Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
626 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 50 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 | #11724377 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11724313 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#64227 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11722830 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11722780 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11722760 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11722707 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10593458 | — | 3 | 1 | no | maximal |
| 9 | C2×D32⋊D3 | — | 2 | 1 | no | — |
| 10 | C4×#1113 | C22 | 1 | 1 | yes | characteristic |
| 11 | C3⋊D3×D12 | C22 | 1 | 1 | yes | characteristic |
| 12 | #89018 | — | 2 | 1 | no | — |
| 13 | C3×#3802 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#3797 | C22 | 1 | 1 | yes | characteristic |
| 15 | C3×#3796 | — | 2 | 1 | no | — |
| 16 | C4⋊(C3⋊#157) | C22 | 1 | 1 | yes | characteristic |
| 17 | C3×#3787 | C22 | 1 | 1 | yes | characteristic |
| 18 | #88962 | — | 2 | 2 | no | — |
| 19 | #88955 | — | 2 | 1 | no | — |
| 20 | D3×#624 | — | 2 | 1 | no | — |
| 21 | D32⋊Dic3 | — | 2 | 1 | no | — |
| 22 | C3×#3775 | — | 2 | 2 | no | — |
| 23 | #88808 | C22 | 1 | 1 | yes | characteristic |
| 24 | #88790 | — | 2 | 1 | no | — |
| 25 | C3×#3713 | — | 2 | 1 | no | — |
| 26 | D3×#239 | — | 6 | 1 | no | — |
| 27 | #64312 | — | 3 | 1 | no | — |
| 28 | #64230 | — | 3 | 1 | no | — |
| 29 | #64227 | D3 | 1 | 1 | yes | characteristic, complemented |
| 30 | #63926 | — | 3 | 1 | no | — |
| 31 | D3×#213 | — | 6 | 1 | no | — |
| 32 | #63782 | — | 3 | 1 | no | — |
| 33 | #63730 | — | 3 | 1 | no | — |
| 34 | D32⋊C8 | — | 3 | 1 | no | — |
| 35 | C2×#1113 | D4 | 1 | 1 | yes | characteristic |
| 36 | C2×D3×C3⋊D3 | — | 2 | 1 | no | — |
| 37 | C2×C3×D32 | — | 2 | 1 | no | — |
| 38 | C2×C3⋊#157 | — | 2 | 1 | no | — |
| 39 | D32⋊D3 | — | 4 | 2 | no | — |
| 40 | C4⋊(C3⋊(C3⋊D3)) | D4 | 1 | 1 | yes | characteristic, complemented |
| 41 | C3×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 42 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 43 | C32×D12 | — | 2 | 1 | no | — |
| 44 | C32×D12 | D4 | 1 | 1 | yes | characteristic, complemented |
| 45 | C32×Dic6 | — | 2 | 1 | no | — |
| 46 | #6294 | — | 2 | 1 | no | — |
| 47 | #6294 | D4 | 1 | 1 | yes | characteristic |
| 48 | #6292 | — | 2 | 2 | no | — |
| 49 | #6291 | — | 2 | 1 | no | — |
| 50 | #6289 | — | 2 | 2 | no | — |
| 51 | C3×#627 | D4 | 1 | 2 | yes | complemented |
| 52 | C3×#626 | — | 2 | 2 | no | — |
| 53 | C3×#625 | — | 2 | 1 | no | — |
| 54 | C3×#624 | — | 2 | 1 | no | — |
| 55 | C3×D3×Dic3 | — | 2 | 2 | no | — |
| 56 | C3×#622 | — | 2 | 1 | no | — |
