Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
996 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 123 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 | #11724618 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#64306 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×C4⋊(C3⋊#157) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11724332 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11724314 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11724313 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11724300 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11724298 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10596513 | — | 3 | 1 | no | maximal |
| 10 | C22×C3⋊#157 | C22 | 1 | 2 | yes | — |
| 11 | C2×D32⋊D3 | C22 | 1 | 4 | yes | — |
| 12 | C3×#3828 | — | 2 | 1 | no | — |
| 13 | C2×C3×C4×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 14 | C32×#235 | — | 2 | 1 | no | — |
| 15 | #89049 | C22 | 1 | 2 | yes | — |
| 16 | #89046 | — | 2 | 1 | no | — |
| 17 | C4⋊#1113 | C22 | 1 | 1 | yes | characteristic |
| 18 | C4×#1113 | C22 | 1 | 2 | yes | — |
| 19 | #89042 | — | 2 | 1 | no | — |
| 20 | #89041 | — | 2 | 1 | no | — |
| 21 | #89040 | C22 | 1 | 1 | yes | characteristic |
| 22 | C3×#3811 | C22 | 1 | 2 | yes | — |
| 23 | C3×#3805 | — | 2 | 1 | no | — |
| 24 | C3×#3802 | C22 | 1 | 1 | yes | characteristic |
| 25 | C3×C4×D32 | C22 | 1 | 2 | yes | — |
| 26 | C3×#3798 | — | 2 | 1 | no | — |
| 27 | C3×#3797 | C22 | 1 | 1 | yes | characteristic |
| 28 | C3×#3796 | — | 2 | 1 | no | — |
| 29 | C4⋊(C3⋊#157) | C22 | 1 | 2 | yes | — |
| 30 | C4⋊(C3⋊#157) | C22 | 1 | 2 | yes | — |
| 31 | #88934 | C22 | 1 | 4 | yes | — |
| 32 | D32⋊Dic3 | C22 | 1 | 4 | yes | — |
| 33 | #88932 | C22 | 1 | 4 | yes | — |
| 34 | C3×D3×#41 | — | 6 | 1 | no | — |
| 35 | #64306 | — | 3 | 1 | no | — |
| 36 | #64306 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | D3×#235 | — | 6 | 1 | no | — |
| 38 | C2×C4⋊#157 | — | 3 | 1 | no | — |
| 39 | #64242 | — | 3 | 4 | no | — |
| 40 | #64230 | — | 3 | 2 | no | — |
| 41 | #64230 | — | 3 | 2 | no | — |
| 42 | D32⋊Q8 | — | 3 | 2 | no | — |
| 43 | D32⋊Q8 | — | 3 | 2 | no | — |
| 44 | C22×C3×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 45 | C2×#1113 | C23 | 1 | 2 | yes | — |
| 46 | C2×C3×D32 | C23 | 1 | 2 | yes | — |
| 47 | C2×C3⋊#157 | — | 4 | 2 | no | — |
| 48 | C2×C3⋊#157 | C23 | 1 | 4 | yes | — |
| 49 | D32⋊D3 | — | 4 | 4 | no | — |
| 50 | C2×C33×C4 | D4 | 1 | 1 | yes | characteristic, complemented |
| 51 | C3×#638 | — | 2 | 2 | no | — |
| 52 | C2×C3×C3⋊Dic3 | D4 | 1 | 1 | yes | characteristic, complemented |
| 53 | C3×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 54 | C3×C4×C3⋊D3 | — | 2 | 2 | no | — |
| 55 | C3×C4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic, complemented |
| 56 | C3×C4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic, complemented |
| 57 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 58 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 59 | C3×#634 | — | 2 | 1 | no | — |
| 60 | C32×#67 | — | 2 | 2 | no | — |
| 61 | C32×D12 | — | 2 | 1 | no | — |
| 62 | C32×C4×D3 | — | 2 | 2 | no | — |
| 63 | C32×Dic6 | — | 2 | 1 | no | — |
| 64 | #6296 | — | 2 | 1 | no | — |
| 65 | #6295 | — | 2 | 2 | no | — |
| 66 | #6295 | — | 2 | 1 | no | — |
| 67 | #6294 | — | 2 | 2 | no | — |
| 68 | #6294 | C23 | 1 | 2 | yes | — |
| 69 | C3×#627 | — | 2 | 1 | no | — |
| 70 | C3×#626 | — | 2 | 2 | no | — |
