Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
1200 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 58 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 | C3×#87521 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#87520 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#73027 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×#73026 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C3×#3027⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11714184 | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 7 | C3×#33559 | — | 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 | C3×D4×S4 | — | 4 | 1 | no | maximal |
| 13 | C3×B(4,𝔽2)⋊C3 | C22 | 1 | 2 | yes | complemented |
| 14 | #87521 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 15 | #87520 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 16 | C3×#3549 | — | 3 | 1 | no | — |
| 17 | C3×#3027 | — | 3 | 1 | no | — |
| 18 | C3×#3027 | D3 | 1 | 1 | yes | characteristic, complemented |
| 19 | C3×#3018 | — | 3 | 1 | no | — |
| 20 | #3027⋊C3 | — | 2 | 1 | no | — |
| 21 | #3027⋊C3 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 22 | #73027 | C2×C3 | 1 | 2 | yes | complemented |
| 23 | #73026 | C2×C3 | 1 | 2 | yes | complemented |
| 24 | C3×#2199 | — | 3 | 2 | no | — |
| 25 | C3×#2199 | — | 3 | 2 | no | — |
| 26 | C3×#2196 | — | 3 | 2 | no | — |
| 27 | C3×#2196 | — | 3 | 2 | no | — |
| 28 | C3×#2126 | — | 3 | 1 | no | — |
| 29 | C3×#2122 | — | 3 | 1 | no | — |
| 30 | C3×#2122 | — | 3 | 1 | no | — |
| 31 | C22×C3×S4 | — | 4 | 2 | no | — |
| 32 | C3×#997 | C23 | 1 | 1 | yes | characteristic |
| 33 | C3×D4×A4 | — | 4 | 1 | no | — |
| 34 | C3×GL(2,ℤ/4) | — | 4 | 2 | no | — |
| 35 | C3×#985 | — | 8 | 1 | no | — |
| 36 | C3×C4⋊S4 | — | 4 | 1 | no | — |
| 37 | C3×C4⋊S4 | — | 8 | 1 | no | — |
| 38 | C3×C4×S4 | — | 4 | 1 | no | — |
| 39 | #33559 | — | 3 | 1 | no | Sylow |
| 40 | C3×#585 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 41 | #5950 | — | 2 | 1 | no | — |
| 42 | #5950 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 43 | #5935 | C22×C3 | 1 | 1 | yes | characteristic |
| 44 | #5934 | C22×C3 | 1 | 2 | yes | complemented |
| 45 | #5933 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 46 | D4×S4 | — | 4 | 1 | no | — |
| 47 | C3×#575 | — | 6 | 1 | no | — |
| 48 | C3×H(3,𝔽4) | — | 3 | 2 | no | — |
| 49 | C3×H(3,𝔽4) | — | 6 | 1 | no | — |
| 50 | C3×#555 | — | 6 | 1 | no | — |
| 51 | C3×#555 | — | 6 | 1 | no | — |
| 52 | C3×#555 | — | 6 | 1 | no | — |
| 53 | C3×D42 | — | 3 | 2 | no | — |
| 54 | C3×D42 | — | 6 | 1 | no | — |
| 55 | C3×D42 | — | 6 | 1 | no | — |
| 56 | C3×#535 | — | 3 | 1 | no | — |
| 57 | C3×#535 | — | 3 | 1 | no | — |
| 58 | C3×#535 | — | 6 | 2 | no | — |
| 59 | C3×#535 | — | 6 | 2 | no | — |
| 60 | C3×#535 | — | 6 | 1 | no | — |
| 61 | C3×#535 | — | 6 | 1 | no | — |
| 62 | C3×#532 | — | 3 | 1 | no | — |
| 63 | C3×#532 | — | 6 | 1 | no | — |
| 64 | C3×B(4,𝔽2) | — | 3 | 2 | no | — |
| 65 | C3×B(4,𝔽2) | — | 3 | 2 | no | — |
| 66 | C3×B(4,𝔽2) | — | 3 | 2 | no | — |
| 67 | C3×B(4,𝔽2) | — | 6 | 2 | no | — |
| 68 | C3×B(4,𝔽2) | C2×D3 | 1 | 2 | yes | complemented |
| 69 | C3×#456 | — | 6 | 1 | no | — |
| 70 | C3×#455 | — | 3 | 1 | no | — |
| 71 | C3×#455 | — | 3 | 1 | no | — |
| 72 | C3×#454 | — | 6 | 1 | no | — |
| 73 | C3×#453 | — | 3 | 1 | no | — |
| 74 | C3×#453 | — | 3 | 1 | no | — |
| 75 | C2×C3×#104 | — | 6 | 1 | no | — |
| 76 | C3×#413 | — | 3 | 1 | no | — |
| 77 | C3×#410 | — | 3 | 1 | no | — |
| 78 | C3×#410 | — | 3 | 1 | no | — |
| 79 | C3×#410 | — | 6 | 1 | no | — |
| 80 | B(4,𝔽2)⋊C3 | — | 2 | 2 | no | — |
| 81 | B(4,𝔽2)⋊C3 | C22×C3 | 1 | 2 | yes | complemented |
| 82 | C3×#354 | — | 3 | 2 | no | — |
| 83 | C3×#353 | — | 3 | 2 | no | — |
| 84 | C3×AΣL(1,𝔽16) | — | 3 | 2 | no | — |
| 85 | C3×AΣL(1,𝔽16) | — | 3 | 2 | no | — |
| 86 | C3×AΣL(1,𝔽16) | — | 3 | 2 | no | — |
| 87 | C3×AΣL(1,𝔽16) | — | 3 | 2 | no | — |
| 88 | C22×C3×A4 | — | 4 | 2 | no | — |
| 89 | C2×C3×S4 | — | 4 | 1 | no | — |
| 90 | C2×C3×S4 | — | 4 | 2 | no | — |
| 91 | C2×C3×S4 | — | 8 | 4 | no | — |
| 92 | C2×C3×S4 | — | 8 | 2 | no | — |
| 93 | C3×D3×D4 | — | 16 | 1 | no | — |
| 94 | C3×#41⋊C3 | — | 8 | 1 | no | — |
| 95 | C3×C4×A4 | — | 4 | 1 | no | — |
| 96 | C3×C4×A4 | — | 8 | 1 | no | — |
| 97 | C3×SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 98 | C3×GL(2,𝔽3) | — | 8 | 1 | no | — |
| 99 | C3×#226 | — | 8 | 1 | no | — |
