← #32911223
Subgroups — #32911223
Order 18176.
10796 conjugacy classes of subgroups.
The subgroup lattice has 434 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#17986835 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22603053 | C2 | 1 | 16 | yes | maximal, complemented |
| 3 | #22603051 | C2 | 1 | 16 | yes | maximal, complemented |
| 4 | C2×#17986766 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#17986765 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #568×D71 | C2 | 1 | 16 | yes | maximal, complemented |
| 7 | C2×#568×C71 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #17986835 | C4 | 1 | 8 | yes | — |
| 9 | #17986835 | C4 | 1 | 8 | yes | — |
| 10 | #17986835 | C22 | 1 | 8 | yes | — |
| 11 | #17986835 | C22 | 1 | 8 | yes | — |
| 12 | C2×#14556176 | C4 | 1 | 2 | yes | — |
| 13 | C2×#14556175 | C4 | 1 | 4 | yes | — |
| 14 | C2×#14556174 | C4 | 1 | 4 | yes | — |
| 15 | C2×#14556173 | C4 | 1 | 6 | yes | — |
| 16 | C22×#11765865 | C22 | 1 | 6 | yes | — |
| 17 | C2×#41×D71 | C22 | 1 | 8 | yes | — |
| 18 | #17986766 | C22 | 1 | 8 | yes | complemented |
| 19 | #17986766 | C22 | 1 | 8 | yes | complemented |
| 20 | #17986765 | C22 | 1 | 48 | yes | complemented |
| 21 | #17986765 | C22 | 1 | 16 | yes | complemented |
| 22 | #17986765 | C22 | 1 | 48 | yes | complemented |
| 23 | #17986765 | C22 | 1 | 48 | yes | complemented |
| 24 | #17986764 | C22 | 1 | 128 | yes | complemented |
| 25 | C2×#14556136 | C22 | 1 | 48 | yes | complemented |
| 26 | C2×#14556135 | C22 | 1 | 8 | yes | complemented |
| 27 | C2×#14556134 | C22 | 1 | 48 | yes | complemented |
| 28 | #131×D71 | C22 | 1 | 128 | yes | complemented |
| 29 | C22×#11765849 | C22 | 1 | 6 | yes | complemented |
| 30 | C2×M16×D71 | C22 | 1 | 48 | yes | complemented |
| 31 | C22×#41×C71 | C22 | 1 | 1 | yes | characteristic |
| 32 | #568×C71 | C22 | 1 | 8 | yes | complemented |
| 33 | #568×C71 | C22 | 1 | 8 | yes | complemented |
| 34 | C2×#131×C71 | C22 | 1 | 8 | yes | complemented |
| 35 | C22×M16×C71 | C22 | 1 | 6 | yes | complemented |
| 36 | #14556176 | C2×C4 | 1 | 16 | yes | — |
| 37 | #14556176 | C2×C4 | 1 | 16 | yes | — |
| 38 | #14556175 | C2×C4 | 1 | 32 | yes | — |
| 39 | #14556175 | C2×C4 | 1 | 32 | yes | — |
| 40 | #14556174 | C2×C4 | 1 | 32 | yes | — |
| 41 | #14556174 | C2×C4 | 1 | 32 | yes | — |
| 42 | #14556173 | C2×C4 | 1 | 48 | yes | — |
| 43 | #14556173 | C2×C4 | 1 | 48 | yes | — |
| 44 | C2×#11765866 | C2×C4 | 1 | 8 | yes | — |
| 45 | C2×#11765865 | C2×C4 | 1 | 12 | yes | — |
| 46 | C2×#11765865 | C2×C4 | 1 | 12 | yes | — |
| 47 | C2×#11765865 | C2×C4 | 1 | 24 | yes | — |
| 48 | C2×#11765865 | C2×C4 | 1 | 24 | yes | — |
| 49 | C2×#11765865 | C23 | 1 | 12 | yes | — |