| 71 | C3×#625 | — | 2 | 1 | no | — |
| 72 | C3×#624 | C23 | 1 | 2 | yes | — |
| 73 | C3×D3×Dic3 | — | 2 | 2 | no | — |
| 74 | #5833 | — | 9 | 1 | no | maximal |
| 75 | C22×#157 | — | 3 | 2 | no | — |
| 76 | C2×GO+(4,𝔽2) | — | 3 | 4 | no | — |
| 77 | C32×#41 | — | 6 | 1 | no | — |
| 78 | #3828 | — | 2 | 1 | no | — |
| 79 | C2×C4×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 80 | C3×#239 | — | 6 | 1 | no | — |
| 81 | C3×D3×Q8 | — | 6 | 1 | no | — |
| 82 | C3×#237 | — | 6 | 1 | no | — |
| 83 | C3×#237 | — | 6 | 2 | no | — |
| 84 | C3×D3×D4 | — | 6 | 1 | no | — |
| 85 | C3×D3×D4 | — | 6 | 2 | no | — |
| 86 | C3×#235 | — | 2 | 1 | no | — |
| 87 | C3×#235 | — | 2 | 1 | no | — |
| 88 | C3×#235 | — | 4 | 1 | no | — |
| 89 | C3×#235 | — | 6 | 2 | no | — |
| 90 | C3×#235 | — | 6 | 1 | no | — |
| 91 | C3×#235 | — | 6 | 1 | no | — |
| 92 | C3×#235 | — | 12 | 1 | no | — |
| 93 | C2×C3×C4×D3 | — | 6 | 2 | no | — |
| 94 | C2×C3×C4×D3 | — | 6 | 1 | no | — |
| 95 | C2×C3×C4×D3 | — | 6 | 1 | no | — |
| 96 | #3811 | — | 3 | 2 | no | — |
| 97 | #3811 | C2×D3 | 1 | 2 | yes | — |
| 98 | D3×#67 | — | 6 | 2 | no | — |
| 99 | #3805 | — | 2 | 1 | no | — |
| 100 | #3805 | — | 6 | 1 | no | — |
| 101 | #3804 | — | 6 | 2 | no | — |
| 102 | #3802 | — | 3 | 1 | no | — |
| 103 | #3802 | C2×D3 | 1 | 1 | yes | characteristic |
| 104 | D3×D12 | — | 6 | 1 | no | — |
| 105 | C4×D32 | — | 3 | 2 | no | — |
| 106 | C4×D32 | — | 6 | 2 | no | — |
| 107 | C4×D32 | C2×D3 | 1 | 2 | yes | — |
| 108 | #3799 | — | 6 | 1 | no | — |
| 109 | #3798 | — | 2 | 1 | no | — |
| 110 | #3798 | — | 6 | 2 | no | — |
| 111 | #3798 | — | 6 | 1 | no | — |
| 112 | #3797 | — | 3 | 1 | no | — |
| 113 | #3797 | C2×D3 | 1 | 1 | yes | characteristic |
| 114 | #3796 | — | 2 | 1 | no | — |
| 115 | #3796 | — | 6 | 1 | no | — |
| 116 | #3795 | — | 6 | 1 | no | — |
| 117 | D3×Dic6 | — | 6 | 1 | no | — |
| 118 | C4⋊#157 | — | 3 | 2 | no | — |
| 119 | C4⋊#157 | — | 3 | 2 | no | — |
| 120 | #3773 | — | 3 | 4 | no | — |
| 121 | D32⋊C4 | — | 3 | 4 | no | — |
| 122 | D32⋊C4 | — | 3 | 4 | no | — |
| 123 | C22×C33 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 125 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 126 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 127 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 128 | C2×C3×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 129 | C2×C32×D3 | — | 2 | 2 | no | — |
| 130 | #1113 | — | 2 | 2 | no | — |
| 131 | #1113 | — | 2 | 2 | no | — |
| 132 | C3×D32 | — | 2 | 2 | no | — |
| 133 | C3×D32 | — | 2 | 2 | no | — |
| 134 | C3⋊#157 | — | 2 | 4 | no | — |
| 135 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 138 | C3×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C3×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 140 | C32×Dic3 | — | 2 | 2 | no | — |
| 141 | C2×C3×#41 | — | 9 | 1 | no | — |
| 142 | D3×#41 | — | 6 | 1 | no | — |
| 143 | D3×#41 | — | 18 | 1 | no | — |
| 144 | C2×#235 | — | 9 | 1 | no | — |
| 145 | #946 | — | 9 | 2 | no | — |
| 146 | #939 | — | 9 | 4 | no | — |
| 147 | #938 | — | 9 | 2 | no | — |
| 148 | #930 | — | 9 | 2 | no | — |
| 149 | C2×C4⋊Dic3 | — | 9 | 1 | no | — |
| 150 | #924 | — | 9 | 2 | no | — |
| 151 | C22×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 152 | C22×C3×D3 | — | 6 | 2 | no | — |
| 153 | C22×C3×D3 | — | 6 | 1 | no | — |
| 154 | C22×C3×D3 | — | 6 | 1 | no | — |
| 155 | C2×D32 | — | 3 | 2 | no | — |
| 156 | C2×D32 | — | 6 | 2 | no | — |
