Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
922 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 922 conjugacy classes of subgroups — too many to draw. Only its 119 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 | #11724620 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#64313 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11724515 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11724328 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×#88937 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11724324 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11724323 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11724310 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11724309 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11724304 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11724303 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10596515 | — | 3 | 1 | no | maximal |
| 13 | C3×#3830 | — | 2 | 1 | no | — |
| 14 | C3×#3830 | C22 | 1 | 1 | yes | characteristic |
| 15 | C32×D3×D4 | — | 2 | 1 | no | — |
| 16 | C2×#6296 | C22 | 1 | 2 | yes | complemented |
| 17 | #89046 | — | 2 | 2 | no | — |
| 18 | #89046 | C22 | 1 | 2 | yes | complemented |
| 19 | #89042 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #89040 | — | 2 | 1 | no | — |
| 21 | #89040 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C3×D3×#67 | — | 2 | 2 | no | — |
| 23 | C2×C3×#625 | C22 | 1 | 2 | yes | — |
| 24 | C3×#3805 | C22 | 1 | 2 | yes | — |
| 25 | C3×#3802 | C22 | 1 | 1 | yes | characteristic |
| 26 | C3×#3798 | C22 | 1 | 1 | yes | characteristic |
| 27 | C3×#3795 | — | 2 | 1 | no | — |
| 28 | #88993 | C22 | 1 | 2 | yes | complemented |
| 29 | C2×C3⋊#622 | C22 | 1 | 2 | yes | complemented |
| 30 | #88989 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #88988 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #88938 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #88938 | C22 | 1 | 2 | yes | complemented |
| 34 | #88937 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #88937 | C22 | 1 | 2 | yes | complemented |
| 36 | #88937 | C22 | 1 | 2 | yes | complemented |
| 37 | #88937 | C22 | 1 | 2 | yes | complemented |
| 38 | #88937 | C22 | 1 | 2 | yes | complemented |
| 39 | #88936 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #88935 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #88935 | C22 | 1 | 2 | yes | complemented |
| 42 | C3×#1004 | — | 6 | 1 | no | — |
| 43 | #64313 | D3 | 1 | 1 | yes | characteristic, complemented |
| 44 | #64309 | — | 3 | 1 | no | — |
| 45 | #64309 | — | 6 | 1 | no | — |
| 46 | #64287 | — | 3 | 1 | no | — |
| 47 | #64239 | — | 3 | 2 | no | — |
| 48 | C2×#3775 | — | 3 | 2 | no | — |
| 49 | #64237 | — | 3 | 2 | no | — |
| 50 | #64236 | — | 3 | 2 | no | — |
| 51 | #64227 | — | 3 | 1 | no | — |
| 52 | #64226 | — | 3 | 1 | no | — |
| 53 | #64224 | — | 3 | 1 | no | — |
| 54 | #64223 | — | 3 | 1 | no | — |
| 55 | C22×C32×D3 | — | 2 | 2 | no | — |
| 56 | C2×C3×D32 | — | 2 | 1 | no | — |
| 57 | C33×D4 | D4 | 1 | 1 | yes | characteristic |
| 58 | C3×#638 | — | 2 | 2 | no | — |
| 59 | C3×#638 | D4 | 1 | 2 | yes | — |
| 60 | C2×C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 61 | C2×C3×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 62 | C3×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 63 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 64 | C3×#634 | — | 2 | 1 | no | — |
| 65 | C3×#634 | D4 | 1 | 1 | yes | characteristic |
