Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
1203 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 1203 conjugacy classes of subgroups — too many to draw. Only its 41 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 | #11923784 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#87520 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #84125⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11920741 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11920735 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11920731 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11920729 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11714162 | — | 3 | 1 | no | maximal |
| 9 | #10949208 | — | 3 | 1 | no | maximal |
| 10 | C3×#5950 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C3⋊#5934 | C22 | 1 | 1 | yes | characteristic |
| 12 | C3⋊#5932 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C3×#5935 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#5933 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C4×D3×S4 | — | 4 | 1 | no | maximal |
| 16 | C3⋊(B(4,𝔽2)⋊C3) | C22 | 1 | 1 | yes | characteristic |
| 17 | C3⋊(#458⋊C3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #87520 | D3 | 1 | 1 | yes | characteristic, complemented |
| 19 | #87519 | — | 3 | 1 | no | — |
| 20 | #87519 | — | 6 | 1 | no | — |
| 21 | #86239 | — | 3 | 1 | no | — |
| 22 | C3×#3018 | — | 3 | 1 | no | — |
| 23 | #84125 | — | 3 | 1 | no | — |
| 24 | #84125 | D3 | 1 | 1 | yes | characteristic, complemented |
| 25 | #3025⋊C3 | — | 3 | 1 | no | — |
| 26 | #73031 | — | 3 | 1 | no | — |
| 27 | #73030 | — | 3 | 1 | no | — |
| 28 | #73026 | — | 3 | 1 | no | — |
| 29 | #73025 | — | 3 | 1 | no | — |
| 30 | #71819 | — | 3 | 1 | no | — |
| 31 | #70990 | — | 3 | 1 | no | — |
| 32 | #70990 | — | 3 | 1 | no | — |
| 33 | #70990 | — | 3 | 1 | no | — |
| 34 | #70990 | — | 3 | 1 | no | — |
| 35 | #70986 | — | 3 | 1 | no | — |
| 36 | #70986 | — | 3 | 1 | no | — |
| 37 | #70984 | — | 3 | 1 | no | — |
| 38 | #70984 | — | 3 | 1 | no | — |
| 39 | #70145 | — | 3 | 1 | no | — |
| 40 | #70145 | — | 3 | 1 | no | — |
| 41 | C2×D3×S4 | — | 4 | 1 | no | — |
| 42 | C3×#997 | C23 | 1 | 1 | yes | characteristic |
| 43 | C4×D3×A4 | — | 4 | 1 | no | — |
| 44 | C4×C3⋊S4 | — | 4 | 1 | no | — |
| 45 | C4×C3⋊S4 | — | 8 | 1 | no | — |
| 46 | C3×#985 | — | 8 | 1 | no | — |
| 47 | C3×C4×S4 | — | 4 | 1 | no | — |
| 48 | D3×SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 49 | (C3⋊S4)⋊C4 | — | 4 | 1 | no | — |
| 50 | Dic3×S4 | — | 4 | 1 | no | — |
| 51 | #33546 | — | 9 | 1 | no | Sylow |
| 52 | C3×#585 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 53 | #5950 | — | 2 | 1 | no | — |
| 54 | #5950 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 55 | #5935 | C2×D3 | 1 | 1 | yes | characteristic |
| 56 | #5934 | — | 3 | 1 | no | — |
| 57 | #5934 | — | 6 | 1 | no | — |
| 58 | #5933 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 59 | #5932 | — | 3 | 1 | no | — |
| 60 | #5932 | — | 6 | 1 | no | — |
| 61 | C2×C4×S4 | — | 12 | 1 | no | — |
| 62 | C3×#575 | — | 6 | 1 | no | — |
| 63 | C3×#532 | — | 3 | 1 | no | — |
| 64 | #5828 | — | 3 | 1 | no | — |
| 65 | #5828 | — | 3 | 1 | no | — |
| 66 | #5828 | — | 6 | 1 | no | — |
| 67 | #5828 | — | 6 | 1 | no | — |
| 68 | #5730 | — | 6 | 1 | no | — |
| 69 | #5717 | — | 3 | 1 | no | — |
| 70 | #5713 | — | 3 | 1 | no | — |
| 71 | #5679 | — | 3 | 1 | no | — |
| 72 | #5679 | — | 3 | 1 | no | — |
| 73 | #5679 | — | 6 | 1 | no | — |
| 74 | #5614 | — | 6 | 1 | no | — |
| 75 | #5614 | — | 6 | 1 | no | — |
| 76 | #5612 | — | 6 | 1 | no | — |
| 77 | #5612 | — | 6 | 1 | no | — |
| 78 | #5557 | — | 6 | 1 | no | — |
| 79 | #5557 | — | 6 | 1 | no | — |
| 80 | C4×D3×D4 | — | 6 | 1 | no | — |
| 81 | C4×D3×D4 | — | 6 | 1 | no | — |
| 82 | C4×#235 | — | 6 | 1 | no | — |
| 83 | C3×#456 | — | 6 | 1 | no | — |
| 84 | C3×#455 | — | 3 | 1 | no | — |
| 85 | C3×#455 | — | 3 | 1 | no | — |
| 86 | C3×#454 | — | 6 | 1 | no | — |
| 87 | C3×#453 | — | 3 | 1 | no | — |
| 88 | C3×#453 | — | 3 | 1 | no | — |
| 89 | C2×C3×#104 | — | 6 | 1 | no | — |
| 90 | C3×#413 | — | 3 | 1 | no | — |
| 91 | #5244 | — | 3 | 1 | no | — |
| 92 | #5244 | — | 3 | 1 | no | — |
| 93 | #5244 | — | 3 | 1 | no | — |
| 94 | #5244 | — | 6 | 1 | no | — |
| 95 | #5244 | C2×D3 | 1 | 1 | yes | characteristic |
| 96 | #5243 | — | 3 | 1 | no | — |
| 97 | #5243 | — | 3 | 1 | no | — |
| 98 | #5243 | — | 3 | 1 | no | — |
| 99 | #5243 | — | 6 | 1 | no | — |
| 100 | #5243 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 101 | #5240 | — | 3 | 1 | no | — |
| 102 | #5240 | — | 3 | 1 | no | — |
| 103 | #5240 | — | 6 | 1 | no | — |
| 104 | #458⋊C3 | — | 3 | 1 | no | — |
| 105 | B(4,𝔽2)⋊C3 | — | 3 | 1 | no | — |
| 106 | #4545 | — | 3 | 1 | no | — |
| 107 | #4545 | — | 3 | 1 | no | — |
| 108 | #4541 | — | 3 | 1 | no | — |
| 109 | #4541 | — | 3 | 1 | no | — |
| 110 | #4476 | — | 3 | 1 | no | — |
| 111 | #4476 | — | 3 | 1 | no | — |
| 112 | #4476 | — | 3 | 1 | no | — |
| 113 | #4476 | — | 3 | 1 | no | — |
| 114 | #4475 | — | 3 | 1 | no | — |
| 115 | #4475 | — | 3 | 1 | no | — |
| 116 | #4475 | — | 3 | 1 | no | — |
| 117 | #4475 | — | 3 | 1 | no | — |
| 118 | C2×D3×A4 | — | 4 | 1 | no | — |
| 119 | C2×C3⋊S4 | — | 4 | 1 | no | — |
| 120 | C2×C3⋊S4 | — | 8 | 1 | no | — |
| 121 | C2×C3×S4 | — | 4 | 1 | no | — |
| 122 | D3×S4 | — | 4 | 4 | no | — |
| 123 | C3×#41⋊C3 | — | 8 | 1 | no | — |
