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 | #11724390 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11724386 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11724340 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11724306 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11724303 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#64224 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11724253 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11724141 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11724140 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11724136 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11724127 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #10596522 | — | 3 | 1 | no | maximal |
| 13 | C4⋊#1113 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #89042 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C3⋊D3×D12 | — | 2 | 1 | no | — |
| 16 | D3×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 17 | #89018 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×#3802 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C3×#3799 | — | 2 | 1 | no | — |
| 20 | C3×#3798 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C3×#3796 | — | 2 | 1 | no | — |
| 22 | #88988 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C3×#3788 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #88965 | C22 | 1 | 2 | yes | complemented |
| 25 | #88959 | C22 | 1 | 2 | yes | complemented |
| 26 | #88955 | — | 2 | 2 | no | — |
| 27 | #88954 | C22 | 1 | 2 | yes | complemented |
| 28 | #88954 | C22 | 1 | 2 | yes | complemented |
| 29 | D3×#626 | — | 2 | 2 | no | — |
| 30 | #88942 | C22 | 1 | 2 | yes | complemented |
| 31 | #88941 | C22 | 1 | 2 | yes | complemented |
| 32 | #88938 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #88937 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #88936 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #88935 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #88935 | C22 | 1 | 2 | yes | complemented |
| 37 | #88935 | C22 | 1 | 2 | yes | complemented |
| 38 | C3×#3775 | C22 | 1 | 2 | yes | complemented |
| 39 | C3×#3774 | C22 | 1 | 2 | yes | complemented |
| 40 | #88926 | C22 | 1 | 2 | yes | complemented |
| 41 | #88924 | C22 | 1 | 2 | yes | complemented |
| 42 | #64320 | — | 3 | 1 | no | — |
| 43 | #64320 | — | 3 | 1 | no | — |
| 44 | #64314 | — | 6 | 1 | no | — |
| 45 | #64308 | — | 6 | 1 | no | — |
| 46 | #64289 | — | 3 | 1 | no | — |
| 47 | #64225 | — | 3 | 1 | no | — |
| 48 | #64225 | — | 3 | 2 | no | — |
| 49 | #64224 | — | 3 | 1 | no | — |
| 50 | #64224 | — | 3 | 2 | no | — |
| 51 | #64224 | — | 3 | 2 | no | — |
| 52 | #64224 | D3 | 1 | 1 | yes | characteristic, complemented |
| 53 | #64223 | — | 3 | 1 | no | — |
| 54 | #64223 | — | 3 | 2 | no | — |
| 55 | C2×#1113 | — | 2 | 1 | no | — |
| 56 | C2×D3×C3⋊D3 | — | 2 | 2 | no | — |
| 57 | C2×D3×C3⋊D3 | — | 2 | 2 | no | — |
| 58 | C2×C3×D32 | — | 2 | 1 | no | — |
| 59 | C4⋊(C3⋊(C3⋊D3)) | D4 | 1 | 1 | yes | characteristic |
| 60 | C3×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 61 | C3×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 62 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 63 | C32×D12 | — | 2 | 1 | no | — |
| 64 | C32×C4×D3 | — | 2 | 1 | no | — |
| 65 | C32×Dic6 | D4 | 1 | 1 | yes | characteristic |
| 66 | #6296 | C23 | 1 | 1 | yes | characteristic |
| 67 | #6295 | — | 2 | 1 | no | — |
| 68 | #6295 | C23 | 1 | 2 | yes | — |
| 69 | #6295 | C23 | 1 | 1 | yes | characteristic |
| 70 | #6292 | — | 2 | 2 | no | — |
| 71 | #6292 | D4 | 1 | 2 | yes | — |
| 72 | #6291 | — | 2 | 2 | no | — |