| 57 | C3×C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 58 | #5172 | — | 9 | 1 | no | maximal |
| 59 | C2×GO+(4,𝔽2) | — | 6 | 1 | no | — |
| 60 | #3832 | — | 6 | 1 | no | — |
| 61 | D4×C3⋊D3 | — | 3 | 1 | no | — |
| 62 | C3×#239 | — | 6 | 1 | no | — |
| 63 | C3×D3×Q8 | — | 6 | 1 | no | — |
| 64 | C3×#237 | — | 6 | 1 | no | — |
| 65 | C3×D3×D4 | — | 6 | 1 | no | — |
| 66 | #3811 | — | 6 | 1 | no | — |
| 67 | C2×#624 | — | 6 | 1 | no | — |
| 68 | #3804 | — | 6 | 2 | no | — |
| 69 | #3802 | C2×D3 | 1 | 1 | yes | characteristic |
| 70 | D3×D12 | — | 6 | 2 | no | — |
| 71 | D3×D12 | — | 6 | 1 | no | — |
| 72 | D3×D12 | — | 6 | 1 | no | — |
| 73 | C4×D32 | — | 3 | 1 | no | — |
| 74 | C4×D32 | — | 6 | 2 | no | — |
| 75 | C4×D32 | — | 6 | 1 | no | — |
| 76 | #3799 | — | 6 | 2 | no | — |
| 77 | #3799 | — | 6 | 1 | no | — |
| 78 | #3799 | — | 6 | 1 | no | — |
| 79 | #3799 | — | 12 | 1 | no | — |
| 80 | #3797 | C2×D3 | 1 | 1 | yes | characteristic |
| 81 | #3796 | — | 2 | 1 | no | — |
| 82 | #3796 | — | 6 | 2 | no | — |
| 83 | C4⋊#157 | — | 3 | 1 | no | — |
| 84 | #3787 | C2×D3 | 1 | 1 | yes | characteristic |
| 85 | #3775 | — | 2 | 2 | no | — |
| 86 | D32⋊C4 | — | 6 | 1 | no | — |
| 87 | #3753 | — | 6 | 1 | no | — |
| 88 | C3×#213 | — | 6 | 1 | no | — |
| 89 | C3×#213 | — | 6 | 1 | no | — |
| 90 | #3714 | — | 6 | 1 | no | — |
| 91 | #3714 | — | 6 | 1 | no | — |
| 92 | #3714 | — | 12 | 1 | no | — |
| 93 | #3713 | — | 2 | 1 | no | — |
| 94 | #3710 | — | 3 | 1 | no | — |
| 95 | D3×C3⋊C8 | — | 6 | 1 | no | — |
| 96 | C2×C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 97 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 98 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | C2×C32×D3 | — | 2 | 1 | no | — |
| 100 | C2×C32×D3 | — | 4 | 1 | no | — |
| 101 | #1113 | — | 2 | 1 | no | — |
| 102 | #1113 | — | 2 | 1 | no | — |
| 103 | D3×C3⋊D3 | — | 4 | 1 | no | — |
| 104 | D3×C3⋊D3 | — | 4 | 1 | no | — |
| 105 | C3×D32 | — | 4 | 1 | no | — |
| 106 | C3×D32 | — | 4 | 1 | no | — |
| 107 | C3⋊#157 | — | 4 | 1 | no | — |
| 108 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 110 | C3×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | C32×Dic3 | — | 2 | 2 | no | — |
| 112 | D3×#41 | — | 18 | 1 | no | — |
| 113 | C2×#239 | — | 9 | 1 | no | — |
| 114 | C2×C3×SD16 | — | 9 | 1 | no | — |
| 115 | #938 | — | 9 | 1 | no | — |
| 116 | C2×#213 | — | 9 | 1 | no | — |
| 117 | D3×D8 | — | 18 | 1 | no | — |
| 118 | #835 | — | 9 | 1 | no | — |
| 119 | #821 | — | 9 | 1 | no | — |
| 120 | (C2×D3)⋊C8 | — | 9 | 1 | no | — |
| 121 | C22×C3⋊D3 | — | 6 | 1 | no | — |
| 122 | C22×C3×D3 | — | 12 | 1 | no | — |
| 123 | C2×D32 | — | 2 | 1 | no | — |
| 124 | C2×D32 | — | 3 | 1 | no | — |
| 125 | C2×D32 | — | 6 | 1 | no | — |
| 126 | C2×D32 | — | 6 | 2 | no | — |
| 127 | C2×D32 | — | 12 | 1 | no | — |
| 128 | C2×#157 | — | 6 | 1 | no | — |
