Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
1340 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 1340 conjugacy classes of subgroups — too many to draw. Only its 57 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 | #11923786 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11923785 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11920983 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11920982 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C3×#3027⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11714184 | — | 3 | 3 | no | maximal |
| 7 | #10949316 | — | 3 | 1 | no | maximal |
| 8 | C3×#5950 | C22 | 1 | 1 | yes | characteristic, complemented |
| 9 | C3⋊#5935 | C22 | 1 | 1 | yes | characteristic |
| 10 | C3⋊#5934 | C22 | 1 | 2 | yes | complemented |
| 11 | C3⋊#5933 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | D4×C3⋊S4 | — | 4 | 1 | no | maximal |
| 13 | C3×B(4,𝔽2)⋊C3 | C22 | 1 | 2 | yes | complemented |
| 14 | #87521 | — | 3 | 3 | no | — |
| 15 | #87520 | — | 3 | 3 | no | — |
| 16 | #86326 | — | 3 | 1 | no | — |
| 17 | C3×#3027 | D3 | 1 | 1 | yes | characteristic, complemented |
| 18 | #84126 | — | 3 | 1 | no | — |
| 19 | #84121 | — | 3 | 1 | no | — |
| 20 | #3027⋊C3 | D3 | 1 | 3 | yes | complemented |
| 21 | #73027 | — | 3 | 6 | no | — |
| 22 | #73026 | — | 3 | 6 | no | — |
| 23 | #71859 | — | 3 | 1 | no | — |
| 24 | #70997 | — | 3 | 2 | no | — |
| 25 | #70997 | — | 3 | 2 | no | — |
| 26 | #70996 | — | 3 | 2 | no | — |
| 27 | #70996 | — | 3 | 2 | no | — |
| 28 | #70060 | — | 3 | 1 | no | — |
| 29 | #70057 | — | 3 | 1 | no | — |
| 30 | C22×C3⋊S4 | — | 4 | 2 | no | — |
| 31 | C3×#997 | C23 | 1 | 1 | yes | characteristic |
| 32 | C3×D4×A4 | — | 4 | 1 | no | — |
| 33 | #64269 | — | 4 | 2 | no | — |
| 34 | #64266 | — | 8 | 1 | no | — |
| 35 | C4⋊(C3⋊S4) | — | 4 | 1 | no | — |
| 36 | C4⋊(C3⋊S4) | — | 8 | 1 | no | — |
| 37 | C4×C3⋊S4 | — | 4 | 1 | no | — |
| 38 | #33559 | — | 9 | 1 | no | Sylow |
| 39 | C3×#585 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 40 | #5950 | C2×D3 | 1 | 3 | yes | complemented |
| 41 | #5935 | — | 3 | 3 | no | — |
| 42 | #5934 | — | 3 | 6 | no | — |
| 43 | #5933 | — | 3 | 3 | no | — |
| 44 | D4×S4 | — | 12 | 3 | no | — |
| 45 | C3×#535 | — | 3 | 1 | no | — |
| 46 | #5832 | — | 3 | 1 | no | — |
| 47 | #5830 | — | 3 | 1 | no | — |
| 48 | #5830 | — | 6 | 1 | no | — |
| 49 | #5822 | — | 6 | 1 | no | — |
| 50 | D4×#67 | — | 6 | 1 | no | — |
| 51 | #5715 | — | 6 | 2 | no | — |
| 52 | #5683 | — | 6 | 1 | no | — |
| 53 | #5670 | — | 6 | 1 | no | — |
| 54 | #5616 | — | 6 | 1 | no | — |
| 55 | #5609 | — | 6 | 1 | no | — |
| 56 | #5607 | — | 6 | 1 | no | — |
| 57 | #5596 | — | 6 | 1 | no | — |
| 58 | #5594 | — | 3 | 2 | no | — |
| 59 | #5592 | — | 6 | 2 | no | — |
| 60 | #5590 | — | 3 | 2 | no | — |
| 61 | #5532 | — | 6 | 1 | no | — |
| 62 | C3×B(4,𝔽2) | — | 3 | 2 | no | — |
| 63 | C3×B(4,𝔽2) | C2×D3 | 1 | 2 | yes | complemented |
| 64 | C3×#410 | — | 3 | 1 | no | — |
| 65 | #5246 | — | 6 | 1 | no | — |
| 66 | #5245 | — | 6 | 1 | no | — |
| 67 | #5244 | — | 3 | 2 | no | — |
| 68 | #5244 | — | 3 | 2 | no | — |
| 69 | #5244 | — | 6 | 2 | no | — |
| 70 | #5242 | — | 3 | 1 | no | — |
| 71 | #5242 | — | 3 | 1 | no | — |
| 72 | #5241 | — | 3 | 1 | no | — |
| 73 | #5241 | — | 3 | 1 | no | — |
| 74 | #5240 | — | 3 | 1 | no | — |
| 75 | #5240 | — | 6 | 1 | no | — |
| 76 | #5237 | — | 3 | 1 | no | — |
| 77 | C2×#837 | — | 6 | 1 | no | — |
| 78 | B(4,𝔽2)⋊C3 | C2×D3 | 1 | 6 | yes | complemented |
| 79 | #4536 | — | 3 | 2 | no | — |
| 80 | #4536 | — | 3 | 2 | no | — |
| 81 | #4474 | — | 3 | 2 | no | — |
| 82 | #4473 | — | 3 | 2 | no | — |
| 83 | #4471 | — | 3 | 2 | no | — |
| 84 | #4471 | — | 3 | 2 | no | — |
| 85 | C22×C3×A4 | — | 4 | 2 | no | — |
| 86 | C2×C3⋊S4 | — | 4 | 1 | no | — |
| 87 | C2×C3⋊S4 | — | 4 | 2 | no | — |
| 88 | C2×C3⋊S4 | — | 8 | 4 | no | — |
| 89 | C2×C3⋊S4 | — | 8 | 2 | no | — |
| 90 | D4×C3⋊D3 | — | 16 | 1 | no | — |
| 91 | C3×#41⋊C3 | — | 8 | 1 | no | — |
| 92 | C3×C4×A4 | — | 4 | 1 | no | — |
| 93 | C3×C4×A4 | — | 8 | 1 | no | — |
| 94 | C3⋊SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 95 | C3⋊GL(2,𝔽3) | — | 8 | 1 | no | — |
