Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
976 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 976 conjugacy classes of subgroups — too many to draw. Only its 108 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 | #11724414 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #11724351 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11724323 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C2×C3×#3774 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11724266 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11724140 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11724138 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11724135 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11724132 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11724127 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | D3×#3774 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10596514 | — | 3 | 1 | no | maximal |
| 13 | #89046 | C22 | 1 | 2 | yes | complemented |
| 14 | D3×#638 | — | 2 | 2 | no | — |
| 15 | #89028 | C22 | 1 | 1 | yes | characteristic |
| 16 | C3×D3×#67 | — | 2 | 2 | no | — |
| 17 | C2×C3×#625 | C22 | 1 | 2 | yes | complemented |
| 18 | #88993 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C2×C3×#622 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #88963 | C22 | 1 | 2 | yes | complemented |
| 21 | #88961 | — | 2 | 2 | no | — |
| 22 | #88959 | C22 | 1 | 2 | yes | complemented |
| 23 | #88954 | C22 | 1 | 2 | yes | complemented |
| 24 | #88952 | — | 2 | 2 | no | — |
| 25 | D3×#625 | C22 | 1 | 2 | yes | complemented |
| 26 | #88943 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #88942 | C22 | 1 | 2 | yes | complemented |
| 28 | #88941 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #88937 | C22 | 1 | 2 | yes | complemented |
| 30 | #88937 | C22 | 1 | 2 | yes | complemented |
| 31 | #88935 | C22 | 1 | 2 | yes | complemented |
| 32 | #88935 | C22 | 1 | 2 | yes | complemented |
| 33 | C3×#3774 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | C3×#3774 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | C3×#3774 | C22 | 1 | 2 | yes | complemented |
| 36 | #88926 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #88925 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #88924 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | D3×#622 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #64330 | — | 6 | 2 | no | — |
| 41 | #64313 | — | 3 | 2 | no | — |
| 42 | #64287 | — | 3 | 1 | no | — |
| 43 | #64237 | — | 3 | 1 | no | — |
| 44 | #64237 | — | 3 | 1 | no | — |
| 45 | #64236 | — | 3 | 2 | no | — |
| 46 | #64236 | — | 3 | 2 | no | — |
| 47 | C2×#3774 | — | 3 | 1 | no | — |
| 48 | C2×#3774 | D3 | 1 | 1 | yes | characteristic, complemented |
| 49 | #64225 | — | 3 | 1 | no | — |
| 50 | #64224 | — | 3 | 2 | no | — |
| 51 | #64223 | — | 3 | 1 | no | — |
| 52 | C22×C32×D3 | — | 2 | 2 | no | — |
| 53 | C2×D3×C3⋊D3 | — | 2 | 2 | no | — |
| 54 | C2×C3×D32 | — | 2 | 2 | no | — |
| 55 | #6312 | D4 | 1 | 1 | yes | characteristic |
| 56 | C3×#638 | — | 2 | 2 | no | — |
