Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1214 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1214 conjugacy classes of subgroups — too many to draw. Only its 187 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 | #20288366 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #20284648 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20277301 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20275933 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #20275161 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #20274932 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #20274676 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C53×#1784 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#13133265 | C22 | 1 | 1 | yes | characteristic |
| 10 | Q8×C22⋊D53 | — | 2 | 4 | no | — |
| 11 | #16811284 | — | 2 | 4 | no | — |
| 12 | #16811197 | — | 2 | 2 | no | — |
| 13 | #16811197 | C22 | 1 | 2 | yes | — |
| 14 | #16811134 | — | 2 | 2 | no | — |
| 15 | #16811134 | C22 | 1 | 2 | yes | — |
| 16 | #16811101 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#13133176 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#13133176 | C22 | 1 | 1 | yes | characteristic |
| 19 | #16810965 | — | 2 | 4 | no | — |
| 20 | #16810948 | — | 2 | 4 | no | — |
| 21 | #16810665 | C22 | 1 | 4 | yes | — |
| 22 | C2×#13133143 | C22 | 1 | 4 | yes | — |
| 23 | #16810625 | C22 | 1 | 4 | yes | — |
| 24 | #16810530 | — | 2 | 2 | no | — |
| 25 | #16810530 | C22 | 1 | 2 | yes | — |
| 26 | #16810530 | C22 | 1 | 2 | yes | — |
| 27 | #16810486 | — | 2 | 2 | no | — |
| 28 | #16810384 | C22 | 1 | 4 | yes | — |
| 29 | C23×Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×#101×C53 | C22 | 1 | 2 | yes | — |
| 31 | C2×#101×C53 | C22 | 1 | 2 | yes | — |
| 32 | C53×#407 | C22 | 1 | 2 | yes | — |
| 33 | #13133265 | — | 2 | 4 | no | — |
| 34 | #13133265 | — | 4 | 2 | no | — |
| 35 | C2×#11719949 | — | 2 | 2 | no | — |
| 36 | C2×#11719945 | — | 2 | 2 | no | — |
| 37 | C2×#11719945 | C23 | 1 | 2 | yes | — |
| 38 | C2×Q8×D53 | — | 2 | 2 | no | — |
| 39 | #13133215 | — | 2 | 4 | no | — |
| 40 | #13133215 | — | 2 | 2 | no | — |
| 41 | #13133206 | — | 2 | 4 | no | — |
| 42 | #13133206 | — | 2 | 2 | no | — |
| 43 | #13133200 | — | 2 | 4 | no | — |
| 44 | #13133200 | — | 2 | 2 | no | — |
| 45 | #13133196 | — | 2 | 4 | no | — |
| 46 | #13133196 | D4 | 1 | 4 | yes | — |
| 47 | #13133193 | — | 2 | 8 | no | — |
| 48 | #13133193 | — | 2 | 4 | no | — |
| 49 | #13133191 | — | 2 | 4 | no | — |
| 50 | #13133191 | D4 | 1 | 4 | yes | — |
