Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3798 conjugacy classes of subgroups; only the 358 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 358 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 | D53⋊#410 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | #20291176 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #20290559 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #585×D53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C2×#13133296 | C22 | 1 | 3 | yes | complemented |
| 6 | C22×C4×#6157 | C22 | 1 | 1 | yes | characteristic, complemented |
| 7 | #16811604 | — | 2 | 3 | no | — |
| 8 | #16811603 | — | 2 | 3 | no | — |
| 9 | #16811602 | — | 2 | 6 | no | — |
| 10 | D53⋊#99 | C22 | 1 | 12 | yes | complemented |
| 11 | (C2×#6157)⋊Q8 | — | 2 | 3 | no | — |
| 12 | #16811575 | — | 2 | 3 | no | — |
| 13 | #16811571 | C22 | 1 | 12 | yes | complemented |
| 14 | C4×C22⋊#6157 | — | 2 | 6 | no | — |
| 15 | #16811460 | — | 2 | 3 | no | — |
| 16 | #16811459 | — | 2 | 6 | no | — |
| 17 | #16811459 | C4 | 1 | 3 | yes | complemented |
| 18 | #16811458 | — | 2 | 3 | no | — |
| 19 | #16811458 | C4 | 1 | 4 | yes | complemented |
| 20 | 2−1+4×D53 | — | 2 | 3 | no | — |
| 21 | H(5,𝔽2)×D53 | — | 2 | 3 | no | — |
| 22 | H(5,𝔽2)×D53 | C22 | 1 | 4 | yes | — |
| 23 | C2×#41×D53 | — | 2 | 6 | no | — |
| 24 | C2×#41×D53 | C22 | 1 | 3 | yes | — |
| 25 | C53×#585 | C4 | 1 | 1 | yes | characteristic, complemented |
| 26 | C23×#6157 | C23 | 1 | 2 | yes | — |
| 27 | #13133296 | — | 2 | 6 | no | — |
| 28 | #13133296 | — | 2 | 6 | no | — |
| 29 | C2×C4⋊#6157 | — | 2 | 3 | no | — |
| 30 | C2×C22⋊#6157 | — | 2 | 12 | no | — |
| 31 | C2×C22⋊#6157 | C23 | 1 | 6 | yes | — |
| 32 | C2×C4×#6157 | — | 2 | 3 | no | — |
| 33 | C2×C4×#6157 | — | 2 | 3 | no | — |
| 34 | C2×C4×#6157 | — | 2 | 3 | no | — |
| 35 | #13133276 | — | 2 | 12 | no | — |
| 36 | #13133275 | — | 2 | 12 | no | — |
| 37 | (C2×#6157)⋊C4 | — | 2 | 12 | no | — |
| 38 | #13133265 | — | 2 | 12 | no | — |
| 39 | #13133265 | — | 2 | 3 | no | — |
| 40 | #13133264 | — | 2 | 12 | no | — |
| 41 | #13133264 | — | 2 | 6 | no | — |
| 42 | #13133264 | — | 2 | 12 | no | — |
| 43 | #13133263 | — | 2 | 12 | no | — |
| 44 | #13133263 | — | 2 | 6 | no | — |
| 45 | #13133263 | — | 2 | 12 | no | — |
| 46 | #13133262 | — | 2 | 12 | no | — |
| 47 | #13133262 | — | 2 | 3 | no | — |
| 48 | #13133262 | — | 2 | 12 | no | — |
| 49 | #13133262 | — | 2 | 12 | no | — |
| 50 | #13133262 | C2×C4 | 1 | 12 | yes | — |
| 51 | C2×#11719949 | — | 2 | 6 | no | — |
| 52 | C2×#11719949 | D4 | 1 | 3 | yes | — |
| 53 | C2×#11719945 | — | 2 | 12 | no | — |
| 54 | C2×#11719945 | — | 2 | 6 | no | — |
| 55 | C2×#11719945 | C2×C4 | 1 | 3 | yes | — |
| 56 | C2×#11719945 | D4 | 1 | 6 | yes | — |
| 57 | C2×#11719947 | — | 2 | 6 | no | — |
| 58 | C2×#11719947 | — | 2 | 12 | no | — |
| 59 | C2×#11719947 | C2×C4 | 1 | 6 | yes | — |
| 60 | C2×#11719947 | D4 | 1 | 3 | yes | — |
