Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
510 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 66 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 | #11723345 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11723343 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11722068 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11722000 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#63551 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#63547 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C3×#63546 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10591049 | — | 3 | 1 | no | maximal |
| 9 | #10591035 | — | 3 | 1 | no | maximal |
| 10 | #10590244 | — | 3 | 1 | no | maximal |
| 11 | #89017 | — | 2 | 1 | no | — |
| 12 | #89015 | — | 2 | 1 | no | — |
| 13 | C8×C3⋊(C3⋊D3) | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#3746 | C22 | 1 | 1 | yes | characteristic |
| 15 | C3×#3745 | C22 | 1 | 1 | yes | characteristic |
| 16 | C32×Dic12 | C22 | 1 | 1 | yes | characteristic |
| 17 | C32×D24 | C22 | 1 | 1 | yes | characteristic |
| 18 | #88793 | — | 2 | 1 | no | — |
| 19 | #88792 | — | 2 | 1 | no | — |
| 20 | C3×C3⋊(C3⋊C16) | C22 | 1 | 1 | yes | characteristic |
| 21 | C32×C3⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 22 | #64128 | — | 3 | 1 | no | — |
| 23 | #64121 | — | 3 | 1 | no | — |
| 24 | #63810 | — | 3 | 1 | no | — |
| 25 | #63810 | — | 3 | 1 | no | — |
| 26 | #63810 | — | 3 | 1 | no | — |
| 27 | #63810 | — | 3 | 1 | no | — |
| 28 | #63810 | — | 6 | 1 | no | — |
| 29 | #63810 | — | 6 | 1 | no | — |
| 30 | C16×C3⋊D3 | — | 3 | 1 | no | — |
| 31 | C3×#829 | — | 3 | 1 | no | — |
| 32 | C3×#828 | — | 3 | 1 | no | — |
| 33 | C3×#827 | — | 3 | 1 | no | — |
| 34 | C3×#826 | — | 3 | 1 | no | — |
| 35 | C3×Dic24 | — | 3 | 1 | no | — |
| 36 | C3×D48 | — | 3 | 1 | no | — |
| 37 | #63551 | D3 | 1 | 1 | yes | characteristic, complemented |
| 38 | #63549 | — | 3 | 1 | no | — |
| 39 | #63548 | — | 3 | 1 | no | — |
| 40 | #63547 | — | 3 | 1 | no | — |
| 41 | #63547 | D3 | 1 | 1 | yes | characteristic, complemented |
| 42 | #63546 | D3 | 1 | 1 | yes | characteristic, complemented |
| 43 | #63542 | — | 3 | 1 | no | — |
| 44 | #63542 | — | 3 | 1 | no | — |
| 45 | #63542 | — | 6 | 1 | no | — |
| 46 | C4×C3⋊(C3⋊D3) | D4 | 1 | 1 | yes | characteristic |
| 47 | C3×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 48 | C3×#634 | — | 2 | 1 | no | — |
| 49 | C32×D12 | — | 2 | 1 | no | — |
| 50 | C32×Dic6 | — | 2 | 1 | no | — |
| 51 | #6292 | — | 4 | 1 | no | — |
| 52 | #6291 | — | 4 | 1 | no | — |