| 129 | GO+(4,𝔽2) | — | 12 | 2 | no | — |
| 130 | C32×Q8 | — | 6 | 1 | no | — |
| 131 | C32×D4 | — | 3 | 1 | no | — |
| 132 | C32×D4 | — | 6 | 1 | no | — |
| 133 | #638 | — | 6 | 1 | no | — |
| 134 | C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 135 | C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 136 | C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 137 | C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 138 | C4⋊(C3⋊D3) | — | 12 | 1 | no | — |
| 139 | C4⋊(C3⋊D3) | — | 12 | 1 | no | — |
| 140 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 141 | C4×C3⋊D3 | — | 6 | 2 | no | — |
| 142 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 143 | C3×#67 | — | 6 | 2 | no | — |
| 144 | C3×#67 | — | 12 | 1 | no | — |
| 145 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 146 | C3×D12 | — | 2 | 1 | no | — |
| 147 | C3×D12 | — | 2 | 1 | no | — |
| 148 | C3×D12 | — | 2 | 1 | no | — |
| 149 | C3×D12 | — | 2 | 1 | no | — |
| 150 | C3×D12 | — | 4 | 1 | no | — |
| 151 | C3×D12 | — | 6 | 2 | no | — |
| 152 | C3×C4×D3 | — | 6 | 1 | no | — |
| 153 | C3×C4×D3 | — | 6 | 1 | no | — |
| 154 | C3×C4×D3 | — | 6 | 2 | no | — |
| 155 | C3×C4×D3 | — | 6 | 1 | no | — |
| 156 | C3×C4×D3 | — | 6 | 2 | no | — |
| 157 | C3×C4×D3 | — | 6 | 1 | no | — |
| 158 | C3×C4×D3 | — | 12 | 1 | no | — |
| 159 | C3×Dic6 | — | 2 | 1 | no | — |
| 160 | C3×Dic6 | — | 2 | 1 | no | — |
| 161 | C3×Dic6 | — | 4 | 1 | no | — |
| 162 | C3×Dic6 | — | 6 | 2 | no | — |
| 163 | #627 | #67 | 1 | 2 | yes | complemented |
| 164 | #626 | — | 2 | 2 | no | — |
| 165 | #626 | — | 6 | 2 | no | — |
| 166 | #626 | — | 6 | 2 | no | — |
| 167 | #626 | — | 6 | 2 | no | — |
| 168 | #626 | — | 12 | 1 | no | — |
| 169 | #626 | — | 12 | 2 | no | — |
| 170 | #625 | — | 2 | 1 | no | — |
| 171 | #624 | — | 2 | 1 | no | — |
| 172 | #624 | — | 3 | 1 | no | — |
| 173 | #624 | — | 6 | 2 | no | — |
| 174 | #624 | — | 6 | 2 | no | — |
| 175 | #624 | — | 6 | 1 | no | — |
| 176 | #624 | — | 12 | 2 | no | — |
| 177 | D3×Dic3 | — | 2 | 2 | no | — |
| 178 | D3×Dic3 | — | 6 | 1 | no | — |
| 179 | D3×Dic3 | — | 6 | 1 | no | — |
| 180 | D3×Dic3 | — | 6 | 1 | no | — |
| 181 | #622 | — | 2 | 1 | no | — |
| 182 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 183 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 184 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 185 | C3×C3⋊C8 | — | 12 | 1 | no | — |
| 186 | #449 | — | 27 | 1 | no | Sylow |
| 187 | C2×C33 | #120 | 1 | 1 | yes | characteristic |
| 188 | C3⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 189 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 190 | C3×C3⋊D3 | #135 | 1 | 1 | yes | characteristic |
| 191 | C3×C3⋊D3 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 192 | C32×D3 | — | 4 | 1 | no | — |
| 193 | C32×D3 | — | 8 | 1 | no | — |