| 61 | #41×D53 | — | 2 | 4 | no | — |
| 62 | #41×D53 | — | 2 | 12 | no | — |
| 63 | #41×D53 | — | 2 | 12 | no | — |
| 64 | #41×D53 | — | 2 | 12 | no | — |
| 65 | #41×D53 | — | 2 | 12 | no | — |
| 66 | #41×D53 | — | 2 | 12 | no | — |
| 67 | #41×D53 | — | 2 | 6 | no | — |
| 68 | #41×D53 | — | 2 | 12 | no | — |
| 69 | #41×D53 | — | 2 | 6 | no | — |
| 70 | #41×D53 | — | 2 | 6 | no | — |
| 71 | #41×D53 | — | 2 | 6 | no | — |
| 72 | C2×Q8×D53 | — | 2 | 6 | no | — |
| 73 | C2×Q8×D53 | D4 | 1 | 3 | yes | — |
| 74 | C2×D4×D53 | — | 2 | 6 | no | — |
| 75 | C2×D4×D53 | — | 2 | 12 | no | — |
| 76 | C2×D4×D53 | D4 | 1 | 3 | yes | — |
| 77 | C2×D4×D53 | C23 | 1 | 6 | yes | — |
| 78 | C22×C4×D53 | — | 2 | 4 | no | — |
| 79 | C22×C4×D53 | D4 | 1 | 6 | yes | — |
| 80 | C22×C4×D53 | C23 | 1 | 1 | yes | characteristic |
| 81 | 2−1+4×C53 | — | 2 | 3 | no | — |
| 82 | H(5,𝔽2)×C53 | — | 2 | 3 | no | — |
| 83 | H(5,𝔽2)×C53 | C2×C4 | 1 | 4 | yes | — |
| 84 | C2×#41×C53 | — | 2 | 6 | no | — |
| 85 | C2×#41×C53 | C2×C4 | 1 | 3 | yes | — |
| 86 | C23×D53 | — | 2 | 4 | no | — |
| 87 | C23×D53 | C2×D4 | 1 | 6 | yes | — |
| 88 | C23×D53 | C24 | 1 | 1 | yes | characteristic |
| 89 | C22×#6157 | — | 2 | 6 | no | — |
| 90 | C22×#6157 | — | 2 | 6 | no | — |
| 91 | C22×#6157 | — | 4 | 4 | no | — |
| 92 | #41×C53 | — | 2 | 4 | no | — |
| 93 | #41×C53 | — | 2 | 12 | no | — |
| 94 | #41×C53 | — | 2 | 6 | no | — |
| 95 | #41×C53 | — | 2 | 12 | no | — |
| 96 | #41×C53 | — | 2 | 6 | no | — |
| 97 | C2×Q8×C53 | — | 2 | 6 | no | — |
| 98 | C2×Q8×C53 | C22⋊C4 | 1 | 3 | yes | complemented |
| 99 | C2×D4×C53 | — | 2 | 6 | no | — |
| 100 | C2×D4×C53 | — | 2 | 12 | no | — |
| 101 | C2×D4×C53 | C22⋊C4 | 1 | 3 | yes | complemented |
| 102 | C2×D4×C53 | C22×C4 | 1 | 6 | yes | — |
| 103 | C22×C4×C53 | — | 2 | 4 | no | — |
| 104 | C22×C4×C53 | C22⋊C4 | 1 | 6 | yes | complemented |
| 105 | C22×C4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 106 | C2×C22⋊D53 | — | 2 | 12 | no | — |
| 107 | C2×C22⋊D53 | — | 2 | 12 | no | — |
| 108 | C2×C22⋊D53 | — | 2 | 12 | no | — |
| 109 | C2×C22⋊D53 | C22⋊C4 | 1 | 6 | yes | complemented |
| 110 | C2×C22⋊D53 | C22×C4 | 1 | 6 | yes | — |
| 111 | C2×C22⋊D53 | C2×D4 | 1 | 6 | yes | — |
| 112 | C22×Dic53 | — | 2 | 4 | no | — |
| 113 | C22×Dic53 | C22⋊C4 | 1 | 6 | yes | complemented |
| 114 | C22×Dic53 | C22×C4 | 1 | 1 | yes | characteristic |
| 115 | #11719949 | — | 2 | 4 | no | — |
| 116 | #11719949 | — | 2 | 12 | no | — |
| 117 | #11719949 | — | 2 | 12 | no | — |
| 118 | #11719949 | — | 2 | 6 | no | — |
| 119 | #11719949 | — | 2 | 6 | no | — |
| 120 | Q8×D53 | — | 2 | 4 | no | — |
| 121 | Q8×D53 | — | 2 | 12 | no | — |
| 122 | Q8×D53 | — | 2 | 12 | no | — |
| 123 | Q8×D53 | — | 2 | 6 | no | — |
| 124 | Q8×D53 | — | 2 | 6 | no | — |
| 125 | #11719947 | — | 2 | 12 | no | — |
| 126 | #11719947 | — | 2 | 12 | no | — |
| 127 | #11719947 | — | 2 | 12 | no | — |
