Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1916 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 1916 conjugacy classes of subgroups — too many to draw. Only its 225 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 | #575×D53 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | #20283157 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #20275820 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20275819 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #20275818 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #338×D53 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C53×#2017 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#41×D53 | C22 | 1 | 3 | yes | — |
| 9 | #16811423 | C22 | 1 | 3 | yes | complemented |
| 10 | #16811422 | — | 2 | 6 | no | — |
| 11 | #16811421 | C22 | 1 | 6 | yes | complemented |
| 12 | #16811420 | — | 2 | 6 | no | — |
| 13 | #16811419 | — | 2 | 6 | no | — |
| 14 | #137×D53 | — | 2 | 6 | no | — |
| 15 | AGL(1,ℤ/8)×D53 | — | 2 | 6 | no | — |
| 16 | #135×D53 | — | 2 | 6 | no | — |
| 17 | C22×#11719912 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×M16×D53 | C22 | 1 | 3 | yes | — |
| 19 | #16810591 | C22 | 1 | 3 | yes | complemented |
| 20 | #16810590 | C22 | 1 | 3 | yes | complemented |
| 21 | #16810589 | C22 | 1 | 3 | yes | complemented |
| 22 | #16810588 | — | 2 | 6 | no | — |
| 23 | #16810585 | — | 2 | 6 | no | — |
| 24 | #16810381 | C22 | 1 | 3 | yes | complemented |
| 25 | C53×#575 | C22 | 1 | 3 | yes | complemented |
| 26 | C53×#408 | C22 | 1 | 3 | yes | complemented |
| 27 | C53×#338 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | C2×#11719949 | D4 | 1 | 3 | yes | — |
| 29 | C2×#11719945 | — | 2 | 3 | no | — |
| 30 | C2×#11719945 | C23 | 1 | 3 | yes | — |
| 31 | C2×#11719947 | — | 2 | 3 | no | — |
| 32 | C2×#11719947 | D4 | 1 | 3 | yes | — |
| 33 | #41×D53 | — | 2 | 6 | no | — |
| 34 | #41×D53 | — | 2 | 6 | no | — |
| 35 | #41×D53 | — | 2 | 6 | no | — |
| 36 | #41×D53 | — | 2 | 6 | no | — |
| 37 | C2×Q8×D53 | D4 | 1 | 3 | yes | — |
| 38 | C2×D4×D53 | — | 2 | 3 | no | — |
| 39 | C2×D4×D53 | D4 | 1 | 3 | yes | — |
| 40 | C22×C4×D53 | — | 2 | 3 | no | — |
| 41 | C22×C4×D53 | C23 | 1 | 1 | yes | characteristic |
| 42 | #13133250 | — | 2 | 6 | no | — |
| 43 | #13133249 | — | 2 | 12 | no | — |
| 44 | #13133248 | — | 2 | 6 | no | — |
| 45 | #13133247 | — | 2 | 6 | no | — |
| 46 | #13133246 | — | 2 | 12 | no | — |
| 47 | #13133245 | — | 2 | 6 | no | — |
| 48 | #13133244 | — | 2 | 12 | no | — |
| 49 | #13133243 | — | 2 | 6 | no | — |
| 50 | #13133242 | — | 2 | 6 | no | — |
| 51 | #13133241 | — | 2 | 12 | no | — |