| 51 | #13133186 | — | 2 | 2 | no | — |
| 52 | Q8×Dic53 | — | 2 | 4 | no | — |
| 53 | C4×C22⋊D53 | — | 2 | 8 | no | — |
| 54 | C4×C22⋊D53 | — | 2 | 4 | no | — |
| 55 | #13133176 | — | 2 | 2 | no | — |
| 56 | #13133176 | — | 2 | 4 | no | — |
| 57 | #13133176 | — | 4 | 2 | no | — |
| 58 | #13133176 | C23 | 1 | 2 | yes | — |
| 59 | C2×C4⋊Dic53 | — | 2 | 1 | no | — |
| 60 | C2×C4⋊Dic53 | C23 | 1 | 2 | yes | — |
| 61 | C2×C22⋊Dic53 | — | 2 | 1 | no | — |
| 62 | C2×C22⋊Dic53 | — | 2 | 1 | no | — |
| 63 | C2×C4×Dic53 | — | 2 | 1 | no | — |
| 64 | C2×C4×Dic53 | C23 | 1 | 2 | yes | — |
| 65 | #13133151 | — | 2 | 4 | no | — |
| 66 | #13133149 | — | 2 | 4 | no | — |
| 67 | #13133143 | — | 4 | 4 | no | — |
| 68 | #13133142 | — | 2 | 4 | no | — |
| 69 | #13133139 | — | 2 | 4 | no | — |
| 70 | #13133124 | — | 2 | 4 | no | — |
| 71 | #13133124 | — | 2 | 4 | no | — |
| 72 | C22×Q8×C53 | — | 2 | 4 | no | — |
| 73 | C22×Q8×C53 | — | 2 | 4 | no | — |
| 74 | C22×Q8×C53 | — | 4 | 2 | no | — |
| 75 | C22×Q8×C53 | D4 | 1 | 2 | yes | — |
| 76 | C22×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 77 | C22×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 78 | C23×C4×C53 | D4 | 1 | 2 | yes | — |
| 79 | C23×C4×C53 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×M16×C53 | C23 | 1 | 4 | yes | — |
| 81 | #101×C53 | — | 2 | 4 | no | — |
| 82 | #101×C53 | — | 4 | 2 | no | — |
| 83 | C22⋊C8×C53 | — | 2 | 4 | no | — |
| 84 | C24×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 85 | C2×Q8×C53 | — | 2 | 4 | no | — |
| 86 | C2×Q8×C53 | — | 2 | 4 | no | — |
| 87 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 88 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 89 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 90 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 91 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 92 | C2×Q8×C53 | — | 4 | 2 | no | — |
| 93 | C2×Q8×C53 | — | 4 | 16 | no | — |
| 94 | C2×Q8×C53 | #41 | 1 | 4 | yes | — |
| 95 | C22×C4×C53 | — | 2 | 2 | no | — |
| 96 | C22×C4×C53 | — | 2 | 2 | no | — |
| 97 | C22×C4×C53 | — | 2 | 4 | no | — |
| 98 | C22×C4×C53 | — | 2 | 4 | no | — |
| 99 | C22×C4×C53 | — | 4 | 2 | no | — |
| 100 | C22×C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 101 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | C22×C4×C53 | C2×D4 | 1 | 4 | yes | — |
| 103 | C22×C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 104 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 105 | C2×C22⋊D53 | — | 2 | 4 | no | — |
| 106 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 107 | C22×Dic53 | — | 2 | 2 | no | — |