| 128 | #11719947 | — | 2 | 24 | no | — |
| 129 | #11719947 | — | 2 | 12 | no | — |
| 130 | #11719947 | — | 2 | 24 | no | — |
| 131 | #11719947 | — | 2 | 12 | no | — |
| 132 | #11719947 | — | 2 | 6 | no | — |
| 133 | #11719947 | — | 2 | 6 | no | — |
| 134 | D4×D53 | — | 2 | 12 | no | — |
| 135 | D4×D53 | — | 2 | 24 | no | — |
| 136 | D4×D53 | — | 2 | 12 | no | — |
| 137 | D4×D53 | — | 2 | 12 | no | — |
| 138 | D4×D53 | — | 2 | 24 | no | — |
| 139 | D4×D53 | — | 2 | 12 | no | — |
| 140 | D4×D53 | — | 2 | 12 | no | — |
| 141 | D4×D53 | — | 2 | 6 | no | — |
| 142 | D4×D53 | — | 2 | 6 | no | — |
| 143 | #11719945 | — | 2 | 12 | no | — |
| 144 | #11719945 | — | 2 | 24 | no | — |
| 145 | #11719945 | — | 2 | 12 | no | — |
| 146 | #11719945 | — | 2 | 24 | no | — |
| 147 | #11719945 | — | 2 | 6 | no | — |
| 148 | #11719945 | — | 2 | 12 | no | — |
| 149 | #11719945 | — | 2 | 6 | no | — |
| 150 | #11719945 | — | 2 | 12 | no | — |
| 151 | #11719945 | — | 2 | 12 | no | — |
| 152 | C2×D212 | — | 2 | 12 | no | — |
| 153 | C2×D212 | — | 2 | 6 | no | — |
| 154 | C2×D212 | C22⋊C4 | 1 | 3 | yes | complemented |
| 155 | C2×D212 | C2×D4 | 1 | 6 | yes | — |
| 156 | C2×C4×D53 | — | 2 | 12 | no | — |
| 157 | C2×C4×D53 | — | 2 | 12 | no | — |
| 158 | C2×C4×D53 | — | 2 | 12 | no | — |
| 159 | C2×C4×D53 | — | 2 | 6 | no | — |
| 160 | C2×C4×D53 | — | 2 | 6 | no | — |
| 161 | C2×C4×D53 | — | 2 | 6 | no | — |
| 162 | C2×C4×D53 | — | 2 | 6 | no | — |
| 163 | C2×C4×D53 | C22⋊C4 | 1 | 6 | yes | complemented |
| 164 | C2×C4×D53 | C22⋊C4 | 1 | 6 | yes | complemented |
| 165 | C2×C4×D53 | C2×D4 | 1 | 6 | yes | — |
| 166 | C2×C4×D53 | C2×D4 | 1 | 3 | yes | — |
| 167 | C2×C4×D53 | C2×D4 | 1 | 3 | yes | — |
| 168 | C2×C4×D53 | C2×D4 | 1 | 3 | yes | — |
| 169 | C2×C4×D53 | C2×D4 | 1 | 3 | yes | — |
| 170 | C2×Dic106 | — | 2 | 6 | no | — |
| 171 | C2×Dic106 | — | 2 | 12 | no | — |
| 172 | C2×Dic106 | C22⋊C4 | 1 | 6 | yes | complemented |
| 173 | C2×Dic106 | C22⋊C4 | 1 | 3 | yes | complemented |
| 174 | C22⋊#6157 | — | 2 | 12 | no | — |
| 175 | C22⋊#6157 | — | 4 | 24 | no | — |
| 176 | C4⋊#6157 | — | 4 | 6 | no | — |
| 177 | C4×#6157 | — | 4 | 1 | no | — |
| 178 | C4×#6157 | — | 4 | 3 | no | — |
| 179 | C4×#6157 | — | 4 | 3 | no | — |
| 180 | C4×#6157 | — | 4 | 3 | no | — |
| 181 | C23×C53 | — | 2 | 4 | no | — |
| 182 | C23×C53 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 183 | C23×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 184 | C22×D53 | — | 2 | 12 | no | — |
| 185 | C22×D53 | — | 2 | 6 | no | — |
| 186 | C22×D53 | — | 2 | 6 | no | — |
| 187 | C22×D53 | — | 4 | 2 | no | — |
| 188 | C22×D53 | — | 4 | 12 | no | — |
| 189 | C22×D53 | — | 8 | 8 | no | — |
| 190 | C22×D53 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 191 | C22×D53 | C22×D4 | 1 | 3 | yes | — |
| 192 | C22×D53 | C22×D4 | 1 | 3 | yes | — |
| 193 | C2×#6157 | — | 2 | 12 | no | — |
| 194 | C2×#6157 | — | 4 | 6 | no | — |
| 195 | C2×#6157 | — | 4 | 2 | no | — |