| 52 | #13133240 | — | 2 | 6 | no | — |
| 53 | #13133239 | — | 2 | 6 | no | — |
| 54 | #13133238 | — | 2 | 12 | no | — |
| 55 | #13133237 | — | 2 | 12 | no | — |
| 56 | #13133236 | — | 2 | 6 | no | — |
| 57 | Q16×D53 | — | 2 | 6 | no | — |
| 58 | SD16×D53 | — | 2 | 12 | no | — |
| 59 | D8×D53 | — | 2 | 6 | no | — |
| 60 | C2×#11719917 | C23 | 1 | 3 | yes | — |
| 61 | C2×#11719912 | — | 2 | 3 | no | — |
| 62 | C2×#11719912 | — | 2 | 3 | no | — |
| 63 | C2×#11719912 | D4 | 1 | 6 | yes | — |
| 64 | M16×D53 | — | 2 | 6 | no | — |
| 65 | M16×D53 | — | 2 | 6 | no | — |
| 66 | C22×#88322 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×C8×D53 | D4 | 1 | 6 | yes | — |
| 68 | C22⋊#88322 | — | 2 | 6 | no | — |
| 69 | #13133129 | — | 2 | 6 | no | — |
| 70 | #13133129 | — | 2 | 6 | no | — |
| 71 | C2×#41×C53 | C23 | 1 | 3 | yes | — |
| 72 | #137×C53 | — | 2 | 6 | no | — |
| 73 | AGL(1,ℤ/8)×C53 | — | 2 | 6 | no | — |
| 74 | #135×C53 | — | 2 | 6 | no | — |
| 75 | C2×M16×C53 | C23 | 1 | 3 | yes | — |
| 76 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 77 | C22⋊C8×C53 | — | 2 | 6 | no | — |
| 78 | C23×D53 | — | 2 | 3 | no | — |
| 79 | C23×D53 | #41 | 1 | 1 | yes | characteristic |
| 80 | #41×C53 | — | 2 | 6 | no | — |
| 81 | #41×C53 | — | 2 | 6 | no | — |
| 82 | C2×Q8×C53 | C2×D4 | 1 | 3 | yes | — |
| 83 | C2×D4×C53 | — | 2 | 3 | no | — |
| 84 | C2×D4×C53 | C2×D4 | 1 | 3 | yes | — |
| 85 | C22×C4×C53 | — | 2 | 3 | no | — |
| 86 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 87 | C2×C22⋊D53 | — | 2 | 3 | no | — |
| 88 | C2×C22⋊D53 | — | 2 | 3 | no | — |
| 89 | C2×C22⋊D53 | — | 2 | 3 | no | — |
| 90 | C22×Dic53 | — | 2 | 3 | no | — |
| 91 | C22×Dic53 | #41 | 1 | 1 | yes | characteristic |
| 92 | #11719949 | — | 2 | 6 | no | — |
| 93 | #11719949 | — | 2 | 6 | no | — |
| 94 | Q8×D53 | — | 2 | 6 | no | — |
| 95 | Q8×D53 | — | 2 | 6 | no | — |
| 96 | #11719947 | — | 2 | 6 | no | — |
| 97 | #11719947 | — | 2 | 6 | no | — |
| 98 | #11719947 | — | 4 | 6 | no | — |
| 99 | #11719947 | — | 4 | 6 | no | — |
| 100 | D4×D53 | — | 2 | 6 | no | — |
| 101 | D4×D53 | — | 2 | 6 | no | — |
| 102 | D4×D53 | — | 4 | 6 | no | — |
| 103 | D4×D53 | — | 4 | 6 | no | — |
| 104 | #11719945 | — | 2 | 6 | no | — |
| 105 | #11719945 | — | 2 | 6 | no | — |
| 106 | #11719945 | — | 4 | 3 | no | — |
| 107 | #11719945 | — | 4 | 3 | no | — |
| 108 | #11719945 | — | 4 | 3 | no | — |
| 109 | #11719945 | — | 4 | 3 | no | — |
| 110 | C2×D212 | — | 2 | 3 | no | — |
| 111 | C2×D212 | C2×D4 | 1 | 3 | yes | — |
| 112 | C2×C4×D53 | — | 2 | 3 | no | — |
| 113 | C2×C4×D53 | — | 2 | 3 | no | — |
| 114 | C2×C4×D53 | — | 2 | 3 | no | — |
| 115 | C2×C4×D53 | — | 4 | 6 | no | — |
