Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
1419 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 1419 conjugacy classes of subgroups — too many to draw. Only its 149 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 | #11906247 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11868704 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #127×#157 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11794264 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11793010 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11791804 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11787871 | C2 | 1 | 2 | yes | maximal |
| 8 | #11786597 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11785132 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10596642 | C22 | 1 | 2 | yes | — |
| 11 | C2×D4×#157 | — | 2 | 2 | no | — |
| 12 | C2×D4×#157 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×D4×#157 | C22 | 1 | 1 | yes | characteristic |
| 14 | #10596550 | — | 2 | 2 | no | — |
| 15 | C2×C22⋊PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 16 | #10596545 | — | 2 | 2 | no | — |
| 17 | #10596545 | — | 2 | 4 | no | — |
| 18 | D4×PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 19 | #10596543 | C22 | 1 | 2 | yes | — |
| 20 | #10596542 | C22 | 1 | 2 | yes | — |
| 21 | C3⋊D3×#127 | C22 | 1 | 1 | yes | characteristic |
| 22 | #10593827 | — | 2 | 2 | no | — |
| 23 | #10593827 | C22 | 1 | 1 | yes | characteristic |
| 24 | #10593827 | C22 | 1 | 1 | yes | characteristic |
| 25 | #10593825 | C22 | 1 | 2 | yes | — |
| 26 | #10593814 | C22 | 1 | 4 | yes | — |
| 27 | #10593735 | C22 | 1 | 1 | yes | characteristic |
| 28 | C42×#157 | C22 | 1 | 1 | yes | characteristic |
| 29 | #10593559 | — | 2 | 2 | no | — |
| 30 | #10593558 | — | 2 | 2 | no | — |
| 31 | #10593557 | — | 2 | 4 | no | — |
| 32 | #10593544 | C22 | 1 | 4 | yes | — |
| 33 | #10593539 | C22 | 1 | 2 | yes | — |
| 34 | #10590151 | C22 | 1 | 4 | yes | — |
| 35 | #10590094 | C22 | 1 | 2 | yes | — |
| 36 | #10590092 | C22 | 1 | 4 | yes | — |
| 37 | C23×#157 | — | 2 | 1 | no | — |
| 38 | C23×#157 | D4 | 1 | 2 | yes | — |
| 39 | C22×PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 40 | C2×D4×C3⋊D3 | — | 2 | 2 | no | — |
| 41 | C2×D4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 42 | C2×D4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 43 | C2×C22⋊#157 | — | 2 | 4 | no | — |
| 44 | C2×C22⋊#157 | — | 2 | 2 | no | — |
| 45 | C2×C22⋊#157 | — | 2 | 2 | no | — |
| 46 | C2×C22⋊#157 | — | 2 | 1 | no | — |
| 47 | C2×C22⋊#157 | D4 | 1 | 2 | yes | — |
| 48 | D4×#157 | — | 2 | 4 | no | — |
| 49 | D4×#157 | — | 2 | 4 | no | — |
| 50 | D4×#157 | — | 2 | 2 | no | — |
| 51 | D4×#157 | — | 2 | 2 | no | — |
| 52 | D4×#157 | — | 2 | 2 | no | — |
| 53 | D4×#157 | — | 2 | 2 | no | — |
| 54 | D4×#157 | — | 4 | 8 | no | — |
| 55 | #64286 | C23 | 1 | 4 | yes | — |
| 56 | C2×C4⋊#157 | — | 2 | 2 | no | — |
| 57 | C2×C4⋊#157 | C23 | 1 | 1 | yes | characteristic |
| 58 | C2×C4⋊#157 | C23 | 1 | 1 | yes | characteristic |
| 59 | C2×C4×#157 | — | 2 | 1 | no | — |
| 60 | C2×C4×#157 | — | 2 | 1 | no | — |
| 61 | C2×C4×#157 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×C4×#157 | C23 | 1 | 1 | yes | characteristic |
| 63 | #64283 | C23 | 1 | 4 | yes | — |
| 64 | C22⋊PSU(3,𝔽2) | — | 2 | 4 | no | — |