| 108 | C22×Dic53 | — | 2 | 2 | no | — |
| 109 | #11719949 | — | 4 | 8 | no | — |
| 110 | Q8×D53 | — | 4 | 8 | no | — |
| 111 | #11719945 | — | 2 | 4 | no | — |
| 112 | #11719945 | — | 2 | 4 | no | — |
| 113 | #11719945 | — | 4 | 4 | no | — |
| 114 | #11719945 | — | 4 | 4 | no | — |
| 115 | C2×D212 | — | 2 | 2 | no | — |
| 116 | C2×D212 | C2×D4 | 1 | 2 | yes | — |
| 117 | C2×C4×D53 | — | 2 | 4 | no | — |
| 118 | C2×C4×D53 | — | 2 | 2 | no | — |
| 119 | C2×Dic106 | — | 2 | 2 | no | — |
| 120 | C2×Dic106 | C2×D4 | 1 | 2 | yes | — |
| 121 | M16×C53 | — | 2 | 4 | no | — |
| 122 | M16×C53 | — | 2 | 4 | no | — |
| 123 | C2×C8×C53 | — | 2 | 4 | no | — |
| 124 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 125 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 126 | C22⋊Dic53 | — | 4 | 2 | no | — |
| 127 | C22⋊Dic53 | — | 4 | 2 | no | — |
| 128 | #11719921 | — | 2 | 8 | no | — |
| 129 | #11719921 | — | 2 | 4 | no | — |
| 130 | C4⋊Dic53 | — | 2 | 4 | no | — |
| 131 | C4⋊Dic53 | — | 2 | 4 | no | — |
| 132 | C4⋊Dic53 | — | 4 | 2 | no | — |
| 133 | C4⋊Dic53 | C2×D4 | 1 | 4 | yes | — |
| 134 | #11719919 | — | 2 | 8 | no | — |
| 135 | #11719919 | — | 2 | 4 | no | — |
| 136 | C4×Dic53 | — | 2 | 4 | no | — |
| 137 | C4×Dic53 | — | 2 | 2 | no | — |
| 138 | C4×Dic53 | — | 2 | 4 | no | — |
| 139 | C4×Dic53 | — | 4 | 2 | no | — |
| 140 | C23×C53 | — | 2 | 1 | no | — |
| 141 | C23×C53 | — | 2 | 1 | no | — |
| 142 | C23×C53 | — | 4 | 2 | no | — |
| 143 | C23×C53 | #120 | 1 | 2 | yes | — |
| 144 | C23×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 145 | C22×D53 | — | 2 | 2 | no | — |
| 146 | Q8×C53 | — | 2 | 8 | no | — |
| 147 | Q8×C53 | — | 4 | 8 | no | — |
| 148 | Q8×C53 | — | 4 | 4 | no | — |
| 149 | C2×C4×C53 | — | 2 | 2 | no | — |
| 150 | C2×C4×C53 | — | 2 | 1 | no | — |
| 151 | C2×C4×C53 | — | 2 | 2 | no | — |
| 152 | C2×C4×C53 | — | 2 | 1 | no | — |
| 153 | C2×C4×C53 | — | 2 | 8 | no | — |
| 154 | C2×C4×C53 | — | 2 | 2 | no | — |
| 155 | C2×C4×C53 | — | 2 | 2 | no | — |
| 156 | C2×C4×C53 | — | 2 | 2 | no | — |
| 157 | C2×C4×C53 | — | 4 | 8 | no | — |
| 158 | C2×C4×C53 | #120 | 1 | 2 | yes | — |
| 159 | C2×C4×C53 | #123 | 1 | 4 | yes | — |
| 160 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 161 | C2×C4×C53 | C2×#41 | 1 | 2 | yes | — |
| 162 | C2×C4×C53 | H(5,𝔽2) | 1 | 2 | yes | — |
| 163 | C22⋊D53 | — | 4 | 8 | no | — |
| 164 | C22⋊D53 | — | 4 | 2 | no | — |
| 165 | C22⋊D53 | — | 4 | 2 | no | — |
| 166 | C2×Dic53 | — | 2 | 2 | no | — |
| 167 | C2×Dic53 | — | 2 | 4 | no | — |
