Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 55 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 | #20282393 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20275945 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20273754 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20273649 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #20272741 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20272658 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C53×#1345 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #16811204 | C22 | 1 | 1 | yes | characteristic |
| 9 | #16810942 | — | 2 | 1 | no | — |
| 10 | #16810757 | — | 2 | 1 | no | — |
| 11 | C2×#13133143 | — | 2 | 1 | no | — |
| 12 | #16810625 | — | 2 | 1 | no | — |
| 13 | #16810563 | — | 2 | 1 | no | — |
| 14 | #16810562 | C22 | 1 | 1 | yes | characteristic |
| 15 | #16810551 | — | 2 | 1 | no | — |
| 16 | #16810511 | — | 2 | 1 | no | — |
| 17 | #16810503 | — | 2 | 1 | no | — |
| 18 | #16810498 | — | 2 | 1 | no | — |
| 19 | #16810498 | — | 2 | 1 | no | — |
| 20 | #16810488 | C22 | 1 | 1 | yes | characteristic |
| 21 | #16810358 | — | 2 | 1 | no | — |
| 22 | #16810356 | — | 2 | 1 | no | — |
| 23 | #16810349 | C22 | 1 | 1 | yes | characteristic |
| 24 | C53×#394 | C22 | 1 | 1 | yes | characteristic |
| 25 | C53×#343 | C22 | 1 | 1 | yes | characteristic |
| 26 | C53×#324 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#11719945 | — | 2 | 1 | no | — |
| 28 | C23×Dic53 | — | 2 | 1 | no | — |
| 29 | C2×#11719922 | — | 4 | 1 | no | — |
| 30 | #13133197 | — | 4 | 1 | no | — |
| 31 | #13133192 | — | 4 | 1 | no | — |
| 32 | #13133191 | — | 2 | 1 | no | — |
| 33 | #13133191 | — | 2 | 1 | no | — |
| 34 | C2×C4⋊Dic53 | — | 2 | 1 | no | — |
| 35 | C2×C4⋊Dic53 | D4 | 1 | 1 | yes | characteristic |
| 36 | C2×C4⋊Dic53 | D4 | 1 | 1 | yes | characteristic |
| 37 | C2×#11719919 | — | 2 | 1 | no | — |
| 38 | C2×C22⋊Dic53 | — | 2 | 1 | no | — |
| 39 | C2×C22⋊Dic53 | — | 2 | 1 | no | — |
| 40 | C2×C22⋊Dic53 | — | 2 | 1 | no | — |
| 41 | C2×C4×Dic53 | D4 | 1 | 1 | yes | characteristic |
| 42 | #13133149 | — | 4 | 1 | no | — |
| 43 | #13133143 | — | 4 | 2 | no | — |
| 44 | #13133142 | — | 4 | 1 | no | — |
| 45 | #13133139 | — | 4 | 1 | no | — |
| 46 | #13133139 | — | 4 | 1 | no | — |
| 47 | #13133138 | — | 4 | 1 | no | — |
| 48 | C22⋊#88322 | — | 2 | 1 | no | — |
| 49 | #13133124 | — | 2 | 1 | no | — |
| 50 | #13133124 | — | 2 | 1 | no | — |
| 51 | #13133124 | — | 2 | 1 | no | — |
| 52 | #13133124 | — | 2 | 1 | no | — |
| 53 | #13133124 | — | 2 | 1 | no | — |
| 54 | #13133124 | — | 2 | 1 | no | — |
| 55 | #13133124 | D4 | 1 | 1 | yes | characteristic |
| 56 | C22×D4×C53 | D4 | 1 | 1 | yes | characteristic |
| 57 | C2×M16×C53 | — | 2 | 1 | no | — |
