Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1190 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 220 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 | #20291328 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20291316 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20290977 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #20290966 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #20288366 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #16811703 | — | 2 | 1 | no | — |
| 7 | #16811691 | — | 2 | 1 | no | — |
| 8 | #16811609 | C22 | 1 | 6 | yes | — |
| 9 | D53⋊#101 | — | 2 | 3 | no | — |
| 10 | #16811604 | — | 2 | 3 | no | — |
| 11 | #16811602 | C22 | 1 | 6 | yes | — |
| 12 | #16811525 | C22 | 1 | 12 | yes | — |
| 13 | #16811523 | C22 | 1 | 4 | yes | — |
| 14 | C2×#13133265 | C22 | 1 | 1 | yes | characteristic |
| 15 | Q8×C22⋊D53 | — | 2 | 3 | no | — |
| 16 | Q8×C22⋊D53 | — | 2 | 1 | no | — |
| 17 | #16811284 | — | 2 | 3 | no | — |
| 18 | #16811284 | — | 2 | 1 | no | — |
| 19 | #16811197 | C4 | 1 | 3 | yes | complemented |
| 20 | #16811197 | C22 | 1 | 3 | yes | — |
| 21 | #16811134 | C4 | 1 | 3 | yes | complemented |
| 22 | #16811134 | C22 | 1 | 3 | yes | — |
| 23 | #16811101 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | C23×Q8×C53 | C4 | 1 | 1 | yes | characteristic, complemented |
| 25 | #13133305 | — | 4 | 4 | no | — |
| 26 | D53⋊M16 | — | 2 | 6 | no | — |
| 27 | Q8×#6157 | — | 4 | 4 | no | — |
| 28 | #13133296 | — | 2 | 6 | no | — |
| 29 | #13133278 | — | 2 | 6 | no | — |
| 30 | #13133277 | C23 | 1 | 4 | yes | — |
| 31 | #13133276 | — | 2 | 6 | no | — |
| 32 | #13133275 | C23 | 1 | 4 | yes | — |
| 33 | #13133265 | — | 4 | 4 | no | — |
| 34 | C2×#11719949 | D4 | 1 | 3 | yes | — |
| 35 | C2×#11719949 | D4 | 1 | 1 | yes | characteristic |
| 36 | C2×#11719945 | C2×C4 | 1 | 3 | yes | — |
| 37 | C2×#11719945 | C23 | 1 | 3 | yes | — |
| 38 | C2×Q8×D53 | D4 | 1 | 1 | yes | characteristic |
| 39 | C2×Q8×D53 | D4 | 1 | 3 | yes | — |
| 40 | #13133215 | — | 2 | 3 | no | — |
| 41 | #13133215 | — | 2 | 3 | no | — |
| 42 | #13133206 | — | 2 | 3 | no | — |
| 43 | #13133206 | — | 2 | 3 | no | — |
| 44 | #13133200 | C2×C4 | 1 | 6 | yes | — |
| 45 | #13133200 | C2×C4 | 1 | 3 | yes | — |
| 46 | #13133200 | C23 | 1 | 3 | yes | — |
| 47 | #13133196 | — | 2 | 3 | no | — |
| 48 | #13133196 | — | 2 | 3 | no | — |
| 49 | #13133193 | — | 2 | 6 | no | — |
| 50 | #13133193 | — | 2 | 3 | no | — |
| 51 | #13133193 | — | 2 | 3 | no | — |
| 52 | #13133191 | — | 2 | 3 | no | — |
| 53 | #13133191 | — | 2 | 3 | no | — |
| 54 | #13133186 | C2×C4 | 1 | 3 | yes | — |