| 157 | C2×D32 | C22×D3 | 1 | 2 | yes | — |
| 158 | C2×#157 | — | 3 | 4 | no | — |
| 159 | C2×#157 | — | 12 | 2 | no | — |
| 160 | GO+(4,𝔽2) | — | 12 | 4 | no | — |
| 161 | C32×Q8 | — | 6 | 1 | no | — |
| 162 | C32×D4 | — | 6 | 1 | no | — |
| 163 | C32×D4 | — | 6 | 2 | no | — |
| 164 | C2×C32×C4 | — | 2 | 1 | no | — |
| 165 | C2×C32×C4 | — | 2 | 1 | no | — |
| 166 | C2×C32×C4 | — | 4 | 1 | no | — |
| 167 | C2×C32×C4 | — | 4 | 1 | no | — |
| 168 | C2×C32×C4 | — | 6 | 2 | no | — |
| 169 | C2×C32×C4 | #67 | 1 | 1 | yes | characteristic, complemented |
| 170 | #638 | — | 2 | 2 | no | — |
| 171 | C2×C3⋊Dic3 | #67 | 1 | 1 | yes | characteristic, complemented |
| 172 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 173 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 174 | C4×C3⋊D3 | #67 | 1 | 1 | yes | characteristic, complemented |
| 175 | C4×C3⋊D3 | #67 | 1 | 1 | yes | characteristic, complemented |
| 176 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 177 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 178 | #634 | — | 2 | 1 | no | — |
| 179 | C3×#67 | — | 2 | 2 | no | — |
| 180 | C3×#67 | — | 2 | 2 | no | — |
| 181 | C3×#67 | — | 4 | 2 | no | — |
| 182 | C3×#67 | — | 6 | 2 | no | — |
| 183 | C3×#67 | — | 6 | 2 | no | — |
| 184 | C3×#67 | — | 6 | 2 | no | — |
| 185 | C3×#67 | — | 6 | 2 | no | — |
| 186 | C3×#67 | — | 12 | 2 | no | — |
| 187 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 188 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 189 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 190 | C3×D12 | — | 2 | 1 | no | — |
| 191 | C3×D12 | — | 2 | 1 | no | — |
| 192 | C3×D12 | — | 4 | 1 | no | — |
| 193 | C3×D12 | — | 6 | 1 | no | — |
| 194 | C3×D12 | — | 6 | 2 | no | — |
| 195 | C3×D12 | — | 6 | 1 | no | — |
| 196 | C3×D12 | — | 12 | 1 | no | — |
| 197 | C3×C4×D3 | — | 2 | 2 | no | — |
| 198 | C3×C4×D3 | — | 2 | 2 | no | — |
| 199 | C3×C4×D3 | — | 4 | 2 | no | — |
| 200 | C3×C4×D3 | — | 6 | 2 | no | — |
| 201 | C3×C4×D3 | — | 6 | 1 | no | — |
| 202 | C3×C4×D3 | — | 6 | 1 | no | — |
| 203 | C3×C4×D3 | — | 6 | 1 | no | — |
| 204 | C3×C4×D3 | — | 6 | 1 | no | — |
| 205 | C3×C4×D3 | — | 6 | 1 | no | — |
| 206 | C3×C4×D3 | — | 6 | 1 | no | — |
| 207 | C3×C4×D3 | — | 6 | 1 | no | — |
| 208 | C3×C4×D3 | — | 6 | 1 | no | — |
| 209 | C3×C4×D3 | — | 6 | 2 | no | — |
| 210 | C3×C4×D3 | — | 6 | 2 | no | — |
| 211 | C3×C4×D3 | — | 6 | 2 | no | — |
| 212 | C3×C4×D3 | — | 12 | 2 | no | — |
| 213 | C3×Dic6 | — | 2 | 1 | no | — |
| 214 | C3×Dic6 | — | 2 | 1 | no | — |
| 215 | C3×Dic6 | — | 4 | 1 | no | — |
| 216 | C3×Dic6 | — | 6 | 2 | no | — |
| 217 | C3×Dic6 | — | 6 | 1 | no | — |
| 218 | C3×Dic6 | — | 6 | 1 | no | — |
| 219 | C3×Dic6 | — | 12 | 1 | no | — |
| 220 | #627 | — | 2 | 1 | no | — |
| 221 | #627 | — | 6 | 2 | no | — |
| 222 | #627 | — | 6 | 1 | no | — |
| 223 | #626 | — | 2 | 2 | no | — |
| 224 | #626 | — | 6 | 2 | no | — |
| 225 | #626 | — | 6 | 2 | no | — |
| 226 | #626 | — | 6 | 2 | no | — |
| 227 | #625 | — | 2 | 1 | no | — |
| 228 | #625 | — | 6 | 2 | no | — |
| 229 | #625 | — | 6 | 1 | no | — |
| 230 | #624 | — | 3 | 2 | no | — |
| 231 | #624 | — | 6 | 2 | no | — |
| 232 | #624 | C22×D3 | 1 | 2 | yes | — |
| 233 | D3×Dic3 | — | 2 | 2 | no | — |
| 234 | D3×Dic3 | — | 6 | 2 | no | — |
| 235 | D3×Dic3 | — | 6 | 2 | no | — |
| 236 | D3×Dic3 | — | 6 | 2 | no | — |
| 237 | #537 | — | 27 | 1 | no | Sylow |
| 238 | C2×C33 | — | 2 | 1 | no | — |
