← #72323229
Subgroups — #72323229
Order 4096.
At least 20808 conjugacy classes of subgroups; only the 893 normal subgroups are shown.
The subgroup lattice has 318 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72323228 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72323226 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72323225 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #72259029 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72259021 | C22 | 1 | 2 | yes | complemented |
| 6 | #72259008 | C22 | 1 | 1 | yes | characteristic, complemented |
| 7 | #72235847 | C22 | 1 | 1 | yes | characteristic, complemented |
| 8 | #72234665 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #72234663 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | #72234659 | C22 | 1 | 2 | yes | — |
| 11 | #72234658 | C4 | 1 | 2 | yes | complemented |
| 12 | #72234619 | C4 | 1 | 2 | yes | complemented |
| 13 | #72232884 | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | #72232592 | C4 | 1 | 2 | yes | complemented |
| 15 | #72225883 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #72225870 | C22 | 1 | 2 | yes | complemented |
| 17 | #72225868 | C22 | 1 | 2 | yes | complemented |
| 18 | #72224136 | C22 | 1 | 2 | yes | — |
| 19 | C2×#7670203 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#72210482 | C2 | 1 | 4 | yes | maximal, complemented |
| 21 | C2×#150393 | C22 | 1 | 8 | yes | complemented |
| 22 | C2×#150393 | C22 | 1 | 8 | yes | complemented |
| 23 | C2×#134033 | C22 | 1 | 2 | yes | complemented |
| 24 | C2×#115690 | C22 | 1 | 2 | yes | complemented |
| 25 | C2×#6499867 | C22 | 1 | 2 | yes | — |
| 26 | #10586404 | C2×C4 | 1 | 2 | yes | — |
| 27 | C2×#62817 | C2×C4 | 1 | 2 | yes | — |
| 28 | #10586069 | C2×C4 | 1 | 2 | yes | — |
| 29 | C22×#3484 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | C22×#3484 | D4 | 1 | 1 | yes | characteristic |
| 31 | C24×#120 | D4 | 1 | 1 | yes | characteristic |
| 32 | C24×#120 | D4 | 1 | 1 | yes | characteristic |
| 33 | C22×#2846 | C23 | 1 | 1 | yes | characteristic |
| 34 | C2×#35390 | D4 | 1 | 1 | yes | characteristic |
| 35 | C2×#35348 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C2×#35348 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | C2×#35346 | D4 | 1 | 1 | yes | characteristic |
| 38 | C2×#34981 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | C2×#34981 | D4 | 1 | 1 | yes | characteristic |
| 40 | C2×#34980 | D4 | 1 | 1 | yes | characteristic |
| 41 | C2×#34980 | C23 | 1 | 1 | yes | characteristic |
| 42 | C2×#34198 | D4 | 1 | 1 | yes | characteristic |
| 43 | C2×#34198 | C23 | 1 | 1 | yes | characteristic |
| 44 | #6499871 | D4 | 1 | 4 | yes | — |
| 45 | #6499870 | D4 | 1 | 4 | yes | — |
| 46 | #6499869 | D4 | 1 | 4 | yes | — |
| 47 | #6499867 | D4 | 1 | 16 | yes | — |
| 48 | #6499867 | D4 | 1 | 4 | yes | — |
| 49 | #6453039 | C2×C4 | 1 | 4 | yes | — |
| 50 | #6451874 | C2×C4 | 1 | 4 | yes | — |
| 51 | C2×#23984 | C2×C4 | 1 | 4 | yes | — |
| 52 | C2×#23984 | C23 | 1 | 4 | yes | — |
| 53 | #6445521 | D4 | 1 | 4 | yes | — |
| 54 | #6442728 | D4 | 1 | 4 | yes | — |
| 55 | #6432106 | D4 | 1 | 8 | yes | — |
| 56 | #6374128 | C2×C4 | 1 | 2 | yes | — |
| 57 | C2×#21746 | C2×C4 | 1 | 2 | yes | — |
| 58 | #6371007 | C2×C4 | 1 | 2 | yes | — |
| 59 | C2×#11499 | C23 | 1 | 4 | yes | complemented |
