Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1164 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 1164 conjugacy classes of subgroups — too many to draw. Only its 205 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 | #20288117 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#16810595 | C2 | 1 | 3 | yes | maximal |
| 3 | #20275893 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #20275892 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #20275891 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20274446 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C53×#2032 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×#11719947 | C22 | 1 | 1 | yes | characteristic |
| 9 | #16811252 | — | 2 | 6 | no | — |
| 10 | #16811249 | C22 | 1 | 3 | yes | — |
| 11 | #16811175 | — | 2 | 6 | no | — |
| 12 | C2×#13133173 | C22 | 1 | 3 | yes | — |
| 13 | C2×#13133173 | C22 | 1 | 3 | yes | — |
| 14 | #16810595 | — | 2 | 6 | no | — |
| 15 | #16810595 | — | 2 | 6 | no | — |
| 16 | C2×#13133132 | C22 | 1 | 3 | yes | — |
| 17 | C2×#13133131 | C22 | 1 | 3 | yes | — |
| 18 | C2×#13133131 | C22 | 1 | 3 | yes | — |
| 19 | #16810390 | C22 | 1 | 3 | yes | — |
| 20 | #16810389 | C22 | 1 | 3 | yes | — |
| 21 | #16810389 | C22 | 1 | 3 | yes | — |
| 22 | C53×#543 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#99×C53 | C22 | 1 | 3 | yes | — |
| 24 | C53×#342 | C22 | 1 | 3 | yes | — |
| 25 | C2×#11719947 | — | 2 | 3 | no | — |
| 26 | C2×#11719947 | — | 2 | 3 | no | — |
| 27 | C2×#11719947 | — | 2 | 3 | no | — |
| 28 | C2×#11719947 | — | 2 | 3 | no | — |
| 29 | C22×Dic106 | Q8 | 1 | 1 | yes | characteristic, complemented |
| 30 | C22×C22⋊D53 | Q8 | 1 | 1 | yes | characteristic, complemented |
| 31 | C22×C22⋊D53 | C23 | 1 | 1 | yes | characteristic |
| 32 | C23×Dic53 | Q8 | 1 | 1 | yes | characteristic, complemented |
| 33 | C23×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 34 | C22×C4×D53 | Q8 | 1 | 1 | yes | characteristic, complemented |
| 35 | #13133216 | — | 2 | 6 | no | — |
| 36 | #13133215 | — | 2 | 6 | no | — |
| 37 | #13133207 | — | 2 | 12 | no | — |
| 38 | #13133196 | — | 2 | 6 | no | — |
| 39 | #13133194 | — | 2 | 6 | no | — |
| 40 | #13133194 | — | 2 | 6 | no | — |
| 41 | Q8×Dic53 | — | 2 | 2 | no | — |
| 42 | #13133182 | — | 2 | 6 | no | — |
| 43 | #13133173 | — | 2 | 3 | no | — |