| 73 | #6289 | C23 | 1 | 2 | yes | — |
| 74 | C3×#627 | C23 | 1 | 1 | yes | characteristic |
| 75 | C3×#626 | — | 2 | 1 | no | — |
| 76 | C3×#626 | — | 2 | 2 | no | — |
| 77 | C3×#626 | — | 2 | 2 | no | — |
| 78 | C3×#625 | C23 | 1 | 1 | yes | characteristic |
| 79 | C3×#625 | C23 | 1 | 2 | yes | — |
| 80 | C3×#624 | — | 2 | 2 | no | — |
| 81 | C3×D3×Dic3 | — | 2 | 2 | no | — |
| 82 | C3⋊#622 | C23 | 1 | 1 | yes | characteristic |
| 83 | C3⋊#622 | C23 | 1 | 1 | yes | characteristic |
| 84 | C3×#622 | C23 | 1 | 2 | yes | — |
| 85 | #5774 | — | 9 | 1 | no | maximal |
| 86 | #3832 | — | 3 | 1 | no | — |
| 87 | D4×C3⋊D3 | — | 6 | 1 | no | — |
| 88 | C2×C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 89 | C3×#239 | — | 6 | 1 | no | — |
| 90 | C3×#239 | — | 6 | 1 | no | — |
| 91 | C3×#237 | — | 6 | 1 | no | — |
| 92 | C3×D3×D4 | — | 6 | 1 | no | — |
| 93 | C3×#235 | — | 6 | 1 | no | — |
| 94 | C3×#235 | — | 6 | 1 | no | — |
| 95 | #3811 | — | 6 | 2 | no | — |
| 96 | #3811 | — | 6 | 2 | no | — |
| 97 | #3811 | — | 6 | 2 | no | — |
| 98 | D3×#67 | — | 6 | 2 | no | — |
| 99 | C2×#626 | — | 6 | 2 | no | — |
| 100 | #3804 | — | 6 | 2 | no | — |
| 101 | #3802 | — | 3 | 1 | no | — |
| 102 | #3802 | — | 3 | 2 | no | — |
| 103 | #3802 | — | 3 | 2 | no | — |
| 104 | #3802 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 105 | D3×D12 | — | 6 | 2 | no | — |
| 106 | D3×D12 | — | 6 | 2 | no | — |
| 107 | D3×D12 | — | 6 | 1 | no | — |
| 108 | D3×D12 | — | 6 | 1 | no | — |
| 109 | D3×D12 | — | 6 | 1 | no | — |
| 110 | D3×D12 | — | 6 | 1 | no | — |
| 111 | D3×D12 | — | 6 | 1 | no | — |
| 112 | D3×D12 | — | 6 | 2 | no | — |
| 113 | D3×D12 | — | 12 | 1 | no | — |
| 114 | D3×D12 | — | 12 | 1 | no | — |
| 115 | #3799 | — | 2 | 1 | no | — |
| 116 | #3799 | — | 6 | 2 | no | — |
| 117 | #3799 | — | 6 | 1 | no | — |
| 118 | #3799 | — | 6 | 1 | no | — |
| 119 | #3798 | — | 3 | 1 | no | — |
| 120 | #3798 | — | 3 | 2 | no | — |
| 121 | #3798 | — | 3 | 2 | no | — |
| 122 | #3798 | — | 6 | 1 | no | — |
| 123 | #3798 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 124 | #3796 | — | 2 | 1 | no | — |
| 125 | #3788 | — | 3 | 2 | no | — |
| 126 | #3788 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 127 | #3787 | — | 3 | 1 | no | — |
| 128 | #3787 | — | 3 | 2 | no | — |
| 129 | #3776 | — | 3 | 1 | no | — |
| 130 | #3775 | — | 3 | 1 | no | — |
| 131 | #3775 | — | 3 | 1 | no | — |
| 132 | #3775 | — | 3 | 2 | no | — |
| 133 | #3775 | C2×D3 | 1 | 2 | yes | complemented |
| 134 | #3774 | — | 3 | 2 | no | — |
| 135 | #3774 | — | 3 | 1 | no | — |
| 136 | #3774 | — | 3 | 2 | no | — |
| 137 | #3774 | — | 3 | 2 | no | — |
| 138 | #3774 | C2×D3 | 1 | 2 | yes | complemented |
| 139 | C2×C3⋊(C3⋊D3) | C2×D4 | 1 | 2 | yes | — |
| 140 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 141 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 142 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C2×C32×D3 | — | 2 | 2 | no | — |
| 144 | C2×C32×D3 | — | 2 | 1 | no | — |
| 145 | #1113 | — | 8 | 1 | no | — |
| 146 | D3×C3⋊D3 | — | 8 | 2 | no | — |
| 147 | D3×C3⋊D3 | — | 8 | 2 | no | — |
| 148 | C3×D32 | — | 8 | 1 | no | — |
| 149 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 150 | C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 151 | C3×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 152 | C32×Dic3 | — | 2 | 1 | no | — |
| 153 | C32×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 154 | #1009 | — | 9 | 1 | no | — |
| 155 | #1009 | — | 18 | 1 | no | — |
| 156 | #1009 | — | 18 | 1 | no | — |
| 157 | #1004 | — | 9 | 1 | no | — |
