Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
468 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 61 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 | #496×D53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #355×D53 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #354×D53 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20272873 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20272872 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20272871 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C53×#1406 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×SD16×D53 | — | 2 | 1 | no | — |
| 9 | C2×D8×D53 | — | 2 | 1 | no | — |
| 10 | #127×D53 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | #124×D53 | C22 | 1 | 1 | yes | characteristic |
| 12 | #16811013 | C22 | 1 | 1 | yes | characteristic |
| 13 | #16811012 | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | #16811011 | — | 2 | 1 | no | — |
| 15 | #16811010 | C4 | 1 | 1 | yes | characteristic, complemented |
| 16 | #16811009 | — | 2 | 1 | no | — |
| 17 | #101×D53 | — | 2 | 1 | no | — |
| 18 | #99×D53 | — | 2 | 1 | no | — |
| 19 | #97×D53 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | #16810420 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #16810419 | — | 2 | 1 | no | — |
| 22 | #16810418 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #16810417 | — | 2 | 1 | no | — |
| 24 | C53×#496 | C22 | 1 | 1 | yes | characteristic |
| 25 | C53×#355 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C53×#354 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×Q8×D53 | D4 | 1 | 1 | yes | characteristic |
| 28 | C2×D4×D53 | — | 2 | 1 | no | — |
| 29 | C2×D4×D53 | — | 4 | 1 | no | — |
| 30 | C2×D4×D53 | D4 | 1 | 1 | yes | characteristic |
| 31 | C2×#11719913 | — | 2 | 1 | no | — |
| 32 | C2×#11719923 | — | 2 | 1 | no | — |
| 33 | C2×#11719924 | — | 2 | 1 | no | — |
| 34 | SD16×D53 | — | 4 | 2 | no | — |
| 35 | SD16×D53 | — | 4 | 2 | no | — |
| 36 | C2×D424 | — | 2 | 1 | no | — |
| 37 | C2×#11719922 | — | 2 | 1 | no | — |
| 38 | C2×#11719922 | — | 2 | 1 | no | — |
| 39 | D8×D53 | — | 4 | 2 | no | — |
| 40 | D8×D53 | — | 4 | 2 | no | — |
| 41 | M16×D53 | — | 4 | 1 | no | — |
| 42 | C2×C8×D53 | — | 2 | 1 | no | — |
| 43 | #13133214 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 44 | #13133213 | — | 2 | 1 | no | — |
| 45 | #13133213 | — | 4 | 1 | no | — |
| 46 | #13133206 | D4 | 1 | 1 | yes | characteristic |
| 47 | #13133205 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | #13133204 | D4 | 1 | 1 | yes | characteristic |
| 49 | #13133203 | — | 4 | 1 | no | — |
| 50 | C22⋊C4×D53 | — | 4 | 1 | no | — |
| 51 | C22⋊C4×D53 | — | 4 | 1 | no | — |
| 52 | C42×D53 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | #13133136 | — | 2 | 1 | no | — |
| 54 | #13133135 | — | 4 | 1 | no | — |
| 55 | #13133132 | — | 2 | 1 | no | — |
| 56 | #13133131 | — | 4 | 1 | no | — |