| 58 | C2×C4⋊C4×C53 | C23 | 1 | 1 | yes | characteristic |
| 59 | C2×C22⋊C4×C53 | — | 2 | 1 | no | — |
| 60 | C2×C22⋊C4×C53 | — | 2 | 1 | no | — |
| 61 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 62 | #95×C53 | D4 | 1 | 1 | yes | characteristic |
| 63 | C24×C53 | — | 2 | 1 | no | — |
| 64 | C2×D4×C53 | — | 4 | 1 | no | — |
| 65 | C2×D4×C53 | — | 4 | 2 | no | — |
| 66 | C22×C4×C53 | — | 2 | 1 | no | — |
| 67 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 68 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 69 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 70 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 71 | C22×Dic53 | — | 2 | 1 | no | — |
| 72 | C22×Dic53 | — | 2 | 1 | no | — |
| 73 | C22×Dic53 | — | 2 | 1 | no | — |
| 74 | C22×Dic53 | — | 2 | 1 | no | — |
| 75 | C22×Dic53 | — | 8 | 1 | no | — |
| 76 | C22×Dic53 | — | 8 | 1 | no | — |
| 77 | C22×Dic53 | — | 8 | 1 | no | — |
| 78 | #11719945 | — | 4 | 1 | no | — |
| 79 | #11719945 | — | 4 | 1 | no | — |
| 80 | #11719945 | — | 4 | 1 | no | — |
| 81 | #11719945 | — | 4 | 1 | no | — |
| 82 | C2×D212 | — | 2 | 1 | no | — |
| 83 | C2×D212 | — | 2 | 1 | no | — |
| 84 | C2×D212 | — | 2 | 1 | no | — |
| 85 | C2×C4×D53 | — | 4 | 1 | no | — |
| 86 | C2×Dic106 | — | 2 | 1 | no | — |
| 87 | M16×C53 | — | 4 | 1 | no | — |
| 88 | M16×C53 | — | 4 | 1 | no | — |
| 89 | C2×C8×C53 | — | 4 | 1 | no | — |
| 90 | C2×C8×C53 | — | 4 | 1 | no | — |
| 91 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 92 | C22⋊C4×C53 | — | 4 | 2 | no | — |
| 93 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 94 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 95 | C22⋊Dic53 | — | 4 | 2 | no | — |
| 96 | C22⋊Dic53 | — | 8 | 1 | no | — |
| 97 | C22⋊Dic53 | — | 8 | 1 | no | — |
| 98 | #11719922 | — | 8 | 2 | no | — |
| 99 | #11719921 | — | 4 | 1 | no | — |
| 100 | #11719921 | — | 4 | 1 | no | — |
| 101 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 102 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 103 | C4⋊Dic53 | — | 4 | 1 | no | — |
| 104 | C4⋊Dic53 | — | 4 | 1 | no | — |
| 105 | C4⋊Dic53 | — | 8 | 1 | no | — |
| 106 | #11719919 | — | 8 | 1 | no | — |
| 107 | C4×Dic53 | — | 2 | 1 | no | — |
| 108 | C4×Dic53 | — | 2 | 1 | no | — |
| 109 | C2×#88322 | — | 4 | 1 | no | — |
| 110 | C23×C53 | — | 2 | 2 | no | — |
| 111 | C23×C53 | — | 4 | 1 | no | — |
| 112 | C23×C53 | — | 4 | 1 | no | — |
| 113 | C23×C53 | — | 4 | 1 | no | — |
| 114 | C23×C53 | — | 4 | 1 | no | — |
| 115 | C23×C53 | — | 4 | 1 | no | — |
| 116 | C23×C53 | — | 4 | 1 | no | — |
| 117 | C23×C53 | #120 | 1 | 1 | yes | characteristic |
| 118 | C22×D53 | — | 4 | 1 | no | — |
| 119 | D4×C53 | — | 4 | 2 | no | — |
| 120 | D4×C53 | — | 8 | 1 | no | — |
| 121 | C2×C4×C53 | — | 2 | 1 | no | — |