| 44 | #13133173 | — | 2 | 3 | no | — |
| 45 | #13133173 | — | 2 | 3 | no | — |
| 46 | #13133173 | — | 2 | 3 | no | — |
| 47 | #13133173 | — | 2 | 3 | no | — |
| 48 | #13133173 | — | 2 | 3 | no | — |
| 49 | #13133173 | D4 | 1 | 6 | yes | — |
| 50 | #13133173 | D4 | 1 | 6 | yes | — |
| 51 | C2×#11719919 | — | 2 | 3 | no | — |
| 52 | C2×#11719919 | — | 2 | 3 | no | — |
| 53 | C2×C22⋊Dic53 | C23 | 1 | 3 | yes | — |
| 54 | C2×C22⋊Dic53 | C23 | 1 | 3 | yes | — |
| 55 | C2×C4×Dic53 | — | 2 | 3 | no | — |
| 56 | C2×C4×Dic53 | — | 2 | 3 | no | — |
| 57 | #13133132 | — | 2 | 6 | no | — |
| 58 | #13133131 | — | 2 | 6 | no | — |
| 59 | #13133131 | — | 2 | 6 | no | — |
| 60 | C22×D4×C53 | C23 | 1 | 1 | yes | characteristic |
| 61 | C22⋊Q8×C53 | — | 2 | 6 | no | — |
| 62 | C2×C22⋊C4×C53 | C23 | 1 | 3 | yes | — |
| 63 | C2×C22⋊C4×C53 | C23 | 1 | 3 | yes | — |
| 64 | #99×C53 | — | 2 | 6 | no | — |
| 65 | C24×C53 | C2×Q8 | 1 | 1 | yes | characteristic |
| 66 | C24×C53 | C24 | 1 | 1 | yes | characteristic |
| 67 | C23×D53 | C2×Q8 | 1 | 1 | yes | characteristic |
| 68 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 69 | C2×D4×C53 | — | 2 | 3 | no | — |
| 70 | C2×D4×C53 | — | 2 | 3 | no | — |
| 71 | C22×C4×C53 | — | 2 | 3 | no | — |
| 72 | C22×C4×C53 | — | 2 | 3 | no | — |
| 73 | C22×C4×C53 | C2×Q8 | 1 | 1 | yes | characteristic |
| 74 | C2×C22⋊D53 | — | 2 | 3 | no | — |
| 75 | C2×C22⋊D53 | — | 2 | 3 | no | — |
| 76 | C2×C22⋊D53 | — | 2 | 3 | no | — |
| 77 | C2×C22⋊D53 | — | 2 | 3 | no | — |
| 78 | C22×Dic53 | — | 2 | 3 | no | — |
| 79 | C22×Dic53 | — | 2 | 3 | no | — |
| 80 | C22×Dic53 | — | 2 | 3 | no | — |
| 81 | C22×Dic53 | — | 2 | 3 | no | — |
| 82 | C22×Dic53 | C2×D4 | 1 | 3 | yes | — |
| 83 | C22×Dic53 | C2×D4 | 1 | 3 | yes | — |
| 84 | C22×Dic53 | C2×Q8 | 1 | 1 | yes | characteristic |
| 85 | C22×Dic53 | C2×Q8 | 1 | 1 | yes | characteristic |
| 86 | C22×Dic53 | C2×Q8 | 1 | 1 | yes | characteristic |
| 87 | C22×Dic53 | #41 | 1 | 3 | yes | — |
| 88 | C22×Dic53 | #41 | 1 | 3 | yes | — |
| 89 | #11719947 | — | 4 | 1 | no | — |
| 90 | #11719947 | — | 4 | 3 | no | — |
| 91 | #11719947 | — | 4 | 3 | no | — |
| 92 | #11719947 | — | 4 | 3 | no | — |
| 93 | #11719947 | — | 4 | 3 | no | — |
| 94 | #11719947 | — | 4 | 3 | no | — |
| 95 | C2×C4×D53 | — | 2 | 3 | no | — |
| 96 | C2×C4×D53 | — | 2 | 3 | no | — |