| 239 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 240 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 241 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 242 | C3×C3⋊D3 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 243 | C3×C3⋊D3 | 2−1+4 | 1 | 1 | yes | characteristic |
| 244 | C32×D3 | — | 4 | 2 | no | — |
| 245 | C3×#41 | — | 6 | 1 | no | — |
| 246 | C3×#41 | — | 6 | 1 | no | — |
| 247 | C3×#41 | — | 12 | 1 | no | — |
| 248 | C3×#41 | — | 18 | 1 | no | — |
| 249 | C3×#41 | — | 18 | 1 | no | — |
| 250 | C3×#41 | — | 18 | 1 | no | — |
| 251 | C3×#41 | — | 18 | 1 | no | — |
| 252 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 253 | C2×C3×D4 | — | 9 | 1 | no | — |
| 254 | C2×C3×D4 | — | 9 | 2 | no | — |
| 255 | C22×C3×C4 | — | 9 | 2 | no | — |
| 256 | C22×C3×C4 | — | 9 | 1 | no | — |
| 257 | C2×#67 | — | 9 | 2 | no | — |
| 258 | C2×#67 | — | 9 | 4 | no | — |
| 259 | C22×Dic3 | — | 9 | 2 | no | — |
| 260 | #239 | — | 6 | 1 | no | — |
| 261 | #239 | — | 18 | 1 | no | — |
| 262 | D3×Q8 | — | 6 | 1 | no | — |
| 263 | D3×Q8 | — | 18 | 1 | no | — |
| 264 | #237 | — | 6 | 1 | no | — |
| 265 | #237 | — | 6 | 2 | no | — |
| 266 | #237 | — | 18 | 1 | no | — |
| 267 | #237 | — | 18 | 2 | no | — |
| 268 | D3×D4 | — | 6 | 1 | no | — |
| 269 | D3×D4 | — | 6 | 2 | no | — |
| 270 | D3×D4 | — | 18 | 1 | no | — |
| 271 | D3×D4 | — | 18 | 2 | no | — |
| 272 | #235 | — | 2 | 1 | no | — |
| 273 | #235 | — | 6 | 2 | no | — |
| 274 | #235 | — | 6 | 1 | no | — |
| 275 | #235 | — | 6 | 1 | no | — |
| 276 | #235 | — | 12 | 1 | no | — |
| 277 | #235 | — | 18 | 1 | no | — |
| 278 | #235 | — | 18 | 1 | no | — |
| 279 | #235 | — | 18 | 2 | no | — |
| 280 | #235 | — | 18 | 1 | no | — |
| 281 | C2×D12 | — | 9 | 1 | no | — |
| 282 | C2×C4×D3 | — | 6 | 2 | no | — |
| 283 | C2×C4×D3 | — | 6 | 1 | no | — |
| 284 | C2×C4×D3 | — | 6 | 1 | no | — |
| 285 | C2×C4×D3 | — | 9 | 2 | no | — |
| 286 | C2×C4×D3 | — | 18 | 2 | no | — |
| 287 | C2×Dic6 | — | 9 | 1 | no | — |
| 288 | #217 | — | 9 | 4 | no | — |
| 289 | (C2×D3)⋊C4 | — | 9 | 4 | no | — |
| 290 | C4⋊Dic3 | — | 9 | 2 | no | — |
| 291 | C4⋊Dic3 | — | 9 | 2 | no | — |
| 292 | Dic3⋊C4 | — | 9 | 4 | no | — |
| 293 | C22×C32 | — | 2 | 1 | no | — |
| 294 | C22×C32 | — | 2 | 1 | no | — |
| 295 | C22×C32 | — | 4 | 1 | no | — |
| 296 | C22×C32 | — | 4 | 1 | no | — |
| 297 | C22×C32 | — | 6 | 2 | no | — |
| 298 | C22×C32 | C2×#67 | 1 | 1 | yes | characteristic |
| 299 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 300 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 301 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 302 | C2×C3⋊D3 | C2×#67 | 1 | 1 | yes | characteristic |
| 303 | C2×C3⋊D3 | C23×D3 | 1 | 1 | yes | characteristic |
| 304 | C2×C3×D3 | — | 2 | 2 | no | — |
| 305 | C2×C3×D3 | — | 2 | 2 | no | — |
| 306 | C2×C3×D3 | — | 4 | 2 | no | — |
| 307 | C2×C3×D3 | — | 6 | 1 | no | — |
| 308 | C2×C3×D3 | — | 6 | 1 | no | — |
| 309 | C2×C3×D3 | — | 6 | 1 | no | — |
| 310 | C2×C3×D3 | — | 6 | 1 | no | — |
| 311 | C2×C3×D3 | — | 6 | 2 | no | — |
| 312 | C2×C3×D3 | — | 6 | 2 | no | — |
| 313 | C2×C3×D3 | — | 12 | 2 | no | — |
| 314 | C2×C3×D3 | — | 12 | 2 | no | — |
| 315 | C2×C3×D3 | — | 12 | 1 | no | — |
| 316 | C2×C3×D3 | — | 12 | 1 | no | — |
| 317 | C2×C3×D3 | — | 12 | 1 | no | — |
| 318 | C2×C3×D3 | — | 12 | 1 | no | — |
| 319 | C2×C3×D3 | — | 12 | 2 | no | — |
| 320 | D32 | — | 2 | 2 | no | — |
| 321 | D32 | — | 2 | 2 | no | — |
| 322 | D32 | — | 6 | 2 | no | — |
