← #27398010
Subgroups — #27398010
Order 13568.
772 conjugacy classes of subgroups.
The subgroup lattice has 436 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #20285210 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #20283632 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #20283582 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20275630 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20275249 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #20275235 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #20275212 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #20275186 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #20274838 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #20274470 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C53×#1976 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C2×#13133247 | C22 | 1 | 2 | yes | — |
| 13 | C22×Dic212 | C22 | 1 | 1 | yes | characteristic |
| 14 | #16811390 | C22 | 1 | 2 | yes | — |
| 15 | #16811194 | C22 | 1 | 2 | yes | — |
| 16 | #16811100 | C22 | 1 | 2 | yes | — |
| 17 | #16811014 | C4 | 1 | 4 | yes | complemented |
| 18 | #16811006 | C4 | 1 | 2 | yes | complemented |
| 19 | #16811001 | C4 | 1 | 2 | yes | complemented |
| 20 | #16810745 | — | 2 | 2 | no | — |
| 21 | #16810740 | — | 2 | 2 | no | — |
| 22 | #16810729 | — | 2 | 2 | no | — |
| 23 | #16810717 | — | 2 | 2 | no | — |
| 24 | C2×#13133153 | C22 | 1 | 1 | yes | characteristic |
| 25 | #16810640 | C22 | 1 | 2 | yes | — |
| 26 | #16810631 | C22 | 1 | 2 | yes | — |
| 27 | #16810631 | C22 | 1 | 2 | yes | — |
| 28 | C2×#13133135 | C22 | 1 | 2 | yes | — |
| 29 | #16810578 | C22 | 1 | 1 | yes | characteristic |
| 30 | #16810578 | C22 | 1 | 1 | yes | characteristic |
| 31 | #16810393 | C22 | 1 | 2 | yes | — |
| 32 | #16810381 | C22 | 1 | 1 | yes | characteristic |
| 33 | #16810380 | C22 | 1 | 1 | yes | characteristic |
| 34 | #16810379 | C22 | 1 | 1 | yes | characteristic |
| 35 | #16810379 | C22 | 1 | 1 | yes | characteristic |
| 36 | #16810379 | C22 | 1 | 2 | yes | — |
| 37 | C2×#135×C53 | C22 | 1 | 1 | yes | characteristic |
| 38 | C53×#427 | C22 | 1 | 1 | yes | characteristic |
| 39 | C53×#421 | C22 | 1 | 2 | yes | — |
| 40 | C53×#410 | C22 | 1 | 2 | yes | — |
| 41 | C53×#405 | C22 | 1 | 1 | yes | characteristic |
| 42 | C22×Dic106 | C23 | 1 | 2 | yes | — |
| 43 | #13133247 | — | 4 | 2 | no | — |
| 44 | #13133247 | — | 4 | 2 | no | — |
| 45 | C2×Dic212 | — | 2 | 1 | no | — |
| 46 | C2×Dic212 | — | 2 | 1 | no | — |
| 47 | C2×Dic212 | — | 2 | 1 | no | — |
| 48 | C2×Dic212 | — | 2 | 1 | no | — |
| 49 | C2×Dic212 | C2×C4 | 1 | 2 | yes | — |
| 50 | C2×Dic212 | C2×C4 | 1 | 2 | yes | — |
| 51 | C2×#11719925 | C2×C4 | 1 | 4 | yes | — |