| 194 | C3×#41 | — | 18 | 1 | no | — |
| 195 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 196 | C2×C3×D4 | — | 9 | 1 | no | — |
| 197 | C2×#67 | — | 18 | 1 | no | — |
| 198 | #239 | — | 6 | 1 | no | — |
| 199 | #239 | — | 18 | 2 | no | — |
| 200 | #239 | — | 18 | 1 | no | — |
| 201 | #239 | — | 18 | 1 | no | — |
| 202 | #239 | — | 36 | 1 | no | — |
| 203 | D3×Q8 | — | 6 | 1 | no | — |
| 204 | #237 | — | 6 | 1 | no | — |
| 205 | #237 | — | 18 | 2 | no | — |
| 206 | D3×D4 | — | 6 | 1 | no | — |
| 207 | D3×D4 | — | 18 | 1 | no | — |
| 208 | D3×D4 | — | 18 | 1 | no | — |
| 209 | D3×D4 | — | 18 | 2 | no | — |
| 210 | #235 | — | 18 | 1 | no | — |
| 211 | #235 | — | 18 | 2 | no | — |
| 212 | C2×D12 | — | 9 | 1 | no | — |
| 213 | C2×D12 | — | 18 | 1 | no | — |
| 214 | C2×C4×D3 | — | 9 | 1 | no | — |
| 215 | C2×C4×D3 | — | 18 | 1 | no | — |
| 216 | C2×C4×D3 | — | 18 | 1 | no | — |
| 217 | C2×C4×D3 | — | 18 | 2 | no | — |
| 218 | C3×SD16 | — | 18 | 2 | no | — |
| 219 | C3×D8 | — | 18 | 1 | no | — |
| 220 | C2×C3×C8 | — | 9 | 1 | no | — |
| 221 | #217 | — | 18 | 1 | no | — |
| 222 | #213 | — | 6 | 1 | no | — |
| 223 | #213 | — | 6 | 1 | no | — |
| 224 | #213 | — | 18 | 1 | no | — |
| 225 | #213 | — | 18 | 1 | no | — |
| 226 | #213 | — | 36 | 1 | no | — |
| 227 | C4⋊Dic3 | — | 9 | 1 | no | — |
| 228 | C2×C3⋊C8 | — | 9 | 1 | no | — |
| 229 | D24 | — | 18 | 1 | no | — |
| 230 | D3×C8 | — | 18 | 1 | no | — |
| 231 | C22×C32 | — | 6 | 1 | no | — |
| 232 | C22×C32 | — | 12 | 1 | no | — |
| 233 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 234 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 235 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 236 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 237 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 238 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 239 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 240 | C2×C3⋊D3 | — | 24 | 1 | no | — |
| 241 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 242 | C2×C3×D3 | — | 2 | 2 | no | — |
| 243 | C2×C3×D3 | — | 4 | 1 | no | — |
| 244 | C2×C3×D3 | — | 4 | 1 | no | — |
| 245 | C2×C3×D3 | — | 4 | 1 | no | — |
| 246 | C2×C3×D3 | — | 6 | 1 | no | — |
| 247 | C2×C3×D3 | — | 6 | 1 | no | — |
| 248 | C2×C3×D3 | — | 6 | 1 | no | — |
| 249 | C2×C3×D3 | — | 6 | 1 | no | — |
| 250 | C2×C3×D3 | — | 8 | 1 | no | — |
| 251 | C2×C3×D3 | — | 12 | 1 | no | — |
| 252 | C2×C3×D3 | — | 24 | 1 | no | — |
| 253 | C2×C3×D3 | — | 24 | 1 | no | — |
| 254 | D32 | — | 4 | 1 | no | — |
| 255 | D32 | — | 4 | 1 | no | — |
| 256 | D32 | — | 6 | 1 | no | — |
| 257 | D32 | — | 6 | 1 | no | — |
| 258 | D32 | — | 12 | 1 | no | — |
| 259 | D32 | — | 12 | 1 | no | — |
| 260 | D32 | — | 12 | 2 | no | — |
| 261 | D32 | — | 12 | 2 | no | — |
| 262 | D32 | — | 24 | 1 | no | — |