| 65 | C22⋊PSU(3,𝔽2) | — | 2 | 8 | no | — |
| 66 | C22⋊PSU(3,𝔽2) | — | 2 | 4 | no | — |
| 67 | C22⋊PSU(3,𝔽2) | — | 2 | 8 | no | — |
| 68 | C22⋊PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 69 | C22⋊PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 70 | C22⋊PSU(3,𝔽2) | — | 2 | 4 | no | — |
| 71 | C2×#3777 | — | 2 | 4 | no | — |
| 72 | C2×#3777 | — | 2 | 2 | no | — |
| 73 | C4⋊PSU(3,𝔽2) | — | 2 | 4 | no | — |
| 74 | C4⋊PSU(3,𝔽2) | D4 | 1 | 2 | yes | complemented |
| 75 | C4⋊PSU(3,𝔽2) | D4 | 1 | 2 | yes | complemented |
| 76 | C4×PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 77 | C4×PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 78 | #64243 | — | 2 | 4 | no | — |
| 79 | #64243 | D4 | 1 | 4 | yes | complemented |
| 80 | C32×#127 | Q8 | 1 | 1 | yes | characteristic, complemented |
| 81 | #64149 | — | 2 | 2 | no | — |
| 82 | #64149 | Q8 | 1 | 1 | yes | characteristic, complemented |
| 83 | #64149 | Q8 | 1 | 1 | yes | characteristic, complemented |
| 84 | #64083 | Q8 | 1 | 1 | yes | characteristic, complemented |
| 85 | C42×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 86 | #63788 | — | 2 | 4 | no | — |
| 87 | #63782 | — | 2 | 4 | no | — |
| 88 | #63782 | — | 2 | 4 | no | — |
| 89 | #63746 | — | 2 | 4 | no | — |
| 90 | #63745 | — | 2 | 4 | no | — |
| 91 | #63744 | — | 2 | 2 | no | — |
| 92 | #63744 | — | 2 | 2 | no | — |
| 93 | #24312 | — | 9 | 1 | no | maximal, Sylow |
| 94 | D3×#127 | — | 12 | 1 | no | — |
| 95 | C23×C3⋊D3 | — | 2 | 1 | no | — |
| 96 | C23×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 97 | C22×#157 | — | 2 | 1 | no | — |
| 98 | C22×#157 | — | 2 | 4 | no | — |
| 99 | C22×#157 | — | 2 | 4 | no | — |
| 100 | C22×#157 | — | 2 | 2 | no | — |
| 101 | C22×#157 | — | 2 | 2 | no | — |
| 102 | C22×#157 | — | 2 | 1 | no | — |
| 103 | C22×#157 | — | 4 | 4 | no | — |
| 104 | C22×#157 | — | 4 | 4 | no | — |
| 105 | C22×#157 | — | 4 | 1 | no | — |
| 106 | C22×#157 | — | 4 | 1 | no | — |
| 107 | C22×#157 | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | C22×#157 | C2×D4 | 1 | 2 | yes | — |
| 109 | C22×#157 | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | C2×PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 111 | C2×PSU(3,𝔽2) | — | 2 | 4 | no | — |
| 112 | C2×PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 113 | C2×PSU(3,𝔽2) | — | 8 | 4 | no | — |
| 114 | C2×C32×D4 | — | 2 | 2 | no | — |
| 115 | C2×C32×D4 | C2×Q8 | 1 | 1 | yes | characteristic |
| 116 | C2×C32×D4 | C2×Q8 | 1 | 1 | yes | characteristic, complemented |
| 117 | C2×#638 | — | 2 | 2 | no | — |
| 118 | C2×#638 | — | 2 | 2 | no | — |
| 119 | C2×#638 | — | 2 | 1 | no | — |
| 120 | C2×#638 | #41 | 1 | 2 | yes | — |
| 121 | D4×C3⋊D3 | — | 2 | 2 | no | — |
| 122 | D4×C3⋊D3 | — | 2 | 2 | no | — |
| 123 | D4×C3⋊D3 | — | 2 | 2 | no | — |
| 124 | D4×C3⋊D3 | — | 2 | 2 | no | — |
| 125 | D4×C3⋊D3 | — | 4 | 4 | no | — |
| 126 | D4×C3⋊D3 | — | 4 | 4 | no | — |
| 127 | C2×C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 128 | C2×C4⋊(C3⋊D3) | C2×Q8 | 1 | 1 | yes | characteristic |
| 129 | C2×C4⋊(C3⋊D3) | C2×Q8 | 1 | 1 | yes | characteristic, complemented |
| 130 | C2×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 131 | C2×C4×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 132 | C22⋊#157 | — | 2 | 8 | no | — |