| 66 | C32×#67 | — | 2 | 2 | no | — |
| 67 | C32×D12 | — | 2 | 1 | no | — |
| 68 | C32×C4×D3 | — | 2 | 1 | no | — |
| 69 | #6296 | — | 2 | 2 | no | — |
| 70 | #6296 | C23 | 1 | 2 | yes | — |
| 71 | #6296 | C23 | 1 | 1 | yes | characteristic |
| 72 | #6295 | — | 2 | 1 | no | — |
| 73 | #6295 | C23 | 1 | 1 | yes | characteristic |
| 74 | #6294 | — | 2 | 1 | no | — |
| 75 | #6294 | — | 2 | 2 | no | — |
| 76 | C3×#627 | C23 | 1 | 1 | yes | characteristic |
| 77 | C3×#626 | — | 2 | 1 | no | — |
| 78 | C3×#625 | — | 2 | 2 | no | — |
| 79 | C3×#625 | C23 | 1 | 1 | yes | characteristic |
| 80 | C3×#625 | C23 | 1 | 2 | yes | — |
| 81 | C3×D3×Dic3 | — | 2 | 2 | no | — |
| 82 | C3⋊#622 | C23 | 1 | 1 | yes | characteristic |
| 83 | C3⋊#622 | C23 | 1 | 2 | yes | — |
| 84 | C3⋊#622 | C23 | 1 | 1 | yes | characteristic |
| 85 | #5836 | — | 9 | 1 | no | maximal |
| 86 | C2×C32×D4 | — | 6 | 1 | no | — |
| 87 | #3830 | — | 2 | 1 | no | — |
| 88 | #3830 | C2×D3 | 1 | 1 | yes | characteristic |
| 89 | C2×C3×#67 | — | 6 | 2 | no | — |
| 90 | C2×C3×#67 | — | 6 | 2 | no | — |
| 91 | C3×#237 | — | 6 | 1 | no | — |
| 92 | C3×#237 | — | 6 | 2 | no | — |
| 93 | C3×#237 | — | 6 | 1 | no | — |
| 94 | C3×#237 | — | 6 | 1 | no | — |
| 95 | C3×#237 | — | 6 | 1 | no | — |
| 96 | C3×#237 | — | 6 | 1 | no | — |
| 97 | C3×#237 | — | 12 | 1 | no | — |
| 98 | C3×D3×D4 | — | 2 | 1 | no | — |
| 99 | C3×D3×D4 | — | 2 | 1 | no | — |
| 100 | C3×D3×D4 | — | 4 | 1 | no | — |
| 101 | C3×D3×D4 | — | 6 | 1 | no | — |
| 102 | C3×D3×D4 | — | 6 | 2 | no | — |
| 103 | C3×#235 | — | 6 | 1 | no | — |
| 104 | C3×#235 | — | 6 | 1 | no | — |
| 105 | D3×#67 | — | 2 | 2 | no | — |
| 106 | C2×#627 | — | 3 | 2 | no | — |
| 107 | C2×#627 | — | 6 | 2 | no | — |
| 108 | C2×#625 | C2×D3 | 1 | 2 | yes | — |
| 109 | #3805 | — | 3 | 2 | no | — |
| 110 | #3805 | — | 6 | 2 | no | — |
| 111 | #3805 | C2×D3 | 1 | 2 | yes | — |
| 112 | #3804 | — | 6 | 2 | no | — |
| 113 | #3804 | — | 6 | 2 | no | — |
| 114 | #3804 | — | 6 | 2 | no | — |
| 115 | #3802 | C2×D3 | 1 | 1 | yes | characteristic |
| 116 | #3798 | — | 3 | 1 | no | — |
| 117 | #3798 | — | 6 | 1 | no | — |
| 118 | #3798 | C2×D3 | 1 | 1 | yes | characteristic |
| 119 | #3797 | — | 3 | 1 | no | — |
| 120 | #3797 | — | 6 | 1 | no | — |
| 121 | #3795 | — | 2 | 1 | no | — |
| 122 | D3×Dic6 | — | 6 | 1 | no | — |
| 123 | D3×Dic6 | — | 6 | 1 | no | — |
| 124 | D3×Dic6 | — | 6 | 1 | no | — |
| 125 | #3792 | — | 3 | 2 | no | — |
| 126 | C2×#622 | — | 3 | 2 | no | — |
| 127 | #3788 | — | 3 | 1 | no | — |
| 128 | #3787 | — | 3 | 1 | no | — |
| 129 | #3776 | — | 3 | 1 | no | — |
| 130 | #3776 | — | 3 | 2 | no | — |
| 131 | #3775 | — | 3 | 1 | no | — |
| 132 | #3775 | — | 3 | 1 | no | — |
| 133 | #3775 | — | 3 | 2 | no | — |
| 134 | #3775 | — | 3 | 2 | no | — |
| 135 | #3775 | — | 3 | 2 | no | — |
| 136 | #3775 | — | 3 | 2 | no | — |
| 137 | #3774 | — | 3 | 1 | no | — |
| 138 | #3774 | — | 3 | 2 | no | — |
| 139 | C22×C33 | C2×D4 | 1 | 2 | yes | — |
| 140 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 141 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C2×C32×D3 | — | 2 | 2 | no | — |
| 143 | C2×C32×D3 | — | 2 | 1 | no | — |
| 144 | C2×C32×D3 | — | 8 | 2 | no | — |
| 145 | C3×D32 | — | 8 | 1 | no | — |
| 146 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 147 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 148 | C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 149 | C3×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 150 | C3×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 151 | C32×Dic3 | — | 2 | 1 | no | — |