| 124 | C3×C4×A4 | — | 4 | 1 | no | — |
| 125 | C3×C4×A4 | — | 8 | 1 | no | — |
| 126 | C4×D32 | — | 16 | 1 | no | — |
| 127 | Dic3×A4 | — | 4 | 1 | no | — |
| 128 | C3⋊SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 129 | C3⋊SL(2,ℤ/4) | — | 8 | 1 | no | — |
| 130 | C3×SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 131 | C3×GL(2,𝔽3) | — | 8 | 1 | no | — |
| 132 | C3×#226 | — | 8 | 1 | no | — |
| 133 | #3481 | — | 9 | 1 | no | — |
| 134 | #3025 | — | 3 | 1 | no | — |
| 135 | #3025 | — | 9 | 1 | no | — |
| 136 | #3018 | — | 3 | 1 | no | — |
| 137 | #2198 | — | 9 | 1 | no | — |
| 138 | #2198 | — | 9 | 1 | no | — |
| 139 | #2197 | — | 9 | 1 | no | — |
| 140 | #2197 | — | 9 | 1 | no | — |
| 141 | #2197 | — | 9 | 1 | no | — |
| 142 | #2197 | — | 9 | 1 | no | — |
| 143 | #2196 | — | 9 | 1 | no | — |
| 144 | #2196 | — | 9 | 1 | no | — |
| 145 | #2126 | — | 9 | 1 | no | — |
| 146 | #2120 | — | 9 | 1 | no | — |
| 147 | #2120 | — | 9 | 1 | no | — |
| 148 | C22×S4 | — | 12 | 1 | no | — |
| 149 | C3×2−1+4 | — | 6 | 1 | no | — |
| 150 | C3×H(5,𝔽2) | — | 3 | 1 | no | — |
| 151 | C3×H(5,𝔽2) | — | 6 | 1 | no | — |
| 152 | C3×H(5,𝔽2) | C22×D3 | 1 | 1 | yes | characteristic |
| 153 | C2×C3×#41 | — | 3 | 1 | no | — |
| 154 | C2×C3×#41 | — | 3 | 1 | no | — |
| 155 | C2×C3×#41 | — | 6 | 1 | no | — |
| 156 | C2×C3×#41 | — | 6 | 1 | no | — |
| 157 | C2×D3×D4 | — | 6 | 1 | no | — |
| 158 | C2×D3×D4 | — | 6 | 1 | no | — |
| 159 | C2×#235 | — | 6 | 1 | no | — |
| 160 | C22×C4×D3 | — | 3 | 1 | no | — |
| 161 | C22×C4×D3 | — | 6 | 1 | no | — |
| 162 | C22×C4×D3 | S4 | 1 | 1 | yes | characteristic, complemented |
| 163 | #997 | — | 2 | 1 | no | — |
| 164 | #997 | C22×D3 | 1 | 1 | yes | characteristic |
| 165 | C2×C4×A4 | — | 12 | 1 | no | — |
| 166 | C2×SL(2,ℤ/4) | — | 12 | 1 | no | — |
| 167 | #985 | — | 8 | 1 | no | — |
| 168 | C4×S4 | — | 4 | 1 | no | — |
| 169 | C4×S4 | — | 12 | 1 | no | — |
| 170 | C4×S4 | — | 12 | 1 | no | — |
| 171 | C4×S4 | — | 12 | 1 | no | — |
| 172 | C4×S4 | — | 24 | 1 | no | — |
| 173 | C4×S4 | — | 24 | 1 | no | — |
| 174 | C4×S4 | — | 24 | 2 | no | — |
| 175 | C3×#137 | — | 6 | 1 | no | — |
| 176 | C3×#137 | — | 6 | 1 | no | — |
| 177 | C3×#137 | — | 12 | 1 | no | — |
| 178 | C3×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 179 | C3×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 180 | C3×AGL(1,ℤ/8) | — | 12 | 1 | no | — |
| 181 | C3×#135 | — | 12 | 1 | no | — |
| 182 | C3×#135 | — | 12 | 1 | no | — |
| 183 | C2×C3×M16 | — | 6 | 1 | no | — |
| 184 | C3×C4⋊Q8 | — | 3 | 1 | no | — |
| 185 | C3×#127 | — | 3 | 1 | no | — |
| 186 | C3×#124 | — | 3 | 1 | no | — |
| 187 | C3×#124 | — | 3 | 1 | no | — |
| 188 | C3×#121 | — | 6 | 1 | no | — |
| 189 | C3×#121 | — | 6 | 1 | no | — |
| 190 | C3×C4×D4 | — | 6 | 1 | no | — |
| 191 | C3×C4×D4 | — | 6 | 1 | no | — |
| 192 | C2×C3×C42 | — | 3 | 1 | no | — |
| 193 | #946 | — | 6 | 1 | no | — |
| 194 | #946 | — | 6 | 1 | no | — |
| 195 | #946 | — | 6 | 1 | no | — |
| 196 | #946 | — | 6 | 1 | no | — |
| 197 | #946 | — | 12 | 1 | no | — |
| 198 | #938 | — | 6 | 1 | no | — |
| 199 | #938 | — | 6 | 1 | no | — |
| 200 | #938 | — | 6 | 1 | no | — |
| 201 | #938 | — | 6 | 1 | no | — |
| 202 | #938 | — | 6 | 1 | no | — |
| 203 | #938 | — | 6 | 1 | no | — |
| 204 | #938 | — | 12 | 1 | no | — |
| 205 | #937 | — | 3 | 1 | no | — |
| 206 | #937 | — | 3 | 1 | no | — |
| 207 | #937 | — | 3 | 1 | no | — |
| 208 | #937 | — | 3 | 1 | no | — |
| 209 | #937 | — | 6 | 1 | no | — |
| 210 | #937 | — | 6 | 1 | no | — |
| 211 | #937 | — | 6 | 1 | no | — |
| 212 | #937 | — | 6 | 1 | no | — |
| 213 | #936 | — | 6 | 1 | no | — |
| 214 | #936 | — | 6 | 1 | no | — |
| 215 | #935 | — | 3 | 1 | no | — |
| 216 | #935 | — | 3 | 1 | no | — |
| 217 | #935 | — | 3 | 1 | no | — |
| 218 | #935 | — | 3 | 1 | no | — |
| 219 | #935 | — | 6 | 1 | no | — |
| 220 | #935 | — | 6 | 1 | no | — |
| 221 | #935 | — | 6 | 1 | no | — |
| 222 | #935 | — | 6 | 1 | no | — |
| 223 | D4×Dic3 | — | 6 | 1 | no | — |
| 224 | D4×Dic3 | — | 6 | 1 | no | — |
| 225 | C4×#67 | — | 6 | 1 | no | — |
| 226 | C4×#67 | — | 6 | 1 | no | — |
| 227 | C4×#67 | — | 6 | 1 | no | — |
| 228 | C4×#67 | — | 6 | 1 | no | — |
| 229 | C4×#67 | — | 6 | 1 | no | — |
| 230 | C4×#67 | — | 6 | 1 | no | — |
| 231 | C4×#67 | — | 6 | 1 | no | — |
| 232 | C4×#67 | — | 6 | 1 | no | — |
| 233 | C4×#67 | — | 12 | 1 | no | — |
| 234 | C4×#67 | — | 12 | 1 | no | — |
| 235 | #926 | — | 3 | 1 | no | — |
| 236 | #926 | — | 3 | 1 | no | — |
| 237 | #926 | — | 6 | 1 | no | — |
| 238 | #926 | — | 6 | 1 | no | — |
| 239 | #926 | — | 6 | 1 | no | — |
| 240 | #897 | — | 6 | 1 | no | — |
| 241 | #897 | — | 6 | 1 | no | — |
| 242 | #893 | — | 6 | 1 | no | — |
| 243 | #893 | — | 6 | 1 | no | — |
| 244 | D3×C4⋊C4 | — | 6 | 1 | no | — |
| 245 | D3×C4⋊C4 | — | 6 | 1 | no | — |
| 246 | #890 | — | 6 | 1 | no | — |
| 247 | #890 | — | 6 | 1 | no | — |
| 248 | #883 | — | 6 | 1 | no | — |
| 249 | #883 | — | 6 | 1 | no | — |
| 250 | #883 | — | 6 | 1 | no | — |
| 251 | #883 | — | 6 | 1 | no | — |
| 252 | #67⋊C4 | — | 6 | 1 | no | — |
| 253 | #67⋊C4 | — | 6 | 1 | no | — |
| 254 | #67⋊C4 | — | 6 | 1 | no | — |
| 255 | #67⋊C4 | — | 6 | 1 | no | — |
| 256 | D3×C22⋊C4 | — | 6 | 1 | no | — |
| 257 | D3×C22⋊C4 | — | 6 | 1 | no | — |
| 258 | D3×C22⋊C4 | — | 6 | 1 | no | — |
| 259 | D3×C22⋊C4 | — | 6 | 1 | no | — |
| 260 | #879 | — | 6 | 1 | no | — |
| 261 | #879 | — | 6 | 1 | no | — |
| 262 | #879 | — | 6 | 1 | no | — |