| 52 | C2×#11719923 | C2×C4 | 1 | 4 | yes | — |
| 53 | #13133224 | — | 2 | 4 | no | — |
| 54 | #13133224 | — | 4 | 2 | no | — |
| 55 | C2×#11719917 | — | 4 | 2 | no | — |
| 56 | C2×#11719917 | C23 | 1 | 2 | yes | — |
| 57 | C2×#11719917 | C23 | 1 | 1 | yes | characteristic |
| 58 | C2×#11719917 | C23 | 1 | 1 | yes | characteristic |
| 59 | #13133215 | C2×C4 | 1 | 4 | yes | — |
| 60 | #13133204 | C2×C4 | 1 | 4 | yes | — |
| 61 | #13133198 | — | 4 | 2 | no | — |
| 62 | #13133196 | — | 4 | 2 | no | — |
| 63 | C4×Dic106 | — | 4 | 2 | no | — |
| 64 | #13133182 | — | 2 | 4 | no | — |
| 65 | #13133176 | C23 | 1 | 1 | yes | characteristic |
| 66 | #13133176 | C23 | 1 | 1 | yes | characteristic |
| 67 | #13133173 | — | 4 | 2 | no | — |
| 68 | #13133153 | — | 2 | 1 | no | — |
| 69 | #13133153 | — | 2 | 1 | no | — |
| 70 | #13133144 | — | 2 | 4 | no | — |
| 71 | #13133140 | — | 2 | 4 | no | — |
| 72 | #13133140 | — | 4 | 2 | no | — |
| 73 | #13133135 | — | 4 | 2 | no | — |
| 74 | #13133127 | C2×C4 | 1 | 2 | yes | — |
| 75 | #13133127 | D4 | 1 | 2 | yes | — |
| 76 | C8×Dic53 | C2×C4 | 1 | 2 | yes | — |
| 77 | C8×Dic53 | D4 | 1 | 2 | yes | — |
| 78 | C2×#41×C53 | C23 | 1 | 2 | yes | — |
| 79 | #135×C53 | — | 2 | 1 | no | — |
| 80 | #135×C53 | — | 2 | 1 | no | — |
| 81 | #135×C53 | — | 2 | 1 | no | — |
| 82 | #135×C53 | — | 2 | 1 | no | — |
| 83 | C2×Q16×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | C2×SD16×C53 | C2×C4 | 1 | 2 | yes | — |
| 85 | C2×D8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 86 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 87 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 88 | #117×C53 | C23 | 1 | 2 | yes | — |
| 89 | #117×C53 | C23 | 1 | 1 | yes | characteristic |
| 90 | #107×C53 | — | 2 | 1 | no | — |
| 91 | #106×C53 | — | 2 | 1 | no | — |
| 92 | #104×C53 | — | 4 | 2 | no | — |
| 93 | #99×C53 | — | 4 | 2 | no | — |
| 94 | #97×C53 | — | 2 | 1 | no | — |
| 95 | C4×C8×C53 | — | 2 | 1 | no | — |
| 96 | #41×C53 | — | 2 | 2 | no | — |
| 97 | #41×C53 | — | 2 | 2 | no | — |
| 98 | #41×C53 | — | 2 | 2 | no | — |
| 99 | #41×C53 | — | 2 | 2 | no | — |
| 100 | C2×Q8×C53 | C22×C4 | 1 | 2 | yes | — |
| 101 | C2×D4×C53 | — | 2 | 2 | no | — |
| 102 | C2×D4×C53 | C22×C4 | 1 | 2 | yes | — |
| 103 | C22×C4×C53 | — | 2 | 2 | no | — |
| 104 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 105 | C22×Dic53 | — | 2 | 2 | no | — |
| 106 | C2×Dic106 | — | 2 | 2 | no | — |
| 107 | C2×Dic106 | — | 2 | 2 | no | — |
| 108 | C2×Dic106 | — | 2 | 2 | no | — |
| 109 | C2×Dic106 | — | 2 | 2 | no | — |
| 110 | C2×Dic106 | — | 2 | 2 | no | — |
| 111 | C2×Dic106 | C22×C4 | 1 | 4 | yes | — |
| 112 | Q16×C53 | — | 2 | 1 | no | — |
| 113 | Q16×C53 | — | 2 | 1 | no | — |