| 196 | C2×#6157 | — | 4 | 12 | no | — |
| 197 | C2×#6157 | — | 4 | 6 | no | — |
| 198 | Q8×C53 | — | 2 | 4 | no | — |
| 199 | Q8×C53 | — | 2 | 6 | no | — |
| 200 | D4×C53 | — | 2 | 12 | no | — |
| 201 | D4×C53 | — | 2 | 12 | no | — |
| 202 | D4×C53 | — | 2 | 6 | no | — |
| 203 | C2×C4×C53 | — | 2 | 12 | no | — |
| 204 | C2×C4×C53 | — | 2 | 6 | no | — |
| 205 | C2×C4×C53 | — | 2 | 6 | no | — |
| 206 | C2×C4×C53 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 207 | C2×C4×C53 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 208 | C2×C4×C53 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 209 | C22⋊D53 | — | 2 | 24 | no | — |
| 210 | C22⋊D53 | — | 2 | 12 | no | — |
| 211 | C22⋊D53 | — | 2 | 12 | no | — |
| 212 | C22⋊D53 | — | 2 | 12 | no | — |
| 213 | C2×Dic53 | — | 2 | 12 | no | — |
| 214 | C2×Dic53 | — | 2 | 6 | no | — |
| 215 | C2×Dic53 | — | 2 | 6 | no | — |
| 216 | C2×Dic53 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 217 | C2×Dic53 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 218 | C2×Dic53 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 219 | D212 | — | 2 | 12 | no | — |
| 220 | D212 | — | 2 | 12 | no | — |
| 221 | D212 | — | 2 | 6 | no | — |
| 222 | C4×D53 | — | 2 | 24 | no | — |
| 223 | C4×D53 | — | 2 | 6 | no | — |
| 224 | C4×D53 | — | 2 | 6 | no | — |
| 225 | C4×D53 | — | 2 | 6 | no | — |
| 226 | C4×D53 | — | 2 | 6 | no | — |
| 227 | C4×D53 | — | 2 | 6 | no | — |
| 228 | C4×D53 | — | 2 | 6 | no | — |
| 229 | C4×D53 | #120 | 1 | 1 | yes | characteristic |
| 230 | C4×D53 | #120 | 1 | 3 | yes | — |
| 231 | C4×D53 | #120 | 1 | 3 | yes | — |
| 232 | C4×D53 | #120 | 1 | 3 | yes | — |
| 233 | C4×D53 | #120 | 1 | 6 | yes | — |
| 234 | Dic106 | — | 2 | 12 | no | — |
| 235 | Dic106 | — | 2 | 6 | no | — |
| 236 | Dic106 | — | 2 | 12 | no | — |
| 237 | #20608 | — | 53 | 1 | no | maximal, Sylow |
| 238 | C22×C53 | — | 2 | 6 | no | — |
| 239 | C22×C53 | — | 4 | 1 | no | — |
| 240 | C22×C53 | — | 4 | 6 | no | — |
| 241 | C22×C53 | — | 8 | 4 | no | — |
| 242 | C22×C53 | C22×C22⋊C4 | 1 | 3 | yes | — |
| 243 | C2×D53 | — | 2 | 6 | no | — |
| 244 | C2×D53 | — | 2 | 6 | no | — |
| 245 | C2×D53 | — | 4 | 3 | no | — |
| 246 | C2×D53 | — | 4 | 12 | no | — |
| 247 | C2×D53 | — | 4 | 6 | no | — |
| 248 | C2×D53 | — | 8 | 6 | no | — |
| 249 | C2×D53 | — | 8 | 12 | no | — |
| 250 | C2×D53 | C2×#120 | 1 | 3 | yes | — |
| 251 | C2×D53 | C2×#120 | 1 | 1 | yes | characteristic |
| 252 | #6157 | — | 4 | 4 | no | — |
| 253 | #6157 | — | 8 | 6 | no | — |
| 254 | C4×C53 | — | 2 | 6 | no | — |
| 255 | C4×C53 | #379 | 1 | 3 | yes | — |
| 256 | C4×C53 | #379 | 1 | 1 | yes | characteristic |
| 257 | Dic53 | — | 2 | 6 | no | — |
| 258 | Dic53 | #379 | 1 | 3 | yes | — |
| 259 | Dic53 | #379 | 1 | 1 | yes | characteristic |
| 260 | C2×#585 | — | 53 | 1 | no | — |
| 261 | C2×#410 | — | 53 | 3 | no | — |
| 262 | #2297 | — | 53 | 3 | no | — |
