Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
1330 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 1330 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 | #11923785 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11923784 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11920987 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11920986 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11920982 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11920981 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C3×#3025⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11714162 | — | 3 | 3 | no | maximal |
| 9 | #10949206 | — | 3 | 1 | no | maximal |
| 10 | C3×#5950 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C3⋊#5935 | C22 | 1 | 1 | yes | characteristic |
| 12 | C3⋊#5934 | C22 | 1 | 1 | yes | characteristic |
| 13 | C3⋊#5933 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C3⋊#5932 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C2×C4×C3⋊S4 | — | 4 | 1 | no | maximal |
| 16 | C3×#458⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C3×B(4,𝔽2)⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 18 | #87520 | — | 3 | 3 | no | — |
| 19 | #87519 | — | 3 | 3 | no | — |
| 20 | #86038 | — | 3 | 1 | no | — |
| 21 | C3×#3025 | D3 | 1 | 1 | yes | characteristic, complemented |
| 22 | #84125 | — | 3 | 1 | no | — |
| 23 | #84121 | — | 3 | 1 | no | — |
| 24 | #3025⋊C3 | D3 | 1 | 3 | yes | complemented |
| 25 | #73031 | — | 3 | 3 | no | — |
| 26 | #73030 | — | 3 | 3 | no | — |
| 27 | #73026 | — | 3 | 3 | no | — |
| 28 | #73025 | — | 3 | 3 | no | — |
| 29 | #71716 | — | 3 | 1 | no | — |
| 30 | #71002 | — | 3 | 1 | no | — |
| 31 | #71002 | — | 3 | 1 | no | — |
| 32 | #71000 | — | 3 | 1 | no | — |
| 33 | #71000 | — | 3 | 1 | no | — |
| 34 | #70998 | — | 3 | 1 | no | — |
| 35 | #70998 | — | 3 | 1 | no | — |
| 36 | #70996 | — | 3 | 1 | no | — |
| 37 | #70996 | — | 3 | 1 | no | — |
| 38 | #70060 | — | 3 | 1 | no | — |
| 39 | #70056 | — | 3 | 1 | no | — |
| 40 | C22×C3⋊S4 | — | 4 | 1 | no | — |
| 41 | C3×#997 | C23 | 1 | 1 | yes | characteristic |
| 42 | C2×C3×C4×A4 | — | 4 | 1 | no | — |
| 43 | C2×C3⋊SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 44 | #64266 | — | 8 | 1 | no | — |
| 45 | C4×C3⋊S4 | — | 4 | 1 | no | — |
| 46 | C4×C3⋊S4 | — | 4 | 1 | no | — |
| 47 | C4×C3⋊S4 | — | 4 | 1 | no | — |
| 48 | C4×C3⋊S4 | — | 4 | 1 | no | — |
| 49 | C4×C3⋊S4 | — | 8 | 1 | no | — |
| 50 | #33546 | — | 9 | 1 | no | Sylow |
| 51 | C3×#585 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 52 | #5950 | C2×D3 | 1 | 3 | yes | complemented |
| 53 | #5935 | — | 3 | 3 | no | — |
| 54 | #5934 | — | 3 | 3 | no | — |
| 55 | #5933 | — | 3 | 3 | no | — |
| 56 | #5932 | — | 3 | 3 | no | — |
| 57 | C2×C4×S4 | — | 12 | 3 | no | — |
| 58 | C3×#525 | — | 3 | 1 | no | — |
| 59 | #5832 | — | 3 | 1 | no | — |
| 60 | #5828 | — | 3 | 1 | no | — |
| 61 | #5828 | — | 6 | 1 | no | — |
| 62 | #5822 | — | 6 | 1 | no | — |
| 63 | C2×C4×#67 | — | 6 | 1 | no | — |
| 64 | #5664 | — | 3 | 1 | no | — |
| 65 | #5661 | — | 6 | 1 | no | — |
| 66 | #5659 | — | 3 | 1 | no | — |
| 67 | #5637 | — | 6 | 1 | no | — |
| 68 | #5636 | — | 6 | 1 | no | — |
| 69 | #5610 | — | 6 | 1 | no | — |
| 70 | #5601 | — | 6 | 1 | no | — |
| 71 | #5591 | — | 6 | 1 | no | — |
| 72 | #5590 | — | 3 | 1 | no | — |
| 73 | #5587 | — | 3 | 1 | no | — |
| 74 | #5547 | — | 6 | 1 | no | — |
| 75 | C4×D3×D4 | — | 6 | 1 | no | — |
| 76 | #5538 | — | 6 | 1 | no | — |
| 77 | C4×#237 | — | 6 | 1 | no | — |
| 78 | #5528 | — | 6 | 1 | no | — |
| 79 | C3×#458 | — | 3 | 1 | no | — |
| 80 | C3×#458 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 81 | C3×B(4,𝔽2) | — | 3 | 1 | no | — |
| 82 | C3×B(4,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 83 | C3×#410 | — | 3 | 1 | no | — |
| 84 | #5246 | — | 6 | 1 | no | — |
| 85 | #5245 | — | 6 | 1 | no | — |
| 86 | #5244 | — | 3 | 1 | no | — |
| 87 | #5244 | — | 3 | 1 | no | — |
| 88 | #5244 | — | 6 | 1 | no | — |
| 89 | #5243 | — | 3 | 1 | no | — |
| 90 | #5243 | — | 3 | 1 | no | — |
| 91 | #5243 | — | 6 | 1 | no | — |
| 92 | #5242 | — | 3 | 1 | no | — |
| 93 | #5242 | — | 3 | 1 | no | — |
| 94 | #5241 | — | 3 | 1 | no | — |
| 95 | #5241 | — | 3 | 1 | no | — |
| 96 | #5240 | — | 3 | 1 | no | — |
| 97 | #5240 | — | 6 | 1 | no | — |
| 98 | #5237 | — | 3 | 1 | no | — |
| 99 | C2×#837 | — | 6 | 1 | no | — |
| 100 | #458⋊C3 | C2×D3 | 1 | 3 | yes | complemented |
| 101 | B(4,𝔽2)⋊C3 | C2×D3 | 1 | 3 | yes | — |
| 102 | #4539 | — | 3 | 1 | no | — |
| 103 | #4539 | — | 3 | 1 | no | — |
| 104 | #4536 | — | 3 | 1 | no | — |
| 105 | #4536 | — | 3 | 1 | no | — |
| 106 | #4474 | — | 3 | 1 | no | — |
| 107 | #4474 | — | 3 | 1 | no | — |
| 108 | #4473 | — | 3 | 1 | no | — |
| 109 | #4473 | — | 3 | 1 | no | — |
| 110 | #4472 | — | 3 | 1 | no | — |
| 111 | #4472 | — | 3 | 1 | no | — |
| 112 | #4471 | — | 3 | 1 | no | — |
| 113 | #4471 | — | 3 | 1 | no | — |
| 114 | C22×C3×A4 | — | 4 | 1 | no | — |
| 115 | C2×C3⋊S4 | — | 4 | 1 | no | — |
| 116 | C2×C3⋊S4 | — | 4 | 1 | no | — |
| 117 | C2×C3⋊S4 | — | 4 | 4 | no | — |
| 118 | C2×C3⋊S4 | — | 8 | 1 | no | — |
| 119 | C2×C4×C3⋊D3 | — | 16 | 1 | no | — |
| 120 | C3×#41⋊C3 | — | 8 | 1 | no | — |
| 121 | C3×C4×A4 | — | 4 | 1 | no | — |
| 122 | C3×C4×A4 | — | 4 | 1 | no | — |
| 123 | C3×C4×A4 | — | 8 | 1 | no | — |