| 96 | C3⋊#226 | — | 8 | 1 | no | — |
| 97 | #3549 | — | 9 | 1 | no | — |
| 98 | #3027 | — | 9 | 1 | no | — |
| 99 | #3027 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 100 | #3018 | — | 9 | 1 | no | — |
| 101 | #2199 | — | 9 | 2 | no | — |
| 102 | #2199 | — | 9 | 2 | no | — |
| 103 | #2196 | — | 9 | 2 | no | — |
| 104 | #2196 | — | 9 | 2 | no | — |
| 105 | #2126 | — | 9 | 1 | no | — |
| 106 | #2122 | — | 9 | 1 | no | — |
| 107 | #2122 | — | 9 | 1 | no | — |
| 108 | C22×S4 | — | 12 | 6 | no | — |
| 109 | C3×2−1+4 | — | 6 | 1 | no | — |
| 110 | C3×H(5,𝔽2) | — | 3 | 1 | no | — |
| 111 | C3×H(5,𝔽2) | — | 6 | 1 | no | — |
| 112 | C3×H(5,𝔽2) | C22×D3 | 1 | 1 | yes | characteristic |
| 113 | C2×C3×#41 | — | 3 | 1 | no | — |
| 114 | C2×C3×#41 | — | 6 | 1 | no | — |
| 115 | C2×C3×#41 | — | 6 | 1 | no | — |
| 116 | C22×C3×D4 | S4 | 1 | 1 | yes | characteristic, complemented |
| 117 | C22×#67 | — | 6 | 2 | no | — |
| 118 | C2×#237 | — | 6 | 2 | no | — |
| 119 | C2×D3×D4 | — | 6 | 2 | no | — |
| 120 | C2×D3×D4 | — | 6 | 1 | no | — |
| 121 | C2×#235 | — | 3 | 1 | no | — |
| 122 | C22×D12 | — | 3 | 1 | no | — |
| 123 | #997 | C22×D3 | 1 | 3 | yes | — |
| 124 | D4×A4 | — | 4 | 3 | no | — |
| 125 | GL(2,ℤ/4) | — | 12 | 6 | no | — |
| 126 | #985 | — | 24 | 3 | no | — |
| 127 | C4⋊S4 | — | 12 | 3 | no | — |
| 128 | C4⋊S4 | — | 24 | 3 | no | — |
| 129 | C4×S4 | — | 12 | 3 | no | — |
| 130 | C3×#127 | — | 6 | 1 | no | — |
| 131 | C3×#124 | — | 6 | 1 | no | — |
| 132 | C3×#121 | — | 6 | 1 | no | — |
| 133 | C3×#121 | — | 6 | 1 | no | — |
| 134 | C3×#120 | — | 3 | 2 | no | — |
| 135 | C3×#120 | — | 3 | 2 | no | — |
| 136 | C3×#117 | — | 3 | 1 | no | — |
| 137 | #953 | — | 6 | 2 | no | — |
| 138 | #951 | — | 6 | 1 | no | — |
| 139 | #951 | — | 6 | 1 | no | — |
| 140 | #950 | — | 12 | 1 | no | — |
| 141 | #950 | — | 12 | 1 | no | — |
| 142 | #949 | — | 6 | 1 | no | — |
| 143 | #949 | — | 6 | 1 | no | — |
| 144 | #947 | — | 3 | 1 | no | — |
| 145 | #947 | — | 6 | 1 | no | — |
| 146 | #947 | — | 12 | 1 | no | — |
| 147 | #944 | — | 3 | 1 | no | — |
| 148 | #942 | — | 12 | 1 | no | — |
| 149 | #940 | — | 3 | 1 | no | — |
| 150 | #940 | — | 6 | 1 | no | — |
| 151 | #940 | — | 6 | 2 | no | — |
| 152 | #940 | — | 6 | 1 | no | — |
| 153 | #940 | — | 12 | 1 | no | — |
| 154 | #939 | — | 6 | 2 | no | — |
| 155 | #939 | — | 6 | 1 | no | — |
| 156 | #939 | — | 6 | 1 | no | — |
| 157 | #939 | — | 6 | 2 | no | — |
| 158 | #939 | — | 6 | 2 | no | — |
| 159 | #938 | — | 6 | 1 | no | — |
| 160 | #937 | — | 3 | 2 | no | — |
| 161 | #937 | — | 3 | 2 | no | — |
| 162 | #937 | — | 6 | 2 | no | — |
| 163 | #937 | — | 6 | 2 | no | — |
| 164 | #937 | — | 6 | 2 | no | — |
| 165 | #937 | — | 6 | 2 | no | — |
| 166 | #937 | — | 6 | 2 | no | — |
| 167 | #936 | — | 3 | 1 | no | — |
| 168 | #936 | — | 6 | 2 | no | — |
| 169 | D4×Dic3 | — | 6 | 1 | no | — |
| 170 | #932 | — | 12 | 1 | no | — |
| 171 | #930 | — | 6 | 1 | no | — |
| 172 | #930 | — | 6 | 1 | no | — |
| 173 | #930 | — | 12 | 1 | no | — |
| 174 | #930 | — | 12 | 1 | no | — |
| 175 | C4×#67 | — | 6 | 1 | no | — |
| 176 | C4×#67 | — | 6 | 1 | no | — |
| 177 | #926 | — | 3 | 1 | no | — |
| 178 | #926 | — | 6 | 1 | no | — |
| 179 | C2×C4×Dic3 | — | 3 | 1 | no | — |
| 180 | C2×#208 | — | 6 | 1 | no | — |
| 181 | #895 | — | 6 | 1 | no | — |
| 182 | #893 | — | 6 | 1 | no | — |
| 183 | #892 | — | 6 | 1 | no | — |
| 184 | #888 | — | 6 | 1 | no | — |
| 185 | #885 | — | 6 | 2 | no | — |
| 186 | #885 | — | 6 | 2 | no | — |
| 187 | #885 | — | 6 | 2 | no | — |
| 188 | #885 | — | 6 | 2 | no | — |
| 189 | #884 | — | 6 | 2 | no | — |
| 190 | #884 | — | 6 | 2 | no | — |
| 191 | #882 | — | 6 | 2 | no | — |
| 192 | #882 | — | 6 | 2 | no | — |
| 193 | #67⋊C4 | — | 6 | 2 | no | — |
| 194 | #877 | — | 6 | 2 | no | — |
| 195 | #875 | — | 6 | 2 | no | — |
| 196 | #872 | — | 6 | 2 | no | — |
| 197 | C3×#99 | — | 3 | 2 | no | — |
| 198 | C3×#99 | — | 6 | 1 | no | — |
| 199 | #837 | — | 6 | 1 | no | — |
| 200 | #837 | — | 6 | 1 | no | — |
| 201 | #837 | — | 6 | 1 | no | — |
| 202 | #837 | — | 6 | 1 | no | — |
| 203 | #836 | — | 6 | 1 | no | — |
| 204 | #834 | — | 3 | 2 | no | — |
| 205 | #834 | — | 6 | 2 | no | — |
| 206 | #834 | — | 6 | 2 | no | — |