| 50 | C2×#11765865 | C23 | 1 | 4 | yes | — |
| 51 | C2×#11765865 | C23 | 1 | 24 | yes | — |
| 52 | C2×#11765865 | C23 | 1 | 24 | yes | — |
| 53 | C2×#11765864 | C2×C4 | 1 | 24 | yes | — |
| 54 | #41×D71 | C2×C4 | 1 | 64 | yes | — |
| 55 | #41×D71 | C23 | 1 | 64 | yes | — |
| 56 | C22×Dic142 | C2×C4 | 1 | 6 | yes | — |
| 57 | C2×Q8×D71 | C2×C4 | 1 | 8 | yes | — |
| 58 | C22×D284 | C2×C4 | 1 | 6 | yes | — |
| 59 | C22×C22⋊D71 | C2×C4 | 1 | 12 | yes | — |
| 60 | C2×D4×D71 | C2×C4 | 1 | 24 | yes | — |
| 61 | C22×C4×D71 | C23 | 1 | 12 | yes | — |
| 62 | #14556136 | C23 | 1 | 192 | yes | complemented |
| 63 | #14556136 | C23 | 1 | 64 | yes | complemented |
| 64 | #14556135 | C23 | 1 | 64 | yes | complemented |
| 65 | #14556134 | C23 | 1 | 192 | yes | complemented |
| 66 | #14556134 | C23 | 1 | 64 | yes | complemented |
| 67 | C2×#11765849 | C23 | 1 | 24 | yes | — |
| 68 | C2×#11765849 | C23 | 1 | 4 | yes | — |
| 69 | C2×#11765849 | C23 | 1 | 24 | yes | complemented |
| 70 | C2×#11765849 | C23 | 1 | 12 | yes | complemented |
| 71 | C2×#11765848 | C23 | 1 | 96 | yes | complemented |
| 72 | M16×D71 | C23 | 1 | 64 | yes | — |
| 73 | M16×D71 | C23 | 1 | 192 | yes | complemented |
| 74 | C22×C71⋊C8 | C23 | 1 | 12 | yes | complemented |
| 75 | C2×C8×D71 | C23 | 1 | 96 | yes | complemented |
| 76 | C2×#41×C71 | C2×C4 | 1 | 4 | yes | — |
| 77 | C2×#41×C71 | C2×C4 | 1 | 4 | yes | — |
| 78 | C2×#41×C71 | C2×C4 | 1 | 4 | yes | — |
| 79 | C2×#41×C71 | C23 | 1 | 4 | yes | — |
| 80 | C2×#41×C71 | C23 | 1 | 4 | yes | — |
| 81 | C2×#41×C71 | C23 | 1 | 4 | yes | — |
| 82 | C22×Q8×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 83 | C22×D4×C71 | C2×C4 | 1 | 3 | yes | — |
| 84 | C23×C4×C71 | C23 | 1 | 3 | yes | — |
| 85 | #131×C71 | C23 | 1 | 64 | yes | complemented |
| 86 | C2×M16×C71 | C23 | 1 | 4 | yes | — |
| 87 | C2×M16×C71 | C23 | 1 | 24 | yes | — |
| 88 | C2×M16×C71 | C23 | 1 | 12 | yes | complemented |
| 89 | C2×M16×C71 | C23 | 1 | 24 | yes | complemented |
| 90 | C22×C8×C71 | C23 | 1 | 12 | yes | complemented |
| 91 | C23×D71 | C22×C4 | 1 | 12 | yes | — |
| 92 | #11765866 | C22×C4 | 1 | 64 | yes | — |
| 93 | #11765865 | C22×C4 | 1 | 48 | yes | — |
| 94 | #11765865 | C22×C4 | 1 | 8 | yes | — |
| 95 | #11765865 | C22×C4 | 1 | 8 | yes | — |
| 96 | #11765865 | C22×C4 | 1 | 48 | yes | — |
| 97 | #11765865 | C22×C4 | 1 | 48 | yes | — |
| 98 | #11765865 | C22×C4 | 1 | 48 | yes | — |
| 99 | #11765865 | C22×C4 | 1 | 48 | yes | — |
| 100 | #11765865 | C24 | 1 | 48 | yes | — |
| 101 | #11765865 | C24 | 1 | 8 | yes | — |
| 102 | #11765865 | C24 | 1 | 8 | yes | — |
| 103 | #11765864 | C22×C4 | 1 | 192 | yes | — |
| 104 | C2×Dic142 | C22×C4 | 1 | 12 | yes | — |
| 105 | C2×Dic142 | C22×C4 | 1 | 4 | yes | — |