| 57 | C2×C3×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 58 | C32×#67 | D4 | 1 | 1 | yes | characteristic |
| 59 | #6296 | C23 | 1 | 2 | yes | — |
| 60 | #6295 | C23 | 1 | 2 | yes | — |
| 61 | #6294 | — | 2 | 2 | no | — |
| 62 | #6293 | D4 | 1 | 1 | yes | characteristic |
| 63 | #6291 | — | 2 | 2 | no | — |
| 64 | #6291 | D4 | 1 | 1 | yes | characteristic |
| 65 | #6290 | — | 2 | 2 | no | — |
| 66 | #6289 | C23 | 1 | 1 | yes | characteristic |
| 67 | D3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 68 | D3×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 69 | C3×#626 | — | 2 | 2 | no | — |
| 70 | C3×#625 | — | 2 | 2 | no | — |
| 71 | C3×#625 | — | 2 | 2 | no | — |
| 72 | C3×#625 | C23 | 1 | 2 | yes | — |
| 73 | C3×#625 | C23 | 1 | 2 | yes | — |
| 74 | C3×D3×Dic3 | — | 2 | 2 | no | — |
| 75 | C3⋊#622 | C23 | 1 | 1 | yes | characteristic |
| 76 | C3⋊#622 | C23 | 1 | 1 | yes | characteristic |
| 77 | C3×#622 | C23 | 1 | 1 | yes | characteristic |
| 78 | C3×#622 | C23 | 1 | 1 | yes | characteristic |
| 79 | #5757 | — | 9 | 1 | no | maximal |
| 80 | C2×#638 | — | 6 | 2 | no | — |
| 81 | #3830 | — | 3 | 1 | no | — |
| 82 | C2×C3×#67 | — | 6 | 2 | no | — |
| 83 | C2×C3×#67 | — | 6 | 2 | no | — |
| 84 | C3×D3×D4 | — | 6 | 2 | no | — |
| 85 | #3811 | — | 6 | 2 | no | — |
| 86 | #3811 | — | 6 | 2 | no | — |
| 87 | D3×#67 | — | 2 | 2 | no | — |
| 88 | D3×#67 | — | 6 | 2 | no | — |
| 89 | D3×#67 | — | 6 | 2 | no | — |
| 90 | D3×#67 | — | 6 | 2 | no | — |
| 91 | D3×#67 | — | 6 | 2 | no | — |
| 92 | D3×#67 | — | 6 | 2 | no | — |
| 93 | D3×#67 | — | 12 | 2 | no | — |
| 94 | C2×#625 | — | 3 | 2 | no | — |
| 95 | C2×#625 | C2×D3 | 1 | 2 | yes | complemented |
| 96 | #3805 | — | 3 | 2 | no | — |
| 97 | #3805 | — | 3 | 2 | no | — |
| 98 | #3805 | — | 6 | 2 | no | — |
| 99 | #3805 | — | 6 | 2 | no | — |
| 100 | #3804 | — | 6 | 2 | no | — |
| 101 | #3804 | — | 6 | 2 | no | — |
| 102 | #3804 | — | 6 | 2 | no | — |
| 103 | #3804 | — | 6 | 2 | no | — |
| 104 | #3802 | — | 3 | 2 | no | — |
| 105 | #3798 | — | 3 | 2 | no | — |
| 106 | #3795 | — | 6 | 2 | no | — |
| 107 | #3792 | — | 3 | 1 | no | — |
| 108 | #3792 | — | 3 | 1 | no | — |
| 109 | C2×#622 | — | 3 | 1 | no | — |
| 110 | C2×#622 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 111 | #3788 | — | 3 | 1 | no | — |
| 112 | #3787 | — | 3 | 1 | no | — |
| 113 | #3776 | — | 3 | 1 | no | — |
| 114 | #3775 | — | 3 | 2 | no | — |
| 115 | #3775 | — | 3 | 2 | no | — |
| 116 | #3775 | — | 3 | 2 | no | — |
| 117 | #3774 | — | 3 | 2 | no | — |
| 118 | #3774 | — | 3 | 2 | no | — |
| 119 | #3774 | — | 3 | 1 | no | — |
| 120 | #3774 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 121 | #3774 | C2×D3 | 1 | 2 | yes | complemented |
| 122 | #3774 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 123 | C22×C33 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C2×C3⋊(C3⋊D3) | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 126 | C2×C32×D3 | — | 2 | 2 | no | — |
| 127 | C2×C32×D3 | — | 2 | 2 | no | — |
| 128 | C2×C32×D3 | — | 8 | 2 | no | — |
| 129 | C2×C32×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | D3×C3⋊D3 | — | 8 | 2 | no | — |
| 131 | C3×D32 | — | 8 | 2 | no | — |