| 122 | C2×C4×C53 | — | 2 | 1 | no | — |
| 123 | C2×C4×C53 | — | 2 | 1 | no | — |
| 124 | C2×C4×C53 | — | 2 | 1 | no | — |
| 125 | C2×C4×C53 | — | 4 | 1 | no | — |
| 126 | C2×C4×C53 | — | 4 | 1 | no | — |
| 127 | C2×C4×C53 | — | 4 | 1 | no | — |
| 128 | C2×C4×C53 | — | 4 | 1 | no | — |
| 129 | C2×C4×C53 | — | 4 | 1 | no | — |
| 130 | C2×C4×C53 | #135 | 1 | 1 | yes | characteristic |
| 131 | C2×C4×C53 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 132 | C22⋊D53 | — | 8 | 1 | no | — |
| 133 | C22⋊D53 | — | 8 | 1 | no | — |
| 134 | C2×Dic53 | — | 4 | 1 | no | — |
| 135 | C2×Dic53 | — | 4 | 1 | no | — |
| 136 | C2×Dic53 | — | 4 | 1 | no | — |
| 137 | C2×Dic53 | — | 4 | 1 | no | — |
| 138 | C2×Dic53 | — | 4 | 1 | no | — |
| 139 | C2×Dic53 | — | 4 | 1 | no | — |
| 140 | C2×Dic53 | — | 4 | 1 | no | — |
| 141 | C2×Dic53 | — | 4 | 1 | no | — |
| 142 | C2×Dic53 | — | 4 | 1 | no | — |
| 143 | C2×Dic53 | — | 4 | 1 | no | — |
| 144 | C2×Dic53 | — | 4 | 1 | no | — |
| 145 | C2×Dic53 | — | 4 | 1 | no | — |
| 146 | C2×Dic53 | — | 4 | 1 | no | — |
| 147 | C2×Dic53 | — | 8 | 4 | no | — |
| 148 | D212 | — | 4 | 1 | no | — |
| 149 | D212 | — | 4 | 1 | no | — |
| 150 | D212 | — | 8 | 1 | no | — |
| 151 | D212 | — | 8 | 1 | no | — |
| 152 | C4×D53 | — | 8 | 1 | no | — |
| 153 | C4×D53 | — | 8 | 1 | no | — |
| 154 | Dic106 | — | 4 | 1 | no | — |
| 155 | Dic106 | — | 4 | 1 | no | — |
| 156 | C8×C53 | — | 8 | 1 | no | — |
| 157 | C8×C53 | — | 8 | 1 | no | — |
| 158 | #88322 | — | 8 | 1 | no | — |
| 159 | #12141 | — | 53 | 1 | no | maximal, Sylow |
| 160 | C22×C53 | — | 2 | 1 | no | — |
| 161 | C22×C53 | — | 2 | 1 | no | — |
| 162 | C22×C53 | — | 4 | 2 | no | — |
| 163 | C22×C53 | — | 4 | 2 | no | — |
| 164 | C22×C53 | — | 4 | 2 | no | — |
| 165 | C22×C53 | — | 8 | 1 | no | — |
| 166 | C22×C53 | — | 8 | 1 | no | — |
| 167 | C22×C53 | — | 8 | 1 | no | — |
| 168 | C22×C53 | — | 8 | 1 | no | — |
| 169 | C22×C53 | #449 | 1 | 1 | yes | characteristic |
| 170 | C22×C53 | #454 | 1 | 1 | yes | characteristic |
| 171 | C22×C53 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 172 | C2×D53 | — | 8 | 1 | no | — |
| 173 | C2×D53 | — | 8 | 1 | no | — |
| 174 | C2×D53 | — | 8 | 1 | no | — |
| 175 | C4×C53 | — | 2 | 1 | no | — |
| 176 | C4×C53 | — | 2 | 1 | no | — |
| 177 | C4×C53 | — | 4 | 1 | no | — |
| 178 | C4×C53 | — | 4 | 1 | no | — |
| 179 | C4×C53 | — | 8 | 1 | no | — |
| 180 | Dic53 | — | 8 | 1 | no | — |
| 181 | Dic53 | — | 8 | 1 | no | — |
| 182 | Dic53 | — | 8 | 1 | no | — |
| 183 | Dic53 | — | 8 | 1 | no | — |
| 184 | Dic53 | — | 8 | 1 | no | — |
| 185 | #2782 | — | 53 | 1 | no | — |
| 186 | #2040 | — | 53 | 1 | no | — |
| 187 | #1616 | — | 53 | 1 | no | — |
| 188 | #1598 | — | 53 | 1 | no | — |
| 189 | #1353 | — | 53 | 1 | no | — |