| 168 | C2×Dic53 | — | 4 | 4 | no | — |
| 169 | C2×Dic53 | — | 4 | 4 | no | — |
| 170 | C2×Dic53 | — | 4 | 2 | no | — |
| 171 | C2×Dic53 | — | 4 | 2 | no | — |
| 172 | D212 | — | 2 | 4 | no | — |
| 173 | D212 | — | 4 | 4 | no | — |
| 174 | C4×D53 | — | 4 | 8 | no | — |
| 175 | C4×D53 | — | 4 | 4 | no | — |
| 176 | Dic106 | — | 2 | 4 | no | — |
| 177 | Dic106 | — | 4 | 4 | no | — |
| 178 | C8×C53 | — | 4 | 4 | no | — |
| 179 | #24023 | — | 53 | 1 | no | maximal, Sylow |
| 180 | C22×C53 | — | 2 | 2 | no | — |
| 181 | C22×C53 | — | 2 | 2 | no | — |
| 182 | C22×C53 | — | 2 | 2 | no | — |
| 183 | C22×C53 | — | 2 | 2 | no | — |
| 184 | C22×C53 | — | 4 | 2 | no | — |
| 185 | C22×C53 | — | 4 | 2 | no | — |
| 186 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 187 | C22×C53 | C2×#123 | 1 | 1 | yes | characteristic |
| 188 | C22×C53 | #534 | 1 | 1 | yes | characteristic |
| 189 | C2×D53 | — | 4 | 2 | no | — |
| 190 | C2×D53 | — | 4 | 4 | no | — |
| 191 | C4×C53 | — | 2 | 4 | no | — |
| 192 | C4×C53 | — | 2 | 2 | no | — |
| 193 | C4×C53 | — | 4 | 2 | no | — |
| 194 | C4×C53 | #546 | 1 | 4 | yes | — |
| 195 | Dic53 | — | 4 | 2 | no | — |
| 196 | Dic53 | — | 4 | 4 | no | — |
| 197 | Dic53 | — | 8 | 2 | no | — |
| 198 | Dic53 | — | 8 | 2 | no | — |
| 199 | #3486 | — | 53 | 1 | no | — |
| 200 | #3093 | — | 53 | 2 | no | — |
| 201 | #2310 | — | 53 | 1 | no | — |
| 202 | #2038 | — | 53 | 4 | no | — |
| 203 | #1897 | — | 53 | 2 | no | — |
| 204 | #1857 | — | 53 | 2 | no | — |
| 205 | #1793 | — | 53 | 2 | no | — |
| 206 | #1784 | D53 | 1 | 1 | yes | characteristic, complemented |
| 207 | C2×C53 | — | 2 | 1 | no | — |
| 208 | C2×C53 | — | 2 | 1 | no | — |
| 209 | C2×C53 | — | 4 | 2 | no | — |
| 210 | C2×C53 | #2405 | 1 | 1 | yes | characteristic |
| 211 | C2×C53 | #3020 | 1 | 2 | yes | — |
| 212 | D53 | — | 8 | 2 | no | — |
| 213 | C2×2−1+4 | — | 53 | 1 | no | — |
| 214 | C23×Q8 | C2×D53 | 1 | 1 | yes | characteristic |
| 215 | D4×Q8 | — | 106 | 4 | no | — |
| 216 | #548 | — | 106 | 4 | no | — |
| 217 | #536 | — | 53 | 2 | no | — |
| 218 | #536 | — | 106 | 2 | no | — |
| 219 | #525 | — | 53 | 2 | no | — |
| 220 | #525 | — | 106 | 2 | no | — |
| 221 | #519 | — | 53 | 1 | no | — |
| 222 | C2×#117 | — | 53 | 1 | no | — |
| 223 | C2×#117 | — | 53 | 1 | no | — |
| 224 | #485 | — | 106 | 4 | no | — |
| 225 | #482 | — | 106 | 4 | no | — |
| 226 | #428 | — | 53 | 4 | no | — |
| 227 | C2×#104 | — | 53 | 4 | no | — |
| 228 | #417 | — | 53 | 4 | no | — |
| 229 | C2×#101 | C2×D53 | 1 | 2 | yes | — |
| 230 | C2×#101 | C2×D53 | 1 | 2 | yes | — |