| 57 | #13133128 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 58 | #13133127 | — | 2 | 1 | no | — |
| 59 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 60 | C2×D8×C53 | — | 2 | 1 | no | — |
| 61 | #127×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 62 | #124×C53 | C23 | 1 | 1 | yes | characteristic |
| 63 | #101×C53 | — | 2 | 1 | no | — |
| 64 | #99×C53 | — | 2 | 1 | no | — |
| 65 | #97×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 66 | C23×D53 | — | 2 | 1 | no | — |
| 67 | C23×D53 | — | 4 | 1 | no | — |
| 68 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 69 | C2×D4×C53 | — | 2 | 1 | no | — |
| 70 | C2×D4×C53 | — | 4 | 1 | no | — |
| 71 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 72 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 73 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 74 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 75 | Q8×D53 | — | 4 | 1 | no | — |
| 76 | Q8×D53 | — | 4 | 1 | no | — |
| 77 | D4×D53 | — | 4 | 1 | no | — |
| 78 | D4×D53 | — | 4 | 1 | no | — |
| 79 | D4×D53 | — | 4 | 1 | no | — |
| 80 | D4×D53 | — | 4 | 1 | no | — |
| 81 | D4×D53 | — | 4 | 1 | no | — |
| 82 | D4×D53 | — | 4 | 1 | no | — |
| 83 | D4×D53 | — | 8 | 4 | no | — |
| 84 | C2×D212 | — | 2 | 1 | no | — |
| 85 | C2×D212 | — | 4 | 1 | no | — |
| 86 | C2×D212 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 87 | C2×C4×D53 | — | 2 | 1 | no | — |
| 88 | C2×C4×D53 | — | 2 | 1 | no | — |
| 89 | C2×C4×D53 | — | 8 | 1 | no | — |
| 90 | C2×C4×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 91 | C2×Dic106 | — | 2 | 1 | no | — |
| 92 | C2×Dic106 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 93 | SD16×C53 | — | 4 | 2 | no | — |
| 94 | D8×C53 | — | 4 | 2 | no | — |
| 95 | M16×C53 | — | 4 | 1 | no | — |
| 96 | C2×C8×C53 | — | 2 | 1 | no | — |
| 97 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 98 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 99 | C42×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 100 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 101 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 102 | #11719924 | — | 4 | 2 | no | — |
| 103 | #11719923 | — | 4 | 2 | no | — |
| 104 | #11719922 | — | 4 | 2 | no | — |
| 105 | #11719922 | — | 4 | 2 | no | — |
| 106 | #11719921 | — | 4 | 1 | no | — |
| 107 | #11719921 | — | 4 | 1 | no | — |
| 108 | #11719921 | — | 8 | 1 | no | — |
| 109 | C4×Dic53 | — | 2 | 1 | no | — |
| 110 | C4×Dic53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 111 | #11719917 | — | 4 | 1 | no | — |
| 112 | C2×#88322 | — | 2 | 1 | no | — |
| 113 | D424 | — | 4 | 2 | no | — |
| 114 | #11719913 | — | 4 | 2 | no | — |
| 115 | #11719912 | — | 8 | 1 | no | — |
| 116 | C8×D53 | — | 2 | 2 | no | — |
| 117 | C8×D53 | — | 2 | 2 | no | — |
| 118 | C8×D53 | — | 8 | 1 | no | — |
| 119 | C23×C53 | — | 2 | 1 | no | — |
| 120 | C23×C53 | — | 4 | 1 | no | — |
| 121 | C22×D53 | — | 2 | 1 | no | — |