| 53 | Dic3×C3⋊D3 | — | 4 | 1 | no | — |
| 54 | D3×C3⋊Dic3 | — | 4 | 1 | no | — |
| 55 | C33×C8 | C23 | 1 | 1 | yes | characteristic |
| 56 | C3⋊(C3⋊(C3⋊C8)) | D4 | 1 | 1 | yes | characteristic |
| 57 | #4919 | — | 9 | 1 | no | — |
| 58 | #4916 | — | 9 | 1 | no | — |
| 59 | #4912 | — | 9 | 1 | no | — |
| 60 | #3832 | — | 6 | 1 | no | — |
| 61 | #3830 | — | 6 | 1 | no | — |
| 62 | #3796 | — | 6 | 1 | no | — |
| 63 | #3796 | — | 6 | 1 | no | — |
| 64 | #3796 | — | 6 | 2 | no | — |
| 65 | #3796 | — | 6 | 1 | no | — |
| 66 | #3796 | — | 6 | 1 | no | — |
| 67 | #3796 | — | 6 | 2 | no | — |
| 68 | C32×Q16 | — | 3 | 1 | no | — |
| 69 | C32×D8 | — | 3 | 1 | no | — |
| 70 | #3755 | — | 6 | 1 | no | — |
| 71 | #3754 | — | 6 | 1 | no | — |
| 72 | #3746 | C2×D3 | 1 | 1 | yes | characteristic |
| 73 | #3745 | C2×D3 | 1 | 1 | yes | characteristic |
| 74 | C8×C3⋊D3 | — | 3 | 1 | no | — |
| 75 | C8×C3⋊D3 | — | 3 | 1 | no | — |
| 76 | C8×C3⋊D3 | — | 3 | 1 | no | — |
| 77 | C8×C3⋊D3 | — | 6 | 1 | no | — |
| 78 | C8×C3⋊D3 | — | 6 | 1 | no | — |
| 79 | C8×C3⋊D3 | — | 6 | 1 | no | — |
| 80 | C8×C3⋊D3 | — | 12 | 1 | no | — |
| 81 | C3×Dic12 | — | 2 | 1 | no | — |
| 82 | C3×Dic12 | — | 3 | 1 | no | — |
| 83 | C3×Dic12 | — | 3 | 1 | no | — |
| 84 | C3×Dic12 | — | 6 | 1 | no | — |
| 85 | C3×Dic12 | C2×D3 | 1 | 1 | yes | characteristic |
| 86 | C3×Dic12 | C2×D3 | 1 | 1 | yes | characteristic |
| 87 | C3×D24 | — | 2 | 1 | no | — |
| 88 | C3×D24 | — | 3 | 1 | no | — |
| 89 | C3×D24 | — | 3 | 1 | no | — |
| 90 | C3×D24 | — | 6 | 1 | no | — |
| 91 | C3×D24 | C2×D3 | 1 | 1 | yes | characteristic |
| 92 | C3×D24 | C2×D3 | 1 | 1 | yes | characteristic |
| 93 | #3715 | — | 6 | 1 | no | — |
| 94 | #3715 | — | 6 | 1 | no | — |
| 95 | #3715 | — | 6 | 1 | no | — |
| 96 | #3715 | — | 6 | 1 | no | — |
| 97 | #3715 | — | 6 | 2 | no | — |
| 98 | #3715 | — | 6 | 2 | no | — |
| 99 | C32×C16 | — | 3 | 1 | no | — |
| 100 | C3⋊(C3⋊C16) | C2×D3 | 1 | 1 | yes | characteristic |
| 101 | C3×C3⋊C16 | — | 2 | 1 | no | — |
| 102 | C3×C3⋊C16 | — | 3 | 1 | no | — |
| 103 | C3×C3⋊C16 | — | 3 | 1 | no | — |
| 104 | C3×C3⋊C16 | — | 6 | 1 | no | — |
| 105 | C3×C3⋊C16 | C2×D3 | 1 | 1 | yes | characteristic |
| 106 | C3×C3⋊C16 | C2×D3 | 1 | 1 | yes | characteristic |
| 107 | C2×C3⋊(C3⋊D3) | D8 | 1 | 1 | yes | characteristic |
| 108 | C2×C3×C3⋊D3 | — | 4 | 1 | no | — |
| 109 | C2×C32×D3 | — | 4 | 1 | no | — |
| 110 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | C3⋊(C3⋊Dic3) | D8 | 1 | 1 | yes | characteristic |
| 112 | C3×C3⋊Dic3 | — | 4 | 1 | no | — |
| 113 | C32×Dic3 | — | 4 | 1 | no | — |