| 158 | C3×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 159 | #950 | — | 9 | 1 | no | — |
| 160 | C2×#213 | — | 9 | 1 | no | — |
| 161 | #916 | — | 9 | 2 | no | — |
| 162 | #914 | — | 9 | 2 | no | — |
| 163 | #911 | — | 9 | 2 | no | — |
| 164 | D3×D8 | — | 9 | 2 | no | — |
| 165 | #908 | — | 9 | 1 | no | — |
| 166 | #907 | — | 9 | 1 | no | — |
| 167 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 168 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 169 | C22×C3×D3 | — | 6 | 2 | no | — |
| 170 | C2×D32 | — | 2 | 1 | no | — |
| 171 | C2×D32 | — | 6 | 2 | no | — |
| 172 | C2×D32 | — | 6 | 2 | no | — |
| 173 | C2×D32 | — | 6 | 2 | no | — |
| 174 | C2×D32 | — | 6 | 2 | no | — |
| 175 | C2×D32 | — | 6 | 2 | no | — |
| 176 | C2×D32 | — | 6 | 1 | no | — |
| 177 | C2×D32 | — | 12 | 2 | no | — |
| 178 | C2×D32 | — | 12 | 2 | no | — |
| 179 | C32×Q8 | — | 3 | 1 | no | — |
| 180 | C32×D4 | — | 6 | 1 | no | — |
| 181 | C2×C32×C4 | — | 6 | 1 | no | — |
| 182 | #638 | — | 6 | 2 | no | — |
| 183 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 184 | C4⋊(C3⋊D3) | — | 3 | 2 | no | — |
| 185 | C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 186 | C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 187 | C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 188 | C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 189 | C4⋊(C3⋊D3) | — | 12 | 1 | no | — |
| 190 | C4⋊(C3⋊D3) | — | 12 | 1 | no | — |
| 191 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 192 | C4×C3⋊D3 | — | 3 | 2 | no | — |
| 193 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 194 | C3×#67 | — | 6 | 2 | no | — |
| 195 | C3×#67 | — | 6 | 1 | no | — |
| 196 | C3×#67 | — | 6 | 2 | no | — |
| 197 | C3×#67 | — | 6 | 1 | no | — |
| 198 | C3×#67 | — | 6 | 2 | no | — |
| 199 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 200 | C3×D12 | — | 2 | 1 | no | — |
| 201 | C3×D12 | — | 2 | 1 | no | — |
| 202 | C3×D12 | — | 4 | 1 | no | — |
| 203 | C3×D12 | — | 6 | 1 | no | — |
| 204 | C3×D12 | — | 6 | 2 | no | — |
| 205 | C3×D12 | — | 6 | 2 | no | — |
| 206 | C3×D12 | — | 6 | 1 | no | — |
| 207 | C3×D12 | — | 6 | 1 | no | — |
| 208 | C3×D12 | — | 12 | 1 | no | — |
| 209 | C3×C4×D3 | — | 2 | 1 | no | — |
| 210 | C3×C4×D3 | — | 2 | 1 | no | — |
| 211 | C3×C4×D3 | — | 4 | 1 | no | — |
| 212 | C3×C4×D3 | — | 6 | 1 | no | — |
| 213 | C3×C4×D3 | — | 6 | 1 | no | — |
| 214 | C3×C4×D3 | — | 6 | 2 | no | — |
| 215 | C3×C4×D3 | — | 6 | 2 | no | — |
| 216 | C3×C4×D3 | — | 6 | 1 | no | — |
| 217 | C3×C4×D3 | — | 6 | 2 | no | — |
| 218 | C3×C4×D3 | — | 6 | 1 | no | — |
| 219 | C3×C4×D3 | — | 12 | 1 | no | — |
| 220 | C3×Dic6 | — | 2 | 1 | no | — |
| 221 | C3×Dic6 | — | 2 | 1 | no | — |
| 222 | C3×Dic6 | — | 6 | 1 | no | — |
| 223 | #627 | — | 3 | 1 | no | — |
| 224 | #627 | — | 6 | 1 | no | — |
| 225 | #627 | C22×D3 | 1 | 1 | yes | characteristic |
| 226 | #626 | — | 2 | 2 | no | — |
| 227 | #626 | — | 2 | 2 | no | — |
| 228 | #626 | — | 2 | 1 | no | — |
| 229 | #626 | — | 6 | 1 | no | — |
| 230 | #626 | — | 6 | 2 | no | — |
| 231 | #626 | — | 6 | 2 | no | — |
| 232 | #626 | — | 6 | 2 | no | — |
| 233 | #626 | — | 6 | 2 | no | — |
| 234 | #626 | — | 6 | 2 | no | — |
| 235 | #626 | — | 6 | 2 | no | — |
| 236 | #626 | — | 6 | 2 | no | — |
| 237 | #626 | — | 6 | 1 | no | — |
| 238 | #626 | — | 6 | 1 | no | — |
| 239 | #626 | — | 12 | 2 | no | — |
| 240 | #626 | — | 12 | 2 | no | — |
| 241 | #625 | — | 3 | 2 | no | — |
| 242 | #625 | — | 3 | 1 | no | — |
| 243 | #625 | — | 6 | 1 | no | — |
| 244 | #625 | C22×D3 | 1 | 2 | yes | — |
| 245 | #625 | C22×D3 | 1 | 1 | yes | characteristic |
| 246 | #624 | — | 2 | 2 | no | — |