| 124 | C3⋊SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 125 | C3⋊SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 126 | C3⋊SL(2,ℤ/4) | — | 8 | 1 | no | — |
| 127 | C3⋊GL(2,𝔽3) | — | 8 | 1 | no | — |
| 128 | C3⋊#226 | — | 8 | 1 | no | — |
| 129 | #3481 | — | 9 | 1 | no | — |
| 130 | #3025 | — | 9 | 1 | no | — |
| 131 | #3025 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 132 | #3018 | — | 9 | 1 | no | — |
| 133 | #2198 | — | 9 | 1 | no | — |
| 134 | #2198 | — | 9 | 1 | no | — |
| 135 | #2197 | — | 9 | 1 | no | — |
| 136 | #2197 | — | 9 | 1 | no | — |
| 137 | #2197 | — | 9 | 1 | no | — |
| 138 | #2197 | — | 9 | 1 | no | — |
| 139 | #2196 | — | 9 | 1 | no | — |
| 140 | #2196 | — | 9 | 1 | no | — |
| 141 | #2126 | — | 9 | 1 | no | — |
| 142 | #2120 | — | 9 | 1 | no | — |
| 143 | #2120 | — | 9 | 1 | no | — |
| 144 | C22×S4 | — | 12 | 3 | no | — |
| 145 | C3×2−1+4 | — | 6 | 1 | no | — |
| 146 | C3×H(5,𝔽2) | — | 3 | 1 | no | — |
| 147 | C3×H(5,𝔽2) | — | 6 | 1 | no | — |
| 148 | C3×H(5,𝔽2) | C22×D3 | 1 | 1 | yes | characteristic |
| 149 | C2×C3×#41 | — | 3 | 1 | no | — |
| 150 | C2×C3×#41 | — | 6 | 1 | no | — |
| 151 | C2×C3×#41 | — | 6 | 1 | no | — |
| 152 | C23×C3×C4 | S4 | 1 | 1 | yes | characteristic, complemented |
| 153 | C22×#67 | — | 6 | 1 | no | — |
| 154 | C2×#237 | — | 6 | 1 | no | — |
| 155 | C2×D3×D4 | — | 6 | 1 | no | — |
| 156 | C2×#235 | — | 3 | 1 | no | — |
| 157 | C22×C4×D3 | — | 3 | 1 | no | — |
| 158 | C22×C4×D3 | — | 6 | 1 | no | — |
| 159 | #997 | C22×D3 | 1 | 3 | yes | — |
| 160 | C2×C4×A4 | — | 4 | 3 | no | — |
| 161 | C2×SL(2,ℤ/4) | — | 12 | 3 | no | — |
| 162 | #985 | — | 24 | 3 | no | — |
| 163 | C4×S4 | — | 12 | 3 | no | — |
| 164 | C4×S4 | — | 12 | 3 | no | — |
| 165 | C4×S4 | — | 12 | 3 | no | — |
| 166 | C4×S4 | — | 12 | 3 | no | — |
| 167 | C4×S4 | — | 24 | 3 | no | — |
| 168 | C3×#123 | — | 3 | 1 | no | — |
| 169 | C3×#123 | — | 3 | 1 | no | — |
| 170 | C3×C22⋊Q8 | — | 6 | 1 | no | — |
| 171 | C3×#121 | — | 6 | 1 | no | — |
| 172 | C3×#120 | — | 3 | 1 | no | — |
| 173 | C3×#120 | — | 3 | 1 | no | — |
| 174 | C3×C4×D4 | — | 6 | 1 | no | — |
| 175 | C3×C4×D4 | — | 6 | 1 | no | — |
| 176 | C3×#117 | — | 3 | 1 | no | — |
| 177 | C2×#217 | — | 6 | 1 | no | — |
| 178 | #951 | — | 6 | 1 | no | — |
| 179 | #951 | — | 6 | 1 | no | — |
| 180 | #950 | — | 12 | 1 | no | — |
| 181 | #950 | — | 12 | 1 | no | — |
| 182 | #949 | — | 6 | 1 | no | — |
| 183 | #949 | — | 6 | 1 | no | — |
| 184 | #947 | — | 3 | 1 | no | — |
| 185 | #946 | — | 6 | 1 | no | — |
| 186 | #946 | — | 12 | 1 | no | — |
| 187 | #944 | — | 3 | 1 | no | — |
| 188 | #942 | — | 12 | 1 | no | — |
| 189 | #940 | — | 3 | 1 | no | — |
| 190 | #939 | — | 6 | 1 | no | — |
| 191 | #939 | — | 6 | 1 | no | — |
| 192 | #939 | — | 6 | 1 | no | — |
| 193 | #939 | — | 6 | 1 | no | — |
| 194 | #938 | — | 6 | 1 | no | — |
| 195 | #938 | — | 12 | 1 | no | — |
| 196 | #937 | — | 3 | 1 | no | — |
| 197 | #937 | — | 3 | 1 | no | — |
| 198 | #937 | — | 6 | 1 | no | — |
| 199 | #937 | — | 6 | 1 | no | — |
| 200 | #937 | — | 6 | 1 | no | — |
| 201 | #936 | — | 3 | 1 | no | — |
| 202 | #935 | — | 3 | 1 | no | — |
| 203 | #935 | — | 3 | 1 | no | — |
| 204 | #935 | — | 6 | 1 | no | — |
| 205 | #935 | — | 6 | 1 | no | — |
| 206 | #935 | — | 6 | 1 | no | — |
| 207 | D4×Dic3 | — | 6 | 1 | no | — |
| 208 | D4×Dic3 | — | 6 | 1 | no | — |
| 209 | #932 | — | 12 | 1 | no | — |
| 210 | C4×#67 | — | 6 | 1 | no | — |
| 211 | C4×#67 | — | 6 | 1 | no | — |
| 212 | C4×#67 | — | 6 | 1 | no | — |
| 213 | C4×#67 | — | 6 | 1 | no | — |
| 214 | C4×#67 | — | 6 | 1 | no | — |
| 215 | C4×#67 | — | 6 | 1 | no | — |
| 216 | C4×#67 | — | 6 | 1 | no | — |
| 217 | C4×#67 | — | 6 | 1 | no | — |
| 218 | C4×#67 | — | 6 | 1 | no | — |
| 219 | C4×#67 | — | 6 | 1 | no | — |
| 220 | C4×#67 | — | 12 | 1 | no | — |
| 221 | C4×#67 | — | 12 | 1 | no | — |
| 222 | C2×(C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 223 | #926 | — | 3 | 1 | no | — |
| 224 | #926 | — | 6 | 1 | no | — |
| 225 | C2×Dic3⋊C4 | — | 6 | 1 | no | — |
| 226 | C2×C4×Dic3 | — | 3 | 1 | no | — |
| 227 | C2×C4×Dic3 | — | 6 | 1 | no | — |
| 228 | C2×#208 | — | 6 | 1 | no | — |
| 229 | #898 | — | 6 | 1 | no | — |
| 230 | #898 | — | 6 | 1 | no | — |
| 231 | #896 | — | 6 | 1 | no | — |
| 232 | #896 | — | 6 | 1 | no | — |
| 233 | #894 | — | 6 | 1 | no | — |
| 234 | #894 | — | 6 | 1 | no | — |
| 235 | #893 | — | 6 | 1 | no | — |
| 236 | #892 | — | 6 | 1 | no | — |
| 237 | D3×C4⋊C4 | — | 6 | 1 | no | — |
| 238 | #889 | — | 6 | 1 | no | — |
| 239 | #889 | — | 6 | 1 | no | — |
| 240 | #887 | — | 6 | 1 | no | — |
| 241 | #886 | — | 6 | 1 | no | — |
| 242 | #885 | — | 6 | 1 | no | — |
| 243 | #885 | — | 6 | 1 | no | — |
| 244 | #884 | — | 6 | 1 | no | — |
| 245 | #884 | — | 6 | 1 | no | — |
| 246 | #883 | — | 6 | 1 | no | — |
| 247 | #883 | — | 6 | 1 | no | — |
| 248 | #882 | — | 6 | 1 | no | — |
| 249 | #67⋊C4 | — | 6 | 1 | no | — |
| 250 | #67⋊C4 | — | 6 | 1 | no | — |
| 251 | #67⋊C4 | — | 6 | 1 | no | — |
| 252 | #67⋊C4 | — | 6 | 1 | no | — |
| 253 | D3×C22⋊C4 | — | 6 | 1 | no | — |
| 254 | D3×C22⋊C4 | — | 6 | 1 | no | — |
| 255 | #879 | — | 6 | 1 | no | — |
| 256 | #879 | — | 6 | 1 | no | — |
| 257 | #878 | — | 6 | 1 | no | — |
| 258 | #878 | — | 6 | 1 | no | — |
| 259 | #877 | — | 6 | 1 | no | — |
| 260 | #877 | — | 6 | 1 | no | — |
| 261 | C4×D12 | — | 6 | 1 | no | — |
| 262 | #872 | — | 6 | 1 | no | — |