| 133 | C22⋊#157 | — | 2 | 4 | no | — |
| 134 | C22⋊#157 | — | 2 | 4 | no | — |
| 135 | C22⋊#157 | — | 4 | 4 | no | — |
| 136 | C22⋊#157 | — | 4 | 4 | no | — |
| 137 | C22⋊#157 | — | 4 | 2 | no | — |
| 138 | #3792 | — | 2 | 4 | no | — |
| 139 | C4⋊#157 | — | 2 | 2 | no | — |
| 140 | C4⋊#157 | — | 2 | 2 | no | — |
| 141 | C4⋊#157 | — | 4 | 4 | no | — |
| 142 | C4⋊#157 | C2×D4 | 1 | 4 | yes | — |
| 143 | C4⋊#157 | C2×D4 | 1 | 4 | yes | — |
| 144 | C4×#157 | — | 2 | 4 | no | — |
| 145 | C4×#157 | — | 2 | 4 | no | — |
| 146 | C4×#157 | — | 2 | 2 | no | — |
| 147 | C4×#157 | — | 4 | 2 | no | — |
| 148 | C4×#157 | C2×D4 | 1 | 2 | yes | — |
| 149 | C4×#157 | C2×D4 | 1 | 2 | yes | — |
| 150 | #3788 | — | 2 | 4 | no | — |
| 151 | #3787 | — | 2 | 4 | no | — |
| 152 | #3777 | — | 2 | 4 | no | — |
| 153 | #3777 | — | 2 | 8 | no | — |
| 154 | #3777 | — | 2 | 4 | no | — |
| 155 | #3777 | — | 2 | 4 | no | — |
| 156 | #3777 | — | 2 | 2 | no | — |
| 157 | #3777 | — | 2 | 2 | no | — |
| 158 | C32×C42 | C2×Q8 | 1 | 1 | yes | characteristic, complemented |
| 159 | C4×C3⋊Dic3 | — | 2 | 1 | no | — |
| 160 | C4×C3⋊Dic3 | C2×Q8 | 1 | 1 | yes | characteristic, complemented |
| 161 | #3501 | — | 9 | 1 | no | — |
| 162 | #3077 | — | 9 | 2 | no | — |
| 163 | C4×#127 | — | 9 | 1 | no | — |
| 164 | #2060 | — | 9 | 2 | no | — |
| 165 | #2027 | — | 9 | 2 | no | — |
| 166 | #1994 | — | 9 | 2 | no | — |
| 167 | #1887 | — | 9 | 2 | no | — |
| 168 | #1856 | — | 9 | 2 | no | — |
| 169 | #1800 | — | 9 | 1 | no | — |
| 170 | C2×D3×D4 | — | 12 | 1 | no | — |
| 171 | C2×D3×D4 | — | 12 | 1 | no | — |
| 172 | C2×D3×D4 | — | 12 | 4 | no | — |
| 173 | C3×#127 | — | 4 | 1 | no | — |
| 174 | #940 | — | 12 | 1 | no | — |
| 175 | #940 | — | 12 | 1 | no | — |
| 176 | #940 | — | 12 | 4 | no | — |
| 177 | #874 | — | 12 | 1 | no | — |
| 178 | C42×D3 | — | 12 | 1 | no | — |
| 179 | C23×C32 | — | 2 | 1 | no | — |
| 180 | C23×C32 | C22⋊Q8 | 1 | 2 | yes | — |
| 181 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 182 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 183 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 184 | C22×C3⋊D3 | — | 4 | 2 | no | — |
| 185 | C22×C3⋊D3 | — | 4 | 2 | no | — |
| 186 | C22×C3⋊D3 | — | 4 | 2 | no | — |
| 187 | C22×C3⋊D3 | — | 4 | 2 | no | — |
| 188 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 189 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 190 | C22×C3⋊D3 | C22⋊Q8 | 1 | 2 | yes | — |
| 191 | C22×C3⋊D3 | C22×D4 | 1 | 1 | yes | characteristic |
| 192 | C2×#157 | — | 2 | 2 | no | — |
| 193 | C2×#157 | — | 2 | 2 | no | — |
| 194 | C2×#157 | — | 2 | 4 | no | — |
| 195 | C2×#157 | — | 2 | 2 | no | — |
| 196 | C2×#157 | — | 2 | 4 | no | — |
| 197 | C2×#157 | — | 4 | 1 | no | — |
| 198 | C2×#157 | — | 4 | 1 | no | — |
| 199 | C2×#157 | — | 4 | 1 | no | — |
| 200 | C2×#157 | — | 4 | 4 | no | — |
| 201 | C2×#157 | — | 4 | 2 | no | — |
| 202 | C2×#157 | — | 4 | 2 | no | — |
| 203 | C2×#157 | — | 4 | 1 | no | — |
| 204 | C2×#157 | — | 8 | 2 | no | — |
| 205 | C2×#157 | — | 8 | 2 | no | — |
| 206 | C2×#157 | — | 8 | 4 | no | — |
| 207 | C2×#157 | — | 8 | 4 | no | — |
| 208 | C2×#157 | — | 8 | 2 | no | — |
| 209 | C2×#157 | #120 | 1 | 2 | yes | — |
| 210 | C2×#157 | #120 | 1 | 1 | yes | characteristic |
| 211 | C2×#157 | #120 | 1 | 1 | yes | characteristic |