| 190 | #1345 | D53 | 1 | 1 | yes | characteristic, complemented |
| 191 | #1324 | — | 53 | 1 | no | — |
| 192 | C2×C53 | — | 2 | 1 | no | — |
| 193 | C2×C53 | — | 2 | 1 | no | — |
| 194 | C2×C53 | — | 8 | 2 | no | — |
| 195 | C2×C53 | #1597 | 1 | 1 | yes | characteristic |
| 196 | C2×C53 | #2197 | 1 | 1 | yes | characteristic |
| 197 | C2×C53 | #2202 | 1 | 1 | yes | characteristic |
| 198 | D53 | — | 16 | 1 | no | — |
| 199 | #537 | — | 53 | 1 | no | — |
| 200 | #481 | — | 106 | 1 | no | — |
| 201 | #447 | — | 106 | 1 | no | — |
| 202 | C2×#104 | — | 106 | 1 | no | — |
| 203 | #417 | — | 106 | 1 | no | — |
| 204 | #400 | — | 53 | 1 | no | — |
| 205 | #400 | — | 106 | 1 | no | — |
| 206 | #397 | — | 106 | 1 | no | — |
| 207 | #394 | C2×D53 | 1 | 1 | yes | characteristic |
| 208 | #388 | — | 106 | 1 | no | — |
| 209 | #386 | — | 106 | 1 | no | — |
| 210 | #385 | — | 106 | 1 | no | — |
| 211 | #385 | — | 106 | 1 | no | — |
| 212 | #382 | — | 53 | 1 | no | — |
| 213 | #343 | C2×D53 | 1 | 1 | yes | characteristic |
| 214 | #327 | — | 106 | 1 | no | — |
| 215 | #327 | — | 106 | 1 | no | — |
| 216 | #324 | — | 53 | 1 | no | — |
| 217 | #324 | C2×D53 | 1 | 1 | yes | characteristic |
| 218 | C53 | #12141 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 219 | C2×#41 | — | 106 | 1 | no | — |
| 220 | C22×D4 | D212 | 1 | 1 | yes | characteristic |
| 221 | C23×C4 | — | 106 | 1 | no | — |
| 222 | C2×D8 | — | 212 | 1 | no | — |
| 223 | C2×M16 | — | 2 | 1 | no | — |
| 224 | C22⋊Q8 | — | 212 | 1 | no | — |
| 225 | #121 | — | 106 | 1 | no | — |
| 226 | #121 | — | 106 | 1 | no | — |
| 227 | #121 | — | 212 | 1 | no | — |
| 228 | C2×C4⋊C4 | — | 53 | 1 | no | — |
| 229 | C2×C4⋊C4 | — | 53 | 1 | no | — |
| 230 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 231 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 232 | C2×C4⋊C4 | C22×D53 | 1 | 1 | yes | characteristic |
| 233 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 234 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 235 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 236 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 237 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 238 | C2×C42 | — | 53 | 1 | no | — |
| 239 | #106 | — | 212 | 1 | no | — |
| 240 | #104 | — | 212 | 2 | no | — |
| 241 | #103 | — | 212 | 1 | no | — |
| 242 | #102 | — | 212 | 1 | no | — |
| 243 | #102 | — | 212 | 1 | no | — |
| 244 | #102 | — | 212 | 1 | no | — |
| 245 | C22⋊C8 | — | 2 | 1 | no | — |
| 246 | C22⋊C8 | — | 106 | 1 | no | — |
| 247 | #95 | — | 53 | 1 | no | — |
| 248 | #95 | — | 106 | 1 | no | — |
| 249 | #95 | — | 106 | 1 | no | — |
| 250 | #95 | — | 106 | 1 | no | — |
| 251 | #95 | — | 106 | 1 | no | — |
| 252 | #95 | — | 106 | 1 | no | — |