| 263 | #879 | — | 6 | 1 | no | — |
| 264 | C4×D12 | — | 6 | 1 | no | — |
| 265 | C4×D12 | — | 6 | 1 | no | — |
| 266 | #872 | — | 6 | 1 | no | — |
| 267 | #872 | — | 6 | 1 | no | — |
| 268 | C42×D3 | — | 6 | 1 | no | — |
| 269 | C42×D3 | — | 6 | 1 | no | — |
| 270 | C4×Dic6 | — | 6 | 1 | no | — |
| 271 | C4×Dic6 | — | 6 | 1 | no | — |
| 272 | C3×#104 | — | 6 | 1 | no | — |
| 273 | C3×#104 | — | 6 | 1 | no | — |
| 274 | C3×#104 | — | 6 | 1 | no | — |
| 275 | C3×#104 | — | 6 | 1 | no | — |
| 276 | C3×#101 | — | 6 | 1 | no | — |
| 277 | C3×#100 | — | 3 | 1 | no | — |
| 278 | C3×#100 | — | 3 | 1 | no | — |
| 279 | #834 | — | 3 | 1 | no | — |
| 280 | #834 | — | 3 | 1 | no | — |
| 281 | #834 | — | 3 | 1 | no | — |
| 282 | #834 | — | 3 | 1 | no | — |
| 283 | #834 | — | 6 | 1 | no | — |
| 284 | #834 | — | 6 | 1 | no | — |
| 285 | #834 | — | 6 | 1 | no | — |
| 286 | #834 | — | 6 | 1 | no | — |
| 287 | #834 | — | 6 | 1 | no | — |
| 288 | #834 | — | 6 | 1 | no | — |
| 289 | C2×C3×A4 | — | 4 | 1 | no | — |
| 290 | C2×C3×A4 | — | 8 | 1 | no | — |
| 291 | C2×D32 | — | 16 | 1 | no | — |
| 292 | D3×A4 | — | 4 | 2 | no | — |
| 293 | C3⋊S4 | — | 4 | 2 | no | — |
| 294 | C3⋊S4 | — | 8 | 2 | no | — |
| 295 | C3×S4 | — | 4 | 2 | no | — |
| 296 | C4×C3⋊D3 | — | 16 | 1 | no | — |
| 297 | C3×C4×D3 | — | 16 | 1 | no | — |
| 298 | C3×C4×D3 | — | 16 | 1 | no | — |
| 299 | C3×SL(2,𝔽3) | — | 8 | 1 | no | — |
| 300 | #624 | — | 16 | 1 | no | — |
| 301 | D3×Dic3 | — | 16 | 1 | no | — |
| 302 | D3×Dic3 | — | 16 | 1 | no | — |
| 303 | #585 | D32 | 1 | 1 | yes | characteristic, complemented |
| 304 | #575 | — | 6 | 1 | no | — |
| 305 | #559 | — | 9 | 1 | no | — |
| 306 | #554 | — | 18 | 1 | no | — |
| 307 | #553 | — | 18 | 1 | no | — |
| 308 | #553 | — | 18 | 1 | no | — |
| 309 | #551 | — | 9 | 1 | no | — |
| 310 | #551 | — | 9 | 1 | no | — |
| 311 | #551 | — | 18 | 1 | no | — |
| 312 | #546 | — | 18 | 1 | no | — |
| 313 | #546 | — | 18 | 1 | no | — |
| 314 | D42 | — | 9 | 1 | no | — |
| 315 | #532 | — | 3 | 1 | no | — |
| 316 | #529 | — | 18 | 1 | no | — |
| 317 | #529 | — | 18 | 1 | no | — |
| 318 | #525 | — | 9 | 1 | no | — |
| 319 | #525 | — | 9 | 1 | no | — |
| 320 | #525 | — | 18 | 1 | no | — |
| 321 | #525 | — | 18 | 1 | no | — |
| 322 | C4×#41 | — | 18 | 1 | no | — |
| 323 | C2×C4×D4 | — | 18 | 1 | no | — |
| 324 | C2×C4×D4 | — | 18 | 1 | no | — |
| 325 | #458 | — | 3 | 1 | no | — |
| 326 | #458 | — | 9 | 1 | no | — |
| 327 | #458 | — | 9 | 1 | no | — |
| 328 | #458 | — | 9 | 1 | no | — |
| 329 | #458 | — | 18 | 1 | no | — |
| 330 | B(4,𝔽2) | — | 3 | 1 | no | — |
| 331 | B(4,𝔽2) | — | 9 | 1 | no | — |
| 332 | B(4,𝔽2) | — | 9 | 1 | no | — |
| 333 | B(4,𝔽2) | — | 9 | 1 | no | — |
| 334 | B(4,𝔽2) | — | 18 | 1 | no | — |
| 335 | #456 | — | 6 | 1 | no | — |
| 336 | #455 | — | 3 | 1 | no | — |
| 337 | #455 | — | 3 | 1 | no | — |
| 338 | #454 | — | 6 | 1 | no | — |
| 339 | #453 | — | 3 | 1 | no | — |
| 340 | #453 | — | 3 | 1 | no | — |
| 341 | C2×#104 | — | 6 | 1 | no | — |
| 342 | #413 | — | 3 | 1 | no | — |
| 343 | #410 | — | 9 | 1 | no | — |
| 344 | #410 | — | 9 | 1 | no | — |
| 345 | #410 | — | 18 | 1 | no | — |
| 346 | #354 | — | 9 | 1 | no | — |
| 347 | #354 | — | 9 | 1 | no | — |
| 348 | #353 | — | 9 | 1 | no | — |
| 349 | #353 | — | 9 | 1 | no | — |
| 350 | #352 | — | 9 | 1 | no | — |
| 351 | #352 | — | 9 | 1 | no | — |
| 352 | #352 | — | 9 | 1 | no | — |
| 353 | #352 | — | 9 | 1 | no | — |
| 354 | AΣL(1,𝔽16) | — | 9 | 1 | no | — |
| 355 | AΣL(1,𝔽16) | — | 9 | 1 | no | — |
| 356 | AΣL(1,𝔽16) | — | 9 | 1 | no | — |
| 357 | AΣL(1,𝔽16) | — | 9 | 1 | no | — |
| 358 | C23×D3 | — | 3 | 1 | no | — |
| 359 | C23×D3 | — | 6 | 1 | no | — |
| 360 | C23×D3 | C2×S4 | 1 | 1 | yes | characteristic |
| 361 | C22×A4 | — | 12 | 1 | no | — |
| 362 | C2×S4 | — | 4 | 1 | no | — |
| 363 | C2×S4 | — | 12 | 1 | no | — |
| 364 | C2×S4 | — | 12 | 4 | no | — |
| 365 | C2×S4 | — | 24 | 1 | no | — |
| 366 | C2×S4 | — | 24 | 1 | no | — |
| 367 | C2×S4 | — | 24 | 2 | no | — |
| 368 | C3×#41 | — | 2 | 1 | no | — |
| 369 | C3×#41 | — | 6 | 1 | no | — |
| 370 | C3×#41 | — | 6 | 1 | no | — |
| 371 | C3×#41 | — | 6 | 1 | no | — |
| 372 | C3×#41 | — | 12 | 1 | no | — |
| 373 | C3×#41 | — | 12 | 1 | no | — |
| 374 | C3×#41 | — | 12 | 1 | no | — |
| 375 | C3×#41 | — | 12 | 1 | no | — |
| 376 | C3×#41 | — | 12 | 1 | no | — |
| 377 | C3×#41 | — | 12 | 1 | no | — |
| 378 | C3×#41 | — | 12 | 1 | no | — |
| 379 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 380 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 381 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 382 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 383 | C2×C3×D4 | — | 3 | 1 | no | — |
| 384 | C2×C3×D4 | — | 3 | 1 | no | — |
| 385 | C2×C3×D4 | — | 3 | 1 | no | — |
| 386 | C2×C3×D4 | — | 3 | 1 | no | — |
| 387 | C2×C3×D4 | — | 6 | 1 | no | — |
| 388 | C2×C3×D4 | — | 6 | 1 | no | — |
| 389 | C2×C3×D4 | — | 6 | 1 | no | — |
| 390 | C2×C3×D4 | — | 6 | 1 | no | — |
| 391 | C2×C3×D4 | — | 6 | 1 | no | — |
| 392 | C2×C3×D4 | — | 6 | 1 | no | — |
| 393 | C2×C3×D4 | — | 6 | 1 | no | — |
| 394 | C2×C3×D4 | — | 12 | 1 | no | — |
| 395 | C22×C3×C4 | — | 2 | 1 | no | — |
| 396 | C22×C3×C4 | — | 3 | 1 | no | — |
| 397 | C22×C3×C4 | — | 3 | 1 | no | — |
| 398 | C22×C3×C4 | — | 6 | 1 | no | — |
| 399 | C22×C3×C4 | — | 6 | 1 | no | — |
| 400 | C22×C3×C4 | — | 6 | 1 | no | — |
| 401 | C22×C3×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 402 | C2×#67 | — | 6 | 1 | no | — |