| 263 | #1790 | — | 53 | 8 | no | — |
| 264 | C2×C53 | — | 2 | 3 | no | — |
| 265 | C2×C53 | — | 4 | 6 | no | — |
| 266 | C2×C53 | C2×#379 | 1 | 1 | yes | characteristic |
| 267 | D53 | — | 2 | 3 | no | — |
| 268 | D53 | — | 4 | 6 | no | — |
| 269 | D53 | #3025 | 1 | 2 | yes | — |
| 270 | #585 | — | 53 | 4 | no | — |
| 271 | #585 | — | 53 | 3 | no | — |
| 272 | #585 | — | 106 | 6 | no | — |
| 273 | #585 | — | 106 | 3 | no | — |
| 274 | #585 | — | 106 | 3 | no | — |
| 275 | #585 | #6157 | 1 | 1 | yes | characteristic, complemented |
| 276 | C2×2−1+4 | — | 106 | 3 | no | — |
| 277 | C2×H(5,𝔽2) | — | 53 | 4 | no | — |
| 278 | C2×H(5,𝔽2) | — | 106 | 3 | no | — |
| 279 | C22×#41 | — | 53 | 3 | no | — |
| 280 | C22×#41 | — | 106 | 6 | no | — |
| 281 | C2×#117 | — | 53 | 3 | no | — |
| 282 | C22×C42 | — | 53 | 1 | no | — |
| 283 | #410 | — | 106 | 6 | no | — |
| 284 | #410 | — | 106 | 3 | no | — |
| 285 | #410 | — | 106 | 3 | no | — |
| 286 | C2×#99 | — | 53 | 12 | no | — |
| 287 | #391 | — | 106 | 3 | no | — |
| 288 | #390 | — | 106 | 3 | no | — |
| 289 | #386 | — | 53 | 12 | no | — |
| 290 | C4×C22⋊C4 | — | 106 | 6 | no | — |
| 291 | C53 | #20608 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 292 | 2−1+4 | — | 2 | 3 | no | — |
| 293 | 2−1+4 | — | 106 | 12 | no | — |
| 294 | 2−1+4 | — | 106 | 12 | no | — |
| 295 | 2−1+4 | — | 106 | 6 | no | — |
| 296 | 2−1+4 | — | 106 | 12 | no | — |
| 297 | 2−1+4 | — | 106 | 3 | no | — |
| 298 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 299 | H(5,𝔽2) | — | 53 | 12 | no | — |
| 300 | H(5,𝔽2) | — | 106 | 12 | no | — |
| 301 | H(5,𝔽2) | — | 106 | 12 | no | — |
| 302 | H(5,𝔽2) | — | 106 | 12 | no | — |
| 303 | H(5,𝔽2) | — | 106 | 12 | no | — |
| 304 | H(5,𝔽2) | — | 106 | 6 | no | — |
| 305 | H(5,𝔽2) | — | 106 | 12 | no | — |
| 306 | H(5,𝔽2) | — | 106 | 3 | no | — |
| 307 | H(5,𝔽2) | C2×#6157 | 1 | 4 | yes | — |
| 308 | C2×#41 | — | 2 | 6 | no | — |
| 309 | C2×#41 | — | 53 | 3 | no | — |
| 310 | C2×#41 | — | 53 | 3 | no | — |
| 311 | C2×#41 | — | 53 | 6 | no | — |
| 312 | C2×#41 | — | 53 | 6 | no | — |
| 313 | C2×#41 | — | 53 | 3 | no | — |
| 314 | C2×#41 | — | 106 | 12 | no | — |
| 315 | C2×#41 | — | 106 | 12 | no | — |
| 316 | C2×#41 | — | 106 | 6 | no | — |
| 317 | C2×#41 | — | 106 | 6 | no | — |
| 318 | C2×#41 | — | 106 | 6 | no | — |
| 319 | C2×#41 | — | 106 | 6 | no | — |
| 320 | C2×#41 | — | 106 | 12 | no | — |
| 321 | C2×#41 | — | 106 | 12 | no | — |
| 322 | C2×#41 | — | 106 | 12 | no | — |
| 323 | C2×#41 | — | 106 | 6 | no | — |
| 324 | C2×#41 | — | 106 | 6 | no | — |
| 325 | C2×#41 | — | 106 | 4 | no | — |
| 326 | C2×#41 | — | 106 | 12 | no | — |
| 327 | C2×#41 | — | 106 | 12 | no | — |
| 328 | C2×#41 | — | 106 | 12 | no | — |
| 329 | C2×#41 | — | 106 | 6 | no | — |
| 330 | C2×#41 | C2×#6157 | 1 | 3 | yes | — |
| 331 | C22×Q8 | — | 53 | 3 | no | — |
| 332 | C22×Q8 | — | 106 | 6 | no | — |
| 333 | C22×D4 | — | 53 | 3 | no | — |