| 132 | C3⋊(C3⋊Dic3) | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 134 | C3×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | C3×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 136 | C32×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | #1004 | — | 9 | 2 | no | — |
| 138 | #1004 | — | 18 | 2 | no | — |
| 139 | C2×C3×D8 | — | 9 | 1 | no | — |
| 140 | #932 | — | 9 | 2 | no | — |
| 141 | #912 | — | 9 | 1 | no | — |
| 142 | #912 | — | 9 | 1 | no | — |
| 143 | #911 | — | 9 | 2 | no | — |
| 144 | #911 | — | 9 | 2 | no | — |
| 145 | D3×D8 | — | 9 | 1 | no | — |
| 146 | D3×D8 | — | 9 | 1 | no | — |
| 147 | #904 | — | 9 | 1 | no | — |
| 148 | #901 | — | 9 | 1 | no | — |
| 149 | C23×C32 | — | 6 | 2 | no | — |
| 150 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 151 | C22×C3×D3 | — | 2 | 2 | no | — |
| 152 | C22×C3×D3 | — | 2 | 2 | no | — |
| 153 | C22×C3×D3 | — | 4 | 2 | no | — |
| 154 | C22×C3×D3 | — | 6 | 2 | no | — |
| 155 | C22×C3×D3 | — | 6 | 2 | no | — |
| 156 | C2×D32 | — | 2 | 2 | no | — |
| 157 | C2×D32 | — | 6 | 2 | no | — |
| 158 | C2×D32 | — | 6 | 2 | no | — |
| 159 | C2×D32 | — | 12 | 2 | no | — |
| 160 | C32×D4 | — | 3 | 1 | no | — |
| 161 | #638 | — | 2 | 2 | no | — |
| 162 | #638 | — | 3 | 1 | no | — |
| 163 | #638 | — | 3 | 1 | no | — |
| 164 | #638 | — | 6 | 2 | no | — |
| 165 | #638 | — | 6 | 2 | no | — |
| 166 | #638 | — | 6 | 2 | no | — |
| 167 | #638 | — | 12 | 2 | no | — |
| 168 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 169 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 170 | C2×C3⋊Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 171 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 172 | #634 | — | 3 | 1 | no | — |
| 173 | C3×#67 | — | 2 | 2 | no | — |
| 174 | C3×#67 | — | 6 | 2 | no | — |
| 175 | C3×#67 | — | 6 | 2 | no | — |
| 176 | C3×#67 | — | 6 | 2 | no | — |
| 177 | C3×#67 | — | 6 | 2 | no | — |
| 178 | C3×#67 | — | 6 | 2 | no | — |
| 179 | C3×#67 | — | 6 | 2 | no | — |
| 180 | C3×#67 | — | 6 | 2 | no | — |
| 181 | C3×#67 | — | 6 | 2 | no | — |
| 182 | C3×#67 | — | 6 | 2 | no | — |
| 183 | C3×#67 | — | 12 | 2 | no | — |
| 184 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 185 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 186 | C3×D12 | — | 6 | 2 | no | — |
| 187 | C3×C4×D3 | — | 6 | 2 | no | — |
| 188 | #627 | — | 3 | 2 | no | — |
| 189 | #627 | — | 6 | 2 | no | — |
| 190 | #627 | — | 6 | 2 | no | — |
| 191 | #626 | — | 2 | 2 | no | — |
| 192 | #626 | — | 6 | 2 | no | — |
| 193 | #626 | — | 6 | 2 | no | — |
| 194 | #626 | — | 6 | 2 | no | — |
| 195 | #626 | — | 6 | 2 | no | — |
| 196 | #626 | — | 12 | 2 | no | — |
| 197 | #625 | — | 2 | 2 | no | — |
| 198 | #625 | — | 2 | 2 | no | — |
| 199 | #625 | — | 3 | 2 | no | — |
| 200 | #625 | — | 6 | 2 | no | — |
| 201 | #625 | — | 6 | 2 | no | — |
| 202 | #625 | — | 12 | 2 | no | — |
| 203 | #625 | C22×D3 | 1 | 2 | yes | — |
| 204 | #625 | C22×D3 | 1 | 2 | yes | — |
| 205 | #624 | — | 6 | 2 | no | — |
| 206 | #624 | — | 6 | 2 | no | — |
| 207 | D3×Dic3 | — | 2 | 2 | no | — |
| 208 | D3×Dic3 | — | 6 | 2 | no | — |
| 209 | D3×Dic3 | — | 6 | 2 | no | — |