| 97 | C2×Dic106 | — | 2 | 3 | no | — |
| 98 | C2×Dic106 | — | 2 | 3 | no | — |
| 99 | C2×Dic106 | — | 2 | 6 | no | — |
| 100 | C4⋊C4×C53 | — | 2 | 6 | no | — |
| 101 | C22⋊C4×C53 | — | 2 | 3 | no | — |
| 102 | C22⋊C4×C53 | — | 2 | 3 | no | — |
| 103 | C22⋊C4×C53 | — | 2 | 3 | no | — |
| 104 | C22⋊C4×C53 | C2×D4 | 1 | 6 | yes | — |
| 105 | C22⋊Dic53 | — | 2 | 3 | no | — |
| 106 | C22⋊Dic53 | — | 2 | 3 | no | — |
| 107 | C22⋊Dic53 | — | 2 | 3 | no | — |
| 108 | C22⋊Dic53 | C2×D4 | 1 | 6 | yes | — |
| 109 | C4⋊Dic53 | — | 2 | 6 | no | — |
| 110 | #11719919 | — | 2 | 12 | no | — |
| 111 | #11719919 | — | 2 | 6 | no | — |
| 112 | #11719919 | — | 2 | 6 | no | — |
| 113 | #11719919 | — | 4 | 3 | no | — |
| 114 | #11719919 | — | 4 | 3 | no | — |
| 115 | C4×Dic53 | — | 2 | 6 | no | — |
| 116 | C4×Dic53 | — | 2 | 6 | no | — |
| 117 | C4×Dic53 | — | 4 | 3 | no | — |
| 118 | C4×Dic53 | — | 4 | 3 | no | — |
| 119 | C23×C53 | — | 2 | 3 | no | — |
| 120 | C23×C53 | — | 8 | 1 | no | — |
| 121 | C23×C53 | — | 8 | 1 | no | — |
| 122 | C23×C53 | C22×D4 | 1 | 3 | yes | — |
| 123 | C23×C53 | C22×Q8 | 1 | 1 | yes | characteristic |
| 124 | C23×C53 | C2×#41 | 1 | 3 | yes | — |
| 125 | C22×D53 | — | 2 | 3 | no | — |
| 126 | C22×D53 | — | 8 | 1 | no | — |
| 127 | Q8×C53 | — | 8 | 2 | no | — |
| 128 | D4×C53 | — | 4 | 1 | no | — |
| 129 | D4×C53 | — | 4 | 3 | no | — |
| 130 | C2×C4×C53 | — | 2 | 6 | no | — |
| 131 | C2×C4×C53 | — | 2 | 3 | no | — |
| 132 | C2×C4×C53 | — | 4 | 3 | no | — |
| 133 | C2×C4×C53 | — | 8 | 3 | no | — |
| 134 | C2×C4×C53 | — | 8 | 3 | no | — |
| 135 | C22⋊D53 | — | 4 | 1 | no | — |
| 136 | C22⋊D53 | — | 4 | 3 | no | — |
| 137 | C22⋊D53 | — | 4 | 1 | no | — |
| 138 | C22⋊D53 | — | 4 | 3 | no | — |
| 139 | C2×Dic53 | — | 2 | 6 | no | — |
| 140 | C2×Dic53 | — | 2 | 3 | no | — |
| 141 | C2×Dic53 | — | 4 | 1 | no | — |
| 142 | C2×Dic53 | — | 4 | 3 | no | — |
| 143 | C2×Dic53 | — | 4 | 3 | no | — |
| 144 | C2×Dic53 | — | 8 | 3 | no | — |
| 145 | C2×Dic53 | — | 8 | 3 | no | — |
| 146 | C2×Dic53 | #120 | 1 | 1 | yes | characteristic |
| 147 | C2×Dic53 | #120 | 1 | 3 | yes | — |
| 148 | C2×Dic53 | C22⋊Q8 | 1 | 3 | yes | — |
| 149 | C2×Dic53 | C22⋊Q8 | 1 | 3 | yes | — |
| 150 | C2×Dic53 | C22⋊Q8 | 1 | 3 | yes | — |
| 151 | C2×Dic53 | C22⋊Q8 | 1 | 3 | yes | — |
| 152 | C2×Dic53 | #124 | 1 | 3 | yes | — |
| 153 | C2×Dic53 | #124 | 1 | 3 | yes | — |