| 114 | #919 | — | 9 | 1 | no | — |
| 115 | #919 | — | 9 | 1 | no | — |
| 116 | #919 | — | 9 | 1 | no | — |
| 117 | #919 | — | 18 | 1 | no | — |
| 118 | #912 | — | 9 | 1 | no | — |
| 119 | #912 | — | 9 | 1 | no | — |
| 120 | #912 | — | 9 | 1 | no | — |
| 121 | #912 | — | 18 | 1 | no | — |
| 122 | C3×Q32 | — | 9 | 1 | no | — |
| 123 | C3×SD32 | — | 9 | 1 | no | — |
| 124 | C3×D16 | — | 9 | 1 | no | — |
| 125 | #829 | — | 3 | 1 | no | — |
| 126 | #828 | — | 3 | 1 | no | — |
| 127 | #828 | — | 9 | 1 | no | — |
| 128 | #827 | — | 3 | 1 | no | — |
| 129 | #827 | — | 9 | 1 | no | — |
| 130 | #826 | — | 3 | 1 | no | — |
| 131 | Dic24 | — | 3 | 1 | no | — |
| 132 | #800 | — | 9 | 1 | no | — |
| 133 | D48 | — | 3 | 1 | no | — |
| 134 | D3×C16 | — | 9 | 1 | no | — |
| 135 | D3×C16 | — | 9 | 1 | no | — |
| 136 | D3×C16 | — | 9 | 1 | no | — |
| 137 | D3×C16 | — | 18 | 1 | no | — |
| 138 | C32×Q8 | — | 6 | 1 | no | — |
| 139 | C32×D4 | — | 6 | 1 | no | — |
| 140 | #638 | — | 12 | 1 | no | — |
| 141 | C2×C3⋊Dic3 | — | 12 | 1 | no | — |
| 142 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 143 | C4⋊(C3⋊D3) | — | 12 | 1 | no | — |
| 144 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 145 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 146 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 147 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 148 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 149 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 150 | C4×C3⋊D3 | — | 12 | 1 | no | — |
| 151 | C4×C3⋊D3 | — | 12 | 1 | no | — |
| 152 | #634 | — | 2 | 1 | no | — |
| 153 | C3×D12 | — | 2 | 2 | no | — |
| 154 | C3×D12 | — | 2 | 1 | no | — |
| 155 | C3×D12 | — | 2 | 1 | no | — |
| 156 | C3×D12 | — | 6 | 2 | no | — |
| 157 | C3×D12 | — | 6 | 1 | no | — |
| 158 | C3×D12 | — | 6 | 1 | no | — |
| 159 | C3×Dic6 | — | 2 | 2 | no | — |
| 160 | C3×Dic6 | — | 2 | 1 | no | — |
| 161 | C3×Dic6 | — | 2 | 1 | no | — |
| 162 | C3×Dic6 | — | 6 | 2 | no | — |
| 163 | C3×Dic6 | — | 6 | 1 | no | — |
| 164 | C3×Dic6 | — | 6 | 1 | no | — |
| 165 | #626 | — | 12 | 1 | no | — |
| 166 | #626 | — | 12 | 1 | no | — |
| 167 | #626 | — | 12 | 2 | no | — |
| 168 | #626 | — | 12 | 1 | no | — |
| 169 | #626 | — | 12 | 1 | no | — |
| 170 | #626 | — | 12 | 2 | no | — |
| 171 | D3×Dic3 | — | 12 | 1 | no | — |
| 172 | D3×Dic3 | — | 12 | 1 | no | — |
| 173 | D3×Dic3 | — | 12 | 2 | no | — |
| 174 | D3×Dic3 | — | 12 | 1 | no | — |
| 175 | D3×Dic3 | — | 12 | 1 | no | — |
| 176 | D3×Dic3 | — | 12 | 2 | no | — |
| 177 | C32×C8 | — | 2 | 1 | no | — |