| 100 | #3549 | — | 3 | 1 | no | — |
| 101 | #3027 | — | 3 | 1 | no | — |
| 102 | #3027 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 103 | #3018 | — | 3 | 1 | no | — |
| 104 | #2199 | — | 3 | 2 | no | — |
| 105 | #2199 | — | 3 | 2 | no | — |
| 106 | #2196 | — | 3 | 2 | no | — |
| 107 | #2196 | — | 3 | 2 | no | — |
| 108 | #2126 | — | 3 | 1 | no | — |
| 109 | #2122 | — | 3 | 1 | no | — |
| 110 | #2122 | — | 3 | 1 | no | — |
| 111 | C22×S4 | — | 4 | 2 | no | — |
| 112 | C3×2−1+4 | — | 6 | 1 | no | — |
| 113 | C3×H(5,𝔽2) | — | 3 | 1 | no | — |
| 114 | C3×H(5,𝔽2) | — | 6 | 1 | no | — |
| 115 | C3×H(5,𝔽2) | C22×D3 | 1 | 1 | yes | characteristic |
| 116 | C2×C3×#41 | — | 3 | 1 | no | — |
| 117 | C2×C3×#41 | — | 3 | 1 | no | — |
| 118 | C2×C3×#41 | — | 6 | 1 | no | — |
| 119 | C2×C3×#41 | — | 6 | 1 | no | — |
| 120 | C2×C3×#41 | — | 6 | 2 | no | — |
| 121 | C22×C3×D4 | — | 3 | 1 | no | — |
| 122 | C22×C3×D4 | — | 6 | 2 | no | — |
| 123 | C22×C3×D4 | — | 6 | 1 | no | — |
| 124 | C22×C3×D4 | — | 6 | 2 | no | — |
| 125 | C22×C3×D4 | S4 | 1 | 1 | yes | characteristic, complemented |
| 126 | #997 | — | 2 | 1 | no | — |
| 127 | #997 | C23×C3 | 1 | 1 | yes | characteristic |
| 128 | D4×A4 | — | 4 | 1 | no | — |
| 129 | D4×A4 | — | 8 | 1 | no | — |
| 130 | GL(2,ℤ/4) | — | 4 | 2 | no | — |
| 131 | #985 | — | 8 | 1 | no | — |
| 132 | C4⋊S4 | — | 4 | 1 | no | — |
| 133 | C4⋊S4 | — | 8 | 1 | no | — |
| 134 | C4×S4 | — | 4 | 1 | no | — |
| 135 | C3×#137 | — | 6 | 1 | no | — |
| 136 | C3×#137 | — | 6 | 1 | no | — |
| 137 | C3×#137 | — | 12 | 1 | no | — |
| 138 | C3×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 139 | C3×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 140 | C3×AGL(1,ℤ/8) | — | 12 | 1 | no | — |
| 141 | C3×#135 | — | 12 | 1 | no | — |
| 142 | C3×#135 | — | 12 | 1 | no | — |
| 143 | C2×C3×M16 | — | 6 | 1 | no | — |
| 144 | C3×C4⋊Q8 | — | 3 | 1 | no | — |
| 145 | C3×C4⋊Q8 | — | 6 | 1 | no | — |
| 146 | C3×#127 | — | 3 | 1 | no | — |
| 147 | C3×#127 | — | 6 | 1 | no | — |
| 148 | C3×#127 | — | 6 | 1 | no | — |
| 149 | C3×#127 | — | 6 | 1 | no | — |
| 150 | C3×#127 | — | 6 | 2 | no | — |
| 151 | C3×#127 | — | 12 | 1 | no | — |
| 152 | C3×#124 | — | 3 | 1 | no | — |
| 153 | C3×#124 | — | 3 | 1 | no | — |
| 154 | C3×#124 | — | 6 | 2 | no | — |
| 155 | C3×#124 | — | 6 | 2 | no | — |
| 156 | C3×#124 | — | 6 | 2 | no | — |
| 157 | C3×#124 | — | 6 | 2 | no | — |
| 158 | C3×#124 | — | 6 | 1 | no | — |
| 159 | C3×#124 | — | 6 | 1 | no | — |
| 160 | C3×#124 | — | 6 | 2 | no | — |
| 161 | C3×#124 | — | 6 | 2 | no | — |
| 162 | C3×#124 | — | 12 | 1 | no | — |
| 163 | C3×#121 | — | 6 | 2 | no | — |
| 164 | C3×#121 | — | 6 | 2 | no | — |
| 165 | C3×#121 | — | 6 | 1 | no | — |
| 166 | C3×#121 | — | 6 | 1 | no | — |
| 167 | C3×#121 | — | 6 | 1 | no | — |
| 168 | C3×#121 | — | 6 | 1 | no | — |
| 169 | C3×#121 | — | 6 | 1 | no | — |
| 170 | C3×#121 | — | 6 | 2 | no | — |
| 171 | C3×#121 | — | 6 | 2 | no | — |
| 172 | C3×#121 | — | 6 | 2 | no | — |
| 173 | C3×#121 | — | 6 | 1 | no | — |
| 174 | C3×#121 | — | 6 | 1 | no | — |
| 175 | C3×#121 | — | 6 | 1 | no | — |
| 176 | C3×#121 | — | 12 | 1 | no | — |
| 177 | C3×#121 | — | 12 | 1 | no | — |
| 178 | C3×#120 | — | 3 | 2 | no | — |
| 179 | C3×#120 | — | 3 | 2 | no | — |
| 180 | C3×#120 | — | 3 | 2 | no | — |
| 181 | C3×#120 | — | 3 | 2 | no | — |
| 182 | C3×#120 | — | 6 | 2 | no | — |
| 183 | C3×#120 | — | 6 | 2 | no | — |
| 184 | C3×#120 | — | 6 | 2 | no | — |
| 185 | C3×#120 | — | 6 | 2 | no | — |
| 186 | C3×#120 | — | 6 | 2 | no | — |
| 187 | C3×#120 | — | 6 | 2 | no | — |
| 188 | C3×#120 | — | 6 | 2 | no | — |
| 189 | C3×#120 | — | 6 | 2 | no | — |
| 190 | C3×C4×D4 | — | 6 | 2 | no | — |
| 191 | C3×C4×D4 | — | 6 | 1 | no | — |
| 192 | C3×C4×D4 | — | 6 | 1 | no | — |
| 193 | C3×C4×D4 | — | 6 | 1 | no | — |
| 194 | C3×C4×D4 | — | 6 | 1 | no | — |
| 195 | C3×#117 | — | 3 | 1 | no | — |
| 196 | C3×#117 | — | 3 | 1 | no | — |
| 197 | C3×#117 | — | 6 | 2 | no | — |
| 198 | C3×#117 | — | 6 | 2 | no | — |
| 199 | C3×#117 | — | 6 | 1 | no | — |
| 200 | C3×#117 | — | 6 | 1 | no | — |
| 201 | C2×C3×C42 | — | 3 | 1 | no | — |
| 202 | C3×#104 | — | 6 | 1 | no | — |
| 203 | C3×#104 | — | 6 | 1 | no | — |
| 204 | C3×#104 | — | 6 | 1 | no | — |
| 205 | C3×#104 | — | 6 | 1 | no | — |
| 206 | C3×#101 | — | 6 | 1 | no | — |
| 207 | C3×#100 | — | 3 | 1 | no | — |
| 208 | C3×#100 | — | 3 | 1 | no | — |
