Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1556 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 1556 conjugacy classes of subgroups — too many to draw. Only its 107 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 | C2×#16811258 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#16810416 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#16810411 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #20275123 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C53×#1887 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C22×D4×D53 | — | 2 | 2 | no | — |
| 7 | #16811258 | — | 2 | 4 | no | — |
| 8 | #16811258 | — | 2 | 2 | no | — |
| 9 | #16811258 | C4 | 1 | 4 | yes | complemented |
| 10 | C2×#13133188 | — | 2 | 2 | no | — |
| 11 | C2×#13133185 | — | 2 | 1 | no | — |
| 12 | C2×#13133185 | C22 | 1 | 2 | yes | — |
| 13 | C2×C4×D212 | — | 2 | 1 | no | — |
| 14 | C2×#13133132 | C22 | 1 | 2 | yes | complemented |
| 15 | #16810478 | — | 2 | 2 | no | — |
| 16 | #16810416 | — | 2 | 2 | no | — |
| 17 | #16810411 | — | 2 | 4 | no | — |
| 18 | #16810390 | — | 2 | 2 | no | — |
| 19 | C2×#127×C53 | C22 | 1 | 1 | yes | characteristic |
| 20 | C53×#518 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C53×#418 | — | 2 | 1 | no | — |
| 22 | C2×#100×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C53×#339 | — | 2 | 1 | no | — |
| 24 | C24×D53 | — | 2 | 1 | no | — |
| 25 | C24×D53 | D4 | 1 | 2 | yes | — |
| 26 | C22×D212 | — | 2 | 1 | no | — |
| 27 | C22×C22⋊D53 | — | 2 | 2 | no | — |
| 28 | C22×C22⋊D53 | — | 2 | 2 | no | — |
| 29 | C2×D4×D53 | — | 2 | 8 | no | — |
| 30 | C2×D4×D53 | — | 2 | 8 | no | — |
| 31 | C2×D4×D53 | — | 4 | 16 | no | — |
| 32 | C22×C4×D53 | — | 2 | 2 | no | — |
| 33 | #13133188 | — | 2 | 8 | no | — |
| 34 | #13133188 | — | 2 | 8 | no | — |
| 35 | #13133185 | — | 2 | 4 | no | — |
| 36 | #13133185 | — | 2 | 4 | no | — |
| 37 | #13133185 | — | 2 | 2 | no | — |
| 38 | #13133185 | — | 2 | 2 | no | — |
| 39 | #13133185 | C2×C4 | 1 | 4 | yes | — |
| 40 | #13133185 | D4 | 1 | 4 | yes | — |
| 41 | C4×D212 | — | 2 | 4 | no | — |
| 42 | C4×D212 | — | 2 | 4 | no | — |
| 43 | C2×C4⋊Dic53 | — | 2 | 1 | no | — |
| 44 | C2×C22⋊Dic53 | — | 2 | 1 | no | — |
| 45 | C2×C22⋊Dic53 | — | 2 | 2 | no | — |
| 46 | C2×C22⋊Dic53 | D4 | 1 | 2 | yes | — |
| 47 | C2×#11719921 | — | 2 | 2 | no | — |
| 48 | C2×#11719921 | — | 4 | 4 | no | — |
| 49 | #13133132 | — | 2 | 2 | no | — |
| 50 | #13133132 | — | 2 | 2 | no | — |
| 51 | C22×D4×C53 | — | 2 | 2 | no | — |
| 52 | C22×D4×C53 | D4 | 1 | 1 | yes | characteristic |
| 53 | C22×D4×C53 | C23 | 1 | 1 | yes | characteristic |