| 178 | C32×C8 | — | 2 | 1 | no | — |
| 179 | C32×C8 | — | 2 | 1 | no | — |
| 180 | C32×C8 | — | 4 | 1 | no | — |
| 181 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 182 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 183 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 184 | C3⋊(C3⋊C8) | — | 3 | 1 | no | — |
| 185 | C3⋊(C3⋊C8) | — | 3 | 1 | no | — |
| 186 | C3⋊(C3⋊C8) | — | 3 | 1 | no | — |
| 187 | C3⋊(C3⋊C8) | — | 6 | 1 | no | — |
| 188 | C3⋊(C3⋊C8) | — | 6 | 1 | no | — |
| 189 | C3⋊(C3⋊C8) | — | 6 | 1 | no | — |
| 190 | C3⋊(C3⋊C8) | — | 12 | 1 | no | — |
| 191 | #508 | — | 27 | 1 | no | Sylow |
| 192 | C2×C33 | C2×D8 | 1 | 1 | yes | characteristic |
| 193 | C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 194 | C3×C3⋊D3 | — | 8 | 1 | no | — |
| 195 | C32×D3 | — | 8 | 1 | no | — |
| 196 | #239 | — | 18 | 1 | no | — |
| 197 | #239 | — | 18 | 1 | no | — |
| 198 | #239 | — | 18 | 1 | no | — |
| 199 | #239 | — | 18 | 2 | no | — |
| 200 | #237 | — | 18 | 1 | no | — |
| 201 | #237 | — | 18 | 1 | no | — |
| 202 | #237 | — | 18 | 1 | no | — |
| 203 | #237 | — | 18 | 2 | no | — |
| 204 | C3×Q16 | — | 3 | 1 | no | — |
| 205 | C3×Q16 | — | 3 | 1 | no | — |
| 206 | C3×Q16 | — | 6 | 1 | no | — |
| 207 | C3×Q16 | — | 9 | 1 | no | — |
| 208 | C3×D8 | — | 3 | 1 | no | — |
| 209 | C3×D8 | — | 3 | 1 | no | — |
| 210 | C3×D8 | — | 6 | 1 | no | — |
| 211 | C3×D8 | — | 9 | 1 | no | — |
| 212 | #215 | — | 18 | 1 | no | — |
| 213 | #215 | — | 18 | 1 | no | — |
| 214 | #215 | — | 18 | 1 | no | — |
| 215 | #215 | — | 18 | 2 | no | — |
| 216 | #214 | — | 18 | 1 | no | — |
| 217 | #214 | — | 18 | 1 | no | — |
| 218 | #214 | — | 18 | 1 | no | — |
| 219 | #214 | — | 18 | 2 | no | — |
| 220 | Dic12 | — | 3 | 1 | no | — |
| 221 | Dic12 | — | 3 | 1 | no | — |
| 222 | Dic12 | — | 6 | 1 | no | — |
| 223 | Dic12 | D32 | 1 | 1 | yes | characteristic |
| 224 | D24 | — | 3 | 1 | no | — |
| 225 | D24 | — | 3 | 1 | no | — |
| 226 | D24 | — | 6 | 1 | no | — |
| 227 | D24 | D32 | 1 | 1 | yes | characteristic |
| 228 | D3×C8 | — | 9 | 1 | no | — |
| 229 | D3×C8 | — | 9 | 1 | no | — |
| 230 | D3×C8 | — | 9 | 1 | no | — |
| 231 | D3×C8 | — | 18 | 1 | no | — |
| 232 | D3×C8 | — | 18 | 1 | no | — |
| 233 | D3×C8 | — | 18 | 1 | no | — |
| 234 | D3×C8 | — | 36 | 1 | no | — |
| 235 | C3×C16 | — | 3 | 1 | no | — |
| 236 | C3×C16 | — | 3 | 1 | no | — |
| 237 | C3×C16 | — | 6 | 1 | no | — |
| 238 | C3×C16 | — | 9 | 1 | no | — |
| 239 | C3⋊C16 | — | 3 | 1 | no | — |
| 240 | C3⋊C16 | — | 3 | 1 | no | — |
| 241 | C3⋊C16 | — | 6 | 1 | no | — |