| 263 | D32 | — | 24 | 1 | no | — |
| 264 | #157 | — | 12 | 1 | no | — |
| 265 | C32×C4 | — | 2 | 1 | no | — |
| 266 | C32×C4 | — | 2 | 1 | no | — |
| 267 | C32×C4 | — | 4 | 1 | no | — |
| 268 | C32×C4 | — | 4 | 1 | no | — |
| 269 | C32×C4 | — | 6 | 2 | no | — |
| 270 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 271 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 272 | C3⋊Dic3 | C2×#67 | 1 | 1 | yes | characteristic |
| 273 | C3×Dic3 | — | 2 | 2 | no | — |
| 274 | C3×Dic3 | — | 2 | 2 | no | — |
| 275 | C3×Dic3 | — | 4 | 2 | no | — |
| 276 | C3×Dic3 | — | 6 | 1 | no | — |
| 277 | C3×Dic3 | — | 6 | 1 | no | — |
| 278 | C3×Dic3 | — | 6 | 1 | no | — |
| 279 | C3×Dic3 | — | 6 | 1 | no | — |
| 280 | C3×Dic3 | — | 12 | 1 | no | — |
| 281 | C2×#41 | — | 27 | 1 | no | — |
| 282 | C2×SD16 | — | 9 | 1 | no | — |
| 283 | C2×D8 | — | 27 | 1 | no | — |
| 284 | #121 | — | 27 | 1 | no | — |
| 285 | #103 | — | 27 | 1 | no | — |
| 286 | #102 | — | 27 | 1 | no | — |
| 287 | C22⋊C8 | — | 27 | 1 | no | — |
| 288 | C33 | #449 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 289 | C23×C3 | — | 18 | 1 | no | — |
| 290 | C22×D3 | — | 9 | 1 | no | — |
| 291 | C22×D3 | — | 12 | 1 | no | — |
| 292 | C22×D3 | — | 18 | 1 | no | — |
| 293 | C22×D3 | — | 18 | 1 | no | — |
| 294 | C22×D3 | — | 18 | 2 | no | — |
| 295 | C22×D3 | — | 36 | 1 | no | — |
| 296 | C3×Q8 | — | 6 | 1 | no | — |
| 297 | C3×Q8 | — | 6 | 1 | no | — |
| 298 | C3×Q8 | — | 9 | 2 | no | — |
| 299 | C3×Q8 | — | 12 | 1 | no | — |
| 300 | C3×D4 | — | 6 | 1 | no | — |
| 301 | C3×D4 | — | 6 | 1 | no | — |
| 302 | C3×D4 | — | 6 | 1 | no | — |
| 303 | C3×D4 | — | 6 | 1 | no | — |
| 304 | C3×D4 | — | 12 | 1 | no | — |
| 305 | C3×D4 | — | 18 | 2 | no | — |
| 306 | C3×D4 | — | 18 | 1 | no | — |
| 307 | C2×C3×C4 | — | 9 | 1 | no | — |
| 308 | C2×C3×C4 | — | 18 | 1 | no | — |
| 309 | C2×C3×C4 | — | 18 | 1 | no | — |
| 310 | C2×C3×C4 | — | 18 | 2 | no | — |
| 311 | #67 | — | 6 | 2 | no | — |
| 312 | #67 | — | 12 | 1 | no | — |
| 313 | #67 | — | 18 | 2 | no | — |
| 314 | #67 | — | 18 | 2 | no | — |
| 315 | #67 | — | 36 | 1 | no | — |
| 316 | #67 | — | 36 | 2 | no | — |
| 317 | C2×Dic3 | — | 6 | 2 | no | — |
| 318 | C2×Dic3 | — | 9 | 1 | no | — |
| 319 | C2×Dic3 | — | 18 | 1 | no | — |
| 320 | C2×Dic3 | — | 18 | 1 | no | — |
| 321 | D12 | — | 2 | 1 | no | — |
| 322 | D12 | — | 6 | 2 | no | — |
| 323 | D12 | — | 9 | 1 | no | — |
| 324 | D12 | — | 18 | 1 | no | — |
| 325 | D12 | — | 18 | 1 | no | — |
| 326 | D12 | — | 18 | 2 | no | — |
| 327 | D12 | — | 18 | 2 | no | — |
| 328 | D12 | — | 18 | 1 | no | — |
| 329 | D12 | — | 36 | 1 | no | — |
| 330 | D12 | — | 36 | 1 | no | — |
| 331 | D12 | — | 36 | 2 | no | — |
| 332 | D12 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 333 | C4×D3 | — | 6 | 1 | no | — |
| 334 | C4×D3 | — | 6 | 1 | no | — |