| 403 | C2×#67 | — | 6 | 1 | no | — |
| 404 | C2×#67 | — | 6 | 1 | no | — |
| 405 | C2×#67 | — | 6 | 1 | no | — |
| 406 | C2×#67 | — | 6 | 1 | no | — |
| 407 | C2×#67 | — | 6 | 1 | no | — |
| 408 | C2×#67 | — | 12 | 1 | no | — |
| 409 | C2×#67 | — | 12 | 1 | no | — |
| 410 | C22×Dic3 | — | 3 | 1 | no | — |
| 411 | C22×Dic3 | — | 6 | 1 | no | — |
| 412 | C22×Dic3 | C2×S4 | 1 | 1 | yes | characteristic |
| 413 | D3×D4 | — | 12 | 4 | no | — |
| 414 | D3×D4 | — | 12 | 4 | no | — |
| 415 | #235 | — | 12 | 4 | no | — |
| 416 | C2×D12 | — | 6 | 1 | no | — |
| 417 | C2×C4×D3 | — | 6 | 1 | no | — |
| 418 | C2×C4×D3 | — | 6 | 1 | no | — |
| 419 | C2×C4×D3 | — | 6 | 1 | no | — |
| 420 | C2×C4×D3 | — | 6 | 1 | no | — |
| 421 | C2×C4×D3 | — | 6 | 1 | no | — |
| 422 | C2×C4×D3 | — | 6 | 1 | no | — |
| 423 | C2×C4×D3 | — | 6 | 1 | no | — |
| 424 | C2×C4×D3 | — | 6 | 1 | no | — |
| 425 | C2×C4×D3 | — | 6 | 1 | no | — |
| 426 | C2×C4×D3 | — | 6 | 1 | no | — |
| 427 | C2×C4×D3 | — | 12 | 1 | no | — |
| 428 | C2×C4×D3 | — | 12 | 1 | no | — |
| 429 | C2×C4×D3 | — | 24 | 1 | no | — |
| 430 | C2×C4×D3 | — | 24 | 1 | no | — |
| 431 | C2×C4×D3 | — | 48 | 1 | no | — |
| 432 | C2×Dic6 | — | 6 | 1 | no | — |
| 433 | #41⋊C3 | — | 8 | 1 | no | — |
| 434 | #41⋊C3 | — | 16 | 1 | no | — |
| 435 | C4×A4 | — | 4 | 1 | no | — |
| 436 | C4×A4 | — | 8 | 1 | no | — |
| 437 | C4×A4 | — | 8 | 2 | no | — |
| 438 | C4×A4 | — | 8 | 1 | no | — |
| 439 | C4×A4 | — | 12 | 1 | no | — |
| 440 | SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 441 | SL(2,ℤ/4) | — | 12 | 1 | no | — |
| 442 | SL(2,ℤ/4) | — | 24 | 1 | no | — |
| 443 | SL(2,ℤ/4) | — | 24 | 1 | no | — |
| 444 | SL(2,ℤ/4) | — | 24 | 2 | no | — |
| 445 | GL(2,𝔽3) | — | 8 | 1 | no | — |
| 446 | #226 | — | 8 | 1 | no | — |
| 447 | C3×Q16 | — | 12 | 1 | no | — |
| 448 | C3×Q16 | — | 12 | 1 | no | — |
| 449 | C3×SD16 | — | 12 | 1 | no | — |
| 450 | C3×SD16 | — | 12 | 1 | no | — |
| 451 | C3×SD16 | — | 12 | 1 | no | — |
| 452 | C3×SD16 | — | 12 | 1 | no | — |
| 453 | C3×D8 | — | 12 | 1 | no | — |
| 454 | C3×D8 | — | 12 | 1 | no | — |
| 455 | C3×M16 | — | 6 | 1 | no | — |
| 456 | C3×M16 | — | 6 | 1 | no | — |
| 457 | C3×M16 | — | 12 | 1 | no | — |
| 458 | C2×C3×C8 | — | 12 | 1 | no | — |
| 459 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 460 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 461 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 462 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 463 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 464 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 465 | C3×C42 | — | 3 | 1 | no | — |
| 466 | C3×C42 | — | 3 | 1 | no | — |
| 467 | C3×C42 | — | 6 | 1 | no | — |
| 468 | #217 | — | 3 | 1 | no | — |
| 469 | #217 | — | 3 | 1 | no | — |
| 470 | #217 | — | 3 | 1 | no | — |
| 471 | #217 | — | 3 | 1 | no | — |
| 472 | #217 | — | 6 | 1 | no | — |
| 473 | #217 | — | 6 | 1 | no | — |
| 474 | #217 | — | 6 | 1 | no | — |
| 475 | #217 | — | 6 | 1 | no | — |
| 476 | #217 | — | 6 | 1 | no | — |
| 477 | #217 | — | 6 | 1 | no | — |
| 478 | #217 | — | 6 | 1 | no | — |
| 479 | #217 | — | 6 | 1 | no | — |
| 480 | #217 | — | 6 | 1 | no | — |
| 481 | #217 | — | 6 | 1 | no | — |
| 482 | #217 | — | 12 | 1 | no | — |
| 483 | #217 | — | 12 | 1 | no | — |
| 484 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 485 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 486 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 487 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 488 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 489 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 490 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 491 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 492 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 493 | (C2×D3)⋊C4 | — | 12 | 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 | — | 6 | 1 | no | — |
| 500 | C4⋊Dic3 | — | 12 | 1 | no | — |
| 501 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 502 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 503 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 504 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 505 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 506 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 507 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 508 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 509 | Dic3⋊C4 | — | 12 | 1 | no | — |
| 510 | Dic3⋊C4 | — | 12 | 1 | no | — |
| 511 | C4×Dic3 | — | 6 | 1 | no | — |
| 512 | C4×Dic3 | — | 6 | 1 | no | — |
| 513 | C4×Dic3 | — | 6 | 1 | no | — |
| 514 | C4×Dic3 | — | 6 | 1 | no | — |
| 515 | C4×Dic3 | — | 6 | 1 | no | — |
| 516 | C4×Dic3 | — | 6 | 1 | no | — |
| 517 | C4×Dic3 | — | 12 | 1 | no | — |
| 518 | C2×C3⋊D3 | — | 16 | 1 | no | — |
| 519 | C2×C3×D3 | — | 16 | 1 | no | — |
| 520 | C2×C3×D3 | — | 16 | 1 | no | — |
| 521 | C3×A4 | — | 4 | 1 | no | — |
| 522 | C3×A4 | — | 8 | 1 | no | — |
| 523 | D32 | — | 16 | 4 | no | — |
| 524 | C32×C4 | — | 16 | 1 | no | — |
| 525 | C3⋊Dic3 | — | 16 | 1 | no | — |
| 526 | C3×Dic3 | — | 16 | 1 | no | — |
| 527 | C3×Dic3 | — | 16 | 1 | no | — |
| 528 | 2−1+4 | — | 6 | 1 | no | — |
| 529 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 530 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 531 | H(5,𝔽2) | C2×D32 | 1 | 1 | yes | characteristic |
| 532 | C2×#41 | — | 3 | 1 | no | — |