| 154 | C2×Dic53 | #124 | 1 | 3 | yes | — |
| 155 | C2×Dic53 | #124 | 1 | 3 | yes | — |
| 156 | C4×D53 | — | 4 | 1 | no | — |
| 157 | C4×D53 | — | 4 | 3 | no | — |
| 158 | Dic106 | — | 4 | 1 | no | — |
| 159 | Dic106 | — | 4 | 3 | no | — |
| 160 | Dic106 | — | 8 | 6 | no | — |
| 161 | #23474 | — | 53 | 1 | no | maximal, Sylow |
| 162 | C22×C53 | — | 4 | 3 | no | — |
| 163 | C22×C53 | — | 4 | 3 | no | — |
| 164 | C22×C53 | — | 4 | 1 | no | — |
| 165 | C22×C53 | — | 4 | 1 | no | — |
| 166 | C22×C53 | — | 8 | 3 | no | — |
| 167 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 168 | C22×C53 | C2×C22⋊Q8 | 1 | 3 | yes | — |
| 169 | C22×C53 | C2×#124 | 1 | 3 | yes | — |
| 170 | C2×D53 | — | 4 | 1 | no | — |
| 171 | C2×D53 | — | 8 | 3 | no | — |
| 172 | C4×C53 | — | 4 | 6 | no | — |
| 173 | C4×C53 | — | 4 | 1 | no | — |
| 174 | C4×C53 | — | 8 | 3 | no | — |
| 175 | Dic53 | — | 4 | 6 | no | — |
| 176 | Dic53 | — | 4 | 1 | no | — |
| 177 | Dic53 | — | 8 | 3 | no | — |
| 178 | Dic53 | #393 | 1 | 1 | yes | characteristic |
| 179 | Dic53 | #393 | 1 | 3 | yes | — |
| 180 | Dic53 | #393 | 1 | 1 | yes | characteristic |
| 181 | Dic53 | #393 | 1 | 3 | yes | — |
| 182 | #3458 | — | 53 | 1 | no | — |
| 183 | C2×#410 | — | 53 | 3 | no | — |
| 184 | #2032 | — | 53 | 3 | no | — |
| 185 | #2032 | — | 53 | 3 | no | — |
| 186 | #2032 | — | 53 | 1 | no | — |
| 187 | #2032 | D53 | 1 | 1 | yes | characteristic, complemented |
| 188 | #1740 | — | 53 | 3 | no | — |
| 189 | C2×C53 | — | 2 | 1 | no | — |
| 190 | C2×C53 | — | 2 | 3 | no | — |
| 191 | C2×C53 | — | 2 | 3 | no | — |
| 192 | C2×C53 | — | 8 | 1 | no | — |
| 193 | C2×C53 | C2×#393 | 1 | 1 | yes | characteristic |
| 194 | D53 | — | 8 | 1 | no | — |
| 195 | C22×#41 | — | 53 | 1 | no | — |
| 196 | #544 | — | 106 | 6 | no | — |
| 197 | #543 | — | 53 | 3 | no | — |
| 198 | #543 | C2×D53 | 1 | 1 | yes | characteristic |
| 199 | #533 | — | 106 | 6 | no | — |
| 200 | C2×#117 | — | 53 | 3 | no | — |
| 201 | C2×#117 | — | 53 | 3 | no | — |
| 202 | #410 | — | 106 | 6 | no | — |
| 203 | #410 | — | 106 | 6 | no | — |
| 204 | C2×#99 | — | 53 | 3 | no | — |
| 205 | C2×#99 | — | 53 | 3 | no | — |
| 206 | C2×#99 | — | 53 | 3 | no | — |
| 207 | C2×#99 | C2×D53 | 1 | 3 | yes | — |
| 208 | #342 | — | 53 | 3 | no | — |
| 209 | #342 | — | 53 | 3 | no | — |