| 212 | PSU(3,𝔽2) | — | 4 | 4 | no | — |
| 213 | PSU(3,𝔽2) | — | 8 | 2 | no | — |
| 214 | PSU(3,𝔽2) | — | 8 | 4 | no | — |
| 215 | C32×D4 | — | 2 | 2 | no | — |
| 216 | C32×D4 | — | 2 | 2 | no | — |
| 217 | C32×D4 | — | 4 | 4 | no | — |
| 218 | C2×C32×C4 | — | 2 | 1 | no | — |
| 219 | C2×C32×C4 | C22×Q8 | 1 | 1 | yes | characteristic |
| 220 | #638 | — | 2 | 4 | no | — |
| 221 | #638 | — | 4 | 4 | no | — |
| 222 | #638 | — | 4 | 4 | no | — |
| 223 | #638 | — | 4 | 2 | no | — |
| 224 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 225 | C2×C3⋊Dic3 | C2×#41 | 1 | 1 | yes | characteristic |
| 226 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 227 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 228 | C4⋊(C3⋊D3) | — | 4 | 4 | no | — |
| 229 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 230 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 231 | C4×C3⋊D3 | C22×D4 | 1 | 2 | yes | — |
| 232 | C4×C3⋊D3 | 2−1+4 | 1 | 2 | yes | — |
| 233 | #622 | — | 4 | 4 | no | — |
| 234 | #554 | — | 18 | 4 | no | — |
| 235 | #554 | — | 18 | 2 | no | — |
| 236 | D4×Q8 | — | 18 | 2 | no | — |
| 237 | #544 | — | 9 | 2 | no | — |
| 238 | #543 | — | 18 | 2 | no | — |
| 239 | #533 | — | 9 | 2 | no | — |
| 240 | C2×#127 | — | 9 | 1 | no | — |
| 241 | C2×C22⋊Q8 | — | 18 | 2 | no | — |
| 242 | #518 | — | 9 | 2 | no | — |
| 243 | C2×C4×D4 | — | 9 | 1 | no | — |
| 244 | C2×C4×D4 | — | 9 | 1 | no | — |
| 245 | C2×C4×D4 | — | 18 | 2 | no | — |
| 246 | #478 | — | 18 | 4 | no | — |
| 247 | #476 | — | 18 | 2 | no | — |
| 248 | #474 | — | 18 | 2 | no | — |
| 249 | #428 | — | 9 | 4 | no | — |
| 250 | #423 | — | 9 | 2 | no | — |
| 251 | #418 | — | 9 | 4 | no | — |
| 252 | C2×#100 | — | 9 | 2 | no | — |
| 253 | #390 | — | 9 | 1 | no | — |
| 254 | #390 | — | 9 | 1 | no | — |
| 255 | #390 | — | 18 | 2 | no | — |
| 256 | #384 | — | 9 | 1 | no | — |
| 257 | C43 | — | 9 | 1 | no | — |
| 258 | #343 | — | 9 | 2 | no | — |
| 259 | #339 | — | 9 | 4 | no | — |
| 260 | #339 | — | 9 | 4 | no | — |
| 261 | C23×D3 | — | 12 | 2 | no | — |
| 262 | C23×D3 | — | 12 | 2 | no | — |
| 263 | C2×C3×D4 | — | 4 | 4 | no | — |
| 264 | C2×C3×D4 | — | 4 | 1 | no | — |
| 265 | C2×C3×D4 | — | 4 | 1 | no | — |
| 266 | C2×#67 | — | 12 | 2 | no | — |
| 267 | C2×#67 | — | 12 | 2 | no | — |
| 268 | C2×#67 | — | 12 | 4 | no | — |
| 269 | C2×#67 | — | 12 | 4 | no | — |
| 270 | D3×D4 | — | 24 | 2 | no | — |
| 271 | D3×D4 | — | 24 | 2 | no | — |
| 272 | D3×D4 | — | 24 | 2 | no | — |
| 273 | D3×D4 | — | 24 | 2 | no | — |
| 274 | D3×D4 | — | 24 | 8 | no | — |
| 275 | D3×D4 | — | 24 | 8 | no | — |
| 276 | C2×D12 | — | 12 | 1 | no | — |
| 277 | C2×D12 | — | 12 | 1 | no | — |
| 278 | C2×D12 | — | 12 | 4 | no | — |
| 279 | C2×C4×D3 | — | 12 | 1 | no | — |
| 280 | C2×C4×D3 | — | 12 | 2 | no | — |
| 281 | C3×C42 | — | 4 | 1 | no | — |
| 282 | C4×Dic3 | — | 12 | 1 | no | — |
| 283 | C4×Dic3 | — | 12 | 2 | no | — |
| 284 | C22×C32 | — | 2 | 2 | no | — |
| 285 | C22×C32 | — | 4 | 2 | no | — |
| 286 | C22×C32 | — | 4 | 2 | no | — |
| 287 | C22×C32 | — | 4 | 1 | no | — |
| 288 | C22×C32 | C2×C22⋊Q8 | 1 | 1 | yes | characteristic |