| 533 | C2×#41 | — | 3 | 1 | no | — |
| 534 | C2×#41 | — | 6 | 1 | no | — |
| 535 | C2×#41 | — | 6 | 1 | no | — |
| 536 | C2×#41 | — | 18 | 1 | no | — |
| 537 | C22×D4 | — | 18 | 1 | no | — |
| 538 | C22×D4 | — | 18 | 1 | no | — |
| 539 | C23×C4 | — | 3 | 1 | no | — |
| 540 | C23×C4 | — | 9 | 1 | no | — |
| 541 | C23×C4 | — | 18 | 1 | no | — |
| 542 | #137 | — | 6 | 1 | no | — |
| 543 | #137 | — | 6 | 1 | no | — |
| 544 | #137 | — | 12 | 1 | no | — |
| 545 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 546 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 547 | AGL(1,ℤ/8) | — | 12 | 1 | no | — |
| 548 | #135 | — | 12 | 1 | no | — |
| 549 | #135 | — | 12 | 1 | no | — |
| 550 | C2×M16 | — | 6 | 1 | no | — |
| 551 | C4⋊Q8 | — | 3 | 1 | no | — |
| 552 | #127 | — | 3 | 1 | no | — |
| 553 | #126 | — | 18 | 1 | no | — |
| 554 | #126 | — | 18 | 1 | no | — |
| 555 | #126 | — | 18 | 1 | no | — |
| 556 | #126 | — | 18 | 1 | no | — |
| 557 | #125 | — | 18 | 1 | no | — |
| 558 | #125 | — | 18 | 1 | no | — |
| 559 | #124 | — | 3 | 1 | no | — |
| 560 | #124 | — | 3 | 1 | no | — |
| 561 | #124 | — | 18 | 1 | no | — |
| 562 | #124 | — | 18 | 1 | no | — |
| 563 | #123 | — | 9 | 1 | no | — |
| 564 | #123 | — | 9 | 1 | no | — |
| 565 | #123 | — | 9 | 1 | no | — |
| 566 | #123 | — | 9 | 1 | no | — |
| 567 | #123 | — | 18 | 1 | no | — |
| 568 | #123 | — | 18 | 1 | no | — |
| 569 | #123 | — | 18 | 1 | no | — |
| 570 | #123 | — | 18 | 1 | no | — |
| 571 | #123 | — | 18 | 1 | no | — |
| 572 | #123 | — | 18 | 1 | no | — |
| 573 | #123 | — | 18 | 1 | no | — |
| 574 | #123 | — | 18 | 1 | no | — |
| 575 | C22⋊Q8 | — | 18 | 1 | no | — |
| 576 | C22⋊Q8 | — | 18 | 1 | no | — |
| 577 | C22⋊Q8 | — | 18 | 1 | no | — |
| 578 | C22⋊Q8 | — | 18 | 1 | no | — |
| 579 | C22⋊Q8 | — | 18 | 1 | no | — |
| 580 | C22⋊Q8 | — | 18 | 1 | no | — |
| 581 | C22⋊Q8 | — | 36 | 1 | no | — |
| 582 | #121 | — | 6 | 1 | no | — |
| 583 | #121 | — | 6 | 1 | no | — |
| 584 | #121 | — | 18 | 1 | no | — |
| 585 | #121 | — | 18 | 1 | no | — |
| 586 | #121 | — | 18 | 1 | no | — |
| 587 | #121 | — | 18 | 1 | no | — |
| 588 | #121 | — | 18 | 1 | no | — |
| 589 | #121 | — | 18 | 1 | no | — |
| 590 | #121 | — | 36 | 1 | no | — |
| 591 | #120 | — | 9 | 1 | no | — |
| 592 | #120 | — | 9 | 1 | no | — |
| 593 | #120 | — | 9 | 1 | no | — |
| 594 | #120 | — | 9 | 1 | no | — |
| 595 | #120 | — | 18 | 1 | no | — |
| 596 | #120 | — | 18 | 1 | no | — |
| 597 | #120 | — | 18 | 1 | no | — |
| 598 | #120 | — | 18 | 1 | no | — |
| 599 | C4×Q8 | — | 18 | 1 | no | — |
| 600 | C4×Q8 | — | 18 | 1 | no | — |
| 601 | C4×D4 | — | 6 | 1 | no | — |
| 602 | C4×D4 | — | 6 | 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 | — | 18 | 1 | no | — |
| 608 | C4×D4 | — | 18 | 1 | no | — |
| 609 | C4×D4 | — | 18 | 1 | no | — |
| 610 | C4×D4 | — | 18 | 1 | no | — |
| 611 | C4×D4 | — | 18 | 1 | no | — |
| 612 | C4×D4 | — | 18 | 1 | no | — |
| 613 | C4×D4 | — | 18 | 1 | no | — |
| 614 | C4×D4 | — | 18 | 1 | no | — |
| 615 | C4×D4 | — | 18 | 1 | no | — |
| 616 | C4×D4 | — | 18 | 1 | no | — |
| 617 | C4×D4 | — | 18 | 1 | no | — |
| 618 | C4×D4 | — | 18 | 1 | no | — |
| 619 | C4×D4 | — | 18 | 1 | no | — |
| 620 | C4×D4 | — | 18 | 1 | no | — |
| 621 | C4×D4 | — | 36 | 1 | no | — |
| 622 | C4×D4 | — | 36 | 1 | no | — |
| 623 | #117 | — | 9 | 1 | no | — |
| 624 | #117 | — | 9 | 1 | no | — |
| 625 | #117 | — | 18 | 1 | no | — |
| 626 | #117 | — | 18 | 1 | no | — |
| 627 | #117 | — | 18 | 1 | no | — |
| 628 | #117 | — | 18 | 1 | no | — |
| 629 | #117 | — | 18 | 1 | no | — |
| 630 | C2×C4⋊C4 | — | 18 | 1 | no | — |
| 631 | C2×C4⋊C4 | — | 18 | 1 | no | — |
| 632 | C2×C22⋊C4 | — | 18 | 1 | no | — |
| 633 | C2×C22⋊C4 | — | 18 | 1 | no | — |
| 634 | C2×C22⋊C4 | — | 18 | 1 | no | — |
| 635 | C2×C22⋊C4 | — | 18 | 1 | no | — |
| 636 | C2×C42 | — | 3 | 1 | no | — |
| 637 | C2×C42 | — | 18 | 1 | no | — |
| 638 | C2×C42 | — | 18 | 1 | no | — |
| 639 | #104 | — | 6 | 1 | no | — |
| 640 | #104 | — | 6 | 1 | no | — |
| 641 | #104 | — | 6 | 1 | no | — |
| 642 | #104 | — | 6 | 1 | no | — |
| 643 | #101 | — | 6 | 1 | no | — |
| 644 | #100 | — | 3 | 1 | no | — |
| 645 | #100 | — | 3 | 1 | no | — |
| 646 | #99 | — | 9 | 1 | no | — |
| 647 | #99 | — | 9 | 1 | no | — |
| 648 | #99 | — | 9 | 1 | no | — |
| 649 | #99 | — | 9 | 1 | no | — |
| 650 | #99 | — | 18 | 1 | no | — |
| 651 | #99 | — | 18 | 1 | no | — |
| 652 | #99 | — | 18 | 1 | no | — |
| 653 | #99 | — | 18 | 1 | no | — |
| 654 | #99 | — | 18 | 1 | no | — |
| 655 | #99 | — | 18 | 1 | no | — |
| 656 | C23×C3 | — | 2 | 1 | no | — |
| 657 | C23×C3 | — | 3 | 1 | no | — |
| 658 | C23×C3 | — | 3 | 1 | no | — |
| 659 | C23×C3 | — | 6 | 1 | no | — |
| 660 | C23×C3 | — | 6 | 1 | no | — |
| 661 | C23×C3 | C22×S4 | 1 | 1 | yes | characteristic |
| 662 | C22×D3 | — | 4 | 2 | no | — |
| 663 | C22×D3 | — | 6 | 1 | no | — |
| 664 | C22×D3 | — | 6 | 1 | no | — |
| 665 | C22×D3 | — | 12 | 2 | no | — |
| 666 | C22×D3 | — | 12 | 2 | no | — |
| 667 | C22×D3 | — | 12 | 2 | no | — |
| 668 | C22×D3 | — | 12 | 1 | no | — |
| 669 | C22×D3 | — | 24 | 1 | no | — |
| 670 | C22×D3 | — | 48 | 1 | no | — |
| 671 | C2×A4 | — | 4 | 1 | no | — |
| 672 | C2×A4 | — | 8 | 1 | no | — |
| 673 | C2×A4 | — | 8 | 2 | no | — |
| 674 | C2×A4 | — | 8 | 1 | no | — |
| 675 | C2×A4 | — | 12 | 2 | no | — |
| 676 | S4 | — | 4 | 2 | no | — |
| 677 | S4 | — | 12 | 2 | no | — |
| 678 | S4 | — | 24 | 2 | no | — |
| 679 | S4 | — | 24 | 2 | no | — |