| 210 | D3×Dic3 | — | 6 | 2 | no | — |
| 211 | D3×Dic3 | — | 6 | 2 | no | — |
| 212 | D3×Dic3 | — | 6 | 2 | no | — |
| 213 | D3×Dic3 | — | 12 | 2 | no | — |
| 214 | #622 | — | 3 | 1 | no | — |
| 215 | #622 | — | 3 | 1 | no | — |
| 216 | #622 | C22×D3 | 1 | 1 | yes | characteristic |
| 217 | #622 | C22×D3 | 1 | 1 | yes | characteristic |
| 218 | #576 | — | 27 | 1 | no | Sylow |
| 219 | C2×C33 | — | 2 | 1 | no | — |
| 220 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 221 | C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 222 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 223 | C32×D3 | — | 2 | 1 | no | — |
| 224 | C32×D3 | — | 4 | 2 | no | — |
| 225 | C32×D3 | — | 4 | 2 | no | — |
| 226 | C2×C3×D4 | — | 9 | 2 | no | — |
| 227 | C2×C3×D4 | — | 18 | 2 | no | — |
| 228 | C2×#67 | — | 6 | 2 | no | — |
| 229 | C2×#67 | — | 6 | 2 | no | — |
| 230 | C2×#67 | — | 18 | 2 | no | — |
| 231 | C2×#67 | — | 18 | 2 | no | — |
| 232 | C2×#67 | — | 18 | 2 | no | — |
| 233 | C2×#67 | — | 18 | 2 | no | — |
| 234 | C2×#67 | — | 36 | 2 | no | — |
| 235 | #237 | — | 9 | 2 | no | — |
| 236 | #237 | — | 9 | 2 | no | — |
| 237 | #237 | — | 18 | 2 | no | — |
| 238 | #237 | — | 18 | 2 | no | — |
| 239 | #237 | — | 18 | 2 | no | — |
| 240 | #237 | — | 18 | 2 | no | — |
| 241 | #237 | — | 18 | 2 | no | — |
| 242 | D3×D4 | — | 6 | 2 | no | — |
| 243 | D3×D4 | — | 9 | 2 | no | — |
| 244 | D3×D4 | — | 9 | 2 | no | — |
| 245 | D3×D4 | — | 18 | 2 | no | — |
| 246 | D3×D4 | — | 18 | 2 | no | — |
| 247 | D3×D4 | — | 18 | 2 | no | — |
| 248 | D3×D4 | — | 18 | 2 | no | — |
| 249 | #235 | — | 9 | 1 | no | — |
| 250 | #235 | — | 9 | 2 | no | — |
| 251 | #235 | — | 18 | 2 | no | — |
| 252 | #235 | — | 18 | 2 | no | — |
| 253 | C3×D8 | — | 9 | 1 | no | — |
| 254 | C3×D8 | — | 9 | 1 | no | — |
| 255 | C3×D8 | — | 9 | 2 | no | — |
| 256 | C2×C3×C8 | — | 9 | 1 | no | — |
| 257 | #214 | — | 9 | 2 | no | — |
| 258 | #214 | — | 9 | 2 | no | — |
| 259 | #213 | — | 9 | 2 | no | — |
| 260 | #213 | — | 9 | 2 | no | — |
| 261 | #208 | — | 9 | 1 | no | — |
| 262 | Dic12 | — | 9 | 1 | no | — |
| 263 | D24 | — | 9 | 1 | no | — |
| 264 | #204 | — | 9 | 2 | no | — |
| 265 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 266 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 267 | D3×C8 | — | 9 | 1 | no | — |
| 268 | D3×C8 | — | 9 | 1 | no | — |
| 269 | C22×C32 | — | 2 | 2 | no | — |
| 270 | C22×C32 | — | 3 | 1 | no | — |
| 271 | C22×C32 | — | 4 | 2 | no | — |
| 272 | C22×C32 | — | 6 | 2 | no | — |
| 273 | C22×C32 | — | 6 | 2 | no | — |
| 274 | C22×C32 | — | 24 | 2 | no | — |
| 275 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 276 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 277 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 278 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 279 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 280 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 281 | C2×C3×D3 | — | 2 | 2 | no | — |
| 282 | C2×C3×D3 | — | 2 | 2 | no | — |
| 283 | C2×C3×D3 | — | 2 | 2 | no | — |
| 284 | C2×C3×D3 | — | 2 | 2 | no | — |
| 285 | C2×C3×D3 | — | 2 | 2 | no | — |