| 242 | C3⋊C16 | D32 | 1 | 1 | yes | characteristic |
| 243 | C22×C32 | — | 12 | 1 | no | — |
| 244 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 245 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 246 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 247 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 248 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 249 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 250 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 251 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 252 | C2×C3×D3 | — | 4 | 2 | no | — |
| 253 | C2×C3×D3 | — | 4 | 1 | no | — |
| 254 | C2×C3×D3 | — | 4 | 1 | no | — |
| 255 | C2×C3×D3 | — | 12 | 2 | no | — |
| 256 | C2×C3×D3 | — | 12 | 1 | no | — |
| 257 | C2×C3×D3 | — | 12 | 1 | no | — |
| 258 | C32×C4 | — | 2 | 1 | no | — |
| 259 | C32×C4 | — | 2 | 1 | no | — |
| 260 | C32×C4 | — | 2 | 1 | no | — |
| 261 | C32×C4 | — | 4 | 1 | no | — |
| 262 | C32×C4 | — | 12 | 1 | no | — |
| 263 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 264 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 265 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 266 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 267 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 268 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 269 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 270 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 271 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 272 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 273 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 274 | C3×Dic3 | — | 4 | 2 | no | — |
| 275 | C3×Dic3 | — | 4 | 1 | no | — |
| 276 | C3×Dic3 | — | 4 | 1 | no | — |
| 277 | C3×Dic3 | — | 12 | 2 | no | — |
| 278 | C3×Dic3 | — | 12 | 1 | no | — |
| 279 | C3×Dic3 | — | 12 | 1 | no | — |
| 280 | #135 | — | 27 | 1 | no | — |
| 281 | #135 | — | 27 | 1 | no | — |
| 282 | Q32 | — | 9 | 1 | no | — |
| 283 | SD32 | — | 9 | 1 | no | — |
| 284 | SD32 | — | 27 | 1 | no | — |
| 285 | D16 | — | 9 | 1 | no | — |
| 286 | C2×C16 | — | 27 | 1 | no | — |
| 287 | C33 | #508 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 288 | C3×Q8 | — | 6 | 2 | no | — |
| 289 | C3×Q8 | — | 6 | 1 | no | — |
| 290 | C3×Q8 | — | 6 | 1 | no | — |
| 291 | C3×Q8 | — | 18 | 1 | no | — |
| 292 | C3×D4 | — | 6 | 2 | no | — |
| 293 | C3×D4 | — | 6 | 1 | no | — |
| 294 | C3×D4 | — | 6 | 1 | no | — |
| 295 | C3×D4 | — | 18 | 1 | no | — |
| 296 | #67 | — | 36 | 1 | no | — |
| 297 | #67 | — | 36 | 1 | no | — |
| 298 | #67 | — | 36 | 1 | no | — |
