Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
426 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 53 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 | #20285551 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20276666 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20275779 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20272704 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20272700 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20272650 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C53×#2190 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #16811133 | — | 2 | 1 | no | — |
| 9 | #16811130 | — | 2 | 1 | no | — |
| 10 | #16811063 | — | 2 | 1 | no | — |
| 11 | #16810967 | — | 2 | 1 | no | — |
| 12 | #16810946 | — | 2 | 1 | no | — |
| 13 | #16810881 | C22 | 1 | 1 | yes | characteristic |
| 14 | #16810867 | — | 2 | 1 | no | — |
| 15 | #16810786 | — | 2 | 1 | no | — |
| 16 | #16810765 | — | 2 | 1 | no | — |
| 17 | #16810640 | — | 2 | 1 | no | — |
| 18 | #16810586 | C22 | 1 | 1 | yes | characteristic |
| 19 | #16810433 | — | 2 | 1 | no | — |
| 20 | #16810405 | C22 | 1 | 1 | yes | characteristic |
| 21 | #16810380 | C22 | 1 | 1 | yes | characteristic |
| 22 | C53×#575 | C22 | 1 | 1 | yes | characteristic |
| 23 | C53×#509 | — | 2 | 1 | no | — |
| 24 | C53×#469 | C22 | 1 | 1 | yes | characteristic |
| 25 | C53×#360 | — | 2 | 1 | no | — |
| 26 | C53×#349 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#11719947 | — | 2 | 1 | no | — |
| 28 | C22×C4×D53 | D4 | 1 | 1 | yes | characteristic |
| 29 | C2×Dic212 | D4 | 1 | 1 | yes | characteristic, complemented |
| 30 | C2×#11719923 | — | 2 | 1 | no | — |
| 31 | C2×#11719917 | D4 | 1 | 1 | yes | characteristic |
| 32 | #13133199 | — | 4 | 1 | no | — |
| 33 | #13133198 | — | 4 | 1 | no | — |
| 34 | #13133197 | — | 2 | 1 | no | — |
| 35 | #13133196 | — | 2 | 1 | no | — |
| 36 | #13133193 | — | 4 | 1 | no | — |
| 37 | #13133188 | — | 2 | 1 | no | — |
| 38 | #13133188 | — | 4 | 1 | no | — |
| 39 | #13133185 | — | 4 | 1 | no | — |
| 40 | #13133185 | — | 4 | 1 | no | — |
| 41 | D4×Dic53 | — | 4 | 1 | no | — |
| 42 | C4×C22⋊D53 | — | 4 | 2 | no | — |
| 43 | #13133177 | — | 4 | 1 | no | — |
| 44 | #13133176 | — | 2 | 1 | no | — |
| 45 | #13133175 | — | 2 | 1 | no | — |
| 46 | #13133163 | — | 4 | 1 | no | — |
| 47 | #13133161 | — | 4 | 1 | no | — |
| 48 | #13133157 | — | 2 | 1 | no | — |
| 49 | #13133150 | — | 2 | 1 | no | — |
| 50 | #13133149 | D4 | 1 | 1 | yes | characteristic, complemented |
| 51 | #13133144 | — | 4 | 2 | no | — |
| 52 | #13133142 | — | 2 | 1 | no | — |
| 53 | #13133140 | — | 2 | 1 | no | — |
| 54 | #13133138 | — | 2 | 1 | no | — |
| 55 | #13133129 | — | 2 | 1 | no | — |
| 56 | #13133129 | — | 2 | 1 | no | — |
| 57 | C2×#41×C53 | — | 2 | 1 | no | — |
| 58 | #137×C53 | — | 4 | 1 | no | — |