| 323 | D32 | — | 6 | 2 | no | — |
| 324 | D32 | — | 12 | 2 | no | — |
| 325 | D32 | — | 12 | 2 | no | — |
| 326 | #157 | — | 6 | 4 | no | — |
| 327 | C32×C4 | — | 2 | 1 | no | — |
| 328 | C32×C4 | — | 2 | 1 | no | — |
| 329 | C32×C4 | — | 2 | 1 | no | — |
| 330 | C32×C4 | — | 2 | 1 | no | — |
| 331 | C32×C4 | — | 4 | 1 | no | — |
| 332 | C32×C4 | — | 4 | 1 | no | — |
| 333 | C32×C4 | — | 4 | 1 | no | — |
| 334 | C32×C4 | — | 4 | 1 | no | — |
| 335 | C32×C4 | — | 6 | 2 | no | — |
| 336 | C32×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 337 | C32×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 338 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 339 | C3⋊Dic3 | C2×#67 | 1 | 1 | yes | characteristic |
| 340 | C3⋊Dic3 | C2×#67 | 1 | 1 | yes | characteristic |
| 341 | C3×Dic3 | — | 2 | 2 | no | — |
| 342 | C3×Dic3 | — | 2 | 2 | no | — |
| 343 | C3×Dic3 | — | 4 | 2 | no | — |
| 344 | C3×Dic3 | — | 6 | 1 | no | — |
| 345 | C3×Dic3 | — | 6 | 1 | no | — |
| 346 | C3×Dic3 | — | 6 | 1 | no | — |
| 347 | C3×Dic3 | — | 6 | 1 | no | — |
| 348 | C3×Dic3 | — | 6 | 2 | no | — |
| 349 | C3×Dic3 | — | 6 | 2 | no | — |
| 350 | C3×Dic3 | — | 12 | 2 | no | — |
| 351 | C2×#41 | — | 9 | 1 | no | — |
| 352 | C2×#41 | — | 27 | 1 | no | — |
| 353 | C22⋊Q8 | — | 27 | 2 | no | — |
| 354 | C22⋊Q8 | — | 27 | 2 | no | — |
| 355 | #121 | — | 27 | 2 | no | — |
| 356 | #121 | — | 27 | 2 | no | — |
| 357 | #121 | — | 27 | 4 | no | — |
| 358 | C2×C4⋊C4 | — | 27 | 1 | no | — |
| 359 | C33 | #537 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 360 | C23×C3 | — | 9 | 2 | no | — |
| 361 | C23×C3 | — | 9 | 1 | no | — |
| 362 | C22×D3 | — | 6 | 2 | no | — |
| 363 | C22×D3 | — | 6 | 1 | no | — |
| 364 | C22×D3 | — | 6 | 1 | no | — |
| 365 | C22×D3 | — | 9 | 2 | no | — |
| 366 | C22×D3 | — | 18 | 2 | no | — |
| 367 | C3×Q8 | — | 6 | 1 | no | — |
| 368 | C3×Q8 | — | 6 | 1 | no | — |
| 369 | C3×Q8 | — | 12 | 1 | no | — |
| 370 | C3×Q8 | — | 18 | 1 | no | — |
| 371 | C3×Q8 | — | 18 | 1 | no | — |
| 372 | C3×D4 | — | 6 | 1 | no | — |
| 373 | C3×D4 | — | 6 | 2 | no | — |
| 374 | C3×D4 | — | 6 | 2 | no | — |
| 375 | C3×D4 | — | 6 | 1 | no | — |
| 376 | C3×D4 | — | 12 | 1 | no | — |
| 377 | C3×D4 | — | 12 | 2 | no | — |
| 378 | C3×D4 | — | 18 | 1 | no | — |
| 379 | C3×D4 | — | 18 | 2 | no | — |
| 380 | C3×D4 | — | 18 | 1 | no | — |
| 381 | C3×D4 | — | 18 | 2 | no | — |
| 382 | C2×C3×C4 | — | 2 | 1 | no | — |
| 383 | C2×C3×C4 | — | 2 | 1 | no | — |
| 384 | C2×C3×C4 | — | 4 | 1 | no | — |
| 385 | C2×C3×C4 | — | 4 | 1 | no | — |
| 386 | C2×C3×C4 | — | 6 | 2 | no | — |
| 387 | C2×C3×C4 | — | 6 | 2 | no | — |
| 388 | C2×C3×C4 | — | 9 | 2 | no | — |
| 389 | C2×C3×C4 | — | 9 | 1 | no | — |
| 390 | C2×C3×C4 | — | 9 | 1 | no | — |
| 391 | C2×C3×C4 | — | 9 | 1 | no | — |
| 392 | C2×C3×C4 | — | 9 | 1 | no | — |
| 393 | C2×C3×C4 | — | 9 | 1 | no | — |
| 394 | C2×C3×C4 | — | 12 | 2 | no | — |
| 395 | C2×C3×C4 | — | 18 | 2 | no | — |
| 396 | C2×C3×C4 | — | 18 | 2 | no | — |
| 397 | C2×C3×C4 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 398 | #67 | — | 2 | 2 | no | — |
| 399 | #67 | — | 6 | 2 | no | — |
| 400 | #67 | — | 6 | 2 | no | — |
| 401 | #67 | — | 6 | 2 | no | — |
| 402 | #67 | — | 6 | 2 | no | — |
| 403 | #67 | — | 12 | 2 | no | — |
| 404 | #67 | — | 18 | 2 | no | — |
| 405 | #67 | — | 18 | 2 | no | — |
| 406 | #67 | — | 18 | 2 | no | — |
| 407 | #67 | — | 36 | 4 | no | — |
| 408 | C2×Dic3 | — | 6 | 1 | no | — |
