← #72266724
Subgroups — #72266724
Order 4096.
At least 14562 conjugacy classes of subgroups; only the 763 normal subgroups are shown.
The subgroup lattice has 332 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72266700 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #72266044 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72266041 | C22 | 1 | 2 | yes | complemented |
| 4 | #72259010 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #72259008 | C22 | 1 | 1 | yes | characteristic, complemented |
| 6 | #72258997 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #72258929 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #72258923 | C4 | 1 | 2 | yes | complemented |
| 9 | #72258921 | C4 | 1 | 2 | yes | complemented |
| 10 | #72258919 | C4 | 1 | 2 | yes | complemented |
| 11 | #72258912 | C22 | 1 | 2 | yes | — |
| 12 | #72258504 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #72238447 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #72238446 | C22 | 1 | 2 | yes | complemented |
| 15 | #72237718 | C2 | 1 | 2 | yes | maximal, complemented |
| 16 | #72235937 | C22 | 1 | 2 | yes | complemented |
| 17 | #72235847 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #72235718 | C22 | 1 | 2 | yes | complemented |
| 19 | #72232723 | C22 | 1 | 4 | yes | complemented |
| 20 | #72232723 | C22 | 1 | 4 | yes | complemented |
| 21 | #72232048 | C4 | 1 | 2 | yes | complemented |
| 22 | #72225737 | C22 | 1 | 1 | yes | characteristic |
| 23 | #72225665 | C22 | 1 | 1 | yes | characteristic |
| 24 | #72219307 | C22 | 1 | 2 | yes | complemented |
| 25 | C2×#139716 | C22 | 1 | 4 | yes | complemented |
| 26 | C2×#139716 | C22 | 1 | 4 | yes | complemented |
| 27 | #72219264 | C22 | 1 | 2 | yes | — |
| 28 | C2×#647656 | C22 | 1 | 1 | yes | characteristic |
| 29 | C22×#3532 | C2×C4 | 1 | 2 | yes | — |
| 30 | C23×D42 | C23 | 1 | 1 | yes | characteristic |
| 31 | C24×#120 | D4 | 1 | 2 | yes | — |
| 32 | C22×#2846 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | C2×#35527 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C2×#35346 | D4 | 1 | 2 | yes | — |
| 35 | C2×#34980 | C23 | 1 | 1 | yes | characteristic |
| 36 | C22×#2403 | D4 | 1 | 2 | yes | — |
| 37 | C2×#21746 | C23 | 1 | 2 | yes | — |
| 38 | C2×#21746 | C23 | 1 | 2 | yes | — |
| 39 | #5063443 | D4 | 1 | 4 | yes | — |
| 40 | #5063442 | D4 | 1 | 4 | yes | — |
| 41 | #5025789 | D4 | 1 | 2 | yes | — |
| 42 | #5025782 | D4 | 1 | 2 | yes | — |
| 43 | #5021140 | D4 | 1 | 2 | yes | — |
| 44 | #5021138 | D4 | 1 | 2 | yes | — |
| 45 | #4464171 | C2×C4 | 1 | 2 | yes | — |
| 46 | #4422949 | D4 | 1 | 2 | yes | — |
| 47 | #4420586 | D4 | 1 | 2 | yes | — |
| 48 | #2356274 | D4 | 1 | 4 | yes | — |
| 49 | #2108839 | D4 | 1 | 4 | yes | — |
| 50 | #763333 | C2×C4 | 1 | 2 | yes | — |
| 51 | #686187 | D4 | 1 | 2 | yes | — |
| 52 | #647656 | D4 | 1 | 2 | yes | — |
| 53 | #618316 | D4 | 1 | 4 | yes | — |
| 54 | #617710 | C2×C4 | 1 | 2 | yes | — |
| 55 | #616961 | C2×C4 | 1 | 2 | yes | — |
| 56 | #616961 | C2×C4 | 1 | 2 | yes | — |
| 57 | #616961 | C23 | 1 | 2 | yes | — |
| 58 | #616960 | C2×C4 | 1 | 2 | yes | — |
| 59 | #616960 | C2×C4 | 1 | 2 | yes | — |
| 60 | #613192 | D4 | 1 | 4 | yes | — |
| 61 | C2×#15947 | C23 | 1 | 2 | yes | — |
| 62 | C2×#15258 | C2×C4 | 1 | 2 | yes | — |
| 63 | C2×#15257 | D4 | 1 | 4 | yes | — |
| 64 | #556752 | C2×C4 | 1 | 2 | yes | — |