| 106 | C2×Dic142 | C22×C4 | 1 | 24 | yes | — |
| 107 | C2×Dic142 | C22×C4 | 1 | 24 | yes | — |
| 108 | Q8×D71 | C22×C4 | 1 | 64 | yes | — |
| 109 | C2×D284 | C22×C4 | 1 | 12 | yes | — |
| 110 | C2×D284 | C22×C4 | 1 | 4 | yes | — |
| 111 | C2×D284 | C22×C4 | 1 | 24 | yes | — |
| 112 | C2×D284 | C22×C4 | 1 | 24 | yes | — |
| 113 | C2×C22⋊D71 | C22×C4 | 1 | 24 | yes | — |
| 114 | C2×C22⋊D71 | C22×C4 | 1 | 8 | yes | — |
| 115 | C2×C22⋊D71 | C22×C4 | 1 | 48 | yes | — |
| 116 | C2×C22⋊D71 | C22×C4 | 1 | 48 | yes | — |
| 117 | D4×D71 | C22×C4 | 1 | 192 | yes | — |
| 118 | C22×Dic71 | C22×C4 | 1 | 12 | yes | — |
| 119 | C2×C4×D71 | C22×C4 | 1 | 24 | yes | — |
| 120 | C2×C4×D71 | C22×C4 | 1 | 48 | yes | — |
| 121 | C2×C4×D71 | C24 | 1 | 8 | yes | — |
| 122 | C2×C4×D71 | C24 | 1 | 48 | yes | — |
| 123 | #11765849 | C24 | 1 | 8 | yes | — |
| 124 | #11765849 | C24 | 1 | 48 | yes | — |
| 125 | #11765849 | C24 | 1 | 8 | yes | — |
| 126 | #11765848 | C24 | 1 | 128 | yes | — |
| 127 | C2×C71⋊C8 | C24 | 1 | 48 | yes | — |
| 128 | C2×C71⋊C8 | C24 | 1 | 8 | yes | — |
| 129 | C8×D71 | C24 | 1 | 128 | yes | — |
| 130 | C24×C71 | C22×C4 | 1 | 3 | yes | — |
| 131 | #41×C71 | C22×C4 | 1 | 16 | yes | — |
| 132 | #41×C71 | C22×C4 | 1 | 16 | yes | — |
| 133 | #41×C71 | C22×C4 | 1 | 16 | yes | — |
| 134 | #41×C71 | C24 | 1 | 16 | yes | — |
| 135 | C2×Q8×C71 | C22×C4 | 1 | 4 | yes | — |
| 136 | C2×Q8×C71 | C22×C4 | 1 | 4 | yes | — |
| 137 | C2×Q8×C71 | C22×C4 | 1 | 4 | yes | — |
| 138 | C2×D4×C71 | C22×C4 | 1 | 12 | yes | — |
| 139 | C2×D4×C71 | C22×C4 | 1 | 12 | yes | — |
| 140 | C2×D4×C71 | C22×C4 | 1 | 12 | yes | — |
| 141 | C22×C4×C71 | C22×C4 | 1 | 6 | yes | — |
| 142 | C22×C4×C71 | C22×C4 | 1 | 3 | yes | — |
| 143 | C22×C4×C71 | C22×C4 | 1 | 6 | yes | — |
| 144 | C22×C4×C71 | C22×C4 | 1 | 6 | yes | — |
| 145 | C22×C4×C71 | C24 | 1 | 6 | yes | — |
| 146 | C22×C4×C71 | C24 | 1 | 6 | yes | — |
| 147 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 148 | C22×C4×C71 | C24 | 1 | 6 | yes | — |
| 149 | M16×C71 | C24 | 1 | 8 | yes | — |
| 150 | M16×C71 | C24 | 1 | 8 | yes | — |
| 151 | M16×C71 | C24 | 1 | 48 | yes | — |
| 152 | C2×C8×C71 | C24 | 1 | 8 | yes | — |
| 153 | C2×C8×C71 | C24 | 1 | 48 | yes | — |
| 154 | C23×C71 | — | 8 | 3 | no | — |
| 155 | C23×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 156 | C23×C71 | C23×C4 | 1 | 6 | yes | — |
| 157 | C23×C71 | C23×C4 | 1 | 6 | yes | — |
| 158 | C23×C71 | C23×C4 | 1 | 6 | yes | — |
| 159 | C22×D71 | — | 8 | 12 | no | — |
| 160 | C22×D71 | C23×C4 | 1 | 8 | yes | — |
| 161 | C22×D71 | C23×C4 | 1 | 48 | yes | — |
| 162 | Q8×C71 | C23×C4 | 1 | 16 | yes | — |
| 163 | D4×C71 | C23×C4 | 1 | 48 | yes | — |