| 55 | #13133186 | C23 | 1 | 1 | yes | characteristic |
| 56 | Q8×Dic53 | — | 2 | 3 | no | — |
| 57 | Q8×Dic53 | — | 2 | 1 | no | — |
| 58 | C4×C22⋊D53 | — | 2 | 6 | no | — |
| 59 | C4×C22⋊D53 | — | 2 | 3 | no | — |
| 60 | C4×C22⋊D53 | — | 2 | 3 | no | — |
| 61 | #13133176 | C2×C4 | 1 | 3 | yes | — |
| 62 | #13133176 | C2×C4 | 1 | 3 | yes | — |
| 63 | C22×Q8×C53 | — | 2 | 3 | no | — |
| 64 | C22×Q8×C53 | — | 2 | 1 | no | — |
| 65 | C22×Q8×C53 | — | 4 | 4 | no | — |
| 66 | C22×Q8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 67 | C22×Q8×C53 | C2×C4 | 1 | 3 | yes | — |
| 68 | C23×C4×C53 | C2×C4 | 1 | 3 | yes | — |
| 69 | C24×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 70 | C2×Q8×C53 | — | 2 | 4 | no | — |
| 71 | C2×Q8×C53 | — | 2 | 3 | no | — |
| 72 | C2×Q8×C53 | — | 2 | 3 | no | — |
| 73 | C2×Q8×C53 | — | 4 | 6 | no | — |
| 74 | C2×Q8×C53 | — | 4 | 12 | no | — |
| 75 | C2×Q8×C53 | — | 4 | 4 | no | — |
| 76 | C2×Q8×C53 | C22⋊C4 | 1 | 3 | yes | — |
| 77 | C2×Q8×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 78 | C22×C4×C53 | — | 2 | 3 | no | — |
| 79 | C22×C4×C53 | — | 2 | 3 | no | — |
| 80 | C22×C4×C53 | — | 4 | 6 | no | — |
| 81 | C22×C4×C53 | C22×C4 | 1 | 3 | yes | — |
| 82 | C22×C4×C53 | C22×C4 | 1 | 3 | yes | — |
| 83 | C2×C22⋊D53 | — | 2 | 3 | no | — |
| 84 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 85 | C2×C22⋊D53 | C22×C4 | 1 | 3 | yes | — |
| 86 | C2×C22⋊D53 | C24 | 1 | 1 | yes | characteristic |
| 87 | #11719949 | — | 2 | 4 | no | — |
| 88 | #11719949 | — | 4 | 6 | no | — |
| 89 | Q8×D53 | — | 2 | 4 | no | — |
| 90 | Q8×D53 | — | 4 | 6 | no | — |
| 91 | #11719945 | — | 4 | 6 | no | — |
| 92 | #11719945 | — | 4 | 6 | no | — |
| 93 | C2×D212 | C22⋊C4 | 1 | 3 | yes | — |
| 94 | C2×D212 | C2×D4 | 1 | 3 | yes | — |
| 95 | C2×C4×D53 | C22⋊C4 | 1 | 6 | yes | — |
| 96 | C2×C4×D53 | C2×D4 | 1 | 3 | yes | — |
| 97 | C2×C4×D53 | C2×D4 | 1 | 3 | yes | — |
| 98 | C2×Dic106 | C22⋊C4 | 1 | 3 | yes | — |
| 99 | C2×Dic106 | C2×D4 | 1 | 3 | yes | — |
| 100 | C22⋊#6157 | — | 2 | 4 | no | — |
| 101 | #11719940 | — | 2 | 4 | no | — |
| 102 | C4⋊#6157 | — | 4 | 6 | no | — |
| 103 | C4×#6157 | — | 4 | 6 | no | — |
| 104 | #11719936 | — | 4 | 6 | no | — |
| 105 | D53⋊C8 | — | 4 | 6 | no | — |
| 106 | C22⋊Dic53 | — | 2 | 3 | no | — |
| 107 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 108 | C22⋊Dic53 | C22×C4 | 1 | 3 | yes | — |
| 109 | C22⋊Dic53 | C22×C4 | 1 | 1 | yes | characteristic |
| 110 | #11719921 | — | 2 | 6 | no | — |
| 111 | #11719921 | — | 2 | 3 | no | — |
| 112 | #11719921 | — | 2 | 3 | no | — |