| 263 | C42×D3 | — | 6 | 1 | no | — |
| 264 | C4×Dic6 | — | 6 | 1 | no | — |
| 265 | C3×#99 | — | 3 | 1 | no | — |
| 266 | C3×#99 | — | 3 | 1 | no | — |
| 267 | C3×#99 | — | 6 | 1 | no | — |
| 268 | #837 | — | 6 | 1 | no | — |
| 269 | #837 | — | 6 | 1 | no | — |
| 270 | #837 | — | 6 | 1 | no | — |
| 271 | #837 | — | 6 | 1 | no | — |
| 272 | #836 | — | 6 | 1 | no | — |
| 273 | #834 | — | 3 | 1 | no | — |
| 274 | #834 | — | 3 | 1 | no | — |
| 275 | #834 | — | 6 | 1 | no | — |
| 276 | #834 | — | 6 | 1 | no | — |
| 277 | #834 | — | 6 | 1 | no | — |
| 278 | #834 | — | 6 | 1 | no | — |
| 279 | #834 | — | 6 | 1 | no | — |
| 280 | #833 | — | 3 | 1 | no | — |
| 281 | #833 | — | 3 | 1 | no | — |
| 282 | C22×C3⋊D3 | — | 16 | 1 | no | — |
| 283 | C2×C3×A4 | — | 4 | 2 | no | — |
| 284 | C2×C3×A4 | — | 4 | 1 | no | — |
| 285 | C2×C3×A4 | — | 8 | 1 | no | — |
| 286 | C3⋊S4 | — | 4 | 2 | no | — |
| 287 | C3⋊S4 | — | 4 | 2 | no | — |
| 288 | C3⋊S4 | — | 8 | 2 | no | — |
| 289 | C2×C32×C4 | — | 16 | 1 | no | — |
| 290 | C2×C3⋊Dic3 | — | 16 | 1 | no | — |
| 291 | C4×C3⋊D3 | — | 16 | 1 | no | — |
| 292 | C4×C3⋊D3 | — | 16 | 1 | no | — |
| 293 | C4×C3⋊D3 | — | 16 | 1 | no | — |
| 294 | C4×C3⋊D3 | — | 16 | 1 | no | — |
| 295 | C3×SL(2,𝔽3) | — | 8 | 1 | no | — |
| 296 | #585 | C2×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 297 | #575 | — | 18 | 1 | no | — |
| 298 | #559 | — | 9 | 1 | no | — |
| 299 | #554 | — | 18 | 1 | no | — |
| 300 | #553 | — | 18 | 1 | no | — |
| 301 | #553 | — | 18 | 1 | no | — |
| 302 | #551 | — | 9 | 1 | no | — |
| 303 | #551 | — | 9 | 1 | no | — |
| 304 | #551 | — | 18 | 1 | no | — |
| 305 | #546 | — | 18 | 1 | no | — |
| 306 | #546 | — | 18 | 1 | no | — |
| 307 | D42 | — | 9 | 1 | no | — |
| 308 | #532 | — | 9 | 1 | no | — |
| 309 | #529 | — | 18 | 1 | no | — |
| 310 | #529 | — | 18 | 1 | no | — |
| 311 | #525 | — | 3 | 1 | no | — |
| 312 | #525 | — | 9 | 1 | no | — |
| 313 | #525 | — | 18 | 1 | no | — |
| 314 | #525 | — | 18 | 1 | no | — |
| 315 | C4×#41 | — | 18 | 1 | no | — |
| 316 | C2×C4×D4 | — | 18 | 1 | no | — |
| 317 | C2×C4×D4 | — | 18 | 1 | no | — |
| 318 | #458 | — | 3 | 1 | no | — |
| 319 | #458 | — | 9 | 1 | no | — |
| 320 | #458 | — | 9 | 1 | no | — |
| 321 | #458 | — | 18 | 1 | no | — |
| 322 | #458 | C2×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 323 | B(4,𝔽2) | — | 3 | 1 | no | — |
| 324 | B(4,𝔽2) | — | 9 | 1 | no | — |
| 325 | B(4,𝔽2) | — | 9 | 1 | no | — |
| 326 | B(4,𝔽2) | — | 18 | 1 | no | — |
| 327 | B(4,𝔽2) | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 328 | #456 | — | 18 | 1 | no | — |
| 329 | #455 | — | 9 | 1 | no | — |
| 330 | #455 | — | 9 | 1 | no | — |
| 331 | #454 | — | 18 | 1 | no | — |
| 332 | #453 | — | 9 | 1 | no | — |
| 333 | #453 | — | 9 | 1 | no | — |
| 334 | C2×#104 | — | 18 | 1 | no | — |
| 335 | #413 | — | 9 | 1 | no | — |
| 336 | #410 | — | 3 | 1 | no | — |
| 337 | #410 | — | 9 | 1 | no | — |
| 338 | #410 | — | 18 | 1 | no | — |
| 339 | #354 | — | 9 | 1 | no | — |
| 340 | #354 | — | 9 | 1 | no | — |
| 341 | #353 | — | 9 | 1 | no | — |
| 342 | #353 | — | 9 | 1 | no | — |
| 343 | #352 | — | 9 | 1 | no | — |
| 344 | #352 | — | 9 | 1 | no | — |
| 345 | #352 | — | 9 | 1 | no | — |
| 346 | #352 | — | 9 | 1 | no | — |
| 347 | AΣL(1,𝔽16) | — | 9 | 1 | no | — |
| 348 | AΣL(1,𝔽16) | — | 9 | 1 | no | — |
| 349 | AΣL(1,𝔽16) | — | 9 | 1 | no | — |
| 350 | AΣL(1,𝔽16) | — | 9 | 1 | no | — |
| 351 | C24×C3 | C2×S4 | 1 | 1 | yes | characteristic |
| 352 | C23×D3 | — | 3 | 1 | no | — |
| 353 | C23×D3 | — | 6 | 1 | no | — |
| 354 | C22×A4 | — | 4 | 3 | no | — |
| 355 | C2×S4 | — | 12 | 3 | no | — |
| 356 | C2×S4 | — | 12 | 3 | no | — |
| 357 | C2×S4 | — | 12 | 12 | no | — |
| 358 | C2×S4 | — | 24 | 3 | no | — |
| 359 | C3×#41 | — | 2 | 1 | no | — |
| 360 | C3×#41 | — | 6 | 1 | no | — |
| 361 | C3×#41 | — | 6 | 1 | no | — |
| 362 | C3×#41 | — | 6 | 1 | no | — |
| 363 | C3×#41 | — | 12 | 1 | no | — |
| 364 | C3×#41 | — | 12 | 1 | no | — |
| 365 | C3×#41 | — | 12 | 1 | no | — |
| 366 | C3×#41 | — | 12 | 1 | no | — |
| 367 | C3×#41 | — | 12 | 1 | no | — |
| 368 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 369 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 370 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 371 | C2×C3×D4 | — | 3 | 1 | no | — |
| 372 | C2×C3×D4 | — | 3 | 1 | no | — |
| 373 | C2×C3×D4 | — | 3 | 1 | no | — |
| 374 | C2×C3×D4 | — | 6 | 1 | no | — |
| 375 | C2×C3×D4 | — | 6 | 1 | no | — |
| 376 | C2×C3×D4 | — | 6 | 1 | no | — |
| 377 | C2×C3×D4 | — | 6 | 1 | no | — |
| 378 | C2×C3×D4 | — | 6 | 1 | no | — |
| 379 | C2×C3×D4 | — | 6 | 1 | no | — |
| 380 | C2×C3×D4 | — | 12 | 1 | no | — |
| 381 | C22×C3×C4 | — | 2 | 1 | no | — |
| 382 | C22×C3×C4 | — | 3 | 1 | no | — |
| 383 | C22×C3×C4 | — | 3 | 1 | no | — |
| 384 | C22×C3×C4 | — | 6 | 1 | no | — |
| 385 | C22×C3×C4 | — | 6 | 1 | no | — |
| 386 | C22×C3×C4 | — | 6 | 1 | no | — |
| 387 | C22×C3×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 388 | C22×C3×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 389 | C2×#67 | — | 6 | 1 | no | — |
| 390 | C2×#67 | — | 6 | 1 | no | — |
| 391 | C2×#67 | — | 6 | 1 | no | — |
| 392 | C2×#67 | — | 6 | 1 | no | — |
| 393 | C2×#67 | — | 6 | 1 | no | — |
| 394 | C2×#67 | — | 6 | 1 | no | — |
| 395 | C2×#67 | — | 6 | 1 | no | — |
| 396 | C2×#67 | — | 12 | 4 | no | — |
| 397 | C2×#67 | — | 12 | 1 | no | — |
| 398 | C2×#67 | — | 12 | 1 | no | — |