| 210 | #342 | — | 53 | 3 | no | — |
| 211 | #342 | C2×D53 | 1 | 3 | yes | — |
| 212 | C53 | #23474 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 213 | C2×#41 | — | 106 | 3 | no | — |
| 214 | C2×#41 | — | 106 | 3 | no | — |
| 215 | C2×#41 | — | 106 | 3 | no | — |
| 216 | C2×#41 | — | 106 | 3 | no | — |
| 217 | C22×Q8 | — | 53 | 1 | no | — |
| 218 | C22×D4 | — | 53 | 1 | no | — |
| 219 | C22×D4 | — | 53 | 1 | no | — |
| 220 | C22×D4 | C22×D53 | 1 | 1 | yes | characteristic |
| 221 | C23×C4 | — | 53 | 1 | no | — |
| 222 | C23×C4 | — | 53 | 1 | no | — |
| 223 | C23×C4 | — | 53 | 1 | no | — |
| 224 | C4⋊Q8 | — | 106 | 6 | no | — |
| 225 | C4⋊Q8 | — | 106 | 6 | no | — |
| 226 | #125 | — | 106 | 12 | no | — |
| 227 | C22⋊Q8 | — | 2 | 6 | no | — |
| 228 | C22⋊Q8 | — | 106 | 6 | no | — |
| 229 | C22⋊Q8 | — | 106 | 6 | no | — |
| 230 | C22⋊Q8 | — | 106 | 6 | no | — |
| 231 | C4×Q8 | — | 106 | 6 | no | — |
| 232 | C4×Q8 | — | 106 | 2 | no | — |
| 233 | #117 | — | 53 | 6 | no | — |
| 234 | #117 | — | 53 | 6 | no | — |
| 235 | #117 | — | 106 | 3 | no | — |
| 236 | #117 | — | 106 | 3 | no | — |
| 237 | #117 | — | 106 | 3 | no | — |
| 238 | #117 | — | 106 | 3 | no | — |
| 239 | #117 | — | 106 | 3 | no | — |
| 240 | #117 | — | 106 | 3 | no | — |
| 241 | C2×C4⋊C4 | — | 106 | 3 | no | — |
| 242 | C2×C4⋊C4 | — | 106 | 3 | no | — |
| 243 | C2×C22⋊C4 | — | 53 | 3 | no | — |
| 244 | C2×C22⋊C4 | — | 53 | 3 | no | — |
| 245 | C2×C22⋊C4 | C22×D53 | 1 | 3 | yes | — |
| 246 | C2×C22⋊C4 | C22×D53 | 1 | 3 | yes | — |
| 247 | C2×C42 | — | 106 | 3 | no | — |
| 248 | C2×C42 | — | 106 | 3 | no | — |
| 249 | #99 | — | 2 | 6 | no | — |
| 250 | #99 | — | 106 | 6 | no | — |
| 251 | #99 | — | 106 | 6 | no | — |
| 252 | #99 | — | 106 | 6 | no | — |
| 253 | C24 | — | 53 | 1 | no | — |
| 254 | C24 | Q8×D53 | 1 | 1 | yes | characteristic |
| 255 | C24 | C23×D53 | 1 | 1 | yes | characteristic |
| 256 | #41 | — | 212 | 1 | no | — |
| 257 | #41 | — | 212 | 3 | no | — |
| 258 | #41 | — | 212 | 3 | no | — |
| 259 | #41 | — | 212 | 3 | no | — |
| 260 | #41 | — | 212 | 3 | no | — |
| 261 | #41 | — | 212 | 3 | no | — |
| 262 | C2×Q8 | — | 2 | 2 | no | — |
| 263 | C2×Q8 | — | 106 | 3 | no | — |
| 264 | C2×Q8 | — | 106 | 3 | no | — |
| 265 | C2×Q8 | — | 106 | 6 | no | — |
| 266 | C2×D4 | — | 2 | 3 | no | — |
| 267 | C2×D4 | — | 2 | 3 | no | — |
| 268 | C2×D4 | — | 106 | 3 | no | — |