| 207 | #834 | — | 6 | 1 | no | — |
| 208 | #833 | — | 3 | 1 | no | — |
| 209 | #833 | — | 3 | 1 | no | — |
| 210 | C22×C3⋊D3 | — | 16 | 2 | no | — |
| 211 | C2×C3×A4 | — | 4 | 1 | no | — |
| 212 | C2×C3×A4 | — | 8 | 1 | no | — |
| 213 | C2×C3×A4 | — | 8 | 2 | no | — |
| 214 | C3⋊S4 | — | 4 | 2 | no | — |
| 215 | C3⋊S4 | — | 8 | 2 | no | — |
| 216 | C3⋊S4 | — | 16 | 2 | no | — |
| 217 | C32×D4 | — | 16 | 1 | no | — |
| 218 | #638 | — | 16 | 2 | no | — |
| 219 | C4⋊(C3⋊D3) | — | 16 | 1 | no | — |
| 220 | C4×C3⋊D3 | — | 16 | 1 | no | — |
| 221 | C3×SL(2,𝔽3) | — | 8 | 1 | no | — |
| 222 | #585 | C2×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 223 | #575 | — | 18 | 1 | no | — |
| 224 | H(3,𝔽4) | — | 9 | 2 | no | — |
| 225 | H(3,𝔽4) | — | 18 | 1 | no | — |
| 226 | #555 | — | 18 | 1 | no | — |
| 227 | #555 | — | 18 | 1 | no | — |
| 228 | #555 | — | 18 | 1 | no | — |
| 229 | D42 | — | 9 | 2 | no | — |
| 230 | D42 | — | 18 | 1 | no | — |
| 231 | D42 | — | 18 | 1 | no | — |
| 232 | #535 | — | 3 | 1 | no | — |
| 233 | #535 | — | 9 | 1 | no | — |
| 234 | #535 | — | 18 | 2 | no | — |
| 235 | #535 | — | 18 | 2 | no | — |
| 236 | #535 | — | 18 | 1 | no | — |
| 237 | #535 | — | 18 | 1 | no | — |
| 238 | #532 | — | 9 | 1 | no | — |
| 239 | #532 | — | 18 | 1 | no | — |
| 240 | B(4,𝔽2) | — | 3 | 2 | no | — |
| 241 | B(4,𝔽2) | — | 9 | 2 | no | — |
| 242 | B(4,𝔽2) | — | 9 | 2 | no | — |
| 243 | B(4,𝔽2) | — | 18 | 2 | no | — |
| 244 | B(4,𝔽2) | C2×C3⋊D3 | 1 | 2 | yes | complemented |
| 245 | #456 | — | 18 | 1 | no | — |
| 246 | #455 | — | 9 | 1 | no | — |
| 247 | #455 | — | 9 | 1 | no | — |
| 248 | #454 | — | 18 | 1 | no | — |
| 249 | #453 | — | 9 | 1 | no | — |
| 250 | #453 | — | 9 | 1 | no | — |
| 251 | C2×#104 | — | 18 | 1 | no | — |
| 252 | #413 | — | 9 | 1 | no | — |
| 253 | #410 | — | 3 | 1 | no | — |
| 254 | #410 | — | 9 | 1 | no | — |
| 255 | #410 | — | 18 | 1 | no | — |
| 256 | #354 | — | 9 | 2 | no | — |
| 257 | #353 | — | 9 | 2 | no | — |
| 258 | AΣL(1,𝔽16) | — | 9 | 2 | no | — |
| 259 | AΣL(1,𝔽16) | — | 9 | 2 | no | — |
| 260 | AΣL(1,𝔽16) | — | 9 | 2 | no | — |
| 261 | AΣL(1,𝔽16) | — | 9 | 2 | no | — |
| 262 | C24×C3 | C2×S4 | 1 | 2 | yes | — |
| 263 | C23×D3 | — | 3 | 2 | no | — |
| 264 | C23×D3 | — | 6 | 2 | no | — |
| 265 | C22×A4 | — | 4 | 6 | no | — |
| 266 | C2×S4 | — | 12 | 3 | no | — |
| 267 | C2×S4 | — | 12 | 6 | no | — |
| 268 | C2×S4 | — | 24 | 6 | no | — |
| 269 | C2×S4 | — | 24 | 12 | no | — |
| 270 | C3×#41 | — | 2 | 1 | no | — |
| 271 | C3×#41 | — | 6 | 1 | no | — |
| 272 | C3×#41 | — | 6 | 1 | no | — |
| 273 | C3×#41 | — | 6 | 1 | no | — |
| 274 | C3×#41 | — | 12 | 1 | no | — |
| 275 | C3×#41 | — | 12 | 1 | no | — |
| 276 | C3×#41 | — | 12 | 1 | no | — |
| 277 | C3×#41 | — | 12 | 1 | no | — |
| 278 | C3×#41 | — | 12 | 1 | no | — |
| 279 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 280 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 281 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 282 | C2×C3×D4 | — | 3 | 1 | no | — |
| 283 | C2×C3×D4 | — | 3 | 1 | no | — |
| 284 | C2×C3×D4 | — | 3 | 1 | no | — |
| 285 | C2×C3×D4 | — | 6 | 1 | no | — |
| 286 | C2×C3×D4 | — | 6 | 1 | no | — |
| 287 | C2×C3×D4 | — | 6 | 1 | no | — |
| 288 | C2×C3×D4 | — | 6 | 1 | no | — |
| 289 | C2×C3×D4 | — | 6 | 1 | no | — |
| 290 | C2×C3×D4 | — | 6 | 1 | no | — |
| 291 | C2×C3×D4 | — | 6 | 2 | no | — |
| 292 | C2×C3×D4 | — | 6 | 2 | no | — |
| 293 | C2×C3×D4 | — | 12 | 1 | no | — |
| 294 | C22×C3×C4 | — | 2 | 1 | no | — |
| 295 | C22×C3×C4 | — | 3 | 1 | no | — |
| 296 | C22×C3×C4 | — | 3 | 1 | no | — |
| 297 | C22×C3×C4 | — | 6 | 1 | no | — |
| 298 | C22×C3×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 299 | C2×#67 | — | 6 | 1 | no | — |
| 300 | C2×#67 | — | 6 | 2 | no | — |
| 301 | C2×#67 | — | 6 | 1 | no | — |
| 302 | C2×#67 | — | 6 | 2 | no | — |
| 303 | C2×#67 | — | 6 | 1 | no | — |
| 304 | C2×#67 | — | 6 | 2 | no | — |
| 305 | C2×#67 | — | 6 | 2 | no | — |
| 306 | C2×#67 | — | 6 | 2 | no | — |
| 307 | C2×#67 | — | 6 | 2 | no | — |
| 308 | C2×#67 | — | 12 | 2 | no | — |
| 309 | C2×#67 | — | 12 | 2 | no | — |
| 310 | C2×#67 | — | 24 | 4 | no | — |
| 311 | C22×Dic3 | — | 6 | 1 | no | — |