| 334 | C22×D4 | — | 53 | 6 | no | — |
| 335 | C22×D4 | — | 106 | 12 | no | — |
| 336 | C22×D4 | — | 106 | 6 | no | — |
| 337 | C23×C4 | — | 53 | 1 | no | — |
| 338 | C23×C4 | — | 53 | 6 | no | — |
| 339 | C23×C4 | — | 53 | 2 | no | — |
| 340 | C23×C4 | — | 106 | 4 | no | — |
| 341 | #117 | — | 106 | 6 | no | — |
| 342 | #117 | — | 106 | 6 | no | — |
| 343 | C2×C4⋊C4 | — | 106 | 3 | no | — |
| 344 | C2×C22⋊C4 | — | 53 | 6 | no | — |
| 345 | C2×C22⋊C4 | — | 106 | 12 | no | — |
| 346 | C2×C42 | — | 106 | 3 | no | — |
| 347 | C2×C42 | — | 106 | 3 | no | — |
| 348 | C2×C42 | — | 106 | 3 | no | — |
| 349 | #99 | — | 106 | 12 | no | — |
| 350 | #99 | — | 106 | 12 | no | — |
| 351 | #95 | — | 106 | 12 | no | — |
| 352 | C24 | — | 53 | 1 | no | — |
| 353 | C24 | — | 53 | 6 | no | — |
| 354 | C24 | — | 106 | 4 | no | — |
| 355 | #41 | — | 2 | 4 | no | — |
| 356 | #41 | — | 2 | 12 | no | — |
| 357 | #41 | — | 2 | 6 | no | — |
| 358 | #41 | — | 2 | 12 | no | — |
| 359 | #41 | — | 2 | 6 | no | — |
| 360 | #41 | — | 106 | 12 | no | — |
| 361 | #41 | — | 106 | 12 | no | — |
| 362 | #41 | — | 106 | 12 | no | — |
| 363 | #41 | — | 106 | 24 | no | — |
| 364 | #41 | — | 106 | 24 | no | — |
| 365 | #41 | — | 106 | 12 | no | — |
| 366 | #41 | — | 106 | 12 | no | — |
| 367 | #41 | — | 106 | 6 | no | — |
| 368 | #41 | — | 106 | 12 | no | — |
| 369 | #41 | — | 106 | 6 | no | — |
| 370 | #41 | — | 106 | 24 | no | — |
| 371 | #41 | — | 106 | 6 | no | — |
| 372 | #41 | — | 106 | 6 | no | — |
| 373 | #41 | — | 106 | 12 | no | — |
| 374 | #41 | — | 106 | 12 | no | — |
| 375 | #41 | — | 106 | 24 | no | — |
| 376 | #41 | — | 106 | 12 | no | — |
| 377 | #41 | — | 106 | 4 | no | — |
| 378 | #41 | — | 106 | 12 | no | — |
| 379 | #41 | — | 106 | 12 | no | — |
| 380 | #41 | — | 106 | 6 | no | — |
| 381 | #41 | — | 106 | 6 | no | — |
| 382 | #41 | — | 106 | 12 | no | — |
| 383 | C2×Q8 | — | 2 | 6 | no | — |
| 384 | C2×Q8 | — | 53 | 6 | no | — |
| 385 | C2×Q8 | — | 53 | 3 | no | — |
| 386 | C2×Q8 | — | 106 | 12 | no | — |
| 387 | C2×Q8 | — | 106 | 6 | no | — |
| 388 | C2×Q8 | — | 106 | 6 | no | — |
| 389 | C2×Q8 | — | 106 | 6 | no | — |
| 390 | C2×Q8 | — | 106 | 4 | no | — |
| 391 | C2×Q8 | — | 106 | 12 | no | — |
| 392 | C2×Q8 | — | 106 | 12 | no | — |
| 393 | C2×Q8 | C22⋊#6157 | 1 | 3 | yes | complemented |
| 394 | C2×D4 | — | 2 | 6 | no | — |
| 395 | C2×D4 | — | 2 | 12 | no | — |
| 396 | C2×D4 | — | 53 | 6 | no | — |
| 397 | C2×D4 | — | 53 | 6 | no | — |
| 398 | C2×D4 | — | 53 | 6 | no | — |
| 399 | C2×D4 | — | 53 | 3 | no | — |
| 400 | C2×D4 | — | 53 | 6 | no | — |
| 401 | C2×D4 | — | 106 | 12 | no | — |
| 402 | C2×D4 | — | 106 | 6 | no | — |
| 403 | C2×D4 | — | 106 | 6 | no | — |
| 404 | C2×D4 | — | 106 | 6 | no | — |
| 405 | C2×D4 | — | 106 | 12 | no | — |
| 406 | C2×D4 | — | 106 | 12 | no | — |
| 407 | C2×D4 | — | 106 | 24 | no | — |
| 408 | C2×D4 | — | 106 | 12 | no | — |
| 409 | C2×D4 | — | 106 | 12 | no | — |