| 399 | C22×Dic3 | — | 3 | 1 | no | — |
| 400 | C22×Dic3 | — | 6 | 1 | no | — |
| 401 | C22×Dic3 | — | 6 | 1 | no | — |
| 402 | C22×Dic3 | — | 6 | 1 | no | — |
| 403 | C22×Dic3 | — | 6 | 1 | no | — |
| 404 | #237 | — | 12 | 4 | no | — |
| 405 | D3×D4 | — | 12 | 4 | no | — |
| 406 | #235 | — | 12 | 1 | no | — |
| 407 | #235 | — | 12 | 1 | no | — |
| 408 | C2×D12 | — | 3 | 1 | no | — |
| 409 | C2×D12 | — | 6 | 1 | no | — |
| 410 | C2×C4×D3 | — | 6 | 1 | no | — |
| 411 | C2×C4×D3 | — | 6 | 1 | no | — |
| 412 | C2×C4×D3 | — | 6 | 1 | no | — |
| 413 | C2×C4×D3 | — | 6 | 1 | no | — |
| 414 | C2×C4×D3 | — | 6 | 1 | no | — |
| 415 | C2×C4×D3 | — | 6 | 1 | no | — |
| 416 | C2×C4×D3 | — | 6 | 1 | no | — |
| 417 | C2×C4×D3 | — | 12 | 1 | no | — |
| 418 | C2×C4×D3 | — | 12 | 1 | no | — |
| 419 | C2×C4×D3 | — | 24 | 1 | no | — |
| 420 | C2×C4×D3 | — | 24 | 1 | no | — |
| 421 | C2×C4×D3 | — | 48 | 3 | no | — |
| 422 | C2×Dic6 | — | 3 | 1 | no | — |
| 423 | C2×Dic6 | — | 6 | 1 | no | — |
| 424 | #41⋊C3 | — | 8 | 3 | no | — |
| 425 | C4×A4 | — | 4 | 3 | no | — |
| 426 | C4×A4 | — | 4 | 3 | no | — |
| 427 | C4×A4 | — | 8 | 3 | no | — |
| 428 | SL(2,ℤ/4) | — | 12 | 3 | no | — |
| 429 | SL(2,ℤ/4) | — | 12 | 3 | no | — |
| 430 | SL(2,ℤ/4) | — | 24 | 3 | no | — |
| 431 | GL(2,𝔽3) | — | 24 | 3 | no | — |
| 432 | #226 | — | 24 | 3 | no | — |
| 433 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 434 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 435 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 436 | C3×C22⋊C4 | — | 3 | 1 | no | — |
| 437 | C3×C22⋊C4 | — | 3 | 1 | no | — |
| 438 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 439 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 440 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 441 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 442 | C3×C42 | — | 6 | 1 | no | — |
| 443 | #217 | — | 3 | 1 | no | — |
| 444 | #217 | — | 3 | 1 | no | — |
| 445 | #217 | — | 6 | 1 | no | — |
| 446 | #217 | — | 6 | 1 | no | — |
| 447 | #217 | — | 6 | 1 | no | — |
| 448 | #217 | — | 6 | 1 | no | — |
| 449 | #217 | — | 6 | 1 | no | — |
| 450 | #217 | — | 6 | 1 | no | — |
| 451 | #217 | — | 6 | 1 | no | — |
| 452 | #217 | — | 6 | 1 | no | — |
| 453 | #217 | — | 12 | 1 | no | — |
| 454 | #217 | — | 12 | 1 | no | — |
| 455 | #216 | — | 12 | 1 | no | — |
| 456 | #216 | — | 12 | 1 | no | — |
| 457 | #215 | — | 12 | 1 | no | — |
| 458 | #215 | — | 12 | 1 | no | — |
| 459 | #214 | — | 12 | 1 | no | — |
| 460 | #214 | — | 12 | 1 | no | — |
| 461 | #213 | — | 12 | 1 | no | — |
| 462 | #213 | — | 12 | 1 | no | — |
| 463 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 464 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 465 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 466 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 467 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 468 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 469 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 470 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 471 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 472 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 473 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 474 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 475 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 476 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 477 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 478 | C4⋊Dic3 | — | 12 | 1 | no | — |
| 479 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 480 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 481 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 482 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 483 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 484 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 485 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 486 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 487 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 488 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 489 | Dic3⋊C4 | — | 12 | 1 | no | — |
| 490 | Dic3⋊C4 | — | 12 | 1 | no | — |
| 491 | C4×Dic3 | — | 3 | 1 | no | — |
| 492 | C4×Dic3 | — | 3 | 1 | no | — |
| 493 | C4×Dic3 | — | 6 | 1 | no | — |
| 494 | C4×Dic3 | — | 6 | 1 | no | — |
| 495 | C4×Dic3 | — | 6 | 1 | no | — |
| 496 | C4×Dic3 | — | 6 | 1 | no | — |
| 497 | C4×Dic3 | — | 6 | 1 | no | — |
| 498 | C4×Dic3 | — | 6 | 1 | no | — |
| 499 | C4×Dic3 | — | 12 | 1 | no | — |
| 500 | #208 | — | 6 | 1 | no | — |
| 501 | #208 | — | 6 | 1 | no | — |
| 502 | #208 | — | 12 | 1 | no | — |
| 503 | C2×C3⋊C8 | — | 12 | 1 | no | — |
| 504 | C22×C32 | — | 16 | 1 | no | — |
| 505 | C2×C3⋊D3 | — | 16 | 1 | no | — |
| 506 | C2×C3⋊D3 | — | 16 | 1 | no | — |
| 507 | C2×C3⋊D3 | — | 16 | 4 | no | — |
| 508 | C3×A4 | — | 4 | 1 | no | — |
| 509 | C3×A4 | — | 8 | 1 | no | — |
| 510 | C32×C4 | — | 16 | 1 | no | — |
| 511 | C32×C4 | — | 16 | 1 | no | — |
| 512 | C3⋊Dic3 | — | 16 | 1 | no | — |
| 513 | C3⋊Dic3 | — | 16 | 1 | no | — |
| 514 | 2−1+4 | — | 6 | 1 | no | — |
| 515 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 516 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 517 | H(5,𝔽2) | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 518 | C2×#41 | — | 3 | 1 | no | — |
| 519 | C2×#41 | — | 6 | 1 | no | — |
