Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
512 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 70 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 | C3⋊D3×D24 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#63810 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11722066 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11722010 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11722005 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#63547 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C3×#63545 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10591038 | — | 3 | 1 | no | maximal |
| 9 | #10591036 | — | 3 | 1 | no | maximal |
| 10 | #10591024 | — | 3 | 1 | no | maximal |
| 11 | C3⋊D3×D12 | — | 2 | 1 | no | — |
| 12 | C3×#3796 | — | 2 | 1 | no | — |
| 13 | #88852 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×C8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 15 | C32×Dic12 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C32×D24 | C22 | 1 | 1 | yes | characteristic |
| 17 | C32×D24 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #88790 | — | 2 | 1 | no | — |
| 19 | C3×#3715 | — | 2 | 1 | no | — |
| 20 | C3×C3⋊(C3⋊C16) | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C3×C3⋊(C3⋊C16) | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | D8×C3⋊D3 | — | 3 | 1 | no | — |
| 23 | C3×#919 | — | 3 | 1 | no | — |
| 24 | C3×#912 | — | 3 | 1 | no | — |
| 25 | #63810 | D3 | 1 | 1 | yes | characteristic, complemented |
| 26 | D3×D24 | — | 3 | 1 | no | — |
| 27 | D3×D24 | — | 3 | 1 | no | — |
| 28 | D3×D24 | — | 6 | 1 | no | — |
| 29 | #63655 | — | 3 | 1 | no | — |
| 30 | #63653 | — | 3 | 1 | no | — |
| 31 | C3×#828 | — | 3 | 1 | no | — |
| 32 | C3×#827 | — | 3 | 1 | no | — |
| 33 | C3×#826 | — | 3 | 1 | no | — |
| 34 | C3×#826 | — | 3 | 1 | no | — |
| 35 | #63549 | — | 3 | 1 | no | — |
| 36 | #63549 | — | 3 | 1 | no | — |
| 37 | #63549 | — | 6 | 1 | no | — |
| 38 | #63547 | D3 | 1 | 1 | yes | characteristic, complemented |
| 39 | #63546 | — | 3 | 1 | no | — |
| 40 | #63546 | — | 3 | 1 | no | — |
| 41 | #63546 | — | 6 | 1 | no | — |
| 42 | #63545 | D3 | 1 | 1 | yes | characteristic, complemented |
| 43 | #63544 | — | 3 | 1 | no | — |
| 44 | #63543 | — | 3 | 1 | no | — |
| 45 | #63543 | — | 3 | 1 | no | — |
| 46 | C2×D3×C3⋊D3 | — | 4 | 1 | no | — |
| 47 | C4⋊(C3⋊(C3⋊D3)) | — | 2 | 1 | no | — |
| 48 | C3×C4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 49 | C32×D12 | — | 2 | 1 | no | — |
| 50 | C32×D12 | — | 2 | 1 | no | — |
| 51 | C32×Dic6 | — | 2 | 1 | no | — |
| 52 | #6291 | — | 4 | 1 | no | — |
| 53 | C3×#626 | — | 4 | 1 | no | — |