| 312 | C22×Dic3 | — | 6 | 2 | no | — |
| 313 | #237 | — | 24 | 4 | no | — |
| 314 | D3×D4 | — | 24 | 1 | no | — |
| 315 | D3×D4 | — | 24 | 1 | no | — |
| 316 | D3×D4 | — | 24 | 4 | no | — |
| 317 | D3×D4 | — | 48 | 3 | no | — |
| 318 | #235 | — | 12 | 1 | no | — |
| 319 | #235 | — | 12 | 1 | no | — |
| 320 | C2×D12 | — | 3 | 1 | no | — |
| 321 | C2×D12 | — | 6 | 1 | no | — |
| 322 | C2×D12 | — | 6 | 1 | no | — |
| 323 | C2×D12 | — | 6 | 2 | no | — |
| 324 | C2×D12 | — | 12 | 1 | no | — |
| 325 | C2×D12 | — | 12 | 1 | no | — |
| 326 | C2×C4×D3 | — | 6 | 1 | no | — |
| 327 | C2×C4×D3 | — | 6 | 2 | no | — |
| 328 | C2×Dic6 | — | 3 | 1 | no | — |
| 329 | C2×Dic6 | — | 6 | 2 | no | — |
| 330 | #41⋊C3 | — | 8 | 3 | no | — |
| 331 | C4×A4 | — | 4 | 3 | no | — |
| 332 | C4×A4 | — | 8 | 3 | no | — |
| 333 | SL(2,ℤ/4) | — | 12 | 3 | no | — |
| 334 | GL(2,𝔽3) | — | 24 | 3 | no | — |
| 335 | #226 | — | 24 | 3 | no | — |
| 336 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 337 | C3×C22⋊C4 | — | 3 | 2 | no | — |
| 338 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 339 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 340 | C3×C42 | — | 6 | 1 | no | — |
| 341 | #217 | — | 3 | 2 | no | — |
| 342 | #217 | — | 6 | 1 | no | — |
| 343 | #217 | — | 6 | 2 | no | — |
| 344 | #217 | — | 6 | 2 | no | — |
| 345 | #217 | — | 6 | 1 | no | — |
| 346 | #217 | — | 6 | 2 | no | — |
| 347 | #216 | — | 12 | 1 | no | — |
| 348 | #216 | — | 12 | 1 | no | — |
| 349 | #215 | — | 12 | 1 | no | — |
| 350 | #215 | — | 12 | 1 | no | — |
| 351 | #214 | — | 12 | 1 | no | — |
| 352 | #214 | — | 12 | 1 | no | — |
| 353 | #213 | — | 12 | 1 | no | — |
| 354 | #213 | — | 12 | 1 | no | — |
| 355 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 356 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 357 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 358 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 359 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 360 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 361 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 362 | (C2×D3)⋊C4 | — | 12 | 2 | no | — |
| 363 | (C2×D3)⋊C4 | — | 12 | 2 | no | — |
| 364 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 365 | C4⋊Dic3 | — | 12 | 1 | no | — |
| 366 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 367 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 368 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 369 | C4×Dic3 | — | 3 | 1 | no | — |
| 370 | C4×Dic3 | — | 3 | 1 | no | — |
| 371 | C4×Dic3 | — | 6 | 1 | no | — |
| 372 | C4×Dic3 | — | 6 | 1 | no | — |
| 373 | C4×Dic3 | — | 6 | 2 | no | — |
| 374 | C4×Dic3 | — | 12 | 1 | no | — |
| 375 | #208 | — | 6 | 1 | no | — |
| 376 | #208 | — | 6 | 1 | no | — |
| 377 | #208 | — | 12 | 1 | no | — |
| 378 | C2×C3⋊C8 | — | 12 | 1 | no | — |
| 379 | C22×C32 | — | 16 | 2 | no | — |
| 380 | C2×C3⋊D3 | — | 16 | 1 | no | — |
| 381 | C2×C3⋊D3 | — | 16 | 2 | no | — |
| 382 | C2×C3⋊D3 | — | 32 | 4 | no | — |
| 383 | C3×A4 | — | 4 | 1 | no | — |
| 384 | C3×A4 | — | 8 | 1 | no | — |
| 385 | C32×C4 | — | 16 | 1 | no | — |
| 386 | C3⋊Dic3 | — | 16 | 1 | no | — |
| 387 | 2−1+4 | — | 6 | 1 | no | — |
| 388 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 389 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 390 | H(5,𝔽2) | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 391 | C2×#41 | — | 3 | 1 | no | — |
| 392 | C2×#41 | — | 6 | 1 | no | — |
| 393 | C2×#41 | — | 6 | 1 | no | — |
| 394 | C2×#41 | — | 9 | 1 | no | — |
| 395 | C2×#41 | — | 18 | 2 | no | — |
| 396 | C22×D4 | — | 9 | 1 | no | — |
| 397 | C22×D4 | — | 18 | 2 | no | — |
| 398 | C22×D4 | — | 18 | 1 | no | — |
| 399 | C22×D4 | — | 18 | 2 | no | — |
| 400 | C22×D4 | C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 401 | #137 | — | 18 | 1 | no | — |
| 402 | #137 | — | 18 | 1 | no | — |
| 403 | #137 | — | 36 | 1 | no | — |
| 404 | AGL(1,ℤ/8) | — | 18 | 1 | no | — |
| 405 | AGL(1,ℤ/8) | — | 18 | 1 | no | — |
| 406 | AGL(1,ℤ/8) | — | 36 | 1 | no | — |
| 407 | #135 | — | 36 | 1 | no | — |
| 408 | #135 | — | 36 | 1 | no | — |
| 409 | C2×M16 | — | 18 | 1 | no | — |
| 410 | C4⋊Q8 | — | 9 | 1 | no | — |
| 411 | C4⋊Q8 | — | 18 | 1 | no | — |