| 247 | #624 | — | 6 | 2 | no | — |
| 248 | #624 | — | 6 | 2 | no | — |
| 249 | D3×Dic3 | — | 2 | 2 | no | — |
| 250 | #622 | — | 3 | 1 | no | — |
| 251 | #622 | — | 3 | 1 | no | — |
| 252 | #622 | C22×D3 | 1 | 2 | yes | — |
| 253 | #576 | — | 27 | 1 | no | Sylow |
| 254 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 255 | C3⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 256 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 257 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 258 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 259 | C32×D3 | — | 4 | 1 | no | — |
| 260 | C32×D3 | — | 4 | 2 | no | — |
| 261 | C3×#41 | — | 9 | 1 | no | — |
| 262 | C3×#41 | — | 18 | 1 | no | — |
| 263 | C3×#41 | — | 18 | 1 | no | — |
| 264 | C2×C3×D4 | — | 9 | 1 | no | — |
| 265 | C2×#67 | — | 18 | 2 | no | — |
| 266 | #239 | — | 6 | 1 | no | — |
| 267 | #239 | — | 6 | 1 | no | — |
| 268 | #239 | — | 9 | 2 | no | — |
| 269 | #239 | — | 18 | 1 | no | — |
| 270 | #239 | — | 18 | 1 | no | — |
| 271 | #237 | — | 6 | 1 | no | — |
| 272 | #237 | — | 9 | 2 | no | — |
| 273 | D3×D4 | — | 6 | 1 | no | — |
| 274 | D3×D4 | — | 9 | 2 | no | — |
| 275 | D3×D4 | — | 9 | 2 | no | — |
| 276 | D3×D4 | — | 18 | 1 | no | — |
| 277 | D3×D4 | — | 18 | 2 | no | — |
| 278 | D3×D4 | — | 18 | 2 | no | — |
| 279 | D3×D4 | — | 18 | 1 | no | — |
| 280 | D3×D4 | — | 18 | 1 | no | — |
| 281 | D3×D4 | — | 18 | 2 | no | — |
| 282 | D3×D4 | — | 18 | 2 | no | — |
| 283 | D3×D4 | — | 18 | 1 | no | — |
| 284 | D3×D4 | — | 18 | 2 | no | — |
| 285 | D3×D4 | — | 36 | 1 | no | — |
| 286 | #235 | — | 6 | 1 | no | — |
| 287 | #235 | — | 6 | 1 | no | — |
| 288 | #235 | — | 9 | 1 | no | — |
| 289 | #235 | — | 9 | 1 | no | — |
| 290 | #235 | — | 18 | 2 | no | — |
| 291 | #235 | — | 18 | 1 | no | — |
| 292 | #235 | — | 18 | 2 | no | — |
| 293 | C2×D12 | — | 9 | 1 | no | — |
| 294 | C2×D12 | — | 18 | 1 | no | — |
| 295 | C2×D12 | — | 18 | 2 | no | — |
| 296 | C2×D12 | — | 18 | 1 | no | — |
| 297 | C2×D12 | — | 18 | 1 | no | — |
| 298 | C2×D12 | — | 18 | 2 | no | — |
| 299 | C2×D12 | — | 36 | 1 | no | — |
| 300 | C3×SD16 | — | 9 | 2 | no | — |
| 301 | C3×D8 | — | 9 | 2 | no | — |
| 302 | C3×M16 | — | 9 | 1 | no | — |
| 303 | #216 | — | 9 | 1 | no | — |
| 304 | #215 | — | 9 | 1 | no | — |
| 305 | #214 | — | 9 | 1 | no | — |
| 306 | #213 | — | 9 | 1 | no | — |
| 307 | #213 | — | 9 | 2 | no | — |
| 308 | #213 | — | 9 | 2 | no | — |
| 309 | C2×C3⋊C8 | — | 9 | 1 | no | — |
| 310 | D24 | — | 9 | 2 | no | — |
| 311 | #204 | — | 9 | 2 | no | — |
| 312 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 313 | D3×C8 | — | 9 | 2 | no | — |
| 314 | C22×C32 | — | 6 | 2 | no | — |
| 315 | C22×C32 | — | 6 | 1 | no | — |
| 316 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 317 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 318 | C2×C3⋊D3 | — | 3 | 2 | no | — |
| 319 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 320 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 321 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 322 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 323 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 324 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 325 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 326 | C2×C3×D3 | — | 2 | 2 | no | — |
| 327 | C2×C3×D3 | — | 2 | 1 | no | — |
| 328 | C2×C3×D3 | — | 2 | 1 | no | — |
| 329 | C2×C3×D3 | — | 2 | 2 | no | — |
| 330 | C2×C3×D3 | — | 4 | 1 | no | — |
| 331 | C2×C3×D3 | — | 4 | 2 | no | — |
| 332 | C2×C3×D3 | — | 6 | 1 | no | — |
| 333 | C2×C3×D3 | — | 6 | 1 | no | — |
| 334 | C2×C3×D3 | — | 6 | 1 | no | — |