| 54 | C3×D3×Dic3 | — | 4 | 1 | no | — |
| 55 | C33×C8 | C23 | 1 | 1 | yes | characteristic |
| 56 | C3×C3⋊(C3⋊C8) | D4 | 1 | 1 | yes | characteristic |
| 57 | #5193 | — | 9 | 1 | no | — |
| 58 | #4914 | — | 9 | 1 | no | — |
| 59 | #4911 | — | 9 | 1 | no | — |
| 60 | D4×C3⋊D3 | — | 6 | 1 | no | — |
| 61 | C3×#239 | — | 6 | 1 | no | — |
| 62 | C3×#237 | — | 6 | 1 | no | — |
| 63 | D3×D12 | — | 6 | 1 | no | — |
| 64 | D3×D12 | — | 6 | 1 | no | — |
| 65 | D3×D12 | — | 6 | 2 | no | — |
| 66 | #3796 | — | 2 | 1 | no | — |
| 67 | C32×Q16 | — | 3 | 1 | no | — |
| 68 | C32×D8 | — | 3 | 1 | no | — |
| 69 | C32×D8 | — | 3 | 1 | no | — |
| 70 | #3753 | — | 6 | 1 | no | — |
| 71 | #3745 | — | 3 | 1 | no | — |
| 72 | #3745 | — | 3 | 1 | no | — |
| 73 | #3745 | — | 3 | 1 | no | — |
| 74 | #3745 | — | 6 | 1 | no | — |
| 75 | #3745 | — | 6 | 1 | no | — |
| 76 | #3745 | — | 6 | 1 | no | — |
| 77 | #3745 | — | 12 | 1 | no | — |
| 78 | C8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 79 | C3×#215 | — | 6 | 1 | no | — |
| 80 | C3×#214 | — | 6 | 1 | no | — |
| 81 | C3×Dic12 | — | 2 | 1 | no | — |
| 82 | C3×Dic12 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 83 | C3×Dic12 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 84 | C3×D24 | — | 2 | 1 | no | — |
| 85 | C3×D24 | — | 2 | 1 | no | — |
| 86 | C3×D24 | C2×D3 | 1 | 1 | yes | characteristic |
| 87 | C3×D24 | C2×D3 | 1 | 1 | yes | characteristic |
| 88 | C3×D24 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 89 | C3×D24 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 90 | C3×D3×C8 | — | 3 | 1 | no | — |
| 91 | C3×D3×C8 | — | 3 | 1 | no | — |
| 92 | C3×D3×C8 | — | 6 | 1 | no | — |
| 93 | #3715 | — | 2 | 1 | no | — |
| 94 | #3714 | — | 6 | 1 | no | — |
| 95 | #3714 | — | 6 | 1 | no | — |
| 96 | #3714 | — | 6 | 2 | no | — |
| 97 | C3⋊(C3⋊C16) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 98 | C3⋊(C3⋊C16) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 99 | C3×C3⋊C16 | — | 3 | 1 | no | — |
| 100 | C3×C3⋊C16 | — | 3 | 1 | no | — |
| 101 | C3×C3⋊C16 | — | 3 | 1 | no | — |
| 102 | C3×C3⋊C16 | — | 3 | 1 | no | — |
| 103 | C3×C3⋊C16 | — | 6 | 1 | no | — |
| 104 | C3×C3⋊C16 | — | 6 | 1 | no | — |
| 105 | C2×C3⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 106 | C2×C3×C3⋊D3 | D8 | 1 | 1 | yes | characteristic |
| 107 | C2×C32×D3 | — | 4 | 1 | no | — |
| 108 | C2×C32×D3 | — | 4 | 1 | no | — |
| 109 | D3×C3⋊D3 | — | 8 | 2 | no | — |
| 110 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | C3×C3⋊Dic3 | D8 | 1 | 1 | yes | characteristic |
| 112 | C32×Dic3 | — | 4 | 1 | no | — |
| 113 | C3×#135 | — | 9 | 1 | no | — |