| 412 | #127 | — | 6 | 1 | no | — |
| 413 | #127 | — | 9 | 1 | no | — |
| 414 | #127 | — | 18 | 1 | no | — |
| 415 | #127 | — | 18 | 1 | no | — |
| 416 | #127 | — | 18 | 2 | no | — |
| 417 | #127 | — | 36 | 1 | no | — |
| 418 | #124 | — | 6 | 1 | no | — |
| 419 | #124 | — | 9 | 1 | no | — |
| 420 | #124 | — | 9 | 1 | no | — |
| 421 | #124 | — | 18 | 2 | no | — |
| 422 | #124 | — | 18 | 2 | no | — |
| 423 | #124 | — | 18 | 2 | no | — |
| 424 | #124 | — | 18 | 2 | no | — |
| 425 | #124 | — | 18 | 2 | no | — |
| 426 | #124 | — | 18 | 2 | no | — |
| 427 | #124 | — | 18 | 1 | no | — |
| 428 | #124 | — | 36 | 1 | no | — |
| 429 | #121 | — | 6 | 1 | no | — |
| 430 | #121 | — | 6 | 1 | no | — |
| 431 | #121 | — | 18 | 2 | no | — |
| 432 | #121 | — | 18 | 2 | no | — |
| 433 | #121 | — | 18 | 2 | no | — |
| 434 | #121 | — | 18 | 1 | no | — |
| 435 | #121 | — | 18 | 1 | no | — |
| 436 | #121 | — | 18 | 1 | no | — |
| 437 | #121 | — | 18 | 1 | no | — |
| 438 | #121 | — | 18 | 2 | no | — |
| 439 | #121 | — | 18 | 1 | no | — |
| 440 | #121 | — | 18 | 2 | no | — |
| 441 | #121 | — | 18 | 1 | no | — |
| 442 | #121 | — | 36 | 1 | no | — |
| 443 | #121 | — | 36 | 1 | no | — |
| 444 | #120 | — | 3 | 2 | no | — |
| 445 | #120 | — | 3 | 2 | no | — |
| 446 | #120 | — | 9 | 2 | no | — |
| 447 | #120 | — | 9 | 2 | no | — |
| 448 | #120 | — | 18 | 2 | no | — |
| 449 | #120 | — | 18 | 2 | no | — |
| 450 | #120 | — | 18 | 2 | no | — |
| 451 | #120 | — | 18 | 2 | no | — |
| 452 | #120 | — | 18 | 2 | no | — |
| 453 | #120 | — | 18 | 2 | no | — |
| 454 | #120 | — | 18 | 2 | no | — |
| 455 | #120 | — | 18 | 2 | no | — |
| 456 | C4×D4 | — | 18 | 2 | no | — |
| 457 | C4×D4 | — | 18 | 1 | no | — |
| 458 | C4×D4 | — | 18 | 1 | no | — |
| 459 | C4×D4 | — | 18 | 1 | no | — |
| 460 | C4×D4 | — | 18 | 1 | no | — |
| 461 | #117 | — | 3 | 1 | no | — |
| 462 | #117 | — | 9 | 1 | no | — |
| 463 | #117 | — | 18 | 2 | no | — |
| 464 | #117 | — | 18 | 2 | no | — |
| 465 | #117 | — | 18 | 1 | no | — |
| 466 | #117 | — | 18 | 1 | no | — |
| 467 | C2×C42 | — | 9 | 1 | no | — |
| 468 | #104 | — | 18 | 1 | no | — |
| 469 | #104 | — | 18 | 1 | no | — |
| 470 | #104 | — | 18 | 1 | no | — |
| 471 | #104 | — | 18 | 1 | no | — |
| 472 | #101 | — | 18 | 1 | no | — |
| 473 | #100 | — | 9 | 1 | no | — |
| 474 | #100 | — | 9 | 1 | no | — |
| 475 | #99 | — | 3 | 2 | no | — |
| 476 | #99 | — | 6 | 1 | no | — |
| 477 | #99 | — | 9 | 2 | no | — |
| 478 | #99 | — | 18 | 2 | no | — |
| 479 | #99 | — | 18 | 2 | no | — |
| 480 | #99 | — | 18 | 1 | no | — |
| 481 | C23×C3 | — | 2 | 1 | no | — |
| 482 | C23×C3 | — | 3 | 1 | no | — |
| 483 | C23×C3 | — | 3 | 1 | no | — |
| 484 | C23×C3 | — | 6 | 2 | no | — |
| 485 | C23×C3 | — | 6 | 1 | no | — |
| 486 | C23×C3 | — | 8 | 2 | no | — |
| 487 | C23×C3 | C22×S4 | 1 | 1 | yes | characteristic |
| 488 | C22×D3 | — | 6 | 1 | no | — |
| 489 | C22×D3 | — | 6 | 2 | no | — |
| 490 | C22×D3 | — | 12 | 2 | no | — |
| 491 | C22×D3 | — | 24 | 2 | no | — |
| 492 | C22×D3 | — | 24 | 2 | no | — |
| 493 | C22×D3 | — | 24 | 2 | no | — |
| 494 | C22×D3 | — | 24 | 2 | no | — |
| 495 | C22×D3 | — | 48 | 6 | no | — |
| 496 | C2×A4 | — | 4 | 3 | no | — |
| 497 | C2×A4 | — | 8 | 3 | no | — |
| 498 | C2×A4 | — | 8 | 6 | no | — |
| 499 | S4 | — | 12 | 6 | no | — |
| 500 | S4 | — | 24 | 6 | no | — |
| 501 | S4 | — | 48 | 6 | no | — |
| 502 | C3×Q8 | — | 2 | 1 | no | — |
| 503 | C3×Q8 | — | 6 | 1 | no | — |
| 504 | C3×Q8 | — | 12 | 1 | no | — |
| 505 | C3×D4 | — | 4 | 1 | no | — |
| 506 | C3×D4 | — | 6 | 1 | no | — |
| 507 | C3×D4 | — | 6 | 1 | no | — |
| 508 | C3×D4 | — | 12 | 1 | no | — |
| 509 | C3×D4 | — | 12 | 1 | no | — |
| 510 | C3×D4 | — | 12 | 1 | no | — |
| 511 | C3×D4 | — | 12 | 1 | no | — |
| 512 | C3×D4 | — | 12 | 1 | no | — |
| 513 | C3×D4 | — | 16 | 3 | no | — |
| 514 | C3×D4 | — | 24 | 2 | no | — |
| 515 | C3×D4 | — | 24 | 2 | no | — |
| 516 | C2×C3×C4 | — | 3 | 1 | no | — |
| 517 | C2×C3×C4 | — | 3 | 1 | no | — |
| 518 | C2×C3×C4 | — | 3 | 1 | no | — |
| 519 | C2×C3×C4 | — | 3 | 1 | no | — |
| 520 | C2×C3×C4 | — | 6 | 1 | no | — |
| 521 | C2×C3×C4 | — | 6 | 1 | no | — |
| 522 | C2×C3×C4 | — | 6 | 1 | no | — |
| 523 | C2×C3×C4 | — | 6 | 1 | no | — |