| 409 | C2×Dic3 | — | 6 | 1 | no | — |
| 410 | C2×Dic3 | — | 6 | 2 | no | — |
| 411 | C2×Dic3 | — | 9 | 2 | no | — |
| 412 | C2×Dic3 | — | 9 | 4 | no | — |
| 413 | C2×Dic3 | — | 18 | 2 | no | — |
| 414 | C2×Dic3 | — | 36 | 2 | no | — |
| 415 | D12 | — | 2 | 1 | no | — |
| 416 | D12 | — | 6 | 1 | no | — |
| 417 | D12 | — | 6 | 2 | no | — |
| 418 | D12 | — | 6 | 1 | no | — |
| 419 | D12 | — | 12 | 1 | no | — |
| 420 | D12 | — | 18 | 1 | no | — |
| 421 | D12 | — | 18 | 2 | no | — |
| 422 | C4×D3 | — | 2 | 2 | no | — |
| 423 | C4×D3 | — | 6 | 2 | no | — |
| 424 | C4×D3 | — | 6 | 1 | no | — |
| 425 | C4×D3 | — | 6 | 1 | no | — |
| 426 | C4×D3 | — | 6 | 1 | no | — |
| 427 | C4×D3 | — | 6 | 1 | no | — |
| 428 | C4×D3 | — | 6 | 1 | no | — |
| 429 | C4×D3 | — | 6 | 1 | no | — |
| 430 | C4×D3 | — | 6 | 1 | no | — |
| 431 | C4×D3 | — | 6 | 1 | no | — |
| 432 | C4×D3 | — | 6 | 2 | no | — |
| 433 | C4×D3 | — | 6 | 2 | no | — |
| 434 | C4×D3 | — | 6 | 2 | no | — |
| 435 | C4×D3 | — | 12 | 2 | no | — |
| 436 | C4×D3 | — | 18 | 2 | no | — |
| 437 | C4×D3 | — | 18 | 2 | no | — |
| 438 | C4×D3 | — | 18 | 2 | no | — |
| 439 | Dic6 | — | 2 | 1 | no | — |
| 440 | Dic6 | — | 6 | 2 | no | — |
| 441 | Dic6 | — | 6 | 1 | no | — |
| 442 | Dic6 | — | 6 | 1 | no | — |
| 443 | Dic6 | — | 12 | 1 | no | — |
| 444 | Dic6 | — | 18 | 1 | no | — |
| 445 | Dic6 | — | 18 | 2 | no | — |
| 446 | C2×C32 | — | 2 | 1 | no | — |
| 447 | C2×C32 | — | 2 | 1 | no | — |
| 448 | C2×C32 | — | 2 | 1 | no | — |
| 449 | C2×C32 | — | 4 | 1 | no | — |
| 450 | C2×C32 | — | 4 | 1 | no | — |
| 451 | C2×C32 | — | 4 | 1 | no | — |
| 452 | C2×C32 | — | 4 | 1 | no | — |
| 453 | C2×C32 | — | 8 | 1 | no | — |
| 454 | C2×C32 | — | 8 | 1 | no | — |
| 455 | C2×C32 | — | 12 | 2 | no | — |
| 456 | C2×C32 | C22×#67 | 1 | 1 | yes | characteristic |
| 457 | C3⋊D3 | — | 2 | 1 | no | — |
| 458 | C3⋊D3 | — | 4 | 2 | no | — |
| 459 | C3⋊D3 | #1009 | 1 | 1 | yes | characteristic |
| 460 | C3⋊D3 | #1010 | 1 | 1 | yes | characteristic |
| 461 | C3×D3 | — | 4 | 2 | no | — |
| 462 | C3×D3 | — | 4 | 2 | no | — |
| 463 | C3×D3 | — | 6 | 1 | no | — |
| 464 | C3×D3 | — | 6 | 1 | no | — |
| 465 | C3×D3 | — | 6 | 1 | no | — |
| 466 | C3×D3 | — | 6 | 1 | no | — |
| 467 | C3×D3 | — | 8 | 2 | no | — |
| 468 | C3×D3 | — | 12 | 1 | no | — |
| 469 | C3×D3 | — | 12 | 1 | no | — |
| 470 | C3×D3 | — | 12 | 2 | no | — |
| 471 | C3×D3 | — | 12 | 2 | no | — |
| 472 | C3×D3 | — | 24 | 2 | no | — |
| 473 | #41 | — | 6 | 1 | no | — |
| 474 | #41 | — | 18 | 1 | no | — |
| 475 | #41 | — | 18 | 1 | no | — |
| 476 | #41 | — | 18 | 1 | no | — |
| 477 | #41 | — | 18 | 1 | no | — |
| 478 | #41 | — | 54 | 1 | no | — |
| 479 | #41 | — | 54 | 1 | no | — |
| 480 | #41 | — | 54 | 1 | no | — |
| 481 | C2×Q8 | — | 9 | 1 | no | — |
| 482 | C2×Q8 | — | 27 | 1 | no | — |
| 483 | C2×D4 | — | 9 | 2 | no | — |
| 484 | C2×D4 | — | 9 | 1 | no | — |
| 485 | C2×D4 | — | 27 | 1 | no | — |
| 486 | C2×D4 | — | 27 | 2 | no | — |
| 487 | C2×D4 | — | 27 | 4 | no | — |
| 488 | C22×C4 | — | 9 | 2 | no | — |
| 489 | C22×C4 | — | 9 | 1 | no | — |
| 490 | C22×C4 | — | 27 | 2 | no | — |
| 491 | C22×C4 | — | 27 | 2 | no | — |
| 492 | C4⋊C4 | — | 27 | 2 | no | — |
| 493 | C4⋊C4 | — | 27 | 2 | no | — |
| 494 | C4⋊C4 | — | 27 | 4 | no | — |
| 495 | C22⋊C4 | — | 27 | 4 | no | — |
| 496 | C22⋊C4 | — | 27 | 4 | no | — |
| 497 | C22×C3 | — | 2 | 1 | no | — |
| 498 | C22×C3 | — | 2 | 1 | no | — |
| 499 | C22×C3 | — | 4 | 1 | no | — |