| 54 | C2×M16×C53 | — | 2 | 1 | no | — |
| 55 | #127×C53 | — | 2 | 2 | no | — |
| 56 | #127×C53 | C2×C4 | 1 | 2 | yes | — |
| 57 | #127×C53 | D4 | 1 | 2 | yes | — |
| 58 | C4×D4×C53 | — | 4 | 2 | no | — |
| 59 | #117×C53 | — | 2 | 1 | no | — |
| 60 | C2×C22⋊C4×C53 | — | 2 | 2 | no | — |
| 61 | C2×C42×C53 | D4 | 1 | 1 | yes | characteristic |
| 62 | #102×C53 | — | 4 | 2 | no | — |
| 63 | #100×C53 | — | 2 | 2 | no | — |
| 64 | C24×C53 | — | 2 | 1 | no | — |
| 65 | C24×C53 | C2×D4 | 1 | 2 | yes | — |
| 66 | C23×D53 | — | 2 | 2 | no | — |
| 67 | C23×D53 | — | 2 | 4 | no | — |
| 68 | C23×D53 | — | 2 | 2 | no | — |
| 69 | C23×D53 | — | 4 | 8 | no | — |
| 70 | C23×D53 | — | 4 | 8 | no | — |
| 71 | C23×D53 | — | 4 | 2 | no | — |
| 72 | C23×D53 | — | 4 | 2 | no | — |
| 73 | C23×D53 | — | 8 | 1 | no | — |
| 74 | C23×D53 | — | 8 | 1 | no | — |
| 75 | C23×D53 | C22⋊C4 | 1 | 4 | yes | complemented |
| 76 | C2×D4×C53 | — | 2 | 4 | no | — |
| 77 | C2×D4×C53 | — | 2 | 4 | no | — |
| 78 | C2×D4×C53 | — | 2 | 1 | no | — |
| 79 | C2×D4×C53 | — | 4 | 1 | no | — |
| 80 | C2×D4×C53 | — | 4 | 1 | no | — |
| 81 | C2×D4×C53 | — | 4 | 8 | no | — |
| 82 | C2×D4×C53 | — | 4 | 1 | no | — |
| 83 | C2×D4×C53 | — | 4 | 1 | no | — |
| 84 | C2×D4×C53 | C22⋊C4 | 1 | 2 | yes | complemented |
| 85 | C2×D4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 86 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 87 | C2×D4×C53 | C2×D4 | 1 | 2 | yes | — |
| 88 | C22×C4×C53 | — | 2 | 1 | no | — |
| 89 | C22×C4×C53 | — | 2 | 4 | no | — |
| 90 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C2×C22⋊D53 | — | 2 | 8 | no | — |
| 92 | C2×C22⋊D53 | — | 2 | 4 | no | — |
| 93 | C2×C22⋊D53 | — | 2 | 4 | no | — |
| 94 | C2×C22⋊D53 | — | 4 | 8 | no | — |
| 95 | C2×C22⋊D53 | — | 4 | 8 | no | — |
| 96 | C22×Dic53 | — | 2 | 2 | no | — |
| 97 | C22×Dic53 | — | 4 | 2 | no | — |
| 98 | D4×D53 | — | 4 | 32 | no | — |
| 99 | D4×D53 | — | 4 | 32 | no | — |
| 100 | C2×D212 | — | 2 | 4 | no | — |
| 101 | C2×D212 | — | 2 | 8 | no | — |
| 102 | C2×C4×D53 | — | 2 | 8 | no | — |
| 103 | C2×C4×D53 | — | 4 | 8 | no | — |
| 104 | M16×C53 | — | 4 | 1 | no | — |
| 105 | M16×C53 | — | 4 | 1 | no | — |
| 106 | C2×C8×C53 | — | 4 | 1 | no | — |
| 107 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 108 | C22⋊C4×C53 | — | 4 | 2 | no | — |
| 109 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 110 | C42×C53 | — | 2 | 1 | no | — |
| 111 | C42×C53 | — | 4 | 1 | no | — |
| 112 | C42×C53 | C22⋊C4 | 1 | 2 | yes | complemented |
| 113 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 114 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 115 | C22⋊Dic53 | — | 4 | 2 | no | — |