| 524 | C2×C3×C4 | — | 6 | 1 | no | — |
| 525 | C2×C3×C4 | — | 6 | 1 | no | — |
| 526 | C2×C3×C4 | — | 6 | 2 | no | — |
| 527 | C2×C3×C4 | — | 12 | 1 | no | — |
| 528 | #67 | — | 12 | 2 | no | — |
| 529 | #67 | — | 12 | 2 | no | — |
| 530 | #67 | — | 12 | 4 | no | — |
| 531 | #67 | — | 24 | 2 | no | — |
| 532 | #67 | — | 24 | 2 | no | — |
| 533 | #67 | — | 24 | 1 | no | — |
| 534 | #67 | — | 24 | 2 | no | — |
| 535 | #67 | — | 24 | 2 | no | — |
| 536 | #67 | — | 24 | 2 | no | — |
| 537 | #67 | — | 48 | 6 | no | — |
| 538 | #67 | — | 48 | 2 | no | — |
| 539 | #67 | — | 48 | 2 | no | — |
| 540 | C2×Dic3 | — | 6 | 1 | no | — |
| 541 | C2×Dic3 | — | 6 | 1 | no | — |
| 542 | C2×Dic3 | — | 6 | 1 | no | — |
| 543 | C2×Dic3 | — | 6 | 2 | no | — |
| 544 | C2×Dic3 | — | 12 | 2 | no | — |
| 545 | C2×Dic3 | — | 12 | 4 | no | — |
| 546 | C2×Dic3 | — | 12 | 2 | no | — |
| 547 | D12 | — | 12 | 1 | no | — |
| 548 | D12 | — | 12 | 1 | no | — |
| 549 | D12 | — | 12 | 1 | no | — |
| 550 | D12 | — | 24 | 1 | no | — |
| 551 | D12 | — | 24 | 2 | no | — |
| 552 | D12 | — | 48 | 3 | no | — |
| 553 | C4×D3 | — | 12 | 4 | no | — |
| 554 | C4×D3 | — | 12 | 1 | no | — |
| 555 | C4×D3 | — | 12 | 1 | no | — |
| 556 | C4×D3 | — | 48 | 3 | no | — |
| 557 | Dic6 | — | 12 | 1 | no | — |
| 558 | Dic6 | — | 24 | 2 | no | — |
| 559 | SL(2,𝔽3) | — | 8 | 3 | no | — |
| 560 | C3⋊C8 | — | 12 | 1 | no | — |
| 561 | C3⋊C8 | — | 12 | 1 | no | — |
| 562 | C2×C32 | — | 16 | 1 | no | — |
| 563 | C2×C32 | — | 32 | 2 | no | — |
| 564 | C3⋊D3 | — | 16 | 2 | no | — |
| 565 | C3⋊D3 | — | 32 | 2 | no | — |
| 566 | C24 | — | 9 | 2 | no | — |
| 567 | C24 | — | 18 | 2 | no | — |
| 568 | C24 | C2×C3⋊S4 | 1 | 2 | yes | — |
| 569 | #41 | — | 2 | 1 | no | — |
| 570 | #41 | — | 6 | 1 | no | — |
| 571 | #41 | — | 6 | 1 | no | — |
| 572 | #41 | — | 6 | 1 | no | — |
| 573 | #41 | — | 12 | 1 | no | — |
| 574 | #41 | — | 12 | 1 | no | — |
| 575 | #41 | — | 12 | 1 | no | — |
| 576 | #41 | — | 12 | 1 | no | — |
| 577 | #41 | — | 12 | 1 | no | — |
| 578 | #41 | — | 36 | 1 | no | — |
| 579 | #41 | — | 36 | 1 | no | — |
| 580 | #41 | — | 72 | 4 | no | — |
| 581 | C2×Q8 | — | 3 | 1 | no | — |
| 582 | C2×Q8 | — | 6 | 1 | no | — |
| 583 | C2×Q8 | — | 6 | 1 | no | — |
| 584 | C2×Q8 | — | 9 | 1 | no | — |
| 585 | C2×Q8 | — | 18 | 2 | no | — |
| 586 | C2×D4 | — | 3 | 1 | no | — |
| 587 | C2×D4 | — | 3 | 1 | no | — |
| 588 | C2×D4 | — | 3 | 1 | no | — |
| 589 | C2×D4 | — | 6 | 1 | no | — |
| 590 | C2×D4 | — | 6 | 1 | no | — |
| 591 | C2×D4 | — | 6 | 1 | no | — |
| 592 | C2×D4 | — | 6 | 1 | no | — |
| 593 | C2×D4 | — | 6 | 1 | no | — |
| 594 | C2×D4 | — | 6 | 1 | no | — |
| 595 | C2×D4 | — | 6 | 2 | no | — |
| 596 | C2×D4 | — | 6 | 2 | no | — |
| 597 | C2×D4 | — | 9 | 1 | no | — |
| 598 | C2×D4 | — | 12 | 1 | no | — |
| 599 | C2×D4 | — | 18 | 1 | no | — |
| 600 | C2×D4 | — | 18 | 1 | no | — |
| 601 | C2×D4 | — | 18 | 2 | no | — |
| 602 | C2×D4 | — | 18 | 1 | no | — |
| 603 | C2×D4 | — | 18 | 2 | no | — |
| 604 | C2×D4 | — | 18 | 1 | no | — |
| 605 | C2×D4 | — | 18 | 2 | no | — |
| 606 | C2×D4 | — | 18 | 1 | no | — |
| 607 | C2×D4 | — | 18 | 2 | no | — |
| 608 | C2×D4 | — | 18 | 2 | no | — |
| 609 | C2×D4 | — | 18 | 2 | no | — |
| 610 | C2×D4 | — | 18 | 2 | no | — |
| 611 | C2×D4 | — | 36 | 1 | no | — |
| 612 | C2×D4 | — | 36 | 1 | no | — |
| 613 | C2×D4 | — | 36 | 2 | no | — |
| 614 | C2×D4 | — | 36 | 2 | no | — |
| 615 | C2×D4 | — | 72 | 1 | no | — |
| 616 | C2×D4 | — | 72 | 1 | no | — |
| 617 | C2×D4 | — | 72 | 4 | no | — |
| 618 | C2×D4 | — | 72 | 4 | no | — |
| 619 | C22×C4 | — | 2 | 1 | no | — |
| 620 | C22×C4 | — | 3 | 1 | no | — |
| 621 | C22×C4 | — | 3 | 1 | no | — |
| 622 | C22×C4 | — | 6 | 1 | no | — |
| 623 | C22×C4 | — | 18 | 1 | no | — |
| 624 | C22×C4 | — | 18 | 2 | no | — |
| 625 | C22×C4 | — | 18 | 1 | no | — |
| 626 | C22×C4 | — | 18 | 2 | no | — |
| 627 | C22×C4 | C2×C3⋊S4 | 1 | 1 | yes | characteristic |
| 628 | Q16 | — | 36 | 1 | no | — |
| 629 | Q16 | — | 36 | 1 | no | — |
| 630 | SD16 | — | 36 | 1 | no | — |
| 631 | SD16 | — | 36 | 1 | no | — |
| 632 | SD16 | — | 36 | 1 | no | — |
| 633 | SD16 | — | 36 | 1 | no | — |
| 634 | D8 | — | 36 | 1 | no | — |
| 635 | D8 | — | 36 | 1 | no | — |