| 113 | C4⋊Dic53 | — | 2 | 3 | no | — |
| 114 | C4⋊Dic53 | — | 2 | 3 | no | — |
| 115 | #11719919 | — | 2 | 6 | no | — |
| 116 | #11719919 | — | 2 | 3 | no | — |
| 117 | #11719919 | — | 2 | 3 | no | — |
| 118 | C4×Dic53 | — | 2 | 3 | no | — |
| 119 | C4×Dic53 | — | 2 | 3 | no | — |
| 120 | C23×C53 | — | 2 | 1 | no | — |
| 121 | C23×C53 | — | 4 | 1 | no | — |
| 122 | C23×C53 | — | 4 | 2 | no | — |
| 123 | C23×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 124 | C22×D53 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 125 | C22×D53 | C22×D4 | 1 | 1 | yes | characteristic |
| 126 | C2×#6157 | — | 4 | 4 | no | — |
| 127 | Q8×C53 | — | 2 | 6 | no | — |
| 128 | Q8×C53 | — | 4 | 6 | no | — |
| 129 | Q8×C53 | — | 4 | 6 | no | — |
| 130 | Q8×C53 | #99 | 1 | 4 | yes | — |
| 131 | C2×C4×C53 | — | 2 | 6 | no | — |
| 132 | C2×C4×C53 | — | 2 | 3 | no | — |
| 133 | C2×C4×C53 | — | 4 | 6 | no | — |
| 134 | C2×C4×C53 | — | 4 | 6 | no | — |
| 135 | C2×C4×C53 | — | 4 | 3 | no | — |
| 136 | C2×C4×C53 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 137 | C2×C4×C53 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 138 | C22⋊D53 | — | 4 | 3 | no | — |
| 139 | C22⋊D53 | — | 4 | 1 | no | — |
| 140 | C22⋊D53 | — | 4 | 6 | no | — |
| 141 | C22⋊D53 | — | 4 | 2 | no | — |
| 142 | C2×Dic53 | — | 2 | 3 | no | — |
| 143 | C2×Dic53 | — | 2 | 1 | no | — |
| 144 | C2×Dic53 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 145 | C2×Dic53 | C22×D4 | 1 | 1 | yes | characteristic |
| 146 | D212 | — | 2 | 6 | no | — |
| 147 | D212 | — | 4 | 3 | no | — |
| 148 | C4×D53 | — | 2 | 6 | no | — |
| 149 | C4×D53 | — | 2 | 6 | no | — |
| 150 | C4×D53 | — | 4 | 6 | no | — |
| 151 | Dic106 | — | 2 | 6 | no | — |
| 152 | Dic106 | — | 4 | 3 | no | — |
| 153 | #88324 | — | 4 | 4 | no | — |
| 154 | #33349 | — | 53 | 1 | no | maximal, Sylow |
| 155 | C22×C53 | — | 2 | 2 | no | — |
| 156 | C22×C53 | — | 2 | 1 | no | — |
| 157 | C22×C53 | — | 4 | 1 | no | — |
| 158 | C22×C53 | — | 4 | 1 | no | — |
| 159 | C22×C53 | — | 4 | 2 | no | — |
| 160 | C22×C53 | — | 4 | 2 | no | — |
| 161 | C22×C53 | — | 4 | 1 | no | — |
| 162 | C22×C53 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 163 | C2×D53 | — | 2 | 1 | no | — |
| 164 | C2×D53 | — | 2 | 3 | no | — |
| 165 | C2×D53 | — | 4 | 3 | no | — |
| 166 | C2×D53 | — | 4 | 1 | no | — |
| 167 | #6157 | — | 8 | 4 | no | — |
| 168 | C4×C53 | — | 2 | 3 | no | — |
| 169 | C4×C53 | — | 4 | 3 | no | — |
| 170 | C4×C53 | C2×#99 | 1 | 6 | yes | — |
| 171 | Dic53 | — | 2 | 1 | no | — |
| 172 | Dic53 | — | 2 | 3 | no | — |
| 173 | Dic53 | — | 4 | 3 | no | — |