| 122 | C22×D53 | — | 4 | 1 | no | — |
| 123 | C22×D53 | — | 4 | 1 | no | — |
| 124 | C22×D53 | — | 4 | 1 | no | — |
| 125 | C22×D53 | — | 8 | 2 | no | — |
| 126 | C22×D53 | — | 8 | 4 | no | — |
| 127 | C22×D53 | — | 8 | 1 | no | — |
| 128 | C22×D53 | — | 8 | 1 | no | — |
| 129 | C22×D53 | #99 | 1 | 1 | yes | characteristic |
| 130 | Q8×C53 | — | 4 | 1 | no | — |
| 131 | D4×C53 | — | 4 | 1 | no | — |
| 132 | D4×C53 | — | 4 | 1 | no | — |
| 133 | D4×C53 | — | 4 | 1 | no | — |
| 134 | D4×C53 | — | 8 | 2 | no | — |
| 135 | C2×C4×C53 | — | 2 | 1 | no | — |
| 136 | C2×C4×C53 | — | 2 | 1 | no | — |
| 137 | C2×C4×C53 | — | 8 | 1 | no | — |
| 138 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 139 | C22⋊D53 | — | 8 | 1 | no | — |
| 140 | C22⋊D53 | — | 8 | 1 | no | — |
| 141 | C22⋊D53 | — | 8 | 1 | no | — |
| 142 | C22⋊D53 | — | 8 | 4 | no | — |
| 143 | C2×Dic53 | — | 2 | 1 | no | — |
| 144 | C2×Dic53 | — | 2 | 1 | no | — |
| 145 | C2×Dic53 | — | 8 | 1 | no | — |
| 146 | C2×Dic53 | #99 | 1 | 1 | yes | characteristic |
| 147 | D212 | — | 4 | 1 | no | — |
| 148 | D212 | — | 4 | 1 | no | — |
| 149 | D212 | — | 4 | 1 | no | — |
| 150 | D212 | — | 8 | 2 | no | — |
| 151 | C4×D53 | — | 2 | 1 | no | — |
| 152 | C4×D53 | — | 2 | 1 | no | — |
| 153 | C4×D53 | — | 4 | 2 | no | — |
| 154 | C4×D53 | — | 4 | 1 | no | — |
| 155 | C4×D53 | — | 4 | 1 | no | — |
| 156 | C4×D53 | — | 16 | 2 | no | — |
| 157 | Dic106 | — | 4 | 1 | no | — |
| 158 | Dic106 | — | 8 | 1 | no | — |
| 159 | C8×C53 | — | 2 | 2 | no | — |
| 160 | C8×C53 | — | 8 | 1 | no | — |
| 161 | #88322 | — | 2 | 2 | no | — |
| 162 | #88322 | — | 8 | 1 | no | — |
| 163 | C2×#1406 | — | 53 | 1 | no | maximal, Sylow |
| 164 | C22×C53 | — | 4 | 1 | no | — |
| 165 | C22×C53 | — | 8 | 1 | no | — |
| 166 | C22×C53 | — | 8 | 2 | no | — |
| 167 | C22×C53 | — | 8 | 1 | no | — |
| 168 | C22×C53 | C2×#99 | 1 | 1 | yes | characteristic |
| 169 | C2×D53 | — | 2 | 2 | no | — |
| 170 | C2×D53 | — | 4 | 1 | no | — |
| 171 | C2×D53 | — | 8 | 2 | no | — |
| 172 | C2×D53 | — | 8 | 1 | no | — |
| 173 | C2×D53 | — | 8 | 2 | no | — |
| 174 | C2×D53 | — | 8 | 1 | no | — |
| 175 | C2×D53 | — | 16 | 1 | no | — |
| 176 | C2×D53 | — | 16 | 2 | no | — |
| 177 | C2×D53 | — | 16 | 2 | no | — |
| 178 | C2×D53 | #353 | 1 | 1 | yes | characteristic |
| 179 | C2×D53 | #353 | 1 | 1 | yes | characteristic |
| 180 | C4×C53 | — | 2 | 1 | no | — |
| 181 | C4×C53 | — | 4 | 1 | no | — |
| 182 | C4×C53 | — | 4 | 1 | no | — |
| 183 | C4×C53 | — | 16 | 1 | no | — |
| 184 | Dic53 | — | 2 | 1 | no | — |
| 185 | Dic53 | — | 4 | 1 | no | — |
| 186 | Dic53 | — | 4 | 1 | no | — |
| 187 | Dic53 | — | 16 | 1 | no | — |
| 188 | C2×#496 | — | 53 | 1 | no | — |
| 189 | C2×#355 | — | 53 | 1 | no | — |
| 190 | C2×#354 | — | 53 | 1 | no | — |
| 191 | #1406 | — | 53 | 1 | no | — |
| 192 | #1406 | — | 53 | 1 | no | — |
| 193 | #1406 | — | 53 | 1 | no | — |
| 194 | #1406 | D53 | 1 | 1 | yes | characteristic, direct product factor |