| 114 | SD16×C53 | — | 2 | 2 | no | — |
| 115 | SD16×C53 | — | 2 | 2 | no | — |
| 116 | D8×C53 | — | 2 | 1 | no | — |
| 117 | D8×C53 | — | 2 | 1 | no | — |
| 118 | M16×C53 | — | 2 | 1 | no | — |
| 119 | M16×C53 | — | 2 | 1 | no | — |
| 120 | C2×C8×C53 | — | 2 | 1 | no | — |
| 121 | C2×C8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 122 | C2×C8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 123 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | C2×C8×C53 | #41 | 1 | 1 | yes | characteristic |
| 126 | C2×C8×C53 | #41 | 1 | 1 | yes | characteristic |
| 127 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 128 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 129 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 130 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 131 | C42×C53 | — | 2 | 1 | no | — |
| 132 | C42×C53 | — | 2 | 2 | no | — |
| 133 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 134 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 135 | C22⋊Dic53 | — | 4 | 4 | no | — |
| 136 | #11719925 | — | 4 | 4 | no | — |
| 137 | #11719923 | — | 4 | 4 | no | — |
| 138 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 139 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 140 | #11719919 | — | 4 | 4 | no | — |
| 141 | #11719919 | — | 4 | 4 | no | — |
| 142 | C4×Dic53 | — | 4 | 4 | no | — |
| 143 | C4×Dic53 | C22×C4 | 1 | 2 | yes | — |
| 144 | C4×Dic53 | C2×D4 | 1 | 2 | yes | — |
| 145 | #11719917 | — | 2 | 1 | no | — |
| 146 | #11719917 | — | 2 | 1 | no | — |
| 147 | #11719917 | — | 2 | 1 | no | — |
| 148 | #11719917 | — | 2 | 1 | no | — |
| 149 | #11719917 | — | 2 | 2 | no | — |
| 150 | #11719917 | — | 2 | 2 | no | — |
| 151 | #11719917 | — | 4 | 4 | no | — |
| 152 | C2×#88322 | — | 2 | 2 | no | — |
| 153 | C2×#88322 | — | 4 | 4 | no | — |
| 154 | C2×#88322 | C22×C4 | 1 | 2 | yes | — |
| 155 | C2×#88322 | C2×D4 | 1 | 2 | yes | — |
| 156 | Dic212 | — | 2 | 2 | no | — |
| 157 | Dic212 | — | 2 | 2 | no | — |
| 158 | Dic212 | — | 2 | 2 | no | — |
| 159 | Dic212 | — | 2 | 2 | no | — |
| 160 | C23×C53 | — | 2 | 2 | no | — |
| 161 | C23×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 162 | Q8×C53 | — | 2 | 2 | no | — |
| 163 | Q8×C53 | — | 2 | 2 | no | — |
| 164 | D4×C53 | — | 2 | 2 | no | — |
| 165 | D4×C53 | — | 2 | 2 | no | — |
| 166 | D4×C53 | — | 4 | 2 | no | — |
| 167 | D4×C53 | — | 4 | 2 | no | — |
| 168 | C2×C4×C53 | — | 2 | 2 | no | — |
| 169 | C2×C4×C53 | — | 4 | 2 | no | — |
| 170 | C2×C4×C53 | — | 4 | 2 | no | — |
| 171 | C2×C4×C53 | — | 4 | 2 | no | — |
| 172 | C2×C4×C53 | — | 4 | 1 | no | — |