| 116 | C2×C4×D53 | — | 4 | 6 | no | — |
| 117 | C2×C4×D53 | C2×D4 | 1 | 3 | yes | — |
| 118 | C2×C4×D53 | C2×D4 | 1 | 3 | yes | — |
| 119 | C2×C4×D53 | C2×D4 | 1 | 3 | yes | — |
| 120 | C2×C4×D53 | C2×D4 | 1 | 3 | yes | — |
| 121 | C2×Dic106 | — | 2 | 3 | no | — |
| 122 | C2×Dic106 | C2×D4 | 1 | 3 | yes | — |
| 123 | Q16×C53 | — | 2 | 6 | no | — |
| 124 | SD16×C53 | — | 2 | 12 | no | — |
| 125 | D8×C53 | — | 2 | 6 | no | — |
| 126 | M16×C53 | — | 2 | 6 | no | — |
| 127 | C2×C8×C53 | — | 2 | 3 | no | — |
| 128 | C2×C8×C53 | C2×D4 | 1 | 6 | yes | — |
| 129 | #11719925 | — | 2 | 12 | no | — |
| 130 | #11719924 | — | 2 | 12 | no | — |
| 131 | #11719923 | — | 2 | 12 | no | — |
| 132 | #11719922 | — | 2 | 12 | no | — |
| 133 | #11719917 | — | 2 | 6 | no | — |
| 134 | C2×#88322 | — | 2 | 3 | no | — |
| 135 | C2×#88322 | C2×D4 | 1 | 6 | yes | — |
| 136 | Dic212 | — | 2 | 6 | no | — |
| 137 | D424 | — | 2 | 6 | no | — |
| 138 | #11719913 | — | 2 | 12 | no | — |
| 139 | #11719912 | — | 2 | 12 | no | — |
| 140 | #11719912 | — | 4 | 3 | no | — |
| 141 | #11719912 | — | 4 | 1 | no | — |
| 142 | C8×D53 | — | 2 | 6 | no | — |
| 143 | C8×D53 | — | 2 | 6 | no | — |
| 144 | C23×C53 | — | 2 | 3 | no | — |
| 145 | C23×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 146 | C22×D53 | — | 2 | 3 | no | — |
| 147 | C22×D53 | — | 4 | 6 | no | — |
| 148 | C22×D53 | — | 8 | 1 | no | — |
| 149 | C22×D53 | — | 8 | 6 | no | — |
| 150 | C22×D53 | #121 | 1 | 3 | yes | — |
| 151 | C22×D53 | #121 | 1 | 3 | yes | — |
| 152 | Q8×C53 | — | 2 | 6 | no | — |
| 153 | D4×C53 | — | 2 | 6 | no | — |
| 154 | D4×C53 | — | 4 | 6 | no | — |
| 155 | C2×C4×C53 | — | 2 | 3 | no | — |
| 156 | C2×C4×C53 | — | 4 | 3 | no | — |
| 157 | C2×C4×C53 | — | 4 | 3 | no | — |
| 158 | C2×C4×C53 | C22×D4 | 1 | 3 | yes | — |
| 159 | C2×C4×C53 | C22×D4 | 1 | 3 | yes | — |
| 160 | C22⋊D53 | — | 4 | 6 | no | — |
| 161 | C22⋊D53 | — | 4 | 3 | no | — |
| 162 | C22⋊D53 | — | 4 | 3 | no | — |
| 163 | C22⋊D53 | — | 4 | 3 | no | — |
| 164 | C22⋊D53 | — | 4 | 3 | no | — |
| 165 | C2×Dic53 | — | 2 | 3 | no | — |
| 166 | C2×Dic53 | — | 4 | 6 | no | — |
| 167 | C2×Dic53 | #121 | 1 | 3 | yes | — |
| 168 | C2×Dic53 | #121 | 1 | 3 | yes | — |
| 169 | D212 | — | 2 | 6 | no | — |
| 170 | D212 | — | 4 | 3 | no | — |
| 171 | D212 | — | 4 | 3 | no | — |
| 172 | C4×D53 | — | 4 | 6 | no | — |
| 173 | C4×D53 | — | 4 | 3 | no | — |
| 174 | C4×D53 | — | 4 | 3 | no | — |
| 175 | C4×D53 | — | 4 | 6 | no | — |
| 176 | C4×D53 | #120 | 1 | 6 | yes | — |
| 177 | C4×D53 | #120 | 1 | 3 | yes | — |
| 178 | C4×D53 | #120 | 1 | 3 | yes | — |
| 179 | C4×D53 | #127 | 1 | 3 | yes | — |