| 299 | #67 | — | 36 | 2 | no | — |
| 300 | C2×Dic3 | — | 36 | 1 | no | — |
| 301 | C2×Dic3 | — | 36 | 1 | no | — |
| 302 | C2×Dic3 | — | 36 | 1 | no | — |
| 303 | C2×Dic3 | — | 36 | 2 | no | — |
| 304 | D12 | — | 2 | 1 | no | — |
| 305 | D12 | — | 6 | 2 | no | — |
| 306 | D12 | — | 6 | 1 | no | — |
| 307 | D12 | — | 6 | 1 | no | — |
| 308 | D12 | — | 36 | 1 | no | — |
| 309 | D12 | — | 36 | 1 | no | — |
| 310 | D12 | — | 36 | 2 | no | — |
| 311 | D12 | — | 36 | 1 | no | — |
| 312 | C4×D3 | — | 9 | 1 | no | — |
| 313 | C4×D3 | — | 9 | 1 | no | — |
| 314 | C4×D3 | — | 9 | 1 | no | — |
| 315 | C4×D3 | — | 18 | 1 | no | — |
| 316 | C4×D3 | — | 18 | 1 | no | — |
| 317 | C4×D3 | — | 18 | 1 | no | — |
| 318 | C4×D3 | — | 36 | 1 | no | — |
| 319 | C4×D3 | — | 36 | 1 | no | — |
| 320 | C4×D3 | — | 36 | 1 | no | — |
| 321 | C4×D3 | — | 36 | 1 | no | — |
| 322 | C4×D3 | — | 36 | 2 | no | — |
| 323 | Dic6 | — | 2 | 1 | no | — |
| 324 | Dic6 | — | 6 | 2 | no | — |
| 325 | Dic6 | — | 6 | 1 | no | — |
| 326 | Dic6 | — | 6 | 1 | no | — |
| 327 | C3×C8 | — | 2 | 1 | no | — |
| 328 | C3×C8 | — | 2 | 1 | no | — |
| 329 | C3×C8 | — | 2 | 1 | no | — |
| 330 | C3×C8 | — | 4 | 1 | no | — |
| 331 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 332 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 333 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 334 | C3⋊C8 | — | 9 | 1 | no | — |
| 335 | C3⋊C8 | — | 9 | 1 | no | — |
| 336 | C3⋊C8 | — | 9 | 1 | no | — |
| 337 | C3⋊C8 | — | 18 | 1 | no | — |
| 338 | C3⋊C8 | — | 18 | 1 | no | — |
| 339 | C3⋊C8 | — | 18 | 1 | no | — |
| 340 | C3⋊C8 | — | 36 | 1 | no | — |
| 341 | C2×C32 | — | 2 | 1 | no | — |
| 342 | C2×C32 | — | 2 | 1 | no | — |
| 343 | C2×C32 | — | 2 | 1 | no | — |
| 344 | C2×C32 | — | 4 | 1 | no | — |
| 345 | C2×C32 | — | 24 | 1 | no | — |
| 346 | C2×C32 | D3×D8 | 1 | 1 | yes | characteristic |
| 347 | C2×C32 | D3×D8 | 1 | 1 | yes | characteristic |
| 348 | C2×C32 | D3×D8 | 1 | 1 | yes | characteristic |
| 349 | C3⋊D3 | — | 6 | 1 | no | — |
| 350 | C3⋊D3 | — | 6 | 2 | no | — |
| 351 | C3⋊D3 | — | 6 | 1 | no | — |
| 352 | C3⋊D3 | — | 6 | 1 | no | — |
| 353 | C3⋊D3 | — | 8 | 1 | no | — |
| 354 | C3⋊D3 | — | 12 | 1 | no | — |
| 355 | C3⋊D3 | — | 12 | 1 | no | — |
| 356 | C3⋊D3 | — | 12 | 2 | no | — |
| 357 | C3×D3 | — | 8 | 2 | no | — |
| 358 | C3×D3 | — | 8 | 1 | no | — |
| 359 | C3×D3 | — | 8 | 1 | no | — |
| 360 | C3×D3 | — | 24 | 2 | no | — |
| 361 | C3×D3 | — | 24 | 1 | no | — |
| 362 | C3×D3 | — | 24 | 1 | no | — |
| 363 | #41 | — | 54 | 1 | no | — |
| 364 | #41 | — | 54 | 1 | no | — |