| 209 | C3×#99 | — | 3 | 2 | no | — |
| 210 | C3×#99 | — | 3 | 2 | no | — |
| 211 | C3×#99 | — | 6 | 1 | no | — |
| 212 | C3×#99 | — | 6 | 2 | no | — |
| 213 | C3×#99 | — | 6 | 2 | no | — |
| 214 | C3×#99 | — | 6 | 1 | no | — |
| 215 | C22×C3×D3 | — | 16 | 2 | no | — |
| 216 | C2×C3×A4 | — | 4 | 1 | no | — |
| 217 | C2×C3×A4 | — | 8 | 1 | no | — |
| 218 | C2×C3×A4 | — | 8 | 2 | no | — |
| 219 | C3×S4 | — | 4 | 2 | no | — |
| 220 | C3×S4 | — | 8 | 2 | no | — |
| 221 | C3×S4 | — | 16 | 2 | no | — |
| 222 | C32×D4 | — | 16 | 1 | no | — |
| 223 | C3×#67 | — | 16 | 2 | no | — |
| 224 | C3×D12 | — | 16 | 1 | no | — |
| 225 | C3×C4×D3 | — | 16 | 1 | no | — |
| 226 | C3×SL(2,𝔽3) | — | 8 | 1 | no | — |
| 227 | #585 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 228 | #575 | — | 6 | 1 | no | — |
| 229 | H(3,𝔽4) | — | 3 | 2 | no | — |
| 230 | H(3,𝔽4) | — | 6 | 1 | no | — |
| 231 | #555 | — | 6 | 1 | no | — |
| 232 | #555 | — | 6 | 1 | no | — |
| 233 | #555 | — | 6 | 1 | no | — |
| 234 | D42 | — | 3 | 2 | no | — |
| 235 | D42 | — | 6 | 1 | no | — |
| 236 | D42 | — | 6 | 1 | no | — |
| 237 | #535 | — | 3 | 1 | no | — |
| 238 | #535 | — | 3 | 1 | no | — |
| 239 | #535 | — | 6 | 2 | no | — |
| 240 | #535 | — | 6 | 2 | no | — |
| 241 | #535 | — | 6 | 1 | no | — |
| 242 | #535 | — | 6 | 1 | no | — |
| 243 | #532 | — | 3 | 1 | no | — |
| 244 | #532 | — | 6 | 1 | no | — |
| 245 | B(4,𝔽2) | — | 3 | 2 | no | — |
| 246 | B(4,𝔽2) | — | 3 | 2 | no | — |
| 247 | B(4,𝔽2) | — | 3 | 2 | no | — |
| 248 | B(4,𝔽2) | — | 6 | 2 | no | — |
| 249 | B(4,𝔽2) | C2×C3×D3 | 1 | 2 | yes | complemented |
| 250 | #456 | — | 6 | 1 | no | — |
| 251 | #455 | — | 3 | 1 | no | — |
| 252 | #455 | — | 3 | 1 | no | — |
| 253 | #454 | — | 6 | 1 | no | — |
| 254 | #453 | — | 3 | 1 | no | — |
| 255 | #453 | — | 3 | 1 | no | — |
| 256 | C2×#104 | — | 6 | 1 | no | — |
| 257 | #413 | — | 3 | 1 | no | — |
| 258 | #410 | — | 3 | 1 | no | — |
| 259 | #410 | — | 3 | 1 | no | — |
| 260 | #410 | — | 6 | 1 | no | — |
| 261 | #354 | — | 3 | 2 | no | — |
| 262 | #353 | — | 3 | 2 | no | — |
| 263 | AΣL(1,𝔽16) | — | 3 | 2 | no | — |
| 264 | AΣL(1,𝔽16) | — | 3 | 2 | no | — |
| 265 | AΣL(1,𝔽16) | — | 3 | 2 | no | — |
| 266 | AΣL(1,𝔽16) | — | 3 | 2 | no | — |
| 267 | C24×C3 | — | 3 | 2 | no | — |
| 268 | C24×C3 | — | 6 | 2 | no | — |
| 269 | C24×C3 | C2×S4 | 1 | 2 | yes | — |
| 270 | C22×A4 | — | 4 | 2 | no | — |
| 271 | C22×A4 | — | 8 | 2 | no | — |
| 272 | C2×S4 | — | 4 | 1 | no | — |
| 273 | C2×S4 | — | 4 | 2 | no | — |
| 274 | C2×S4 | — | 8 | 2 | no | — |
| 275 | C2×S4 | — | 8 | 4 | no | — |
| 276 | C3×#41 | — | 2 | 1 | no | — |
| 277 | C3×#41 | — | 6 | 1 | no | — |
| 278 | C3×#41 | — | 6 | 1 | no | — |
| 279 | C3×#41 | — | 6 | 1 | no | — |
| 280 | C3×#41 | — | 12 | 1 | no | — |
| 281 | C3×#41 | — | 12 | 1 | no | — |
| 282 | C3×#41 | — | 12 | 1 | no | — |
| 283 | C3×#41 | — | 12 | 1 | no | — |
| 284 | C3×#41 | — | 12 | 1 | no | — |
| 285 | C3×#41 | — | 12 | 1 | no | — |
| 286 | C3×#41 | — | 12 | 1 | no | — |
| 287 | C3×#41 | — | 24 | 4 | no | — |
| 288 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 289 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 290 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 291 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 292 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 293 | C2×C3×D4 | — | 3 | 1 | no | — |
| 294 | C2×C3×D4 | — | 3 | 1 | no | — |
| 295 | C2×C3×D4 | — | 3 | 1 | no | — |
| 296 | C2×C3×D4 | — | 3 | 1 | no | — |
| 297 | C2×C3×D4 | — | 6 | 1 | no | — |
| 298 | C2×C3×D4 | — | 6 | 1 | no | — |
| 299 | C2×C3×D4 | — | 6 | 1 | no | — |
| 300 | C2×C3×D4 | — | 6 | 1 | no | — |
| 301 | C2×C3×D4 | — | 6 | 1 | no | — |
| 302 | C2×C3×D4 | — | 6 | 1 | no | — |
| 303 | C2×C3×D4 | — | 6 | 1 | no | — |
| 304 | C2×C3×D4 | — | 6 | 1 | no | — |
| 305 | C2×C3×D4 | — | 6 | 1 | no | — |
| 306 | C2×C3×D4 | — | 6 | 2 | no | — |
| 307 | C2×C3×D4 | — | 6 | 1 | no | — |
| 308 | C2×C3×D4 | — | 6 | 2 | no | — |
| 309 | C2×C3×D4 | — | 6 | 2 | no | — |
| 310 | C2×C3×D4 | — | 6 | 2 | no | — |
| 311 | C2×C3×D4 | — | 6 | 1 | no | — |
| 312 | C2×C3×D4 | — | 6 | 2 | no | — |
| 313 | C2×C3×D4 | — | 6 | 2 | no | — |
| 314 | C2×C3×D4 | — | 6 | 2 | no | — |
| 315 | C2×C3×D4 | — | 6 | 2 | no | — |
| 316 | C2×C3×D4 | — | 6 | 2 | no | — |
| 317 | C2×C3×D4 | — | 12 | 1 | no | — |
| 318 | C2×C3×D4 | — | 12 | 1 | no | — |