| 60 | C2×#8101 | C23 | 1 | 2 | yes | complemented |
| 61 | C2×#8101 | C23 | 1 | 2 | yes | complemented |
| 62 | C28 | C2×D4 | 1 | 1 | yes | characteristic |
| 63 | C23×H(5,𝔽2) | C22⋊C4 | 1 | 1 | yes | characteristic |
| 64 | C25×D4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 65 | C25×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 66 | #62844 | C22⋊C4 | 1 | 4 | yes | complemented |
| 67 | #62843 | C22⋊C4 | 1 | 2 | yes | complemented |
| 68 | #62842 | C22⋊C4 | 1 | 2 | yes | complemented |
| 69 | #62820 | C22⋊C4 | 1 | 4 | yes | complemented |
| 70 | #62817 | C22⋊C4 | 1 | 8 | yes | complemented |
| 71 | #62817 | C22⋊C4 | 1 | 4 | yes | complemented |
| 72 | C2×#3490 | C22×C4 | 1 | 4 | yes | — |
| 73 | C22×#534 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 74 | C22×#534 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 75 | C22×#534 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 76 | C22×#534 | C22×C4 | 1 | 1 | yes | characteristic |
| 77 | C22×#534 | C2×D4 | 1 | 1 | yes | characteristic |
| 78 | C23×#120 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 79 | C23×#120 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 80 | C23×#120 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 81 | C23×#120 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 82 | C23×#120 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 83 | C23×#120 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 84 | C23×#120 | C22×C4 | 1 | 1 | yes | characteristic |
| 85 | C23×#120 | C2×D4 | 1 | 1 | yes | characteristic |
| 86 | C23×#120 | C2×D4 | 1 | 1 | yes | characteristic |
| 87 | C23×#120 | C2×D4 | 1 | 1 | yes | characteristic |
| 88 | C23×#120 | C2×D4 | 1 | 1 | yes | characteristic |
| 89 | C22×#518 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 90 | C22×#518 | C22×C4 | 1 | 1 | yes | characteristic |
| 91 | C24×C22⋊C4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 92 | C24×C22⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 93 | C2×#2849 | C2×D4 | 1 | 2 | yes | — |
| 94 | C2×#2846 | C2×D4 | 1 | 2 | yes | — |
| 95 | C2×#2846 | C2×D4 | 1 | 8 | yes | — |
| 96 | C2×#2613 | C2×D4 | 1 | 2 | yes | — |
| 97 | C2×#2613 | C2×D4 | 1 | 2 | yes | — |
| 98 | #34198 | C2×D4 | 1 | 4 | yes | — |
| 99 | #34198 | C2×D4 | 1 | 4 | yes | — |
| 100 | C2×#2315 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 101 | C2×#2315 | C22×C4 | 1 | 1 | yes | characteristic |
| 102 | C2×#2308 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 103 | C2×#2308 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 104 | C2×#2308 | C22×C4 | 1 | 1 | yes | characteristic |
| 105 | C2×#2308 | C2×D4 | 1 | 1 | yes | characteristic |
| 106 | C2×#2308 | C2×D4 | 1 | 1 | yes | characteristic |
| 107 | C22×#379 | C22×C4 | 1 | 1 | yes | characteristic |
| 108 | C22×#379 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C22×#379 | C24 | 1 | 1 | yes | characteristic |
| 110 | C2×#2273 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | #23985 | C22⋊C4 | 1 | 8 | yes | complemented |
| 112 | #23984 | C22⋊C4 | 1 | 16 | yes | complemented |
| 113 | #23984 | C22⋊C4 | 1 | 8 | yes | complemented |
| 114 | #23984 | C2×D4 | 1 | 8 | yes | — |
| 115 | #23984 | C2×D4 | 1 | 8 | yes | — |
| 116 | #23984 | C2×D4 | 1 | 16 | yes | — |
| 117 | #23565 | C22⋊C4 | 1 | 8 | yes | complemented |