| 500 | C22×C3 | — | 4 | 1 | no | — |
| 501 | C22×C3 | — | 6 | 2 | no | — |
| 502 | C22×C3 | — | 6 | 2 | no | — |
| 503 | C22×C3 | — | 9 | 1 | no | — |
| 504 | C22×C3 | — | 9 | 1 | no | — |
| 505 | C22×C3 | — | 12 | 2 | no | — |
| 506 | C22×C3 | — | 18 | 1 | no | — |
| 507 | C22×C3 | — | 18 | 1 | no | — |
| 508 | C22×C3 | — | 18 | 2 | no | — |
| 509 | C22×C3 | — | 18 | 2 | no | — |
| 510 | C22×C3 | — | 18 | 2 | no | — |
| 511 | C22×C3 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 512 | C2×D3 | — | 2 | 2 | no | — |
| 513 | C2×D3 | — | 6 | 1 | no | — |
| 514 | C2×D3 | — | 6 | 1 | no | — |
| 515 | C2×D3 | — | 6 | 1 | no | — |
| 516 | C2×D3 | — | 6 | 1 | no | — |
| 517 | C2×D3 | — | 6 | 2 | no | — |
| 518 | C2×D3 | — | 6 | 2 | no | — |
| 519 | C2×D3 | — | 12 | 2 | no | — |
| 520 | C2×D3 | — | 12 | 2 | no | — |
| 521 | C2×D3 | — | 12 | 1 | no | — |
| 522 | C2×D3 | — | 12 | 1 | no | — |
| 523 | C2×D3 | — | 12 | 1 | no | — |
| 524 | C2×D3 | — | 12 | 1 | no | — |
| 525 | C2×D3 | — | 12 | 2 | no | — |
| 526 | C2×D3 | — | 18 | 2 | no | — |
| 527 | C2×D3 | — | 18 | 2 | no | — |
| 528 | C2×D3 | — | 36 | 2 | no | — |
| 529 | C2×D3 | — | 36 | 2 | no | — |
| 530 | C3×C4 | — | 2 | 1 | no | — |
| 531 | C3×C4 | — | 2 | 1 | no | — |
| 532 | C3×C4 | — | 2 | 1 | no | — |
| 533 | C3×C4 | — | 2 | 1 | no | — |
| 534 | C3×C4 | — | 4 | 1 | no | — |
| 535 | C3×C4 | — | 4 | 1 | no | — |
| 536 | C3×C4 | — | 4 | 1 | no | — |
| 537 | C3×C4 | — | 4 | 1 | no | — |
| 538 | C3×C4 | — | 6 | 2 | no | — |
| 539 | C3×C4 | — | 6 | 2 | no | — |
| 540 | C3×C4 | — | 9 | 1 | no | — |
| 541 | C3×C4 | — | 9 | 1 | no | — |
| 542 | C3×C4 | — | 12 | 2 | no | — |
| 543 | C3×C4 | — | 18 | 2 | no | — |
| 544 | C3×C4 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 545 | C3×C4 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 546 | Dic3 | — | 2 | 2 | no | — |
| 547 | Dic3 | — | 6 | 1 | no | — |
| 548 | Dic3 | — | 6 | 1 | no | — |
| 549 | Dic3 | — | 6 | 1 | no | — |
| 550 | Dic3 | — | 6 | 1 | no | — |
| 551 | Dic3 | — | 6 | 2 | no | — |
| 552 | Dic3 | — | 6 | 2 | no | — |
| 553 | Dic3 | — | 12 | 2 | no | — |
| 554 | Dic3 | — | 18 | 4 | no | — |
| 555 | C32 | — | 2 | 1 | no | — |
| 556 | C32 | — | 2 | 1 | no | — |
| 557 | C32 | — | 4 | 1 | no | — |
| 558 | C32 | — | 4 | 1 | no | — |
| 559 | C32 | #5833 | 1 | 1 | yes | characteristic, complemented |
| 560 | C23 | — | 9 | 2 | no | — |
| 561 | C23 | — | 9 | 1 | no | — |
| 562 | C23 | — | 27 | 2 | no | — |
| 563 | Q8 | — | 6 | 1 | no | — |
| 564 | Q8 | — | 18 | 1 | no | — |
| 565 | Q8 | — | 18 | 1 | no | — |
| 566 | Q8 | — | 54 | 1 | no | — |
| 567 | D4 | — | 6 | 2 | no | — |
| 568 | D4 | — | 6 | 1 | no | — |
| 569 | D4 | — | 18 | 2 | no | — |
| 570 | D4 | — | 18 | 1 | no | — |
| 571 | D4 | — | 18 | 2 | no | — |
| 572 | D4 | — | 18 | 1 | no | — |
| 573 | D4 | — | 54 | 1 | no | — |
| 574 | D4 | — | 54 | 2 | no | — |
| 575 | D4 | — | 108 | 4 | no | — |
| 576 | C2×C4 | — | 6 | 2 | no | — |
| 577 | C2×C4 | — | 9 | 2 | no | — |
| 578 | C2×C4 | — | 9 | 1 | no | — |
| 579 | C2×C4 | — | 9 | 1 | no | — |
| 580 | C2×C4 | — | 9 | 1 | no | — |
| 581 | C2×C4 | — | 9 | 1 | no | — |
| 582 | C2×C4 | — | 9 | 1 | no | — |
| 583 | C2×C4 | — | 18 | 2 | no | — |
| 584 | C2×C4 | — | 18 | 2 | no | — |
| 585 | C2×C4 | — | 27 | 2 | no | — |
| 586 | C2×C4 | — | 27 | 4 | no | — |
| 587 | C2×C4 | — | 54 | 2 | no | — |
| 588 | C2×C4 | — | 108 | 2 | no | — |
| 589 | C2×C4 | D32⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 590 | C2×C3 | — | 2 | 1 | no | — |