| 636 | M16 | — | 18 | 1 | no | — |
| 637 | M16 | — | 18 | 1 | no | — |
| 638 | M16 | — | 36 | 1 | no | — |
| 639 | C2×C8 | — | 36 | 1 | no | — |
| 640 | C4⋊C4 | — | 6 | 1 | no | — |
| 641 | C4⋊C4 | — | 18 | 1 | no | — |
| 642 | C4⋊C4 | — | 18 | 1 | no | — |
| 643 | C4⋊C4 | — | 18 | 1 | no | — |
| 644 | C4⋊C4 | — | 18 | 2 | no | — |
| 645 | C4⋊C4 | — | 36 | 1 | no | — |
| 646 | C22⋊C4 | — | 3 | 2 | no | — |
| 647 | C22⋊C4 | — | 6 | 2 | no | — |
| 648 | C22⋊C4 | — | 6 | 2 | no | — |
| 649 | C22⋊C4 | — | 9 | 2 | no | — |
| 650 | C22⋊C4 | — | 18 | 2 | no | — |
| 651 | C22⋊C4 | — | 18 | 2 | no | — |
| 652 | C22⋊C4 | — | 18 | 1 | no | — |
| 653 | C22⋊C4 | — | 18 | 1 | no | — |
| 654 | C22⋊C4 | — | 18 | 2 | no | — |
| 655 | C22⋊C4 | — | 18 | 2 | no | — |
| 656 | C22⋊C4 | — | 18 | 2 | no | — |
| 657 | C22⋊C4 | — | 18 | 1 | no | — |
| 658 | C22⋊C4 | — | 18 | 2 | no | — |
| 659 | C22⋊C4 | — | 18 | 2 | no | — |
| 660 | C22⋊C4 | — | 18 | 1 | no | — |
| 661 | C22⋊C4 | — | 18 | 2 | no | — |
| 662 | C22⋊C4 | — | 36 | 2 | no | — |
| 663 | C22⋊C4 | — | 36 | 2 | no | — |
| 664 | C42 | — | 6 | 1 | no | — |
| 665 | C42 | — | 9 | 1 | no | — |
| 666 | C42 | — | 9 | 1 | no | — |
| 667 | C42 | — | 18 | 1 | no | — |
| 668 | C42 | — | 18 | 1 | no | — |
| 669 | C42 | — | 18 | 2 | no | — |
| 670 | C42 | — | 36 | 1 | no | — |
| 671 | C22×C3 | — | 3 | 1 | no | — |
| 672 | C22×C3 | — | 4 | 1 | no | — |
| 673 | C22×C3 | — | 4 | 2 | no | — |
| 674 | C22×C3 | — | 6 | 1 | no | — |
| 675 | C22×C3 | — | 6 | 1 | no | — |
| 676 | C22×C3 | — | 8 | 1 | no | — |
| 677 | C22×C3 | — | 12 | 2 | no | — |
| 678 | C22×C3 | — | 12 | 2 | no | — |
| 679 | C22×C3 | — | 12 | 1 | no | — |
| 680 | C22×C3 | — | 12 | 1 | no | — |
| 681 | C22×C3 | — | 16 | 6 | no | — |
| 682 | C22×C3 | — | 24 | 1 | no | — |
| 683 | C2×D3 | — | 12 | 2 | no | — |
| 684 | C2×D3 | — | 12 | 1 | no | — |
| 685 | C2×D3 | — | 12 | 2 | no | — |
| 686 | C2×D3 | — | 12 | 1 | no | — |
| 687 | C2×D3 | — | 12 | 1 | no | — |
| 688 | C2×D3 | — | 12 | 2 | no | — |
| 689 | C2×D3 | — | 24 | 2 | no | — |
| 690 | C2×D3 | — | 24 | 2 | no | — |
| 691 | C2×D3 | — | 48 | 3 | no | — |
| 692 | C2×D3 | — | 48 | 6 | no | — |
| 693 | C2×D3 | — | 48 | 4 | no | — |
| 694 | C2×D3 | — | 96 | 12 | no | — |
| 695 | A4 | — | 4 | 3 | no | — |
| 696 | A4 | — | 8 | 3 | no | — |
| 697 | C3×C4 | — | 3 | 1 | no | — |
| 698 | C3×C4 | — | 6 | 1 | no | — |
| 699 | C3×C4 | — | 6 | 1 | no | — |
| 700 | C3×C4 | — | 12 | 2 | no | — |
| 701 | C3×C4 | — | 16 | 3 | no | — |
| 702 | C3×C4 | #1020⋊C2 | 1 | 1 | yes | characteristic |
| 703 | Dic3 | — | 6 | 2 | no | — |
| 704 | Dic3 | — | 12 | 1 | no | — |
| 705 | Dic3 | — | 12 | 2 | no | — |
| 706 | Dic3 | — | 12 | 1 | no | — |
| 707 | Dic3 | — | 24 | 2 | no | — |
| 708 | Dic3 | — | 48 | 3 | no | — |
| 709 | C32 | — | 16 | 1 | no | Sylow |
| 710 | C23 | — | 2 | 1 | no | — |
| 711 | C23 | — | 3 | 1 | no | — |
| 712 | C23 | — | 3 | 1 | no | — |
| 713 | C23 | — | 6 | 2 | no | — |
| 714 | C23 | — | 6 | 1 | no | — |
| 715 | C23 | — | 8 | 2 | no | — |
| 716 | C23 | — | 18 | 1 | no | — |
| 717 | C23 | — | 18 | 2 | no | — |
| 718 | C23 | — | 36 | 2 | no | — |
| 719 | C23 | — | 72 | 2 | no | — |
| 720 | C23 | — | 72 | 2 | no | — |
| 721 | C23 | — | 72 | 2 | no | — |
| 722 | C23 | — | 72 | 2 | no | — |
| 723 | C23 | C22×C3⋊S4 | 1 | 1 | yes | characteristic |
| 724 | Q8 | — | 2 | 1 | no | — |
| 725 | Q8 | — | 6 | 1 | no | — |
| 726 | Q8 | — | 12 | 1 | no | — |
| 727 | Q8 | — | 36 | 1 | no | — |
| 728 | Q8 | — | 72 | 2 | no | — |
| 729 | D4 | — | 4 | 1 | no | — |
| 730 | D4 | — | 6 | 1 | no | — |
| 731 | D4 | — | 6 | 1 | no | — |
| 732 | D4 | — | 12 | 1 | no | — |
| 733 | D4 | — | 12 | 1 | no | — |
| 734 | D4 | — | 12 | 1 | no | — |
| 735 | D4 | — | 12 | 1 | no | — |
| 736 | D4 | — | 12 | 1 | no | — |
| 737 | D4 | — | 24 | 2 | no | — |
| 738 | D4 | — | 24 | 2 | no | — |
| 739 | D4 | — | 36 | 1 | no | — |
| 740 | D4 | — | 36 | 1 | no | — |
| 741 | D4 | — | 36 | 2 | no | — |
| 742 | D4 | — | 36 | 4 | no | — |
| 743 | D4 | — | 36 | 2 | no | — |
| 744 | D4 | — | 36 | 1 | no | — |
| 745 | D4 | — | 72 | 1 | no | — |
| 746 | D4 | — | 72 | 2 | no | — |
| 747 | D4 | — | 72 | 2 | no | — |
| 748 | D4 | — | 72 | 2 | no | — |