| 319 | C2×C3×D4 | — | 12 | 1 | no | — |
| 320 | C2×C3×D4 | — | 12 | 2 | no | — |
| 321 | C2×C3×D4 | — | 12 | 2 | no | — |
| 322 | C2×C3×D4 | — | 24 | 1 | no | — |
| 323 | C2×C3×D4 | — | 24 | 4 | no | — |
| 324 | C2×C3×D4 | — | 24 | 1 | no | — |
| 325 | C2×C3×D4 | — | 24 | 4 | no | — |
| 326 | C22×C3×C4 | — | 2 | 1 | no | — |
| 327 | C22×C3×C4 | — | 3 | 1 | no | — |
| 328 | C22×C3×C4 | — | 3 | 1 | no | — |
| 329 | C22×C3×C4 | — | 6 | 1 | no | — |
| 330 | C22×C3×C4 | — | 6 | 1 | no | — |
| 331 | C22×C3×C4 | — | 6 | 1 | no | — |
| 332 | C22×C3×C4 | — | 6 | 2 | no | — |
| 333 | C22×C3×C4 | — | 6 | 2 | no | — |
| 334 | C22×C3×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 335 | D3×D4 | — | 16 | 1 | no | — |
| 336 | #41⋊C3 | — | 8 | 1 | no | — |
| 337 | #41⋊C3 | — | 16 | 1 | no | — |
| 338 | C4×A4 | — | 4 | 1 | no | — |
| 339 | C4×A4 | — | 8 | 1 | no | — |
| 340 | C4×A4 | — | 8 | 1 | no | — |
| 341 | C4×A4 | — | 16 | 1 | no | — |
| 342 | SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 343 | GL(2,𝔽3) | — | 8 | 1 | no | — |
| 344 | #226 | — | 8 | 1 | no | — |
| 345 | C3×Q16 | — | 12 | 1 | no | — |
| 346 | C3×Q16 | — | 12 | 1 | no | — |
| 347 | C3×SD16 | — | 12 | 1 | no | — |
| 348 | C3×SD16 | — | 12 | 1 | no | — |
| 349 | C3×SD16 | — | 12 | 1 | no | — |
| 350 | C3×SD16 | — | 12 | 1 | no | — |
| 351 | C3×D8 | — | 12 | 1 | no | — |
| 352 | C3×D8 | — | 12 | 1 | no | — |
| 353 | C3×M16 | — | 6 | 1 | no | — |
| 354 | C3×M16 | — | 6 | 1 | no | — |
| 355 | C3×M16 | — | 12 | 1 | no | — |
| 356 | C2×C3×C8 | — | 12 | 1 | no | — |
| 357 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 358 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 359 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 360 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 361 | C3×C4⋊C4 | — | 6 | 2 | no | — |
| 362 | C3×C4⋊C4 | — | 12 | 1 | no | — |
| 363 | C3×C22⋊C4 | — | 3 | 2 | no | — |
| 364 | C3×C22⋊C4 | — | 3 | 2 | no | — |
| 365 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 366 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 367 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 368 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 369 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 370 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 371 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 372 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 373 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 374 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 375 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 376 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 377 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 378 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 379 | C3×C22⋊C4 | — | 12 | 2 | no | — |
| 380 | C3×C22⋊C4 | — | 12 | 2 | no | — |
| 381 | C3×C42 | — | 3 | 1 | no | — |
| 382 | C3×C42 | — | 3 | 1 | no | — |
| 383 | C3×C42 | — | 6 | 1 | no | — |
| 384 | C3×C42 | — | 6 | 1 | no | — |
| 385 | C3×C42 | — | 6 | 1 | no | — |
| 386 | C3×C42 | — | 6 | 2 | no | — |
| 387 | C3×C42 | — | 12 | 1 | no | — |
| 388 | C22×C32 | — | 16 | 2 | no | — |
| 389 | C2×C3×D3 | — | 16 | 1 | no | — |
| 390 | C2×C3×D3 | — | 16 | 2 | no | — |
| 391 | C2×C3×D3 | — | 32 | 4 | no | — |
| 392 | C3×A4 | — | 4 | 1 | no | — |
| 393 | C3×A4 | — | 8 | 1 | no | — |
| 394 | C32×C4 | — | 16 | 1 | no | — |
| 395 | C3×Dic3 | — | 16 | 1 | no | — |
| 396 | 2−1+4 | — | 6 | 1 | no | — |
| 397 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 398 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 399 | H(5,𝔽2) | C22×C3×D3 | 1 | 1 | yes | characteristic |
| 400 | C2×#41 | — | 3 | 1 | no | — |
| 401 | C2×#41 | — | 3 | 1 | no | — |
| 402 | C2×#41 | — | 6 | 1 | no | — |
| 403 | C2×#41 | — | 6 | 1 | no | — |
| 404 | C2×#41 | — | 6 | 2 | no | — |
| 405 | C22×D4 | — | 3 | 1 | no | — |
| 406 | C22×D4 | — | 6 | 2 | no | — |
| 407 | C22×D4 | — | 6 | 1 | no | — |
| 408 | C22×D4 | — | 6 | 2 | no | — |
| 409 | C22×D4 | C3×S4 | 1 | 1 | yes | characteristic, complemented |
| 410 | #137 | — | 6 | 1 | no | — |
| 411 | #137 | — | 6 | 1 | no | — |
| 412 | #137 | — | 12 | 1 | no | — |
| 413 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 414 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 415 | AGL(1,ℤ/8) | — | 12 | 1 | no | — |
| 416 | #135 | — | 12 | 1 | no | — |
| 417 | #135 | — | 12 | 1 | no | — |
