |
| 336 | C2×Dic3 | — | 18 | 1 | no | — |
| 337 | C2×Dic3 | — | 36 | 2 | no | — |
| 338 | C2×Dic3 | — | 36 | 2 | no | — |
| 339 | D12 | — | 2 | 1 | no | — |
| 340 | D12 | C2×D32 | 1 | 2 | yes | — |
| 341 | C4×D3 | — | 3 | 4 | no | — |
| 342 | C4×D3 | — | 3 | 4 | no | — |
| 343 | C4×D3 | — | 6 | 2 | no | — |
| 344 | C4×D3 | — | 6 | 2 | no | — |
| 345 | C4×D3 | — | 18 | 8 | no | — |
| 346 | C4×D3 | — | 18 | 4 | no | — |
| 347 | Dic6 | — | 3 | 4 | no | — |
| 348 | Dic6 | — | 3 | 4 | no | — |
| 349 | Dic6 | — | 6 | 4 | no | — |
| 350 | Dic6 | — | 6 | 2 | no | — |
| 351 | Dic6 | — | 6 | 2 | no | — |
| 352 | Dic6 | — | 9 | 2 | no | — |
| 353 | Dic6 | — | 9 | 4 | no | — |
| 354 | Dic6 | — | 12 | 2 | no | — |
| 355 | Dic6 | — | 18 | 2 | no | — |
| 356 | Dic6 | — | 18 | 4 | no | — |
| 357 | Dic6 | — | 18 | 8 | no | — |
| 358 | Dic6 | — | 18 | 4 | no | — |
| 359 | Dic6 | — | 18 | 2 | no | — |
| 360 | Dic6 | — | 18 | 2 | no | — |
| 361 | Dic6 | — | 18 | 1 | no | — |
| 362 | Dic6 | — | 36 | 2 | no | — |
| 363 | Dic6 | — | 36 | 2 | no | — |
| 364 | Dic6 | — | 36 | 2 | no | — |
| 365 | C3×C8 | — | 3 | 4 | no | — |
| 366 | C3×C8 | — | 3 | 4 | no | — |
| 367 | C3×C8 | — | 6 | 4 | no | — |
| 368 | C3⋊C8 | C2×D32 | 1 | 4 | yes | — |
| 369 | C2×C32 | — | 2 | 2 | no | — |
| 370 | C2×C32 | — | 2 | 4 | no | — |
| 371 | C2×C32 | — | 2 | 1 | no | — |
| 372 | C2×C32 | — | 2 | 2 | no | — |
| 373 | C2×C32 | — | 4 | 2 | no | — |
| 374 | C2×C32 | — | 4 | 1 | no | — |
| 375 | C2×C32 | — | 12 | 2 | no | — |
| 376 | C2×C32 | #909 | 1 | 2 | yes | complemented |
| 377 | C2×C32 | #915 | 1 | 4 | yes | complemented |
| 378 | C2×C32 | C22×D12 | 1 | 1 | yes | characteristic |
| 379 | C2×C32 | C2×D3×D4 | 1 | 2 | yes | — |
| 380 | C3⋊D3 | — | 2 | 2 | no | — |
| 381 | C3×D3 | — | 4 | 4 | no | — |
| 382 | C3×D3 | — | 4 | 4 | no | — |
| 383 | C3×D3 | — | 6 | 4 | no | — |
| 384 | C3×D3 | — | 12 | 2 | no | — |
| 385 | #41 | — | 27 | 4 | no | — |
| 386 | #41 | — | 54 | 2 | no | — |
| 387 | C2×Q8 | — | 9 | 2 | no | — |
| 388 | C2×Q8 | — | 27 | 4 | no | — |
| 389 | C2×Q8 | — | 27 | 1 | no | — |
| 390 | C2×Q8 | — | 54 | 1 | no | — |
| 391 | C2×Q8 | — | 54 | 2 | no | — |
| 392 | C2×D4 | — | 3 | 1 | no | — |
| 393 | C2×D4 | — | 54 | 1 | no | — |
| 394 | C22×C4 | — | 9 | 1 | no | — |
| 395 | C22×C4 | — | 54 | 1 | no | — |
| 396 | C22×C4 | — | 54 | 1 | no | — |
| 397 | Q16 | — | 27 | 8 | no | — |
| 398 | SD16 | — | 9 | 8 | no | — |
| 399 | M16 | — | 9 | 4 | no | — |
| 400 | C2×C8 | — | 3 | 2 | no | — |