| 116 | C22⋊Dic53 | — | 4 | 2 | no | — |
| 117 | C22⋊Dic53 | C22⋊C4 | 1 | 4 | yes | complemented |
| 118 | #11719921 | — | 2 | 4 | no | — |
| 119 | #11719921 | — | 2 | 4 | no | — |
| 120 | #11719921 | — | 8 | 8 | no | — |
| 121 | C4⋊Dic53 | — | 2 | 4 | no | — |
| 122 | C23×C53 | — | 2 | 2 | no | — |
| 123 | C23×C53 | — | 2 | 2 | no | — |
| 124 | C23×C53 | — | 2 | 2 | no | — |
| 125 | C23×C53 | — | 4 | 4 | no | — |
| 126 | C23×C53 | — | 4 | 4 | no | — |
| 127 | C23×C53 | — | 4 | 1 | no | — |
| 128 | C23×C53 | — | 4 | 1 | no | — |
| 129 | C23×C53 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 130 | C23×C53 | #120 | 1 | 1 | yes | characteristic |
| 131 | C23×C53 | #120 | 1 | 2 | yes | — |
| 132 | C22×D53 | — | 2 | 8 | no | — |
| 133 | C22×D53 | — | 2 | 4 | no | — |
| 134 | C22×D53 | — | 4 | 8 | no | — |
| 135 | C22×D53 | — | 4 | 8 | no | — |
| 136 | C22×D53 | — | 4 | 16 | no | — |
| 137 | C22×D53 | — | 4 | 4 | no | — |
| 138 | C22×D53 | — | 4 | 2 | no | — |
| 139 | C22×D53 | — | 4 | 2 | no | — |
| 140 | C22×D53 | — | 4 | 4 | no | — |
| 141 | C22×D53 | — | 4 | 8 | no | — |
| 142 | C22×D53 | — | 8 | 8 | no | — |
| 143 | C22×D53 | — | 8 | 2 | no | — |
| 144 | C22×D53 | — | 8 | 4 | no | — |
| 145 | C22×D53 | — | 8 | 4 | no | — |
| 146 | C22×D53 | — | 8 | 8 | no | — |
| 147 | C22×D53 | — | 8 | 8 | no | — |
| 148 | D4×C53 | — | 4 | 1 | no | — |
| 149 | D4×C53 | — | 4 | 1 | no | — |
| 150 | D4×C53 | — | 4 | 2 | no | — |
| 151 | D4×C53 | — | 4 | 2 | no | — |
| 152 | D4×C53 | — | 4 | 8 | no | — |
| 153 | D4×C53 | — | 4 | 8 | no | — |
| 154 | D4×C53 | — | 8 | 1 | no | — |
| 155 | C2×C4×C53 | — | 2 | 4 | no | — |
| 156 | C2×C4×C53 | — | 2 | 2 | no | — |
| 157 | C2×C4×C53 | — | 2 | 1 | no | — |
| 158 | C2×C4×C53 | — | 2 | 1 | no | — |
| 159 | C2×C4×C53 | — | 4 | 2 | no | — |
| 160 | C2×C4×C53 | — | 8 | 4 | no | — |
| 161 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 162 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 163 | C22⋊D53 | — | 4 | 8 | no | — |
| 164 | C22⋊D53 | — | 4 | 8 | no | — |
| 165 | C22⋊D53 | — | 4 | 16 | no | — |
| 166 | C2×Dic53 | — | 2 | 4 | no | — |
| 167 | C2×Dic53 | — | 4 | 4 | no | — |
| 168 | C2×Dic53 | — | 8 | 2 | no | — |
| 169 | C2×Dic53 | — | 8 | 4 | no | — |
| 170 | D212 | — | 2 | 16 | no | — |
| 171 | C4×D53 | — | 4 | 16 | no | — |
| 172 | C8×C53 | — | 8 | 1 | no | — |
| 173 | #12759 | — | 53 | 1 | no | maximal, Sylow |
| 174 | C22×C53 | — | 2 | 2 | no | — |
| 175 | C22×C53 | — | 2 | 2 | no | — |
| 176 | C22×C53 | — | 2 | 2 | no | — |
| 177 | C22×C53 | — | 4 | 2 | no | — |
| 178 | C22×C53 | — | 4 | 2 | no | — |
| 179 | C22×C53 | — | 4 | 4 | no | — |