| 749 | D4 | — | 72 | 1 | no | — |
| 750 | D4 | — | 72 | 2 | no | — |
| 751 | D4 | — | 72 | 2 | no | — |
| 752 | D4 | — | 72 | 2 | no | — |
| 753 | D4 | — | 144 | 2 | no | — |
| 754 | D4 | — | 144 | 2 | no | — |
| 755 | C2×C4 | — | 3 | 1 | no | — |
| 756 | C2×C4 | — | 3 | 1 | no | — |
| 757 | C2×C4 | — | 3 | 1 | no | — |
| 758 | C2×C4 | — | 3 | 1 | no | — |
| 759 | C2×C4 | — | 6 | 1 | no | — |
| 760 | C2×C4 | — | 6 | 1 | no | — |
| 761 | C2×C4 | — | 6 | 1 | no | — |
| 762 | C2×C4 | — | 6 | 1 | no | — |
| 763 | C2×C4 | — | 6 | 1 | no | — |
| 764 | C2×C4 | — | 6 | 1 | no | — |
| 765 | C2×C4 | — | 6 | 2 | no | — |
| 766 | C2×C4 | — | 12 | 1 | no | — |
| 767 | C2×C4 | — | 18 | 1 | no | — |
| 768 | C2×C4 | — | 18 | 1 | no | — |
| 769 | C2×C4 | — | 18 | 2 | no | — |
| 770 | C2×C4 | — | 18 | 1 | no | — |
| 771 | C2×C4 | — | 36 | 1 | no | — |
| 772 | C2×C4 | — | 36 | 4 | no | — |
| 773 | C2×C4 | — | 36 | 4 | no | — |
| 774 | C2×C4 | — | 36 | 2 | no | — |
| 775 | C2×C4 | — | 36 | 1 | no | — |
| 776 | C2×C4 | — | 36 | 2 | no | — |
| 777 | C8 | — | 36 | 1 | no | — |
| 778 | C8 | — | 36 | 1 | no | — |
| 779 | C2×C3 | — | 6 | 1 | no | — |
| 780 | C2×C3 | — | 8 | 2 | no | — |
| 781 | C2×C3 | — | 12 | 1 | no | — |
| 782 | C2×C3 | — | 12 | 1 | no | — |
| 783 | C2×C3 | — | 16 | 3 | no | — |
| 784 | C2×C3 | — | 32 | 6 | no | — |
| 785 | C2×C3 | C2×#1020⋊C2 | 1 | 1 | yes | characteristic |
| 786 | D3 | — | 24 | 2 | no | — |
| 787 | D3 | — | 24 | 1 | no | — |
| 788 | D3 | — | 48 | 6 | no | — |
| 789 | D3 | — | 96 | 6 | no | — |
| 790 | C22 | — | 3 | 1 | no | — |
| 791 | C22 | — | 4 | 1 | no | — |
| 792 | C22 | — | 4 | 2 | no | — |
| 793 | C22 | — | 6 | 1 | no | — |
| 794 | C22 | — | 6 | 1 | no | — |
| 795 | C22 | — | 8 | 1 | no | — |
| 796 | C22 | — | 12 | 2 | no | — |
| 797 | C22 | — | 12 | 2 | no | — |
| 798 | C22 | — | 12 | 1 | no | — |
| 799 | C22 | — | 12 | 1 | no | — |
| 800 | C22 | — | 24 | 1 | no | — |
| 801 | C22 | — | 36 | 2 | no | — |
| 802 | C22 | — | 36 | 2 | no | — |
| 803 | C22 | — | 36 | 1 | no | — |
| 804 | C22 | — | 36 | 1 | no | — |
| 805 | C22 | — | 36 | 1 | no | — |
| 806 | C22 | — | 36 | 2 | no | — |
| 807 | C22 | — | 72 | 2 | no | — |
| 808 | C22 | — | 72 | 2 | no | — |
| 809 | C22 | — | 144 | 4 | no | — |
| 810 | C4 | — | 3 | 1 | no | — |
| 811 | C4 | — | 6 | 1 | no | — |
| 812 | C4 | — | 6 | 1 | no | — |
| 813 | C4 | — | 12 | 2 | no | — |
| 814 | C4 | — | 18 | 2 | no | — |
| 815 | C4 | — | 36 | 2 | no | — |
| 816 | C4 | — | 36 | 1 | no | — |
| 817 | C4 | — | 36 | 1 | no | — |
| 818 | C4 | — | 72 | 2 | no | — |
| 819 | C4 | #10593630 | 1 | 1 | yes | characteristic |
| 820 | C3 | — | 16 | 3 | no | — |
| 821 | C3 | #11714184 | 1 | 1 | yes | characteristic, complemented |
| 822 | C2 | — | 6 | 1 | no | — |
| 823 | C2 | — | 8 | 2 | no | — |
| 824 | C2 | — | 12 | 1 | no | — |
| 825 | C2 | — | 12 | 1 | no | — |
| 826 | C2 | — | 72 | 2 | no | — |
| 827 | C2 | — | 72 | 1 | no | — |
| 828 | C2 | C2×#10593630 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#10593630 |
| commutator, cosocle, hypocenter | C3×#997 | C23 |
| Frattini | C23 | C22×C3⋊S4 |
| Fitting | C3×#3027 | D3 |
| socle | C2×C3 | C2×#1020⋊C2 |
| hypercenter | C4 | #10593630 |
| LCS | G ▷ C3×#997 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11923786 | C2 | semidirect |
| 2. #11923785 | C2 | semidirect |
| 3. #11920983 | C2 | semidirect |
| 4. #11920982 | C2 | semidirect |
| 5. C3×#3027⋊C3 | C2 | semidirect |
| 8. C3×#5950 | C22 | semidirect |
| 10. C3⋊#5934 | C22 | semidirect |
| 11. C3⋊#5933 | C22 | semidirect |
| 13. C3×B(4,𝔽2)⋊C3 | C22 | semidirect |
| 17. C3×#3027 | D3 | semidirect |
| 20. #3027⋊C3 | D3 | semidirect |
| 39. C3×#585 | C2×D3 | semidirect |
| 40. #5950 | C2×D3 | semidirect |
| 63. C3×B(4,𝔽2) | C2×D3 | semidirect |
| 78. B(4,𝔽2)⋊C3 | C2×D3 | semidirect |
| 99. #3027 | C3⋊D3 | semidirect |
| 116. C22×C3×D4 | S4 | semidirect |
| 222. #585 | C2×C3⋊D3 | semidirect |
| 244. B(4,𝔽2) | C2×C3⋊D3 | semidirect |
| 400. C22×D4 | C3⋊S4 | semidirect |
| 821. C3 | #11714184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11923786 | 2 |
| #11923785 | 2 |
| #11920983 | 2 |
| #11920982 | 2 |
| C3×#3027⋊C3 | 2 |
| #11714184 | 3 |
| #10949316 | 3 |
| D4×C3⋊S4 | 4 |