| 173 | C2×C4×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 174 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 175 | C2×C4×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 176 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 177 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 178 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 179 | C2×Dic53 | — | 2 | 4 | no | — |
| 180 | C2×Dic53 | — | 2 | 2 | no | — |
| 181 | C2×Dic53 | — | 2 | 2 | no | — |
| 182 | C2×Dic53 | — | 4 | 2 | no | — |
| 183 | C2×Dic53 | — | 4 | 2 | no | — |
| 184 | Dic106 | — | 2 | 4 | no | — |
| 185 | Dic106 | — | 2 | 4 | no | — |
| 186 | Dic106 | — | 4 | 2 | no | — |
| 187 | Dic106 | — | 4 | 2 | no | — |
| 188 | C8×C53 | — | 4 | 1 | no | — |
| 189 | C8×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 190 | C8×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 191 | C8×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 192 | C8×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 193 | #88322 | — | 2 | 2 | no | — |
| 194 | #88322 | — | 2 | 2 | no | — |
| 195 | #88322 | — | 4 | 2 | no | — |
| 196 | #22285 | — | 53 | 1 | no | maximal, Sylow |
| 197 | C22×C53 | — | 4 | 1 | no | — |
| 198 | C22×C53 | — | 4 | 2 | no | — |
| 199 | C22×C53 | — | 8 | 2 | no | — |
| 200 | C22×C53 | #518 | 1 | 1 | yes | characteristic |
| 201 | C22×C53 | #535 | 1 | 1 | yes | characteristic |
| 202 | C22×C53 | #540 | 1 | 1 | yes | characteristic |
| 203 | C4×C53 | — | 4 | 2 | no | — |
| 204 | C4×C53 | — | 8 | 2 | no | — |
| 205 | C4×C53 | — | 8 | 1 | no | — |
| 206 | C4×C53 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 207 | C4×C53 | #518 | 1 | 1 | yes | characteristic |
| 208 | C4×C53 | #535 | 1 | 1 | yes | characteristic |
| 209 | C4×C53 | #540 | 1 | 1 | yes | characteristic |
| 210 | Dic53 | — | 4 | 2 | no | — |
| 211 | Dic53 | — | 4 | 2 | no | — |
| 212 | Dic53 | — | 4 | 4 | no | — |
| 213 | #3156 | — | 53 | 1 | no | — |
| 214 | #2957 | — | 53 | 1 | no | — |
| 215 | #2950 | — | 53 | 1 | no | — |
| 216 | #1979 | — | 53 | 1 | no | — |
| 217 | #1976 | D53 | 1 | 1 | yes | characteristic |
| 218 | #1912 | — | 53 | 2 | no | — |
| 219 | #1909 | — | 53 | 2 | no | — |
| 220 | #1905 | — | 53 | 2 | no | — |
| 221 | #1902 | — | 53 | 2 | no | — |
| 222 | #1833 | — | 53 | 1 | no | — |
| 223 | #1747 | — | 53 | 1 | no | — |
| 224 | C2×C53 | — | 2 | 1 | no | — |
| 225 | C2×C53 | — | 2 | 1 | no | — |
| 226 | C2×C53 | — | 2 | 1 | no | — |
| 227 | C2×C53 | — | 8 | 2 | no | — |
| 228 | C2×C53 | #2328 | 1 | 1 | yes | characteristic |
| 229 | C2×#137 | — | 53 | 2 | no | — |
| 230 | C2×#135 | C2×D53 | 1 | 1 | yes | characteristic |
| 231 | C22×Q16 | — | 53 | 1 | no | — |
| 232 | #568 | — | 53 | 2 | no | — |
| 233 | #536 | — | 53 | 2 | no | — |
| 234 | #519 | — | 53 | 2 | no | — |
| 235 | #497 | — | 53 | 4 | no | — |