| 520 | C2×#41 | — | 6 | 1 | no | — |
| 521 | C2×#41 | — | 9 | 1 | no | — |
| 522 | C2×#41 | — | 18 | 1 | no | — |
| 523 | C22×D4 | — | 18 | 1 | no | — |
| 524 | C22×D4 | — | 18 | 1 | no | — |
| 525 | C23×C4 | — | 9 | 1 | no | — |
| 526 | C23×C4 | — | 18 | 1 | no | — |
| 527 | C23×C4 | C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 528 | #137 | — | 18 | 1 | no | — |
| 529 | #137 | — | 18 | 1 | no | — |
| 530 | #137 | — | 36 | 1 | no | — |
| 531 | AGL(1,ℤ/8) | — | 18 | 1 | no | — |
| 532 | AGL(1,ℤ/8) | — | 18 | 1 | no | — |
| 533 | AGL(1,ℤ/8) | — | 36 | 1 | no | — |
| 534 | #135 | — | 36 | 1 | no | — |
| 535 | #135 | — | 36 | 1 | no | — |
| 536 | C2×M16 | — | 18 | 1 | no | — |
| 537 | C4⋊Q8 | — | 9 | 1 | no | — |
| 538 | #127 | — | 9 | 1 | no | — |
| 539 | #126 | — | 18 | 1 | no | — |
| 540 | #126 | — | 18 | 1 | no | — |
| 541 | #126 | — | 18 | 1 | no | — |
| 542 | #126 | — | 18 | 1 | no | — |
| 543 | #125 | — | 18 | 1 | no | — |
| 544 | #125 | — | 18 | 1 | no | — |
| 545 | #124 | — | 9 | 1 | no | — |
| 546 | #124 | — | 9 | 1 | no | — |
| 547 | #124 | — | 18 | 1 | no | — |
| 548 | #124 | — | 18 | 1 | no | — |
| 549 | #123 | — | 3 | 1 | no | — |
| 550 | #123 | — | 3 | 1 | no | — |
| 551 | #123 | — | 9 | 1 | no | — |
| 552 | #123 | — | 9 | 1 | no | — |
| 553 | #123 | — | 18 | 1 | no | — |
| 554 | #123 | — | 18 | 1 | no | — |
| 555 | #123 | — | 18 | 1 | no | — |
| 556 | #123 | — | 18 | 1 | no | — |
| 557 | #123 | — | 18 | 1 | no | — |
| 558 | #123 | — | 18 | 1 | no | — |
| 559 | #123 | — | 18 | 1 | no | — |
| 560 | #123 | — | 18 | 1 | no | — |
| 561 | C22⋊Q8 | — | 6 | 1 | no | — |
| 562 | C22⋊Q8 | — | 18 | 1 | no | — |
| 563 | C22⋊Q8 | — | 18 | 1 | no | — |
| 564 | C22⋊Q8 | — | 18 | 1 | no | — |
| 565 | C22⋊Q8 | — | 18 | 1 | no | — |
| 566 | C22⋊Q8 | — | 18 | 1 | no | — |
| 567 | C22⋊Q8 | — | 36 | 1 | no | — |
| 568 | #121 | — | 6 | 1 | no | — |
| 569 | #121 | — | 18 | 1 | no | — |
| 570 | #121 | — | 18 | 1 | no | — |
| 571 | #121 | — | 18 | 1 | no | — |
| 572 | #121 | — | 18 | 1 | no | — |
| 573 | #121 | — | 18 | 1 | no | — |
| 574 | #121 | — | 18 | 1 | no | — |
| 575 | #121 | — | 18 | 1 | no | — |
| 576 | #121 | — | 36 | 1 | no | — |
| 577 | #120 | — | 3 | 1 | no | — |
| 578 | #120 | — | 3 | 1 | no | — |
| 579 | #120 | — | 9 | 1 | no | — |
| 580 | #120 | — | 9 | 1 | no | — |
| 581 | #120 | — | 18 | 1 | no | — |
| 582 | #120 | — | 18 | 1 | no | — |
| 583 | #120 | — | 18 | 1 | no | — |
| 584 | #120 | — | 18 | 1 | no | — |
| 585 | C4×Q8 | — | 18 | 1 | no | — |
| 586 | C4×Q8 | — | 18 | 1 | no | — |
| 587 | C4×D4 | — | 6 | 1 | no | — |
| 588 | C4×D4 | — | 6 | 1 | no | — |
| 589 | C4×D4 | — | 18 | 1 | no | — |
| 590 | C4×D4 | — | 18 | 1 | no | — |
| 591 | C4×D4 | — | 18 | 1 | no | — |
| 592 | C4×D4 | — | 18 | 1 | no | — |
| 593 | C4×D4 | — | 18 | 1 | no | — |
| 594 | C4×D4 | — | 18 | 1 | no | — |
| 595 | C4×D4 | — | 18 | 1 | no | — |
| 596 | C4×D4 | — | 18 | 1 | no | — |
| 597 | C4×D4 | — | 18 | 1 | no | — |
| 598 | C4×D4 | — | 18 | 1 | no | — |
| 599 | C4×D4 | — | 18 | 1 | no | — |
| 600 | C4×D4 | — | 18 | 1 | no | — |
| 601 | C4×D4 | — | 18 | 1 | no | — |
| 602 | C4×D4 | — | 18 | 1 | no | — |
| 603 | C4×D4 | — | 18 | 1 | no | — |
| 604 | C4×D4 | — | 18 | 1 | no | — |
| 605 | C4×D4 | — | 18 | 1 | no | — |
| 606 | C4×D4 | — | 18 | 1 | no | — |
| 607 | C4×D4 | — | 36 | 1 | no | — |
| 608 | C4×D4 | — | 36 | 1 | no | — |
| 609 | #117 | — | 3 | 1 | no | — |
| 610 | #117 | — | 9 | 1 | no | — |
| 611 | #117 | — | 18 | 1 | no | — |
| 612 | #117 | — | 18 | 1 | no | — |
| 613 | #117 | — | 18 | 1 | no | — |
| 614 | #117 | — | 18 | 1 | no | — |
| 615 | #117 | — | 18 | 1 | no | — |
| 616 | C2×C4⋊C4 | — | 18 | 1 | no | — |
| 617 | C2×C4⋊C4 | — | 18 | 1 | no | — |
| 618 | C2×C22⋊C4 | — | 18 | 1 | no | — |
| 619 | C2×C22⋊C4 | — | 18 | 1 | no | — |
| 620 | C2×C22⋊C4 | — | 18 | 1 | no | — |
| 621 | C2×C22⋊C4 | — | 18 | 1 | no | — |
| 622 | C2×C42 | — | 9 | 1 | no | — |
| 623 | C2×C42 | — | 18 | 1 | no | — |
| 624 | C2×C42 | — | 18 | 1 | no | — |
| 625 | #104 | — | 18 | 1 | no | — |
| 626 | #104 | — | 18 | 1 | no | — |
| 627 | #104 | — | 18 | 1 | no | — |
| 628 | #104 | — | 18 | 1 | no | — |
| 629 | #101 | — | 18 | 1 | no | — |
| 630 | #100 | — | 9 | 1 | no | — |
| 631 | #100 | — | 9 | 1 | no | — |
| 632 | #99 | — | 3 | 1 | no | — |
| 633 | #99 | — | 3 | 1 | no | — |
| 634 | #99 | — | 6 | 1 | no | — |
| 635 | #99 | — | 9 | 1 | no | — |
| 636 | #99 | — | 9 | 1 | no | — |
| 637 | #99 | — | 18 | 1 | no | — |
| 638 | #99 | — | 18 | 1 | no | — |
| 639 | #99 | — | 18 | 1 | no | — |
| 640 | #99 | — | 18 | 1 | no | — |
| 641 | #99 | — | 18 | 1 | no | — |
| 642 | C23×C3 | — | 2 | 1 | no | — |
| 643 | C23×C3 | — | 3 | 1 | no | — |
| 644 | C23×C3 | — | 3 | 1 | no | — |
| 645 | C23×C3 | — | 4 | 2 | no | — |
| 646 | C23×C3 | — | 6 | 1 | no | — |
| 647 | C23×C3 | — | 6 | 1 | no | — |
| 648 | C23×C3 | C22×S4 | 1 | 1 | yes | characteristic |
| 649 | C22×D3 | — | 6 | 1 | no | — |
| 650 | C22×D3 | — | 6 | 1 | no | — |
| 651 | C22×D3 | — | 12 | 2 | no | — |
| 652 | C22×D3 | — | 12 | 2 | no | — |
| 653 | C22×D3 | — | 12 | 1 | no | — |
| 654 | C22×D3 | — | 12 | 2 | no | — |
| 655 | C22×D3 | — | 24 | 1 | no | — |
| 656 | C22×D3 | — | 48 | 3 | no | — |
| 657 | C2×A4 | — | 4 | 6 | no | — |
| 658 | C2×A4 | — | 4 | 3 | no | — |
| 659 | C2×A4 | — | 8 | 3 | no | — |
| 660 | S4 | — | 12 | 6 | no | — |
| 661 | S4 | — | 12 | 6 | no | — |
| 662 | S4 | — | 24 | 6 | no | — |