| 286 | C2×C3×D3 | — | 4 | 2 | no | — |
| 287 | C2×C3×D3 | — | 4 | 2 | no | — |
| 288 | C2×C3×D3 | — | 6 | 2 | no | — |
| 289 | C2×C3×D3 | — | 6 | 2 | no | — |
| 290 | C2×C3×D3 | — | 8 | 2 | no | — |
| 291 | C2×C3×D3 | — | 8 | 2 | no | — |
| 292 | C2×C3×D3 | — | 8 | 4 | no | — |
| 293 | C2×C3×D3 | — | 12 | 2 | no | — |
| 294 | C2×C3×D3 | — | 24 | 2 | no | — |
| 295 | C2×C3×D3 | — | 24 | 2 | no | — |
| 296 | D32 | — | 8 | 2 | no | — |
| 297 | D32 | — | 24 | 2 | no | — |
| 298 | D32 | — | 24 | 2 | no | — |
| 299 | D32 | — | 24 | 4 | no | — |
| 300 | C32×C4 | — | 3 | 1 | no | — |
| 301 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 302 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 303 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 304 | C3⋊Dic3 | — | 12 | 2 | no | — |
| 305 | C3⋊Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 306 | C3⋊Dic3 | C23×D3 | 1 | 1 | yes | characteristic |
| 307 | C3×Dic3 | — | 2 | 2 | no | — |
| 308 | C3×Dic3 | — | 6 | 2 | no | — |
| 309 | C3×Dic3 | — | 6 | 2 | no | — |
| 310 | C3×Dic3 | — | 6 | 2 | no | — |
| 311 | C3×Dic3 | — | 6 | 2 | no | — |
| 312 | C3×Dic3 | — | 12 | 2 | no | — |
| 313 | H(5,𝔽2) | — | 27 | 2 | no | — |
| 314 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 315 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 316 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 317 | #135 | — | 27 | 1 | no | — |
| 318 | #135 | — | 27 | 1 | no | — |
| 319 | #135 | — | 27 | 1 | no | — |
| 320 | C2×D8 | — | 9 | 1 | no | — |
| 321 | C2×D8 | — | 27 | 1 | no | — |
| 322 | C2×D8 | — | 27 | 1 | no | — |
| 323 | #131 | — | 27 | 1 | no | — |
| 324 | C33 | #576 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 325 | C23×C3 | — | 6 | 2 | no | — |
| 326 | C23×C3 | — | 6 | 2 | no | — |
| 327 | C23×C3 | — | 12 | 2 | no | — |
| 328 | C23×C3 | — | 18 | 2 | no | — |
| 329 | C22×D3 | — | 2 | 2 | no | — |
| 330 | C22×D3 | — | 6 | 2 | no | — |
| 331 | C22×D3 | — | 6 | 2 | no | — |
| 332 | C22×D3 | — | 18 | 2 | no | — |
| 333 | C22×D3 | — | 18 | 2 | no | — |
| 334 | C22×D3 | — | 18 | 2 | no | — |
| 335 | C22×D3 | — | 36 | 2 | no | — |
| 336 | C3×D4 | — | 6 | 2 | no | — |
| 337 | C3×D4 | — | 9 | 2 | no | — |
| 338 | C3×D4 | — | 9 | 2 | no | — |
| 339 | C3×D4 | — | 18 | 2 | no | — |
| 340 | C3×D4 | — | 18 | 2 | no | — |
| 341 | C3×D4 | — | 18 | 2 | no | — |
| 342 | C3×D4 | — | 18 | 2 | no | — |
| 343 | C2×C3×C4 | — | 9 | 1 | no | — |
| 344 | C2×C3×C4 | — | 18 | 2 | no | — |
| 345 | #67 | — | 6 | 2 | no | — |
| 346 | #67 | — | 6 | 2 | no | — |
| 347 | #67 | — | 6 | 2 | no | — |
| 348 | #67 | — | 6 | 2 | no | — |
| 349 | #67 | — | 6 | 2 | no | — |
| 350 | #67 | — | 6 | 2 | no | — |
| 351 | #67 | — | 6 | 2 | no | — |
| 352 | #67 | — | 6 | 2 | no | — |
| 353 | #67 | — | 6 | 2 | no | — |
| 354 | #67 | — | 9 | 1 | no | — |
| 355 | #67 | — | 12 | 2 | no | — |
| 356 | #67 | — | 18 | 2 | no | — |
| 357 | #67 | — | 18 | 2 | no | — |
| 358 | #67 | — | 18 | 2 | no | — |
| 359 | #67 | — | 18 | 2 | no | — |
| 360 | #67 | — | 18 | 2 | no | — |
| 361 | #67 | — | 18 | 2 | no | — |
| 362 | #67 | — | 18 | 2 | no | — |
| 363 | #67 | — | 18 | 2 | no | — |