| 335 | C4×D3 | — | 6 | 2 | no | — |
| 336 | C4×D3 | — | 6 | 1 | no | — |
| 337 | C4×D3 | — | 6 | 2 | no | — |
| 338 | C4×D3 | — | 6 | 1 | no | — |
| 339 | C4×D3 | — | 12 | 1 | no | — |
| 340 | C4×D3 | — | 18 | 1 | no | — |
| 341 | C4×D3 | — | 18 | 2 | no | — |
| 342 | C4×D3 | — | 18 | 2 | no | — |
| 343 | C4×D3 | — | 18 | 2 | no | — |
| 344 | C4×D3 | — | 18 | 1 | no | — |
| 345 | C4×D3 | — | 18 | 1 | no | — |
| 346 | C4×D3 | — | 36 | 2 | no | — |
| 347 | Dic6 | — | 2 | 1 | no | — |
| 348 | Dic6 | — | 6 | 2 | no | — |
| 349 | C3×C8 | — | 18 | 1 | no | — |
| 350 | C3×C8 | — | 18 | 1 | no | — |
| 351 | C3⋊C8 | — | 6 | 1 | no | — |
| 352 | C3⋊C8 | — | 6 | 1 | no | — |
| 353 | C3⋊C8 | — | 12 | 1 | no | — |
| 354 | C2×C32 | — | 2 | 1 | no | — |
| 355 | C2×C32 | — | 2 | 1 | no | — |
| 356 | C2×C32 | — | 4 | 1 | no | — |
| 357 | C2×C32 | — | 4 | 1 | no | — |
| 358 | C2×C32 | — | 12 | 1 | no | — |
| 359 | C2×C32 | — | 24 | 1 | no | — |
| 360 | C2×C32 | #937 | 1 | 1 | yes | characteristic |
| 361 | C3⋊D3 | — | 4 | 1 | no | — |
| 362 | C3⋊D3 | — | 12 | 2 | no | — |
| 363 | C3⋊D3 | — | 12 | 1 | no | — |
| 364 | C3⋊D3 | — | 24 | 1 | no | — |
| 365 | C3⋊D3 | — | 24 | 2 | no | — |
| 366 | C3⋊D3 | — | 48 | 1 | no | — |
| 367 | C3⋊D3 | #914 | 1 | 1 | yes | characteristic |
| 368 | C3⋊D3 | #916 | 1 | 1 | yes | characteristic |
| 369 | C3×D3 | — | 4 | 2 | no | — |
| 370 | C3×D3 | — | 6 | 1 | no | — |
| 371 | C3×D3 | — | 6 | 1 | no | — |
| 372 | C3×D3 | — | 6 | 1 | no | — |
| 373 | C3×D3 | — | 6 | 1 | no | — |
| 374 | C3×D3 | — | 8 | 1 | no | — |
| 375 | C3×D3 | — | 8 | 1 | no | — |
| 376 | C3×D3 | — | 8 | 1 | no | — |
| 377 | C3×D3 | — | 12 | 1 | no | — |
| 378 | C3×D3 | — | 12 | 1 | no | — |
| 379 | C3×D3 | — | 16 | 1 | no | — |
| 380 | C3×D3 | — | 24 | 1 | no | — |
| 381 | #41 | — | 18 | 1 | no | — |
| 382 | #41 | — | 54 | 2 | no | — |
| 383 | #41 | — | 54 | 1 | no | — |
| 384 | C2×Q8 | — | 9 | 1 | no | — |
| 385 | C2×D4 | — | 9 | 1 | no | — |
| 386 | C2×D4 | — | 27 | 1 | no | — |
| 387 | C2×D4 | — | 54 | 1 | no | — |
| 388 | C2×D4 | — | 54 | 1 | no | — |
| 389 | C22×C4 | — | 27 | 1 | no | — |
| 390 | C22×C4 | — | 54 | 1 | no | — |
| 391 | SD16 | — | 18 | 2 | no | — |
| 392 | D8 | — | 18 | 1 | no | — |
| 393 | D8 | — | 54 | 1 | no | — |
| 394 | C2×C8 | — | 9 | 1 | no | — |
| 395 | C2×C8 | — | 27 | 1 | no | — |
| 396 | C4⋊C4 | — | 27 | 1 | no | — |
| 397 | C22⋊C4 | — | 54 | 1 | no | — |
| 398 | C22×C3 | — | 6 | 2 | no | — |
| 399 | C22×C3 | — | 9 | 1 | no | — |
| 400 | C22×C3 | — | 12 | 1 | no | — |
| 401 | C22×C3 | — | 12 | 1 | no | — |
| 402 | C22×C3 | — | 12 | 1 | no | — |
| 403 | C22×C3 | — | 18 | 1 | no | — |
| 404 | C22×C3 | — | 24 | 1 | no | — |
| 405 | C22×C3 | — | 36 | 1 | no | — |
| 406 | C22×C3 | — | 36 | 1 | no | — |
| 407 | C2×D3 | — | 2 | 1 | no | — |