| 65 | #556752 | C23 | 1 | 1 | yes | characteristic |
| 66 | #555905 | C2×C4 | 1 | 1 | yes | characteristic |
| 67 | #555894 | D4 | 1 | 2 | yes | — |
| 68 | #552671 | C2×C4 | 1 | 2 | yes | — |
| 69 | #552670 | C2×C4 | 1 | 2 | yes | — |
| 70 | #517411 | D4 | 1 | 2 | yes | — |
| 71 | C2×#14134 | C2×C4 | 1 | 1 | yes | characteristic |
| 72 | C2×#13867 | D4 | 1 | 2 | yes | — |
| 73 | C2×#8547 | C23 | 1 | 4 | yes | — |
| 74 | C28 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 75 | C23×H(5,𝔽2) | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 76 | C25×D4 | C2×D4 | 1 | 2 | yes | — |
| 77 | C25×D4 | C2×D4 | 1 | 2 | yes | — |
| 78 | C25×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 79 | C22×#551 | C22⋊C4 | 1 | 2 | yes | complemented |
| 80 | C22×D42 | C22⋊C4 | 1 | 2 | yes | complemented |
| 81 | C22×H(3,𝔽4) | C22⋊C4 | 1 | 2 | yes | complemented |
| 82 | C22×#560 | C22⋊C4 | 1 | 2 | yes | complemented |
| 83 | C22×#535 | C22×C4 | 1 | 2 | yes | — |
| 84 | C22×#534 | C22×C4 | 1 | 2 | yes | — |
| 85 | C23×#127 | C22×C4 | 1 | 1 | yes | characteristic |
| 86 | C23×#121 | C2×D4 | 1 | 2 | yes | — |
| 87 | C23×#121 | C2×D4 | 1 | 2 | yes | — |
| 88 | C23×#120 | C22⋊C4 | 1 | 4 | yes | complemented |
| 89 | C23×#120 | C22×C4 | 1 | 2 | yes | — |
| 90 | C23×#120 | C22×C4 | 1 | 1 | yes | characteristic |
| 91 | C23×#120 | C2×D4 | 1 | 4 | yes | — |
| 92 | C23×#120 | C2×D4 | 1 | 2 | yes | — |
| 93 | C23×#120 | C24 | 1 | 1 | yes | characteristic |
| 94 | C23×C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 95 | C24×C22⋊C4 | C22⋊C4 | 1 | 2 | yes | complemented |
| 96 | C2×#2849 | C2×D4 | 1 | 2 | yes | — |
| 97 | C2×#2846 | C2×D4 | 1 | 2 | yes | — |
| 98 | C2×#2404 | C22⋊C4 | 1 | 4 | yes | complemented |
| 99 | C2×#2404 | C2×D4 | 1 | 4 | yes | — |
| 100 | C2×#2403 | C22⋊C4 | 1 | 4 | yes | — |
| 101 | C2×#2403 | C22⋊C4 | 1 | 4 | yes | — |
| 102 | C2×#2613 | C2×D4 | 1 | 2 | yes | — |
| 103 | C2×#2613 | C2×D4 | 1 | 2 | yes | — |
| 104 | C2×#2309 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 105 | C2×#2308 | C22⋊C4 | 1 | 2 | yes | complemented |
| 106 | C2×#2308 | C2×D4 | 1 | 2 | yes | — |
| 107 | C2×#2297 | C22⋊C4 | 1 | 2 | yes | complemented |
| 108 | C22×#379 | C22⋊C4 | 1 | 2 | yes | complemented |
| 109 | C22×#379 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 110 | C22×#379 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | C22×#379 | C2×D4 | 1 | 2 | yes | — |
| 112 | #17271 | C22⋊C4 | 1 | 4 | yes | complemented |
| 113 | #17137 | C22⋊C4 | 1 | 4 | yes | complemented |
| 114 | #15948 | C22⋊C4 | 1 | 2 | yes | complemented |
| 115 | #15948 | C22⋊C4 | 1 | 2 | yes | complemented |
| 116 | #15947 | C22⋊C4 | 1 | 2 | yes | complemented |
| 117 | #15947 | C22⋊C4 | 1 | 2 | yes | complemented |
| 118 | #15947 | C2×D4 | 1 | 4 | yes | — |
| 119 | #15947 | C2×D4 | 1 | 2 | yes | — |
| 120 | #15947 | C2×D4 | 1 | 2 | yes | — |
| 121 | #15947 | C2×D4 | 1 | 4 | yes | — |
| 122 | #15947 | C2×D4 | 1 | 2 | yes | — |
| 123 | #15947 | C2×D4 | 1 | 2 | yes | — |
| 124 | #15262 | C22⋊C4 | 1 | 2 | yes | complemented |
| 125 | #15261 | C22⋊C4 | 1 | 2 | yes | complemented |
| 126 | #15259 | C22⋊C4 | 1 | 2 | yes | complemented |
| 127 | #15259 | C22⋊C4 | 1 | 2 | yes | complemented |
| 128 | #15259 | C22⋊C4 | 1 | 2 | yes | complemented |
| 129 | #15259 | C2×D4 | 1 | 2 | yes | — |
| 130 | #15259 | C2×D4 | 1 | 4 | yes | — |