| 164 | C2×C4×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 165 | C2×C4×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 166 | C2×C4×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 167 | C2×C4×C71 | C23×C4 | 1 | 6 | yes | — |
| 168 | C2×C4×C71 | C23×C4 | 1 | 6 | yes | — |
| 169 | C2×C4×C71 | C23×C4 | 1 | 6 | yes | — |
| 170 | C2×C4×C71 | C23×C4 | 1 | 12 | yes | — |
| 171 | C2×C4×C71 | C23×C4 | 1 | 12 | yes | — |
| 172 | C2×C4×C71 | C23×C4 | 1 | 12 | yes | — |
| 173 | C2×C4×C71 | C25 | 1 | 1 | yes | characteristic |
| 174 | C2×C4×C71 | C25 | 1 | 12 | yes | — |
| 175 | C2×C4×C71 | C25 | 1 | 1 | yes | characteristic |
| 176 | C2×C4×C71 | C25 | 1 | 1 | yes | characteristic |
| 177 | C22⋊D71 | C23×C4 | 1 | 96 | yes | — |
| 178 | C22⋊D71 | C23×C4 | 1 | 16 | yes | — |
| 179 | C22⋊D71 | C23×C4 | 1 | 16 | yes | — |
| 180 | C2×Dic71 | C23×C4 | 1 | 8 | yes | — |
| 181 | C2×Dic71 | C23×C4 | 1 | 48 | yes | — |
| 182 | D284 | C23×C4 | 1 | 48 | yes | — |
| 183 | D284 | C23×C4 | 1 | 8 | yes | — |
| 184 | D284 | C23×C4 | 1 | 8 | yes | — |
| 185 | C4×D71 | C23×C4 | 1 | 16 | yes | — |
| 186 | C4×D71 | C23×C4 | 1 | 96 | yes | — |
| 187 | C4×D71 | C25 | 1 | 16 | yes | — |
| 188 | Dic142 | C23×C4 | 1 | 48 | yes | — |
| 189 | Dic142 | C23×C4 | 1 | 8 | yes | — |
| 190 | Dic142 | C23×C4 | 1 | 8 | yes | — |
| 191 | C8×C71 | C25 | 1 | 16 | yes | — |
| 192 | C71⋊C8 | C25 | 1 | 16 | yes | — |
| 193 | C22×C71 | — | 4 | 6 | no | — |
| 194 | C22×C71 | — | 4 | 1 | no | — |
| 195 | C22×C71 | — | 4 | 6 | no | — |
| 196 | C22×C71 | — | 4 | 6 | no | — |
| 197 | C22×C71 | C24×C4 | 1 | 1 | yes | characteristic |
| 198 | C22×C71 | C24×C4 | 1 | 12 | yes | — |
| 199 | C22×C71 | C24×C4 | 1 | 1 | yes | characteristic |
| 200 | C22×C71 | C24×C4 | 1 | 1 | yes | characteristic |
| 201 | C2×D71 | — | 4 | 8 | no | — |
| 202 | C2×D71 | — | 4 | 48 | no | — |
| 203 | C2×D71 | C24×C4 | 1 | 16 | yes | — |
| 204 | C4×C71 | C24×C4 | 1 | 1 | yes | characteristic |
| 205 | C4×C71 | C24×C4 | 1 | 1 | yes | characteristic |
| 206 | C4×C71 | C24×C4 | 1 | 12 | yes | — |
| 207 | C4×C71 | C24×C4 | 1 | 1 | yes | characteristic |
| 208 | C4×C71 | C26 | 1 | 1 | yes | characteristic |
| 209 | Dic71 | C24×C4 | 1 | 16 | yes | — |
| 210 | #63076 | — | 71 | 1 | no | maximal, Sylow |
| 211 | C2×C71 | — | 2 | 1 | no | — |
| 212 | C2×C71 | — | 2 | 12 | no | — |
| 213 | C2×C71 | — | 2 | 1 | no | — |
| 214 | C2×C71 | — | 2 | 1 | no | — |
| 215 | C2×C71 | C25×C4 | 1 | 1 | yes | characteristic |
| 216 | D71 | — | 2 | 16 | no | — |
| 217 | C2×#585 | — | 71 | 1 | no | — |
| 218 | #3573 | — | 71 | 16 | no | — |
| 219 | #3573 | — | 71 | 16 | no | — |
| 220 | C2×#568 | — | 71 | 1 | no | — |
| 221 | C2×#568 | — | 71 | 16 | no | — |
| 222 | C2×#568 | — | 71 | 12 | no | — |