| 418 | C2×M16 | — | 6 | 1 | no | — |
| 419 | C4⋊Q8 | — | 3 | 1 | no | — |
| 420 | C4⋊Q8 | — | 6 | 1 | no | — |
| 421 | #127 | — | 3 | 1 | no | — |
| 422 | #127 | — | 6 | 1 | no | — |
| 423 | #127 | — | 6 | 1 | no | — |
| 424 | #127 | — | 6 | 1 | no | — |
| 425 | #127 | — | 6 | 2 | no | — |
| 426 | #127 | — | 12 | 1 | no | — |
| 427 | #124 | — | 3 | 1 | no | — |
| 428 | #124 | — | 3 | 1 | no | — |
| 429 | #124 | — | 6 | 2 | no | — |
| 430 | #124 | — | 6 | 2 | no | — |
| 431 | #124 | — | 6 | 2 | no | — |
| 432 | #124 | — | 6 | 1 | no | — |
| 433 | #124 | — | 6 | 1 | no | — |
| 434 | #124 | — | 6 | 2 | no | — |
| 435 | #124 | — | 6 | 2 | no | — |
| 436 | #124 | — | 6 | 2 | no | — |
| 437 | #124 | — | 12 | 1 | no | — |
| 438 | #121 | — | 6 | 2 | no | — |
| 439 | #121 | — | 6 | 2 | no | — |
| 440 | #121 | — | 6 | 1 | no | — |
| 441 | #121 | — | 6 | 1 | no | — |
| 442 | #121 | — | 6 | 1 | no | — |
| 443 | #121 | — | 6 | 1 | no | — |
| 444 | #121 | — | 6 | 1 | no | — |
| 445 | #121 | — | 6 | 2 | no | — |
| 446 | #121 | — | 6 | 2 | no | — |
| 447 | #121 | — | 6 | 2 | no | — |
| 448 | #121 | — | 6 | 1 | no | — |
| 449 | #121 | — | 6 | 1 | no | — |
| 450 | #121 | — | 6 | 1 | no | — |
| 451 | #121 | — | 12 | 1 | no | — |
| 452 | #121 | — | 12 | 1 | no | — |
| 453 | #120 | — | 3 | 2 | no | — |
| 454 | #120 | — | 3 | 2 | no | — |
| 455 | #120 | — | 3 | 2 | no | — |
| 456 | #120 | — | 3 | 2 | no | — |
| 457 | #120 | — | 6 | 2 | no | — |
| 458 | #120 | — | 6 | 2 | no | — |
| 459 | #120 | — | 6 | 2 | no | — |
| 460 | #120 | — | 6 | 2 | no | — |
| 461 | #120 | — | 6 | 2 | no | — |
| 462 | #120 | — | 6 | 2 | no | — |
| 463 | #120 | — | 6 | 2 | no | — |
| 464 | #120 | — | 6 | 2 | no | — |
| 465 | C4×D4 | — | 6 | 2 | no | — |
| 466 | C4×D4 | — | 6 | 1 | no | — |
| 467 | C4×D4 | — | 6 | 1 | no | — |
| 468 | C4×D4 | — | 6 | 1 | no | — |
| 469 | C4×D4 | — | 6 | 1 | no | — |
| 470 | #117 | — | 3 | 1 | no | — |
| 471 | #117 | — | 3 | 1 | no | — |
| 472 | #117 | — | 6 | 2 | no | — |
| 473 | #117 | — | 6 | 2 | no | — |
| 474 | #117 | — | 6 | 1 | no | — |
| 475 | #117 | — | 6 | 1 | no | — |
| 476 | C2×C42 | — | 3 | 1 | no | — |
| 477 | #104 | — | 6 | 1 | no | — |
| 478 | #104 | — | 6 | 1 | no | — |
| 479 | #104 | — | 6 | 1 | no | — |
| 480 | #104 | — | 6 | 1 | no | — |
| 481 | #101 | — | 6 | 1 | no | — |
| 482 | #100 | — | 3 | 1 | no | — |
| 483 | #100 | — | 3 | 1 | no | — |
| 484 | #99 | — | 3 | 2 | no | — |
| 485 | #99 | — | 3 | 2 | no | — |
| 486 | #99 | — | 6 | 1 | no | — |
| 487 | #99 | — | 6 | 2 | no | — |
| 488 | #99 | — | 6 | 2 | no | — |
| 489 | #99 | — | 6 | 1 | no | — |
| 490 | C23×C3 | — | 2 | 1 | no | — |
| 491 | C23×C3 | — | 3 | 1 | no | — |
| 492 | C23×C3 | — | 3 | 1 | no | — |
| 493 | C23×C3 | — | 6 | 2 | no | — |
| 494 | C23×C3 | — | 6 | 1 | no | — |
| 495 | C23×C3 | — | 6 | 2 | no | — |
| 496 | C23×C3 | — | 6 | 1 | no | — |
| 497 | C23×C3 | — | 8 | 2 | no | — |
| 498 | C23×C3 | — | 12 | 2 | no | — |
| 499 | C23×C3 | — | 24 | 2 | no | — |
| 500 | C23×C3 | — | 24 | 2 | no | — |
| 501 | C23×C3 | — | 24 | 2 | no | — |
| 502 | C23×C3 | — | 24 | 2 | no | — |
| 503 | C23×C3 | C22×S4 | 1 | 1 | yes | characteristic |
| 504 | C22×D3 | — | 16 | 2 | no | — |
| 505 | C2×A4 | — | 4 | 1 | no | — |
| 506 | C2×A4 | — | 8 | 1 | no | — |
| 507 | C2×A4 | — | 8 | 2 | no | — |
| 508 | C2×A4 | — | 8 | 1 | no | — |
| 509 | C2×A4 | — | 16 | 1 | no | — |
| 510 | C2×A4 | — | 16 | 2 | no | — |
| 511 | S4 | — | 4 | 2 | no | — |
| 512 | S4 | — | 8 | 2 | no | — |
| 513 | S4 | — | 16 | 2 | no | — |
| 514 | C3×Q8 | — | 2 | 1 | no | — |
| 515 | C3×Q8 | — | 6 | 1 | no | — |
| 516 | C3×Q8 | — | 12 | 1 | no | — |
| 517 | C3×Q8 | — | 12 | 1 | no | — |
| 518 | C3×Q8 | — | 24 | 2 | no | — |
| 519 | C3×D4 | — | 4 | 1 | no | — |
| 520 | C3×D4 | — | 6 | 1 | no | — |
| 521 | C3×D4 | — | 6 | 1 | no | — |
| 522 | C3×D4 | — | 12 | 1 | no | — |
| 523 | C3×D4 | — | 12 | 1 | no | — |
| 524 | C3×D4 | — | 12 | 1 | no | — |
| 525 | C3×D4 | — | 12 | 1 | no | — |
| 526 | C3×D4 | — | 12 | 1 | no | — |
| 527 | C3×D4 | — | 12 | 2 | no | — |
| 528 | C3×D4 | — | 12 | 1 | no | — |
| 529 | C3×D4 | — | 12 | 1 | no | — |
| 530 | C3×D4 | — | 12 | 4 | no | — |
| 531 | C3×D4 | — | 12 | 2 | no | — |
| 532 | C3×D4 | — | 12 | 1 | no | — |
| 533 | C3×D4 | — | 16 | 1 | no | — |
| 534 | C3×D4 | — | 24 | 1 | no | — |
| 535 | C3×D4 | — | 24 | 2 | no | — |
| 536 | C3×D4 | — | 24 | 2 | no | — |
| 537 | C3×D4 | — | 24 | 1 | no | — |