| 131 | #15259 | C2×D4 | 1 | 2 | yes | — |
| 132 | #15258 | C22⋊C4 | 1 | 2 | yes | complemented |
| 133 | #15258 | C22⋊C4 | 1 | 2 | yes | complemented |
| 134 | #15258 | C22⋊C4 | 1 | 2 | yes | complemented |
| 135 | #15258 | C2×D4 | 1 | 2 | yes | — |
| 136 | #15258 | C2×D4 | 1 | 4 | yes | — |
| 137 | #15258 | C2×D4 | 1 | 2 | yes | — |
| 138 | #14684 | C22⋊C4 | 1 | 2 | yes | complemented |
| 139 | #14658 | C22⋊C4 | 1 | 2 | yes | complemented |
| 140 | #14657 | C22⋊C4 | 1 | 4 | yes | complemented |
| 141 | #14657 | C22⋊C4 | 1 | 2 | yes | complemented |
| 142 | #14492 | C22⋊C4 | 1 | 4 | yes | complemented |
| 143 | #14419 | C22⋊C4 | 1 | 4 | yes | complemented |
| 144 | #14341 | C2×D4 | 1 | 2 | yes | — |
| 145 | #14335 | C22×C4 | 1 | 2 | yes | — |
| 146 | #14335 | C22×C4 | 1 | 2 | yes | — |
| 147 | #14255 | C2×D4 | 1 | 4 | yes | — |
| 148 | #14255 | C2×D4 | 1 | 4 | yes | — |
| 149 | #14167 | C22⋊C4 | 1 | 2 | yes | complemented |
| 150 | #14134 | C22⋊C4 | 1 | 2 | yes | complemented |
| 151 | #14134 | C22⋊C4 | 1 | 4 | yes | complemented |
| 152 | #13868 | C22⋊C4 | 1 | 4 | yes | complemented |
| 153 | #13868 | C2×D4 | 1 | 4 | yes | — |
| 154 | #13867 | C22⋊C4 | 1 | 4 | yes | — |
| 155 | #13867 | C22⋊C4 | 1 | 4 | yes | — |
| 156 | C2×#1440 | C22⋊C4 | 1 | 2 | yes | complemented |
| 157 | C2×#1438 | C22⋊C4 | 1 | 4 | yes | complemented |
| 158 | C2×#1438 | C22×C4 | 1 | 2 | yes | — |
| 159 | C2×#1438 | C2×D4 | 1 | 4 | yes | — |
| 160 | C27 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 161 | C27 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 162 | C27 | #120 | 1 | 2 | yes | — |
| 163 | C27 | #120 | 1 | 1 | yes | characteristic |
| 164 | C27 | C22×D4 | 1 | 1 | yes | characteristic |
| 165 | C23×#41 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 166 | C24×D4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 167 | C24×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 168 | C24×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 169 | C24×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 170 | C24×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 171 | C24×D4 | #120 | 1 | 2 | yes | — |
| 172 | C24×D4 | #120 | 1 | 2 | yes | — |
| 173 | C24×D4 | #120 | 1 | 2 | yes | — |
| 174 | C24×D4 | #120 | 1 | 2 | yes | — |
| 175 | C24×D4 | C23×C4 | 1 | 1 | yes | characteristic |
| 176 | C24×D4 | C22×D4 | 1 | 2 | yes | — |
| 177 | C25×C4 | #120 | 1 | 2 | yes | — |
| 178 | C25×C4 | #120 | 1 | 2 | yes | — |
| 179 | C25×C4 | #120 | 1 | 1 | yes | characteristic |
| 180 | C22×#127 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 181 | C22×#127 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 182 | C22×#124 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 183 | C22×#124 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 184 | C22×#123 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 185 | C22×#123 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 186 | C22×#120 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 187 | C22×#120 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 188 | C22×#120 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 189 | C22×#120 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 190 | C22×#120 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 191 | C22×#120 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 192 | C22×#120 | #120 | 1 | 4 | yes | — |