| 174 | Dic53 | — | 4 | 1 | no | — |
| 175 | #3486 | — | 53 | 1 | no | — |
| 176 | #2889 | — | 53 | 1 | no | — |
| 177 | #2884 | — | 53 | 1 | no | — |
| 178 | #2123 | — | 53 | 6 | no | — |
| 179 | #2120 | — | 53 | 6 | no | — |
| 180 | C2×C53 | — | 2 | 1 | no | — |
| 181 | C2×C53 | — | 4 | 2 | no | — |
| 182 | C2×C53 | — | 4 | 1 | no | — |
| 183 | C2×C53 | C22×#99 | 1 | 1 | yes | characteristic |
| 184 | D53 | — | 4 | 1 | no | — |
| 185 | D53 | — | 4 | 3 | no | — |
| 186 | C2×2−1+4 | — | 53 | 1 | no | — |
| 187 | C23×Q8 | #6157 | 1 | 1 | yes | characteristic, complemented |
| 188 | #568 | — | 106 | 1 | no | — |
| 189 | D4×Q8 | — | 106 | 3 | no | — |
| 190 | D4×Q8 | — | 106 | 1 | no | — |
| 191 | #548 | — | 106 | 3 | no | — |
| 192 | #548 | — | 106 | 1 | no | — |
| 193 | #536 | — | 53 | 3 | no | — |
| 194 | #536 | — | 53 | 3 | no | — |
| 195 | #525 | — | 53 | 3 | no | — |
| 196 | #525 | — | 53 | 3 | no | — |
| 197 | #519 | — | 53 | 1 | no | — |
| 198 | #519 | — | 106 | 1 | no | — |
| 199 | #413 | — | 53 | 6 | no | — |
| 200 | C2×#101 | — | 106 | 3 | no | — |
| 201 | #410 | — | 53 | 6 | no | — |
| 202 | #410 | — | 106 | 3 | no | — |
| 203 | #352 | — | 53 | 12 | no | — |
| 204 | AΣL(1,𝔽16) | — | 53 | 4 | no | — |
| 205 | C53 | #33349 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 206 | 2−1+4 | — | 212 | 4 | no | — |
| 207 | C2×#41 | — | 53 | 3 | no | — |
| 208 | C2×#41 | — | 53 | 1 | no | — |
| 209 | C2×#41 | — | 53 | 3 | no | — |
| 210 | C2×#41 | — | 53 | 3 | no | — |
| 211 | C22×Q8 | — | 2 | 3 | no | — |
| 212 | C22×Q8 | — | 2 | 1 | no | — |
| 213 | C22×Q8 | — | 4 | 4 | no | — |
| 214 | C22×Q8 | — | 53 | 1 | no | — |
| 215 | C22×Q8 | — | 53 | 3 | no | — |
| 216 | C22×Q8 | C2×#6157 | 1 | 3 | yes | — |
| 217 | C22×Q8 | C2×#6157 | 1 | 1 | yes | characteristic |
| 218 | C23×C4 | C2×#6157 | 1 | 3 | yes | — |
| 219 | #131 | — | 212 | 4 | no | — |
| 220 | C2×M16 | — | 106 | 6 | no | — |
| 221 | C4⋊Q8 | — | 106 | 3 | no | — |
| 222 | C4⋊Q8 | — | 106 | 3 | no | — |
| 223 | #124 | — | 106 | 3 | no | — |
| 224 | #124 | — | 106 | 3 | no | — |
| 225 | #123 | — | 53 | 3 | no | — |
| 226 | #123 | — | 53 | 3 | no | — |
| 227 | #123 | — | 53 | 6 | no | — |
| 228 | C22⋊Q8 | — | 106 | 3 | no | — |
| 229 | C22⋊Q8 | — | 106 | 3 | no | — |
| 230 | C22⋊Q8 | — | 106 | 3 | no | — |
| 231 | C22⋊Q8 | — | 106 | 3 | no | — |
| 232 | C22⋊Q8 | — | 106 | 6 | no | — |
| 233 | #121 | — | 106 | 3 | no | — |
| 234 | #121 | — | 106 | 3 | no | — |
| 235 | #120 | — | 53 | 1 | no | — |
| 236 | #120 | — | 53 | 3 | no | — |
| 237 | C4×Q8 | — | 106 | 3 | no | — |
| 238 | C4×Q8 | — | 106 | 1 | no | — |