| 114 | #919 | — | 3 | 1 | no | — |
| 115 | #912 | — | 3 | 1 | no | — |
| 116 | D3×D8 | — | 9 | 1 | no | — |
| 117 | D3×D8 | — | 9 | 1 | no | — |
| 118 | D3×D8 | — | 18 | 1 | no | — |
| 119 | C2×D24 | — | 9 | 1 | no | — |
| 120 | C3×SD32 | — | 9 | 1 | no | — |
| 121 | C3×D16 | — | 9 | 1 | no | — |
| 122 | #828 | — | 3 | 1 | no | — |
| 123 | #828 | — | 9 | 1 | no | — |
| 124 | #828 | — | 9 | 1 | no | — |
| 125 | #828 | — | 18 | 1 | no | — |
| 126 | #827 | — | 3 | 1 | no | — |
| 127 | #826 | — | 3 | 1 | no | — |
| 128 | #826 | — | 3 | 1 | no | — |
| 129 | #826 | — | 9 | 1 | no | — |
| 130 | #826 | — | 9 | 1 | no | — |
| 131 | #826 | — | 18 | 1 | no | — |
| 132 | #812 | — | 9 | 1 | no | — |
| 133 | #800 | — | 9 | 1 | no | — |
| 134 | D48 | — | 9 | 1 | no | — |
| 135 | #798 | — | 9 | 1 | no | — |
| 136 | #798 | — | 9 | 1 | no | — |
| 137 | C22×C3⋊D3 | — | 12 | 1 | no | — |
| 138 | C2×D32 | — | 12 | 1 | no | — |
| 139 | C2×D32 | — | 12 | 1 | no | — |
| 140 | C2×D32 | — | 12 | 2 | no | — |
| 141 | C32×Q8 | — | 6 | 1 | no | — |
| 142 | C32×D4 | — | 6 | 1 | no | — |
| 143 | C32×D4 | — | 6 | 1 | no | — |
| 144 | #638 | — | 12 | 1 | no | — |
| 145 | C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 146 | C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 147 | C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 148 | C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 149 | C4⋊(C3⋊D3) | — | 12 | 1 | no | — |
| 150 | C4⋊(C3⋊D3) | — | 12 | 1 | no | — |
| 151 | C4⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 152 | C4×C3⋊D3 | #67 | 1 | 1 | yes | characteristic |
| 153 | C3×#67 | — | 12 | 1 | no | — |
| 154 | C2×C3×Dic3 | — | 12 | 1 | no | — |
| 155 | C3×D12 | — | 2 | 2 | no | — |
| 156 | C3×D12 | — | 2 | 1 | no | — |
| 157 | C3×D12 | — | 2 | 1 | no | — |
| 158 | C3×D12 | — | 2 | 1 | no | — |
| 159 | C3×D12 | — | 2 | 1 | no | — |
| 160 | C3×D12 | — | 4 | 1 | no | — |
| 161 | C3×D12 | — | 12 | 1 | no | — |
| 162 | C3×C4×D3 | — | 3 | 1 | no | — |
| 163 | C3×C4×D3 | — | 3 | 1 | no | — |
| 164 | C3×C4×D3 | — | 6 | 1 | no | — |
| 165 | C3×C4×D3 | — | 12 | 1 | no | — |
| 166 | C3×Dic6 | — | 2 | 1 | no | — |
| 167 | C3×Dic6 | — | 2 | 1 | no | — |
| 168 | C3×Dic6 | — | 4 | 1 | no | — |
| 169 | #626 | — | 4 | 1 | no | — |
| 170 | #626 | — | 12 | 1 | no | — |
| 171 | #626 | — | 12 | 1 | no | — |
| 172 | #626 | — | 12 | 2 | no | — |
| 173 | D3×Dic3 | — | 4 | 1 | no | — |
| 174 | C32×C8 | — | 2 | 1 | no | — |
| 175 | C32×C8 | — | 2 | 1 | no | — |
| 176 | C32×C8 | — | 2 | 1 | no | — |
| 177 | C32×C8 | — | 4 | 1 | no | — |