| 538 | C3×D4 | — | 24 | 2 | no | — |
| 539 | C3×D4 | — | 24 | 2 | no | — |
| 540 | C3×D4 | — | 24 | 2 | no | — |
| 541 | C3×D4 | — | 24 | 2 | no | — |
| 542 | C3×D4 | — | 24 | 2 | no | — |
| 543 | C3×D4 | — | 24 | 2 | no | — |
| 544 | C3×D4 | — | 32 | 1 | no | — |
| 545 | C3×D4 | — | 48 | 2 | no | — |
| 546 | C3×D4 | — | 48 | 2 | no | — |
| 547 | C2×C3×C4 | — | 3 | 1 | no | — |
| 548 | C2×C3×C4 | — | 3 | 1 | no | — |
| 549 | C2×C3×C4 | — | 3 | 1 | no | — |
| 550 | C2×C3×C4 | — | 3 | 1 | no | — |
| 551 | C2×C3×C4 | — | 6 | 1 | no | — |
| 552 | C2×C3×C4 | — | 6 | 1 | no | — |
| 553 | C2×C3×C4 | — | 6 | 1 | no | — |
| 554 | C2×C3×C4 | — | 6 | 1 | no | — |
| 555 | C2×C3×C4 | — | 6 | 1 | no | — |
| 556 | C2×C3×C4 | — | 6 | 1 | no | — |
| 557 | C2×C3×C4 | — | 6 | 1 | no | — |
| 558 | C2×C3×C4 | — | 6 | 1 | no | — |
| 559 | C2×C3×C4 | — | 6 | 2 | no | — |
| 560 | C2×C3×C4 | — | 6 | 2 | no | — |
| 561 | C2×C3×C4 | — | 6 | 1 | no | — |
| 562 | C2×C3×C4 | — | 12 | 1 | no | — |
| 563 | C2×C3×C4 | — | 12 | 1 | no | — |
| 564 | C2×C3×C4 | — | 12 | 4 | no | — |
| 565 | C2×C3×C4 | — | 12 | 4 | no | — |
| 566 | C2×C3×C4 | — | 12 | 2 | no | — |
| 567 | C2×C3×C4 | — | 12 | 1 | no | — |
| 568 | C2×C3×C4 | — | 12 | 2 | no | — |
| 569 | #67 | — | 16 | 2 | no | — |
| 570 | D12 | — | 16 | 1 | no | — |
| 571 | C4×D3 | — | 16 | 1 | no | — |
| 572 | SL(2,𝔽3) | — | 8 | 1 | no | — |
| 573 | SL(2,𝔽3) | — | 16 | 1 | no | — |
| 574 | C3×C8 | — | 12 | 1 | no | — |
| 575 | C3×C8 | — | 12 | 1 | no | — |
| 576 | C2×C32 | — | 16 | 1 | no | — |
| 577 | C2×C32 | — | 32 | 2 | no | — |
| 578 | C3×D3 | — | 16 | 2 | no | — |
| 579 | C3×D3 | — | 32 | 2 | no | — |
| 580 | C24 | — | 3 | 2 | no | — |
| 581 | C24 | — | 6 | 2 | no | — |
| 582 | C24 | C2×C3×S4 | 1 | 2 | yes | — |
| 583 | #41 | — | 2 | 1 | no | — |
| 584 | #41 | — | 6 | 1 | no | — |
| 585 | #41 | — | 6 | 1 | no | — |
| 586 | #41 | — | 6 | 1 | no | — |
| 587 | #41 | — | 12 | 1 | no | — |
| 588 | #41 | — | 12 | 1 | no | — |
| 589 | #41 | — | 12 | 1 | no | — |
| 590 | #41 | — | 12 | 1 | no | — |
| 591 | #41 | — | 12 | 1 | no | — |
| 592 | #41 | — | 12 | 1 | no | — |
| 593 | #41 | — | 12 | 1 | no | — |
| 594 | #41 | — | 24 | 4 | no | — |
| 595 | C2×Q8 | — | 3 | 1 | no | — |
| 596 | C2×Q8 | — | 3 | 1 | no | — |
| 597 | C2×Q8 | — | 6 | 1 | no | — |
| 598 | C2×Q8 | — | 6 | 2 | no | — |
| 599 | C2×Q8 | — | 6 | 1 | no | — |
| 600 | C2×D4 | — | 3 | 1 | no | — |
| 601 | C2×D4 | — | 3 | 1 | no | — |
| 602 | C2×D4 | — | 3 | 1 | no | — |
| 603 | C2×D4 | — | 3 | 1 | no | — |
| 604 | C2×D4 | — | 6 | 1 | no | — |
| 605 | C2×D4 | — | 6 | 1 | no | — |
| 606 | C2×D4 | — | 6 | 1 | no | — |
| 607 | C2×D4 | — | 6 | 1 | no | — |
| 608 | C2×D4 | — | 6 | 1 | no | — |
| 609 | C2×D4 | — | 6 | 1 | no | — |
| 610 | C2×D4 | — | 6 | 1 | no | — |
| 611 | C2×D4 | — | 6 | 1 | no | — |
| 612 | C2×D4 | — | 6 | 1 | no | — |
| 613 | C2×D4 | — | 6 | 2 | no | — |
| 614 | C2×D4 | — | 6 | 1 | no | — |
| 615 | C2×D4 | — | 6 | 2 | no | — |
| 616 | C2×D4 | — | 6 | 2 | no | — |
| 617 | C2×D4 | — | 6 | 2 | no | — |
| 618 | C2×D4 | — | 6 | 1 | no | — |
| 619 | C2×D4 | — | 6 | 2 | no | — |
| 620 | C2×D4 | — | 6 | 2 | no | — |
| 621 | C2×D4 | — | 6 | 2 | no | — |
| 622 | C2×D4 | — | 6 | 2 | no | — |
| 623 | C2×D4 | — | 6 | 2 | no | — |
| 624 | C2×D4 | — | 12 | 1 | no | — |
| 625 | C2×D4 | — | 12 | 1 | no | — |
| 626 | C2×D4 | — | 12 | 1 | no | — |
| 627 | C2×D4 | — | 12 | 2 | no | — |
| 628 | C2×D4 | — | 12 | 2 | no | — |
| 629 | C2×D4 | — | 24 | 1 | no | — |
| 630 | C2×D4 | — | 24 | 4 | no | — |
| 631 | C2×D4 | — | 24 | 1 | no | — |
| 632 | C2×D4 | — | 24 | 4 | no | — |
| 633 | C22×C4 | — | 2 | 1 | no | — |
| 634 | C22×C4 | — | 3 | 1 | no | — |
| 635 | C22×C4 | — | 3 | 1 | no | — |
| 636 | C22×C4 | — | 6 | 1 | no | — |
| 637 | C22×C4 | — | 6 | 1 | no | — |
| 638 | C22×C4 | — | 6 | 1 | no | — |
| 639 | C22×C4 | — | 6 | 2 | no | — |
| 640 | C22×C4 | — | 6 | 2 | no | — |
| 641 | C22×C4 | C2×C3×S4 | 1 | 1 | yes | characteristic |
| 642 | Q16 | — | 12 | 1 | no | — |
| 643 | Q16 | — | 12 | 1 | no | — |
| 644 | SD16 | — | 12 | 1 | no | — |
| 645 | SD16 | — | 12 | 1 | no | — |
| 646 | SD16 | — | 12 | 1 | no | — |
| 647 | SD16 | — | 12 | 1 | no | — |
| 648 | D8 | — | 12 | 1 | no | — |
| 649 | D8 | — | 12 | 1 | no | — |
| 650 | M16 | — | 6 | 1 | no | — |
| 651 | M16 | — | 6 | 1 | no | — |
| 652 | M16 | — | 12 | 1 | no | — |
| 653 | C2×C8 | — | 12 | 1 | no | — |