| 335 | C2×C3×D3 | — | 6 | 2 | no | — |
| 336 | C2×C3×D3 | — | 6 | 2 | no | — |
| 337 | C2×C3×D3 | — | 6 | 1 | no | — |
| 338 | C2×C3×D3 | — | 12 | 1 | no | — |
| 339 | C2×C3×D3 | — | 12 | 2 | no | — |
| 340 | C2×C3×D3 | — | 24 | 2 | no | — |
| 341 | D32 | — | 8 | 1 | no | — |
| 342 | D32 | — | 24 | 2 | no | — |
| 343 | D32 | — | 24 | 2 | no | — |
| 344 | D32 | — | 24 | 2 | no | — |
| 345 | D32 | — | 24 | 2 | no | — |
| 346 | D32 | — | 24 | 4 | no | — |
| 347 | D32 | — | 24 | 4 | no | — |
| 348 | D32 | — | 24 | 1 | no | — |
| 349 | D32 | — | 24 | 2 | no | — |
| 350 | C32×C4 | — | 2 | 1 | no | — |
| 351 | C32×C4 | — | 2 | 1 | no | — |
| 352 | C32×C4 | — | 3 | 2 | no | — |
| 353 | C32×C4 | — | 4 | 1 | no | — |
| 354 | C32×C4 | — | 4 | 1 | no | — |
| 355 | C32×C4 | — | 6 | 1 | no | — |
| 356 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 357 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 358 | C3⋊Dic3 | C23×D3 | 1 | 1 | yes | characteristic |
| 359 | C3×Dic3 | — | 2 | 1 | no | — |
| 360 | C3×Dic3 | — | 2 | 1 | no | — |
| 361 | C3×Dic3 | — | 2 | 2 | no | — |
| 362 | C3×Dic3 | — | 2 | 2 | no | — |
| 363 | C3×Dic3 | — | 4 | 1 | no | — |
| 364 | C3×Dic3 | — | 6 | 1 | no | — |
| 365 | C3×Dic3 | — | 6 | 1 | no | — |
| 366 | C3×Dic3 | — | 6 | 1 | no | — |
| 367 | C3×Dic3 | — | 6 | 1 | no | — |
| 368 | C3×Dic3 | — | 12 | 1 | no | — |
| 369 | H(5,𝔽2) | — | 27 | 1 | no | — |
| 370 | H(5,𝔽2) | — | 27 | 1 | no | — |
| 371 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 372 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 373 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 374 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 375 | #135 | — | 27 | 2 | no | — |
| 376 | #135 | — | 27 | 1 | no | — |
| 377 | C2×D8 | — | 27 | 2 | no | — |
| 378 | C2×D8 | — | 27 | 1 | no | — |
| 379 | #131 | — | 27 | 1 | no | — |
| 380 | C33 | #576 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 381 | C23×C3 | — | 18 | 1 | no | — |
| 382 | C22×D3 | — | 6 | 2 | no | — |
| 383 | C22×D3 | — | 18 | 2 | no | — |
| 384 | C22×D3 | — | 18 | 2 | no | — |
| 385 | C22×D3 | — | 18 | 1 | no | — |
| 386 | C22×D3 | — | 18 | 2 | no | — |
| 387 | C22×D3 | — | 18 | 2 | no | — |
| 388 | C22×D3 | — | 18 | 2 | no | — |
| 389 | C22×D3 | — | 18 | 2 | no | — |
| 390 | C22×D3 | — | 18 | 2 | no | — |
| 391 | C22×D3 | — | 36 | 2 | no | — |
| 392 | C22×D3 | — | 36 | 2 | no | — |
| 393 | C3×Q8 | — | 6 | 1 | no | — |
| 394 | C3×Q8 | — | 6 | 1 | no | — |
| 395 | C3×Q8 | — | 9 | 1 | no | — |
| 396 | C3×D4 | — | 6 | 1 | no | — |
| 397 | C3×D4 | — | 6 | 1 | no | — |
| 398 | C3×D4 | — | 9 | 2 | no | — |
| 399 | C3×D4 | — | 9 | 1 | no | — |
| 400 | C3×D4 | — | 12 | 1 | no | — |
| 401 | C3×D4 | — | 18 | 1 | no | — |
| 402 | C3×D4 | — | 18 | 1 | no | — |
| 403 | C3×D4 | — | 18 | 2 | no | — |
| 404 | C3×D4 | — | 18 | 2 | no | — |
| 405 | C2×C3×C4 | — | 6 | 1 | no | — |
| 406 | C2×C3×C4 | — | 6 | 1 | no | — |
| 407 | C2×C3×C4 | — | 9 | 1 | no | — |
| 408 | C2×C3×C4 | — | 12 | 1 | no | — |
| 409 | C2×C3×C4 | — | 18 | 1 | no | — |
| 410 | C2×C3×C4 | — | 18 | 2 | no | — |
| 411 | C2×C3×C4 | — | 18 | 2 | no | — |
| 412 | #67 | — | 6 | 1 | no | — |
| 413 | #67 | — | 6 | 2 | no | — |
| 414 | #67 | — | 6 | 1 | no | — |
| 415 | #67 | — | 6 | 2 | no | — |
| 416 | #67 | — | 6 | 2 | no | — |
| 417 | #67 | — | 9 | 2 | no | — |
| 418 | #67 | — | 18 | 2 | no | — |
| 419 | #67 | — | 18 | 1 | no | — |
| 420 | #67 | — | 18 | 2 | no | — |
| 421 | #67 | — | 18 | 1 | no | — |
| 422 | #67 | — | 18 | 1 | no | — |
| 423 | #67 | — | 18 | 2 | no | — |
| 424 | #67 | — | 18 | 2 | no | — |
| 425 | #67 | — | 36 | 2 | no | — |