| 680 | S4 | — | 24 | 4 | no | — |
| 681 | C3×Q8 | — | 2 | 1 | no | — |
| 682 | C3×Q8 | — | 6 | 1 | no | — |
| 683 | C3×Q8 | — | 12 | 1 | no | — |
| 684 | C3×Q8 | — | 12 | 1 | no | — |
| 685 | C3×D4 | — | 6 | 1 | no | — |
| 686 | C3×D4 | — | 6 | 1 | no | — |
| 687 | C3×D4 | — | 12 | 1 | no | — |
| 688 | C3×D4 | — | 12 | 1 | no | — |
| 689 | C3×D4 | — | 12 | 1 | no | — |
| 690 | C3×D4 | — | 12 | 2 | no | — |
| 691 | C3×D4 | — | 12 | 1 | no | — |
| 692 | C3×D4 | — | 12 | 1 | no | — |
| 693 | C3×D4 | — | 12 | 2 | no | — |
| 694 | C3×D4 | — | 24 | 1 | no | — |
| 695 | C2×C3×C4 | — | 3 | 1 | no | — |
| 696 | C2×C3×C4 | — | 3 | 1 | no | — |
| 697 | C2×C3×C4 | — | 3 | 1 | no | — |
| 698 | C2×C3×C4 | — | 3 | 1 | no | — |
| 699 | C2×C3×C4 | — | 6 | 1 | no | — |
| 700 | C2×C3×C4 | — | 6 | 1 | no | — |
| 701 | C2×C3×C4 | — | 6 | 1 | no | — |
| 702 | C2×C3×C4 | — | 6 | 1 | no | — |
| 703 | C2×C3×C4 | — | 6 | 1 | no | — |
| 704 | C2×C3×C4 | — | 6 | 1 | no | — |
| 705 | C2×C3×C4 | — | 6 | 1 | no | — |
| 706 | C2×C3×C4 | — | 6 | 1 | no | — |
| 707 | C2×C3×C4 | — | 6 | 1 | no | — |
| 708 | C2×C3×C4 | — | 12 | 1 | no | — |
| 709 | C2×C3×C4 | — | 12 | 1 | no | — |
| 710 | C2×C3×C4 | — | 12 | 2 | no | — |
| 711 | C2×C3×C4 | — | 12 | 1 | no | — |
| 712 | C2×C3×C4 | — | 48 | 1 | no | — |
| 713 | #67 | — | 12 | 2 | no | — |
| 714 | #67 | — | 12 | 2 | no | — |
| 715 | #67 | — | 12 | 2 | no | — |
| 716 | #67 | — | 12 | 2 | no | — |
| 717 | #67 | — | 12 | 2 | no | — |
| 718 | #67 | — | 12 | 2 | no | — |
| 719 | #67 | — | 24 | 2 | no | — |
| 720 | #67 | — | 24 | 2 | no | — |
| 721 | C2×Dic3 | — | 6 | 1 | no | — |
| 722 | C2×Dic3 | — | 6 | 1 | no | — |
| 723 | C2×Dic3 | — | 6 | 1 | no | — |
| 724 | C2×Dic3 | — | 6 | 1 | no | — |
| 725 | C2×Dic3 | — | 6 | 1 | no | — |
| 726 | C2×Dic3 | — | 6 | 1 | no | — |
| 727 | C2×Dic3 | — | 12 | 1 | no | — |
| 728 | C2×Dic3 | — | 12 | 1 | no | — |
| 729 | C2×Dic3 | — | 12 | 1 | no | — |
| 730 | C2×Dic3 | — | 24 | 1 | no | — |
| 731 | C2×Dic3 | — | 48 | 1 | no | — |
| 732 | D12 | — | 6 | 4 | no | — |
| 733 | C4×D3 | — | 4 | 1 | no | — |
| 734 | C4×D3 | — | 12 | 1 | no | — |
| 735 | C4×D3 | — | 12 | 1 | no | — |
| 736 | C4×D3 | — | 12 | 2 | no | — |
| 737 | C4×D3 | — | 12 | 2 | no | — |
| 738 | C4×D3 | — | 12 | 2 | no | — |
| 739 | C4×D3 | — | 12 | 2 | no | — |
| 740 | C4×D3 | — | 12 | 1 | no | — |
| 741 | C4×D3 | — | 16 | 1 | no | — |
| 742 | C4×D3 | — | 24 | 1 | no | — |
| 743 | C4×D3 | — | 24 | 1 | no | — |
| 744 | C4×D3 | — | 24 | 1 | no | — |
| 745 | C4×D3 | — | 48 | 1 | no | — |
| 746 | C4×D3 | — | 48 | 1 | no | — |
| 747 | C4×D3 | — | 48 | 1 | no | — |
| 748 | C4×D3 | — | 96 | 1 | no | — |
| 749 | Dic6 | — | 12 | 2 | no | — |
| 750 | SL(2,𝔽3) | — | 8 | 1 | no | — |
| 751 | SL(2,𝔽3) | — | 16 | 1 | no | — |
| 752 | C3×C8 | — | 12 | 1 | no | — |
| 753 | C3×C8 | — | 12 | 1 | no | — |
| 754 | C2×C32 | — | 16 | 1 | no | — |
| 755 | C3⋊D3 | — | 16 | 2 | no | — |
| 756 | C3×D3 | — | 16 | 2 | no | — |
| 757 | C3×D3 | — | 16 | 2 | no | — |
| 758 | C24 | — | 3 | 1 | no | — |
| 759 | C24 | — | 9 | 1 | no | — |
| 760 | C24 | — | 18 | 1 | no | — |
| 761 | #41 | — | 2 | 1 | no | — |
| 762 | #41 | — | 6 | 1 | no | — |
| 763 | #41 | — | 6 | 1 | no | — |
| 764 | #41 | — | 6 | 1 | no | — |
| 765 | #41 | — | 12 | 1 | no | — |
| 766 | #41 | — | 12 | 1 | no | — |
| 767 | #41 | — | 12 | 1 | no | — |
| 768 | #41 | — | 12 | 1 | no | — |
| 769 | #41 | — | 12 | 1 | no | — |
| 770 | #41 | — | 12 | 1 | no | — |
| 771 | #41 | — | 12 | 1 | no | — |
| 772 | #41 | — | 36 | 4 | no | — |
| 773 | C2×Q8 | — | 3 | 1 | no | — |
| 774 | C2×Q8 | — | 3 | 1 | no | — |
| 775 | C2×Q8 | — | 6 | 1 | no | — |
| 776 | C2×Q8 | — | 6 | 1 | no | — |
| 777 | C2×Q8 | — | 18 | 1 | no | — |
| 778 | C2×D4 | — | 3 | 1 | no | — |
| 779 | C2×D4 | — | 3 | 1 | no | — |
| 780 | C2×D4 | — | 3 | 1 | no | — |
| 781 | C2×D4 | — | 3 | 1 | no | — |
| 782 | C2×D4 | — | 6 | 1 | no | — |
| 783 | C2×D4 | — | 6 | 1 | no | — |
| 784 | C2×D4 | — | 6 | 1 | no | — |
| 785 | C2×D4 | — | 6 | 1 | no | — |
| 786 | C2×D4 | — | 6 | 1 | no | — |
| 787 | C2×D4 | — | 6 | 1 | no | — |
| 788 | C2×D4 | — | 6 | 1 | no | — |
| 789 | C2×D4 | — | 12 | 1 | no | — |
| 790 | C2×D4 | — | 18 | 1 | no | — |
| 791 | C2×D4 | — | 18 | 1 | no | — |
| 792 | C2×D4 | — | 18 | 1 | no | — |
| 793 | C2×D4 | — | 18 | 1 | no | — |
| 794 | C2×D4 | — | 18 | 1 | no | — |
| 795 | C2×D4 | — | 18 | 1 | no | — |
| 796 | C2×D4 | — | 18 | 1 | no | — |
| 797 | C2×D4 | — | 36 | 4 | no | — |
| 798 | C2×D4 | — | 36 | 4 | no | — |
| 799 | C2×D4 | — | 36 | 1 | no | — |
| 800 | C2×D4 | — | 36 | 1 | no | — |
| 801 | C22×C4 | — | 2 | 1 | no | — |
| 802 | C22×C4 | — | 3 | 1 | no | — |
| 803 | C22×C4 | — | 3 | 1 | no | — |
| 804 | C22×C4 | — | 3 | 1 | no | — |
| 805 | C22×C4 | — | 6 | 1 | no | — |
| 806 | C22×C4 | — | 6 | 1 | no | — |
| 807 | C22×C4 | — | 6 | 1 | no | — |
| 808 | C22×C4 | — | 9 | 1 | no | — |
| 809 | C22×C4 | — | 18 | 1 | no | — |
| 810 | C22×C4 | — | 18 | 1 | no | — |
| 811 | C22×C4 | — | 18 | 1 | no | — |
| 812 | C22×C4 | — | 18 | 1 | no | — |
| 813 | C22×C4 | — | 18 | 1 | no | — |
| 814 | C22×C4 | — | 18 | 1 | no | — |
| 815 | C22×C4 | — | 18 | 1 | no | — |
| 816 | C22×C4 | — | 18 | 1 | no | — |
| 817 | C22×C4 | — | 18 | 1 | no | — |
| 818 | C22×C4 | — | 18 | 1 | no | — |
| 819 | C22×C4 | — | 18 | 1 | no | — |
| 820 | C22×C4 | — | 36 | 1 | no | — |
| 821 | C22×C4 | — | 36 | 1 | no | — |
| 822 | C22×C4 | — | 72 | 1 | no | — |
| 823 | C22×C4 | — | 72 | 1 | no | — |