| 195 | C2×C53 | — | 2 | 1 | no | — |
| 196 | C2×C53 | — | 8 | 1 | no | — |
| 197 | C2×C53 | — | 16 | 1 | no | — |
| 198 | C2×C53 | C2×#353 | 1 | 1 | yes | characteristic |
| 199 | D53 | — | 2 | 1 | no | — |
| 200 | D53 | — | 8 | 1 | no | — |
| 201 | D53 | — | 16 | 1 | no | — |
| 202 | D53 | #1406 | 1 | 2 | yes | direct product factor |
| 203 | C22×SD16 | — | 106 | 1 | no | — |
| 204 | C22×D8 | — | 106 | 1 | no | — |
| 205 | C2×#127 | — | 53 | 1 | no | — |
| 206 | C2×#124 | — | 53 | 1 | no | — |
| 207 | #496 | — | 53 | 1 | no | — |
| 208 | #496 | — | 53 | 1 | no | — |
| 209 | #496 | — | 53 | 1 | no | — |
| 210 | #496 | — | 106 | 1 | no | — |
| 211 | #496 | — | 106 | 1 | no | — |
| 212 | #496 | C2×D53 | 1 | 1 | yes | characteristic |
| 213 | C2×#101 | — | 106 | 1 | no | — |
| 214 | C2×#99 | — | 106 | 1 | no | — |
| 215 | C2×#97 | — | 53 | 1 | no | — |
| 216 | #355 | — | 53 | 1 | no | — |
| 217 | #355 | — | 106 | 1 | no | — |
| 218 | #355 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 219 | #354 | — | 53 | 1 | no | — |
| 220 | #354 | — | 106 | 1 | no | — |
| 221 | #354 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 222 | C53 | C2×#1406 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 223 | C22×Q8 | — | 53 | 1 | no | — |
| 224 | C22×D4 | — | 53 | 1 | no | — |
| 225 | C22×D4 | — | 106 | 1 | no | — |
| 226 | C22×D4 | — | 212 | 1 | no | — |
| 227 | C2×SD16 | — | 2 | 1 | no | — |
| 228 | C2×SD16 | — | 106 | 1 | no | — |
| 229 | C2×SD16 | — | 106 | 1 | no | — |
| 230 | C2×SD16 | — | 106 | 1 | no | — |
| 231 | C2×SD16 | — | 212 | 2 | no | — |
| 232 | C2×SD16 | — | 212 | 2 | no | — |
| 233 | C2×D8 | — | 2 | 1 | no | — |
| 234 | C2×D8 | — | 106 | 1 | no | — |
| 235 | C2×D8 | — | 106 | 1 | no | — |
| 236 | C2×D8 | — | 106 | 1 | no | — |
| 237 | C2×D8 | — | 212 | 2 | no | — |
| 238 | C2×D8 | — | 212 | 2 | no | — |
| 239 | C2×M16 | — | 212 | 1 | no | — |
| 240 | C22×C8 | — | 106 | 1 | no | — |
| 241 | #127 | — | 53 | 1 | no | — |
| 242 | #127 | — | 106 | 1 | no | — |
| 243 | #127 | — | 212 | 1 | no | — |
| 244 | #127 | C4×D53 | 1 | 1 | yes | characteristic, complemented |
| 245 | #124 | — | 53 | 1 | no | — |
| 246 | #124 | — | 53 | 1 | no | — |
| 247 | #124 | — | 53 | 1 | no | — |
| 248 | #124 | — | 212 | 1 | no | — |
| 249 | #124 | C22×D53 | 1 | 1 | yes | characteristic |
| 250 | C2×C22⋊C4 | — | 212 | 1 | no | — |
| 251 | C2×C22⋊C4 | — | 212 | 1 | no | — |
| 252 | C2×C42 | — | 53 | 1 | no | — |
| 253 | #101 | — | 2 | 1 | no | — |
| 254 | #101 | — | 106 | 1 | no | — |
| 255 | #101 | — | 212 | 1 | no | — |
| 256 | #99 | — | 2 | 1 | no | — |
| 257 | #99 | — | 106 | 1 | no | — |
| 258 | #99 | — | 212 | 1 | no | — |
| 259 | #97 | — | 53 | 1 | no | — |
| 260 | #97 | — | 106 | 1 | no | — |
| 261 | #97 | C4×D53 | 1 | 1 | yes | characteristic, complemented |
| 262 | C24 | — | 106 | 1 | no | — |
| 263 | C24 | — | 212 | 1 | no | — |
| 264 | C2×Q8 | — | 53 | 1 | no | — |