| 663 | C3×Q8 | — | 2 | 1 | no | — |
| 664 | C3×Q8 | — | 6 | 1 | no | — |
| 665 | C3×Q8 | — | 12 | 1 | no | — |
| 666 | C3×D4 | — | 6 | 1 | no | — |
| 667 | C3×D4 | — | 6 | 1 | no | — |
| 668 | C3×D4 | — | 12 | 1 | no | — |
| 669 | C3×D4 | — | 12 | 1 | no | — |
| 670 | C3×D4 | — | 12 | 1 | no | — |
| 671 | C3×D4 | — | 12 | 1 | no | — |
| 672 | C3×D4 | — | 12 | 2 | no | — |
| 673 | C3×D4 | — | 12 | 2 | no | — |
| 674 | C2×C3×C4 | — | 3 | 1 | no | — |
| 675 | C2×C3×C4 | — | 3 | 1 | no | — |
| 676 | C2×C3×C4 | — | 3 | 1 | no | — |
| 677 | C2×C3×C4 | — | 3 | 1 | no | — |
| 678 | C2×C3×C4 | — | 4 | 1 | no | — |
| 679 | C2×C3×C4 | — | 6 | 1 | no | — |
| 680 | C2×C3×C4 | — | 6 | 1 | no | — |
| 681 | C2×C3×C4 | — | 6 | 1 | no | — |
| 682 | C2×C3×C4 | — | 6 | 1 | no | — |
| 683 | C2×C3×C4 | — | 6 | 1 | no | — |
| 684 | C2×C3×C4 | — | 6 | 1 | no | — |
| 685 | C2×C3×C4 | — | 6 | 1 | no | — |
| 686 | C2×C3×C4 | — | 6 | 1 | no | — |
| 687 | C2×C3×C4 | — | 6 | 1 | no | — |
| 688 | C2×C3×C4 | — | 12 | 1 | no | — |
| 689 | C2×C3×C4 | — | 12 | 1 | no | — |
| 690 | C2×C3×C4 | — | 16 | 3 | no | — |
| 691 | #67 | — | 6 | 4 | no | — |
| 692 | #67 | — | 12 | 2 | no | — |
| 693 | #67 | — | 12 | 2 | no | — |
| 694 | #67 | — | 12 | 2 | no | — |
| 695 | #67 | — | 12 | 2 | no | — |
| 696 | #67 | — | 12 | 2 | no | — |
| 697 | #67 | — | 24 | 1 | no | — |
| 698 | #67 | — | 24 | 2 | no | — |
| 699 | #67 | — | 24 | 2 | no | — |
| 700 | C2×Dic3 | — | 6 | 1 | no | — |
| 701 | C2×Dic3 | — | 6 | 1 | no | — |
| 702 | C2×Dic3 | — | 6 | 1 | no | — |
| 703 | C2×Dic3 | — | 6 | 1 | no | — |
| 704 | C2×Dic3 | — | 6 | 1 | no | — |
| 705 | C2×Dic3 | — | 6 | 1 | no | — |
| 706 | C2×Dic3 | — | 12 | 2 | no | — |
| 707 | C2×Dic3 | — | 12 | 2 | no | — |
| 708 | C2×Dic3 | — | 12 | 2 | no | — |
| 709 | C2×Dic3 | — | 12 | 1 | no | — |
| 710 | C2×Dic3 | — | 12 | 1 | no | — |
| 711 | C2×Dic3 | — | 12 | 1 | no | — |
| 712 | C2×Dic3 | — | 24 | 1 | no | — |
| 713 | C2×Dic3 | — | 48 | 3 | no | — |
| 714 | D12 | — | 12 | 1 | no | — |
| 715 | D12 | — | 12 | 2 | no | — |
| 716 | C4×D3 | — | 12 | 2 | no | — |
| 717 | C4×D3 | — | 12 | 1 | no | — |
| 718 | C4×D3 | — | 12 | 1 | no | — |
| 719 | C4×D3 | — | 12 | 2 | no | — |
| 720 | C4×D3 | — | 12 | 1 | no | — |
| 721 | C4×D3 | — | 12 | 1 | no | — |
| 722 | C4×D3 | — | 24 | 1 | no | — |
| 723 | C4×D3 | — | 24 | 1 | no | — |
| 724 | C4×D3 | — | 24 | 1 | no | — |
| 725 | C4×D3 | — | 48 | 3 | no | — |
| 726 | C4×D3 | — | 48 | 3 | no | — |
| 727 | C4×D3 | — | 48 | 3 | no | — |
| 728 | C4×D3 | — | 48 | 3 | no | — |
| 729 | Dic6 | — | 12 | 2 | no | — |
| 730 | Dic6 | — | 12 | 1 | no | — |
| 731 | SL(2,𝔽3) | — | 8 | 3 | no | — |
| 732 | C3⋊C8 | — | 12 | 1 | no | — |
| 733 | C3⋊C8 | — | 12 | 1 | no | — |
| 734 | C2×C32 | — | 16 | 2 | no | — |
| 735 | C2×C32 | — | 16 | 1 | no | — |
| 736 | C3⋊D3 | — | 16 | 2 | no | — |
| 737 | C3⋊D3 | — | 16 | 2 | no | — |
| 738 | C24 | — | 9 | 1 | no | — |
| 739 | C24 | — | 18 | 1 | no | — |
| 740 | C24 | C2×C3⋊S4 | 1 | 1 | yes | characteristic |
| 741 | #41 | — | 2 | 1 | no | — |
| 742 | #41 | — | 6 | 1 | no | — |
| 743 | #41 | — | 6 | 1 | no | — |
| 744 | #41 | — | 6 | 1 | no | — |
| 745 | #41 | — | 12 | 1 | no | — |
| 746 | #41 | — | 12 | 1 | no | — |
| 747 | #41 | — | 12 | 1 | no | — |
| 748 | #41 | — | 12 | 1 | no | — |
| 749 | #41 | — | 12 | 1 | no | — |
| 750 | #41 | — | 36 | 1 | no | — |
| 751 | #41 | — | 36 | 1 | no | — |
| 752 | #41 | — | 36 | 4 | no | — |
| 753 | C2×Q8 | — | 3 | 1 | no | — |
| 754 | C2×Q8 | — | 6 | 1 | no | — |
| 755 | C2×Q8 | — | 6 | 1 | no | — |
| 756 | C2×Q8 | — | 9 | 1 | no | — |
| 757 | C2×Q8 | — | 18 | 1 | no | — |
| 758 | C2×D4 | — | 3 | 1 | no | — |
| 759 | C2×D4 | — | 3 | 1 | no | — |
| 760 | C2×D4 | — | 3 | 1 | no | — |
| 761 | C2×D4 | — | 6 | 1 | no | — |
| 762 | C2×D4 | — | 6 | 1 | no | — |
| 763 | C2×D4 | — | 6 | 1 | no | — |
| 764 | C2×D4 | — | 6 | 1 | no | — |
| 765 | C2×D4 | — | 6 | 1 | no | — |
| 766 | C2×D4 | — | 6 | 1 | no | — |
| 767 | C2×D4 | — | 9 | 1 | no | — |
| 768 | C2×D4 | — | 12 | 1 | no | — |
| 769 | C2×D4 | — | 18 | 1 | no | — |
| 770 | C2×D4 | — | 18 | 1 | no | — |
| 771 | C2×D4 | — | 18 | 1 | no | — |
| 772 | C2×D4 | — | 18 | 1 | no | — |
| 773 | C2×D4 | — | 18 | 1 | no | — |
| 774 | C2×D4 | — | 18 | 1 | no | — |
| 775 | C2×D4 | — | 18 | 1 | no | — |
| 776 | C2×D4 | — | 18 | 1 | no | — |
| 777 | C2×D4 | — | 36 | 4 | no | — |
| 778 | C2×D4 | — | 36 | 4 | no | — |
| 779 | C2×D4 | — | 36 | 1 | no | — |
| 780 | C2×D4 | — | 36 | 1 | no | — |
| 781 | C22×C4 | — | 2 | 1 | no | — |
| 782 | C22×C4 | — | 3 | 1 | no | — |
| 783 | C22×C4 | — | 3 | 1 | no | — |
| 784 | C22×C4 | — | 6 | 1 | no | — |
| 785 | C22×C4 | — | 6 | 1 | no | — |
| 786 | C22×C4 | — | 6 | 1 | no | — |
| 787 | C22×C4 | — | 9 | 1 | no | — |
| 788 | C22×C4 | — | 18 | 1 | no | — |
| 789 | C22×C4 | — | 18 | 1 | no | — |
| 790 | C22×C4 | — | 18 | 1 | no | — |
| 791 | C22×C4 | — | 18 | 1 | no | — |
| 792 | C22×C4 | — | 18 | 1 | no | — |
| 793 | C22×C4 | — | 18 | 1 | no | — |
| 794 | C22×C4 | — | 18 | 1 | no | — |
| 795 | C22×C4 | — | 18 | 1 | no | — |
| 796 | C22×C4 | — | 18 | 1 | no | — |
| 797 | C22×C4 | — | 18 | 1 | no | — |
| 798 | C22×C4 | — | 18 | 1 | no | — |
| 799 | C22×C4 | — | 36 | 1 | no | — |
| 800 | C22×C4 | — | 36 | 1 | no | — |
| 801 | C22×C4 | — | 72 | 1 | no | — |
| 802 | C22×C4 | — | 72 | 1 | no | — |
| 803 | C22×C4 | C2×C3⋊S4 | 1 | 1 | yes | characteristic |