| 180 | C22×C53 | — | 4 | 4 | no | — |
| 181 | C22×C53 | — | 4 | 2 | no | — |
| 182 | C22×C53 | — | 8 | 2 | no | — |
| 183 | C22×C53 | — | 8 | 2 | no | — |
| 184 | C22×C53 | — | 8 | 2 | no | — |
| 185 | C22×C53 | #379 | 1 | 1 | yes | characteristic |
| 186 | C22×C53 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 187 | C22×C53 | #458 | 1 | 1 | yes | characteristic |
| 188 | C2×D53 | — | 2 | 8 | no | — |
| 189 | C2×D53 | — | 4 | 4 | no | — |
| 190 | C2×D53 | — | 4 | 8 | no | — |
| 191 | C2×D53 | — | 4 | 8 | no | — |
| 192 | C2×D53 | — | 4 | 4 | no | — |
| 193 | C2×D53 | — | 4 | 8 | no | — |
| 194 | C2×D53 | — | 8 | 8 | no | — |
| 195 | C2×D53 | — | 8 | 4 | no | — |
| 196 | C2×D53 | — | 8 | 16 | no | — |
| 197 | C4×C53 | — | 2 | 4 | no | — |
| 198 | C4×C53 | — | 2 | 1 | no | — |
| 199 | C4×C53 | — | 2 | 1 | no | — |
| 200 | C4×C53 | — | 8 | 2 | no | — |
| 201 | Dic53 | — | 4 | 4 | no | — |
| 202 | Dic53 | — | 16 | 2 | no | — |
| 203 | C2×D42 | — | 53 | 1 | no | — |
| 204 | C2×#353 | — | 53 | 1 | no | — |
| 205 | C2×AΣL(1,𝔽16) | — | 53 | 2 | no | — |
| 206 | #1889 | — | 53 | 2 | no | — |
| 207 | #1887 | D53 | 1 | 1 | yes | characteristic, complemented |
| 208 | C2×C53 | — | 2 | 1 | no | — |
| 209 | C2×C53 | — | 2 | 1 | no | — |
| 210 | C2×C53 | — | 4 | 2 | no | — |
| 211 | C2×C53 | — | 4 | 2 | no | — |
| 212 | C2×C53 | — | 8 | 2 | no | — |
| 213 | C2×C53 | #1790 | 1 | 1 | yes | characteristic |
| 214 | C2×C53 | #2196 | 1 | 2 | yes | — |
| 215 | D53 | — | 4 | 8 | no | — |
| 216 | C23×D4 | — | 106 | 2 | no | — |
| 217 | D42 | — | 53 | 4 | no | — |
| 218 | D42 | — | 106 | 4 | no | — |
| 219 | D42 | — | 106 | 2 | no | — |
| 220 | C2×#127 | C2×D53 | 1 | 1 | yes | characteristic |
| 221 | C2×#121 | — | 106 | 2 | no | — |
| 222 | C2×#120 | — | 53 | 2 | no | — |
| 223 | C2×#120 | — | 106 | 1 | no | — |
| 224 | #518 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 225 | C2×C4×D4 | — | 106 | 1 | no | — |
| 226 | #418 | — | 2 | 1 | no | — |
| 227 | C2×#100 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 228 | C2×#99 | — | 53 | 2 | no | — |
| 229 | #379 | — | 106 | 2 | no | — |
| 230 | #353 | — | 106 | 2 | no | — |
| 231 | AΣL(1,𝔽16) | — | 106 | 4 | no | — |
| 232 | #342 | — | 106 | 2 | no | — |
| 233 | #339 | — | 2 | 1 | no | — |
| 234 | C53 | #12759 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 235 | C25 | — | 53 | 2 | no | — |
| 236 | C25 | — | 106 | 1 | no | — |
| 237 | C22×D4 | — | 2 | 2 | no | — |
| 238 | C22×D4 | — | 106 | 1 | no | — |
| 239 | C22×D4 | — | 106 | 8 | no | — |
| 240 | C22×D4 | — | 106 | 8 | no | — |
| 241 | C22×D4 | — | 106 | 2 | no | — |
| 242 | C22×D4 | — | 106 | 2 | no | — |