| 152 | C3×H(5,𝔽2) | — | 9 | 1 | no | — |
| 153 | #1010 | — | 9 | 1 | no | — |
| 154 | #1010 | — | 18 | 1 | no | — |
| 155 | #1004 | — | 6 | 1 | no | — |
| 156 | #951 | — | 9 | 1 | no | — |
| 157 | #951 | — | 9 | 2 | no | — |
| 158 | #950 | — | 9 | 1 | no | — |
| 159 | #950 | — | 9 | 2 | no | — |
| 160 | #948 | — | 9 | 1 | no | — |
| 161 | C2×#214 | — | 9 | 1 | no | — |
| 162 | C2×#214 | — | 9 | 2 | no | — |
| 163 | #932 | — | 9 | 1 | no | — |
| 164 | #932 | — | 9 | 2 | no | — |
| 165 | C23×C32 | — | 6 | 2 | no | — |
| 166 | C22×C3×D3 | — | 2 | 2 | no | — |
| 167 | C22×C3×D3 | — | 2 | 2 | no | — |
| 168 | C22×C3×D3 | — | 4 | 2 | no | — |
| 169 | C22×C3×D3 | — | 6 | 2 | no | — |
| 170 | C2×D32 | — | 2 | 1 | no | — |
| 171 | C32×D4 | — | 2 | 1 | no | — |
| 172 | C32×D4 | — | 2 | 1 | no | — |
| 173 | C32×D4 | — | 4 | 1 | no | — |
| 174 | C32×D4 | — | 4 | 1 | no | — |
| 175 | C32×D4 | — | 6 | 1 | no | — |
| 176 | C32×D4 | — | 6 | 2 | no | — |
| 177 | C32×D4 | #67 | 1 | 1 | yes | characteristic |
| 178 | C2×C32×C4 | — | 6 | 1 | no | — |
| 179 | #638 | — | 2 | 2 | no | — |
| 180 | #638 | #67 | 1 | 2 | yes | — |
| 181 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 182 | C2×C3⋊Dic3 | C22×D3 | 1 | 2 | yes | — |
| 183 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 184 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 185 | #634 | — | 2 | 1 | no | — |
| 186 | #634 | #67 | 1 | 1 | yes | characteristic |
| 187 | C3×#67 | — | 2 | 2 | no | — |
| 188 | C3×#67 | — | 2 | 2 | no | — |
| 189 | C3×#67 | — | 4 | 2 | no | — |
| 190 | C3×#67 | — | 6 | 1 | no | — |
| 191 | C3×#67 | — | 6 | 2 | no | — |
| 192 | C3×#67 | — | 6 | 2 | no | — |
| 193 | C3×#67 | — | 6 | 2 | no | — |
| 194 | C3×#67 | — | 6 | 1 | no | — |
| 195 | C3×#67 | — | 6 | 2 | no | — |
| 196 | C3×#67 | — | 6 | 2 | no | — |
| 197 | C3×#67 | — | 6 | 2 | no | — |
| 198 | C3×#67 | — | 6 | 2 | no | — |
| 199 | C3×#67 | — | 12 | 2 | no | — |
| 200 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 201 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 202 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 203 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 204 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 205 | C2×C3×Dic3 | — | 12 | 2 | no | — |
| 206 | C3×D12 | — | 2 | 1 | no | — |
| 207 | C3×D12 | — | 2 | 1 | no | — |
| 208 | C3×D12 | — | 4 | 1 | no | — |
| 209 | C3×D12 | — | 6 | 1 | no | — |
| 210 | C3×C4×D3 | — | 2 | 1 | no | — |
| 211 | C3×C4×D3 | — | 2 | 1 | no | — |
| 212 | C3×C4×D3 | — | 4 | 1 | no | — |
| 213 | C3×C4×D3 | — | 6 | 1 | no | — |
| 214 | C3×C4×D3 | — | 6 | 1 | no | — |
| 215 | C3×C4×D3 | — | 6 | 1 | no | — |
| 216 | C3×C4×D3 | — | 6 | 2 | no | — |
| 217 | C3×C4×D3 | — | 6 | 1 | no | — |
| 218 | C3×C4×D3 | — | 12 | 1 | no | — |
| 219 | C3×Dic6 | — | 6 | 1 | no | — |
| 220 | C3×Dic6 | — | 6 | 1 | no | — |
| 221 | C3×Dic6 | — | 6 | 1 | no | — |
| 222 | C3×Dic6 | — | 6 | 1 | no | — |
| 223 | C3×Dic6 | — | 6 | 1 | no | — |
| 224 | C3×Dic6 | — | 12 | 1 | no | — |
| 225 | #627 | — | 3 | 2 | no | — |
| 226 | #627 | — | 3 | 1 | no | — |
| 227 | #627 | — | 6 | 2 | no | — |
| 228 | #627 | — | 6 | 1 | no | — |
| 229 | #627 | — | 6 | 2 | no | — |
| 230 | #627 | — | 6 | 2 | no | — |
| 231 | #627 | — | 6 | 2 | no | — |
| 232 | #627 | C22×D3 | 1 | 1 | yes | characteristic |
| 233 | #626 | — | 2 | 1 | no | — |
| 234 | #626 | — | 6 | 1 | no | — |