| 118 | #23515 | C22⋊C4 | 1 | 8 | yes | complemented |
| 119 | C2×#2029 | C2×D4 | 1 | 8 | yes | — |
| 120 | C2×#2021 | C2×D4 | 1 | 8 | yes | — |
| 121 | #21747 | C22⋊C4 | 1 | 4 | yes | complemented |
| 122 | #21746 | C22⋊C4 | 1 | 8 | yes | complemented |
| 123 | #21746 | C22⋊C4 | 1 | 4 | yes | complemented |
| 124 | C2×#1819 | C22×C4 | 1 | 4 | yes | — |
| 125 | #20633 | C22⋊C4 | 1 | 4 | yes | complemented |
| 126 | #20392 | C22⋊C4 | 1 | 4 | yes | complemented |
| 127 | C27 | #99 | 1 | 1 | yes | characteristic |
| 128 | C27 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 129 | C27 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 130 | C27 | #120 | 1 | 1 | yes | characteristic |
| 131 | C27 | #120 | 1 | 4 | yes | — |
| 132 | C27 | C22×D4 | 1 | 1 | yes | characteristic |
| 133 | C22×H(5,𝔽2) | #99 | 1 | 2 | yes | — |
| 134 | C22×H(5,𝔽2) | #99 | 1 | 2 | yes | — |
| 135 | C24×D4 | #99 | 1 | 1 | yes | characteristic |
| 136 | C24×D4 | #99 | 1 | 1 | yes | characteristic |
| 137 | C24×D4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 138 | C24×D4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 139 | C24×D4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 140 | C24×D4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 141 | C24×D4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 142 | C24×D4 | #120 | 1 | 1 | yes | characteristic |
| 143 | C24×D4 | #120 | 1 | 1 | yes | characteristic |
| 144 | C25×C4 | #99 | 1 | 1 | yes | characteristic |
| 145 | C25×C4 | #120 | 1 | 1 | yes | characteristic |
| 146 | #3490 | C2×C22⋊C4 | 1 | 8 | yes | — |
| 147 | #3490 | C2×C22⋊C4 | 1 | 8 | yes | — |
| 148 | C2×#543 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 149 | C2×#534 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 150 | C22×#123 | #99 | 1 | 2 | yes | — |
| 151 | C22×#123 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 152 | C22×#123 | #120 | 1 | 2 | yes | — |
| 153 | C22×#120 | #99 | 1 | 4 | yes | — |
| 154 | C22×#120 | #99 | 1 | 2 | yes | — |
| 155 | C22×#120 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 156 | C22×#120 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 157 | C22×#120 | #120 | 1 | 4 | yes | — |
| 158 | C22×#120 | #120 | 1 | 2 | yes | — |
| 159 | C22×#120 | #120 | 1 | 2 | yes | — |
| 160 | C22×#120 | #120 | 1 | 2 | yes | — |
| 161 | C22×#120 | #120 | 1 | 4 | yes | — |
| 162 | C22×#120 | #120 | 1 | 2 | yes | — |
| 163 | C22×#120 | #120 | 1 | 2 | yes | — |
| 164 | C2×#518 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 165 | C2×#518 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 166 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 167 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 168 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 169 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 170 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 171 | C23×C22⋊C4 | #120 | 1 | 4 | yes | — |
| 172 | C23×C22⋊C4 | C23×C4 | 1 | 1 | yes | characteristic |
| 173 | C23×C22⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 174 | #2315 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 175 | #2308 | #120 | 1 | 2 | yes | — |
| 176 | #2308 | #120 | 1 | 2 | yes | — |
| 177 | C2×#381 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 178 | C2×#381 | #120 | 1 | 2 | yes | — |