| 243 | C22×D4 | — | 212 | 16 | no | — |
| 244 | C22×D4 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 245 | C22×D4 | C22×D53 | 1 | 1 | yes | characteristic |
| 246 | C23×C4 | — | 106 | 2 | no | — |
| 247 | C2×M16 | — | 2 | 1 | no | — |
| 248 | #127 | — | 2 | 2 | no | — |
| 249 | #127 | C4×D53 | 1 | 2 | yes | — |
| 250 | #127 | D212 | 1 | 2 | yes | — |
| 251 | #121 | — | 106 | 8 | no | — |
| 252 | #121 | — | 106 | 8 | no | — |
| 253 | #120 | — | 53 | 4 | no | — |
| 254 | #120 | — | 53 | 4 | no | — |
| 255 | #120 | — | 106 | 4 | no | — |
| 256 | #120 | — | 106 | 2 | no | — |
| 257 | #120 | — | 106 | 2 | no | — |
| 258 | #120 | — | 106 | 4 | no | — |
| 259 | C4×D4 | — | 4 | 2 | no | — |
| 260 | C4×D4 | — | 106 | 4 | no | — |
| 261 | C4×D4 | — | 106 | 4 | no | — |
| 262 | #117 | — | 2 | 1 | no | — |
| 263 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 264 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 265 | C2×C22⋊C4 | — | 53 | 2 | no | — |
| 266 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 267 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 268 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 269 | C2×C22⋊C4 | — | 212 | 4 | no | — |
| 270 | C2×C42 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 271 | #102 | — | 4 | 2 | no | — |
| 272 | #100 | — | 2 | 2 | no | — |
| 273 | #99 | — | 106 | 2 | no | — |
| 274 | #99 | — | 106 | 2 | no | — |
| 275 | C24 | — | 2 | 1 | no | — |
| 276 | C24 | — | 53 | 4 | no | — |
| 277 | C24 | — | 106 | 4 | no | — |
| 278 | C24 | — | 106 | 2 | no | — |
| 279 | C24 | — | 106 | 2 | no | — |
| 280 | C24 | — | 424 | 1 | no | — |
| 281 | C24 | — | 424 | 1 | no | — |
| 282 | C24 | — | 212 | 2 | no | — |
| 283 | C24 | — | 212 | 2 | no | — |
| 284 | C24 | — | 212 | 8 | no | — |
| 285 | C24 | — | 212 | 8 | no | — |
| 286 | C24 | D4×D53 | 1 | 2 | yes | — |
| 287 | C2×D4 | — | 2 | 4 | no | — |
| 288 | C2×D4 | — | 2 | 4 | no | — |
| 289 | C2×D4 | — | 2 | 1 | no | — |
| 290 | C2×D4 | — | 4 | 1 | no | — |
| 291 | C2×D4 | — | 4 | 1 | no | — |
| 292 | C2×D4 | — | 4 | 8 | no | — |
| 293 | C2×D4 | — | 4 | 1 | no | — |
| 294 | C2×D4 | — | 4 | 1 | no | — |
| 295 | C2×D4 | — | 106 | 4 | no | — |
| 296 | C2×D4 | — | 106 | 8 | no | — |
| 297 | C2×D4 | — | 106 | 8 | no | — |
| 298 | C2×D4 | — | 106 | 4 | no | — |
| 299 | C2×D4 | — | 106 | 4 | no | — |
| 300 | C2×D4 | — | 212 | 32 | no | — |
| 301 | C2×D4 | — | 212 | 32 | no | — |
| 302 | C2×D4 | — | 212 | 8 | no | — |
| 303 | C2×D4 | — | 212 | 8 | no | — |
| 304 | C2×D4 | #11719921 | 1 | 2 | yes | complemented |
| 305 | C2×D4 | C2×C4×D53 | 1 | 1 | yes | characteristic |