| 235 | #626 | — | 6 | 1 | no | — |
| 236 | #626 | — | 6 | 1 | no | — |
| 237 | #625 | — | 2 | 2 | no | — |
| 238 | #625 | — | 3 | 1 | no | — |
| 239 | #625 | — | 6 | 1 | no | — |
| 240 | #625 | C22×D3 | 1 | 1 | yes | characteristic |
| 241 | #625 | C22×D3 | 1 | 2 | yes | — |
| 242 | #624 | — | 6 | 2 | no | — |
| 243 | #624 | — | 6 | 1 | no | — |
| 244 | D3×Dic3 | — | 2 | 2 | no | — |
| 245 | D3×Dic3 | — | 6 | 2 | no | — |
| 246 | D3×Dic3 | — | 6 | 2 | no | — |
| 247 | D3×Dic3 | — | 6 | 2 | no | — |
| 248 | #622 | — | 3 | 1 | no | — |
| 249 | #622 | — | 3 | 2 | no | — |
| 250 | #622 | — | 3 | 1 | no | — |
| 251 | #577 | — | 27 | 1 | no | Sylow |
| 252 | C2×C33 | — | 2 | 2 | no | — |
| 253 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 254 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 255 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 256 | C32×D3 | — | 4 | 1 | no | — |
| 257 | C32×D3 | — | 4 | 2 | no | — |
| 258 | C3×#41 | — | 9 | 1 | no | — |
| 259 | C3×#41 | — | 9 | 1 | no | — |
| 260 | C3×#41 | — | 9 | 2 | no | — |
| 261 | C3×#41 | — | 18 | 1 | no | — |
| 262 | C3×#41 | — | 18 | 1 | no | — |
| 263 | C2×C3×D4 | — | 6 | 1 | no | — |
| 264 | C2×C3×D4 | — | 6 | 1 | no | — |
| 265 | C2×C3×D4 | — | 9 | 1 | no | — |
| 266 | C2×C3×D4 | — | 9 | 2 | no | — |
| 267 | C2×C3×D4 | — | 12 | 1 | no | — |
| 268 | C2×C3×D4 | — | 18 | 2 | no | — |
| 269 | C2×#67 | — | 6 | 2 | no | — |
| 270 | C2×#67 | — | 6 | 2 | no | — |
| 271 | D3×Q8 | — | 18 | 1 | no | — |
| 272 | D3×Q8 | — | 18 | 1 | no | — |
| 273 | D3×Q8 | — | 18 | 1 | no | — |
| 274 | #237 | — | 6 | 2 | no | — |
| 275 | #237 | — | 6 | 1 | no | — |
| 276 | #237 | — | 6 | 1 | no | — |
| 277 | #237 | — | 6 | 1 | no | — |
| 278 | #237 | — | 6 | 1 | no | — |
| 279 | #237 | — | 6 | 1 | no | — |
| 280 | #237 | — | 12 | 1 | no | — |
| 281 | #237 | — | 18 | 2 | no | — |
| 282 | #237 | — | 18 | 2 | no | — |
| 283 | #237 | — | 18 | 2 | no | — |
| 284 | D3×D4 | — | 2 | 1 | no | — |
| 285 | D3×D4 | — | 6 | 1 | no | — |
| 286 | D3×D4 | — | 6 | 2 | no | — |
| 287 | #235 | — | 6 | 1 | no | — |
| 288 | #235 | — | 6 | 1 | no | — |
| 289 | #235 | — | 9 | 1 | no | — |
| 290 | #235 | — | 9 | 2 | no | — |
| 291 | #235 | — | 18 | 1 | no | — |
| 292 | #235 | — | 18 | 2 | no | — |
| 293 | C2×Dic6 | — | 9 | 1 | no | — |
| 294 | C2×Dic6 | — | 9 | 2 | no | — |
| 295 | C2×Dic6 | — | 18 | 2 | no | — |
| 296 | C2×Dic6 | — | 18 | 1 | no | — |
| 297 | #216 | — | 9 | 1 | no | — |
| 298 | #216 | — | 9 | 2 | no | — |
| 299 | #215 | — | 9 | 1 | no | — |
| 300 | #214 | — | 9 | 2 | no | — |
| 301 | #214 | — | 9 | 2 | no | — |
| 302 | #214 | — | 9 | 2 | no | — |
| 303 | #214 | — | 9 | 1 | no | — |
| 304 | #214 | — | 9 | 2 | no | — |
| 305 | #213 | — | 9 | 1 | no | — |
| 306 | #213 | — | 9 | 2 | no | — |
| 307 | #208 | — | 9 | 1 | no | — |
| 308 | #208 | — | 9 | 2 | no | — |
| 309 | C2×C3⋊C8 | — | 9 | 1 | no | — |
| 310 | C2×C3⋊C8 | — | 9 | 2 | no | — |
| 311 | C22×C32 | — | 2 | 2 | no | — |
| 312 | C22×C32 | — | 2 | 2 | no | — |
| 313 | C22×C32 | — | 4 | 2 | no | — |
| 314 | C22×C32 | — | 4 | 2 | no | — |
| 315 | C22×C32 | — | 6 | 2 | no | — |
| 316 | C22×C32 | — | 6 | 1 | no | — |
| 317 | C22×C32 | — | 24 | 2 | no | — |
| 318 | C22×C32 | C2×#67 | 1 | 2 | yes | — |
| 319 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 320 | C2×C3⋊D3 | C2×#67 | 1 | 1 | yes | characteristic |
| 321 | C2×C3×D3 | — | 2 | 1 | no | — |
| 322 | C2×C3×D3 | — | 2 | 2 | no | — |
| 323 | C2×C3×D3 | — | 2 | 2 | no | — |
| 324 | C2×C3×D3 | — | 2 | 1 | no | — |