| 178 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 179 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 180 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 181 | C3⋊(C3⋊C8) | #67 | 1 | 1 | yes | characteristic |
| 182 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 183 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 184 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 185 | #509 | — | 27 | 1 | no | Sylow |
| 186 | C2×C33 | C2×D8 | 1 | 1 | yes | characteristic |
| 187 | C3⋊(C3⋊D3) | — | 8 | 1 | no | — |
| 188 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 189 | C32×D3 | — | 8 | 1 | no | — |
| 190 | C32×D3 | — | 8 | 1 | no | — |
| 191 | C3×#41 | — | 18 | 1 | no | — |
| 192 | #239 | — | 6 | 1 | no | — |
| 193 | #237 | — | 6 | 1 | no | — |
| 194 | D3×D4 | — | 18 | 1 | no | — |
| 195 | D3×D4 | — | 18 | 1 | no | — |
| 196 | D3×D4 | — | 18 | 2 | no | — |
| 197 | C2×D12 | — | 18 | 1 | no | — |
| 198 | C3×Q16 | — | 3 | 1 | no | — |
| 199 | C3×Q16 | — | 3 | 1 | no | — |
| 200 | C3×Q16 | — | 6 | 1 | no | — |
| 201 | C3×SD16 | — | 18 | 1 | no | — |
| 202 | C3×D8 | — | 3 | 1 | no | — |
| 203 | C3×D8 | — | 3 | 1 | no | — |
| 204 | C3×D8 | — | 3 | 1 | no | — |
| 205 | C3×D8 | — | 3 | 1 | no | — |
| 206 | C3×D8 | — | 6 | 1 | no | — |
| 207 | C3×D8 | — | 6 | 1 | no | — |
| 208 | C2×C3×C8 | — | 9 | 1 | no | — |
| 209 | #215 | — | 6 | 1 | no | — |
| 210 | #214 | — | 6 | 1 | no | — |
| 211 | #213 | — | 18 | 1 | no | — |
| 212 | #213 | — | 18 | 1 | no | — |
| 213 | #213 | — | 18 | 2 | no | — |
| 214 | Dic12 | D32 | 1 | 1 | yes | characteristic, complemented |
| 215 | D24 | — | 9 | 1 | no | — |
| 216 | D24 | — | 9 | 1 | no | — |
| 217 | D24 | — | 9 | 1 | no | — |
| 218 | D24 | — | 18 | 1 | no | — |
| 219 | D24 | — | 18 | 1 | no | — |
| 220 | D24 | — | 18 | 1 | no | — |
| 221 | D24 | — | 18 | 1 | no | — |
| 222 | D24 | — | 36 | 1 | no | — |
| 223 | D24 | D32 | 1 | 1 | yes | characteristic |
| 224 | D24 | D32 | 1 | 1 | yes | characteristic, complemented |
| 225 | D3×C8 | — | 3 | 1 | no | — |
| 226 | D3×C8 | — | 3 | 1 | no | — |
| 227 | D3×C8 | — | 6 | 1 | no | — |
| 228 | C3×C16 | — | 9 | 1 | no | — |
| 229 | C3×C16 | — | 9 | 1 | no | — |
| 230 | C3⋊C16 | — | 3 | 1 | no | — |
| 231 | C3⋊C16 | — | 3 | 1 | no | — |
| 232 | C3⋊C16 | — | 3 | 1 | no | — |
| 233 | C3⋊C16 | — | 3 | 1 | no | — |
| 234 | C3⋊C16 | — | 6 | 1 | no | — |
| 235 | C3⋊C16 | — | 6 | 1 | no | — |
| 236 | C22×C32 | — | 12 | 1 | no | — |
| 237 | C22×C32 | — | 12 | 1 | no | — |
| 238 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 239 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 240 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 241 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 242 | C2×C3⋊D3 | — | 24 | 1 | no | — |