| 289 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 290 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 291 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 292 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 293 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 294 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 295 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 296 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 297 | C2×C3⋊D3 | — | 8 | 2 | no | — |
| 298 | C2×C3⋊D3 | — | 8 | 2 | no | — |
| 299 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 300 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 301 | C2×C3⋊D3 | C2×#120 | 1 | 1 | yes | characteristic |
| 302 | C2×C3⋊D3 | #536 | 1 | 1 | yes | characteristic |
| 303 | #157 | — | 2 | 1 | no | — |
| 304 | #157 | — | 2 | 2 | no | — |
| 305 | #157 | — | 4 | 2 | no | — |
| 306 | #157 | — | 4 | 4 | no | — |
| 307 | #157 | — | 4 | 2 | no | — |
| 308 | #157 | — | 4 | 4 | no | — |
| 309 | #157 | — | 8 | 1 | no | — |
| 310 | #157 | #453 | 1 | 2 | yes | — |
| 311 | C32×C4 | — | 2 | 2 | no | — |
| 312 | C32×C4 | D4×Q8 | 1 | 2 | yes | — |
| 313 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 314 | C3⋊Dic3 | #548 | 1 | 2 | yes | — |
| 315 | C22×Q8 | — | 18 | 2 | no | — |
| 316 | C22×D4 | — | 9 | 1 | no | — |
| 317 | C22×D4 | — | 9 | 1 | no | — |
| 318 | C22×D4 | — | 18 | 2 | no | — |
| 319 | C23×C4 | — | 9 | 2 | no | — |
| 320 | C23×C4 | — | 18 | 1 | no | — |
| 321 | C2×M16 | — | 9 | 4 | no | — |
| 322 | C4⋊Q8 | — | 9 | 2 | no | — |
| 323 | C4⋊Q8 | — | 9 | 2 | no | — |
| 324 | C4⋊Q8 | — | 18 | 4 | no | — |
| 325 | #127 | — | 9 | 1 | no | — |
| 326 | #127 | — | 9 | 1 | no | — |
| 327 | #127 | — | 9 | 1 | no | — |
| 328 | #127 | — | 18 | 2 | no | — |
| 329 | #127 | PSU(3,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 330 | #125 | — | 9 | 4 | no | — |
| 331 | #125 | — | 18 | 4 | no | — |
| 332 | C22⋊Q8 | — | 18 | 2 | no | — |
| 333 | C22⋊Q8 | — | 18 | 4 | no | — |
| 334 | C22⋊Q8 | — | 18 | 2 | no | — |
| 335 | C22⋊Q8 | — | 18 | 4 | no | — |
| 336 | C22⋊Q8 | — | 18 | 4 | no | — |
| 337 | C22⋊Q8 | — | 18 | 8 | no | — |
| 338 | C22⋊Q8 | — | 18 | 8 | no | — |
| 339 | C4×Q8 | — | 18 | 2 | no | — |
| 340 | C4×Q8 | — | 18 | 2 | no | — |
| 341 | C4×D4 | — | 18 | 2 | no | — |
| 342 | C4×D4 | — | 18 | 2 | no | — |
| 343 | C4×D4 | — | 18 | 2 | no | — |
| 344 | C4×D4 | — | 18 | 2 | no | — |
| 345 | C4×D4 | — | 18 | 4 | no | — |
| 346 | C4×D4 | — | 18 | 4 | no | — |
| 347 | C4×D4 | — | 36 | 8 | no | — |
| 348 | #117 | — | 9 | 4 | no | — |
| 349 | C2×C4⋊C4 | — | 9 | 1 | no | — |
| 350 | C2×C4⋊C4 | — | 9 | 1 | no | — |
| 351 | C2×C4⋊C4 | — | 18 | 4 | no | — |
| 352 | C2×C4⋊C4 | — | 18 | 2 | no | — |
| 353 | C2×C4⋊C4 | — | 18 | 2 | no | — |
| 354 | C2×C22⋊C4 | — | 9 | 2 | no | — |
| 355 | C2×C22⋊C4 | — | 18 | 4 | no | — |
| 356 | C2×C22⋊C4 | — | 18 | 1 | no | — |
| 357 | C2×C22⋊C4 | — | 18 | 2 | no | — |
| 358 | C2×C22⋊C4 | — | 18 | 2 | no | — |
| 359 | C2×C42 | — | 9 | 1 | no | — |
| 360 | C2×C42 | — | 9 | 1 | no | — |
| 361 | C2×C42 | — | 9 | 1 | no | — |
| 362 | C2×C42 | — | 18 | 1 | no | — |
| 363 | C2×C42 | — | 18 | 1 | no | — |
| 364 | #107 | — | 18 | 4 | no | — |
| 365 | #106 | — | 18 | 4 | no | — |
| 366 | C4⋊C8 | — | 18 | 2 | no | — |
| 367 | C4⋊C8 | — | 18 | 2 | no | — |
| 368 | #102 | — | 18 | 4 | no | — |
| 369 | #102 | — | 18 | 4 | no | — |
| 370 | #100 | — | 18 | 4 | no | — |
| 371 | C23×C3 | — | 4 | 2 | no | — |
| 372 | C23×C3 | — | 4 | 2 | no | — |