| 180 | C4×D53 | #127 | 1 | 1 | yes | characteristic |
| 181 | Dic106 | — | 2 | 6 | no | — |
| 182 | Dic106 | — | 4 | 3 | no | — |
| 183 | Dic106 | — | 4 | 3 | no | — |
| 184 | C8×C53 | — | 2 | 6 | no | — |
| 185 | C8×C53 | — | 4 | 1 | no | — |
| 186 | #88322 | — | 2 | 6 | no | — |
| 187 | #88322 | — | 4 | 1 | no | — |
| 188 | #23434 | — | 53 | 1 | no | maximal, Sylow |
| 189 | C22×C53 | — | 4 | 1 | no | — |
| 190 | C22×C53 | — | 4 | 6 | no | — |
| 191 | C22×C53 | — | 4 | 3 | no | — |
| 192 | C22×C53 | C2×#121 | 1 | 3 | yes | — |
| 193 | C2×D53 | — | 4 | 3 | no | — |
| 194 | C2×D53 | — | 4 | 3 | no | — |
| 195 | C2×D53 | — | 4 | 6 | no | — |
| 196 | C2×D53 | — | 4 | 3 | no | — |
| 197 | C2×D53 | — | 8 | 12 | no | — |
| 198 | C2×D53 | #392 | 1 | 3 | yes | — |
| 199 | C2×D53 | #392 | 1 | 1 | yes | characteristic |
| 200 | C4×C53 | — | 4 | 3 | no | — |
| 201 | C4×C53 | C2×#120 | 1 | 3 | yes | — |
| 202 | C4×C53 | C2×#127 | 1 | 1 | yes | characteristic |
| 203 | Dic53 | — | 4 | 3 | no | — |
| 204 | Dic53 | #392 | 1 | 1 | yes | characteristic |
| 205 | Dic53 | #392 | 1 | 3 | yes | — |
| 206 | C2×#575 | — | 53 | 3 | no | — |
| 207 | #2879 | — | 53 | 3 | no | — |
| 208 | #2017 | — | 53 | 3 | no | — |
| 209 | #2017 | — | 53 | 1 | no | — |
| 210 | #2017 | — | 53 | 3 | no | — |
| 211 | #2017 | D53 | 1 | 1 | yes | characteristic, complemented |
| 212 | C2×#338 | — | 53 | 1 | no | — |
| 213 | C2×C53 | — | 2 | 3 | no | — |
| 214 | C2×C53 | — | 8 | 3 | no | — |
| 215 | C2×C53 | C2×#392 | 1 | 1 | yes | characteristic |
| 216 | D53 | — | 2 | 3 | no | — |
| 217 | D53 | — | 2 | 1 | no | — |
| 218 | D53 | — | 8 | 3 | no | — |
| 219 | C22×#41 | — | 53 | 3 | no | — |
| 220 | #575 | — | 53 | 6 | no | — |
| 221 | #575 | — | 53 | 3 | no | — |
| 222 | #575 | — | 106 | 6 | no | — |
| 223 | #575 | — | 106 | 6 | no | — |
| 224 | #575 | — | 106 | 6 | no | — |
| 225 | #575 | C2×D53 | 1 | 3 | yes | complemented |
| 226 | C2×#137 | — | 106 | 6 | no | — |
| 227 | C2×AGL(1,ℤ/8) | — | 106 | 6 | no | — |
| 228 | C2×#135 | — | 106 | 6 | no | — |
| 229 | C22×M16 | — | 53 | 3 | no | — |
| 230 | C22×M16 | — | 53 | 1 | no | — |
| 231 | #408 | — | 53 | 3 | no | — |
| 232 | #408 | — | 53 | 3 | no | — |
| 233 | #408 | — | 53 | 3 | no | — |
| 234 | #408 | — | 106 | 6 | no | — |
| 235 | #408 | C2×D53 | 1 | 3 | yes | complemented |
| 236 | #407 | — | 106 | 6 | no | — |
| 237 | #338 | — | 53 | 3 | no | — |
| 238 | #338 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 239 | C53 | #23434 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 240 | C2×#41 | — | 53 | 3 | no | — |
| 241 | C2×#41 | — | 53 | 3 | no | — |
| 242 | C2×#41 | — | 53 | 3 | no | — |
| 243 | C2×#41 | — | 106 | 3 | no | — |
| 244 | C2×#41 | — | 106 | 3 | no | — |
| 245 | C2×#41 | — | 106 | 6 | no | — |
| 246 | C2×#41 | — | 106 | 6 | no | — |
| 247 | C2×#41 | — | 106 | 6 | no | — |
| 248 | C2×#41 | — | 106 | 6 | no | — |
| 249 | C2×#41 | C22×D53 | 1 | 3 | yes | — |
| 250 | C22×Q8 | — | 53 | 3 | no | — |
| 251 | C22×D4 | — | 53 | 3 | no | — |
| 252 | C22×D4 | — | 106 | 3 | no | — |
| 253 | C23×C4 | — | 53 | 1 | no | — |
| 254 | C23×C4 | — | 106 | 3 | no | — |
| 255 | #137 | — | 2 | 6 | no | — |
| 256 | #137 | — | 106 | 6 | no | — |
| 257 | #137 | — | 106 | 12 | no | — |
| 258 | #137 | — | 106 | 12 | no | — |
| 259 | #137 | — | 106 | 6 | no | — |
| 260 | #137 | — | 106 | 6 | no | — |
| 261 | AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 262 | AGL(1,ℤ/8) | — | 106 | 6 | no | — |
| 263 | AGL(1,ℤ/8) | — | 106 | 12 | no | — |
| 264 | AGL(1,ℤ/8) | — | 106 | 12 | no | — |
| 265 | AGL(1,ℤ/8) | — | 106 | 6 | no | — |
| 266 | AGL(1,ℤ/8) | — | 106 | 6 | no | — |
| 267 | #135 | — | 2 | 6 | no | — |
| 268 | #135 | — | 106 | 12 | no | — |
| 269 | #135 | — | 106 | 6 | no | — |
| 270 | #135 | — | 106 | 12 | no | — |
| 271 | #135 | — | 106 | 6 | no | — |
| 272 | #135 | — | 106 | 6 | no | — |
| 273 | C2×Q16 | — | 106 | 6 | no | — |
| 274 | C2×SD16 | — | 106 | 12 | no | — |
| 275 | C2×D8 | — | 106 | 6 | no | — |
| 276 | C2×M16 | — | 53 | 3 | no | — |
| 277 | C2×M16 | — | 53 | 6 | no | — |
| 278 | C2×M16 | — | 106 | 3 | no | — |
| 279 | C2×M16 | — | 106 | 3 | no | — |
| 280 | C2×M16 | — | 106 | 6 | no | — |
| 281 | C2×M16 | — | 106 | 6 | no | — |
| 282 | C2×M16 | C22×D53 | 1 | 3 | yes | — |
| 283 | C22×C8 | — | 53 | 6 | no | — |
| 284 | C22×C8 | — | 53 | 1 | no | — |
| 285 | C22×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 286 | C22⋊C8 | — | 2 | 6 | no | — |
| 287 | C22⋊C8 | — | 106 | 6 | no | — |
| 288 | C22⋊C8 | — | 106 | 6 | no | — |
| 289 | C22⋊C8 | — | 106 | 6 | no | — |
| 290 | C24 | — | 53 | 1 | no | — |
| 291 | C24 | — | 106 | 3 | no | — |
| 292 | #41 | — | 2 | 6 | no | — |
| 293 | #41 | — | 2 | 6 | no | — |
| 294 | #41 | — | 106 | 6 | no | — |
| 295 | #41 | — | 106 | 6 | no | — |
| 296 | #41 | — | 106 | 6 | no | — |
| 297 | #41 | — | 106 | 6 | no | — |
| 298 | #41 | — | 106 | 6 | no | — |
| 299 | #41 | — | 106 | 6 | no | — |
| 300 | #41 | — | 212 | 3 | no | — |
| 301 | #41 | — | 212 | 3 | no | — |
| 302 | #41 | — | 212 | 3 | no | — |
| 303 | #41 | — | 212 | 3 | no | — |
| 304 | #41 | — | 212 | 6 | no | — |
| 305 | #41 | — | 212 | 6 | no | — |
| 306 | C2×Q8 | — | 53 | 3 | no | — |
| 307 | C2×Q8 | — | 106 | 3 | no | — |
| 308 | C2×Q8 | — | 106 | 6 | no | — |