| 654 | C4⋊C4 | — | 6 | 1 | no | — |
| 655 | C4⋊C4 | — | 6 | 1 | no | — |
| 656 | C4⋊C4 | — | 6 | 1 | no | — |
| 657 | C4⋊C4 | — | 6 | 1 | no | — |
| 658 | C4⋊C4 | — | 6 | 2 | no | — |
| 659 | C4⋊C4 | — | 12 | 1 | no | — |
| 660 | C22⋊C4 | — | 3 | 2 | no | — |
| 661 | C22⋊C4 | — | 3 | 2 | no | — |
| 662 | C22⋊C4 | — | 6 | 2 | no | — |
| 663 | C22⋊C4 | — | 6 | 2 | no | — |
| 664 | C22⋊C4 | — | 6 | 2 | no | — |
| 665 | C22⋊C4 | — | 6 | 2 | no | — |
| 666 | C22⋊C4 | — | 6 | 1 | no | — |
| 667 | C22⋊C4 | — | 6 | 1 | no | — |
| 668 | C22⋊C4 | — | 6 | 1 | no | — |
| 669 | C22⋊C4 | — | 6 | 2 | no | — |
| 670 | C22⋊C4 | — | 6 | 2 | no | — |
| 671 | C22⋊C4 | — | 6 | 2 | no | — |
| 672 | C22⋊C4 | — | 6 | 2 | no | — |
| 673 | C22⋊C4 | — | 6 | 2 | no | — |
| 674 | C22⋊C4 | — | 6 | 1 | no | — |
| 675 | C22⋊C4 | — | 6 | 2 | no | — |
| 676 | C22⋊C4 | — | 12 | 2 | no | — |
| 677 | C22⋊C4 | — | 12 | 2 | no | — |
| 678 | C42 | — | 3 | 1 | no | — |
| 679 | C42 | — | 3 | 1 | no | — |
| 680 | C42 | — | 6 | 1 | no | — |
| 681 | C42 | — | 6 | 1 | no | — |
| 682 | C42 | — | 6 | 1 | no | — |
| 683 | C42 | — | 6 | 2 | no | — |
| 684 | C42 | — | 12 | 1 | no | — |
| 685 | C22×C3 | — | 3 | 1 | no | — |
| 686 | C22×C3 | — | 4 | 1 | no | — |
| 687 | C22×C3 | — | 4 | 2 | no | — |
| 688 | C22×C3 | — | 6 | 1 | no | — |
| 689 | C22×C3 | — | 6 | 1 | no | — |
| 690 | C22×C3 | — | 8 | 1 | no | — |
| 691 | C22×C3 | — | 12 | 2 | no | — |
| 692 | C22×C3 | — | 12 | 2 | no | — |
| 693 | C22×C3 | — | 12 | 1 | no | — |
| 694 | C22×C3 | — | 12 | 1 | no | — |
| 695 | C22×C3 | — | 12 | 2 | no | — |
| 696 | C22×C3 | — | 12 | 2 | no | — |
| 697 | C22×C3 | — | 12 | 1 | no | — |
| 698 | C22×C3 | — | 12 | 1 | no | — |
| 699 | C22×C3 | — | 12 | 1 | no | — |
| 700 | C22×C3 | — | 12 | 2 | no | — |
| 701 | C22×C3 | — | 16 | 2 | no | — |
| 702 | C22×C3 | — | 24 | 1 | no | — |
| 703 | C22×C3 | — | 24 | 2 | no | — |
| 704 | C22×C3 | — | 24 | 2 | no | — |
| 705 | C22×C3 | — | 32 | 2 | no | — |
| 706 | C22×C3 | — | 48 | 4 | no | — |
| 707 | C2×D3 | — | 16 | 1 | no | — |
| 708 | C2×D3 | — | 16 | 2 | no | — |
| 709 | C2×D3 | — | 32 | 4 | no | — |
| 710 | A4 | — | 4 | 1 | no | — |
| 711 | A4 | — | 8 | 1 | no | — |
| 712 | A4 | — | 8 | 1 | no | — |
| 713 | A4 | — | 16 | 1 | no | — |
| 714 | C3×C4 | — | 3 | 1 | no | — |
| 715 | C3×C4 | — | 6 | 2 | no | — |
| 716 | C3×C4 | — | 6 | 1 | no | — |
| 717 | C3×C4 | — | 6 | 1 | no | — |
| 718 | C3×C4 | — | 12 | 2 | no | — |
| 719 | C3×C4 | — | 12 | 2 | no | — |
| 720 | C3×C4 | — | 12 | 1 | no | — |
| 721 | C3×C4 | — | 12 | 1 | no | — |
| 722 | C3×C4 | — | 16 | 1 | no | — |
| 723 | C3×C4 | — | 24 | 2 | no | — |
| 724 | C3×C4 | — | 32 | 1 | no | — |
| 725 | C3×C4 | #1020⋊C2 | 1 | 1 | yes | characteristic |
| 726 | Dic3 | — | 16 | 1 | no | — |
| 727 | C32 | — | 16 | 1 | no | Sylow |
| 728 | C23 | — | 2 | 1 | no | — |
| 729 | C23 | — | 3 | 1 | no | — |
| 730 | C23 | — | 3 | 1 | no | — |
| 731 | C23 | — | 6 | 2 | no | — |
| 732 | C23 | — | 6 | 1 | no | — |
| 733 | C23 | — | 6 | 2 | no | — |
| 734 | C23 | — | 6 | 1 | no | — |
| 735 | C23 | — | 8 | 2 | no | — |
| 736 | C23 | — | 12 | 2 | no | — |
| 737 | C23 | — | 24 | 2 | no | — |
| 738 | C23 | — | 24 | 2 | no | — |
| 739 | C23 | — | 24 | 2 | no | — |
| 740 | C23 | — | 24 | 2 | no | — |
| 741 | C23 | C22×C3×S4 | 1 | 1 | yes | characteristic |
| 742 | Q8 | — | 2 | 1 | no | — |
| 743 | Q8 | — | 6 | 1 | no | — |
| 744 | Q8 | — | 12 | 1 | no | — |
| 745 | Q8 | — | 12 | 1 | no | — |
| 746 | Q8 | — | 24 | 2 | no | — |
| 747 | D4 | — | 4 | 1 | no | — |
| 748 | D4 | — | 6 | 1 | no | — |
| 749 | D4 | — | 6 | 1 | no | — |
| 750 | D4 | — | 12 | 1 | no | — |
| 751 | D4 | — | 12 | 1 | no | — |
| 752 | D4 | — | 12 | 1 | no | — |
| 753 | D4 | — | 12 | 1 | no | — |
| 754 | D4 | — | 12 | 1 | no | — |
| 755 | D4 | — | 12 | 2 | no | — |
| 756 | D4 | — | 12 | 1 | no | — |
| 757 | D4 | — | 12 | 1 | no | — |
| 758 | D4 | — | 12 | 4 | no | — |
| 759 | D4 | — | 12 | 2 | no | — |
| 760 | D4 | — | 12 | 1 | no | — |
| 761 | D4 | — | 24 | 1 | no | — |
| 762 | D4 | — | 24 | 2 | no | — |
| 763 | D4 | — | 24 | 2 | no | — |
| 764 | D4 | — | 24 | 1 | no | — |
| 765 | D4 | — | 24 | 2 | no | — |
| 766 | D4 | — | 24 | 2 | no | — |
| 767 | D4 | — | 24 | 2 | no | — |
| 768 | D4 | — | 24 | 2 | no | — |
| 769 | D4 | — | 24 | 2 | no | — |
| 770 | D4 | — | 24 | 2 | no | — |
| 771 | D4 | — | 48 | 2 | no | — |