| 239 | C4×Q8 | — | 212 | 4 | no | — |
| 240 | C4×D4 | — | 106 | 3 | no | — |
| 241 | C4×D4 | — | 106 | 3 | no | — |
| 242 | C4×D4 | — | 106 | 6 | no | — |
| 243 | #117 | — | 53 | 3 | no | — |
| 244 | #117 | — | 53 | 3 | no | — |
| 245 | #117 | — | 106 | 6 | no | — |
| 246 | #101 | — | 106 | 6 | no | — |
| 247 | #100 | — | 53 | 4 | no | — |
| 248 | #99 | — | 53 | 4 | no | — |
| 249 | #99 | — | 106 | 6 | no | — |
| 250 | C24 | C22×#6157 | 1 | 1 | yes | characteristic |
| 251 | #41 | — | 106 | 4 | no | — |
| 252 | #41 | — | 212 | 6 | no | — |
| 253 | #41 | — | 212 | 6 | no | — |
| 254 | #41 | — | 212 | 6 | no | — |
| 255 | C2×Q8 | — | 2 | 4 | no | — |
| 256 | C2×Q8 | — | 2 | 3 | no | — |
| 257 | C2×Q8 | — | 2 | 3 | no | — |
| 258 | C2×Q8 | — | 4 | 6 | no | — |
| 259 | C2×Q8 | — | 4 | 12 | no | — |
| 260 | C2×Q8 | — | 4 | 4 | no | — |
| 261 | C2×Q8 | — | 53 | 3 | no | — |
| 262 | C2×Q8 | — | 53 | 3 | no | — |
| 263 | C2×Q8 | — | 106 | 4 | no | — |
| 264 | C2×Q8 | — | 212 | 6 | no | — |
| 265 | C2×Q8 | C22⋊#6157 | 1 | 3 | yes | — |
| 266 | C2×Q8 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 267 | C2×D4 | — | 53 | 3 | no | — |
| 268 | C2×D4 | — | 53 | 1 | no | — |
| 269 | C2×D4 | — | 53 | 3 | no | — |
| 270 | C2×D4 | — | 53 | 3 | no | — |
| 271 | C2×D4 | — | 106 | 3 | no | — |
| 272 | C2×D4 | — | 106 | 1 | no | — |
| 273 | C22×C4 | — | 2 | 3 | no | — |
| 274 | C22×C4 | — | 2 | 3 | no | — |
| 275 | C22×C4 | — | 4 | 6 | no | — |
| 276 | C22×C4 | — | 53 | 3 | no | — |
| 277 | C22×C4 | — | 53 | 3 | no | — |
| 278 | C22×C4 | — | 53 | 6 | no | — |
| 279 | C22×C4 | C22×#6157 | 1 | 3 | yes | — |
| 280 | C22×C4 | C22×#6157 | 1 | 3 | yes | — |
| 281 | M16 | — | 106 | 4 | no | — |
| 282 | M16 | — | 212 | 6 | no | — |
| 283 | C2×C8 | — | 212 | 6 | no | — |
| 284 | C4⋊C4 | — | 106 | 3 | no | — |
| 285 | C4⋊C4 | — | 106 | 6 | no | — |
| 286 | C4⋊C4 | — | 106 | 3 | no | — |
| 287 | C4⋊C4 | — | 106 | 3 | no | — |
| 288 | C4⋊C4 | — | 106 | 3 | no | — |
| 289 | C4⋊C4 | — | 212 | 6 | no | — |
| 290 | C22⋊C4 | — | 53 | 1 | no | — |
| 291 | C22⋊C4 | — | 53 | 3 | no | — |
| 292 | C22⋊C4 | — | 106 | 3 | no | — |
| 293 | C22⋊C4 | — | 106 | 6 | no | — |
| 294 | C22⋊C4 | — | 106 | 3 | no | — |
| 295 | C22⋊C4 | — | 106 | 3 | no | — |
| 296 | C22⋊C4 | — | 106 | 1 | no | — |
| 297 | C22⋊C4 | — | 106 | 4 | no | — |
| 298 | C42 | — | 106 | 3 | no | — |
| 299 | C42 | — | 106 | 3 | no | — |
| 300 | C42 | — | 212 | 6 | no | — |
| 301 | C23 | — | 2 | 1 | no | — |
| 302 | C23 | — | 4 | 1 | no | — |
| 303 | C23 | — | 4 | 2 | no | — |
| 304 | C23 | — | 53 | 3 | no | — |
| 305 | C23 | — | 53 | 1 | no | — |