| 410 | C2×D4 | — | 106 | 24 | no | — |
| 411 | C2×D4 | — | 106 | 12 | no | — |
| 412 | C2×D4 | — | 106 | 12 | no | — |
| 413 | C2×D4 | — | 106 | 12 | no | — |
| 414 | C2×D4 | — | 106 | 12 | no | — |
| 415 | C2×D4 | C22⋊#6157 | 1 | 3 | yes | complemented |
| 416 | C2×D4 | C22×#6157 | 1 | 6 | yes | — |
| 417 | C22×C4 | — | 2 | 4 | no | — |
| 418 | C22×C4 | — | 53 | 1 | no | — |
| 419 | C22×C4 | — | 53 | 3 | no | — |
| 420 | C22×C4 | — | 53 | 3 | no | — |
| 421 | C22×C4 | — | 53 | 3 | no | — |
| 422 | C22×C4 | — | 53 | 3 | no | — |
| 423 | C22×C4 | — | 53 | 6 | no | — |
| 424 | C22×C4 | — | 53 | 6 | no | — |
| 425 | C22×C4 | — | 53 | 6 | no | — |
| 426 | C22×C4 | — | 53 | 6 | no | — |
| 427 | C22×C4 | — | 106 | 6 | no | — |
| 428 | C22×C4 | — | 106 | 6 | no | — |
| 429 | C22×C4 | — | 106 | 6 | no | — |
| 430 | C22×C4 | — | 106 | 6 | no | — |
| 431 | C22×C4 | — | 106 | 12 | no | — |
| 432 | C22×C4 | — | 106 | 12 | no | — |
| 433 | C22×C4 | — | 106 | 12 | no | — |
| 434 | C22×C4 | — | 106 | 4 | no | — |
| 435 | C22×C4 | — | 106 | 6 | no | — |
| 436 | C22×C4 | — | 106 | 6 | no | — |
| 437 | C22×C4 | — | 212 | 4 | no | — |
| 438 | C22×C4 | C22⋊#6157 | 1 | 6 | yes | complemented |
| 439 | C22×C4 | C22×#6157 | 1 | 1 | yes | characteristic |
| 440 | C4⋊C4 | — | 212 | 6 | no | — |
| 441 | C22⋊C4 | — | 106 | 12 | no | — |
| 442 | C22⋊C4 | — | 212 | 24 | no | — |
| 443 | C42 | — | 212 | 3 | no | — |
| 444 | C42 | — | 212 | 1 | no | — |
| 445 | C42 | — | 212 | 3 | no | — |
| 446 | C42 | — | 212 | 3 | no | — |
| 447 | C23 | — | 2 | 4 | no | — |
| 448 | C23 | — | 53 | 3 | no | — |
| 449 | C23 | — | 53 | 3 | no | — |
| 450 | C23 | — | 53 | 6 | no | — |
| 451 | C23 | — | 106 | 6 | no | — |
| 452 | C23 | — | 106 | 6 | no | — |
| 453 | C23 | — | 106 | 12 | no | — |
| 454 | C23 | — | 424 | 8 | no | — |
| 455 | C23 | — | 212 | 2 | no | — |
| 456 | C23 | — | 212 | 12 | no | — |
| 457 | C23 | C2×C22⋊#6157 | 1 | 6 | yes | — |
| 458 | C23 | C23×#6157 | 1 | 1 | yes | characteristic |
| 459 | Q8 | — | 2 | 4 | no | — |
| 460 | Q8 | — | 2 | 6 | no | — |
| 461 | Q8 | — | 106 | 12 | no | — |
| 462 | Q8 | — | 106 | 12 | no | — |
| 463 | Q8 | — | 106 | 6 | no | — |
| 464 | D4 | — | 2 | 12 | no | — |
| 465 | D4 | — | 2 | 12 | no | — |
| 466 | D4 | — | 2 | 6 | no | — |
| 467 | D4 | — | 106 | 12 | no | — |
| 468 | D4 | — | 106 | 12 | no | — |
| 469 | D4 | — | 106 | 12 | no | — |
| 470 | D4 | — | 106 | 12 | no | — |
| 471 | D4 | — | 106 | 24 | no | — |
| 472 | D4 | — | 106 | 12 | no | — |
| 473 | D4 | — | 106 | 6 | no | — |
| 474 | C2×C4 | — | 2 | 12 | no | — |
| 475 | C2×C4 | — | 2 | 6 | no | — |
| 476 | C2×C4 | — | 2 | 6 | no | — |
| 477 | C2×C4 | — | 53 | 3 | no | — |
| 478 | C2×C4 | — | 53 | 3 | no | — |
| 479 | C2×C4 | — | 53 | 3 | no | — |
| 480 | C2×C4 | — | 53 | 3 | no | — |
| 481 | C2×C4 | — | 53 | 6 | no | — |
| 482 | C2×C4 | — | 53 | 1 | no | — |
| 483 | C2×C4 | — | 53 | 3 | no | — |