| 804 | C22×C4 | C2×C3⋊S4 | 1 | 1 | yes | characteristic |
| 805 | Q16 | — | 36 | 1 | no | — |
| 806 | Q16 | — | 36 | 1 | no | — |
| 807 | SD16 | — | 36 | 1 | no | — |
| 808 | SD16 | — | 36 | 1 | no | — |
| 809 | SD16 | — | 36 | 1 | no | — |
| 810 | SD16 | — | 36 | 1 | no | — |
| 811 | D8 | — | 36 | 1 | no | — |
| 812 | D8 | — | 36 | 1 | no | — |
| 813 | M16 | — | 18 | 1 | no | — |
| 814 | M16 | — | 18 | 1 | no | — |
| 815 | M16 | — | 36 | 1 | no | — |
| 816 | C2×C8 | — | 36 | 1 | no | — |
| 817 | C4⋊C4 | — | 6 | 1 | no | — |
| 818 | C4⋊C4 | — | 6 | 1 | no | — |
| 819 | C4⋊C4 | — | 6 | 1 | no | — |
| 820 | C4⋊C4 | — | 18 | 1 | no | — |
| 821 | C4⋊C4 | — | 18 | 1 | no | — |
| 822 | C4⋊C4 | — | 18 | 1 | no | — |
| 823 | C4⋊C4 | — | 18 | 1 | no | — |
| 824 | C4⋊C4 | — | 18 | 1 | no | — |
| 825 | C4⋊C4 | — | 18 | 1 | no | — |
| 826 | C4⋊C4 | — | 18 | 1 | no | — |
| 827 | C4⋊C4 | — | 18 | 1 | no | — |
| 828 | C4⋊C4 | — | 18 | 1 | no | — |
| 829 | C4⋊C4 | — | 18 | 1 | no | — |
| 830 | C4⋊C4 | — | 18 | 1 | no | — |
| 831 | C4⋊C4 | — | 18 | 1 | no | — |
| 832 | C4⋊C4 | — | 18 | 1 | no | — |
| 833 | C4⋊C4 | — | 36 | 1 | no | — |
| 834 | C4⋊C4 | — | 36 | 1 | no | — |
| 835 | C4⋊C4 | — | 36 | 1 | no | — |
| 836 | C22⋊C4 | — | 3 | 1 | no | — |
| 837 | C22⋊C4 | — | 3 | 1 | no | — |
| 838 | C22⋊C4 | — | 6 | 1 | no | — |
| 839 | C22⋊C4 | — | 6 | 1 | no | — |
| 840 | C22⋊C4 | — | 6 | 1 | no | — |
| 841 | C22⋊C4 | — | 6 | 1 | no | — |
| 842 | C22⋊C4 | — | 9 | 1 | no | — |
| 843 | C22⋊C4 | — | 9 | 1 | no | — |
| 844 | C22⋊C4 | — | 18 | 1 | no | — |
| 845 | C22⋊C4 | — | 18 | 1 | no | — |
| 846 | C22⋊C4 | — | 18 | 1 | no | — |
| 847 | C22⋊C4 | — | 18 | 1 | no | — |
| 848 | C22⋊C4 | — | 18 | 1 | no | — |
| 849 | C22⋊C4 | — | 18 | 1 | no | — |
| 850 | C22⋊C4 | — | 18 | 1 | no | — |
| 851 | C22⋊C4 | — | 18 | 1 | no | — |
| 852 | C22⋊C4 | — | 18 | 1 | no | — |
| 853 | C22⋊C4 | — | 18 | 1 | no | — |
| 854 | C22⋊C4 | — | 18 | 1 | no | — |
| 855 | C22⋊C4 | — | 18 | 1 | no | — |
| 856 | C22⋊C4 | — | 18 | 1 | no | — |
| 857 | C22⋊C4 | — | 18 | 1 | no | — |
| 858 | C22⋊C4 | — | 18 | 1 | no | — |
| 859 | C22⋊C4 | — | 18 | 1 | no | — |
| 860 | C22⋊C4 | — | 18 | 1 | no | — |
| 861 | C22⋊C4 | — | 18 | 1 | no | — |
| 862 | C22⋊C4 | — | 36 | 1 | no | — |
| 863 | C22⋊C4 | — | 36 | 1 | no | — |
| 864 | C22⋊C4 | — | 36 | 1 | no | — |
| 865 | C22⋊C4 | — | 36 | 1 | no | — |
| 866 | C42 | — | 6 | 1 | no | — |
| 867 | C42 | — | 9 | 1 | no | — |
| 868 | C42 | — | 9 | 1 | no | — |
| 869 | C42 | — | 18 | 1 | no | — |
| 870 | C42 | — | 18 | 1 | no | — |
| 871 | C42 | — | 18 | 1 | no | — |
| 872 | C42 | — | 18 | 1 | no | — |
| 873 | C42 | — | 18 | 1 | no | — |
| 874 | C42 | — | 18 | 1 | no | — |
| 875 | C42 | — | 36 | 1 | no | — |
| 876 | C22×C3 | — | 3 | 1 | no | — |
| 877 | C22×C3 | — | 4 | 1 | no | — |
| 878 | C22×C3 | — | 4 | 1 | no | — |
| 879 | C22×C3 | — | 6 | 2 | no | — |
| 880 | C22×C3 | — | 6 | 1 | no | — |
| 881 | C22×C3 | — | 6 | 1 | no | — |
| 882 | C22×C3 | — | 8 | 1 | no | — |
| 883 | C22×C3 | — | 12 | 1 | no | — |
| 884 | C22×C3 | — | 12 | 1 | no | — |
| 885 | C22×C3 | — | 12 | 1 | no | — |
| 886 | C22×C3 | — | 16 | 3 | no | — |
| 887 | C22×C3 | — | 24 | 1 | no | — |
| 888 | C2×D3 | — | 6 | 2 | no | — |
| 889 | C2×D3 | — | 12 | 1 | no | — |
| 890 | C2×D3 | — | 12 | 1 | no | — |
| 891 | C2×D3 | — | 12 | 2 | no | — |
| 892 | C2×D3 | — | 12 | 1 | no | — |
| 893 | C2×D3 | — | 12 | 1 | no | — |
| 894 | C2×D3 | — | 12 | 1 | no | — |
| 895 | C2×D3 | — | 24 | 1 | no | — |
| 896 | C2×D3 | — | 24 | 4 | no | — |
| 897 | C2×D3 | — | 48 | 3 | no | — |
| 898 | C2×D3 | — | 48 | 3 | no | — |
| 899 | C2×D3 | — | 48 | 12 | no | — |
| 900 | A4 | — | 4 | 3 | no | — |
| 901 | A4 | — | 8 | 3 | no | — |
| 902 | C3×C4 | — | 3 | 1 | no | — |
| 903 | C3×C4 | — | 4 | 1 | no | — |
| 904 | C3×C4 | — | 6 | 1 | no | — |
| 905 | C3×C4 | — | 6 | 1 | no | — |
| 906 | C3×C4 | — | 12 | 1 | no | — |
| 907 | C3×C4 | — | 12 | 1 | no | — |
| 908 | C3×C4 | — | 16 | 3 | no | — |
| 909 | C3×C4 | — | 16 | 3 | no | — |
| 910 | C3×C4 | #1020⋊C2 | 1 | 1 | yes | characteristic |
| 911 | Dic3 | — | 6 | 2 | no | — |
| 912 | Dic3 | — | 12 | 1 | no | — |
| 913 | Dic3 | — | 12 | 1 | no | — |
| 914 | Dic3 | — | 12 | 1 | no | — |
| 915 | Dic3 | — | 12 | 1 | no | — |
| 916 | Dic3 | — | 12 | 1 | no | — |
| 917 | Dic3 | — | 24 | 1 | no | — |
| 918 | Dic3 | — | 24 | 1 | no | — |
| 919 | Dic3 | — | 48 | 3 | no | — |
| 920 | Dic3 | — | 48 | 3 | no | — |
| 921 | C32 | — | 16 | 1 | no | Sylow |
| 922 | C23 | — | 2 | 1 | no | — |
| 923 | C23 | — | 3 | 1 | no | — |
| 924 | C23 | — | 3 | 1 | no | — |
| 925 | C23 | — | 4 | 2 | no | — |
| 926 | C23 | — | 6 | 1 | no | — |
| 927 | C23 | — | 6 | 1 | no | — |
| 928 | C23 | — | 18 | 1 | no | — |
| 929 | C23 | — | 18 | 1 | no | — |
| 930 | C23 | — | 36 | 1 | no | — |
| 931 | C23 | — | 36 | 2 | no | — |
| 932 | C23 | — | 36 | 2 | no | — |
| 933 | C23 | — | 36 | 2 | no | — |
| 934 | C23 | — | 72 | 1 | no | — |
| 935 | C23 | C22×C3⋊S4 | 1 | 1 | yes | characteristic |
| 936 | Q8 | — | 2 | 1 | no | — |
| 937 | Q8 | — | 6 | 1 | no | — |
| 938 | Q8 | — | 12 | 1 | no | — |
| 939 | Q8 | — | 36 | 1 | no | — |
| 940 | Q8 | — | 36 | 2 | no | — |
| 941 | D4 | — | 6 | 1 | no | — |
| 942 | D4 | — | 6 | 1 | no | — |
| 943 | D4 | — | 12 | 1 | no | — |
| 944 | D4 | — | 12 | 1 | no | — |
| 945 | D4 | — | 12 | 1 | no | — |