| 243 | C2×C3⋊D3 | — | 24 | 1 | no | — |
| 244 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 245 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 246 | C2×C3⋊D3 | #213 | 1 | 1 | yes | characteristic |
| 247 | C2×C3×D3 | — | 3 | 1 | no | — |
| 248 | C2×C3×D3 | — | 3 | 1 | no | — |
| 249 | C2×C3×D3 | — | 4 | 2 | no | — |
| 250 | C2×C3×D3 | — | 4 | 1 | no | — |
| 251 | C2×C3×D3 | — | 4 | 1 | no | — |
| 252 | C2×C3×D3 | — | 4 | 1 | no | — |
| 253 | C2×C3×D3 | — | 4 | 1 | no | — |
| 254 | C2×C3×D3 | — | 6 | 1 | no | — |
| 255 | C2×C3×D3 | — | 8 | 1 | no | — |
| 256 | D32 | — | 24 | 4 | no | — |
| 257 | D32 | — | 24 | 2 | no | — |
| 258 | D32 | — | 24 | 2 | no | — |
| 259 | C32×C4 | — | 2 | 1 | no | — |
| 260 | C32×C4 | — | 2 | 1 | no | — |
| 261 | C32×C4 | — | 2 | 1 | no | — |
| 262 | C32×C4 | — | 4 | 1 | no | — |
| 263 | C32×C4 | — | 12 | 1 | no | — |
| 264 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 265 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 266 | C32×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 267 | C3⋊Dic3 | #213 | 1 | 1 | yes | characteristic |
| 268 | C3×Dic3 | — | 3 | 1 | no | — |
| 269 | C3×Dic3 | — | 3 | 1 | no | — |
| 270 | C3×Dic3 | — | 4 | 1 | no | — |
| 271 | C3×Dic3 | — | 4 | 1 | no | — |
| 272 | C3×Dic3 | — | 6 | 1 | no | — |
| 273 | C3×Dic3 | — | 8 | 1 | no | — |
| 274 | #135 | — | 9 | 1 | no | — |
| 275 | C2×D8 | — | 27 | 1 | no | — |
| 276 | SD32 | — | 9 | 1 | no | — |
| 277 | SD32 | — | 27 | 1 | no | — |
| 278 | D16 | — | 9 | 1 | no | — |
| 279 | D16 | — | 27 | 1 | no | — |
| 280 | M32 | — | 27 | 1 | no | — |
| 281 | C33 | #509 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 282 | C22×D3 | — | 36 | 1 | no | — |
| 283 | C22×D3 | — | 36 | 1 | no | — |
| 284 | C22×D3 | — | 36 | 1 | no | — |
| 285 | C22×D3 | — | 36 | 2 | no | — |
| 286 | C3×Q8 | — | 6 | 1 | no | — |
| 287 | C3×Q8 | — | 6 | 1 | no | — |
| 288 | C3×Q8 | — | 12 | 1 | no | — |
| 289 | C3×D4 | — | 6 | 2 | no | — |
| 290 | C3×D4 | — | 6 | 1 | no | — |
| 291 | C3×D4 | — | 6 | 1 | no | — |
| 292 | C3×D4 | — | 6 | 1 | no | — |
| 293 | C3×D4 | — | 6 | 1 | no | — |
| 294 | C3×D4 | — | 12 | 1 | no | — |
| 295 | C3×D4 | — | 36 | 1 | no | — |
| 296 | C2×C3×C4 | — | 9 | 1 | no | — |
| 297 | C2×C3×C4 | — | 36 | 1 | no | — |
| 298 | #67 | — | 12 | 1 | no | — |
| 299 | #67 | — | 36 | 1 | no | — |
| 300 | #67 | — | 36 | 1 | no | — |
| 301 | #67 | — | 36 | 2 | no | — |
| 302 | C2×Dic3 | — | 12 | 1 | no | — |
| 303 | D12 | — | 2 | 1 | no | — |
| 304 | D12 | — | 2 | 1 | no | — |
| 305 | D12 | — | 12 | 1 | no | — |