| 401 | C22×C3 | — | 2 | 1 | no | — |
| 402 | C22×C3 | — | 2 | 2 | no | — |
| 403 | C22×C3 | — | 4 | 1 | no | — |
| 404 | C22×C3 | — | 6 | 4 | no | — |
| 405 | C22×C3 | — | 6 | 4 | no | — |
| 406 | C22×C3 | — | 9 | 2 | no | — |
| 407 | C22×C3 | — | 12 | 4 | no | — |
| 408 | C22×C3 | — | 12 | 4 | no | — |
| 409 | C22×C3 | — | 18 | 2 | no | — |
| 410 | C22×C3 | D3×D12 | 1 | 2 | yes | — |
| 411 | C22×C3 | #3811 | 1 | 1 | yes | characteristic |
| 412 | C2×D3 | — | 2 | 2 | no | — |
| 413 | C2×D3 | — | 3 | 4 | no | — |
| 414 | C2×D3 | — | 4 | 2 | no | — |
| 415 | C2×D3 | — | 6 | 2 | no | — |
| 416 | C2×D3 | — | 6 | 4 | no | — |
| 417 | C2×D3 | — | 12 | 2 | no | — |
| 418 | C3×C4 | — | 2 | 2 | no | — |
| 419 | C3×C4 | — | 2 | 1 | no | — |
| 420 | C3×C4 | — | 2 | 2 | no | — |
| 421 | C3×C4 | — | 2 | 1 | no | — |
| 422 | C3×C4 | — | 4 | 1 | no | — |
| 423 | C3×C4 | — | 4 | 1 | no | — |
| 424 | C3×C4 | — | 9 | 2 | no | — |
| 425 | C3×C4 | — | 18 | 4 | no | — |
| 426 | C3×C4 | D3×D12 | 1 | 2 | yes | — |
| 427 | C3×C4 | #3811 | 1 | 1 | yes | characteristic |
| 428 | C3×C4 | C22×D32 | 1 | 2 | yes | — |
| 429 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 430 | Dic3 | — | 3 | 4 | no | — |
| 431 | Dic3 | — | 6 | 2 | no | — |
| 432 | Dic3 | — | 6 | 4 | no | — |
| 433 | Dic3 | — | 6 | 4 | no | — |
| 434 | Dic3 | — | 12 | 4 | no | — |
| 435 | Dic3 | — | 18 | 4 | no | — |
| 436 | Dic3 | — | 18 | 4 | no | — |
| 437 | Dic3 | — | 18 | 2 | no | — |
| 438 | Dic3 | — | 36 | 4 | no | — |
| 439 | Dic3 | — | 36 | 4 | no | — |
| 440 | C32 | — | 2 | 1 | no | — |
| 441 | C32 | — | 2 | 2 | no | — |
| 442 | C32 | — | 4 | 1 | no | — |
| 443 | C32 | C2×#909 | 1 | 1 | yes | characteristic, complemented |
| 444 | C32 | C2×#915 | 1 | 2 | yes | complemented |
| 445 | C23 | — | 6 | 1 | no | — |
| 446 | C23 | — | 9 | 1 | no | — |
| 447 | Q8 | — | 9 | 4 | no | — |
| 448 | Q8 | — | 18 | 2 | no | — |
| 449 | Q8 | — | 27 | 2 | no | — |
| 450 | Q8 | — | 54 | 4 | no | — |
| 451 | Q8 | — | 54 | 1 | no | — |
| 452 | D4 | — | 3 | 2 | no | — |
| 453 | D4 | — | 6 | 1 | no | — |
| 454 | D4 | — | 54 | 4 | no | — |
| 455 | C2×C4 | — | 9 | 1 | no | — |
| 456 | C2×C4 | — | 9 | 2 | no | — |
| 457 | C2×C4 | — | 9 | 2 | no | — |
| 458 | C2×C4 | — | 18 | 2 | no | — |
| 459 | C2×C4 | — | 54 | 4 | no | — |
| 460 | C2×C4 | — | 54 | 4 | no | — |
| 461 | C2×C4 | — | 54 | 1 | no | — |
| 462 | C2×C4 | D33 | 1 | 1 | yes | characteristic |
| 463 | C8 | — | 3 | 4 | no | — |
| 464 | C2×C3 | — | 2 | 1 | no | — |