| 946 | D4 | — | 12 | 1 | no | — |
| 947 | D4 | — | 12 | 2 | no | — |
| 948 | D4 | — | 12 | 2 | no | — |
| 949 | D4 | — | 18 | 4 | no | — |
| 950 | D4 | — | 36 | 1 | no | — |
| 951 | D4 | — | 36 | 2 | no | — |
| 952 | D4 | — | 36 | 2 | no | — |
| 953 | D4 | — | 36 | 2 | no | — |
| 954 | D4 | — | 36 | 2 | no | — |
| 955 | D4 | — | 36 | 2 | no | — |
| 956 | D4 | — | 36 | 2 | no | — |
| 957 | D4 | — | 72 | 1 | no | — |
| 958 | D4 | — | 72 | 2 | no | — |
| 959 | D4 | — | 72 | 2 | no | — |
| 960 | C2×C4 | — | 3 | 1 | no | — |
| 961 | C2×C4 | — | 3 | 1 | no | — |
| 962 | C2×C4 | — | 3 | 1 | no | — |
| 963 | C2×C4 | — | 3 | 1 | no | — |
| 964 | C2×C4 | — | 4 | 1 | no | — |
| 965 | C2×C4 | — | 6 | 1 | no | — |
| 966 | C2×C4 | — | 6 | 1 | no | — |
| 967 | C2×C4 | — | 6 | 1 | no | — |
| 968 | C2×C4 | — | 6 | 1 | no | — |
| 969 | C2×C4 | — | 6 | 1 | no | — |
| 970 | C2×C4 | — | 6 | 1 | no | — |
| 971 | C2×C4 | — | 6 | 1 | no | — |
| 972 | C2×C4 | — | 6 | 1 | no | — |
| 973 | C2×C4 | — | 6 | 1 | no | — |
| 974 | C2×C4 | — | 12 | 1 | no | — |
| 975 | C2×C4 | — | 12 | 1 | no | — |
| 976 | C2×C4 | — | 18 | 1 | no | — |
| 977 | C2×C4 | — | 18 | 1 | no | — |
| 978 | C2×C4 | — | 18 | 1 | no | — |
| 979 | C2×C4 | — | 18 | 1 | no | — |
| 980 | C2×C4 | — | 18 | 1 | no | — |
| 981 | C2×C4 | — | 18 | 1 | no | — |
| 982 | C2×C4 | — | 36 | 1 | no | — |
| 983 | C2×C4 | — | 36 | 1 | no | — |
| 984 | C2×C4 | — | 36 | 2 | no | — |
| 985 | C2×C4 | — | 36 | 2 | no | — |
| 986 | C2×C4 | — | 36 | 2 | no | — |
| 987 | C2×C4 | — | 36 | 2 | no | — |
| 988 | C2×C4 | — | 36 | 2 | no | — |
| 989 | C2×C4 | — | 36 | 1 | no | — |
| 990 | C2×C4 | — | 36 | 1 | no | — |
| 991 | C2×C4 | — | 36 | 1 | no | — |
| 992 | C2×C4 | — | 36 | 1 | no | — |
| 993 | C2×C4 | — | 36 | 1 | no | — |
| 994 | C2×C4 | — | 72 | 1 | no | — |
| 995 | C2×C4 | — | 72 | 1 | no | — |
| 996 | C2×C4 | — | 72 | 1 | no | — |
| 997 | C2×C4 | — | 72 | 1 | no | — |
| 998 | C8 | — | 36 | 1 | no | — |
| 999 | C8 | — | 36 | 1 | no | — |
| 1000 | C2×C3 | — | 4 | 2 | no | — |
| 1001 | C2×C3 | — | 6 | 1 | no | — |
| 1002 | C2×C3 | — | 12 | 1 | no | — |
| 1003 | C2×C3 | — | 12 | 1 | no | — |
| 1004 | C2×C3 | — | 16 | 6 | no | — |
| 1005 | C2×C3 | — | 16 | 3 | no | — |
| 1006 | C2×C3 | C2×#1020⋊C2 | 1 | 1 | yes | characteristic |
| 1007 | D3 | — | 12 | 2 | no | — |
| 1008 | D3 | — | 24 | 1 | no | — |
| 1009 | D3 | — | 48 | 6 | no | — |
| 1010 | D3 | — | 48 | 6 | no | — |
| 1011 | C22 | — | 3 | 1 | no | — |
| 1012 | C22 | — | 4 | 1 | no | — |
| 1013 | C22 | — | 4 | 1 | no | — |
| 1014 | C22 | — | 6 | 2 | no | — |
| 1015 | C22 | — | 6 | 1 | no | — |
| 1016 | C22 | — | 6 | 1 | no | — |
| 1017 | C22 | — | 8 | 1 | no | — |
| 1018 | C22 | — | 12 | 1 | no | — |
| 1019 | C22 | — | 12 | 1 | no | — |
| 1020 | C22 | — | 12 | 1 | no | — |
| 1021 | C22 | — | 18 | 2 | no | — |
| 1022 | C22 | — | 24 | 1 | no | — |
| 1023 | C22 | — | 36 | 1 | no | — |
| 1024 | C22 | — | 36 | 1 | no | — |
| 1025 | C22 | — | 36 | 1 | no | — |
| 1026 | C22 | — | 36 | 2 | no | — |
| 1027 | C22 | — | 36 | 1 | no | — |
| 1028 | C22 | — | 36 | 1 | no | — |
| 1029 | C22 | — | 72 | 4 | no | — |
| 1030 | C22 | — | 72 | 1 | no | — |
| 1031 | C4 | — | 3 | 1 | no | — |
| 1032 | C4 | — | 4 | 1 | no | — |
| 1033 | C4 | — | 6 | 1 | no | — |
| 1034 | C4 | — | 6 | 1 | no | — |
| 1035 | C4 | — | 12 | 1 | no | — |
| 1036 | C4 | — | 12 | 1 | no | — |
| 1037 | C4 | — | 18 | 2 | no | — |
| 1038 | C4 | — | 36 | 1 | no | — |
| 1039 | C4 | — | 36 | 1 | no | — |
| 1040 | C4 | — | 36 | 1 | no | — |
| 1041 | C4 | — | 36 | 1 | no | — |
| 1042 | C4 | — | 36 | 1 | no | — |
| 1043 | C4 | — | 72 | 1 | no | — |
| 1044 | C4 | — | 72 | 1 | no | — |
| 1045 | C4 | #10593630 | 1 | 1 | yes | characteristic |
| 1046 | C3 | — | 16 | 3 | no | — |
| 1047 | C3 | #11714162 | 1 | 1 | yes | characteristic, complemented |
| 1048 | C2 | — | 4 | 2 | no | — |
| 1049 | C2 | — | 6 | 1 | no | — |
| 1050 | C2 | — | 12 | 1 | no | — |
| 1051 | C2 | — | 12 | 1 | no | — |
| 1052 | C2 | — | 36 | 2 | no | — |
| 1053 | C2 | — | 72 | 1 | no | — |
| 1054 | C2 | C2×#10593630 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #10593630 |
| commutator, cosocle, hypocenter | C3×#997 | C23 |
| Frattini | C23 | C22×C3⋊S4 |
| Fitting | C3×#3025 | D3 |
| socle | C2×C3 | C2×#1020⋊C2 |
| LCS | G ▷ C3×#997 | |
| UCS | C1 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11923785 | C2 | semidirect |
| 2. #11923784 | C2 | semidirect |
| 3. #11920987 | C2 | semidirect |
| 4. #11920986 | C2 | semidirect |
| 5. #11920982 | C2 | semidirect |
| 6. #11920981 | C2 | semidirect |
| 7. C3×#3025⋊C3 | C2 | semidirect |
| 10. C3×#5950 | C22 | semidirect |
| 13. C3⋊#5933 | C22 | semidirect |
| 14. C3⋊#5932 | C22 | semidirect |
| 16. C3×#458⋊C3 | C22 | semidirect |
| 21. C3×#3025 | D3 | semidirect |
| 24. #3025⋊C3 | D3 | semidirect |
| 51. C3×#585 | C2×D3 | semidirect |
| 52. #5950 | C2×D3 | semidirect |
| 80. C3×#458 | C2×D3 | semidirect |
| 100. #458⋊C3 | C2×D3 | semidirect |
| 131. #3025 | C3⋊D3 | semidirect |
| 152. C23×C3×C4 | S4 | semidirect |
| 296. #585 | C2×C3⋊D3 | semidirect |
| 322. #458 | C2×C3⋊D3 | semidirect |
| 527. C23×C4 | C3⋊S4 | semidirect |
| 1047. C3 | #11714162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11923785 | 2 |
| #11923784 | 2 |
| #11920987 | 2 |
| #11920986 | 2 |
| #11920982 | 2 |
| #11920981 | 2 |
| C3×#3025⋊C3 | 2 |
| #11714162 | 3 |
| #10949206 | 3 |
| C2×C4×C3⋊S4 | 4 |