| 824 | C22×C4 | D3×S4 | 1 | 1 | yes | characteristic |
| 825 | Q16 | — | 12 | 1 | no | — |
| 826 | Q16 | — | 12 | 1 | no | — |
| 827 | SD16 | — | 12 | 1 | no | — |
| 828 | SD16 | — | 12 | 1 | no | — |
| 829 | SD16 | — | 12 | 1 | no | — |
| 830 | SD16 | — | 12 | 1 | no | — |
| 831 | D8 | — | 12 | 1 | no | — |
| 832 | D8 | — | 12 | 1 | no | — |
| 833 | M16 | — | 6 | 1 | no | — |
| 834 | M16 | — | 6 | 1 | no | — |
| 835 | M16 | — | 12 | 1 | no | — |
| 836 | C2×C8 | — | 12 | 1 | no | — |
| 837 | C4⋊C4 | — | 6 | 1 | no | — |
| 838 | C4⋊C4 | — | 6 | 1 | no | — |
| 839 | C4⋊C4 | — | 18 | 1 | no | — |
| 840 | C4⋊C4 | — | 18 | 1 | no | — |
| 841 | C4⋊C4 | — | 18 | 1 | no | — |
| 842 | C4⋊C4 | — | 18 | 1 | no | — |
| 843 | C4⋊C4 | — | 18 | 1 | no | — |
| 844 | C4⋊C4 | — | 18 | 1 | no | — |
| 845 | C4⋊C4 | — | 18 | 1 | no | — |
| 846 | C4⋊C4 | — | 18 | 1 | no | — |
| 847 | C4⋊C4 | — | 18 | 1 | no | — |
| 848 | C4⋊C4 | — | 18 | 1 | no | — |
| 849 | C4⋊C4 | — | 18 | 1 | no | — |
| 850 | C4⋊C4 | — | 18 | 1 | no | — |
| 851 | C4⋊C4 | — | 18 | 1 | no | — |
| 852 | C4⋊C4 | — | 18 | 1 | no | — |
| 853 | C4⋊C4 | — | 36 | 1 | no | — |
| 854 | C4⋊C4 | — | 36 | 1 | no | — |
| 855 | C4⋊C4 | — | 36 | 1 | no | — |
| 856 | C22⋊C4 | — | 6 | 1 | no | — |
| 857 | C22⋊C4 | — | 6 | 1 | no | — |
| 858 | C22⋊C4 | — | 6 | 1 | no | — |
| 859 | C22⋊C4 | — | 6 | 1 | no | — |
| 860 | C22⋊C4 | — | 9 | 1 | no | — |
| 861 | C22⋊C4 | — | 9 | 1 | no | — |
| 862 | C22⋊C4 | — | 9 | 1 | no | — |
| 863 | C22⋊C4 | — | 9 | 1 | no | — |
| 864 | C22⋊C4 | — | 18 | 1 | no | — |
| 865 | C22⋊C4 | — | 18 | 1 | no | — |
| 866 | C22⋊C4 | — | 18 | 1 | no | — |
| 867 | C22⋊C4 | — | 18 | 1 | no | — |
| 868 | C22⋊C4 | — | 18 | 1 | no | — |
| 869 | C22⋊C4 | — | 18 | 1 | no | — |
| 870 | C22⋊C4 | — | 18 | 1 | no | — |
| 871 | C22⋊C4 | — | 18 | 1 | no | — |
| 872 | C22⋊C4 | — | 18 | 1 | no | — |
| 873 | C22⋊C4 | — | 18 | 1 | no | — |
| 874 | C22⋊C4 | — | 18 | 1 | no | — |
| 875 | C22⋊C4 | — | 18 | 1 | no | — |
| 876 | C22⋊C4 | — | 18 | 1 | no | — |
| 877 | C22⋊C4 | — | 18 | 1 | no | — |
| 878 | C22⋊C4 | — | 18 | 1 | no | — |
| 879 | C22⋊C4 | — | 18 | 1 | no | — |
| 880 | C22⋊C4 | — | 18 | 1 | no | — |
| 881 | C22⋊C4 | — | 18 | 1 | no | — |
| 882 | C22⋊C4 | — | 36 | 1 | no | — |
| 883 | C22⋊C4 | — | 36 | 1 | no | — |
| 884 | C22⋊C4 | — | 36 | 1 | no | — |
| 885 | C22⋊C4 | — | 36 | 1 | no | — |
| 886 | C42 | — | 3 | 1 | no | — |
| 887 | C42 | — | 3 | 1 | no | — |
| 888 | C42 | — | 6 | 1 | no | — |
| 889 | C42 | — | 18 | 1 | no | — |
| 890 | C42 | — | 18 | 1 | no | — |
| 891 | C42 | — | 18 | 1 | no | — |
| 892 | C42 | — | 18 | 1 | no | — |
| 893 | C42 | — | 18 | 1 | no | — |
| 894 | C42 | — | 18 | 1 | no | — |
| 895 | C42 | — | 36 | 1 | no | — |
| 896 | C22×C3 | — | 3 | 1 | no | — |
| 897 | C22×C3 | — | 4 | 1 | no | — |
| 898 | C22×C3 | — | 6 | 1 | no | — |
| 899 | C22×C3 | — | 6 | 1 | no | — |
| 900 | C22×C3 | — | 8 | 1 | no | — |
| 901 | C22×C3 | — | 12 | 1 | no | — |
| 902 | C22×C3 | — | 12 | 1 | no | — |
| 903 | C22×C3 | — | 12 | 1 | no | — |
| 904 | C22×C3 | — | 12 | 1 | no | — |
| 905 | C22×C3 | — | 12 | 1 | no | — |
| 906 | C22×C3 | — | 24 | 1 | no | — |
| 907 | C22×C3 | — | 48 | 1 | no | — |
| 908 | C2×D3 | — | 4 | 1 | no | — |
| 909 | C2×D3 | — | 6 | 2 | no | — |
| 910 | C2×D3 | — | 6 | 2 | no | — |
| 911 | C2×D3 | — | 12 | 1 | no | — |
| 912 | C2×D3 | — | 12 | 1 | no | — |
| 913 | C2×D3 | — | 12 | 1 | no | — |
| 914 | C2×D3 | — | 12 | 2 | no | — |
| 915 | C2×D3 | — | 16 | 1 | no | — |
| 916 | C2×D3 | — | 24 | 4 | no | — |
| 917 | C2×D3 | — | 24 | 1 | no | — |
| 918 | C2×D3 | — | 48 | 1 | no | — |
| 919 | C2×D3 | — | 48 | 4 | no | — |
| 920 | C2×D3 | — | 96 | 1 | no | — |
| 921 | A4 | — | 4 | 1 | no | — |
| 922 | A4 | — | 8 | 1 | no | — |
| 923 | A4 | — | 8 | 1 | no | — |
| 924 | A4 | — | 8 | 2 | no | — |
| 925 | C3×C4 | — | 3 | 1 | no | — |
| 926 | C3×C4 | — | 6 | 2 | no | — |
| 927 | C3×C4 | — | 6 | 1 | no | — |
| 928 | C3×C4 | — | 6 | 1 | no | — |
| 929 | C3×C4 | — | 12 | 1 | no | — |
| 930 | C3×C4 | — | 12 | 1 | no | — |
| 931 | C3×C4 | — | 16 | 1 | no | — |
| 932 | C3×C4 | — | 32 | 1 | no | — |
| 933 | C3×C4 | — | 48 | 1 | no | — |
| 934 | C3×C4 | #1020⋊C2 | 1 | 1 | yes | characteristic |
| 935 | Dic3 | — | 4 | 1 | no | — |
| 936 | Dic3 | — | 12 | 1 | no | — |
| 937 | Dic3 | — | 12 | 1 | no | — |
| 938 | Dic3 | — | 12 | 1 | no | — |
| 939 | Dic3 | — | 12 | 1 | no | — |
| 940 | Dic3 | — | 12 | 1 | no | — |
| 941 | Dic3 | — | 16 | 1 | no | — |
| 942 | Dic3 | — | 24 | 1 | no | — |
| 943 | Dic3 | — | 24 | 1 | no | — |
| 944 | Dic3 | — | 48 | 1 | no | — |
| 945 | Dic3 | — | 96 | 1 | no | — |
| 946 | C32 | — | 16 | 1 | no | Sylow |
| 947 | C23 | — | 2 | 1 | no | — |
| 948 | C23 | — | 3 | 1 | no | — |
| 949 | C23 | — | 3 | 1 | no | — |
| 950 | C23 | — | 6 | 1 | no | — |
| 951 | C23 | — | 6 | 1 | no | — |
| 952 | C23 | — | 12 | 2 | no | — |
| 953 | C23 | — | 18 | 1 | no | — |
| 954 | C23 | — | 18 | 1 | no | — |
| 955 | C23 | — | 36 | 1 | no | — |
| 956 | C23 | — | 36 | 2 | no | — |
| 957 | C23 | — | 36 | 2 | no | — |
| 958 | C23 | — | 36 | 2 | no | — |
| 959 | C23 | — | 72 | 1 | no | — |
| 960 | C23 | C2×D3×S4 | 1 | 1 | yes | characteristic |
| 961 | Q8 | — | 2 | 1 | no | — |
| 962 | Q8 | — | 6 | 1 | no | — |
| 963 | Q8 | — | 12 | 1 | no | — |
| 964 | Q8 | — | 12 | 1 | no | — |
| 965 | Q8 | — | 36 | 2 | no | — |
| 966 | D4 | — | 6 | 1 | no | — |
| 967 | D4 | — | 6 | 1 | no | — |