| 365 | Q16 | — | 3 | 1 | no | — |
| 366 | Q16 | — | 9 | 1 | no | — |
| 367 | SD16 | — | 54 | 1 | no | — |
| 368 | SD16 | — | 54 | 1 | no | — |
| 369 | D8 | — | 3 | 1 | no | — |
| 370 | D8 | — | 9 | 1 | no | — |
| 371 | C2×C8 | — | 27 | 1 | no | — |
| 372 | C16 | — | 3 | 1 | no | — |
| 373 | C16 | — | 9 | 1 | no | — |
| 374 | C22×C3 | — | 12 | 2 | no | — |
| 375 | C22×C3 | — | 12 | 1 | no | — |
| 376 | C22×C3 | — | 12 | 1 | no | — |
| 377 | C22×C3 | — | 36 | 1 | no | — |
| 378 | C2×D3 | — | 4 | 1 | no | — |
| 379 | C2×D3 | — | 9 | 1 | no | — |
| 380 | C2×D3 | — | 9 | 1 | no | — |
| 381 | C2×D3 | — | 9 | 1 | no | — |
| 382 | C2×D3 | — | 12 | 2 | no | — |
| 383 | C2×D3 | — | 12 | 1 | no | — |
| 384 | C2×D3 | — | 12 | 1 | no | — |
| 385 | C2×D3 | — | 18 | 1 | no | — |
| 386 | C2×D3 | — | 18 | 1 | no | — |
| 387 | C2×D3 | — | 18 | 1 | no | — |
| 388 | C2×D3 | — | 36 | 1 | no | — |
| 389 | C3×C4 | — | 2 | 1 | no | — |
| 390 | C3×C4 | — | 2 | 1 | no | — |
| 391 | C3×C4 | — | 2 | 1 | no | — |
| 392 | C3×C4 | — | 4 | 1 | no | — |
| 393 | C3×C4 | — | 12 | 2 | no | — |
| 394 | C3×C4 | — | 12 | 1 | no | — |
| 395 | C3×C4 | — | 12 | 1 | no | — |
| 396 | C3×C4 | — | 36 | 1 | no | — |
| 397 | C3×C4 | #3802 | 1 | 1 | yes | characteristic |
| 398 | C3×C4 | #3811 | 1 | 1 | yes | characteristic |
| 399 | C3×C4 | #3811 | 1 | 1 | yes | characteristic |
| 400 | Dic3 | — | 4 | 1 | no | — |
| 401 | Dic3 | — | 9 | 1 | no | — |
| 402 | Dic3 | — | 9 | 1 | no | — |
| 403 | Dic3 | — | 9 | 1 | no | — |
| 404 | Dic3 | — | 12 | 2 | no | — |
| 405 | Dic3 | — | 12 | 1 | no | — |
| 406 | Dic3 | — | 12 | 1 | no | — |
| 407 | Dic3 | — | 18 | 1 | no | — |
| 408 | Dic3 | — | 18 | 1 | no | — |
| 409 | Dic3 | — | 18 | 1 | no | — |
| 410 | Dic3 | — | 36 | 1 | no | — |
| 411 | C32 | — | 2 | 1 | no | — |
| 412 | C32 | — | 2 | 1 | no | — |
| 413 | C32 | — | 2 | 1 | no | — |
| 414 | C32 | — | 4 | 1 | no | — |
| 415 | C32 | #4912 | 1 | 1 | yes | characteristic, complemented |
| 416 | C32 | #4916 | 1 | 1 | yes | characteristic, complemented |
| 417 | C32 | #4919 | 1 | 1 | yes | characteristic, complemented |
| 418 | Q8 | — | 6 | 1 | no | — |
| 419 | Q8 | — | 18 | 1 | no | — |
| 420 | D4 | — | 6 | 1 | no | — |
| 421 | D4 | — | 18 | 1 | no | — |
| 422 | D4 | — | 108 | 1 | no | — |
| 423 | D4 | — | 108 | 1 | no | — |
| 424 | C2×C4 | — | 27 | 1 | no | — |
| 425 | C2×C4 | — | 108 | 1 | no | — |
| 426 | C2×C4 | — | 108 | 1 | no | — |
| 427 | C8 | — | 27 | 1 | no | — |
| 428 | C8 | D33 | 1 | 1 | yes | characteristic |
| 429 | C2×C3 | — | 2 | 1 | no | — |
| 430 | C2×C3 | — | 2 | 1 | no | — |