| 325 | C2×C3×D3 | — | 4 | 1 | no | — |
| 326 | C2×C3×D3 | — | 4 | 2 | no | — |
| 327 | C2×C3×D3 | — | 6 | 1 | no | — |
| 328 | C2×C3×D3 | — | 6 | 1 | no | — |
| 329 | C2×C3×D3 | — | 6 | 1 | no | — |
| 330 | C2×C3×D3 | — | 6 | 1 | no | — |
| 331 | C2×C3×D3 | — | 8 | 2 | no | — |
| 332 | C2×C3×D3 | — | 8 | 2 | no | — |
| 333 | C2×C3×D3 | — | 8 | 4 | no | — |
| 334 | C2×C3×D3 | — | 12 | 1 | no | — |
| 335 | C2×C3×D3 | — | 24 | 2 | no | — |
| 336 | D32 | — | 8 | 1 | no | — |
| 337 | C32×C4 | — | 2 | 1 | no | — |
| 338 | C32×C4 | — | 2 | 1 | no | — |
| 339 | C32×C4 | — | 4 | 1 | no | — |
| 340 | C32×C4 | — | 4 | 1 | no | — |
| 341 | C32×C4 | — | 6 | 1 | no | — |
| 342 | C32×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 343 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 344 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 345 | C3⋊Dic3 | C2×#67 | 1 | 2 | yes | — |
| 346 | C3⋊Dic3 | C23×D3 | 1 | 1 | yes | characteristic |
| 347 | C3×Dic3 | — | 2 | 1 | no | — |
| 348 | C3×Dic3 | — | 2 | 1 | no | — |
| 349 | C3×Dic3 | — | 4 | 1 | no | — |
| 350 | C3×Dic3 | — | 6 | 2 | no | — |
| 351 | C3×Dic3 | — | 6 | 2 | no | — |
| 352 | C3×Dic3 | — | 6 | 1 | no | — |
| 353 | C3×Dic3 | — | 6 | 1 | no | — |
| 354 | C3×Dic3 | — | 6 | 2 | no | — |
| 355 | C3×Dic3 | — | 6 | 1 | no | — |
| 356 | C3×Dic3 | — | 6 | 2 | no | — |
| 357 | C3×Dic3 | — | 6 | 1 | no | — |
| 358 | C3×Dic3 | — | 12 | 2 | no | — |
| 359 | C3×Dic3 | — | 12 | 1 | no | — |
| 360 | 2−1+4 | — | 27 | 1 | no | — |
| 361 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 362 | #137 | — | 27 | 1 | no | — |
| 363 | #137 | — | 27 | 2 | no | — |
| 364 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 365 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 366 | #135 | — | 27 | 1 | no | — |
| 367 | #135 | — | 27 | 2 | no | — |
| 368 | C2×SD16 | — | 27 | 1 | no | — |
| 369 | C2×SD16 | — | 27 | 2 | no | — |
| 370 | #131 | — | 27 | 1 | no | — |
| 371 | C33 | #577 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 372 | C23×C3 | — | 6 | 2 | no | — |
| 373 | C23×C3 | — | 6 | 2 | no | — |
| 374 | C23×C3 | — | 12 | 2 | no | — |
| 375 | C23×C3 | — | 18 | 1 | no | — |
| 376 | C22×D3 | — | 2 | 2 | no | — |
| 377 | C22×D3 | — | 6 | 2 | no | — |
| 378 | C3×Q8 | — | 9 | 1 | no | — |
| 379 | C3×Q8 | — | 9 | 1 | no | — |
| 380 | C3×Q8 | — | 18 | 1 | no | — |
| 381 | C3×D4 | — | 2 | 1 | no | — |
| 382 | C3×D4 | — | 2 | 1 | no | — |
| 383 | C3×D4 | — | 4 | 1 | no | — |
| 384 | C3×D4 | — | 4 | 1 | no | — |
| 385 | C3×D4 | — | 6 | 1 | no | — |
| 386 | C3×D4 | — | 6 | 2 | no | — |
| 387 | C3×D4 | — | 6 | 2 | no | — |
| 388 | C3×D4 | — | 6 | 1 | no | — |
| 389 | C3×D4 | — | 9 | 1 | no | — |
| 390 | C3×D4 | — | 9 | 2 | no | — |
| 391 | C3×D4 | — | 9 | 2 | no | — |
| 392 | C3×D4 | — | 12 | 1 | no | — |
| 393 | C3×D4 | — | 12 | 2 | no | — |
| 394 | C3×D4 | — | 18 | 1 | no | — |
| 395 | C3×D4 | — | 18 | 2 | no | — |
| 396 | C3×D4 | — | 18 | 2 | no | — |
| 397 | C3×D4 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 398 | C2×C3×C4 | — | 6 | 1 | no | — |
| 399 | C2×C3×C4 | — | 6 | 1 | no | — |
| 400 | C2×C3×C4 | — | 9 | 2 | no | — |
| 401 | C2×C3×C4 | — | 9 | 1 | no | — |
| 402 | C2×C3×C4 | — | 12 | 1 | no | — |
| 403 | C2×C3×C4 | — | 18 | 1 | no | — |
| 404 | C2×C3×C4 | — | 18 | 2 | no | — |
| 405 | C2×C3×C4 | — | 18 | 2 | no | — |
| 406 | #67 | — | 2 | 2 | no | — |
| 407 | #67 | — | 6 | 1 | no | — |
| 408 | #67 | — | 6 | 2 | no | — |
| 409 | #67 | — | 6 | 2 | no | — |