| 373 | C22×D3 | — | 12 | 1 | no | — |
| 374 | C22×D3 | — | 12 | 2 | no | — |
| 375 | C22×D3 | — | 12 | 2 | no | — |
| 376 | C22×D3 | — | 24 | 2 | no | — |
| 377 | C22×D3 | — | 24 | 2 | no | — |
| 378 | C22×D3 | — | 24 | 2 | no | — |
| 379 | C22×D3 | — | 24 | 2 | no | — |
| 380 | C22×D3 | — | 24 | 4 | no | — |
| 381 | C22×D3 | — | 24 | 4 | no | — |
| 382 | C22×D3 | — | 24 | 4 | no | — |
| 383 | C22×D3 | — | 24 | 4 | no | — |
| 384 | C3×D4 | — | 8 | 2 | no | — |
| 385 | C3×D4 | — | 8 | 2 | no | — |
| 386 | C3×D4 | — | 8 | 8 | no | — |
| 387 | C2×C3×C4 | — | 4 | 2 | no | — |
| 388 | C2×C3×C4 | — | 4 | 1 | no | — |
| 389 | #67 | — | 24 | 4 | no | — |
| 390 | #67 | — | 24 | 4 | no | — |
| 391 | #67 | — | 24 | 8 | no | — |
| 392 | #67 | — | 24 | 8 | no | — |
| 393 | C2×Dic3 | — | 12 | 1 | no | — |
| 394 | C2×Dic3 | — | 12 | 2 | no | — |
| 395 | D12 | — | 24 | 2 | no | — |
| 396 | D12 | — | 24 | 2 | no | — |
| 397 | D12 | — | 24 | 8 | no | — |
| 398 | C4×D3 | — | 12 | 2 | no | — |
| 399 | C4×D3 | — | 12 | 2 | no | — |
| 400 | C4×D3 | — | 12 | 4 | no | — |
| 401 | C4×D3 | — | 12 | 4 | no | — |
| 402 | C2×C32 | — | 2 | 1 | no | — |
| 403 | C2×C32 | — | 4 | 2 | no | — |
| 404 | C2×C32 | — | 8 | 1 | no | — |
| 405 | C2×C32 | #2409 | 1 | 1 | yes | characteristic |
| 406 | C3⋊D3 | — | 2 | 1 | no | — |
| 407 | C3⋊D3 | — | 4 | 2 | no | — |
| 408 | C3⋊D3 | — | 8 | 1 | no | — |
| 409 | C3⋊D3 | C2×#453 | 1 | 1 | yes | characteristic |
| 410 | C3⋊D3 | #3018 | 1 | 1 | yes | characteristic |
| 411 | C24 | — | 9 | 2 | no | — |
| 412 | C24 | — | 18 | 1 | no | — |
| 413 | C2×Q8 | — | 18 | 2 | no | — |
| 414 | C2×Q8 | — | 18 | 2 | no | — |
| 415 | C2×Q8 | — | 18 | 4 | no | — |
| 416 | C2×Q8 | — | 72 | 4 | no | — |
| 417 | C2×D4 | — | 2 | 2 | no | — |
| 418 | C2×D4 | — | 9 | 2 | no | — |
| 419 | C2×D4 | — | 9 | 1 | no | — |
| 420 | C2×D4 | — | 9 | 1 | no | — |
| 421 | C2×D4 | — | 18 | 2 | no | — |
| 422 | C2×D4 | — | 18 | 2 | no | — |
| 423 | C2×D4 | — | 18 | 2 | no | — |
| 424 | C2×D4 | — | 18 | 2 | no | — |
| 425 | C2×D4 | — | 18 | 2 | no | — |
| 426 | C2×D4 | — | 18 | 1 | no | — |
| 427 | C2×D4 | — | 18 | 2 | no | — |
| 428 | C2×D4 | — | 18 | 2 | no | — |
| 429 | C2×D4 | — | 36 | 4 | no | — |
| 430 | C2×D4 | — | 36 | 4 | no | — |
| 431 | C2×D4 | C2×PSU(3,𝔽2) | 1 | 1 | yes | characteristic |
| 432 | C2×D4 | C2×PSU(3,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 433 | C22×C4 | — | 9 | 1 | no | — |
| 434 | C22×C4 | — | 9 | 1 | no | — |
| 435 | C22×C4 | — | 9 | 1 | no | — |
| 436 | C22×C4 | — | 9 | 2 | no | — |
| 437 | C22×C4 | — | 18 | 1 | no | — |
| 438 | C22×C4 | — | 18 | 2 | no | — |
| 439 | C22×C4 | — | 18 | 2 | no | — |
| 440 | C22×C4 | — | 18 | 1 | no | — |
| 441 | C22×C4 | — | 18 | 4 | no | — |
| 442 | C22×C4 | — | 18 | 4 | no | — |
| 443 | C22×C4 | — | 18 | 1 | no | — |
| 444 | C22×C4 | — | 36 | 1 | no | — |
| 445 | C22×C4 | — | 36 | 1 | no | — |
| 446 | C22×C4 | — | 36 | 4 | no | — |
| 447 | C22×C4 | — | 36 | 4 | no | — |
| 448 | M16 | — | 18 | 4 | no | — |
| 449 | M16 | — | 18 | 4 | no | — |
| 450 | C2×C8 | — | 18 | 4 | no | — |
| 451 | C4⋊C4 | — | 9 | 4 | no | — |
| 452 | C4⋊C4 | — | 9 | 4 | no | — |
| 453 | C4⋊C4 | — | 18 | 2 | no | — |
| 454 | C4⋊C4 | — | 18 | 4 | no | — |
| 455 | C4⋊C4 | — | 18 | 2 | no | — |
| 456 | C4⋊C4 | — | 18 | 4 | no | — |