| 59 | AGL(1,ℤ/8)×C53 | — | 4 | 1 | no | — |
| 60 | #135×C53 | — | 2 | 1 | no | — |
| 61 | #135×C53 | — | 2 | 1 | no | — |
| 62 | C2×D8×C53 | D4 | 1 | 1 | yes | characteristic, complemented |
| 63 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 64 | #121×C53 | — | 2 | 1 | no | — |
| 65 | SD32×C53 | — | 4 | 1 | no | — |
| 66 | D16×C53 | — | 4 | 1 | no | — |
| 67 | M32×C53 | — | 2 | 1 | no | — |
| 68 | #106×C53 | D4 | 1 | 1 | yes | characteristic, complemented |
| 69 | #102×C53 | — | 2 | 1 | no | — |
| 70 | C23×D53 | D8 | 1 | 1 | yes | characteristic |
| 71 | #41×C53 | — | 4 | 1 | no | — |
| 72 | #41×C53 | — | 4 | 1 | no | — |
| 73 | #41×C53 | — | 4 | 1 | no | — |
| 74 | #41×C53 | — | 4 | 1 | no | — |
| 75 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 76 | C2×D4×C53 | — | 2 | 1 | no | — |
| 77 | C2×D4×C53 | — | 2 | 1 | no | — |
| 78 | C2×D4×C53 | — | 4 | 1 | no | — |
| 79 | C2×D4×C53 | — | 4 | 1 | no | — |
| 80 | C22×C4×C53 | — | 4 | 1 | no | — |
| 81 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 82 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 83 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 84 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 85 | C22×Dic53 | — | 4 | 1 | no | — |
| 86 | C22×Dic53 | D8 | 1 | 1 | yes | characteristic |
| 87 | #11719947 | — | 8 | 1 | no | — |
| 88 | #11719947 | — | 8 | 1 | no | — |
| 89 | C2×C4×D53 | — | 2 | 1 | no | — |
| 90 | C2×C4×D53 | — | 2 | 1 | no | — |
| 91 | C2×C4×D53 | — | 4 | 1 | no | — |
| 92 | C2×C4×D53 | — | 4 | 1 | no | — |
| 93 | C2×Dic106 | — | 2 | 1 | no | — |
| 94 | Q16×C53 | — | 2 | 1 | no | — |
| 95 | Q16×C53 | — | 2 | 1 | no | — |
| 96 | SD16×C53 | — | 4 | 1 | no | — |
| 97 | SD16×C53 | — | 4 | 1 | no | — |
| 98 | D8×C53 | — | 2 | 1 | no | — |
| 99 | D8×C53 | — | 2 | 1 | no | — |
| 100 | D8×C53 | — | 4 | 1 | no | — |
| 101 | M16×C53 | — | 4 | 1 | no | — |
| 102 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 103 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 104 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 105 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 106 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 107 | C22⋊Dic53 | — | 4 | 2 | no | — |
| 108 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 109 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 110 | #11719923 | — | 8 | 1 | no | — |
| 111 | #11719921 | — | 4 | 1 | no | — |
| 112 | #11719921 | — | 4 | 1 | no | — |
| 113 | #11719921 | — | 4 | 2 | no | — |
| 114 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 115 | C4⋊Dic53 | — | 4 | 1 | no | — |
| 116 | C4⋊Dic53 | — | 4 | 1 | no | — |
| 117 | #11719919 | — | 4 | 2 | no | — |
| 118 | #11719919 | — | 4 | 1 | no | — |
| 119 | C4×Dic53 | — | 2 | 2 | no | — |
| 120 | C4×Dic53 | — | 4 | 1 | no | — |
| 121 | #11719917 | — | 4 | 1 | no | — |