| 306 | D12 | — | 18 | 2 | no | — |
| 307 | D12 | — | 18 | 1 | no | — |
| 308 | D12 | — | 18 | 1 | no | — |
| 309 | D12 | — | 18 | 1 | no | — |
| 310 | D12 | — | 36 | 1 | no | — |
| 311 | D12 | — | 36 | 1 | no | — |
| 312 | D12 | — | 36 | 2 | no | — |
| 313 | D12 | — | 36 | 1 | no | — |
| 314 | C4×D3 | — | 3 | 1 | no | — |
| 315 | C4×D3 | — | 3 | 1 | no | — |
| 316 | C4×D3 | — | 6 | 1 | no | — |
| 317 | C4×D3 | — | 12 | 1 | no | — |
| 318 | Dic6 | — | 2 | 1 | no | — |
| 319 | C3×C8 | — | 2 | 1 | no | — |
| 320 | C3×C8 | — | 2 | 1 | no | — |
| 321 | C3×C8 | — | 2 | 1 | no | — |
| 322 | C3×C8 | — | 4 | 1 | no | — |
| 323 | C3×C8 | — | 9 | 1 | no | — |
| 324 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 325 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 326 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 327 | C3⋊C8 | — | 3 | 1 | no | — |
| 328 | C3⋊C8 | — | 3 | 1 | no | — |
| 329 | C3⋊C8 | — | 6 | 1 | no | — |
| 330 | C2×C32 | — | 2 | 1 | no | — |
| 331 | C2×C32 | — | 2 | 1 | no | — |
| 332 | C2×C32 | — | 2 | 1 | no | — |
| 333 | C2×C32 | — | 4 | 1 | no | — |
| 334 | C2×C32 | — | 24 | 1 | no | — |
| 335 | C2×C32 | — | 24 | 1 | no | — |
| 336 | C2×C32 | D3×D8 | 1 | 1 | yes | characteristic |
| 337 | C2×C32 | D3×D8 | 1 | 1 | yes | characteristic |
| 338 | C2×C32 | C2×#213 | 1 | 1 | yes | characteristic |
| 339 | C3⋊D3 | — | 2 | 1 | no | — |
| 340 | C3⋊D3 | — | 24 | 1 | no | — |
| 341 | C3⋊D3 | — | 24 | 2 | no | — |
| 342 | C3⋊D3 | — | 24 | 1 | no | — |
| 343 | C3⋊D3 | — | 24 | 1 | no | — |
| 344 | C3⋊D3 | — | 48 | 1 | no | — |
| 345 | C3⋊D3 | — | 48 | 1 | no | — |
| 346 | C3⋊D3 | — | 48 | 2 | no | — |
| 347 | C3×D3 | — | 6 | 2 | no | — |
| 348 | C3×D3 | — | 6 | 1 | no | — |
| 349 | C3×D3 | — | 6 | 1 | no | — |
| 350 | C3×D3 | — | 8 | 2 | no | — |
| 351 | C3×D3 | — | 8 | 1 | no | — |
| 352 | C3×D3 | — | 8 | 1 | no | — |
| 353 | C3×D3 | — | 8 | 1 | no | — |
| 354 | C3×D3 | — | 8 | 1 | no | — |
| 355 | C3×D3 | — | 16 | 1 | no | — |
| 356 | #41 | — | 18 | 1 | no | — |
| 357 | C2×D4 | — | 54 | 1 | no | — |
| 358 | Q16 | — | 3 | 1 | no | — |
| 359 | SD16 | — | 18 | 1 | no | — |
| 360 | D8 | — | 3 | 1 | no | — |
| 361 | D8 | — | 3 | 1 | no | — |
| 362 | D8 | — | 27 | 1 | no | — |
| 363 | D8 | — | 54 | 1 | no | — |
| 364 | C2×C8 | — | 9 | 1 | no | — |
| 365 | C16 | — | 9 | 1 | no | — |
| 366 | C16 | — | 9 | 1 | no | — |
| 367 | C22×C3 | — | 9 | 1 | no | — |
| 368 | C22×C3 | — | 12 | 2 | no | — |
| 369 | C22×C3 | — | 12 | 1 | no | — |
| 370 | C22×C3 | — | 12 | 1 | no | — |
| 371 | C22×C3 | — | 12 | 1 | no | — |
| 372 | C22×C3 | — | 12 | 1 | no | — |
| 373 | C22×C3 | — | 24 | 1 | no | — |