| 426 | C2×Dic3 | — | 6 | 2 | no | — |
| 427 | D12 | — | 2 | 1 | no | — |
| 428 | D12 | — | 6 | 1 | no | — |
| 429 | D12 | — | 6 | 1 | no | — |
| 430 | D12 | — | 6 | 2 | no | — |
| 431 | D12 | — | 6 | 2 | no | — |
| 432 | D12 | — | 6 | 1 | no | — |
| 433 | D12 | — | 9 | 2 | no | — |
| 434 | D12 | — | 9 | 1 | no | — |
| 435 | D12 | — | 9 | 1 | no | — |
| 436 | D12 | — | 12 | 1 | no | — |
| 437 | D12 | — | 18 | 1 | no | — |
| 438 | D12 | — | 18 | 1 | no | — |
| 439 | D12 | — | 18 | 2 | no | — |
| 440 | D12 | — | 18 | 2 | no | — |
| 441 | D12 | — | 18 | 2 | no | — |
| 442 | D12 | — | 18 | 2 | no | — |
| 443 | D12 | — | 18 | 2 | no | — |
| 444 | D12 | — | 18 | 1 | no | — |
| 445 | D12 | — | 36 | 1 | no | — |
| 446 | D12 | — | 36 | 1 | no | — |
| 447 | D12 | — | 36 | 2 | no | — |
| 448 | C4×D3 | — | 2 | 1 | no | — |
| 449 | C4×D3 | — | 6 | 1 | no | — |
| 450 | C4×D3 | — | 6 | 1 | no | — |
| 451 | C4×D3 | — | 6 | 2 | no | — |
| 452 | C4×D3 | — | 6 | 1 | no | — |
| 453 | C4×D3 | — | 6 | 2 | no | — |
| 454 | C4×D3 | — | 6 | 1 | no | — |
| 455 | C4×D3 | — | 6 | 2 | no | — |
| 456 | C4×D3 | — | 9 | 2 | no | — |
| 457 | C4×D3 | — | 12 | 1 | no | — |
| 458 | C4×D3 | — | 18 | 2 | no | — |
| 459 | C4×D3 | — | 18 | 2 | no | — |
| 460 | Dic6 | — | 6 | 1 | no | — |
| 461 | Dic6 | — | 9 | 1 | no | — |
| 462 | Dic6 | — | 18 | 1 | no | — |
| 463 | Dic6 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 464 | C3×C8 | — | 9 | 2 | no | — |
| 465 | C3⋊C8 | — | 9 | 1 | no | — |
| 466 | C3⋊C8 | — | 9 | 1 | no | — |
| 467 | C2×C32 | — | 2 | 1 | no | — |
| 468 | C2×C32 | — | 2 | 1 | no | — |
| 469 | C2×C32 | — | 4 | 1 | no | — |
| 470 | C2×C32 | — | 4 | 1 | no | — |
| 471 | C2×C32 | — | 12 | 1 | no | — |
| 472 | C2×C32 | — | 12 | 2 | no | — |
| 473 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 474 | C3⋊D3 | — | 2 | 1 | no | — |
| 475 | C3⋊D3 | — | 4 | 1 | no | — |
| 476 | C3⋊D3 | — | 4 | 2 | no | — |
| 477 | C3⋊D3 | — | 6 | 2 | no | — |
| 478 | C3⋊D3 | — | 12 | 2 | no | — |
| 479 | C3⋊D3 | — | 12 | 2 | no | — |
| 480 | C3⋊D3 | — | 24 | 2 | no | — |
| 481 | C3⋊D3 | — | 24 | 2 | no | — |
| 482 | C3×D3 | — | 4 | 1 | no | — |
| 483 | C3×D3 | — | 4 | 2 | no | — |
| 484 | C3×D3 | — | 4 | 2 | no | — |
| 485 | C3×D3 | — | 4 | 2 | no | — |
| 486 | C3×D3 | — | 4 | 1 | no | — |
| 487 | C3×D3 | — | 8 | 2 | no | — |
| 488 | C3×D3 | — | 12 | 1 | no | — |
| 489 | C3×D3 | — | 12 | 1 | no | — |
| 490 | C3×D3 | — | 12 | 1 | no | — |
| 491 | C3×D3 | — | 12 | 2 | no | — |
| 492 | C3×D3 | — | 12 | 2 | no | — |
| 493 | C3×D3 | — | 12 | 1 | no | — |
| 494 | C3×D3 | — | 12 | 2 | no | — |
| 495 | C3×D3 | — | 24 | 2 | no | — |
| 496 | #41 | — | 9 | 1 | no | — |
| 497 | #41 | — | 18 | 1 | no | — |
| 498 | #41 | — | 18 | 1 | no | — |
| 499 | #41 | — | 27 | 1 | no | — |
| 500 | #41 | — | 27 | 1 | no | — |
| 501 | #41 | — | 27 | 2 | no | — |
| 502 | #41 | — | 27 | 2 | no | — |
| 503 | C2×D4 | — | 9 | 1 | no | — |
| 504 | C2×D4 | — | 27 | 1 | no | — |
| 505 | C2×D4 | — | 27 | 2 | no | — |
| 506 | C2×D4 | — | 27 | 2 | no | — |
| 507 | C2×D4 | — | 54 | 1 | no | — |
| 508 | C2×D4 | — | 54 | 1 | no | — |
| 509 | C2×D4 | — | 54 | 2 | no | — |
| 510 | C2×D4 | — | 54 | 2 | no | — |
| 511 | Q16 | — | 27 | 1 | no | — |
| 512 | SD16 | — | 9 | 2 | no | — |
| 513 | SD16 | — | 27 | 2 | no | — |
| 514 | SD16 | — | 27 | 1 | no | — |
| 515 | SD16 | — | 27 | 1 | no | — |
| 516 | D8 | — | 9 | 2 | no | — |
| 517 | D8 | — | 27 | 2 | no | — |
| 518 | D8 | — | 27 | 1 | no | — |
| 519 | D8 | — | 27 | 2 | no | — |
| 520 | D8 | — | 27 | 2 | no | — |
| 521 | M16 | — | 9 | 1 | no | — |
| 522 | M16 | — | 27 | 2 | no | — |
| 523 | C2×C8 | — | 27 | 2 | no | — |