| 306 | C23 | C23×#6157 | 1 | 1 | yes | characteristic |
| 307 | Q8 | — | 2 | 6 | no | — |
| 308 | Q8 | — | 4 | 6 | no | — |
| 309 | Q8 | — | 4 | 6 | no | — |
| 310 | Q8 | — | 106 | 6 | no | — |
| 311 | Q8 | — | 212 | 3 | no | — |
| 312 | Q8 | #13133275 | 1 | 4 | yes | — |
| 313 | D4 | — | 106 | 6 | no | — |
| 314 | D4 | — | 212 | 3 | no | — |
| 315 | D4 | — | 212 | 1 | no | — |
| 316 | D4 | — | 212 | 3 | no | — |
| 317 | D4 | — | 212 | 2 | no | — |
| 318 | D4 | — | 212 | 6 | no | — |
| 319 | C2×C4 | — | 2 | 6 | no | — |
| 320 | C2×C4 | — | 2 | 3 | no | — |
| 321 | C2×C4 | — | 4 | 6 | no | — |
| 322 | C2×C4 | — | 4 | 6 | no | — |
| 323 | C2×C4 | — | 4 | 3 | no | — |
| 324 | C2×C4 | — | 53 | 3 | no | — |
| 325 | C2×C4 | — | 53 | 1 | no | — |
| 326 | C2×C4 | — | 106 | 6 | no | — |
| 327 | C2×C4 | — | 106 | 6 | no | — |
| 328 | C2×C4 | — | 106 | 3 | no | — |
| 329 | C2×C4 | — | 106 | 1 | no | — |
| 330 | C2×C4 | — | 212 | 6 | no | — |
| 331 | C2×C4 | — | 212 | 4 | no | — |
| 332 | C2×C4 | C2×C22⋊#6157 | 1 | 3 | yes | — |
| 333 | C2×C4 | C2×C22⋊#6157 | 1 | 3 | yes | — |
| 334 | C8 | — | 212 | 4 | no | — |
| 335 | C22 | — | 2 | 2 | no | — |
| 336 | C22 | — | 2 | 1 | no | — |
| 337 | C22 | — | 4 | 1 | no | — |
| 338 | C22 | — | 4 | 1 | no | — |
| 339 | C22 | — | 4 | 2 | no | — |
| 340 | C22 | — | 4 | 2 | no | — |
| 341 | C22 | — | 4 | 1 | no | — |
| 342 | C22 | — | 106 | 1 | no | — |
| 343 | C22 | — | 106 | 3 | no | — |
| 344 | C22 | — | 212 | 1 | no | — |
| 345 | C22 | — | 212 | 3 | no | — |
| 346 | C22 | C22×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 347 | C4 | — | 2 | 3 | no | — |
| 348 | C4 | — | 4 | 3 | no | — |
| 349 | C4 | — | 106 | 1 | no | — |
| 350 | C4 | — | 106 | 3 | no | — |
| 351 | C4 | — | 424 | 4 | no | — |
| 352 | C4 | — | 212 | 3 | no | — |
| 353 | C4 | — | 212 | 1 | no | — |
| 354 | C4 | C2×#13133275 | 1 | 6 | yes | — |
| 355 | C2 | — | 2 | 1 | no | — |
| 356 | C2 | — | 4 | 2 | no | — |
| 357 | C2 | — | 4 | 1 | no | — |
| 358 | C2 | — | 212 | 1 | no | — |
| 359 | C2 | — | 212 | 3 | no | — |
| 360 | C2 | C22×#13133275 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20291328 | C2 | semidirect |
| 2. #20291316 | C2 | semidirect |
| 3. #20290977 | C2 | semidirect |
| 4. #20290966 | C2 | semidirect |
| 19. #16811197 | C4 | semidirect |
| 21. #16811134 | C4 | semidirect |
| 23. #16811101 | C4 | semidirect |
| 24. C23×Q8×C53 | C4 | semidirect |
| 187. C23×Q8 | #6157 | semidirect |
| 205. C53 | #33349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291328 | 2 |
| #20291316 | 2 |
| #20290977 | 2 |
| #20290966 | 2 |
| #20288366 | 2 |
| #33349 | 53 |