| 269 | C2×D4 | — | 106 | 3 | no | — |
| 270 | C2×D4 | — | 106 | 3 | no | — |
| 271 | C2×D4 | — | 106 | 3 | no | — |
| 272 | C22×C4 | — | 2 | 3 | no | — |
| 273 | C22×C4 | — | 2 | 3 | no | — |
| 274 | C22×C4 | — | 53 | 3 | no | — |
| 275 | C22×C4 | — | 53 | 3 | no | — |
| 276 | C22×C4 | — | 53 | 1 | no | — |
| 277 | C22×C4 | — | 53 | 1 | no | — |
| 278 | C22×C4 | — | 53 | 3 | no | — |
| 279 | C22×C4 | — | 53 | 3 | no | — |
| 280 | C22×C4 | — | 53 | 1 | no | — |
| 281 | C22×C4 | — | 106 | 3 | no | — |
| 282 | C22×C4 | — | 106 | 3 | no | — |
| 283 | C22×C4 | — | 106 | 3 | no | — |
| 284 | C22×C4 | — | 106 | 3 | no | — |
| 285 | C22×C4 | — | 106 | 3 | no | — |
| 286 | C22×C4 | — | 106 | 3 | no | — |
| 287 | C22×C4 | Q8×D53 | 1 | 1 | yes | characteristic |
| 288 | C4⋊C4 | — | 2 | 6 | no | — |
| 289 | C4⋊C4 | — | 106 | 6 | no | — |
| 290 | C4⋊C4 | — | 106 | 6 | no | — |
| 291 | C4⋊C4 | — | 106 | 12 | no | — |
| 292 | C4⋊C4 | — | 106 | 6 | no | — |
| 293 | C4⋊C4 | — | 212 | 3 | no | — |
| 294 | C4⋊C4 | — | 212 | 3 | no | — |
| 295 | C22⋊C4 | — | 2 | 3 | no | — |
| 296 | C22⋊C4 | — | 2 | 3 | no | — |
| 297 | C22⋊C4 | — | 2 | 3 | no | — |
| 298 | C22⋊C4 | — | 53 | 6 | no | — |
| 299 | C22⋊C4 | — | 106 | 3 | no | — |
| 300 | C22⋊C4 | — | 106 | 3 | no | — |
| 301 | C22⋊C4 | — | 106 | 3 | no | — |
| 302 | C22⋊C4 | D4×D53 | 1 | 6 | yes | — |
| 303 | C42 | — | 106 | 6 | no | — |
| 304 | C42 | — | 106 | 6 | no | — |
| 305 | C42 | — | 212 | 3 | no | — |
| 306 | C42 | — | 212 | 3 | no | — |
| 307 | C23 | — | 2 | 3 | no | — |
| 308 | C23 | — | 8 | 1 | no | — |
| 309 | C23 | — | 8 | 1 | no | — |
| 310 | C23 | — | 106 | 3 | no | — |
| 311 | C23 | — | 424 | 1 | no | — |
| 312 | C23 | C2×D4×D53 | 1 | 3 | yes | — |
| 313 | C23 | C2×Q8×D53 | 1 | 1 | yes | characteristic |
| 314 | C23 | #41×D53 | 1 | 3 | yes | — |
| 315 | Q8 | — | 8 | 2 | no | — |
| 316 | Q8 | — | 424 | 6 | no | — |
| 317 | Q8 | — | 212 | 1 | no | — |
| 318 | Q8 | — | 212 | 3 | no | — |
| 319 | D4 | — | 4 | 1 | no | — |
| 320 | D4 | — | 4 | 3 | no | — |
| 321 | D4 | — | 212 | 1 | no | — |
| 322 | D4 | — | 212 | 3 | no | — |
| 323 | D4 | — | 212 | 1 | no | — |
| 324 | D4 | — | 212 | 3 | no | — |
| 325 | C2×C4 | — | 2 | 6 | no | — |
| 326 | C2×C4 | — | 2 | 3 | no | — |
| 327 | C2×C4 | — | 4 | 3 | no | — |
| 328 | C2×C4 | — | 8 | 3 | no | — |