| 122 | C2×#88322 | — | 2 | 1 | no | — |
| 123 | Dic212 | — | 4 | 1 | no | — |
| 124 | C16×C53 | — | 4 | 1 | no | — |
| 125 | #11719908 | — | 4 | 1 | no | — |
| 126 | C23×C53 | — | 4 | 1 | no | — |
| 127 | C23×C53 | — | 4 | 1 | no | — |
| 128 | C23×C53 | C2×D8 | 1 | 1 | yes | characteristic |
| 129 | C22×D53 | — | 2 | 1 | no | — |
| 130 | C22×D53 | — | 4 | 1 | no | — |
| 131 | C22×D53 | — | 8 | 1 | no | — |
| 132 | Q8×C53 | — | 4 | 1 | no | — |
| 133 | Q8×C53 | — | 4 | 1 | no | — |
| 134 | D4×C53 | — | 4 | 1 | no | — |
| 135 | D4×C53 | — | 4 | 1 | no | — |
| 136 | D4×C53 | — | 4 | 1 | no | — |
| 137 | D4×C53 | — | 4 | 1 | no | — |
| 138 | D4×C53 | — | 8 | 1 | no | — |
| 139 | D4×C53 | — | 8 | 2 | no | — |
| 140 | D4×C53 | — | 8 | 1 | no | — |
| 141 | C2×C4×C53 | — | 2 | 1 | no | — |
| 142 | C2×C4×C53 | — | 2 | 1 | no | — |
| 143 | C2×C4×C53 | — | 4 | 1 | no | — |
| 144 | C2×C4×C53 | — | 4 | 1 | no | — |
| 145 | C2×C4×C53 | — | 8 | 1 | no | — |
| 146 | C2×C4×C53 | — | 8 | 1 | no | — |
| 147 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 148 | C2×C4×C53 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 149 | C22⋊D53 | — | 8 | 2 | no | — |
| 150 | C22⋊D53 | — | 8 | 2 | no | — |
| 151 | C22⋊D53 | — | 8 | 4 | no | — |
| 152 | C2×Dic53 | — | 2 | 1 | no | — |
| 153 | C2×Dic53 | — | 4 | 1 | no | — |
| 154 | C2×Dic53 | — | 4 | 2 | no | — |
| 155 | C2×Dic53 | — | 4 | 1 | no | — |
| 156 | C2×Dic53 | — | 4 | 1 | no | — |
| 157 | C2×Dic53 | — | 8 | 2 | no | — |
| 158 | C4×D53 | — | 4 | 1 | no | — |
| 159 | C4×D53 | — | 4 | 1 | no | — |
| 160 | C4×D53 | — | 8 | 1 | no | — |
| 161 | Dic106 | — | 4 | 1 | no | — |
| 162 | Dic106 | — | 4 | 1 | no | — |
| 163 | C8×C53 | — | 2 | 1 | no | — |
| 164 | C8×C53 | — | 2 | 1 | no | — |
| 165 | #88322 | — | 4 | 1 | no | — |
| 166 | #12116 | — | 53 | 1 | no | maximal, Sylow |
| 167 | C22×C53 | — | 2 | 1 | no | — |
| 168 | C22×C53 | — | 4 | 1 | no | — |
| 169 | C22×C53 | — | 8 | 1 | no | — |
| 170 | C22×C53 | — | 8 | 1 | no | — |
| 171 | C22×C53 | — | 8 | 2 | no | — |
| 172 | C22×C53 | — | 8 | 1 | no | — |
| 173 | C22×C53 | — | 8 | 1 | no | — |
| 174 | C22×C53 | #447 | 1 | 1 | yes | characteristic |
| 175 | C2×D53 | — | 4 | 1 | no | — |
| 176 | C2×D53 | — | 4 | 1 | no | — |
| 177 | C2×D53 | — | 4 | 2 | no | — |
| 178 | C2×D53 | — | 4 | 1 | no | — |
| 179 | C2×D53 | — | 8 | 1 | no | — |
| 180 | C4×C53 | — | 2 | 1 | no | — |
| 181 | C4×C53 | — | 8 | 1 | no | — |
| 182 | C4×C53 | — | 8 | 1 | no | — |
| 183 | C4×C53 | #453 | 1 | 1 | yes | characteristic |
| 184 | C4×C53 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 185 | Dic53 | — | 4 | 1 | no | — |
| 186 | Dic53 | — | 8 | 1 | no | — |
| 187 | Dic53 | — | 8 | 2 | no | — |
| 188 | Dic53 | — | 8 | 1 | no | — |
| 189 | #3197 | — | 53 | 1 | no | — |
| 190 | #2191 | — | 53 | 1 | no | — |