| 408 | C2×D3 | — | 4 | 1 | no | — |
| 409 | C2×D3 | — | 6 | 1 | no | — |
| 410 | C2×D3 | — | 6 | 1 | no | — |
| 411 | C2×D3 | — | 6 | 1 | no | — |
| 412 | C2×D3 | — | 6 | 1 | no | — |
| 413 | C2×D3 | — | 12 | 1 | no | — |
| 414 | C2×D3 | — | 18 | 1 | no | — |
| 415 | C2×D3 | — | 18 | 1 | no | — |
| 416 | C2×D3 | — | 18 | 2 | no | — |
| 417 | C2×D3 | — | 18 | 1 | no | — |
| 418 | C2×D3 | — | 24 | 1 | no | — |
| 419 | C2×D3 | — | 24 | 1 | no | — |
| 420 | C2×D3 | — | 36 | 1 | no | — |
| 421 | C2×D3 | — | 36 | 1 | no | — |
| 422 | C2×D3 | — | 36 | 1 | no | — |
| 423 | C2×D3 | — | 36 | 2 | no | — |
| 424 | C2×D3 | — | 36 | 1 | no | — |
| 425 | C2×D3 | — | 36 | 1 | no | — |
| 426 | C2×D3 | — | 36 | 2 | no | — |
| 427 | C2×D3 | — | 36 | 2 | no | — |
| 428 | C2×D3 | — | 72 | 1 | no | — |
| 429 | C2×D3 | — | 72 | 1 | no | — |
| 430 | C2×D3 | — | 72 | 1 | no | — |
| 431 | C3×C4 | — | 2 | 1 | no | — |
| 432 | C3×C4 | — | 2 | 1 | no | — |
| 433 | C3×C4 | — | 4 | 1 | no | — |
| 434 | C3×C4 | — | 4 | 1 | no | — |
| 435 | C3×C4 | — | 6 | 2 | no | — |
| 436 | C3×C4 | — | 6 | 2 | no | — |
| 437 | C3×C4 | — | 9 | 1 | no | — |
| 438 | C3×C4 | — | 12 | 2 | no | — |
| 439 | C3×C4 | — | 18 | 1 | no | — |
| 440 | C3×C4 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 441 | Dic3 | — | 2 | 2 | no | — |
| 442 | Dic3 | — | 6 | 1 | no | — |
| 443 | Dic3 | — | 6 | 1 | no | — |
| 444 | Dic3 | — | 6 | 1 | no | — |
| 445 | Dic3 | — | 6 | 1 | no | — |
| 446 | Dic3 | — | 12 | 1 | no | — |
| 447 | Dic3 | — | 36 | 1 | no | — |
| 448 | C32 | — | 2 | 1 | no | — |
| 449 | C32 | — | 2 | 1 | no | — |
| 450 | C32 | — | 4 | 1 | no | — |
| 451 | C32 | — | 4 | 1 | no | — |
| 452 | C32 | #5172 | 1 | 1 | yes | characteristic, complemented |
| 453 | C23 | — | 18 | 1 | no | — |
| 454 | C23 | — | 27 | 1 | no | — |
| 455 | C23 | — | 54 | 1 | no | — |
| 456 | Q8 | — | 6 | 1 | no | — |
| 457 | Q8 | — | 9 | 2 | no | — |
| 458 | D4 | — | 3 | 1 | no | — |
| 459 | D4 | — | 6 | 1 | no | — |
| 460 | D4 | — | 18 | 2 | no | — |
| 461 | D4 | — | 18 | 1 | no | — |
| 462 | D4 | — | 27 | 1 | no | — |
| 463 | D4 | — | 54 | 2 | no | — |
| 464 | D4 | — | 54 | 1 | no | — |
| 465 | D4 | — | 108 | 2 | no | — |
| 466 | C2×C4 | — | 9 | 1 | no | — |
| 467 | C2×C4 | — | 18 | 1 | no | — |
| 468 | C2×C4 | — | 18 | 2 | no | — |
| 469 | C2×C4 | — | 18 | 1 | no | — |
| 470 | C2×C4 | — | 27 | 1 | no | — |
| 471 | C2×C4 | — | 54 | 2 | no | — |
| 472 | C2×C4 | — | 54 | 1 | no | — |
| 473 | C2×C4 | — | 54 | 1 | no | — |
| 474 | C8 | — | 18 | 1 | no | — |
| 475 | C8 | — | 18 | 1 | no | — |
| 476 | C2×C3 | — | 2 | 1 | no | — |
| 477 | C2×C3 | — | 2 | 1 | no | — |
| 478 | C2×C3 | — | 4 | 1 | no | — |
| 479 | C2×C3 | — | 4 | 1 | no | — |
| 480 | C2×C3 | — | 9 | 1 | no | — |
| 481 | C2×C3 | — | 9 | 1 | no | — |
| 482 | C2×C3 | — | 12 | 2 | no | — |