| 231 | #407 | C2×D53 | 1 | 2 | yes | — |
| 232 | #391 | — | 53 | 2 | no | — |
| 233 | #391 | — | 53 | 2 | no | — |
| 234 | #391 | — | 106 | 2 | no | — |
| 235 | #381 | — | 106 | 2 | no | — |
| 236 | #339 | — | 53 | 4 | no | — |
| 237 | C53 | #24023 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 238 | 2−1+4 | — | 106 | 4 | no | — |
| 239 | 2−1+4 | — | 212 | 2 | no | — |
| 240 | C2×#41 | — | 53 | 2 | no | — |
| 241 | C2×#41 | — | 106 | 2 | no | — |
| 242 | C2×#41 | — | 106 | 2 | no | — |
| 243 | C22×Q8 | — | 2 | 4 | no | — |
| 244 | C22×Q8 | — | 2 | 4 | no | — |
| 245 | C22×Q8 | — | 4 | 2 | no | — |
| 246 | C22×Q8 | — | 106 | 2 | no | — |
| 247 | C22×Q8 | D212 | 1 | 2 | yes | — |
| 248 | C22×Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 249 | C22×Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 250 | C23×C4 | D212 | 1 | 2 | yes | — |
| 251 | C23×C4 | C22×D53 | 1 | 1 | yes | characteristic |
| 252 | C2×M16 | C22×D53 | 1 | 4 | yes | — |
| 253 | C4⋊Q8 | — | 106 | 2 | no | — |
| 254 | C4⋊Q8 | — | 106 | 4 | no | — |
| 255 | #124 | — | 106 | 2 | no | — |
| 256 | #124 | — | 106 | 4 | no | — |
| 257 | #123 | — | 106 | 2 | no | — |
| 258 | #123 | — | 106 | 4 | no | — |
| 259 | C22⋊Q8 | — | 53 | 4 | no | — |
| 260 | C22⋊Q8 | — | 106 | 4 | no | — |
| 261 | C22⋊Q8 | — | 106 | 4 | no | — |
| 262 | C22⋊Q8 | — | 106 | 8 | no | — |
| 263 | #121 | — | 53 | 4 | no | — |
| 264 | #121 | — | 106 | 4 | no | — |
| 265 | #120 | — | 106 | 2 | no | — |
| 266 | C4×Q8 | — | 106 | 4 | no | — |
| 267 | C4×D4 | — | 106 | 8 | no | — |
| 268 | C4×D4 | — | 106 | 4 | no | — |
| 269 | #117 | — | 53 | 2 | no | — |
| 270 | #117 | — | 106 | 2 | no | — |
| 271 | #117 | — | 106 | 4 | no | — |
| 272 | #117 | — | 212 | 2 | no | — |
| 273 | C2×C4⋊C4 | — | 53 | 2 | no | — |
| 274 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 275 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 276 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 277 | C2×C42 | — | 53 | 2 | no | — |
| 278 | C2×C42 | — | 106 | 1 | no | — |
| 279 | #107 | — | 106 | 4 | no | — |
| 280 | #106 | — | 106 | 4 | no | — |
| 281 | #104 | — | 212 | 4 | no | — |
| 282 | #103 | — | 106 | 4 | no | — |
| 283 | #102 | — | 106 | 4 | no | — |
| 284 | #101 | — | 2 | 4 | no | — |
| 285 | #101 | — | 4 | 2 | no | — |
| 286 | C22⋊C8 | — | 2 | 4 | no | — |
| 287 | #95 | — | 106 | 4 | no | — |
| 288 | #95 | — | 106 | 4 | no | — |
| 289 | C24 | C2×D212 | 1 | 1 | yes | characteristic |
| 290 | #41 | — | 106 | 4 | no | — |
| 291 | #41 | — | 106 | 4 | no | — |