| 265 | C2×Q8 | — | 106 | 1 | no | — |
| 266 | C2×Q8 | — | 212 | 1 | no | — |
| 267 | C2×Q8 | — | 212 | 1 | no | — |
| 268 | C2×Q8 | D4×D53 | 1 | 1 | yes | characteristic |
| 269 | C2×D4 | — | 2 | 1 | no | — |
| 270 | C2×D4 | — | 4 | 1 | no | — |
| 271 | C2×D4 | — | 53 | 1 | no | — |
| 272 | C2×D4 | — | 106 | 1 | no | — |
| 273 | C2×D4 | — | 106 | 1 | no | — |
| 274 | C2×D4 | — | 424 | 4 | no | — |
| 275 | C2×D4 | — | 212 | 1 | no | — |
| 276 | C2×D4 | — | 212 | 1 | no | — |
| 277 | C2×D4 | — | 212 | 1 | no | — |
| 278 | C2×D4 | — | 212 | 1 | no | — |
| 279 | C2×D4 | — | 212 | 1 | no | — |
| 280 | C2×D4 | — | 212 | 1 | no | — |
| 281 | C2×D4 | — | 212 | 1 | no | — |
| 282 | C2×D4 | — | 212 | 1 | no | — |
| 283 | C2×D4 | — | 212 | 2 | no | — |
| 284 | C2×D4 | D4×D53 | 1 | 1 | yes | characteristic |
| 285 | C22×C4 | — | 53 | 1 | no | — |
| 286 | C22×C4 | — | 106 | 1 | no | — |
| 287 | C22×C4 | — | 106 | 1 | no | — |
| 288 | C22×C4 | — | 424 | 1 | no | — |
| 289 | SD16 | — | 4 | 2 | no | — |
| 290 | SD16 | — | 212 | 2 | no | — |
| 291 | SD16 | — | 212 | 2 | no | — |
| 292 | SD16 | — | 212 | 2 | no | — |
| 293 | D8 | — | 4 | 2 | no | — |
| 294 | D8 | — | 212 | 2 | no | — |
| 295 | D8 | — | 212 | 2 | no | — |
| 296 | D8 | — | 212 | 2 | no | — |
| 297 | M16 | — | 4 | 1 | no | — |
| 298 | M16 | — | 424 | 1 | no | — |
| 299 | M16 | — | 212 | 1 | no | — |
| 300 | C2×C8 | — | 2 | 1 | no | — |
| 301 | C2×C8 | — | 106 | 2 | no | — |
| 302 | C2×C8 | — | 106 | 2 | no | — |
| 303 | C2×C8 | — | 106 | 1 | no | — |
| 304 | C2×C8 | — | 424 | 1 | no | — |
| 305 | C22⋊C4 | — | 4 | 1 | no | — |
| 306 | C22⋊C4 | — | 4 | 1 | no | — |
| 307 | C22⋊C4 | — | 424 | 1 | no | — |
| 308 | C22⋊C4 | — | 212 | 1 | no | — |
| 309 | C22⋊C4 | — | 212 | 1 | no | — |
| 310 | C22⋊C4 | — | 212 | 1 | no | — |
| 311 | C22⋊C4 | — | 212 | 1 | no | — |
| 312 | C42 | — | 53 | 1 | no | — |
| 313 | C42 | — | 106 | 1 | no | — |
| 314 | C42 | C2×C4×D53 | 1 | 1 | yes | characteristic |
| 315 | C23 | — | 2 | 1 | no | — |
| 316 | C23 | — | 4 | 1 | no | — |
| 317 | C23 | — | 53 | 1 | no | — |
| 318 | C23 | — | 106 | 1 | no | — |
| 319 | C23 | — | 424 | 1 | no | — |
| 320 | C23 | — | 424 | 1 | no | — |
| 321 | C23 | — | 424 | 4 | no | — |
| 322 | C23 | — | 424 | 2 | no | — |
| 323 | C23 | — | 212 | 1 | no | — |
| 324 | C23 | — | 212 | 1 | no | — |
| 325 | C23 | — | 212 | 1 | no | — |
| 326 | Q8 | — | 4 | 1 | no | — |
| 327 | Q8 | — | 424 | 1 | no | — |
| 328 | Q8 | — | 212 | 1 | no | — |
| 329 | D4 | — | 4 | 1 | no | — |
| 330 | D4 | — | 4 | 1 | no | — |
| 331 | D4 | — | 4 | 1 | no | — |
| 332 | D4 | — | 8 | 2 | no | — |
| 333 | D4 | — | 424 | 2 | no | — |
| 334 | D4 | — | 424 | 1 | no | — |
| 335 | D4 | — | 424 | 1 | no | — |
| 336 | D4 | — | 424 | 1 | no | — |
| 337 | D4 | — | 424 | 4 | no | — |
| 338 | D4 | — | 212 | 1 | no | — |
| 339 | D4 | — | 212 | 1 | no | — |
| 340 | D4 | — | 212 | 1 | no | — |
| 341 | C2×C4 | — | 2 | 1 | no | — |