| 191 | #2190 | D53 | 1 | 1 | yes | characteristic, complemented |
| 192 | #2010 | — | 53 | 1 | no | — |
| 193 | #1340 | — | 53 | 1 | no | — |
| 194 | #1339 | — | 53 | 1 | no | — |
| 195 | #1320 | — | 53 | 1 | no | — |
| 196 | C2×C53 | — | 2 | 1 | no | — |
| 197 | C2×C53 | — | 4 | 1 | no | — |
| 198 | C2×C53 | — | 16 | 1 | no | — |
| 199 | C2×C53 | — | 16 | 1 | no | — |
| 200 | C2×C53 | #1595 | 1 | 1 | yes | characteristic |
| 201 | D53 | — | 8 | 1 | no | — |
| 202 | #575 | C2×D53 | 1 | 1 | yes | characteristic |
| 203 | #525 | — | 106 | 1 | no | — |
| 204 | #525 | — | 106 | 1 | no | — |
| 205 | #510 | — | 106 | 1 | no | — |
| 206 | #509 | — | 2 | 1 | no | — |
| 207 | #485 | — | 106 | 1 | no | — |
| 208 | #482 | — | 106 | 1 | no | — |
| 209 | #470 | — | 53 | 1 | no | — |
| 210 | #469 | C2×D53 | 1 | 1 | yes | characteristic |
| 211 | #468 | — | 106 | 1 | no | — |
| 212 | #452 | — | 106 | 1 | no | — |
| 213 | #449 | — | 106 | 1 | no | — |
| 214 | #421 | — | 106 | 1 | no | — |
| 215 | #407 | — | 53 | 1 | no | — |
| 216 | #360 | — | 2 | 1 | no | — |
| 217 | #360 | — | 106 | 1 | no | — |
| 218 | #349 | — | 53 | 1 | no | — |
| 219 | #349 | C2×D53 | 1 | 1 | yes | characteristic |
| 220 | H(3,ℤ/4) | — | 53 | 1 | no | — |
| 221 | C53 | #12116 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 222 | C2×#41 | — | 2 | 1 | no | — |
| 223 | C2×#41 | — | 106 | 1 | no | — |
| 224 | C23×C4 | — | 53 | 1 | no | — |
| 225 | #137 | — | 4 | 1 | no | — |
| 226 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 227 | #135 | — | 2 | 1 | no | — |
| 228 | #135 | — | 2 | 1 | no | — |
| 229 | C2×Q16 | — | 53 | 1 | no | — |
| 230 | C2×SD16 | — | 106 | 1 | no | — |
| 231 | C2×D8 | C22⋊D53 | 1 | 1 | yes | characteristic, complemented |
| 232 | C2×M16 | — | 53 | 1 | no | — |
| 233 | C2×M16 | C22×D53 | 1 | 1 | yes | characteristic |
| 234 | #123 | — | 212 | 1 | no | — |
| 235 | #123 | — | 212 | 1 | no | — |
| 236 | C22⋊Q8 | — | 106 | 1 | no | — |
| 237 | C22⋊Q8 | — | 106 | 1 | no | — |
| 238 | C22⋊Q8 | — | 212 | 1 | no | — |
| 239 | #121 | — | 2 | 1 | no | — |
| 240 | #121 | — | 106 | 1 | no | — |
| 241 | #121 | — | 212 | 1 | no | — |
| 242 | #120 | — | 212 | 1 | no | — |
| 243 | #120 | — | 212 | 1 | no | — |
| 244 | C4×D4 | — | 212 | 2 | no | — |
| 245 | C4×D4 | — | 212 | 1 | no | — |
| 246 | C4×D4 | — | 212 | 1 | no | — |
| 247 | #117 | — | 106 | 1 | no | — |
| 248 | #117 | — | 106 | 1 | no | — |
| 249 | Q32 | — | 212 | 1 | no | — |
| 250 | SD32 | — | 4 | 1 | no | — |
| 251 | SD32 | — | 212 | 1 | no | — |
| 252 | D16 | — | 4 | 1 | no | — |
| 253 | M32 | — | 2 | 1 | no | — |
| 254 | M32 | — | 106 | 1 | no | — |
| 255 | #107 | — | 106 | 1 | no | — |
| 256 | #106 | — | 53 | 1 | no | — |
| 257 | #106 | C22⋊D53 | 1 | 1 | yes | characteristic, complemented |
| 258 | #104 | — | 212 | 2 | no | — |
| 259 | #103 | — | 106 | 1 | no | — |