| 193 | C22×#120 | #120 | 1 | 4 | yes | — |
| 194 | C22×#120 | #120 | 1 | 4 | yes | — |
| 195 | C22×#120 | #120 | 1 | 4 | yes | — |
| 196 | C22×#120 | C22×D4 | 1 | 2 | yes | — |
| 197 | C22×#120 | C22×D4 | 1 | 2 | yes | — |
| 198 | C22×#120 | C22×D4 | 1 | 4 | yes | — |
| 199 | C22×#117 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 200 | C23×C4⋊C4 | #120 | 1 | 2 | yes | — |
| 201 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 202 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 203 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 204 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 205 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 206 | C23×C22⋊C4 | #120 | 1 | 2 | yes | — |
| 207 | C23×C22⋊C4 | #120 | 1 | 2 | yes | — |
| 208 | C23×C22⋊C4 | #120 | 1 | 2 | yes | — |
| 209 | C23×C22⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 210 | C23×C22⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 211 | C23×C42 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 212 | C2×#393 | #120 | 1 | 4 | yes | — |
| 213 | C2×#393 | #120 | 1 | 4 | yes | — |
| 214 | C2×#392 | #120 | 1 | 4 | yes | — |
| 215 | C2×#392 | #120 | 1 | 4 | yes | — |
| 216 | C2×#381 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 217 | C2×#381 | #120 | 1 | 2 | yes | — |
| 218 | C2×#381 | #120 | 1 | 2 | yes | — |
| 219 | C2×#379 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 220 | C2×#379 | #120 | 1 | 2 | yes | — |
| 221 | C2×#379 | #120 | 1 | 2 | yes | — |
| 222 | C2×#379 | #120 | 1 | 2 | yes | — |
| 223 | C2×#379 | #120 | 1 | 4 | yes | — |
| 224 | C2×#379 | #120 | 1 | 1 | yes | characteristic |
| 225 | C2×#379 | #120 | 1 | 1 | yes | characteristic |
| 226 | #1440 | #120 | 1 | 2 | yes | — |
| 227 | #1440 | #120 | 1 | 4 | yes | — |
| 228 | #1440 | #120 | 1 | 2 | yes | — |
| 229 | #1438 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 230 | #1438 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 231 | #1438 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 232 | #1438 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 233 | #1438 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 234 | #1438 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 235 | #1438 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 236 | #1438 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 237 | #1438 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 238 | #1438 | #120 | 1 | 4 | yes | — |
| 239 | #1438 | #120 | 1 | 4 | yes | — |
| 240 | #1438 | #120 | 1 | 4 | yes | — |
| 241 | #1438 | #120 | 1 | 4 | yes | — |
| 242 | #1437 | #120 | 1 | 4 | yes | — |
| 243 | #1437 | #120 | 1 | 4 | yes | — |
| 244 | #1437 | #120 | 1 | 4 | yes | — |
| 245 | #1437 | #120 | 1 | 4 | yes | — |
| 246 | C26 | #379 | 1 | 2 | yes | — |
| 247 | C26 | #379 | 1 | 2 | yes | — |
| 248 | C26 | #379 | 1 | 2 | yes | — |
| 249 | C26 | #379 | 1 | 2 | yes | — |
| 250 | C26 | #379 | 1 | 2 | yes | — |
| 251 | C26 | B(4,𝔽2) | 1 | 4 | yes | — |
| 252 | C26 | #458 | 1 | 4 | yes | — |
| 253 | C26 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 254 | C26 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 255 | C26 | C2×#120 | 1 | 1 | yes | characteristic |
| 256 | C26 | C2×#120 | 1 | 2 | yes | — |
| 257 | C26 | C2×#120 | 1 | 1 | yes | characteristic |
| 258 | C26 | C2×#120 | 1 | 2 | yes | — |