| 236 | #495 | — | 53 | 2 | no | — |
| 237 | #494 | — | 53 | 2 | no | — |
| 238 | #444 | — | 106 | 2 | no | — |
| 239 | #443 | — | 106 | 2 | no | — |
| 240 | #441 | — | 106 | 2 | no | — |
| 241 | C4×Q16 | — | 106 | 2 | no | — |
| 242 | C2×#108 | — | 53 | 1 | no | — |
| 243 | #427 | C2×D53 | 1 | 1 | yes | characteristic |
| 244 | #421 | — | 53 | 2 | no | — |
| 245 | #421 | C2×D53 | 1 | 2 | yes | — |
| 246 | #419 | — | 53 | 2 | no | — |
| 247 | #419 | — | 53 | 2 | no | — |
| 248 | C2×#101 | — | 53 | 2 | no | — |
| 249 | #410 | C2×D53 | 1 | 2 | yes | — |
| 250 | #405 | — | 53 | 1 | no | — |
| 251 | #405 | — | 53 | 1 | no | — |
| 252 | #405 | C2×D53 | 1 | 1 | yes | characteristic |
| 253 | #344 | — | 53 | 2 | no | — |
| 254 | #338 | — | 53 | 1 | no | — |
| 255 | H(3,ℤ/4) | — | 53 | 1 | no | — |
| 256 | H(3,ℤ/4) | — | 53 | 2 | no | — |
| 257 | H(3,ℤ/4) | — | 53 | 1 | no | — |
| 258 | H(3,ℤ/4) | — | 53 | 1 | no | — |
| 259 | C53 | #22285 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 260 | C2×#41 | C22×D53 | 1 | 2 | yes | — |
| 261 | C22×Q8 | — | 53 | 2 | no | — |
| 262 | #137 | — | 212 | 2 | no | — |
| 263 | #137 | — | 212 | 2 | no | — |
| 264 | #135 | — | 2 | 1 | no | — |
| 265 | #135 | — | 2 | 1 | no | — |
| 266 | #135 | — | 2 | 1 | no | — |
| 267 | #135 | — | 2 | 1 | no | — |
| 268 | C2×Q16 | — | 53 | 4 | no | — |
| 269 | C2×Q16 | — | 53 | 2 | no | — |
| 270 | C2×Q16 | — | 53 | 2 | no | — |
| 271 | C2×Q16 | — | 106 | 1 | no | — |
| 272 | C2×Q16 | — | 106 | 1 | no | — |
| 273 | C2×Q16 | — | 106 | 1 | no | — |
| 274 | C2×Q16 | — | 106 | 1 | no | — |
| 275 | C2×Q16 | C4×D53 | 1 | 1 | yes | characteristic |
| 276 | C2×SD16 | — | 53 | 4 | no | — |
| 277 | C2×SD16 | C4×D53 | 1 | 2 | yes | — |
| 278 | C2×D8 | C4×D53 | 1 | 1 | yes | characteristic |
| 279 | #131 | — | 106 | 4 | no | — |
| 280 | #131 | — | 212 | 2 | no | — |
| 281 | C2×M16 | — | 53 | 1 | no | — |
| 282 | C2×M16 | — | 53 | 1 | no | — |
| 283 | C2×M16 | — | 53 | 2 | no | — |
| 284 | C2×M16 | — | 212 | 2 | no | — |
| 285 | C2×M16 | C22×D53 | 1 | 1 | yes | characteristic |
| 286 | C22×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 287 | C4⋊Q8 | — | 53 | 4 | no | — |
| 288 | #124 | — | 53 | 4 | no | — |
| 289 | #123 | — | 212 | 2 | no | — |
| 290 | C22⋊Q8 | — | 212 | 2 | no | — |
| 291 | C4×Q8 | — | 106 | 4 | no | — |
| 292 | C4×Q8 | — | 212 | 2 | no | — |
| 293 | #117 | — | 53 | 1 | no | — |
| 294 | #117 | — | 53 | 1 | no | — |
| 295 | #117 | — | 212 | 2 | no | — |
| 296 | #117 | C22×D53 | 1 | 2 | yes | — |
| 297 | #117 | C22×D53 | 1 | 1 | yes | characteristic |
| 298 | #108 | — | 106 | 1 | no | — |
| 299 | #108 | — | 106 | 1 | no | — |
| 300 | #107 | — | 2 | 1 | no | — |
| 301 | #106 | — | 2 | 1 | no | — |