| 260 | #103 | — | 106 | 1 | no | — |
| 261 | #102 | — | 2 | 1 | no | — |
| 262 | #102 | — | 106 | 1 | no | — |
| 263 | C22⋊C8 | — | 106 | 1 | no | — |
| 264 | C22⋊C8 | — | 106 | 1 | no | — |
| 265 | C24 | — | 53 | 1 | no | — |
| 266 | #41 | — | 4 | 1 | no | — |
| 267 | #41 | — | 4 | 1 | no | — |
| 268 | #41 | — | 4 | 1 | no | — |
| 269 | #41 | — | 4 | 1 | no | — |
| 270 | #41 | — | 424 | 1 | no | — |
| 271 | #41 | — | 424 | 1 | no | — |
| 272 | C2×Q8 | — | 2 | 1 | no | — |
| 273 | C2×Q8 | — | 106 | 1 | no | — |
| 274 | C2×D4 | — | 2 | 1 | no | — |
| 275 | C2×D4 | — | 2 | 1 | no | — |
| 276 | C2×D4 | — | 4 | 1 | no | — |
| 277 | C2×D4 | — | 4 | 1 | no | — |
| 278 | C2×D4 | — | 212 | 1 | no | — |
| 279 | C2×D4 | — | 212 | 1 | no | — |
| 280 | C2×D4 | — | 212 | 2 | no | — |
| 281 | C22×C4 | — | 4 | 1 | no | — |
| 282 | C22×C4 | — | 53 | 1 | no | — |
| 283 | C22×C4 | — | 106 | 1 | no | — |
| 284 | C22×C4 | — | 106 | 1 | no | — |
| 285 | C22×C4 | — | 212 | 1 | no | — |
| 286 | C22×C4 | — | 212 | 1 | no | — |
| 287 | C22×C4 | — | 212 | 1 | no | — |
| 288 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 289 | Q16 | — | 2 | 1 | no | — |
| 290 | Q16 | — | 2 | 1 | no | — |
| 291 | Q16 | — | 212 | 1 | no | — |
| 292 | SD16 | — | 4 | 1 | no | — |
| 293 | SD16 | — | 4 | 1 | no | — |
| 294 | SD16 | — | 424 | 1 | no | — |
| 295 | D8 | — | 2 | 1 | no | — |
| 296 | D8 | — | 2 | 1 | no | — |
| 297 | D8 | — | 4 | 1 | no | — |
| 298 | M16 | — | 4 | 1 | no | — |
| 299 | M16 | — | 212 | 1 | no | — |
| 300 | C2×C8 | — | 106 | 1 | no | — |
| 301 | C2×C8 | D4×D53 | 1 | 1 | yes | characteristic |
| 302 | C2×C8 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 303 | C4⋊C4 | — | 2 | 1 | no | — |
| 304 | C4⋊C4 | — | 106 | 1 | no | — |
| 305 | C4⋊C4 | — | 212 | 1 | no | — |
| 306 | C4⋊C4 | — | 212 | 1 | no | — |
| 307 | C4⋊C4 | — | 212 | 2 | no | — |
| 308 | C4⋊C4 | — | 212 | 1 | no | — |
| 309 | C22⋊C4 | — | 4 | 1 | no | — |
| 310 | C22⋊C4 | — | 212 | 1 | no | — |
| 311 | C22⋊C4 | — | 212 | 1 | no | — |
| 312 | C22⋊C4 | — | 212 | 2 | no | — |
| 313 | C22⋊C4 | — | 212 | 1 | no | — |
| 314 | C22⋊C4 | — | 212 | 2 | no | — |
| 315 | C22⋊C4 | — | 212 | 1 | no | — |
| 316 | C22⋊C4 | — | 212 | 1 | no | — |
| 317 | C42 | — | 106 | 2 | no | — |
| 318 | C42 | — | 212 | 1 | no | — |
| 319 | C16 | — | 4 | 1 | no | — |
| 320 | C16 | — | 212 | 1 | no | — |
| 321 | C23 | — | 4 | 1 | no | — |
| 322 | C23 | — | 4 | 1 | no | — |
| 323 | C23 | — | 106 | 1 | no | — |
| 324 | C23 | — | 424 | 1 | no | — |
| 325 | C23 | — | 212 | 1 | no | — |
| 326 | C23 | D8×D53 | 1 | 1 | yes | characteristic |
| 327 | Q8 | — | 4 | 1 | no | — |
| 328 | Q8 | — | 4 | 1 | no | — |
| 329 | Q8 | — | 212 | 1 | no | — |
| 330 | Q8 | — | 212 | 1 | no | — |
| 331 | D4 | — | 4 | 1 | no | — |
| 332 | D4 | — | 4 | 1 | no | — |
| 333 | D4 | — | 4 | 1 | no | — |