| 259 | C23×Q8 | #379 | 1 | 2 | yes | — |
| 260 | C23×D4 | #379 | 1 | 2 | yes | — |
| 261 | C23×D4 | C22×C22⋊C4 | 1 | 2 | yes | — |
| 262 | C23×D4 | C22×C22⋊C4 | 1 | 2 | yes | — |
| 263 | C23×D4 | C2×#120 | 1 | 4 | yes | — |
| 264 | C23×D4 | C2×#120 | 1 | 4 | yes | — |
| 265 | C24×C4 | #379 | 1 | 2 | yes | — |
| 266 | C24×C4 | #379 | 1 | 2 | yes | — |
| 267 | C24×C4 | #379 | 1 | 2 | yes | — |
| 268 | C24×C4 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 269 | C24×C4 | C2×#120 | 1 | 2 | yes | — |
| 270 | C22×C22⋊C4 | #379 | 1 | 2 | yes | — |
| 271 | C22×C22⋊C4 | #379 | 1 | 2 | yes | — |
| 272 | C22×C22⋊C4 | #379 | 1 | 4 | yes | — |
| 273 | C22×C22⋊C4 | #379 | 1 | 4 | yes | — |
| 274 | C22×C22⋊C4 | #379 | 1 | 4 | yes | — |
| 275 | C22×C22⋊C4 | #379 | 1 | 4 | yes | — |
| 276 | C22×C22⋊C4 | #379 | 1 | 2 | yes | — |
| 277 | C22×C22⋊C4 | #379 | 1 | 2 | yes | — |
| 278 | C22×C22⋊C4 | C2×#120 | 1 | 2 | yes | — |
| 279 | C22×C22⋊C4 | C2×#120 | 1 | 2 | yes | — |
| 280 | C22×C22⋊C4 | C2×#120 | 1 | 4 | yes | — |
| 281 | C22×C22⋊C4 | C2×#120 | 1 | 4 | yes | — |
| 282 | C22×C42 | #379 | 1 | 2 | yes | — |
| 283 | C22×C42 | #379 | 1 | 2 | yes | — |
| 284 | C2×#95 | #379 | 1 | 4 | yes | — |
| 285 | C2×#95 | #379 | 1 | 4 | yes | — |
| 286 | C25 | #1790 | 1 | 4 | yes | — |
| 287 | C25 | #1790 | 1 | 4 | yes | — |
| 288 | C25 | C2×#379 | 1 | 2 | yes | — |
| 289 | C25 | C2×#379 | 1 | 1 | yes | characteristic |
| 290 | C25 | C2×#379 | 1 | 1 | yes | characteristic |
| 291 | C25 | C2×#379 | 1 | 1 | yes | characteristic |
| 292 | C25 | #2846 | 1 | 2 | yes | — |
| 293 | C25 | #2846 | 1 | 2 | yes | — |
| 294 | C25 | #2883 | 1 | 1 | yes | characteristic |
| 295 | C25 | #2883 | 1 | 1 | yes | characteristic |
| 296 | C25 | #2883 | 1 | 1 | yes | characteristic |
| 297 | C25 | #2883 | 1 | 1 | yes | characteristic |
| 298 | C25 | C2×B(4,𝔽2) | 1 | 2 | yes | — |
| 299 | C25 | C2×#458 | 1 | 2 | yes | — |
| 300 | C25 | #3026 | 1 | 2 | yes | — |
| 301 | C25 | #3026 | 1 | 2 | yes | — |
| 302 | C23×C4 | C2×#379 | 1 | 2 | yes | — |
| 303 | C23×C4 | #2846 | 1 | 4 | yes | — |
| 304 | C24 | #14679 | 1 | 1 | yes | characteristic |
| 305 | C24 | #20585 | 1 | 1 | yes | characteristic |
| 306 | C24 | #20585 | 1 | 1 | yes | characteristic |
| 307 | C24 | #20585 | 1 | 1 | yes | characteristic |
| 308 | C24 | #20585 | 1 | 1 | yes | characteristic |
| 309 | C24 | #20586 | 1 | 1 | yes | characteristic |
| 310 | C24 | #20586 | 1 | 1 | yes | characteristic |
| 311 | C24 | C2×#1790 | 1 | 2 | yes | — |
| 312 | C24 | #20609 | 1 | 2 | yes | — |
| 313 | C24 | #32898 | 1 | 2 | yes | — |
| 314 | C24 | #32898 | 1 | 2 | yes | — |
| 315 | C24 | #32900 | 1 | 2 | yes | — |
| 316 | C24 | #32900 | 1 | 2 | yes | — |
| 317 | C23 | #187934 | 1 | 2 | yes | — |
| 318 | C23 | #187940 | 1 | 1 | yes | characteristic |
| 319 | C23 | #187949 | 1 | 1 | yes | characteristic |
| 320 | C23 | #392111 | 1 | 1 | yes | characteristic |
| 321 | C23 | #392125 | 1 | 2 | yes | — |
| 322 | C23 | #493474 | 1 | 4 | yes | — |
| 323 | C23 | #511790 | 1 | 4 | yes | — |
| 324 | C22 | #72218475 | 1 | 2 | yes | — |
| 325 | C22 | #72219393 | 1 | 2 | yes | — |
| 326 | C22 | #72225624 | 1 | 1 | yes | characteristic |
| 327 | C22 | #72237472 | 1 | 2 | yes | — |
| 328 | C22 | #72256144 | 1 | 4 | yes | — |
| 329 | C2 | #72265776 | 1 | 2 | yes | — |
| 330 | C2 | #72265984 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta