Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
476 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #20291494 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20291042 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#16811541 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20290876 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20289793 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20289767 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #509×D53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #16811702 | — | 2 | 1 | no | — |
| 9 | C2×#13133292 | C22 | 1 | 1 | yes | characteristic |
| 10 | #16811670 | — | 2 | 1 | no | — |
| 11 | #16811669 | — | 2 | 1 | no | — |
| 12 | #16811666 | — | 2 | 2 | no | — |
| 13 | D53⋊#108 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#13133287 | C22 | 1 | 1 | yes | characteristic |
| 15 | #16811620 | — | 2 | 1 | no | — |
| 16 | #16811615 | — | 2 | 1 | no | — |
| 17 | D53⋊#100 | — | 2 | 1 | no | — |
| 18 | #16811586 | C22 | 1 | 1 | yes | characteristic |
| 19 | #16811542 | — | 2 | 1 | no | — |
| 20 | #16811541 | — | 2 | 2 | no | — |
| 21 | #16811541 | — | 2 | 1 | no | — |
| 22 | #135×D53 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×D8×D53 | C22 | 1 | 1 | yes | characteristic |
| 24 | #16811061 | C4 | 1 | 1 | yes | characteristic, complemented |
| 25 | #16811060 | — | 2 | 1 | no | — |
| 26 | #16811059 | C4 | 1 | 1 | yes | characteristic, complemented |
| 27 | #16811058 | C4 | 1 | 1 | yes | characteristic, complemented |
| 28 | #16811057 | — | 2 | 1 | no | — |
| 29 | SD32×D53 | — | 2 | 1 | no | — |
| 30 | D16×D53 | — | 2 | 1 | no | — |
| 31 | M32×D53 | C22 | 1 | 1 | yes | characteristic |
| 32 | C53×#509 | C4 | 1 | 1 | yes | characteristic, complemented |
| 33 | #13133305 | — | 2 | 2 | no | — |
| 34 | #13133304 | — | 2 | 2 | no | — |
| 35 | #13133304 | — | 4 | 2 | no | — |
| 36 | C2×#11719936 | — | 2 | 1 | no | — |
| 37 | C2×#11719936 | — | 4 | 1 | no | — |
| 38 | D53⋊M16 | — | 2 | 1 | no | — |
| 39 | D53⋊M16 | — | 4 | 1 | no | — |
| 40 | D53⋊M16 | D4 | 1 | 1 | yes | characteristic |
| 41 | #13133296 | D4 | 1 | 1 | yes | characteristic |
| 42 | #13133292 | — | 2 | 1 | no | — |
| 43 | #13133292 | — | 2 | 1 | no | — |
| 44 | C2×#11719910 | — | 2 | 1 | no | — |
| 45 | #13133288 | — | 2 | 1 | no | — |
| 46 | #13133287 | — | 2 | 1 | no | — |
| 47 | #13133287 | — | 2 | 1 | no | — |
| 48 | #13133287 | D4 | 1 | 2 | yes | — |
| 49 | #13133282 | — | 2 | 2 | no | — |
| 50 | #13133281 | — | 2 | 2 | no | — |
| 51 | #13133279 | — | 4 | 2 | no | — |
| 52 | #13133277 | — | 4 | 2 | no | — |
| 53 | #13133271 | — | 2 | 1 | no | — |
| 54 | C8×#6157 | — | 2 | 1 | no | — |
| 55 | #41×D53 | — | 2 | 1 | no | — |
| 56 | C2×D4×D53 | — | 2 | 1 | no | — |
| 57 | #13133240 | D4 | 1 | 1 | yes | characteristic |
| 58 | #13133239 | C2×C4 | 1 | 1 | yes | characteristic |
| 59 | #13133238 | — | 2 | 1 | no | — |
| 60 | #13133237 | — | 2 | 1 | no | — |
| 61 | #13133236 | D4 | 1 | 1 | yes | characteristic |
| 62 | Q16×D53 | D4 | 1 | 1 | yes | characteristic |
| 63 | SD16×D53 | — | 2 | 1 | no | — |
| 64 | C2×D424 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | C2×#11719922 | — | 2 | 1 | no | — |
| 66 | D8×D53 | — | 2 | 1 | no | — |
| 67 | D8×D53 | — | 2 | 1 | no | — |
| 68 | D8×D53 | — | 2 | 1 | no | — |
| 69 | D8×D53 | — | 2 | 1 | no | — |
| 70 | D8×D53 | D4 | 1 | 1 | yes | characteristic |
| 71 | C2×C8×D53 | C23 | 1 | 1 | yes | characteristic |
| 72 | #13133162 | — | 2 | 1 | no | — |
| 73 | #13133161 | — | 2 | 1 | no | — |
| 74 | #13133160 | — | 2 | 1 | no | — |
| 75 | D848 | — | 2 | 1 | no | — |
| 76 | #13133158 | — | 2 | 1 | no | — |
| 77 | #13133158 | — | 2 | 1 | no | — |
| 78 | #13133157 | C2×C4 | 1 | 1 | yes | characteristic |
| 79 | #13133156 | — | 2 | 1 | no | — |
| 80 | C16×D53 | — | 2 | 1 | no | — |
| 81 | #135×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 82 | C2×D8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 83 | SD32×C53 | — | 2 | 1 | no | — |
| 84 | D16×C53 | — | 2 | 1 | no | — |
| 85 | M32×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 86 | C23×D53 | — | 4 | 1 | no | — |
| 87 | #41×C53 | — | 2 | 1 | no | — |
| 88 | C2×D4×C53 | — | 2 | 1 | no | — |
| 89 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 90 | #11719949 | — | 2 | 1 | no | — |
| 91 | Q8×D53 | — | 2 | 1 | no | — |
| 92 | #11719947 | — | 2 | 1 | no | — |
| 93 | #11719947 | — | 4 | 1 | no | — |
| 94 | D4×D53 | — | 2 | 1 | no | — |
| 95 | D4×D53 | — | 4 | 1 | no | — |
| 96 | D4×D53 | — | 4 | 1 | no | — |
| 97 | D4×D53 | — | 4 | 1 | no | — |
| 98 | D4×D53 | — | 4 | 1 | no | — |
| 99 | D4×D53 | — | 4 | 1 | no | — |
| 100 | #11719945 | — | 2 | 1 | no | — |
| 101 | #11719945 | — | 4 | 1 | no | — |
| 102 | C2×D212 | — | 2 | 1 | no | — |
| 103 | C2×C4×D53 | — | 4 | 1 | no | — |
| 104 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | C22⋊#6157 | — | 2 | 1 | no | — |
| 106 | #11719940 | — | 4 | 2 | no | — |
| 107 | #11719940 | — | 4 | 1 | no | — |
| 108 | #11719940 | D8 | 1 | 2 | yes | — |
| 109 | C2×#88324 | — | 4 | 2 | no | — |
| 110 | C2×#88324 | — | 4 | 1 | no | — |
| 111 | C4⋊#6157 | — | 2 | 1 | no | — |
| 112 | C4×#6157 | — | 2 | 1 | no | — |
| 113 | #11719936 | — | 2 | 1 | no | — |
| 114 | #11719936 | — | 2 | 2 | no | — |
| 115 | #11719936 | — | 4 | 2 | no | — |
| 116 | #11719936 | — | 4 | 1 | no | — |
| 117 | #11719936 | — | 4 | 1 | no | — |
| 118 | D53⋊C8 | — | 2 | 1 | no | — |
| 119 | D53⋊C8 | — | 4 | 2 | no | — |
| 120 | D53⋊C8 | — | 4 | 1 | no | — |
| 121 | Q16×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 122 | SD16×C53 | — | 2 | 1 | no | — |
| 123 | D8×C53 | — | 2 | 1 | no | — |
| 124 | D8×C53 | — | 2 | 1 | no | — |
| 125 | D8×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 126 | C2×C8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 127 | #11719925 | — | 2 | 1 | no | — |
| 128 | #11719924 | — | 2 | 1 | no | — |
| 129 | #11719923 | — | 2 | 1 | no | — |
| 130 | #11719922 | — | 2 | 1 | no | — |
| 131 | #11719922 | — | 4 | 1 | no | — |
| 132 | #11719922 | — | 4 | 1 | no | — |
| 133 | C2×#88322 | #41 | 1 | 1 | yes | characteristic |
| 134 | Dic212 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 135 | D424 | — | 2 | 1 | no | — |
| 136 | D424 | — | 2 | 1 | no | — |
| 137 | D424 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 138 | #11719913 | — | 2 | 1 | no | — |
| 139 | C8×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 140 | C8×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C8×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C8×D53 | #41 | 1 | 1 | yes | characteristic |
| 143 | #11719910 | — | 4 | 1 | no | — |
| 144 | C16×C53 | — | 2 | 1 | no | — |
| 145 | #11719908 | — | 2 | 1 | no | — |
| 146 | C23×C53 | — | 4 | 1 | no | — |
| 147 | C22×D53 | — | 4 | 1 | no | — |
| 148 | C22×D53 | — | 4 | 1 | no | — |
| 149 | C22×D53 | — | 8 | 1 | no | — |
| 150 | C22×D53 | — | 8 | 1 | no | — |
| 151 | C22×D53 | — | 16 | 2 | no | — |
| 152 | C22×D53 | #135 | 1 | 1 | yes | characteristic |
| 153 | C2×#6157 | — | 4 | 1 | no | — |
| 154 | Q8×C53 | — | 2 | 1 | no | — |
| 155 | D4×C53 | — | 2 | 1 | no | — |
| 156 | D4×C53 | — | 4 | 1 | no | — |
| 157 | D4×C53 | — | 4 | 1 | no | — |
| 158 | D4×C53 | — | 4 | 1 | no | — |
| 159 | C2×C4×C53 | — | 4 | 1 | no | — |
| 160 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 161 | C22⋊D53 | — | 4 | 1 | no | — |
| 162 | C22⋊D53 | — | 4 | 1 | no | — |
| 163 | C22⋊D53 | — | 4 | 1 | no | — |
| 164 | C22⋊D53 | — | 8 | 1 | no | — |
| 165 | C22⋊D53 | — | 8 | 1 | no | — |
| 166 | C2×Dic53 | — | 4 | 1 | no | — |
| 167 | C2×Dic53 | C2×D8 | 1 | 1 | yes | characteristic |
| 168 | D212 | — | 2 | 1 | no | — |
| 169 | D212 | — | 4 | 1 | no | — |
| 170 | D212 | — | 4 | 1 | no | — |
| 171 | D212 | — | 4 | 1 | no | — |
| 172 | C4×D53 | — | 4 | 1 | no | — |
| 173 | C4×D53 | — | 4 | 1 | no | — |
| 174 | C4×D53 | — | 4 | 1 | no | — |
| 175 | C4×D53 | #120 | 1 | 1 | yes | characteristic |
| 176 | C4×D53 | #121 | 1 | 1 | yes | characteristic |
| 177 | C4×D53 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 178 | C4×D53 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 179 | Dic106 | — | 2 | 1 | no | — |
| 180 | Dic106 | — | 4 | 1 | no | — |
| 181 | #88324 | — | 2 | 2 | no | — |
| 182 | #88324 | — | 4 | 2 | no | — |
| 183 | #88324 | — | 8 | 1 | no | — |
| 184 | C8×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 185 | C8×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 186 | #88322 | #121 | 1 | 1 | yes | characteristic |
| 187 | #88322 | #123 | 1 | 1 | yes | characteristic |
| 188 | #13032 | — | 53 | 1 | no | maximal, Sylow |
| 189 | C22×C53 | — | 4 | 1 | no | — |
| 190 | C22×C53 | — | 8 | 1 | no | — |
| 191 | C22×C53 | — | 16 | 1 | no | — |
| 192 | C22×C53 | C4×D8 | 1 | 1 | yes | characteristic |
| 193 | C2×D53 | — | 4 | 1 | no | — |
| 194 | C2×D53 | — | 4 | 1 | no | — |
| 195 | C2×D53 | — | 8 | 1 | no | — |
| 196 | C2×D53 | — | 16 | 1 | no | — |
| 197 | C2×D53 | — | 16 | 2 | no | — |
| 198 | C2×D53 | — | 16 | 2 | no | — |
| 199 | C2×D53 | — | 16 | 1 | no | — |
| 200 | C2×D53 | #449 | 1 | 1 | yes | characteristic |
| 201 | C2×D53 | #463 | 1 | 1 | yes | characteristic |
| 202 | #6157 | — | 8 | 1 | no | — |
| 203 | C4×C53 | — | 4 | 1 | no | — |
| 204 | C4×C53 | #386 | 1 | 1 | yes | characteristic |
| 205 | C4×C53 | #442 | 1 | 1 | yes | characteristic |
| 206 | Dic53 | — | 4 | 1 | no | — |
| 207 | Dic53 | #447 | 1 | 1 | yes | characteristic |
| 208 | Dic53 | #459 | 1 | 1 | yes | characteristic |
| 209 | C2×#509 | — | 53 | 1 | no | — |
| 210 | #2957 | — | 53 | 1 | no | — |
| 211 | #2148 | — | 53 | 1 | no | — |
| 212 | C2×#361 | — | 53 | 1 | no | — |
| 213 | #1978 | — | 53 | 1 | no | — |
| 214 | #1388 | — | 53 | 1 | no | — |
| 215 | #1378 | — | 53 | 1 | no | — |
| 216 | C2×C53 | — | 2 | 1 | no | — |
| 217 | C2×C53 | — | 8 | 1 | no | — |
| 218 | C2×C53 | — | 16 | 1 | no | — |
| 219 | C2×C53 | #1879 | 1 | 1 | yes | characteristic |
| 220 | D53 | — | 2 | 1 | no | — |
| 221 | D53 | — | 2 | 1 | no | — |
| 222 | D53 | — | 8 | 1 | no | — |
| 223 | D53 | — | 16 | 1 | no | — |
| 224 | C2×#135 | — | 53 | 1 | no | — |
| 225 | C22×D8 | — | 53 | 1 | no | — |
| 226 | #568 | — | 106 | 1 | no | — |
| 227 | #509 | — | 53 | 1 | no | — |
| 228 | #509 | — | 53 | 1 | no | — |
| 229 | #509 | — | 53 | 1 | no | — |
| 230 | #509 | — | 106 | 1 | no | — |
| 231 | #509 | — | 106 | 1 | no | — |
| 232 | #509 | #6157 | 1 | 1 | yes | characteristic, complemented |
| 233 | C2×SD32 | — | 106 | 1 | no | — |
| 234 | C2×D16 | — | 106 | 1 | no | — |
| 235 | C2×M32 | — | 53 | 1 | no | — |
| 236 | C2×M32 | — | 53 | 1 | no | — |
| 237 | #444 | — | 106 | 1 | no | — |
| 238 | #444 | — | 106 | 1 | no | — |
| 239 | #443 | — | 106 | 2 | no | — |
| 240 | C2×#108 | — | 53 | 1 | no | — |
| 241 | C2×#108 | — | 53 | 1 | no | — |
| 242 | #421 | — | 106 | 1 | no | — |
| 243 | #418 | — | 106 | 1 | no | — |
| 244 | C2×#100 | — | 106 | 1 | no | — |
| 245 | #405 | — | 53 | 1 | no | — |
| 246 | #362 | — | 106 | 1 | no | — |
| 247 | #361 | — | 106 | 2 | no | — |
| 248 | #361 | — | 106 | 1 | no | — |
| 249 | C53 | #13032 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 250 | C2×#41 | — | 106 | 1 | no | — |
| 251 | C22×D4 | — | 106 | 1 | no | — |
| 252 | #135 | — | 53 | 1 | no | — |
| 253 | #135 | — | 53 | 1 | no | — |
| 254 | #135 | — | 53 | 1 | no | — |
| 255 | #135 | — | 106 | 1 | no | — |
| 256 | #135 | — | 106 | 1 | no | — |
| 257 | #135 | C2×#6157 | 1 | 1 | yes | characteristic |
| 258 | C2×Q16 | — | 53 | 1 | no | — |
| 259 | C2×SD16 | — | 106 | 1 | no | — |
| 260 | C2×D8 | — | 53 | 1 | no | — |
| 261 | C2×D8 | — | 53 | 1 | no | — |
| 262 | C2×D8 | — | 106 | 1 | no | — |
| 263 | C2×D8 | — | 106 | 1 | no | — |
| 264 | C2×D8 | — | 106 | 1 | no | — |
| 265 | C2×D8 | — | 106 | 1 | no | — |
| 266 | C2×D8 | — | 106 | 1 | no | — |
| 267 | C2×D8 | C2×#6157 | 1 | 1 | yes | characteristic |
| 268 | #131 | — | 106 | 2 | no | — |
| 269 | #131 | — | 106 | 2 | no | — |
| 270 | #131 | — | 212 | 2 | no | — |
| 271 | C2×M16 | — | 53 | 1 | no | — |
| 272 | C2×M16 | — | 106 | 1 | no | — |
| 273 | C2×M16 | — | 106 | 1 | no | — |
| 274 | C2×M16 | — | 212 | 1 | no | — |
| 275 | C2×M16 | — | 212 | 1 | no | — |
| 276 | C22×C8 | — | 53 | 1 | no | — |
| 277 | #117 | — | 53 | 1 | no | — |
| 278 | SD32 | — | 2 | 1 | no | — |
| 279 | SD32 | — | 106 | 1 | no | — |
| 280 | SD32 | — | 106 | 1 | no | — |
| 281 | SD32 | — | 106 | 1 | no | — |
| 282 | D16 | — | 2 | 1 | no | — |
| 283 | D16 | — | 106 | 1 | no | — |
| 284 | D16 | — | 106 | 1 | no | — |
| 285 | D16 | — | 106 | 1 | no | — |
| 286 | M32 | — | 53 | 1 | no | — |
| 287 | M32 | — | 106 | 1 | no | — |
| 288 | M32 | — | 106 | 1 | no | — |
| 289 | M32 | — | 106 | 1 | no | — |
| 290 | M32 | C2×#6157 | 1 | 1 | yes | characteristic |
| 291 | C2×C16 | — | 106 | 1 | no | — |
| 292 | C2×C16 | — | 106 | 1 | no | — |
| 293 | #108 | — | 53 | 2 | no | — |
| 294 | #108 | — | 106 | 1 | no | — |
| 295 | #108 | — | 106 | 1 | no | — |
| 296 | #108 | — | 106 | 1 | no | — |
| 297 | #104 | — | 106 | 2 | no | — |
| 298 | #104 | — | 106 | 2 | no | — |
| 299 | #102 | — | 212 | 2 | no | — |
| 300 | #100 | — | 212 | 2 | no | — |
| 301 | #97 | — | 106 | 1 | no | — |
| 302 | C4×C8 | — | 106 | 1 | no | — |
| 303 | C24 | — | 212 | 1 | no | — |
| 304 | #41 | — | 2 | 1 | no | — |
| 305 | #41 | — | 106 | 1 | no | — |
| 306 | #41 | — | 106 | 1 | no | — |
| 307 | #41 | — | 106 | 1 | no | — |
| 308 | #41 | — | 212 | 1 | no | — |
| 309 | #41 | — | 212 | 1 | no | — |
| 310 | C2×Q8 | — | 106 | 1 | no | — |
| 311 | C2×D4 | — | 2 | 1 | no | — |
| 312 | C2×D4 | — | 106 | 1 | no | — |
| 313 | C2×D4 | — | 106 | 1 | no | — |
| 314 | C2×D4 | — | 212 | 1 | no | — |
| 315 | C2×D4 | — | 212 | 1 | no | — |
| 316 | C2×D4 | — | 212 | 1 | no | — |
| 317 | C2×D4 | — | 212 | 1 | no | — |
| 318 | C2×D4 | — | 212 | 1 | no | — |
| 319 | C2×D4 | — | 212 | 1 | no | — |
| 320 | C22×C4 | — | 53 | 1 | no | — |
| 321 | C22×C4 | — | 212 | 1 | no | — |
| 322 | Q16 | — | 53 | 1 | no | — |
| 323 | Q16 | — | 106 | 1 | no | — |
| 324 | Q16 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 325 | SD16 | — | 2 | 1 | no | — |
| 326 | SD16 | — | 106 | 1 | no | — |
| 327 | SD16 | — | 106 | 1 | no | — |
| 328 | SD16 | — | 106 | 1 | no | — |
| 329 | D8 | — | 2 | 1 | no | — |
| 330 | D8 | — | 2 | 1 | no | — |
| 331 | D8 | — | 53 | 1 | no | — |
| 332 | D8 | — | 106 | 1 | no | — |
| 333 | D8 | — | 106 | 1 | no | — |
| 334 | D8 | — | 106 | 1 | no | — |
| 335 | D8 | — | 212 | 1 | no | — |
| 336 | D8 | — | 212 | 1 | no | — |
| 337 | D8 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 338 | M16 | — | 53 | 2 | no | — |
| 339 | M16 | — | 106 | 1 | no | — |
| 340 | M16 | — | 106 | 2 | no | — |
| 341 | M16 | — | 212 | 2 | no | — |
| 342 | M16 | — | 212 | 2 | no | — |
| 343 | M16 | — | 212 | 1 | no | — |
| 344 | M16 | — | 212 | 1 | no | — |
| 345 | M16 | — | 212 | 1 | no | — |
| 346 | C2×C8 | — | 53 | 1 | no | — |
| 347 | C2×C8 | — | 53 | 1 | no | — |
| 348 | C2×C8 | — | 53 | 1 | no | — |
| 349 | C2×C8 | — | 53 | 1 | no | — |
| 350 | C2×C8 | — | 53 | 1 | no | — |
| 351 | C2×C8 | — | 106 | 1 | no | — |
| 352 | C2×C8 | — | 212 | 2 | no | — |
| 353 | C2×C8 | — | 212 | 2 | no | — |
| 354 | C2×C8 | — | 212 | 1 | no | — |
| 355 | C2×C8 | — | 212 | 1 | no | — |
| 356 | C2×C8 | C22×#6157 | 1 | 1 | yes | characteristic |
| 357 | C4⋊C4 | — | 106 | 1 | no | — |
| 358 | C22⋊C4 | — | 106 | 1 | no | — |
| 359 | C42 | — | 106 | 1 | no | — |
| 360 | C16 | — | 2 | 1 | no | — |
| 361 | C16 | — | 106 | 1 | no | — |
| 362 | C16 | — | 212 | 1 | no | — |
| 363 | C23 | — | 4 | 1 | no | — |
| 364 | C23 | — | 53 | 1 | no | — |
| 365 | C23 | — | 848 | 2 | no | — |
| 366 | C23 | — | 424 | 1 | no | — |
| 367 | C23 | — | 424 | 1 | no | — |
| 368 | C23 | — | 212 | 1 | no | — |
| 369 | C23 | — | 212 | 1 | no | — |
| 370 | Q8 | — | 2 | 1 | no | — |
| 371 | Q8 | — | 106 | 1 | no | — |
| 372 | Q8 | — | 212 | 1 | no | — |
| 373 | D4 | — | 2 | 1 | no | — |
| 374 | D4 | — | 4 | 1 | no | — |
| 375 | D4 | — | 4 | 1 | no | — |
| 376 | D4 | — | 4 | 1 | no | — |
| 377 | D4 | — | 106 | 1 | no | — |
| 378 | D4 | — | 424 | 1 | no | — |
| 379 | D4 | — | 424 | 1 | no | — |
| 380 | D4 | — | 212 | 1 | no | — |
| 381 | D4 | — | 212 | 1 | no | — |
| 382 | D4 | — | 212 | 1 | no | — |
| 383 | D4 | — | 212 | 1 | no | — |
| 384 | D4 | — | 212 | 1 | no | — |
| 385 | D4 | — | 212 | 1 | no | — |
| 386 | C2×C4 | — | 4 | 1 | no | — |
| 387 | C2×C4 | — | 53 | 1 | no | — |
| 388 | C2×C4 | — | 53 | 1 | no | — |
| 389 | C2×C4 | — | 53 | 1 | no | — |
| 390 | C2×C4 | — | 53 | 1 | no | — |
| 391 | C2×C4 | — | 53 | 1 | no | — |
| 392 | C2×C4 | — | 212 | 1 | no | — |
| 393 | C2×C4 | — | 212 | 1 | no | — |
| 394 | C2×C4 | — | 212 | 1 | no | — |
| 395 | C2×C4 | — | 212 | 1 | no | — |
| 396 | C2×C4 | — | 212 | 1 | no | — |
| 397 | C2×C4 | D4×#6157 | 1 | 1 | yes | characteristic |
| 398 | C8 | — | 53 | 1 | no | — |
| 399 | C8 | — | 53 | 1 | no | — |
| 400 | C8 | — | 106 | 2 | no | — |
| 401 | C8 | — | 424 | 1 | no | — |
| 402 | C8 | — | 212 | 2 | no | — |
| 403 | C8 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 404 | C8 | D4×#6157 | 1 | 1 | yes | characteristic |
| 405 | C22 | — | 4 | 1 | no | — |
| 406 | C22 | — | 8 | 1 | no | — |
| 407 | C22 | — | 16 | 1 | no | — |
| 408 | C22 | — | 53 | 1 | no | — |
| 409 | C22 | — | 53 | 1 | no | — |
| 410 | C22 | — | 848 | 1 | no | — |
| 411 | C22 | — | 848 | 1 | no | — |
| 412 | C22 | — | 848 | 2 | no | — |
| 413 | C22 | — | 848 | 2 | no | — |
| 414 | C22 | — | 424 | 1 | no | — |
| 415 | C22 | — | 212 | 1 | no | — |
| 416 | C22 | — | 212 | 1 | no | — |
| 417 | C22 | D8×#6157 | 1 | 1 | yes | characteristic |
| 418 | C4 | — | 4 | 1 | no | — |
| 419 | C4 | — | 53 | 1 | no | — |
| 420 | C4 | — | 53 | 1 | no | — |
| 421 | C4 | — | 424 | 1 | no | — |
| 422 | C4 | — | 212 | 1 | no | — |
| 423 | C4 | #16811571 | 1 | 1 | yes | characteristic |
| 424 | C4 | #16811664 | 1 | 1 | yes | characteristic |
| 425 | C2 | — | 2 | 1 | no | — |
| 426 | C2 | — | 8 | 1 | no | — |
| 427 | C2 | — | 16 | 1 | no | — |
| 428 | C2 | — | 848 | 1 | no | — |
| 429 | C2 | — | 106 | 1 | no | — |
| 430 | C2 | — | 106 | 1 | no | — |
| 431 | C2 | — | 424 | 1 | no | — |
| 432 | C2 | #20290710 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20291494 | C2 | semidirect |
| 2. #20291042 | C2 | semidirect |
| 3. C2×#16811541 | C2 | semidirect |
| 4. #20290876 | C2 | semidirect |
| 5. #20289793 | C2 | semidirect |
| 6. #20289767 | C2 | semidirect |
| 24. #16811061 | C4 | semidirect |
| 26. #16811059 | C4 | semidirect |
| 27. #16811058 | C4 | semidirect |
| 32. C53×#509 | C4 | semidirect |
| 232. #509 | #6157 | semidirect |
| 249. C53 | #13032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291494 | 2 |
| #20291042 | 2 |
| C2×#16811541 | 2 |
| #20290876 | 2 |
| #20289793 | 2 |
| #20289767 | 2 |
| #509×D53 | 2 |
| #13032 | 53 |