| 292 | #41 | — | 212 | 4 | no | — |
| 293 | #41 | — | 212 | 8 | no | — |
| 294 | #41 | — | 212 | 4 | no | — |
| 295 | C2×Q8 | — | 2 | 4 | no | — |
| 296 | C2×Q8 | — | 2 | 4 | no | — |
| 297 | C2×Q8 | — | 2 | 2 | no | — |
| 298 | C2×Q8 | — | 2 | 2 | no | — |
| 299 | C2×Q8 | — | 2 | 2 | no | — |
| 300 | C2×Q8 | — | 2 | 2 | no | — |
| 301 | C2×Q8 | — | 2 | 2 | no | — |
| 302 | C2×Q8 | — | 4 | 2 | no | — |
| 303 | C2×Q8 | — | 4 | 16 | no | — |
| 304 | C2×Q8 | — | 53 | 2 | no | — |
| 305 | C2×Q8 | — | 106 | 2 | no | — |
| 306 | C2×Q8 | — | 212 | 8 | no | — |
| 307 | C2×Q8 | #11719947 | 1 | 4 | yes | — |
| 308 | C2×D4 | — | 53 | 2 | no | — |
| 309 | C2×D4 | — | 106 | 2 | no | — |
| 310 | C2×D4 | — | 106 | 4 | no | — |
| 311 | C2×D4 | — | 106 | 2 | no | — |
| 312 | C22×C4 | — | 2 | 2 | no | — |
| 313 | C22×C4 | — | 2 | 2 | no | — |
| 314 | C22×C4 | — | 2 | 4 | no | — |
| 315 | C22×C4 | — | 2 | 4 | no | — |
| 316 | C22×C4 | — | 4 | 2 | no | — |
| 317 | C22×C4 | — | 106 | 4 | no | — |
| 318 | C22×C4 | — | 106 | 2 | no | — |
| 319 | C22×C4 | — | 106 | 2 | no | — |
| 320 | C22×C4 | — | 106 | 2 | no | — |
| 321 | C22×C4 | C2×D212 | 1 | 2 | yes | — |
| 322 | C22×C4 | C2×D212 | 1 | 1 | yes | characteristic |
| 323 | C22×C4 | C2×D212 | 1 | 2 | yes | — |
| 324 | C22×C4 | D4×D53 | 1 | 4 | yes | — |
| 325 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 326 | M16 | — | 2 | 4 | no | — |
| 327 | M16 | — | 2 | 4 | no | — |
| 328 | C2×C8 | — | 2 | 4 | no | — |
| 329 | C4⋊C4 | — | 53 | 4 | no | — |
| 330 | C4⋊C4 | — | 106 | 4 | no | — |
| 331 | C4⋊C4 | — | 106 | 8 | no | — |
| 332 | C4⋊C4 | — | 106 | 4 | no | — |
| 333 | C4⋊C4 | — | 106 | 4 | no | — |
| 334 | C4⋊C4 | — | 212 | 2 | no | — |
| 335 | C22⋊C4 | — | 106 | 8 | no | — |
| 336 | C22⋊C4 | — | 106 | 4 | no | — |
| 337 | C22⋊C4 | — | 106 | 2 | no | — |
| 338 | C22⋊C4 | — | 106 | 4 | no | — |
| 339 | C22⋊C4 | — | 212 | 2 | no | — |
| 340 | C22⋊C4 | — | 212 | 2 | no | — |
| 341 | C42 | — | 106 | 4 | no | — |
| 342 | C42 | — | 106 | 2 | no | — |
| 343 | C42 | — | 106 | 4 | no | — |
| 344 | C42 | — | 212 | 2 | no | — |
| 345 | C23 | — | 2 | 1 | no | — |
| 346 | C23 | — | 2 | 1 | no | — |
| 347 | C23 | — | 4 | 2 | no | — |
| 348 | C23 | — | 106 | 2 | no | — |
| 349 | C23 | #13133187 | 1 | 2 | yes | — |
| 350 | C23 | C22×D212 | 1 | 1 | yes | characteristic |
| 351 | Q8 | — | 2 | 8 | no | — |
| 352 | Q8 | — | 4 | 8 | no | — |
| 353 | Q8 | — | 4 | 4 | no | — |
| 354 | Q8 | — | 106 | 4 | no | — |
| 355 | Q8 | — | 212 | 4 | no | — |
| 356 | D4 | — | 106 | 4 | no | — |
| 357 | D4 | — | 212 | 4 | no | — |