| 309 | C2×Q8 | — | 106 | 6 | no | — |
| 310 | C2×Q8 | D4×D53 | 1 | 3 | yes | — |
| 311 | C2×D4 | — | 2 | 3 | no | — |
| 312 | C2×D4 | — | 53 | 3 | no | — |
| 313 | C2×D4 | — | 106 | 3 | no | — |
| 314 | C2×D4 | — | 106 | 6 | no | — |
| 315 | C2×D4 | — | 106 | 6 | no | — |
| 316 | C2×D4 | — | 106 | 3 | no | — |
| 317 | C2×D4 | — | 106 | 3 | no | — |
| 318 | C2×D4 | — | 106 | 3 | no | — |
| 319 | C2×D4 | — | 212 | 6 | no | — |
| 320 | C2×D4 | — | 212 | 6 | no | — |
| 321 | C2×D4 | D4×D53 | 1 | 3 | yes | — |
| 322 | C22×C4 | — | 2 | 3 | no | — |
| 323 | C22×C4 | — | 53 | 1 | no | — |
| 324 | C22×C4 | — | 53 | 3 | no | — |
| 325 | C22×C4 | — | 53 | 3 | no | — |
| 326 | C22×C4 | — | 53 | 3 | no | — |
| 327 | C22×C4 | — | 53 | 3 | no | — |
| 328 | C22×C4 | — | 106 | 3 | no | — |
| 329 | C22×C4 | — | 106 | 3 | no | — |
| 330 | C22×C4 | — | 106 | 3 | no | — |
| 331 | C22×C4 | — | 106 | 3 | no | — |
| 332 | C22×C4 | — | 212 | 6 | no | — |
| 333 | C22×C4 | — | 212 | 6 | no | — |
| 334 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 335 | Q16 | — | 2 | 6 | no | — |
| 336 | Q16 | — | 106 | 6 | no | — |
| 337 | Q16 | — | 106 | 12 | no | — |
| 338 | SD16 | — | 2 | 12 | no | — |
| 339 | SD16 | — | 106 | 12 | no | — |
| 340 | SD16 | — | 106 | 12 | no | — |
| 341 | SD16 | — | 106 | 12 | no | — |
| 342 | D8 | — | 2 | 6 | no | — |
| 343 | D8 | — | 106 | 6 | no | — |
| 344 | D8 | — | 106 | 12 | no | — |
| 345 | M16 | — | 2 | 6 | no | — |
| 346 | M16 | — | 106 | 12 | no | — |
| 347 | M16 | — | 106 | 6 | no | — |
| 348 | M16 | — | 212 | 3 | no | — |
| 349 | M16 | — | 212 | 1 | no | — |
| 350 | C2×C8 | — | 2 | 3 | no | — |
| 351 | C2×C8 | — | 53 | 6 | no | — |
| 352 | C2×C8 | — | 106 | 6 | no | — |
| 353 | C2×C8 | — | 106 | 6 | no | — |
| 354 | C2×C8 | — | 106 | 3 | no | — |
| 355 | C2×C8 | D4×D53 | 1 | 6 | yes | — |
| 356 | C23 | — | 2 | 3 | no | — |
| 357 | C23 | — | 53 | 3 | no | — |
| 358 | C23 | — | 53 | 3 | no | — |
| 359 | C23 | — | 106 | 3 | no | — |
| 360 | C23 | — | 424 | 6 | no | — |
| 361 | C23 | — | 424 | 1 | no | — |
| 362 | C23 | — | 212 | 6 | no | — |
| 363 | C23 | #41×D53 | 1 | 1 | yes | characteristic |
| 364 | Q8 | — | 2 | 6 | no | — |
| 365 | Q8 | — | 106 | 6 | no | — |
| 366 | Q8 | — | 212 | 3 | no | — |
| 367 | Q8 | — | 212 | 3 | no | — |
| 368 | D4 | — | 2 | 6 | no | — |
| 369 | D4 | — | 4 | 6 | no | — |
| 370 | D4 | — | 106 | 6 | no | — |
| 371 | D4 | — | 212 | 3 | no | — |
| 372 | D4 | — | 212 | 3 | no | — |
| 373 | D4 | — | 212 | 3 | no | — |
| 374 | D4 | — | 212 | 3 | no | — |
| 375 | D4 | — | 212 | 3 | no | — |
| 376 | D4 | — | 212 | 3 | no | — |
| 377 | D4 | — | 212 | 6 | no | — |