| 410 | #67 | — | 6 | 2 | no | — |
| 411 | #67 | — | 6 | 1 | no | — |
| 412 | #67 | — | 6 | 2 | no | — |
| 413 | #67 | — | 6 | 2 | no | — |
| 414 | #67 | — | 6 | 2 | no | — |
| 415 | #67 | — | 6 | 2 | no | — |
| 416 | #67 | — | 12 | 2 | no | — |
| 417 | #67 | — | 18 | 1 | no | — |
| 418 | #67 | — | 18 | 1 | no | — |
| 419 | #67 | — | 18 | 1 | no | — |
| 420 | C2×Dic3 | — | 6 | 2 | no | — |
| 421 | C2×Dic3 | — | 6 | 2 | no | — |
| 422 | C2×Dic3 | — | 6 | 2 | no | — |
| 423 | C2×Dic3 | — | 6 | 2 | no | — |
| 424 | C2×Dic3 | — | 6 | 2 | no | — |
| 425 | C2×Dic3 | — | 12 | 2 | no | — |
| 426 | C2×Dic3 | — | 18 | 1 | no | — |
| 427 | C2×Dic3 | — | 18 | 2 | no | — |
| 428 | D12 | — | 2 | 1 | no | — |
| 429 | D12 | — | 6 | 1 | no | — |
| 430 | D12 | — | 9 | 1 | no | — |
| 431 | D12 | — | 18 | 1 | no | — |
| 432 | C4×D3 | — | 2 | 1 | no | — |
| 433 | C4×D3 | — | 6 | 1 | no | — |
| 434 | C4×D3 | — | 6 | 1 | no | — |
| 435 | C4×D3 | — | 6 | 1 | no | — |
| 436 | C4×D3 | — | 6 | 2 | no | — |
| 437 | C4×D3 | — | 6 | 1 | no | — |
| 438 | C4×D3 | — | 12 | 1 | no | — |
| 439 | C4×D3 | — | 18 | 2 | no | — |
| 440 | C4×D3 | — | 18 | 2 | no | — |
| 441 | C4×D3 | — | 18 | 2 | no | — |
| 442 | Dic6 | — | 6 | 1 | no | — |
| 443 | Dic6 | — | 6 | 1 | no | — |
| 444 | Dic6 | — | 6 | 1 | no | — |
| 445 | Dic6 | — | 6 | 1 | no | — |
| 446 | Dic6 | — | 6 | 1 | no | — |
| 447 | Dic6 | — | 9 | 2 | no | — |
| 448 | Dic6 | — | 9 | 1 | no | — |
| 449 | Dic6 | — | 12 | 1 | no | — |
| 450 | Dic6 | — | 18 | 1 | no | — |
| 451 | Dic6 | — | 18 | 2 | no | — |
| 452 | Dic6 | — | 18 | 2 | no | — |
| 453 | Dic6 | — | 18 | 2 | no | — |
| 454 | Dic6 | — | 18 | 2 | no | — |
| 455 | C3⋊C8 | — | 9 | 1 | no | — |
| 456 | C3⋊C8 | — | 9 | 1 | no | — |
| 457 | C3⋊C8 | — | 9 | 2 | no | — |
| 458 | C2×C32 | — | 2 | 1 | no | — |
| 459 | C2×C32 | — | 2 | 1 | no | — |
| 460 | C2×C32 | — | 2 | 2 | no | — |
| 461 | C2×C32 | — | 4 | 1 | no | — |
| 462 | C2×C32 | — | 4 | 1 | no | — |
| 463 | C2×C32 | — | 4 | 2 | no | — |
| 464 | C2×C32 | — | 4 | 2 | no | — |
| 465 | C2×C32 | — | 8 | 2 | no | — |
| 466 | C2×C32 | — | 8 | 2 | no | — |
| 467 | C2×C32 | — | 12 | 1 | no | — |
| 468 | C2×C32 | — | 12 | 2 | no | — |
| 469 | C2×C32 | C22×#67 | 1 | 1 | yes | characteristic |
| 470 | C3⋊D3 | — | 2 | 1 | no | — |
| 471 | C3⋊D3 | — | 4 | 1 | no | — |
| 472 | C3×D3 | — | 4 | 1 | no | — |
| 473 | C3×D3 | — | 4 | 2 | no | — |
| 474 | C3×D3 | — | 4 | 2 | no | — |
| 475 | C3×D3 | — | 4 | 2 | no | — |
| 476 | C3×D3 | — | 4 | 1 | no | — |
| 477 | C3×D3 | — | 8 | 2 | no | — |
| 478 | C3×D3 | — | 12 | 1 | no | — |
| 479 | C3×D3 | — | 12 | 1 | no | — |
| 480 | C3×D3 | — | 12 | 1 | no | — |
| 481 | C3×D3 | — | 12 | 1 | no | — |
| 482 | C3×D3 | — | 24 | 1 | no | — |
| 483 | #41 | — | 9 | 1 | no | — |
| 484 | #41 | — | 9 | 1 | no | — |
| 485 | #41 | — | 9 | 2 | no | — |
| 486 | #41 | — | 18 | 1 | no | — |
| 487 | #41 | — | 18 | 1 | no | — |
| 488 | #41 | — | 27 | 1 | no | — |
| 489 | #41 | — | 27 | 2 | no | — |
| 490 | #41 | — | 54 | 2 | no | — |
| 491 | C2×Q8 | — | 27 | 2 | no | — |
| 492 | C2×Q8 | — | 27 | 1 | no | — |
| 493 | C2×Q8 | — | 54 | 1 | no | — |
| 494 | C2×D4 | — | 6 | 1 | no | — |
| 495 | C2×D4 | — | 9 | 1 | no | — |
| 496 | C2×D4 | — | 9 | 2 | no | — |
| 497 | C2×D4 | — | 18 | 2 | no | — |
| 498 | Q16 | — | 27 | 1 | no | — |
| 499 | Q16 | — | 27 | 2 | no | — |
| 500 | SD16 | — | 27 | 2 | no | — |
| 501 | SD16 | — | 27 | 1 | no | — |
| 502 | SD16 | — | 27 | 2 | no | — |
| 503 | SD16 | — | 27 | 2 | no | — |