| 358 | D4 | — | 212 | 8 | no | — |
| 359 | D4 | — | 212 | 2 | no | — |
| 360 | D4 | — | 212 | 2 | no | — |
| 361 | C2×C4 | — | 2 | 2 | no | — |
| 362 | C2×C4 | — | 2 | 1 | no | — |
| 363 | C2×C4 | — | 2 | 1 | no | — |
| 364 | C2×C4 | — | 2 | 2 | no | — |
| 365 | C2×C4 | — | 2 | 8 | no | — |
| 366 | C2×C4 | — | 2 | 2 | no | — |
| 367 | C2×C4 | — | 2 | 2 | no | — |
| 368 | C2×C4 | — | 2 | 2 | no | — |
| 369 | C2×C4 | — | 4 | 8 | no | — |
| 370 | C2×C4 | — | 106 | 4 | no | — |
| 371 | C2×C4 | — | 106 | 2 | no | — |
| 372 | C2×C4 | — | 212 | 8 | no | — |
| 373 | C2×C4 | — | 212 | 4 | no | — |
| 374 | C2×C4 | — | 212 | 4 | no | — |
| 375 | C2×C4 | — | 212 | 2 | no | — |
| 376 | C2×C4 | — | 212 | 2 | no | — |
| 377 | C2×C4 | — | 212 | 4 | no | — |
| 378 | C2×C4 | #13133187 | 1 | 2 | yes | — |
| 379 | C2×C4 | #13133201 | 1 | 4 | yes | — |
| 380 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 381 | C2×C4 | C2×#11719947 | 1 | 2 | yes | — |
| 382 | C2×C4 | #13133262 | 1 | 2 | yes | — |
| 383 | C8 | — | 4 | 4 | no | — |
| 384 | C22 | — | 2 | 2 | no | — |
| 385 | C22 | — | 2 | 2 | no | — |
| 386 | C22 | — | 2 | 2 | no | — |
| 387 | C22 | — | 2 | 2 | no | — |
| 388 | C22 | — | 4 | 2 | no | — |
| 389 | C22 | — | 4 | 2 | no | — |
| 390 | C22 | — | 212 | 2 | no | — |
| 391 | C22 | — | 212 | 4 | no | — |
| 392 | C22 | C2×#13133187 | 1 | 1 | yes | characteristic |
| 393 | C22 | C2×#13133201 | 1 | 1 | yes | characteristic |
| 394 | C22 | #16811185 | 1 | 1 | yes | characteristic |
| 395 | C4 | — | 2 | 2 | no | — |
| 396 | C4 | — | 2 | 4 | no | — |
| 397 | C4 | — | 4 | 2 | no | — |
| 398 | C4 | — | 424 | 2 | no | — |
| 399 | C4 | — | 424 | 2 | no | — |
| 400 | C4 | — | 212 | 2 | no | — |
| 401 | C4 | — | 212 | 4 | no | — |
| 402 | C4 | #16811260 | 1 | 4 | yes | — |
| 403 | C2 | — | 2 | 1 | no | — |
| 404 | C2 | — | 2 | 1 | no | — |
| 405 | C2 | — | 4 | 2 | no | — |
| 406 | C2 | — | 424 | 2 | no | — |
| 407 | C2 | #20278043 | 1 | 1 | yes | characteristic |
| 408 | C2 | #20284082 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20284648 | C2 | semidirect |
| 3. #20277301 | C2 | semidirect |
| 4. #20275933 | C2 | semidirect |
| 5. #20275161 | C2 | semidirect |
| 6. #20274932 | C2 | semidirect |
| 7. #20274676 | C2 | semidirect |
| 8. C53×#1784 | C2 | semidirect |
| 206. #1784 | D53 | semidirect |
| 237. C53 | #24023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288366 | 2 |
| #20284648 | 2 |
| #20277301 | 2 |
| #20275933 | 2 |
| #20275161 | 2 |
| #20274932 | 2 |
| #20274676 | 2 |
| C53×#1784 | 2 |
| #24023 | 53 |