| 374 | C2×D3 | — | 3 | 1 | no | — |
| 375 | C2×D3 | — | 3 | 1 | no | — |
| 376 | C2×D3 | — | 4 | 1 | no | — |
| 377 | C2×D3 | — | 4 | 1 | no | — |
| 378 | C2×D3 | — | 6 | 1 | no | — |
| 379 | C2×D3 | — | 36 | 2 | no | — |
| 380 | C2×D3 | — | 36 | 1 | no | — |
| 381 | C2×D3 | — | 36 | 1 | no | — |
| 382 | C2×D3 | — | 36 | 1 | no | — |
| 383 | C2×D3 | — | 72 | 1 | no | — |
| 384 | C2×D3 | — | 72 | 1 | no | — |
| 385 | C2×D3 | — | 72 | 2 | no | — |
| 386 | C2×D3 | — | 72 | 4 | no | — |
| 387 | C2×D3 | — | 72 | 2 | no | — |
| 388 | C2×D3 | — | 72 | 2 | no | — |
| 389 | C2×D3 | — | 72 | 2 | no | — |
| 390 | C3×C4 | — | 2 | 1 | no | — |
| 391 | C3×C4 | — | 2 | 1 | no | — |
| 392 | C3×C4 | — | 2 | 1 | no | — |
| 393 | C3×C4 | — | 4 | 1 | no | — |
| 394 | C3×C4 | — | 9 | 1 | no | — |
| 395 | C3×C4 | — | 12 | 1 | no | — |
| 396 | C3×C4 | — | 12 | 1 | no | — |
| 397 | C3×C4 | — | 24 | 1 | no | — |
| 398 | C3×C4 | D3×#67 | 1 | 1 | yes | characteristic |
| 399 | C3×C4 | D3×#67 | 1 | 1 | yes | characteristic |
| 400 | C3×C4 | #3811 | 1 | 1 | yes | characteristic |
| 401 | Dic3 | — | 3 | 1 | no | — |
| 402 | Dic3 | — | 3 | 1 | no | — |
| 403 | Dic3 | — | 4 | 1 | no | — |
| 404 | Dic3 | — | 6 | 1 | no | — |
| 405 | C32 | — | 2 | 1 | no | — |
| 406 | C32 | — | 2 | 1 | no | — |
| 407 | C32 | — | 2 | 1 | no | — |
| 408 | C32 | — | 4 | 1 | no | — |
| 409 | C32 | #4911 | 1 | 1 | yes | characteristic, complemented |
| 410 | C32 | #4914 | 1 | 1 | yes | characteristic, complemented |
| 411 | C32 | #5193 | 1 | 1 | yes | characteristic, complemented |
| 412 | C23 | — | 108 | 1 | no | — |
| 413 | Q8 | — | 6 | 1 | no | — |
| 414 | D4 | — | 6 | 1 | no | — |
| 415 | D4 | — | 6 | 1 | no | — |
| 416 | D4 | — | 36 | 1 | no | — |
| 417 | D4 | — | 54 | 1 | no | — |
| 418 | D4 | — | 108 | 1 | no | — |
| 419 | C2×C4 | — | 9 | 1 | no | — |
| 420 | C2×C4 | — | 36 | 1 | no | — |
| 421 | C8 | — | 9 | 1 | no | — |
| 422 | C8 | D33 | 1 | 1 | yes | characteristic |
| 423 | C2×C3 | — | 2 | 1 | no | — |
| 424 | C2×C3 | — | 2 | 1 | no | — |
| 425 | C2×C3 | — | 2 | 1 | no | — |
| 426 | C2×C3 | — | 4 | 1 | no | — |
| 427 | C2×C3 | — | 18 | 1 | no | — |
| 428 | C2×C3 | — | 24 | 2 | no | — |
| 429 | C2×C3 | — | 24 | 1 | no | — |
| 430 | C2×C3 | — | 24 | 1 | no | — |
| 431 | C2×C3 | — | 24 | 1 | no | — |
| 432 | C2×C3 | — | 24 | 1 | no | — |
| 433 | C2×C3 | — | 48 | 1 | no | — |
| 434 | C2×C3 | D3×#213 | 1 | 1 | yes | characteristic |
| 435 | C2×C3 | D3×#213 | 1 | 1 | yes | characteristic |
| 436 | C2×C3 | #63926 | 1 | 1 | yes | characteristic |
| 437 | D3 | — | 6 | 2 | no | — |
| 438 | D3 | — | 6 | 1 | no | — |
| 439 | D3 | — | 6 | 1 | no | — |