| 504 | SD16 | — | 27 | 2 | no | — |
| 505 | SD16 | — | 27 | 1 | no | — |
| 506 | D8 | — | 27 | 1 | no | — |
| 507 | D8 | — | 27 | 2 | no | — |
| 508 | M16 | — | 27 | 1 | no | — |
| 509 | M16 | — | 27 | 2 | no | — |
| 510 | C2×C8 | — | 27 | 1 | no | — |
| 511 | C2×C8 | — | 27 | 2 | no | — |
| 512 | C22×C3 | — | 2 | 2 | no | — |
| 513 | C22×C3 | — | 2 | 2 | no | — |
| 514 | C22×C3 | — | 4 | 2 | no | — |
| 515 | C22×C3 | — | 4 | 2 | no | — |
| 516 | C22×C3 | — | 6 | 2 | no | — |
| 517 | C22×C3 | — | 6 | 1 | no | — |
| 518 | C22×C3 | — | 6 | 1 | no | — |
| 519 | C22×C3 | — | 6 | 2 | no | — |
| 520 | C22×C3 | — | 9 | 1 | no | — |
| 521 | C22×C3 | — | 12 | 1 | no | — |
| 522 | C22×C3 | — | 12 | 2 | no | — |
| 523 | C22×C3 | — | 18 | 1 | no | — |
| 524 | C22×C3 | — | 24 | 2 | no | — |
| 525 | C22×C3 | — | 24 | 2 | no | — |
| 526 | C22×C3 | — | 24 | 4 | no | — |
| 527 | C22×C3 | — | 72 | 1 | no | — |
| 528 | C22×C3 | C2×GO+(4,𝔽2) | 1 | 2 | yes | — |
| 529 | C2×D3 | — | 2 | 1 | no | — |
| 530 | C2×D3 | — | 2 | 2 | no | — |
| 531 | C2×D3 | — | 6 | 1 | no | — |
| 532 | C2×D3 | — | 6 | 1 | no | — |
| 533 | C2×D3 | — | 6 | 1 | no | — |
| 534 | C2×D3 | — | 6 | 1 | no | — |
| 535 | C2×D3 | — | 8 | 2 | no | — |
| 536 | C2×D3 | — | 12 | 1 | no | — |
| 537 | C2×D3 | — | 24 | 2 | no | — |
| 538 | C3×C4 | — | 2 | 1 | no | — |
| 539 | C3×C4 | — | 2 | 1 | no | — |
| 540 | C3×C4 | — | 4 | 1 | no | — |
| 541 | C3×C4 | — | 4 | 1 | no | — |
| 542 | C3×C4 | — | 6 | 1 | no | — |
| 543 | C3×C4 | — | 6 | 1 | no | — |
| 544 | C3×C4 | — | 9 | 1 | no | — |
| 545 | C3×C4 | — | 9 | 2 | no | — |
| 546 | C3×C4 | — | 12 | 1 | no | — |
| 547 | C3×C4 | — | 18 | 1 | no | — |
| 548 | C3×C4 | — | 18 | 2 | no | — |
| 549 | C3×C4 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 550 | Dic3 | — | 2 | 1 | no | — |
| 551 | Dic3 | — | 6 | 2 | no | — |
| 552 | Dic3 | — | 6 | 2 | no | — |
| 553 | Dic3 | — | 6 | 1 | no | — |
| 554 | Dic3 | — | 6 | 1 | no | — |
| 555 | Dic3 | — | 6 | 2 | no | — |
| 556 | Dic3 | — | 6 | 1 | no | — |
| 557 | Dic3 | — | 6 | 2 | no | — |
| 558 | Dic3 | — | 6 | 1 | no | — |
| 559 | Dic3 | — | 12 | 2 | no | — |
| 560 | Dic3 | — | 12 | 1 | no | — |
| 561 | C32 | — | 2 | 1 | no | — |
| 562 | C32 | — | 2 | 1 | no | — |
| 563 | C32 | — | 4 | 1 | no | — |
| 564 | C32 | — | 4 | 1 | no | — |
| 565 | C32 | #5836 | 1 | 1 | yes | characteristic, complemented |
| 566 | C23 | — | 6 | 2 | no | — |
| 567 | C23 | — | 18 | 1 | no | — |
| 568 | Q8 | — | 9 | 1 | no | — |
| 569 | Q8 | — | 9 | 1 | no | — |
| 570 | Q8 | — | 18 | 1 | no | — |
| 571 | Q8 | — | 27 | 1 | no | — |
| 572 | Q8 | — | 27 | 2 | no | — |
| 573 | Q8 | — | 54 | 2 | no | — |
| 574 | D4 | — | 6 | 2 | no | — |
| 575 | D4 | — | 6 | 1 | no | — |
| 576 | D4 | — | 9 | 1 | no | — |
| 577 | D4 | — | 9 | 2 | no | — |
| 578 | D4 | — | 9 | 2 | no | — |
| 579 | D4 | — | 18 | 1 | no | — |
| 580 | D4 | — | 18 | 2 | no | — |
| 581 | D4 | — | 18 | 2 | no | — |
| 582 | D4 | — | 27 | 1 | no | — |
| 583 | D4 | — | 54 | 1 | no | — |
| 584 | D4 | D32⋊D3 | 1 | 1 | yes | characteristic |
| 585 | C2×C4 | — | 6 | 1 | no | — |
| 586 | C2×C4 | — | 9 | 2 | no | — |
| 587 | C2×C4 | — | 9 | 1 | no | — |
| 588 | C2×C4 | — | 18 | 2 | no | — |
| 589 | C2×C4 | — | 18 | 2 | no | — |
| 590 | C2×C4 | — | 18 | 1 | no | — |
| 591 | C2×C4 | — | 54 | 2 | no | — |
| 592 | C2×C4 | — | 54 | 1 | no | — |
| 593 | C8 | — | 27 | 1 | no | — |
| 594 | C8 | — | 27 | 1 | no | — |
| 595 | C8 | — | 27 | 2 | no | — |
| 596 | C2×C3 | — | 2 | 2 | no | — |