| 591 | C2×C3 | — | 2 | 1 | no | — |
| 592 | C2×C3 | — | 2 | 1 | no | — |
| 593 | C2×C3 | — | 4 | 1 | no | — |
| 594 | C2×C3 | — | 4 | 1 | no | — |
| 595 | C2×C3 | — | 4 | 1 | no | — |
| 596 | C2×C3 | — | 4 | 1 | no | — |
| 597 | C2×C3 | — | 8 | 1 | no | — |
| 598 | C2×C3 | — | 8 | 1 | no | — |
| 599 | C2×C3 | — | 9 | 1 | no | — |
| 600 | C2×C3 | — | 9 | 1 | no | — |
| 601 | C2×C3 | — | 12 | 2 | no | — |
| 602 | C2×C3 | — | 12 | 2 | no | — |
| 603 | C2×C3 | — | 18 | 1 | no | — |
| 604 | C2×C3 | — | 24 | 2 | no | — |
| 605 | C2×C3 | — | 36 | 2 | no | — |
| 606 | C2×C3 | C22×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 607 | D3 | — | 4 | 2 | no | — |
| 608 | D3 | — | 6 | 1 | no | — |
| 609 | D3 | — | 6 | 1 | no | — |
| 610 | D3 | — | 6 | 1 | no | — |
| 611 | D3 | — | 6 | 1 | no | — |
| 612 | D3 | — | 12 | 1 | no | — |
| 613 | D3 | — | 12 | 1 | no | — |
| 614 | D3 | — | 12 | 2 | no | — |
| 615 | D3 | — | 12 | 2 | no | — |
| 616 | D3 | — | 24 | 2 | no | — |
| 617 | C22 | — | 6 | 2 | no | — |
| 618 | C22 | — | 9 | 1 | no | — |
| 619 | C22 | — | 9 | 1 | no | — |
| 620 | C22 | — | 18 | 1 | no | — |
| 621 | C22 | — | 18 | 1 | no | — |
| 622 | C22 | — | 18 | 2 | no | — |
| 623 | C22 | — | 18 | 2 | no | — |
| 624 | C22 | — | 18 | 2 | no | — |
| 625 | C22 | — | 54 | 2 | no | — |
| 626 | C22 | — | 54 | 2 | no | — |
| 627 | C22 | C2×D32⋊D3 | 1 | 1 | yes | characteristic |
| 628 | C4 | — | 6 | 2 | no | — |
| 629 | C4 | — | 9 | 1 | no | — |
| 630 | C4 | — | 9 | 1 | no | — |
| 631 | C4 | — | 18 | 2 | no | — |
| 632 | C4 | — | 54 | 4 | no | — |
| 633 | C4 | C2×D32⋊D3 | 1 | 1 | yes | characteristic |
| 634 | C4 | C2×D32⋊D3 | 1 | 1 | yes | characteristic |
| 635 | C3 | — | 2 | 1 | no | — |
| 636 | C3 | — | 2 | 1 | no | — |
| 637 | C3 | — | 4 | 1 | no | — |
| 638 | C3 | — | 4 | 1 | no | — |
| 639 | C3 | #10596513 | 1 | 1 | yes | characteristic, complemented |
| 640 | C2 | — | 2 | 1 | no | — |
| 641 | C2 | — | 9 | 1 | no | — |
| 642 | C2 | — | 9 | 1 | no | — |
| 643 | C2 | — | 12 | 2 | no | — |
| 644 | C2 | — | 18 | 1 | no | — |
| 645 | C2 | — | 36 | 2 | no | — |
| 646 | C2 | C22×D32⋊D3 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D32⋊D3 |
| commutator, cosocle | C2×C3×C3⋊D3 | C24 |
| Fitting | C2×C33×C4 | D4 |
| socle | C2×C33 | C22×D4 |
| hypercenter | C2×C4 | D32⋊D3 |
| hypocenter | C33 | #537 |
| LCS | G ▷ C2×C3×C3⋊D3 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11724618 | C2 | semidirect |
| 2. C3×#64306 | C2 | semidirect |
| 3. C2×C4⋊(C3⋊#157) | C2 | semidirect |
| 4. #11724332 | C2 | semidirect |
| 5. #11724314 | C2 | semidirect |
| 6. #11724313 | C2 | semidirect |
| 7. #11724300 | C2 | semidirect |
| 8. #11724298 | C2 | semidirect |
| 36. #64306 | D3 | semidirect |
| 50. C2×C33×C4 | D4 | semidirect |
| 52. C2×C3×C3⋊Dic3 | D4 | semidirect |
| 55. C3×C4×C3⋊D3 | D4 | semidirect |
| 56. C3×C4×C3⋊D3 | D4 | semidirect |
| 169. C2×C32×C4 | #67 | semidirect |
| 171. C2×C3⋊Dic3 | #67 | semidirect |
| 174. C4×C3⋊D3 | #67 | semidirect |
| 175. C4×C3⋊D3 | #67 | semidirect |
| 359. C33 | #537 | semidirect |
| 397. C2×C3×C4 | GO+(4,𝔽2) | semidirect |
| 559. C32 | #5833 | semidirect |
| 589. C2×C4 | D32⋊D3 | semidirect |
| 639. C3 | #10596513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724618 | 2 |
| C3×#64306 | 2 |
| C2×C4⋊(C3⋊#157) | 2 |
| #11724332 | 2 |
| #11724314 | 2 |
| #11724313 | 2 |
| #11724300 | 2 |
| #11724298 | 2 |
| #10596513 | 3 |
| #5833 | 9 |