| 440 | D3 | — | 8 | 1 | no | — |
| 441 | D3 | — | 8 | 1 | no | — |
| 442 | D3 | — | 72 | 2 | no | — |
| 443 | D3 | — | 72 | 1 | no | — |
| 444 | D3 | — | 72 | 1 | no | — |
| 445 | D3 | — | 72 | 1 | no | — |
| 446 | D3 | — | 144 | 1 | no | — |
| 447 | D3 | — | 144 | 1 | no | — |
| 448 | D3 | — | 144 | 2 | no | — |
| 449 | C22 | — | 9 | 1 | no | — |
| 450 | C22 | — | 12 | 1 | no | — |
| 451 | C22 | — | 12 | 1 | no | — |
| 452 | C22 | — | 108 | 1 | no | — |
| 453 | C22 | — | 216 | 2 | no | — |
| 454 | C4 | — | 9 | 1 | no | — |
| 455 | C4 | — | 12 | 1 | no | — |
| 456 | C4 | #88952 | 1 | 1 | yes | characteristic |
| 457 | C3 | — | 2 | 1 | no | — |
| 458 | C3 | — | 2 | 1 | no | — |
| 459 | C3 | — | 2 | 1 | no | — |
| 460 | C3 | — | 4 | 1 | no | — |
| 461 | C3 | #10591024 | 1 | 1 | yes | characteristic, complemented |
| 462 | C3 | #10591036 | 1 | 1 | yes | characteristic, complemented |
| 463 | C3 | #10591038 | 1 | 1 | yes | characteristic, complemented |
| 464 | C2 | — | 18 | 1 | no | — |
| 465 | C2 | — | 24 | 1 | no | — |
| 466 | C2 | — | 24 | 1 | no | — |
| 467 | C2 | — | 216 | 1 | no | — |
| 468 | C2 | #11722830 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11722830 |
| commutator, Fitting, cosocle | C33×C8 | C23 |
| Frattini, hypercenter | C8 | D33 |
| socle | C2×C33 | C2×D8 |
| hypocenter | C33 | #509 |
| LCS | G ▷ C33×C8 ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊D3×D24 | C2 | semidirect |
| 2. C3×#63810 | C2 | semidirect |
| 3. #11722066 | C2 | semidirect |
| 4. #11722010 | C2 | semidirect |
| 5. #11722005 | C2 | semidirect |
| 6. C3×#63547 | C2 | semidirect |
| 7. C3×#63545 | C2 | semidirect |
| 15. C32×Dic12 | C22 | semidirect |
| 17. C32×D24 | C22 | semidirect |
| 20. C3×C3⋊(C3⋊C16) | C22 | semidirect |
| 21. C3×C3⋊(C3⋊C16) | C22 | semidirect |
| 25. #63810 | D3 | semidirect |
| 38. #63547 | D3 | semidirect |
| 42. #63545 | D3 | semidirect |
| 82. C3×Dic12 | C2×D3 | semidirect |
| 83. C3×Dic12 | C2×D3 | semidirect |
| 88. C3×D24 | C2×D3 | semidirect |
| 89. C3×D24 | C2×D3 | semidirect |
| 97. C3⋊(C3⋊C16) | C2×D3 | semidirect |
| 98. C3⋊(C3⋊C16) | C2×D3 | semidirect |
| 214. Dic12 | D32 | semidirect |
| 224. D24 | D32 | semidirect |
| 281. C33 | #509 | semidirect |
| 409. C32 | #4911 | semidirect |
| 410. C32 | #4914 | semidirect |
| 411. C32 | #5193 | semidirect |
| 461. C3 | #10591024 | semidirect |
| 462. C3 | #10591036 | semidirect |
| 463. C3 | #10591038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×D24 | 2 |
| C3×#63810 | 2 |
| #11722066 | 2 |
| #11722010 | 2 |
| #11722005 | 2 |
| C3×#63547 | 2 |
| C3×#63545 | 2 |
| #10591038 | 3 |
| #10591036 | 3 |
| #10591024 | 3 |