| 364 | #67 | — | 36 | 2 | no | — |
| 365 | #67 | — | 36 | 2 | no | — |
| 366 | #67 | — | 36 | 2 | no | — |
| 367 | #67 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 368 | C2×Dic3 | — | 6 | 2 | no | — |
| 369 | C2×Dic3 | — | 6 | 2 | no | — |
| 370 | C2×Dic3 | — | 18 | 2 | no | — |
| 371 | C2×Dic3 | — | 18 | 2 | no | — |
| 372 | C2×Dic3 | — | 18 | 2 | no | — |
| 373 | C2×Dic3 | — | 18 | 2 | no | — |
| 374 | C2×Dic3 | — | 36 | 2 | no | — |
| 375 | D12 | — | 6 | 2 | no | — |
| 376 | D12 | — | 9 | 2 | no | — |
| 377 | D12 | — | 9 | 1 | no | — |
| 378 | D12 | — | 18 | 2 | no | — |
| 379 | C4×D3 | — | 6 | 2 | no | — |
| 380 | C4×D3 | — | 9 | 1 | no | — |
| 381 | C4×D3 | — | 9 | 1 | no | — |
| 382 | C4×D3 | — | 18 | 2 | no | — |
| 383 | C4×D3 | — | 18 | 2 | no | — |
| 384 | C4×D3 | — | 18 | 2 | no | — |
| 385 | C4×D3 | — | 18 | 2 | no | — |
| 386 | Dic6 | — | 9 | 2 | no | — |
| 387 | Dic6 | — | 9 | 1 | no | — |
| 388 | Dic6 | — | 18 | 2 | no | — |
| 389 | Dic6 | — | 18 | 2 | no | — |
| 390 | C3×C8 | — | 9 | 1 | no | — |
| 391 | C3×C8 | — | 9 | 1 | no | — |
| 392 | C3⋊C8 | — | 9 | 1 | no | — |
| 393 | C3⋊C8 | — | 9 | 1 | no | — |
| 394 | C2×C32 | — | 2 | 2 | no | — |
| 395 | C2×C32 | — | 2 | 1 | no | — |
| 396 | C2×C32 | — | 4 | 2 | no | — |
| 397 | C2×C32 | — | 4 | 2 | no | — |
| 398 | C2×C32 | — | 6 | 1 | no | — |
| 399 | C2×C32 | — | 8 | 2 | no | — |
| 400 | C2×C32 | — | 12 | 2 | no | — |
| 401 | C2×C32 | — | 12 | 2 | no | — |
| 402 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 403 | C3⋊D3 | — | 4 | 2 | no | — |
| 404 | C3⋊D3 | — | 6 | 1 | no | — |
| 405 | C3⋊D3 | — | 12 | 2 | no | — |
| 406 | C3⋊D3 | — | 24 | 2 | no | — |
| 407 | C3×D3 | — | 4 | 2 | no | — |
| 408 | C3×D3 | — | 4 | 2 | no | — |
| 409 | C3×D3 | — | 4 | 2 | no | — |
| 410 | C3×D3 | — | 4 | 4 | no | — |
| 411 | C3×D3 | — | 4 | 2 | no | — |
| 412 | C3×D3 | — | 4 | 2 | no | — |
| 413 | C3×D3 | — | 8 | 2 | no | — |
| 414 | C3×D3 | — | 12 | 2 | no | — |
| 415 | C3×D3 | — | 12 | 2 | no | — |
| 416 | C3×D3 | — | 24 | 2 | no | — |
| 417 | #41 | — | 27 | 1 | no | — |
| 418 | #41 | — | 27 | 2 | no | — |
| 419 | #41 | — | 27 | 2 | no | — |
| 420 | #41 | — | 27 | 2 | no | — |
| 421 | #41 | — | 54 | 2 | no | — |
| 422 | C2×D4 | — | 9 | 2 | no | — |
| 423 | C2×D4 | — | 18 | 2 | no | — |
| 424 | C2×D4 | — | 27 | 2 | no | — |
| 425 | C2×D4 | — | 27 | 2 | no | — |
| 426 | C2×D4 | — | 54 | 2 | no | — |
| 427 | C2×D4 | — | 54 | 2 | no | — |
| 428 | Q16 | — | 27 | 1 | no | — |
| 429 | SD16 | — | 27 | 2 | no | — |
| 430 | SD16 | — | 27 | 2 | no | — |
| 431 | SD16 | — | 27 | 2 | no | — |
| 432 | D8 | — | 9 | 1 | no | — |
| 433 | D8 | — | 9 | 1 | no | — |
| 434 | D8 | — | 9 | 2 | no | — |
| 435 | D8 | — | 27 | 1 | no | — |
| 436 | D8 | — | 27 | 2 | no | — |
| 437 | D8 | — | 27 | 2 | no | — |
| 438 | M16 | — | 27 | 1 | no | — |
| 439 | M16 | — | 27 | 1 | no | — |
| 440 | M16 | — | 27 | 1 | no | — |
| 441 | C2×C8 | — | 9 | 1 | no | — |
| 442 | C2×C8 | — | 27 | 1 | no | — |
| 443 | C2×C8 | — | 27 | 1 | no | — |
| 444 | C22×C3 | — | 2 | 2 | no | — |
| 445 | C22×C3 | — | 4 | 2 | no | — |
| 446 | C22×C3 | — | 6 | 2 | no | — |