| 342 | C2×C4 | — | 2 | 1 | no | — |
| 343 | C2×C4 | — | 8 | 1 | no | — |
| 344 | C2×C4 | — | 53 | 1 | no | — |
| 345 | C2×C4 | — | 848 | 2 | no | — |
| 346 | C2×C4 | — | 106 | 1 | no | — |
| 347 | C2×C4 | — | 106 | 1 | no | — |
| 348 | C2×C4 | — | 106 | 1 | no | — |
| 349 | C2×C4 | — | 106 | 1 | no | — |
| 350 | C2×C4 | — | 424 | 1 | no | — |
| 351 | C2×C4 | — | 212 | 1 | no | — |
| 352 | C2×C4 | — | 212 | 1 | no | — |
| 353 | C2×C4 | — | 212 | 2 | no | — |
| 354 | C2×C4 | C22⋊C4×D53 | 1 | 1 | yes | characteristic |
| 355 | C8 | — | 2 | 2 | no | — |
| 356 | C8 | — | 8 | 1 | no | — |
| 357 | C8 | — | 106 | 2 | no | — |
| 358 | C8 | — | 424 | 1 | no | — |
| 359 | C22 | — | 4 | 1 | no | — |
| 360 | C22 | — | 8 | 1 | no | — |
| 361 | C22 | — | 8 | 2 | no | — |
| 362 | C22 | — | 8 | 1 | no | — |
| 363 | C22 | — | 53 | 1 | no | — |
| 364 | C22 | — | 53 | 1 | no | — |
| 365 | C22 | — | 848 | 1 | no | — |
| 366 | C22 | — | 848 | 2 | no | — |
| 367 | C22 | — | 848 | 2 | no | — |
| 368 | C22 | — | 106 | 2 | no | — |
| 369 | C22 | — | 424 | 2 | no | — |
| 370 | C22 | — | 424 | 1 | no | — |
| 371 | C22 | — | 424 | 2 | no | — |
| 372 | C22 | — | 424 | 1 | no | — |
| 373 | C22 | — | 212 | 1 | no | — |
| 374 | C22 | #99×D53 | 1 | 1 | yes | characteristic |
| 375 | C4 | — | 2 | 1 | no | — |
| 376 | C4 | — | 4 | 1 | no | — |
| 377 | C4 | — | 4 | 1 | no | — |
| 378 | C4 | — | 16 | 1 | no | — |
| 379 | C4 | — | 848 | 1 | no | — |
| 380 | C4 | — | 106 | 1 | no | — |
| 381 | C4 | — | 212 | 1 | no | — |
| 382 | C4 | — | 212 | 1 | no | — |
| 383 | C2 | — | 2 | 1 | no | — |
| 384 | C2 | — | 8 | 1 | no | — |
| 385 | C2 | — | 16 | 1 | no | — |
| 386 | C2 | — | 53 | 2 | no | — |
| 387 | C2 | — | 848 | 1 | no | — |
| 388 | C2 | — | 106 | 1 | no | — |
| 389 | C2 | — | 424 | 1 | no | — |
| 390 | C2 | #353×D53 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #355×D53 | C2 | semidirect |
| 3. #354×D53 | C2 | semidirect |
| 4. #20272873 | C2 | semidirect |
| 5. #20272872 | C2 | semidirect |
| 6. #20272871 | C2 | semidirect |
| 7. C53×#1406 | C2 | semidirect |
| 10. #127×D53 | C4 | semidirect |
| 13. #16811012 | C4 | semidirect |
| 15. #16811010 | C4 | semidirect |
| 19. #97×D53 | C4 | semidirect |
| 20. #16810420 | C22 | semidirect |
| 22. #16810418 | C22 | semidirect |
| 25. C53×#355 | C22 | semidirect |
| 26. C53×#354 | C22 | semidirect |
| 43. #13133214 | C2×C4 | semidirect |
| 57. #13133128 | C2×C4 | semidirect |
| 61. #127×C53 | C2×C4 | semidirect |
| 65. #97×C53 | C2×C4 | semidirect |
| 194. #1406 | D53 | direct (N × H) |
| 202. D53 | #1406 | direct (N × H) |
| 218. #355 | C2×D53 | semidirect |
| 221. #354 | C2×D53 | semidirect |
| 222. C53 | C2×#1406 | semidirect |
| 244. #127 | C4×D53 | semidirect |
| 261. #97 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #496×D53 | 2 |
| #355×D53 | 2 |
| #354×D53 | 2 |
| #20272873 | 2 |
| #20272872 | 2 |
| #20272871 | 2 |
| C53×#1406 | 2 |
| C2×#1406 | 53 |