| 431 | C2×C3 | — | 2 | 1 | no | — |
| 432 | C2×C3 | — | 4 | 1 | no | — |
| 433 | C2×C3 | — | 24 | 2 | no | — |
| 434 | C2×C3 | — | 24 | 1 | no | — |
| 435 | C2×C3 | — | 24 | 1 | no | — |
| 436 | C2×C3 | — | 72 | 1 | no | — |
| 437 | C2×C3 | #63797 | 1 | 1 | yes | characteristic |
| 438 | C2×C3 | #63926 | 1 | 1 | yes | characteristic |
| 439 | C2×C3 | #63926 | 1 | 1 | yes | characteristic |
| 440 | D3 | — | 8 | 1 | no | — |
| 441 | D3 | — | 18 | 2 | no | — |
| 442 | D3 | — | 18 | 1 | no | — |
| 443 | D3 | — | 18 | 1 | no | — |
| 444 | D3 | — | 18 | 1 | no | — |
| 445 | D3 | — | 24 | 2 | no | — |
| 446 | D3 | — | 24 | 1 | no | — |
| 447 | D3 | — | 24 | 1 | no | — |
| 448 | D3 | — | 36 | 1 | no | — |
| 449 | D3 | — | 36 | 1 | no | — |
| 450 | D3 | — | 36 | 2 | no | — |
| 451 | C22 | — | 12 | 1 | no | — |
| 452 | C22 | — | 27 | 1 | no | — |
| 453 | C22 | — | 36 | 1 | no | — |
| 454 | C4 | — | 12 | 1 | no | — |
| 455 | C4 | — | 27 | 1 | no | — |
| 456 | C4 | — | 36 | 1 | no | — |
| 457 | C4 | #88954 | 1 | 1 | yes | characteristic |
| 458 | C3 | — | 2 | 1 | no | — |
| 459 | C3 | — | 2 | 1 | no | — |
| 460 | C3 | — | 2 | 1 | no | — |
| 461 | C3 | — | 4 | 1 | no | — |
| 462 | C3 | #10590244 | 1 | 1 | yes | characteristic, complemented |
| 463 | C3 | #10591035 | 1 | 1 | yes | characteristic, complemented |
| 464 | C3 | #10591049 | 1 | 1 | yes | characteristic, complemented |
| 465 | C2 | — | 24 | 1 | no | — |
| 466 | C2 | — | 54 | 1 | no | — |
| 467 | C2 | — | 72 | 1 | no | — |
| 468 | C2 | #11722832 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11722832 |
| commutator, Fitting, cosocle | C33×C8 | C23 |
| Frattini, hypercenter | C8 | D33 |
| socle | C2×C33 | C2×D8 |
| hypocenter | C33 | #508 |
| 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. #11723345 | C2 | semidirect |
| 2. #11723343 | C2 | semidirect |
| 3. #11722068 | C2 | semidirect |
| 4. #11722000 | C2 | semidirect |
| 5. C3×#63551 | C2 | semidirect |
| 6. C3×#63547 | C2 | semidirect |
| 7. C3×#63546 | C2 | semidirect |
| 37. #63551 | D3 | semidirect |
| 41. #63547 | D3 | semidirect |
| 42. #63546 | D3 | semidirect |
| 287. C33 | #508 | semidirect |
| 415. C32 | #4912 | semidirect |
| 416. C32 | #4916 | semidirect |
| 417. C32 | #4919 | semidirect |
| 462. C3 | #10590244 | semidirect |
| 463. C3 | #10591035 | semidirect |
| 464. C3 | #10591049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723345 | 2 |
| #11723343 | 2 |
| #11722068 | 2 |
| #11722000 | 2 |
| C3×#63551 | 2 |
| C3×#63547 | 2 |
| C3×#63546 | 2 |
| #10591049 | 3 |
| #10591035 | 3 |
| #10590244 | 3 |