| 597 | C2×C3 | — | 2 | 1 | no | — |
| 598 | C2×C3 | — | 2 | 1 | no | — |
| 599 | C2×C3 | — | 4 | 2 | no | — |
| 600 | C2×C3 | — | 4 | 2 | no | — |
| 601 | C2×C3 | — | 4 | 1 | no | — |
| 602 | C2×C3 | — | 4 | 1 | no | — |
| 603 | C2×C3 | — | 8 | 2 | no | — |
| 604 | C2×C3 | — | 8 | 2 | no | — |
| 605 | C2×C3 | — | 12 | 2 | no | — |
| 606 | C2×C3 | — | 12 | 1 | no | — |
| 607 | C2×C3 | — | 12 | 2 | no | — |
| 608 | C2×C3 | — | 12 | 1 | no | — |
| 609 | C2×C3 | — | 12 | 2 | no | — |
| 610 | C2×C3 | — | 18 | 1 | no | — |
| 611 | C2×C3 | — | 24 | 2 | no | — |
| 612 | C2×C3 | — | 36 | 1 | no | — |
| 613 | C2×C3 | C22×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 614 | D3 | — | 4 | 1 | no | — |
| 615 | D3 | — | 4 | 2 | no | — |
| 616 | D3 | — | 12 | 1 | no | — |
| 617 | D3 | — | 12 | 1 | no | — |
| 618 | D3 | — | 12 | 1 | no | — |
| 619 | D3 | — | 12 | 1 | no | — |
| 620 | D3 | — | 24 | 1 | no | — |
| 621 | C22 | — | 6 | 1 | no | — |
| 622 | C22 | — | 6 | 2 | no | — |
| 623 | C22 | — | 9 | 1 | no | — |
| 624 | C22 | — | 18 | 1 | no | — |
| 625 | C22 | — | 24 | 2 | no | — |
| 626 | C22 | — | 72 | 1 | no | — |
| 627 | C22 | C2×D32⋊D3 | 1 | 2 | yes | — |
| 628 | C4 | — | 6 | 1 | no | — |
| 629 | C4 | — | 9 | 1 | no | — |
| 630 | C4 | — | 9 | 2 | no | — |
| 631 | C4 | — | 18 | 1 | no | — |
| 632 | C4 | — | 18 | 2 | no | — |
| 633 | C4 | C2×D32⋊D3 | 1 | 1 | yes | characteristic |
| 634 | C3 | — | 2 | 1 | no | — |
| 635 | C3 | — | 2 | 1 | no | — |
| 636 | C3 | — | 4 | 1 | no | — |
| 637 | C3 | — | 4 | 1 | no | — |
| 638 | C3 | #10596515 | 1 | 1 | yes | characteristic, complemented |
| 639 | C2 | — | 2 | 2 | no | — |
| 640 | C2 | — | 12 | 1 | no | — |
| 641 | C2 | — | 12 | 2 | no | — |
| 642 | C2 | — | 18 | 1 | no | — |
| 643 | C2 | — | 36 | 1 | no | — |
| 644 | C2 | C22×D32⋊D3 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D32⋊D3 |
| commutator, cosocle | C3×C3⋊Dic3 | C24 |
| Fitting | C33×D4 | D4 |
| socle | C2×C33 | C22×D4 |
| hypercenter | D4 | D32⋊D3 |
| hypocenter | C33 | #577 |
| LCS | G ▷ C3×C3⋊Dic3 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11724620 | C2 | semidirect |
| 2. C3×#64313 | C2 | semidirect |
| 3. #11724515 | C2 | semidirect |
| 4. #11724328 | C2 | semidirect |
| 5. C2×#88937 | C2 | semidirect |
| 6. #11724324 | C2 | semidirect |
| 7. #11724323 | C2 | semidirect |
| 8. #11724310 | C2 | semidirect |
| 9. #11724309 | C2 | semidirect |
| 10. #11724304 | C2 | semidirect |
| 11. #11724303 | C2 | semidirect |
| 16. C2×#6296 | C22 | semidirect |
| 18. #89046 | C22 | semidirect |
| 19. #89042 | C22 | semidirect |
| 21. #89040 | C22 | semidirect |
| 28. #88993 | C22 | semidirect |
| 29. C2×C3⋊#622 | C22 | semidirect |
| 30. #88989 | C22 | semidirect |
| 31. #88988 | C22 | semidirect |
| 32. #88938 | C22 | semidirect |
| 33. #88938 | C22 | semidirect |
| 34. #88937 | C22 | semidirect |
| 35. #88937 | C22 | semidirect |
| 36. #88937 | C22 | semidirect |
| 37. #88937 | C22 | semidirect |
| 38. #88937 | C22 | semidirect |
| 39. #88936 | C22 | semidirect |
| 40. #88935 | C22 | semidirect |
| 41. #88935 | C22 | semidirect |
| 43. #64313 | D3 | semidirect |
| 371. C33 | #577 | semidirect |
| 565. C32 | #5836 | semidirect |
| 638. C3 | #10596515 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724620 | 2 |
| C3×#64313 | 2 |
| #11724515 | 2 |
| #11724328 | 2 |
| C2×#88937 | 2 |
| #11724324 | 2 |
| #11724323 | 2 |
| #11724310 | 2 |
| #11724309 | 2 |
| #11724304 | 2 |
| #11724303 | 2 |
| #10596515 | 3 |
| #5836 | 9 |