| 772 | D4 | — | 48 | 2 | no | — |
| 773 | C2×C4 | — | 3 | 1 | no | — |
| 774 | C2×C4 | — | 3 | 1 | no | — |
| 775 | C2×C4 | — | 3 | 1 | no | — |
| 776 | C2×C4 | — | 3 | 1 | no | — |
| 777 | C2×C4 | — | 6 | 1 | no | — |
| 778 | C2×C4 | — | 6 | 1 | no | — |
| 779 | C2×C4 | — | 6 | 1 | no | — |
| 780 | C2×C4 | — | 6 | 1 | no | — |
| 781 | C2×C4 | — | 6 | 1 | no | — |
| 782 | C2×C4 | — | 6 | 1 | no | — |
| 783 | C2×C4 | — | 6 | 1 | no | — |
| 784 | C2×C4 | — | 6 | 1 | no | — |
| 785 | C2×C4 | — | 6 | 2 | no | — |
| 786 | C2×C4 | — | 6 | 2 | no | — |
| 787 | C2×C4 | — | 6 | 1 | no | — |
| 788 | C2×C4 | — | 12 | 1 | no | — |
| 789 | C2×C4 | — | 12 | 1 | no | — |
| 790 | C2×C4 | — | 12 | 4 | no | — |
| 791 | C2×C4 | — | 12 | 4 | no | — |
| 792 | C2×C4 | — | 12 | 2 | no | — |
| 793 | C2×C4 | — | 12 | 1 | no | — |
| 794 | C2×C4 | — | 12 | 2 | no | — |
| 795 | C8 | — | 12 | 1 | no | — |
| 796 | C8 | — | 12 | 1 | no | — |
| 797 | C2×C3 | — | 6 | 1 | no | — |
| 798 | C2×C3 | — | 8 | 2 | no | — |
| 799 | C2×C3 | — | 12 | 1 | no | — |
| 800 | C2×C3 | — | 12 | 1 | no | — |
| 801 | C2×C3 | — | 16 | 1 | no | — |
| 802 | C2×C3 | — | 24 | 2 | no | — |
| 803 | C2×C3 | — | 24 | 1 | no | — |
| 804 | C2×C3 | — | 32 | 2 | no | — |
| 805 | C2×C3 | — | 32 | 1 | no | — |
| 806 | C2×C3 | — | 64 | 2 | no | — |
| 807 | C2×C3 | C2×#1020⋊C2 | 1 | 1 | yes | characteristic |
| 808 | D3 | — | 16 | 2 | no | — |
| 809 | D3 | — | 32 | 2 | no | — |
| 810 | C22 | — | 3 | 1 | no | — |
| 811 | C22 | — | 4 | 1 | no | — |
| 812 | C22 | — | 4 | 2 | no | — |
| 813 | C22 | — | 6 | 1 | no | — |
| 814 | C22 | — | 6 | 1 | no | — |
| 815 | C22 | — | 8 | 1 | no | — |
| 816 | C22 | — | 12 | 2 | no | — |
| 817 | C22 | — | 12 | 2 | no | — |
| 818 | C22 | — | 12 | 1 | no | — |
| 819 | C22 | — | 12 | 1 | no | — |
| 820 | C22 | — | 12 | 2 | no | — |
| 821 | C22 | — | 12 | 2 | no | — |
| 822 | C22 | — | 12 | 1 | no | — |
| 823 | C22 | — | 12 | 1 | no | — |
| 824 | C22 | — | 12 | 1 | no | — |
| 825 | C22 | — | 12 | 2 | no | — |
| 826 | C22 | — | 24 | 1 | no | — |
| 827 | C22 | — | 24 | 2 | no | — |
| 828 | C22 | — | 24 | 2 | no | — |
| 829 | C22 | — | 48 | 4 | no | — |
| 830 | C4 | — | 3 | 1 | no | — |
| 831 | C4 | — | 6 | 2 | no | — |
| 832 | C4 | — | 6 | 1 | no | — |
| 833 | C4 | — | 6 | 1 | no | — |
| 834 | C4 | — | 12 | 2 | no | — |
| 835 | C4 | — | 12 | 2 | no | — |
| 836 | C4 | — | 12 | 1 | no | — |
| 837 | C4 | — | 12 | 1 | no | — |
| 838 | C4 | — | 24 | 2 | no | — |
| 839 | C4 | C3×#1020⋊C2 | 1 | 1 | yes | characteristic |
| 840 | C3 | — | 16 | 1 | no | — |
| 841 | C3 | — | 32 | 1 | no | — |
| 842 | C3 | #11714184 | 1 | 1 | yes | characteristic, direct product factor |
| 843 | C2 | — | 6 | 1 | no | — |
| 844 | C2 | — | 8 | 2 | no | — |
| 845 | C2 | — | 12 | 1 | no | — |
| 846 | C2 | — | 12 | 1 | no | — |
| 847 | C2 | — | 24 | 2 | no | — |
| 848 | C2 | — | 24 | 1 | no | — |
| 849 | C2 | C2×C3×#1020⋊C2 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | C2×#1020⋊C2 |
| commutator, cosocle, hypocenter | #997 | C23×C3 |
| Frattini | C23 | C22×C3×S4 |
| Fitting | C3×#3027 | D3 |
| hypercenter | C3×C4 | #1020⋊C2 |
| LCS | G ▷ #997 | |
| UCS | C1 ◁ C2×C3 ◁ C3×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#87521 | C2 | semidirect |
| 2. C3×#87520 | C2 | semidirect |
| 3. C3×#73027 | C2 | semidirect |
| 4. C3×#73026 | C2 | semidirect |
| 5. C3×#3027⋊C3 | C2 | semidirect |
| 6. #11714184 | C3 | direct (N × H) |
| 8. C3×#5950 | C22 | semidirect |
| 10. C3×#5934 | C22 | semidirect |
| 11. C3×#5933 | C22 | semidirect |
| 13. C3×B(4,𝔽2)⋊C3 | C22 | semidirect |
| 14. #87521 | C2×C3 | semidirect |
| 15. #87520 | C2×C3 | semidirect |
| 18. C3×#3027 | D3 | semidirect |
| 21. #3027⋊C3 | C2×C3 | semidirect |
| 22. #73027 | C2×C3 | semidirect |
| 23. #73026 | C2×C3 | semidirect |
| 40. C3×#585 | C2×D3 | semidirect |
| 42. #5950 | C22×C3 | semidirect |
| 44. #5934 | C22×C3 | semidirect |
| 45. #5933 | C22×C3 | semidirect |
| 68. C3×B(4,𝔽2) | C2×D3 | semidirect |
| 81. B(4,𝔽2)⋊C3 | C22×C3 | semidirect |
| 102. #3027 | C3×D3 | semidirect |
| 125. C22×C3×D4 | S4 | semidirect |
| 227. #585 | C2×C3×D3 | semidirect |
| 249. B(4,𝔽2) | C2×C3×D3 | semidirect |
| 409. C22×D4 | C3×S4 | semidirect |
| 842. C3 | #11714184 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#87521 | 2 |
| C3×#87520 | 2 |
| C3×#73027 | 2 |
| C3×#73026 | 2 |
| C3×#3027⋊C3 | 2 |
| #11714184 | 3 |
| C3×#33559 | 3 |
| C3×D4×S4 | 4 |