| 968 | D4 | — | 12 | 1 | no | — |
| 969 | D4 | — | 12 | 1 | no | — |
| 970 | D4 | — | 12 | 1 | no | — |
| 971 | D4 | — | 12 | 2 | no | — |
| 972 | D4 | — | 12 | 1 | no | — |
| 973 | D4 | — | 12 | 1 | no | — |
| 974 | D4 | — | 12 | 2 | no | — |
| 975 | D4 | — | 18 | 4 | no | — |
| 976 | D4 | — | 24 | 1 | no | — |
| 977 | D4 | — | 36 | 2 | no | — |
| 978 | D4 | — | 36 | 2 | no | — |
| 979 | D4 | — | 36 | 2 | no | — |
| 980 | D4 | — | 36 | 2 | no | — |
| 981 | D4 | — | 36 | 2 | no | — |
| 982 | D4 | — | 36 | 2 | no | — |
| 983 | D4 | — | 72 | 2 | no | — |
| 984 | D4 | — | 72 | 2 | no | — |
| 985 | C2×C4 | — | 3 | 1 | no | — |
| 986 | C2×C4 | — | 3 | 1 | no | — |
| 987 | C2×C4 | — | 3 | 1 | no | — |
| 988 | C2×C4 | — | 3 | 1 | no | — |
| 989 | C2×C4 | — | 6 | 1 | no | — |
| 990 | C2×C4 | — | 6 | 1 | no | — |
| 991 | C2×C4 | — | 6 | 1 | no | — |
| 992 | C2×C4 | — | 6 | 1 | no | — |
| 993 | C2×C4 | — | 6 | 1 | no | — |
| 994 | C2×C4 | — | 6 | 1 | no | — |
| 995 | C2×C4 | — | 6 | 1 | no | — |
| 996 | C2×C4 | — | 6 | 1 | no | — |
| 997 | C2×C4 | — | 6 | 1 | no | — |
| 998 | C2×C4 | — | 12 | 1 | no | — |
| 999 | C2×C4 | — | 12 | 1 | no | — |
| 1000 | C2×C4 | — | 12 | 2 | no | — |
| 1001 | C2×C4 | — | 12 | 1 | no | — |
| 1002 | C2×C4 | — | 12 | 1 | no | — |
| 1003 | C2×C4 | — | 18 | 1 | no | — |
| 1004 | C2×C4 | — | 18 | 1 | no | — |
| 1005 | C2×C4 | — | 18 | 1 | no | — |
| 1006 | C2×C4 | — | 18 | 1 | no | — |
| 1007 | C2×C4 | — | 18 | 1 | no | — |
| 1008 | C2×C4 | — | 18 | 1 | no | — |
| 1009 | C2×C4 | — | 36 | 1 | no | — |
| 1010 | C2×C4 | — | 36 | 1 | no | — |
| 1011 | C2×C4 | — | 36 | 2 | no | — |
| 1012 | C2×C4 | — | 36 | 2 | no | — |
| 1013 | C2×C4 | — | 36 | 2 | no | — |
| 1014 | C2×C4 | — | 36 | 2 | no | — |
| 1015 | C2×C4 | — | 36 | 1 | no | — |
| 1016 | C2×C4 | — | 36 | 1 | no | — |
| 1017 | C2×C4 | — | 36 | 1 | no | — |
| 1018 | C2×C4 | — | 36 | 1 | no | — |
| 1019 | C2×C4 | — | 72 | 1 | no | — |
| 1020 | C2×C4 | — | 72 | 1 | no | — |
| 1021 | C2×C4 | — | 72 | 1 | no | — |
| 1022 | C2×C4 | — | 72 | 1 | no | — |
| 1023 | C8 | — | 12 | 1 | no | — |
| 1024 | C8 | — | 12 | 1 | no | — |
| 1025 | C2×C3 | — | 6 | 1 | no | — |
| 1026 | C2×C3 | — | 12 | 1 | no | — |
| 1027 | C2×C3 | — | 12 | 1 | no | — |
| 1028 | C2×C3 | — | 16 | 1 | no | — |
| 1029 | C2×C3 | — | 24 | 1 | no | — |
| 1030 | C2×C3 | — | 32 | 1 | no | — |
| 1031 | C2×C3 | — | 48 | 2 | no | — |
| 1032 | C2×C3 | C2×#1020⋊C2 | 1 | 1 | yes | characteristic |
| 1033 | D3 | — | 4 | 2 | no | — |
| 1034 | D3 | — | 12 | 2 | no | — |
| 1035 | D3 | — | 16 | 2 | no | — |
| 1036 | D3 | — | 48 | 2 | no | — |
| 1037 | D3 | — | 96 | 2 | no | — |
| 1038 | C22 | — | 3 | 1 | no | — |
| 1039 | C22 | — | 4 | 1 | no | — |
| 1040 | C22 | — | 6 | 1 | no | — |
| 1041 | C22 | — | 6 | 1 | no | — |
| 1042 | C22 | — | 8 | 1 | no | — |
| 1043 | C22 | — | 12 | 1 | no | — |
| 1044 | C22 | — | 12 | 1 | no | — |
| 1045 | C22 | — | 12 | 1 | no | — |
| 1046 | C22 | — | 12 | 1 | no | — |
| 1047 | C22 | — | 12 | 1 | no | — |
| 1048 | C22 | — | 12 | 1 | no | — |
| 1049 | C22 | — | 18 | 2 | no | — |
| 1050 | C22 | — | 18 | 2 | no | — |
| 1051 | C22 | — | 24 | 1 | no | — |
| 1052 | C22 | — | 36 | 1 | no | — |
| 1053 | C22 | — | 36 | 1 | no | — |
| 1054 | C22 | — | 36 | 2 | no | — |
| 1055 | C22 | — | 36 | 1 | no | — |
| 1056 | C22 | — | 72 | 4 | no | — |
| 1057 | C22 | — | 72 | 1 | no | — |
| 1058 | C4 | — | 3 | 1 | no | — |
| 1059 | C4 | — | 6 | 2 | no | — |
| 1060 | C4 | — | 6 | 1 | no | — |
| 1061 | C4 | — | 6 | 1 | no | — |
| 1062 | C4 | — | 12 | 1 | no | — |
| 1063 | C4 | — | 12 | 1 | no | — |
| 1064 | C4 | — | 12 | 1 | no | — |
| 1065 | C4 | — | 36 | 1 | no | — |
| 1066 | C4 | — | 36 | 1 | no | — |
| 1067 | C4 | — | 36 | 1 | no | — |
| 1068 | C4 | — | 36 | 1 | no | — |
| 1069 | C4 | — | 36 | 1 | no | — |
| 1070 | C4 | — | 72 | 1 | no | — |
| 1071 | C4 | — | 72 | 1 | no | — |
| 1072 | C4 | #10593244 | 1 | 1 | yes | characteristic |
| 1073 | C3 | — | 16 | 1 | no | — |
| 1074 | C3 | — | 32 | 1 | no | — |
| 1075 | C3 | #11714162 | 1 | 1 | yes | characteristic, complemented |
| 1076 | C2 | — | 6 | 1 | no | — |
| 1077 | C2 | — | 12 | 1 | no | — |
| 1078 | C2 | — | 12 | 1 | no | — |
| 1079 | C2 | — | 12 | 2 | no | — |
| 1080 | C2 | — | 24 | 1 | no | — |
| 1081 | C2 | — | 36 | 2 | no | — |
| 1082 | C2 | C2×#10593244 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #10593244 |
| commutator, cosocle, hypocenter | C3×#997 | C23 |
| Frattini | C23 | C2×D3×S4 |
| Fitting | C3×#585 | C2×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. #11923784 | C2 | semidirect |
| 2. C3×#87520 | C2 | semidirect |
| 3. #84125⋊C3 | C2 | semidirect |
| 4. #11920741 | C2 | semidirect |
| 5. #11920735 | C2 | semidirect |
| 6. #11920731 | C2 | semidirect |
| 7. #11920729 | C2 | semidirect |
| 10. C3×#5950 | C22 | semidirect |
| 12. C3⋊#5932 | C22 | semidirect |
| 14. C3×#5933 | C22 | semidirect |
| 17. C3⋊(#458⋊C3) | C22 | semidirect |
| 18. #87520 | D3 | semidirect |
| 24. #84125 | D3 | semidirect |
| 52. C3×#585 | C2×D3 | semidirect |
| 54. #5950 | C2×D3 | semidirect |
| 58. #5933 | C2×D3 | semidirect |
| 100. #5243 | C2×D3 | semidirect |
| 162. C22×C4×D3 | S4 | semidirect |
| 303. #585 | D32 | semidirect |
| 1075. C3 | #11714162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11923784 | 2 |
| C3×#87520 | 2 |
| #84125⋊C3 | 2 |
| #11920741 | 2 |
| #11920735 | 2 |
| #11920731 | 2 |
| #11920729 | 2 |
| #11714162 | 3 |
| #10949208 | 3 |
| C4×D3×S4 | 4 |