| 524 | C2×C8 | — | 27 | 1 | no | — |
| 525 | C22×C3 | — | 6 | 1 | no | — |
| 526 | C22×C3 | — | 6 | 2 | no | — |
| 527 | C22×C3 | — | 6 | 2 | no | — |
| 528 | C22×C3 | — | 6 | 1 | no | — |
| 529 | C22×C3 | — | 9 | 1 | no | — |
| 530 | C22×C3 | — | 12 | 1 | no | — |
| 531 | C22×C3 | — | 12 | 2 | no | — |
| 532 | C22×C3 | — | 18 | 2 | no | — |
| 533 | C22×C3 | — | 18 | 1 | no | — |
| 534 | C22×C3 | — | 72 | 1 | no | — |
| 535 | C2×D3 | — | 2 | 1 | no | — |
| 536 | C2×D3 | — | 2 | 2 | no | — |
| 537 | C2×D3 | — | 6 | 1 | no | — |
| 538 | C2×D3 | — | 6 | 1 | no | — |
| 539 | C2×D3 | — | 6 | 2 | no | — |
| 540 | C2×D3 | — | 6 | 1 | no | — |
| 541 | C2×D3 | — | 6 | 2 | no | — |
| 542 | C2×D3 | — | 6 | 1 | no | — |
| 543 | C2×D3 | — | 9 | 2 | no | — |
| 544 | C2×D3 | — | 12 | 1 | no | — |
| 545 | C2×D3 | — | 12 | 2 | no | — |
| 546 | C2×D3 | — | 18 | 2 | no | — |
| 547 | C2×D3 | — | 18 | 2 | no | — |
| 548 | C2×D3 | — | 24 | 2 | no | — |
| 549 | C2×D3 | — | 36 | 2 | no | — |
| 550 | C2×D3 | — | 36 | 2 | no | — |
| 551 | C2×D3 | — | 72 | 2 | no | — |
| 552 | C2×D3 | — | 72 | 2 | no | — |
| 553 | C2×D3 | — | 72 | 1 | no | — |
| 554 | C2×D3 | — | 72 | 2 | no | — |
| 555 | C2×D3 | — | 72 | 2 | no | — |
| 556 | C2×D3 | — | 72 | 2 | no | — |
| 557 | C2×D3 | — | 72 | 2 | no | — |
| 558 | C2×D3 | — | 72 | 2 | no | — |
| 559 | C2×D3 | — | 72 | 4 | no | — |
| 560 | C2×D3 | — | 72 | 4 | no | — |
| 561 | C3×C4 | — | 2 | 1 | no | — |
| 562 | C3×C4 | — | 2 | 1 | no | — |
| 563 | C3×C4 | — | 4 | 1 | no | — |
| 564 | C3×C4 | — | 4 | 1 | no | — |
| 565 | C3×C4 | — | 6 | 2 | no | — |
| 566 | C3×C4 | — | 6 | 2 | no | — |
| 567 | C3×C4 | — | 6 | 1 | no | — |
| 568 | C3×C4 | — | 6 | 1 | no | — |
| 569 | C3×C4 | — | 9 | 1 | no | — |
| 570 | C3×C4 | — | 12 | 1 | no | — |
| 571 | C3×C4 | — | 18 | 1 | no | — |
| 572 | C3×C4 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 573 | Dic3 | — | 2 | 1 | no | — |
| 574 | Dic3 | — | 6 | 1 | no | — |
| 575 | Dic3 | — | 6 | 1 | no | — |
| 576 | Dic3 | — | 6 | 1 | no | — |
| 577 | Dic3 | — | 6 | 1 | no | — |
| 578 | Dic3 | — | 12 | 1 | no | — |
| 579 | Dic3 | C2×GO+(4,𝔽2) | 1 | 2 | yes | — |
| 580 | C32 | — | 2 | 1 | no | — |
| 581 | C32 | — | 2 | 1 | no | — |
| 582 | C32 | — | 4 | 1 | no | — |
| 583 | C32 | — | 4 | 1 | no | — |
| 584 | C32 | #5774 | 1 | 1 | yes | characteristic, complemented |
| 585 | C23 | — | 18 | 1 | no | — |
| 586 | C23 | — | 54 | 2 | no | — |
| 587 | C23 | — | 54 | 2 | no | — |
| 588 | C23 | — | 54 | 1 | no | — |
| 589 | Q8 | — | 3 | 1 | no | — |
| 590 | Q8 | — | 9 | 1 | no | — |
| 591 | Q8 | — | 27 | 1 | no | — |
| 592 | D4 | — | 6 | 1 | no | — |
| 593 | D4 | — | 9 | 1 | no | — |
| 594 | D4 | — | 9 | 2 | no | — |
| 595 | D4 | — | 18 | 2 | no | — |
| 596 | D4 | — | 18 | 2 | no | — |
| 597 | D4 | — | 18 | 1 | no | — |
| 598 | D4 | — | 18 | 1 | no | — |
| 599 | D4 | — | 27 | 2 | no | — |
| 600 | D4 | — | 27 | 1 | no | — |
| 601 | D4 | — | 27 | 2 | no | — |
| 602 | D4 | — | 27 | 1 | no | — |
| 603 | D4 | — | 54 | 2 | no | — |
| 604 | D4 | — | 54 | 2 | no | — |
| 605 | D4 | — | 54 | 1 | no | — |
| 606 | C2×C4 | — | 6 | 1 | no | — |
| 607 | C2×C4 | — | 9 | 1 | no | — |
| 608 | C2×C4 | — | 18 | 2 | no | — |
| 609 | C2×C4 | — | 18 | 2 | no | — |
| 610 | C2×C4 | — | 18 | 1 | no | — |
| 611 | C2×C4 | — | 27 | 2 | no | — |
| 612 | C8 | — | 9 | 2 | no | — |
| 613 | C8 | — | 27 | 1 | no | — |
| 614 | C8 | — | 27 | 1 | no | — |
| 615 | C2×C3 | — | 2 | 1 | no | — |
| 616 | C2×C3 | — | 2 | 1 | no | — |
| 617 | C2×C3 | — | 4 | 1 | no | — |
| 618 | C2×C3 | — | 4 | 1 | no | — |
| 619 | C2×C3 | — | 12 | 2 | no | — |
| 620 | C2×C3 | — | 12 | 1 | no | — |