| 334 | D4 | — | 4 | 1 | no | — |
| 335 | D4 | — | 8 | 1 | no | — |
| 336 | D4 | — | 8 | 2 | no | — |
| 337 | D4 | — | 8 | 1 | no | — |
| 338 | D4 | — | 424 | 2 | no | — |
| 339 | D4 | — | 424 | 4 | no | — |
| 340 | D4 | — | 424 | 2 | no | — |
| 341 | C2×C4 | — | 2 | 1 | no | — |
| 342 | C2×C4 | — | 2 | 1 | no | — |
| 343 | C2×C4 | — | 4 | 1 | no | — |
| 344 | C2×C4 | — | 4 | 1 | no | — |
| 345 | C2×C4 | — | 8 | 1 | no | — |
| 346 | C2×C4 | — | 8 | 1 | no | — |
| 347 | C2×C4 | — | 106 | 1 | no | — |
| 348 | C2×C4 | — | 424 | 1 | no | — |
| 349 | C2×C4 | — | 424 | 2 | no | — |
| 350 | C2×C4 | — | 212 | 2 | no | — |
| 351 | C2×C4 | — | 212 | 1 | no | — |
| 352 | C2×C4 | — | 212 | 1 | no | — |
| 353 | C2×C4 | — | 212 | 1 | no | — |
| 354 | C2×C4 | — | 212 | 1 | no | — |
| 355 | C2×C4 | — | 212 | 1 | no | — |
| 356 | C2×C4 | #13133185 | 1 | 1 | yes | characteristic |
| 357 | C2×C4 | #13133241 | 1 | 1 | yes | characteristic |
| 358 | C8 | — | 2 | 1 | no | — |
| 359 | C8 | — | 2 | 1 | no | — |
| 360 | C8 | — | 212 | 1 | no | — |
| 361 | C22 | — | 2 | 1 | no | — |
| 362 | C22 | — | 4 | 1 | no | — |
| 363 | C22 | — | 8 | 1 | no | — |
| 364 | C22 | — | 8 | 1 | no | — |
| 365 | C22 | — | 8 | 2 | no | — |
| 366 | C22 | — | 8 | 1 | no | — |
| 367 | C22 | — | 8 | 1 | no | — |
| 368 | C22 | — | 424 | 1 | no | — |
| 369 | C22 | — | 212 | 1 | no | — |
| 370 | C22 | — | 212 | 1 | no | — |
| 371 | C22 | — | 212 | 2 | no | — |
| 372 | C22 | — | 212 | 1 | no | — |
| 373 | C22 | #16810755 | 1 | 1 | yes | characteristic |
| 374 | C4 | — | 2 | 1 | no | — |
| 375 | C4 | — | 8 | 1 | no | — |
| 376 | C4 | — | 8 | 1 | no | — |
| 377 | C4 | — | 424 | 1 | no | — |
| 378 | C4 | — | 424 | 2 | no | — |
| 379 | C4 | — | 424 | 1 | no | — |
| 380 | C4 | — | 212 | 1 | no | — |
| 381 | C4 | #16810789 | 1 | 1 | yes | characteristic |
| 382 | C4 | #16810809 | 1 | 1 | yes | characteristic |
| 383 | C2 | — | 2 | 1 | no | — |
| 384 | C2 | — | 4 | 1 | no | — |
| 385 | C2 | — | 16 | 1 | no | — |
| 386 | C2 | — | 16 | 1 | no | — |
| 387 | C2 | — | 424 | 1 | no | — |
| 388 | C2 | #20273631 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20285551 | C2 | semidirect |
| 2. #20276666 | C2 | semidirect |
| 3. #20275779 | C2 | semidirect |
| 4. #20272704 | C2 | semidirect |
| 5. #20272700 | C2 | semidirect |
| 6. #20272650 | C2 | semidirect |
| 7. C53×#2190 | C2 | semidirect |
| 29. C2×Dic212 | D4 | semidirect |
| 50. #13133149 | D4 | semidirect |
| 62. C2×D8×C53 | D4 | semidirect |
| 68. #106×C53 | D4 | semidirect |
| 191. #2190 | D53 | semidirect |
| 221. C53 | #12116 | semidirect |
| 231. C2×D8 | C22⋊D53 | semidirect |
| 257. #106 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285551 | 2 |
| #20276666 | 2 |
| #20275779 | 2 |
| #20272704 | 2 |
| #20272700 | 2 |
| #20272650 | 2 |
| C53×#2190 | 2 |
| #12116 | 53 |