| 306 | C2×D4 | C2×D212 | 1 | 1 | yes | characteristic |
| 307 | C2×D4 | D4×D53 | 1 | 2 | yes | — |
| 308 | C22×C4 | — | 2 | 1 | no | — |
| 309 | C22×C4 | — | 2 | 4 | no | — |
| 310 | C22×C4 | — | 106 | 8 | no | — |
| 311 | C22×C4 | — | 106 | 2 | no | — |
| 312 | C22×C4 | — | 212 | 8 | no | — |
| 313 | C22×C4 | — | 212 | 2 | no | — |
| 314 | C22×C4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 315 | M16 | — | 4 | 1 | no | — |
| 316 | M16 | — | 4 | 1 | no | — |
| 317 | C2×C8 | — | 4 | 1 | no | — |
| 318 | C4⋊C4 | — | 2 | 2 | no | — |
| 319 | C4⋊C4 | — | 106 | 4 | no | — |
| 320 | C22⋊C4 | — | 4 | 2 | no | — |
| 321 | C22⋊C4 | — | 4 | 1 | no | — |
| 322 | C22⋊C4 | — | 53 | 4 | no | — |
| 323 | C22⋊C4 | — | 106 | 4 | no | — |
| 324 | C22⋊C4 | — | 106 | 2 | no | — |
| 325 | C22⋊C4 | — | 106 | 4 | no | — |
| 326 | C22⋊C4 | — | 106 | 4 | no | — |
| 327 | C22⋊C4 | — | 424 | 8 | no | — |
| 328 | C22⋊C4 | — | 212 | 2 | no | — |
| 329 | C22⋊C4 | — | 212 | 2 | no | — |
| 330 | C42 | — | 2 | 1 | no | — |
| 331 | C42 | — | 4 | 1 | no | — |
| 332 | C42 | #11719921 | 1 | 2 | yes | complemented |
| 333 | C23 | — | 2 | 2 | no | — |
| 334 | C23 | — | 2 | 2 | no | — |
| 335 | C23 | — | 2 | 2 | no | — |
| 336 | C23 | — | 4 | 4 | no | — |
| 337 | C23 | — | 4 | 4 | no | — |
| 338 | C23 | — | 4 | 1 | no | — |
| 339 | C23 | — | 4 | 1 | no | — |
| 340 | C23 | — | 106 | 8 | no | — |
| 341 | C23 | — | 106 | 4 | no | — |
| 342 | C23 | — | 424 | 2 | no | — |
| 343 | C23 | — | 424 | 4 | no | — |
| 344 | C23 | — | 424 | 4 | no | — |
| 345 | C23 | — | 424 | 8 | no | — |
| 346 | C23 | — | 424 | 8 | no | — |
| 347 | C23 | — | 424 | 8 | no | — |
| 348 | C23 | — | 212 | 4 | no | — |
| 349 | C23 | — | 212 | 4 | no | — |
| 350 | C23 | — | 212 | 8 | no | — |
| 351 | C23 | — | 212 | 16 | no | — |
| 352 | C23 | — | 212 | 8 | no | — |
| 353 | C23 | — | 212 | 8 | no | — |
| 354 | C23 | — | 212 | 2 | no | — |
| 355 | C23 | — | 212 | 2 | no | — |
| 356 | C23 | C22⋊C4×D53 | 1 | 2 | yes | — |
| 357 | C23 | #13133185 | 1 | 1 | yes | characteristic |
| 358 | C23 | #13133187 | 1 | 2 | yes | — |
| 359 | D4 | — | 4 | 1 | no | — |
| 360 | D4 | — | 4 | 1 | no | — |
| 361 | D4 | — | 4 | 2 | no | — |
| 362 | D4 | — | 4 | 2 | no | — |
| 363 | D4 | — | 4 | 8 | no | — |
| 364 | D4 | — | 4 | 8 | no | — |
| 365 | D4 | — | 8 | 1 | no | — |
| 366 | D4 | — | 106 | 16 | no | — |
| 367 | D4 | — | 212 | 8 | no | — |
| 368 | D4 | — | 212 | 8 | no | — |
| 369 | D4 | — | 212 | 16 | no | — |
| 370 | C2×C4 | — | 2 | 4 | no | — |
| 371 | C2×C4 | — | 2 | 1 | no | — |
| 372 | C2×C4 | — | 2 | 1 | no | — |
| 373 | C2×C4 | — | 2 | 2 | no | — |
| 374 | C2×C4 | — | 4 | 2 | no | — |