| 484 | C2×C4 | — | 53 | 6 | no | — |
| 485 | C2×C4 | — | 106 | 6 | no | — |
| 486 | C2×C4 | — | 106 | 6 | no | — |
| 487 | C2×C4 | — | 106 | 6 | no | — |
| 488 | C2×C4 | — | 106 | 6 | no | — |
| 489 | C2×C4 | — | 106 | 24 | no | — |
| 490 | C2×C4 | — | 106 | 6 | no | — |
| 491 | C2×C4 | — | 106 | 6 | no | — |
| 492 | C2×C4 | — | 106 | 12 | no | — |
| 493 | C2×C4 | — | 106 | 6 | no | — |
| 494 | C2×C4 | — | 106 | 6 | no | — |
| 495 | C2×C4 | — | 106 | 12 | no | — |
| 496 | C2×C4 | — | 212 | 6 | no | — |
| 497 | C2×C4 | — | 212 | 12 | no | — |
| 498 | C2×C4 | — | 212 | 2 | no | — |
| 499 | C2×C4 | — | 212 | 6 | no | — |
| 500 | C2×C4 | C2×C22⋊#6157 | 1 | 6 | yes | — |
| 501 | C2×C4 | C2×C22⋊#6157 | 1 | 3 | yes | — |
| 502 | C2×C4 | C2×C22⋊#6157 | 1 | 3 | yes | — |
| 503 | C22 | — | 2 | 6 | no | — |
| 504 | C22 | — | 4 | 1 | no | — |
| 505 | C22 | — | 4 | 6 | no | — |
| 506 | C22 | — | 8 | 4 | no | — |
| 507 | C22 | — | 53 | 1 | no | — |
| 508 | C22 | — | 53 | 3 | no | — |
| 509 | C22 | — | 106 | 6 | no | — |
| 510 | C22 | — | 106 | 6 | no | — |
| 511 | C22 | — | 424 | 6 | no | — |
| 512 | C22 | — | 424 | 12 | no | — |
| 513 | C22 | — | 212 | 3 | no | — |
| 514 | C22 | — | 212 | 6 | no | — |
| 515 | C22 | — | 212 | 12 | no | — |
| 516 | C22 | C22×C22⋊#6157 | 1 | 3 | yes | — |
| 517 | C4 | — | 2 | 6 | no | — |
| 518 | C4 | — | 53 | 1 | no | — |
| 519 | C4 | — | 53 | 3 | no | — |
| 520 | C4 | — | 106 | 6 | no | — |
| 521 | C4 | — | 424 | 6 | no | — |
| 522 | C4 | — | 212 | 4 | no | — |
| 523 | C4 | #16811564 | 1 | 3 | yes | — |
| 524 | C4 | #16811564 | 1 | 1 | yes | characteristic |
| 525 | C2 | — | 2 | 3 | no | — |
| 526 | C2 | — | 4 | 6 | no | — |
| 527 | C2 | — | 53 | 2 | no | — |
| 528 | C2 | — | 106 | 3 | no | — |
| 529 | C2 | — | 212 | 6 | no | — |
| 530 | C2 | C2×#16811564 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D53⋊#410 | C2 | semidirect |
| 2. #20291176 | C2 | semidirect |
| 3. #20290559 | C2 | semidirect |
| 5. C2×#13133296 | C22 | semidirect |
| 6. C22×C4×#6157 | C22 | semidirect |
| 10. D53⋊#99 | C22 | semidirect |
| 13. #16811571 | C22 | semidirect |
| 17. #16811459 | C4 | semidirect |
| 19. #16811458 | C4 | semidirect |
| 25. C53×#585 | C4 | semidirect |
| 98. C2×Q8×C53 | C22⋊C4 | semidirect |
| 101. C2×D4×C53 | C22⋊C4 | semidirect |
| 104. C22×C4×C53 | C22⋊C4 | semidirect |
| 109. C2×C22⋊D53 | C22⋊C4 | semidirect |
| 113. C22×Dic53 | C22⋊C4 | semidirect |
| 154. C2×D212 | C22⋊C4 | semidirect |
| 163. C2×C4×D53 | C22⋊C4 | semidirect |
| 164. C2×C4×D53 | C22⋊C4 | semidirect |
| 172. C2×Dic106 | C22⋊C4 | semidirect |
| 173. C2×Dic106 | C22⋊C4 | semidirect |
| 275. #585 | #6157 | semidirect |
| 291. C53 | #20608 | semidirect |
| 393. C2×Q8 | C22⋊#6157 | semidirect |
| 415. C2×D4 | C22⋊#6157 | semidirect |
| 438. C22×C4 | C22⋊#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#410 | 2 |
| #20291176 | 2 |
| #20290559 | 2 |
| #585×D53 | 2 |
| #20608 | 53 |