| 253 | #95 | — | 106 | 1 | no | — |
| 254 | #95 | D212 | 1 | 1 | yes | characteristic |
| 255 | C24 | — | 2 | 1 | no | — |
| 256 | #41 | — | 212 | 1 | no | — |
| 257 | #41 | — | 212 | 1 | no | — |
| 258 | #41 | — | 212 | 1 | no | — |
| 259 | #41 | — | 212 | 1 | no | — |
| 260 | C2×Q8 | — | 106 | 1 | no | — |
| 261 | C2×D4 | — | 4 | 1 | no | — |
| 262 | C2×D4 | — | 4 | 2 | no | — |
| 263 | C2×D4 | — | 106 | 1 | no | — |
| 264 | C2×D4 | — | 106 | 1 | no | — |
| 265 | C2×D4 | — | 106 | 1 | no | — |
| 266 | C2×D4 | — | 212 | 1 | no | — |
| 267 | C22×C4 | — | 2 | 1 | no | — |
| 268 | C22×C4 | — | 106 | 1 | no | — |
| 269 | C22×C4 | — | 106 | 1 | no | — |
| 270 | C22×C4 | — | 106 | 1 | no | — |
| 271 | C22×C4 | — | 106 | 1 | no | — |
| 272 | C22×C4 | — | 424 | 1 | no | — |
| 273 | C22×C4 | — | 424 | 1 | no | — |
| 274 | C22×C4 | — | 424 | 1 | no | — |
| 275 | C22×C4 | — | 212 | 1 | no | — |
| 276 | C22×C4 | C2×D212 | 1 | 1 | yes | characteristic |
| 277 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 278 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 279 | D8 | — | 424 | 2 | no | — |
| 280 | M16 | — | 4 | 1 | no | — |
| 281 | M16 | — | 4 | 1 | no | — |
| 282 | C2×C8 | — | 4 | 1 | no | — |
| 283 | C2×C8 | — | 4 | 1 | no | — |
| 284 | C2×C8 | — | 212 | 1 | no | — |
| 285 | C4⋊C4 | — | 4 | 1 | no | — |
| 286 | C4⋊C4 | — | 106 | 1 | no | — |
| 287 | C4⋊C4 | — | 106 | 1 | no | — |
| 288 | C4⋊C4 | — | 424 | 1 | no | — |
| 289 | C4⋊C4 | — | 424 | 1 | no | — |
| 290 | C4⋊C4 | — | 212 | 1 | no | — |
| 291 | C4⋊C4 | — | 212 | 1 | no | — |
| 292 | C22⋊C4 | — | 4 | 2 | no | — |
| 293 | C22⋊C4 | — | 4 | 1 | no | — |
| 294 | C22⋊C4 | — | 4 | 1 | no | — |
| 295 | C22⋊C4 | — | 424 | 1 | no | — |
| 296 | C22⋊C4 | — | 424 | 1 | no | — |
| 297 | C22⋊C4 | — | 212 | 1 | no | — |
| 298 | C22⋊C4 | — | 212 | 1 | no | — |
| 299 | C22⋊C4 | — | 212 | 2 | no | — |
| 300 | C42 | — | 106 | 1 | no | — |
| 301 | C42 | — | 106 | 1 | no | — |
| 302 | C23 | — | 2 | 2 | no | — |
| 303 | C23 | — | 4 | 1 | no | — |
| 304 | C23 | — | 4 | 1 | no | — |
| 305 | C23 | — | 4 | 1 | no | — |
| 306 | C23 | — | 4 | 1 | no | — |
| 307 | C23 | — | 4 | 1 | no | — |
| 308 | C23 | — | 4 | 1 | no | — |
| 309 | C23 | — | 212 | 1 | no | — |
| 310 | C23 | #13133187 | 1 | 1 | yes | characteristic |
| 311 | Q8 | — | 212 | 1 | no | — |
| 312 | Q8 | — | 212 | 1 | no | — |
| 313 | D4 | — | 4 | 2 | no | — |
| 314 | D4 | — | 8 | 1 | no | — |
| 315 | D4 | — | 424 | 1 | no | — |
| 316 | D4 | — | 424 | 1 | no | — |
| 317 | D4 | — | 424 | 1 | no | — |
| 318 | D4 | — | 424 | 1 | no | — |
| 319 | D4 | — | 212 | 1 | no | — |
| 320 | D4 | — | 212 | 1 | no | — |
| 321 | C2×C4 | — | 2 | 1 | no | — |
| 322 | C2×C4 | — | 2 | 1 | no | — |
| 323 | C2×C4 | — | 2 | 1 | no | — |
| 324 | C2×C4 | — | 2 | 1 | no | — |