| 375 | C2×C4 | — | 8 | 4 | no | — |
| 376 | C2×C4 | — | 106 | 4 | no | — |
| 377 | C2×C4 | — | 424 | 2 | no | — |
| 378 | C2×C4 | — | 424 | 4 | no | — |
| 379 | C2×C4 | — | 212 | 16 | no | — |
| 380 | C2×C4 | — | 212 | 4 | no | — |
| 381 | C2×C4 | C2×#11719921 | 1 | 1 | yes | characteristic |
| 382 | C2×C4 | #13133185 | 1 | 1 | yes | characteristic |
| 383 | C8 | — | 8 | 1 | no | — |
| 384 | C22 | — | 2 | 2 | no | — |
| 385 | C22 | — | 2 | 2 | no | — |
| 386 | C22 | — | 2 | 2 | no | — |
| 387 | C22 | — | 4 | 2 | no | — |
| 388 | C22 | — | 4 | 2 | no | — |
| 389 | C22 | — | 4 | 4 | no | — |
| 390 | C22 | — | 4 | 4 | no | — |
| 391 | C22 | — | 4 | 2 | no | — |
| 392 | C22 | — | 8 | 2 | no | — |
| 393 | C22 | — | 8 | 2 | no | — |
| 394 | C22 | — | 8 | 2 | no | — |
| 395 | C22 | — | 106 | 8 | no | — |
| 396 | C22 | — | 424 | 8 | no | — |
| 397 | C22 | — | 424 | 4 | no | — |
| 398 | C22 | — | 424 | 16 | no | — |
| 399 | C22 | — | 212 | 4 | no | — |
| 400 | C22 | — | 212 | 8 | no | — |
| 401 | C22 | — | 212 | 8 | no | — |
| 402 | C22 | — | 212 | 8 | no | — |
| 403 | C22 | — | 212 | 4 | no | — |
| 404 | C22 | #16810478 | 1 | 1 | yes | characteristic |
| 405 | C22 | #16810809 | 1 | 1 | yes | characteristic |
| 406 | C22 | #16810812 | 1 | 1 | yes | characteristic |
| 407 | C4 | — | 2 | 4 | no | — |
| 408 | C4 | — | 2 | 1 | no | — |
| 409 | C4 | — | 2 | 1 | no | — |
| 410 | C4 | — | 8 | 2 | no | — |
| 411 | C4 | — | 848 | 2 | no | — |
| 412 | C4 | — | 212 | 4 | no | — |
| 413 | C2 | — | 2 | 1 | no | — |
| 414 | C2 | — | 2 | 1 | no | — |
| 415 | C2 | — | 4 | 2 | no | — |
| 416 | C2 | — | 4 | 2 | no | — |
| 417 | C2 | — | 8 | 2 | no | — |
| 418 | C2 | — | 212 | 8 | no | — |
| 419 | C2 | #20274662 | 1 | 1 | yes | characteristic |
| 420 | C2 | #20276698 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#16810416 | C2 | semidirect |
| 3. C2×#16810411 | C2 | semidirect |
| 4. #20275123 | C2 | semidirect |
| 5. C53×#1887 | C2 | semidirect |
| 9. #16811258 | C4 | semidirect |
| 14. C2×#13133132 | C22 | semidirect |
| 20. C53×#518 | C22 | semidirect |
| 22. C2×#100×C53 | C22 | semidirect |
| 75. C23×D53 | C22⋊C4 | semidirect |
| 84. C2×D4×C53 | C22⋊C4 | semidirect |
| 112. C42×C53 | C22⋊C4 | semidirect |
| 117. C22⋊Dic53 | C22⋊C4 | semidirect |
| 207. #1887 | D53 | semidirect |
| 224. #518 | C2×D53 | semidirect |
| 227. C2×#100 | C2×D53 | semidirect |
| 234. C53 | #12759 | semidirect |
| 304. C2×D4 | #11719921 | semidirect |
| 332. C42 | #11719921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811258 | 2 |
| C2×#16810416 | 2 |
| C2×#16810411 | 2 |
| #20275123 | 2 |
| C53×#1887 | 2 |
| #12759 | 53 |