| 457 | C4⋊C4 | — | 18 | 2 | no | — |
| 458 | C4⋊C4 | — | 18 | 2 | no | — |
| 459 | C4⋊C4 | — | 18 | 4 | no | — |
| 460 | C4⋊C4 | — | 18 | 8 | no | — |
| 461 | C4⋊C4 | — | 36 | 4 | no | — |
| 462 | C22⋊C4 | — | 18 | 4 | no | — |
| 463 | C22⋊C4 | — | 18 | 4 | no | — |
| 464 | C22⋊C4 | — | 18 | 8 | no | — |
| 465 | C22⋊C4 | — | 36 | 2 | no | — |
| 466 | C22⋊C4 | — | 36 | 4 | no | — |
| 467 | C22⋊C4 | — | 36 | 4 | no | — |
| 468 | C42 | — | 9 | 2 | no | — |
| 469 | C42 | — | 9 | 2 | no | — |
| 470 | C42 | — | 9 | 1 | no | — |
| 471 | C42 | — | 18 | 1 | no | — |
| 472 | C42 | — | 18 | 4 | no | — |
| 473 | C42 | — | 18 | 2 | no | — |
| 474 | C42 | — | 18 | 4 | no | — |
| 475 | C42 | — | 36 | 2 | no | — |
| 476 | C42 | C2×PSU(3,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 477 | C22×C3 | — | 4 | 1 | no | — |
| 478 | C22×C3 | — | 8 | 2 | no | — |
| 479 | C22×C3 | — | 8 | 4 | no | — |
| 480 | C22×C3 | — | 8 | 4 | no | — |
| 481 | C22×C3 | — | 8 | 2 | no | — |
| 482 | C2×D3 | — | 12 | 1 | no | — |
| 483 | C2×D3 | — | 12 | 1 | no | — |
| 484 | C2×D3 | — | 12 | 2 | no | — |
| 485 | C2×D3 | — | 12 | 2 | no | — |
| 486 | C2×D3 | — | 24 | 2 | no | — |
| 487 | C2×D3 | — | 24 | 4 | no | — |
| 488 | C2×D3 | — | 24 | 4 | no | — |
| 489 | C2×D3 | — | 24 | 2 | no | — |
| 490 | C2×D3 | — | 48 | 2 | no | — |
| 491 | C2×D3 | — | 48 | 2 | no | — |
| 492 | C2×D3 | — | 48 | 4 | no | — |
| 493 | C2×D3 | — | 48 | 2 | no | — |
| 494 | C2×D3 | — | 48 | 2 | no | — |
| 495 | C2×D3 | — | 48 | 4 | no | — |
| 496 | C3×C4 | — | 4 | 4 | no | — |
| 497 | C3×C4 | — | 4 | 2 | no | — |
| 498 | Dic3 | — | 12 | 2 | no | — |
| 499 | Dic3 | — | 12 | 4 | no | — |
| 500 | C32 | #24312 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 501 | C23 | — | 2 | 1 | no | — |
| 502 | C23 | — | 9 | 1 | no | — |
| 503 | C23 | — | 9 | 2 | no | — |
| 504 | C23 | — | 18 | 2 | no | — |
| 505 | C23 | — | 18 | 2 | no | — |
| 506 | C23 | — | 18 | 1 | no | — |
| 507 | C23 | — | 36 | 1 | no | — |
| 508 | C23 | — | 36 | 1 | no | — |
| 509 | C23 | — | 36 | 2 | no | — |
| 510 | C23 | — | 36 | 2 | no | — |
| 511 | C23 | — | 36 | 2 | no | — |
| 512 | C23 | — | 36 | 2 | no | — |
| 513 | C23 | C22⋊PSU(3,𝔽2) | 1 | 2 | yes | — |
| 514 | Q8 | — | 36 | 4 | no | — |
| 515 | Q8 | — | 72 | 2 | no | — |
| 516 | Q8 | — | 72 | 4 | no | — |
| 517 | D4 | — | 2 | 2 | no | — |
| 518 | D4 | — | 2 | 2 | no | — |
| 519 | D4 | — | 4 | 4 | no | — |
| 520 | D4 | — | 18 | 4 | no | — |
| 521 | D4 | — | 18 | 2 | no | — |
| 522 | D4 | — | 18 | 2 | no | — |
| 523 | D4 | — | 36 | 4 | no | — |
| 524 | D4 | — | 36 | 2 | no | — |
| 525 | D4 | — | 36 | 4 | no | — |
| 526 | D4 | — | 36 | 4 | no | — |
| 527 | C2×C4 | — | 2 | 1 | no | — |
| 528 | C2×C4 | — | 9 | 1 | no | — |
| 529 | C2×C4 | — | 9 | 1 | no | — |
| 530 | C2×C4 | — | 9 | 2 | no | — |
| 531 | C2×C4 | — | 9 | 2 | no | — |
| 532 | C2×C4 | — | 9 | 2 | no | — |
| 533 | C2×C4 | — | 9 | 1 | no | — |
| 534 | C2×C4 | — | 18 | 2 | no | — |
| 535 | C2×C4 | — | 18 | 2 | no | — |
| 536 | C2×C4 | — | 18 | 2 | no | — |
| 537 | C2×C4 | — | 18 | 1 | no | — |
| 538 | C2×C4 | — | 18 | 4 | no | — |
| 539 | C2×C4 | — | 18 | 4 | no | — |
| 540 | C2×C4 | — | 18 | 2 | no | — |
| 541 | C2×C4 | — | 18 | 2 | no | — |
| 542 | C2×C4 | — | 36 | 4 | no | — |
| 543 | C2×C4 | — | 36 | 1 | no | — |
| 544 | C2×C4 | — | 36 | 1 | no | — |