| 325 | C2×C4 | — | 4 | 1 | no | — |
| 326 | C2×C4 | — | 4 | 1 | no | — |
| 327 | C2×C4 | — | 4 | 1 | no | — |
| 328 | C2×C4 | — | 4 | 1 | no | — |
| 329 | C2×C4 | — | 4 | 1 | no | — |
| 330 | C2×C4 | — | 424 | 1 | no | — |
| 331 | C2×C4 | — | 424 | 1 | no | — |
| 332 | C2×C4 | — | 424 | 4 | no | — |
| 333 | C2×C4 | — | 212 | 1 | no | — |
| 334 | C2×C4 | — | 212 | 1 | no | — |
| 335 | C2×C4 | — | 212 | 1 | no | — |
| 336 | C2×C4 | — | 212 | 1 | no | — |
| 337 | C2×C4 | — | 212 | 1 | no | — |
| 338 | C2×C4 | — | 212 | 1 | no | — |
| 339 | C2×C4 | — | 212 | 1 | no | — |
| 340 | C2×C4 | — | 212 | 1 | no | — |
| 341 | C2×C4 | — | 212 | 1 | no | — |
| 342 | C2×C4 | — | 212 | 1 | no | — |
| 343 | C2×C4 | — | 212 | 1 | no | — |
| 344 | C2×C4 | — | 212 | 1 | no | — |
| 345 | C2×C4 | — | 212 | 1 | no | — |
| 346 | C2×C4 | #13133238 | 1 | 1 | yes | characteristic |
| 347 | C2×C4 | #13133241 | 1 | 1 | yes | characteristic |
| 348 | C8 | — | 8 | 1 | no | — |
| 349 | C8 | — | 8 | 1 | no | — |
| 350 | C8 | — | 424 | 1 | no | — |
| 351 | C22 | — | 2 | 1 | no | — |
| 352 | C22 | — | 2 | 1 | no | — |
| 353 | C22 | — | 4 | 2 | no | — |
| 354 | C22 | — | 4 | 2 | no | — |
| 355 | C22 | — | 4 | 2 | no | — |
| 356 | C22 | — | 8 | 1 | no | — |
| 357 | C22 | — | 8 | 1 | no | — |
| 358 | C22 | — | 8 | 1 | no | — |
| 359 | C22 | — | 8 | 1 | no | — |
| 360 | C22 | — | 424 | 1 | no | — |
| 361 | C22 | — | 424 | 1 | no | — |
| 362 | C22 | — | 424 | 1 | no | — |
| 363 | C22 | #16810769 | 1 | 1 | yes | characteristic |
| 364 | C22 | #16810797 | 1 | 1 | yes | characteristic |
| 365 | C22 | #16810811 | 1 | 1 | yes | characteristic |
| 366 | C4 | — | 2 | 1 | no | — |
| 367 | C4 | — | 2 | 1 | no | — |
| 368 | C4 | — | 4 | 1 | no | — |
| 369 | C4 | — | 4 | 1 | no | — |
| 370 | C4 | — | 8 | 1 | no | — |
| 371 | C4 | — | 424 | 1 | no | — |
| 372 | C4 | — | 424 | 1 | no | — |
| 373 | C4 | — | 424 | 1 | no | — |
| 374 | C4 | — | 424 | 1 | no | — |
| 375 | C4 | — | 424 | 1 | no | — |
| 376 | C2 | — | 2 | 1 | no | — |
| 377 | C2 | — | 2 | 1 | no | — |
| 378 | C2 | — | 8 | 2 | no | — |
| 379 | C2 | — | 848 | 1 | no | — |
| 380 | C2 | #20273645 | 1 | 1 | yes | characteristic |
| 381 | C2 | #20276707 | 1 | 1 | yes | characteristic |
| 382 | C2 | #20276733 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20282393 | C2 | semidirect |
| 2. #20275945 | C2 | semidirect |
| 3. #20273754 | C2 | semidirect |
| 5. #20272741 | C2 | semidirect |
| 6. #20272658 | C2 | semidirect |
| 7. C53×#1345 | C2 | semidirect |
| 190. #1345 | D53 | semidirect |
| 218. C53 | #12141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20282393 | 2 |
| #20275945 | 2 |
| #20273754 | 2 |
| #20273649 | 2 |
| #20272741 | 2 |
| #20272658 | 2 |
| C53×#1345 | 2 |
| #12141 | 53 |