| 447 | C22×C3 | — | 6 | 2 | no | — |
| 448 | C22×C3 | — | 6 | 2 | no | — |
| 449 | C22×C3 | — | 6 | 2 | no | — |
| 450 | C22×C3 | — | 6 | 2 | no | — |
| 451 | C22×C3 | — | 12 | 2 | no | — |
| 452 | C22×C3 | — | 12 | 2 | no | — |
| 453 | C22×C3 | — | 18 | 2 | no | — |
| 454 | C22×C3 | — | 24 | 2 | no | — |
| 455 | C22×C3 | — | 24 | 2 | no | — |
| 456 | C22×C3 | — | 24 | 4 | no | — |
| 457 | C22×C3 | — | 72 | 2 | no | — |
| 458 | C22×C3 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 459 | C2×D3 | — | 2 | 2 | no | — |
| 460 | C2×D3 | — | 2 | 2 | no | — |
| 461 | C2×D3 | — | 6 | 2 | no | — |
| 462 | C2×D3 | — | 6 | 2 | no | — |
| 463 | C2×D3 | — | 8 | 2 | no | — |
| 464 | C2×D3 | — | 9 | 1 | no | — |
| 465 | C2×D3 | — | 12 | 2 | no | — |
| 466 | C2×D3 | — | 18 | 2 | no | — |
| 467 | C2×D3 | — | 24 | 2 | no | — |
| 468 | C2×D3 | — | 24 | 2 | no | — |
| 469 | C2×D3 | — | 36 | 2 | no | — |
| 470 | C2×D3 | — | 72 | 2 | no | — |
| 471 | C2×D3 | — | 72 | 2 | no | — |
| 472 | C2×D3 | — | 72 | 2 | no | — |
| 473 | C2×D3 | — | 72 | 4 | no | — |
| 474 | C2×D3 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 475 | C3×C4 | — | 6 | 2 | no | — |
| 476 | C3×C4 | — | 9 | 1 | no | — |
| 477 | C3×C4 | — | 9 | 1 | no | — |
| 478 | C3×C4 | — | 18 | 2 | no | — |
| 479 | Dic3 | — | 6 | 2 | no | — |
| 480 | Dic3 | — | 6 | 2 | no | — |
| 481 | Dic3 | — | 6 | 2 | no | — |
| 482 | Dic3 | — | 6 | 2 | no | — |
| 483 | Dic3 | — | 9 | 1 | no | — |
| 484 | Dic3 | — | 12 | 2 | no | — |
| 485 | Dic3 | — | 18 | 2 | no | — |
| 486 | Dic3 | — | 36 | 2 | no | — |
| 487 | Dic3 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 488 | C32 | — | 2 | 2 | no | — |
| 489 | C32 | — | 4 | 2 | no | — |
| 490 | C32 | #5757 | 1 | 1 | yes | characteristic, complemented |
| 491 | C23 | — | 6 | 2 | no | — |
| 492 | C23 | — | 18 | 2 | no | — |
| 493 | C23 | — | 54 | 2 | no | — |
| 494 | Q8 | — | 27 | 1 | no | — |
| 495 | Q8 | — | 27 | 2 | no | — |
| 496 | D4 | — | 3 | 1 | no | — |
| 497 | D4 | — | 9 | 2 | no | — |
| 498 | D4 | — | 9 | 2 | no | — |
| 499 | D4 | — | 18 | 2 | no | — |
| 500 | D4 | — | 18 | 2 | no | — |
| 501 | D4 | — | 18 | 2 | no | — |
| 502 | D4 | — | 18 | 2 | no | — |
| 503 | D4 | — | 27 | 1 | no | — |
| 504 | D4 | — | 27 | 2 | no | — |
| 505 | D4 | — | 27 | 1 | no | — |
| 506 | D4 | — | 54 | 2 | no | — |
| 507 | D4 | — | 54 | 2 | no | — |
| 508 | C2×C4 | — | 9 | 1 | no | — |
| 509 | C2×C4 | — | 18 | 2 | no | — |
| 510 | C2×C4 | — | 27 | 1 | no | — |
| 511 | C2×C4 | — | 27 | 1 | no | — |
| 512 | C2×C4 | — | 54 | 2 | no | — |
| 513 | C2×C4 | — | 54 | 2 | no | — |
| 514 | C8 | — | 9 | 1 | no | — |
| 515 | C8 | — | 9 | 1 | no | — |
| 516 | C8 | — | 27 | 1 | no | — |
| 517 | C8 | — | 27 | 1 | no | — |
| 518 | C2×C3 | — | 2 | 1 | no | — |
| 519 | C2×C3 | — | 2 | 2 | no | — |
| 520 | C2×C3 | — | 4 | 2 | no | — |
| 521 | C2×C3 | — | 4 | 2 | no | — |
| 522 | C2×C3 | — | 8 | 2 | no | — |
| 523 | C2×C3 | — | 12 | 2 | no | — |
| 524 | C2×C3 | — | 12 | 2 | no | — |
| 525 | C2×C3 | — | 12 | 2 | no | — |
| 526 | C2×C3 | — | 12 | 4 | no | — |
| 527 | C2×C3 | — | 12 | 2 | no | — |
| 528 | C2×C3 | — | 12 | 2 | no | — |