| 545 | C2×C4 | — | 36 | 1 | no | — |
| 546 | C2×C4 | — | 36 | 2 | no | — |
| 547 | C2×C4 | — | 36 | 1 | no | — |
| 548 | C2×C4 | — | 36 | 2 | no | — |
| 549 | C2×C4 | — | 72 | 2 | no | — |
| 550 | C2×C4 | — | 72 | 2 | no | — |
| 551 | C2×C4 | — | 72 | 2 | no | — |
| 552 | C2×C4 | — | 72 | 4 | no | — |
| 553 | C2×C4 | — | 72 | 4 | no | — |
| 554 | C2×C4 | C22×PSU(3,𝔽2) | 1 | 1 | yes | characteristic |
| 555 | C8 | — | 36 | 4 | no | — |
| 556 | C2×C3 | — | 4 | 2 | no | — |
| 557 | C2×C3 | — | 4 | 1 | no | — |
| 558 | C2×C3 | — | 16 | 2 | no | — |
| 559 | C2×C3 | — | 16 | 2 | no | — |
| 560 | D3 | — | 12 | 1 | no | — |
| 561 | D3 | — | 12 | 1 | no | — |
| 562 | D3 | — | 12 | 2 | no | — |
| 563 | D3 | — | 48 | 2 | no | — |
| 564 | D3 | — | 48 | 2 | no | — |
| 565 | C22 | — | 2 | 2 | no | — |
| 566 | C22 | — | 4 | 2 | no | — |
| 567 | C22 | — | 4 | 2 | no | — |
| 568 | C22 | — | 4 | 1 | no | — |
| 569 | C22 | — | 9 | 1 | no | — |
| 570 | C22 | — | 9 | 1 | no | — |
| 571 | C22 | — | 18 | 1 | no | — |
| 572 | C22 | — | 18 | 1 | no | — |
| 573 | C22 | — | 18 | 2 | no | — |
| 574 | C22 | — | 36 | 2 | no | — |
| 575 | C22 | — | 36 | 2 | no | — |
| 576 | C22 | — | 36 | 2 | no | — |
| 577 | C22 | — | 36 | 2 | no | — |
| 578 | C22 | — | 36 | 1 | no | — |
| 579 | C22 | — | 72 | 2 | no | — |
| 580 | C22 | — | 72 | 1 | no | — |
| 581 | C22 | — | 72 | 1 | no | — |
| 582 | C22 | — | 72 | 2 | no | — |
| 583 | C22 | C2×C22⋊PSU(3,𝔽2) | 1 | 1 | yes | characteristic |
| 584 | C4 | — | 2 | 2 | no | — |
| 585 | C4 | — | 9 | 2 | no | — |
| 586 | C4 | — | 9 | 2 | no | — |
| 587 | C4 | — | 18 | 2 | no | — |
| 588 | C4 | — | 18 | 1 | no | — |
| 589 | C4 | — | 18 | 2 | no | — |
| 590 | C4 | — | 36 | 2 | no | — |
| 591 | C4 | — | 36 | 4 | no | — |
| 592 | C4 | — | 36 | 4 | no | — |
| 593 | C4 | — | 36 | 2 | no | — |
| 594 | C4 | — | 72 | 1 | no | — |
| 595 | C4 | D4×PSU(3,𝔽2) | 1 | 2 | yes | — |
| 596 | C3 | — | 4 | 1 | no | — |
| 597 | C2 | — | 2 | 1 | no | — |
| 598 | C2 | — | 4 | 2 | no | — |
| 599 | C2 | — | 8 | 1 | no | — |
| 600 | C2 | — | 9 | 1 | no | — |
| 601 | C2 | — | 9 | 1 | no | — |
| 602 | C2 | — | 18 | 1 | no | — |
| 603 | C2 | — | 36 | 2 | no | — |
| 604 | C2 | — | 72 | 1 | no | — |
| 605 | C2 | #11809470 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11906247 | C2 | semidirect |
| 2. #11868704 | C2 | semidirect |
| 4. #11794264 | C2 | semidirect |
| 5. #11793010 | C2 | semidirect |
| 6. #11791804 | C2 | semidirect |
| 8. #11786597 | C2 | semidirect |
| 9. #11785132 | C2 | semidirect |
| 74. C4⋊PSU(3,𝔽2) | D4 | semidirect |
| 75. C4⋊PSU(3,𝔽2) | D4 | semidirect |
| 79. #64243 | D4 | semidirect |
| 80. C32×#127 | Q8 | semidirect |
| 82. #64149 | Q8 | semidirect |
| 83. #64149 | Q8 | semidirect |
| 84. #64083 | Q8 | semidirect |
| 116. C2×C32×D4 | C2×Q8 | semidirect |
| 129. C2×C4⋊(C3⋊D3) | C2×Q8 | semidirect |
| 158. C32×C42 | C2×Q8 | semidirect |
| 160. C4×C3⋊Dic3 | C2×Q8 | semidirect |
| 329. #127 | PSU(3,𝔽2) | semidirect |
| 432. C2×D4 | C2×PSU(3,𝔽2) | semidirect |
| 476. C42 | C2×PSU(3,𝔽2) | semidirect |
| 500. C32 | #24312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11906247 | 2 |
| #11868704 | 2 |
| #127×#157 | 2 |
| #11794264 | 2 |
| #11793010 | 2 |
| #11791804 | 2 |
| #11787871 | 2 |
| #11786597 | 2 |
| #11785132 | 2 |
| #24312 | 9 |