| 302 | #104 | — | 4 | 2 | no | — |
| 303 | #104 | — | 106 | 4 | no | — |
| 304 | #103 | — | 106 | 4 | no | — |
| 305 | #103 | — | 212 | 2 | no | — |
| 306 | #101 | — | 212 | 2 | no | — |
| 307 | #99 | — | 4 | 2 | no | — |
| 308 | #97 | — | 2 | 1 | no | — |
| 309 | #97 | — | 53 | 2 | no | — |
| 310 | #97 | — | 53 | 2 | no | — |
| 311 | C4×C8 | — | 2 | 1 | no | — |
| 312 | C4×C8 | — | 53 | 2 | no | — |
| 313 | C4×C8 | — | 53 | 2 | no | — |
| 314 | #41 | — | 2 | 2 | no | — |
| 315 | #41 | — | 2 | 2 | no | — |
| 316 | #41 | — | 2 | 2 | no | — |
| 317 | #41 | — | 2 | 2 | no | — |
| 318 | C2×Q8 | — | 53 | 4 | no | — |
| 319 | C2×Q8 | — | 106 | 2 | no | — |
| 320 | C2×Q8 | — | 106 | 2 | no | — |
| 321 | C2×Q8 | — | 106 | 2 | no | — |
| 322 | C2×Q8 | — | 106 | 2 | no | — |
| 323 | C2×Q8 | — | 106 | 2 | no | — |
| 324 | C2×Q8 | C2×C4×D53 | 1 | 2 | yes | — |
| 325 | C2×D4 | — | 2 | 2 | no | — |
| 326 | C2×D4 | C2×C4×D53 | 1 | 2 | yes | — |
| 327 | C22×C4 | — | 2 | 2 | no | — |
| 328 | C22×C4 | — | 106 | 2 | no | — |
| 329 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 330 | Q16 | — | 2 | 1 | no | — |
| 331 | Q16 | — | 2 | 1 | no | — |
| 332 | Q16 | — | 106 | 2 | no | — |
| 333 | Q16 | — | 106 | 2 | no | — |
| 334 | Q16 | — | 106 | 2 | no | — |
| 335 | Q16 | — | 106 | 2 | no | — |
| 336 | Q16 | — | 212 | 4 | no | — |
| 337 | SD16 | — | 2 | 2 | no | — |
| 338 | SD16 | — | 2 | 2 | no | — |
| 339 | SD16 | — | 212 | 4 | no | — |
| 340 | D8 | — | 2 | 1 | no | — |
| 341 | D8 | — | 2 | 1 | no | — |
| 342 | M16 | — | 2 | 1 | no | — |
| 343 | M16 | — | 2 | 1 | no | — |
| 344 | M16 | — | 106 | 1 | no | — |
| 345 | M16 | — | 106 | 1 | no | — |
| 346 | M16 | — | 106 | 1 | no | — |
| 347 | M16 | — | 106 | 1 | no | — |
| 348 | M16 | — | 106 | 2 | no | — |
| 349 | M16 | — | 106 | 2 | no | — |
| 350 | M16 | — | 212 | 4 | no | — |
| 351 | C2×C8 | — | 2 | 1 | no | — |
| 352 | C2×C8 | — | 53 | 2 | no | — |
| 353 | C2×C8 | — | 53 | 2 | no | — |
| 354 | C2×C8 | — | 106 | 2 | no | — |
| 355 | C2×C8 | — | 212 | 4 | no | — |
| 356 | C2×C8 | C2×C4×D53 | 1 | 1 | yes | characteristic |
| 357 | C2×C8 | C2×C4×D53 | 1 | 1 | yes | characteristic |
| 358 | C2×C8 | D4×D53 | 1 | 1 | yes | characteristic |
| 359 | C2×C8 | D4×D53 | 1 | 1 | yes | characteristic |
| 360 | C2×C8 | #11719947 | 1 | 1 | yes | characteristic |
| 361 | C2×C8 | #11719947 | 1 | 1 | yes | characteristic |
| 362 | C4⋊C4 | — | 2 | 2 | no | — |
| 363 | C4⋊C4 | — | 2 | 1 | no | — |
| 364 | C4⋊C4 | — | 106 | 1 | no | — |
| 365 | C4⋊C4 | — | 106 | 1 | no | — |
| 366 | C4⋊C4 | — | 212 | 4 | no | — |
| 367 | C4⋊C4 | — | 212 | 4 | no | — |
| 368 | C22⋊C4 | — | 2 | 1 | no | — |
| 369 | C22⋊C4 | — | 2 | 2 | no | — |
| 370 | C22⋊C4 | — | 106 | 1 | no | — |