| 378 | C2×C4 | — | 2 | 3 | no | — |
| 379 | C2×C4 | — | 4 | 3 | no | — |
| 380 | C2×C4 | — | 4 | 3 | no | — |
| 381 | C2×C4 | — | 53 | 3 | no | — |
| 382 | C2×C4 | — | 53 | 3 | no | — |
| 383 | C2×C4 | — | 53 | 3 | no | — |
| 384 | C2×C4 | — | 53 | 3 | no | — |
| 385 | C2×C4 | — | 53 | 6 | no | — |
| 386 | C2×C4 | — | 53 | 3 | no | — |
| 387 | C2×C4 | — | 53 | 1 | no | — |
| 388 | C2×C4 | — | 106 | 3 | no | — |
| 389 | C2×C4 | — | 212 | 6 | no | — |
| 390 | C2×C4 | — | 212 | 6 | no | — |
| 391 | C2×C4 | — | 212 | 6 | no | — |
| 392 | C2×C4 | — | 212 | 3 | no | — |
| 393 | C2×C4 | — | 212 | 3 | no | — |
| 394 | C2×C4 | C2×D4×D53 | 1 | 3 | yes | — |
| 395 | C2×C4 | C2×D4×D53 | 1 | 3 | yes | — |
| 396 | C8 | — | 2 | 6 | no | — |
| 397 | C8 | — | 4 | 1 | no | — |
| 398 | C8 | — | 106 | 6 | no | — |
| 399 | C8 | — | 212 | 1 | no | — |
| 400 | C22 | — | 4 | 1 | no | — |
| 401 | C22 | — | 4 | 6 | no | — |
| 402 | C22 | — | 4 | 3 | no | — |
| 403 | C22 | — | 53 | 3 | no | — |
| 404 | C22 | — | 53 | 1 | no | — |
| 405 | C22 | — | 424 | 12 | no | — |
| 406 | C22 | — | 212 | 3 | no | — |
| 407 | C22 | — | 212 | 3 | no | — |
| 408 | C22 | — | 212 | 6 | no | — |
| 409 | C22 | — | 212 | 3 | no | — |
| 410 | C22 | #121×D53 | 1 | 3 | yes | — |
| 411 | C4 | — | 4 | 3 | no | — |
| 412 | C4 | — | 53 | 3 | no | — |
| 413 | C4 | — | 53 | 1 | no | — |
| 414 | C4 | — | 212 | 3 | no | — |
| 415 | C4 | #120×D53 | 1 | 3 | yes | — |
| 416 | C4 | #127×D53 | 1 | 1 | yes | characteristic |
| 417 | C2 | — | 2 | 3 | no | — |
| 418 | C2 | — | 8 | 3 | no | — |
| 419 | C2 | — | 106 | 3 | no | — |
| 420 | C2 | — | 106 | 1 | no | — |
| 421 | C2 | — | 424 | 3 | no | — |
| 422 | C2 | #392×D53 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #575×D53 | C2 | semidirect |
| 2. #20283157 | C2 | semidirect |
| 3. #20275820 | C2 | semidirect |
| 4. #20275819 | C2 | semidirect |
| 5. #20275818 | C2 | semidirect |
| 6. #338×D53 | C2 | semidirect |
| 7. C53×#2017 | C2 | semidirect |
| 9. #16811423 | C22 | semidirect |
| 11. #16811421 | C22 | semidirect |
| 19. #16810591 | C22 | semidirect |
| 20. #16810590 | C22 | semidirect |
| 21. #16810589 | C22 | semidirect |
| 24. #16810381 | C22 | semidirect |
| 25. C53×#575 | C22 | semidirect |
| 26. C53×#408 | C22 | semidirect |
| 27. C53×#338 | C22 | semidirect |
| 211. #2017 | D53 | semidirect |
| 225. #575 | C2×D53 | semidirect |
| 235. #408 | C2×D53 | semidirect |
| 238. #338 | C2×D53 | semidirect |
| 239. C53 | #23434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #575×D53 | 2 |
| #20283157 | 2 |
| #20275820 | 2 |
| #20275819 | 2 |
| #20275818 | 2 |
| #338×D53 | 2 |
| C53×#2017 | 2 |
| #23434 | 53 |