| 179 | C2×#379 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 180 | C2×#379 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 181 | C2×#379 | #120 | 1 | 4 | yes | — |
| 182 | C2×#379 | #120 | 1 | 2 | yes | — |
| 183 | C2×#379 | C22×D4 | 1 | 2 | yes | — |
| 184 | C2×#379 | C22×D4 | 1 | 2 | yes | — |
| 185 | C2×#379 | C22×D4 | 1 | 4 | yes | — |
| 186 | C2×#379 | C22×D4 | 1 | 4 | yes | — |
| 187 | #2273 | #120 | 1 | 4 | yes | — |
| 188 | #2029 | #120 | 1 | 16 | yes | — |
| 189 | #2029 | #120 | 1 | 16 | yes | — |
| 190 | #2021 | #120 | 1 | 16 | yes | — |
| 191 | #2021 | #120 | 1 | 16 | yes | — |
| 192 | #1819 | C2×C22⋊C4 | 1 | 8 | yes | — |
| 193 | #1819 | C2×C22⋊C4 | 1 | 8 | yes | — |
| 194 | C2×#342 | C2×C22⋊C4 | 1 | 8 | yes | — |
| 195 | C26 | #379 | 1 | 1 | yes | characteristic |
| 196 | C26 | #379 | 1 | 2 | yes | — |
| 197 | C26 | #379 | 1 | 1 | yes | characteristic |
| 198 | C26 | #379 | 1 | 2 | yes | — |
| 199 | C26 | C2×#99 | 1 | 1 | yes | characteristic |
| 200 | C26 | C2×#99 | 1 | 1 | yes | characteristic |
| 201 | C26 | C2×#99 | 1 | 2 | yes | — |
| 202 | C26 | C2×#99 | 1 | 1 | yes | characteristic |
| 203 | C26 | C2×#99 | 1 | 1 | yes | characteristic |
| 204 | C26 | C2×#99 | 1 | 1 | yes | characteristic |
| 205 | C26 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 206 | C26 | C2×#120 | 1 | 1 | yes | characteristic |
| 207 | C26 | C2×#120 | 1 | 2 | yes | — |
| 208 | C26 | C2×#120 | 1 | 1 | yes | characteristic |
| 209 | C26 | C2×#120 | 1 | 2 | yes | — |
| 210 | C23×D4 | #379 | 1 | 1 | yes | characteristic |
| 211 | C23×D4 | #379 | 1 | 1 | yes | characteristic |
| 212 | C23×D4 | #379 | 1 | 2 | yes | — |
| 213 | C23×D4 | #379 | 1 | 2 | yes | — |
| 214 | C23×D4 | C2×#99 | 1 | 2 | yes | — |
| 215 | C23×D4 | C2×#99 | 1 | 2 | yes | — |
| 216 | C23×D4 | C2×#99 | 1 | 1 | yes | characteristic |
| 217 | C23×D4 | C2×#99 | 1 | 1 | yes | characteristic |
| 218 | C23×D4 | C2×#99 | 1 | 2 | yes | — |
| 219 | C23×D4 | C2×#99 | 1 | 2 | yes | — |
| 220 | C24×C4 | #379 | 1 | 1 | yes | characteristic |
| 221 | C24×C4 | #379 | 1 | 1 | yes | characteristic |
| 222 | C24×C4 | C2×#99 | 1 | 1 | yes | characteristic |
| 223 | C24×C4 | C2×#99 | 1 | 1 | yes | characteristic |
| 224 | C24×C4 | C2×#99 | 1 | 1 | yes | characteristic |
| 225 | #543 | #379 | 1 | 8 | yes | — |
| 226 | #534 | #379 | 1 | 8 | yes | — |
| 227 | C2×#120 | AΣL(1,𝔽16) | 1 | 8 | yes | — |
| 228 | C2×#120 | AΣL(1,𝔽16) | 1 | 8 | yes | — |
| 229 | C2×#120 | #453 | 1 | 4 | yes | — |
| 230 | C2×#120 | #455 | 1 | 4 | yes | — |
| 231 | C22×C22⋊C4 | #379 | 1 | 2 | yes | — |
| 232 | C22×C22⋊C4 | #379 | 1 | 2 | yes | — |
| 233 | C22×C22⋊C4 | #379 | 1 | 2 | yes | — |
| 234 | C22×C22⋊C4 | #379 | 1 | 2 | yes | — |
| 235 | C22×C22⋊C4 | #379 | 1 | 2 | yes | — |
| 236 | C22×C22⋊C4 | C2×#99 | 1 | 2 | yes | — |
| 237 | C22×C22⋊C4 | C2×#99 | 1 | 2 | yes | — |
| 238 | C22×C22⋊C4 | C22×C22⋊C4 | 1 | 2 | yes | — |
| 239 | C22×C22⋊C4 | C22×C22⋊C4 | 1 | 2 | yes | — |
| 240 | C22×C22⋊C4 | C22×C22⋊C4 | 1 | 2 | yes | — |
| 241 | C22×C22⋊C4 | C2×#120 | 1 | 2 | yes | — |
| 242 | C22×C22⋊C4 | C2×#120 | 1 | 2 | yes | — |
| 243 | C22×C22⋊C4 | C2×#120 | 1 | 2 | yes | — |
| 244 | #379 | C2×#120 | 1 | 8 | yes | — |
| 245 | #379 | C2×#120 | 1 | 8 | yes | — |
| 246 | #342 | #379 | 1 | 16 | yes | — |