| 371 | C22⋊C4 | — | 106 | 1 | no | — |
| 372 | C22⋊C4 | — | 212 | 4 | no | — |
| 373 | C42 | — | 2 | 1 | no | — |
| 374 | C42 | — | 2 | 2 | no | — |
| 375 | C42 | — | 53 | 2 | no | — |
| 376 | C42 | — | 53 | 2 | no | — |
| 377 | C42 | — | 212 | 4 | no | — |
| 378 | C23 | — | 2 | 2 | no | — |
| 379 | C23 | #13133262 | 1 | 1 | yes | characteristic |
| 380 | Q8 | — | 2 | 2 | no | — |
| 381 | Q8 | — | 2 | 2 | no | — |
| 382 | Q8 | — | 106 | 4 | no | — |
| 383 | Q8 | — | 106 | 4 | no | — |
| 384 | Q8 | — | 212 | 2 | no | — |
| 385 | Q8 | — | 212 | 2 | no | — |
| 386 | D4 | — | 2 | 2 | no | — |
| 387 | D4 | — | 2 | 2 | no | — |
| 388 | D4 | — | 4 | 2 | no | — |
| 389 | D4 | — | 4 | 2 | no | — |
| 390 | C2×C4 | — | 2 | 2 | no | — |
| 391 | C2×C4 | — | 4 | 2 | no | — |
| 392 | C2×C4 | — | 4 | 2 | no | — |
| 393 | C2×C4 | — | 4 | 2 | no | — |
| 394 | C2×C4 | — | 4 | 1 | no | — |
| 395 | C2×C4 | — | 106 | 2 | no | — |
| 396 | C2×C4 | — | 106 | 4 | no | — |
| 397 | C2×C4 | — | 106 | 2 | no | — |
| 398 | C2×C4 | — | 212 | 2 | no | — |
| 399 | C2×C4 | — | 212 | 2 | no | — |
| 400 | C2×C4 | C22×C4×D53 | 1 | 1 | yes | characteristic |
| 401 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 402 | C2×C4 | C2×#11719947 | 1 | 1 | yes | characteristic |
| 403 | C2×C4 | #13133262 | 1 | 1 | yes | characteristic |
| 404 | C2×C4 | #13133263 | 1 | 1 | yes | characteristic |
| 405 | C2×C4 | #13133263 | 1 | 1 | yes | characteristic |
| 406 | C8 | — | 4 | 1 | no | — |
| 407 | C8 | — | 106 | 2 | no | — |
| 408 | C8 | — | 106 | 2 | no | — |
| 409 | C8 | — | 212 | 2 | no | — |
| 410 | C8 | #13133177 | 1 | 1 | yes | characteristic |
| 411 | C8 | #13133177 | 1 | 1 | yes | characteristic |
| 412 | C8 | #13133177 | 1 | 1 | yes | characteristic |
| 413 | C8 | #13133177 | 1 | 1 | yes | characteristic |
| 414 | C22 | — | 4 | 1 | no | — |
| 415 | C22 | — | 4 | 2 | no | — |
| 416 | C22 | — | 8 | 2 | no | — |
| 417 | C22 | #16811095 | 1 | 1 | yes | characteristic |
| 418 | C22 | #16811186 | 1 | 1 | yes | characteristic |
| 419 | C22 | #16811226 | 1 | 1 | yes | characteristic |
| 420 | C4 | — | 4 | 2 | no | — |
| 421 | C4 | — | 8 | 2 | no | — |
| 422 | C4 | — | 8 | 1 | no | — |
| 423 | C4 | — | 212 | 2 | no | — |
| 424 | C4 | — | 212 | 2 | no | — |
| 425 | C4 | — | 212 | 4 | no | — |
| 426 | C4 | C2×#13133177 | 1 | 1 | yes | characteristic |
| 427 | C4 | #16811095 | 1 | 1 | yes | characteristic |
| 428 | C4 | #16811191 | 1 | 1 | yes | characteristic |
| 429 | C4 | #16811226 | 1 | 1 | yes | characteristic |
| 430 | C2 | — | 2 | 1 | no | — |
| 431 | C2 | — | 2 | 1 | no | — |
| 432 | C2 | — | 2 | 1 | no | — |
| 433 | C2 | — | 8 | 2 | no | — |
| 434 | C2 | #20277439 | 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