| 465 | C2×C3 | — | 2 | 2 | no | — |
| 466 | C2×C3 | — | 2 | 2 | no | — |
| 467 | C2×C3 | — | 2 | 4 | no | — |
| 468 | C2×C3 | — | 4 | 1 | no | — |
| 469 | C2×C3 | — | 4 | 2 | no | — |
| 470 | C2×C3 | — | 12 | 4 | no | — |
| 471 | C2×C3 | — | 12 | 4 | no | — |
| 472 | C2×C3 | — | 18 | 2 | no | — |
| 473 | C2×C3 | #63800 | 1 | 4 | yes | complemented |
| 474 | C2×C3 | #63931 | 1 | 2 | yes | complemented |
| 475 | C2×C3 | C2×D3×D12 | 1 | 2 | yes | — |
| 476 | C2×C3 | C2×#3811 | 1 | 1 | yes | characteristic |
| 477 | D3 | — | 4 | 2 | no | — |
| 478 | D3 | — | 6 | 4 | no | — |
| 479 | D3 | — | 12 | 2 | no | — |
| 480 | C22 | — | 6 | 2 | no | — |
| 481 | C22 | — | 9 | 2 | no | — |
| 482 | C22 | — | 12 | 2 | no | — |
| 483 | C22 | — | 18 | 2 | no | — |
| 484 | C22 | #88955 | 1 | 1 | yes | characteristic |
| 485 | C4 | — | 9 | 2 | no | — |
| 486 | C4 | — | 18 | 4 | no | — |
| 487 | C4 | — | 54 | 2 | no | — |
| 488 | C4 | #88955 | 1 | 1 | yes | characteristic |
| 489 | C4 | C2×D33 | 1 | 1 | yes | characteristic |
| 490 | C3 | — | 2 | 1 | no | — |
| 491 | C3 | — | 2 | 2 | no | — |
| 492 | C3 | — | 4 | 1 | no | — |
| 493 | C3 | C2×#63800 | 1 | 2 | yes | complemented |
| 494 | C3 | C2×#63931 | 1 | 1 | yes | characteristic, complemented |
| 495 | C2 | — | 12 | 2 | no | — |
| 496 | C2 | — | 18 | 2 | no | — |
| 497 | C2 | #11722895 | 1 | 2 | yes | direct product factor |
| 498 | C2 | C2×#88955 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#89040 | C2 | semidirect |
| 3. C2×#88800 | C2 | semidirect |
| 4. C2×C3×#3716 | C2 | semidirect |
| 5. C2×C3×#3712 | C2 | semidirect |
| 6. #11722895 | C2 | direct (N × H) |
| 16. #89040 | C22 | semidirect |
| 22. #88800 | C22 | semidirect |
| 23. C3×#3716 | C22 | semidirect |
| 24. C3×#3712 | C22 | semidirect |
| 38. C2×#3716 | D3 | semidirect |
| 39. C2×#3712 | D3 | semidirect |
| 108. #3716 | C2×D3 | semidirect |
| 109. #3712 | C2×D3 | semidirect |
| 204. C2×C33 | #137 | semidirect |
| 301. C33 | C2×#137 | semidirect |
| 376. C2×C32 | #909 | semidirect |
| 377. C2×C32 | #915 | semidirect |
| 443. C32 | C2×#909 | semidirect |
| 444. C32 | C2×#915 | semidirect |
| 473. C2×C3 | #63800 | semidirect |
| 474. C2×C3 | #63931 | semidirect |
| 493. C3 | C2×#63800 | semidirect |
| 494. C3 | C2×#63931 | semidirect |
| 497. C2 | #11722895 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89040 | 2 |
| C2×#89014 | 2 |
| C2×#88800 | 2 |
| C2×C3×#3716 | 2 |
| C2×C3×#3712 | 2 |
| #11722895 | 2 |
| C2×#63931 | 3 |
| C2×#63800 | 3 |