| 483 | C2×C3 | — | 24 | 1 | no | — |
| 484 | C2×C3 | — | 24 | 1 | no | — |
| 485 | C2×C3 | — | 24 | 1 | no | — |
| 486 | C2×C3 | — | 36 | 1 | no | — |
| 487 | C2×C3 | — | 48 | 1 | no | — |
| 488 | C2×C3 | #64241 | 1 | 1 | yes | characteristic |
| 489 | D3 | — | 4 | 1 | no | — |
| 490 | D3 | — | 6 | 1 | no | — |
| 491 | D3 | — | 6 | 1 | no | — |
| 492 | D3 | — | 6 | 1 | no | — |
| 493 | D3 | — | 6 | 1 | no | — |
| 494 | D3 | — | 8 | 1 | no | — |
| 495 | D3 | — | 12 | 1 | no | — |
| 496 | D3 | — | 12 | 1 | no | — |
| 497 | D3 | — | 24 | 1 | no | — |
| 498 | D3 | — | 36 | 2 | no | — |
| 499 | D3 | — | 36 | 1 | no | — |
| 500 | D3 | — | 72 | 1 | no | — |
| 501 | D3 | — | 72 | 2 | no | — |
| 502 | D3 | — | 144 | 1 | no | — |
| 503 | C22 | — | 6 | 1 | no | — |
| 504 | C22 | — | 9 | 1 | no | — |
| 505 | C22 | — | 12 | 1 | no | — |
| 506 | C22 | — | 18 | 1 | no | — |
| 507 | C22 | — | 36 | 1 | no | — |
| 508 | C22 | — | 36 | 1 | no | — |
| 509 | C22 | — | 54 | 1 | no | — |
| 510 | C22 | — | 54 | 1 | no | — |
| 511 | C22 | — | 54 | 1 | no | — |
| 512 | C22 | — | 108 | 1 | no | — |
| 513 | C22 | — | 108 | 1 | no | — |
| 514 | C4 | — | 6 | 2 | no | — |
| 515 | C4 | — | 9 | 1 | no | — |
| 516 | C4 | — | 18 | 1 | no | — |
| 517 | C4 | — | 108 | 1 | no | — |
| 518 | C4 | D3×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 519 | C3 | — | 2 | 1 | no | — |
| 520 | C3 | — | 2 | 1 | no | — |
| 521 | C3 | — | 4 | 1 | no | — |
| 522 | C3 | — | 4 | 1 | no | — |
| 523 | C3 | #10593458 | 1 | 1 | yes | characteristic, complemented |
| 524 | C2 | — | 9 | 1 | no | — |
| 525 | C2 | — | 9 | 1 | no | — |
| 526 | C2 | — | 12 | 1 | no | — |
| 527 | C2 | — | 24 | 1 | no | — |
| 528 | C2 | — | 36 | 1 | no | — |
| 529 | C2 | — | 108 | 1 | no | — |
| 530 | C2 | #11724112 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11724112 |
| commutator, cosocle | C3×C4×C3⋊D3 | C23 |
| Frattini, hypercenter | C4 | D3×GO+(4,𝔽2) |
| Fitting | C33×C4 | C2×D4 |
| socle | C2×C33 | #120 |
| hypocenter | C33 | #449 |
| LCS | G ▷ C3×C4×C3⋊D3 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11724377 | C2 | semidirect |
| 2. #11724313 | C2 | semidirect |
| 3. C3×#64227 | C2 | semidirect |
| 4. #11722830 | C2 | semidirect |
| 5. #11722780 | C2 | semidirect |
| 6. #11722760 | C2 | semidirect |
| 7. #11722707 | C2 | semidirect |
| 29. #64227 | D3 | semidirect |
| 40. C4⋊(C3⋊(C3⋊D3)) | D4 | semidirect |
| 44. C32×D12 | D4 | semidirect |
| 51. C3×#627 | D4 | semidirect |
| 163. #627 | #67 | semidirect |
| 288. C33 | #449 | semidirect |
| 332. D12 | GO+(4,𝔽2) | semidirect |
| 452. C32 | #5172 | semidirect |
| 523. C3 | #10593458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724377 | 2 |
| #11724313 | 2 |
| C3×#64227 | 2 |
| #11722830 | 2 |
| #11722780 | 2 |
| #11722760 | 2 |
| #11722707 | 2 |
| #10593458 | 3 |
| #5172 | 9 |