| 329 | C2×C4 | — | 8 | 3 | no | — |
| 330 | C2×C4 | — | 53 | 1 | no | — |
| 331 | C2×C4 | — | 53 | 3 | no | — |
| 332 | C2×C4 | — | 53 | 3 | no | — |
| 333 | C2×C4 | — | 53 | 3 | no | — |
| 334 | C2×C4 | — | 53 | 3 | no | — |
| 335 | C2×C4 | — | 53 | 3 | no | — |
| 336 | C2×C4 | — | 53 | 3 | no | — |
| 337 | C2×C4 | — | 53 | 3 | no | — |
| 338 | C2×C4 | — | 53 | 3 | no | — |
| 339 | C2×C4 | — | 53 | 3 | no | — |
| 340 | C2×C4 | — | 106 | 6 | no | — |
| 341 | C2×C4 | — | 106 | 3 | no | — |
| 342 | C2×C4 | — | 424 | 3 | no | — |
| 343 | C2×C4 | — | 424 | 3 | no | — |
| 344 | C2×C4 | — | 212 | 1 | no | — |
| 345 | C2×C4 | — | 212 | 3 | no | — |
| 346 | C2×C4 | — | 212 | 1 | no | — |
| 347 | C2×C4 | — | 212 | 3 | no | — |
| 348 | C2×C4 | — | 212 | 3 | no | — |
| 349 | C22 | — | 4 | 3 | no | — |
| 350 | C22 | — | 4 | 3 | no | — |
| 351 | C22 | — | 4 | 1 | no | — |
| 352 | C22 | — | 4 | 1 | no | — |
| 353 | C22 | — | 8 | 3 | no | — |
| 354 | C22 | — | 424 | 3 | no | — |
| 355 | C22 | — | 212 | 1 | no | — |
| 356 | C22 | #120×D53 | 1 | 1 | yes | characteristic |
| 357 | C22 | C22⋊Q8×D53 | 1 | 3 | yes | — |
| 358 | C22 | #124×D53 | 1 | 3 | yes | — |
| 359 | C4 | — | 4 | 6 | no | — |
| 360 | C4 | — | 4 | 1 | no | — |
| 361 | C4 | — | 8 | 3 | no | — |
| 362 | C4 | — | 53 | 1 | no | — |
| 363 | C4 | — | 53 | 3 | no | — |
| 364 | C4 | — | 53 | 1 | no | — |
| 365 | C4 | — | 53 | 3 | no | — |
| 366 | C4 | — | 424 | 3 | no | — |
| 367 | C4 | — | 212 | 6 | no | — |
| 368 | C4 | — | 212 | 1 | no | — |
| 369 | C2 | — | 2 | 1 | no | — |
| 370 | C2 | — | 2 | 3 | no | — |
| 371 | C2 | — | 2 | 3 | no | — |
| 372 | C2 | — | 8 | 1 | no | — |
| 373 | C2 | — | 424 | 1 | no | — |
| 374 | C2 | #393×D53 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20288117 | C2 | semidirect |
| 3. #20275893 | C2 | semidirect |
| 4. #20275892 | C2 | semidirect |
| 5. #20275891 | C2 | semidirect |
| 6. #20274446 | C2 | semidirect |
| 7. C53×#2032 | C2 | semidirect |
| 29. C22×Dic106 | Q8 | semidirect |
| 30. C22×C22⋊D53 | Q8 | semidirect |
| 32. C23×Dic53 | Q8 | semidirect |
| 34. C22×C4×D53 | Q8 | semidirect |
| 187. #2032 | D53 | semidirect |
| 212. C53 | #23474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288117 | 2 |
| C2×#16810595 | 2 |
| #20275893 | 2 |
| #20275892 | 2 |
| #20275891 | 2 |
| #20274446 | 2 |
| C53×#2032 | 2 |
| #23474 | 53 |