| 247 | C25 | #1781 | 1 | 1 | yes | characteristic |
| 248 | C25 | #1781 | 1 | 2 | yes | — |
| 249 | C25 | #1781 | 1 | 1 | yes | characteristic |
| 250 | C25 | #1781 | 1 | 2 | yes | — |
| 251 | C25 | #1781 | 1 | 2 | yes | — |
| 252 | C25 | #1781 | 1 | 2 | yes | — |
| 253 | C25 | #1781 | 1 | 2 | yes | — |
| 254 | C25 | C2×AΣL(1,𝔽16) | 1 | 4 | yes | — |
| 255 | C25 | C2×AΣL(1,𝔽16) | 1 | 4 | yes | — |
| 256 | C25 | C2×#379 | 1 | 1 | yes | characteristic |
| 257 | C25 | C2×#379 | 1 | 1 | yes | characteristic |
| 258 | C25 | C2×#379 | 1 | 1 | yes | characteristic |
| 259 | C25 | #2846 | 1 | 2 | yes | — |
| 260 | C25 | #2846 | 1 | 2 | yes | — |
| 261 | C25 | C22×#99 | 1 | 1 | yes | characteristic |
| 262 | C25 | C22×#99 | 1 | 1 | yes | characteristic |
| 263 | C25 | C22×#99 | 1 | 1 | yes | characteristic |
| 264 | C25 | C22×#99 | 1 | 1 | yes | characteristic |
| 265 | C25 | C2×#453 | 1 | 2 | yes | — |
| 266 | C25 | C2×#455 | 1 | 2 | yes | — |
| 267 | C25 | #3019 | 1 | 2 | yes | — |
| 268 | C25 | #3019 | 1 | 2 | yes | — |
| 269 | C22×D4 | #1792 | 1 | 4 | yes | — |
| 270 | C22×D4 | C2×AΣL(1,𝔽16) | 1 | 8 | yes | — |
| 271 | C23×C4 | #1781 | 1 | 1 | yes | characteristic |
| 272 | C23×C4 | #1781 | 1 | 1 | yes | characteristic |
| 273 | C23×C4 | #1781 | 1 | 2 | yes | — |
| 274 | C23×C4 | #1781 | 1 | 2 | yes | — |
| 275 | C23×C4 | #1781 | 1 | 2 | yes | — |
| 276 | C2×C22⋊C4 | #1781 | 1 | 4 | yes | — |
| 277 | C2×C22⋊C4 | #1792 | 1 | 4 | yes | — |
| 278 | C2×C22⋊C4 | C2×AΣL(1,𝔽16) | 1 | 8 | yes | — |
| 279 | C2×C22⋊C4 | C2×#379 | 1 | 4 | yes | — |
| 280 | C2×C22⋊C4 | #2846 | 1 | 4 | yes | — |
| 281 | C24 | #8453 | 1 | 2 | yes | — |
| 282 | C24 | #12687 | 1 | 2 | yes | — |
| 283 | C24 | #12687 | 1 | 4 | yes | — |
| 284 | C24 | #12687 | 1 | 4 | yes | — |
| 285 | C24 | #12687 | 1 | 2 | yes | — |
| 286 | C24 | #14679 | 1 | 1 | yes | characteristic |
| 287 | C24 | C2×#1781 | 1 | 1 | yes | characteristic |
| 288 | C24 | C2×#1781 | 1 | 1 | yes | characteristic |
| 289 | C24 | C2×#1781 | 1 | 1 | yes | characteristic |
| 290 | C24 | C2×#1781 | 1 | 1 | yes | characteristic |
| 291 | C24 | C2×#1781 | 1 | 1 | yes | characteristic |
| 292 | C24 | C2×#1781 | 1 | 1 | yes | characteristic |
| 293 | C24 | C2×#1792 | 1 | 2 | yes | — |
| 294 | C24 | #20616 | 1 | 2 | yes | — |
| 295 | C24 | #32888 | 1 | 2 | yes | — |
| 296 | C24 | #32888 | 1 | 2 | yes | — |
| 297 | C24 | #32891 | 1 | 2 | yes | — |
| 298 | C24 | #32891 | 1 | 2 | yes | — |
| 299 | C24 | C22×AΣL(1,𝔽16) | 1 | 4 | yes | — |
| 300 | C22×C4 | #8453 | 1 | 2 | yes | — |
| 301 | C22×C4 | #12687 | 1 | 4 | yes | — |
| 302 | C22⋊C4 | #12687 | 1 | 8 | yes | — |
| 303 | C23 | C2×#8453 | 1 | 1 | yes | characteristic |
| 304 | C23 | #186808 | 1 | 2 | yes | — |
| 305 | C23 | #186835 | 1 | 1 | yes | characteristic |
| 306 | C23 | #392109 | 1 | 1 | yes | characteristic |
| 307 | C23 | #392128 | 1 | 2 | yes | — |
| 308 | C23 | C2×#12687 | 1 | 2 | yes | — |
| 309 | C23 | C2×#12687 | 1 | 2 | yes | — |
| 310 | C23 | C2×#12687 | 1 | 2 | yes | — |
| 311 | C23 | #493398 | 1 | 2 | yes | — |
| 312 | C22 | #72215179 | 1 | 1 | yes | characteristic |
| 313 | C22 | #72219245 | 1 | 1 | yes | characteristic |
| 314 | C22 | #72258026 | 1 | 1 | yes | characteristic |
| 315 | C22 | #72266291 | 1 | 4 | yes | — |
| 316 | C2 | #72266293 | 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