| 529 | C2×C3 | — | 24 | 2 | no | — |
| 530 | C2×C3 | — | 36 | 2 | no | — |
| 531 | C2×C3 | C22×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 532 | D3 | — | 2 | 1 | no | — |
| 533 | D3 | — | 4 | 2 | no | — |
| 534 | D3 | — | 4 | 2 | no | — |
| 535 | D3 | — | 12 | 2 | no | — |
| 536 | D3 | — | 12 | 2 | no | — |
| 537 | D3 | — | 18 | 1 | no | — |
| 538 | D3 | — | 24 | 2 | no | — |
| 539 | D3 | — | 36 | 2 | no | — |
| 540 | D3 | — | 72 | 2 | no | — |
| 541 | C22 | — | 3 | 1 | no | — |
| 542 | C22 | — | 6 | 2 | no | — |
| 543 | C22 | — | 6 | 2 | no | — |
| 544 | C22 | — | 18 | 2 | no | — |
| 545 | C22 | — | 24 | 2 | no | — |
| 546 | C22 | — | 27 | 1 | no | — |
| 547 | C22 | — | 72 | 2 | no | — |
| 548 | C22 | — | 216 | 2 | no | — |
| 549 | C22 | D3×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 550 | C4 | — | 3 | 1 | no | — |
| 551 | C4 | — | 9 | 1 | no | — |
| 552 | C4 | — | 9 | 1 | no | — |
| 553 | C4 | — | 18 | 2 | no | — |
| 554 | C4 | — | 27 | 1 | no | — |
| 555 | C3 | — | 2 | 2 | no | — |
| 556 | C3 | — | 4 | 2 | no | — |
| 557 | C3 | #10596514 | 1 | 1 | yes | characteristic, complemented |
| 558 | C2 | — | 2 | 1 | no | — |
| 559 | C2 | — | 6 | 1 | no | — |
| 560 | C2 | — | 12 | 2 | no | — |
| 561 | C2 | — | 12 | 2 | no | — |
| 562 | C2 | — | 36 | 2 | no | — |
| 563 | C2 | — | 54 | 1 | no | — |
| 564 | C2 | C2×D3×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11724414 | C2 | semidirect |
| 2. #11724351 | C2 | semidirect |
| 3. #11724323 | C2 | semidirect |
| 4. C2×C3×#3774 | C2 | semidirect |
| 5. #11724266 | C2 | semidirect |
| 6. #11724140 | C2 | semidirect |
| 7. #11724138 | C2 | semidirect |
| 8. #11724135 | C2 | semidirect |
| 9. #11724132 | C2 | semidirect |
| 10. #11724127 | C2 | semidirect |
| 11. D3×#3774 | C2 | semidirect |
| 13. #89046 | C22 | semidirect |
| 17. C2×C3×#625 | C22 | semidirect |
| 18. #88993 | C22 | semidirect |
| 19. C2×C3×#622 | C22 | semidirect |
| 20. #88963 | C22 | semidirect |
| 22. #88959 | C22 | semidirect |
| 23. #88954 | C22 | semidirect |
| 25. D3×#625 | C22 | semidirect |
| 26. #88943 | C22 | semidirect |
| 27. #88942 | C22 | semidirect |
| 28. #88941 | C22 | semidirect |
| 29. #88937 | C22 | semidirect |
| 30. #88937 | C22 | semidirect |
| 31. #88935 | C22 | semidirect |
| 32. #88935 | C22 | semidirect |
| 33. C3×#3774 | C22 | semidirect |
| 34. C3×#3774 | C22 | semidirect |
| 35. C3×#3774 | C22 | semidirect |
| 36. #88926 | C22 | semidirect |
| 37. #88925 | C22 | semidirect |
| 38. #88924 | C22 | semidirect |
| 39. D3×#622 | C22 | semidirect |
| 48. C2×#3774 | D3 | semidirect |
| 95. C2×#625 | C2×D3 | semidirect |
| 110. C2×#622 | C2×D3 | semidirect |
| 120. #3774 | C2×D3 | semidirect |
| 121. #3774 | C2×D3 | semidirect |
| 122. #3774 | C2×D3 | semidirect |
| 324. C33 | #576 | semidirect |
| 490. C32 | #5757 | semidirect |
| 557. C3 | #10596514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724414 | 2 |
| #11724351 | 2 |
| #11724323 | 2 |
| C2×C3×#3774 | 2 |
| #11724266 | 2 |
| #11724140 | 2 |
| #11724138 | 2 |
| #11724135 | 2 |
| #11724132 | 2 |
| #11724127 | 2 |
| D3×#3774 | 2 |
| #10596514 | 3 |
| #5757 | 9 |