| 621 | C2×C3 | — | 12 | 2 | no | — |
| 622 | C2×C3 | — | 12 | 1 | no | — |
| 623 | C2×C3 | — | 12 | 2 | no | — |
| 624 | C2×C3 | — | 18 | 1 | no | — |
| 625 | C2×C3 | — | 24 | 2 | no | — |
| 626 | C2×C3 | — | 36 | 1 | no | — |
| 627 | C2×C3 | — | 36 | 2 | no | — |
| 628 | C2×C3 | C22×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 629 | D3 | — | 4 | 2 | no | — |
| 630 | D3 | — | 4 | 1 | no | — |
| 631 | D3 | — | 12 | 1 | no | — |
| 632 | D3 | — | 12 | 1 | no | — |
| 633 | D3 | — | 12 | 1 | no | — |
| 634 | D3 | — | 12 | 2 | no | — |
| 635 | D3 | — | 12 | 2 | no | — |
| 636 | D3 | — | 12 | 1 | no | — |
| 637 | D3 | — | 12 | 2 | no | — |
| 638 | D3 | — | 18 | 2 | no | — |
| 639 | D3 | — | 24 | 2 | no | — |
| 640 | D3 | — | 36 | 2 | no | — |
| 641 | D3 | — | 36 | 2 | no | — |
| 642 | D3 | — | 72 | 2 | no | — |
| 643 | D3 | — | 72 | 2 | no | — |
| 644 | C22 | — | 6 | 1 | no | — |
| 645 | C22 | — | 6 | 2 | no | — |
| 646 | C22 | — | 9 | 1 | no | — |
| 647 | C22 | — | 18 | 1 | no | — |
| 648 | C22 | — | 18 | 2 | no | — |
| 649 | C22 | — | 27 | 2 | no | — |
| 650 | C22 | — | 72 | 1 | no | — |
| 651 | C22 | — | 216 | 2 | no | — |
| 652 | C22 | — | 216 | 2 | no | — |
| 653 | C22 | — | 216 | 1 | no | — |
| 654 | C4 | — | 3 | 2 | no | — |
| 655 | C4 | — | 6 | 1 | no | — |
| 656 | C4 | — | 9 | 1 | no | — |
| 657 | C4 | — | 18 | 1 | no | — |
| 658 | C4 | D3×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 659 | C3 | — | 2 | 1 | no | — |
| 660 | C3 | — | 2 | 1 | no | — |
| 661 | C3 | — | 4 | 1 | no | — |
| 662 | C3 | — | 4 | 1 | no | — |
| 663 | C3 | #10596522 | 1 | 1 | yes | characteristic, complemented |
| 664 | C2 | — | 12 | 2 | no | — |
| 665 | C2 | — | 12 | 1 | no | — |
| 666 | C2 | — | 18 | 1 | no | — |
| 667 | C2 | — | 36 | 1 | no | — |
| 668 | C2 | — | 36 | 2 | no | — |
| 669 | C2 | — | 54 | 2 | no | — |
| 670 | 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. #11724390 | C2 | semidirect |
| 2. #11724386 | C2 | semidirect |
| 3. #11724340 | C2 | semidirect |
| 4. #11724306 | C2 | semidirect |
| 5. #11724303 | C2 | semidirect |
| 6. C3×#64224 | C2 | semidirect |
| 7. #11724253 | C2 | semidirect |
| 8. #11724141 | C2 | semidirect |
| 9. #11724140 | C2 | semidirect |
| 10. #11724136 | C2 | semidirect |
| 11. #11724127 | C2 | semidirect |
| 13. C4⋊#1113 | C22 | semidirect |
| 14. #89042 | C22 | semidirect |
| 18. C3×#3802 | C22 | semidirect |
| 20. C3×#3798 | C22 | semidirect |
| 22. #88988 | C22 | semidirect |
| 23. C3×#3788 | C22 | semidirect |
| 24. #88965 | C22 | semidirect |
| 25. #88959 | C22 | semidirect |
| 27. #88954 | C22 | semidirect |
| 28. #88954 | C22 | semidirect |
| 30. #88942 | C22 | semidirect |
| 31. #88941 | C22 | semidirect |
| 32. #88938 | C22 | semidirect |
| 33. #88937 | C22 | semidirect |
| 34. #88936 | C22 | semidirect |
| 35. #88935 | C22 | semidirect |
| 36. #88935 | C22 | semidirect |
| 37. #88935 | C22 | semidirect |
| 38. C3×#3775 | C22 | semidirect |
| 39. C3×#3774 | C22 | semidirect |
| 40. #88926 | C22 | semidirect |
| 41. #88924 | C22 | semidirect |
| 52. #64224 | D3 | semidirect |
| 104. #3802 | C2×D3 | semidirect |
| 123. #3798 | C2×D3 | semidirect |
| 126. #3788 | C2×D3 | semidirect |
| 133. #3775 | C2×D3 | semidirect |
| 138. #3774 | C2×D3 | semidirect |
| 380. C33 | #576 | semidirect |
| 584. C32 | #5774 | semidirect |
| 663. C3 | #10596522 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724390 | 2 |
| #11724386 | 2 |
| #11724340 | 2 |
| #11724306 | 2 |
| #11724303 | 2 |
| C3×#64224 | 2 |
| #11724253 | 2 |
| #11724141 | 2 |
| #11724140 | 2 |
| #11724136 | 2 |
| #11724127 | 2 |
| #10596522 | 3 |
| #5774 | 9 |