| 223 | C2×#568 | D71 | 1 | 1 | yes | characteristic, complemented |
| 224 | C71 | #63076 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 225 | #585 | — | 71 | 8 | no | — |
| 226 | #585 | — | 71 | 8 | no | — |
| 227 | #585 | — | 71 | 8 | no | — |
| 228 | #585 | — | 71 | 8 | no | — |
| 229 | C2×2−1+4 | — | 71 | 4 | no | — |
| 230 | C2×2−1+4 | — | 71 | 2 | no | — |
| 231 | C2×H(5,𝔽2) | — | 71 | 4 | no | — |
| 232 | C2×H(5,𝔽2) | — | 71 | 6 | no | — |
| 233 | C22×#41 | — | 71 | 8 | no | — |
| 234 | C22×#41 | — | 71 | 6 | no | — |
| 235 | C22×#41 | C2×D71 | 1 | 1 | yes | characteristic |
| 236 | #568 | — | 71 | 8 | no | — |
| 237 | #568 | — | 71 | 8 | no | — |
| 238 | #568 | — | 71 | 128 | no | — |
| 239 | #568 | — | 71 | 48 | no | — |
| 240 | #568 | — | 71 | 16 | no | — |
| 241 | #568 | — | 71 | 48 | no | — |
| 242 | #568 | — | 71 | 48 | no | — |
| 243 | #568 | C2×D71 | 1 | 8 | yes | complemented |
| 244 | #568 | C2×D71 | 1 | 8 | yes | complemented |
| 245 | C2×#131 | — | 71 | 8 | no | — |
| 246 | C2×#131 | — | 71 | 128 | no | — |
| 247 | C2×#131 | — | 71 | 48 | no | — |
| 248 | C2×#131 | — | 71 | 48 | no | — |
| 249 | C2×#131 | C2×D71 | 1 | 8 | yes | complemented |
| 250 | C22×M16 | — | 71 | 6 | no | — |
| 251 | C22×M16 | — | 71 | 48 | no | — |
| 252 | C22×M16 | C2×D71 | 1 | 6 | yes | complemented |
| 253 | 2−1+4 | — | 71 | 32 | no | — |
| 254 | 2−1+4 | — | 71 | 32 | no | — |
| 255 | 2−1+4 | — | 71 | 16 | no | — |
| 256 | 2−1+4 | — | 71 | 16 | no | — |
| 257 | H(5,𝔽2) | — | 71 | 32 | no | — |
| 258 | H(5,𝔽2) | — | 71 | 32 | no | — |
| 259 | H(5,𝔽2) | — | 71 | 48 | no | — |
| 260 | H(5,𝔽2) | — | 71 | 48 | no | — |
| 261 | C2×#41 | — | 71 | 64 | no | — |
| 262 | C2×#41 | — | 71 | 64 | no | — |
| 263 | C2×#41 | — | 71 | 8 | no | — |
| 264 | C2×#41 | — | 71 | 24 | no | — |
| 265 | C2×#41 | — | 71 | 12 | no | — |
| 266 | C2×#41 | — | 71 | 12 | no | — |
| 267 | C2×#41 | — | 71 | 24 | no | — |
| 268 | C2×#41 | — | 71 | 24 | no | — |
| 269 | C2×#41 | — | 71 | 24 | no | — |
| 270 | C2×#41 | — | 71 | 24 | no | — |
| 271 | C2×#41 | — | 71 | 12 | no | — |
| 272 | C2×#41 | — | 71 | 4 | no | — |
| 273 | C2×#41 | C4×D71 | 1 | 4 | yes | — |
| 274 | C2×#41 | C4×D71 | 1 | 4 | yes | — |
| 275 | C2×#41 | C4×D71 | 1 | 4 | yes | — |
| 276 | C2×#41 | C22×D71 | 1 | 4 | yes | — |
| 277 | C2×#41 | C22×D71 | 1 | 4 | yes | — |
| 278 | C2×#41 | C22×D71 | 1 | 4 | yes | — |
| 279 | C22×Q8 | — | 71 | 8 | no | — |
| 280 | C22×Q8 | — | 71 | 6 | no | — |
| 281 | C22×Q8 | C4×D71 | 1 | 1 | yes | characteristic |
| 282 | C22×D4 | — | 71 | 12 | no | — |
| 283 | C22×D4 | — | 71 | 24 | no | — |
| 284 | C22×D4 | — | 71 | 6 | no | — |
| 285 | C22×D4 | C4×D71 | 1 | 3 | yes | — |
| 286 | C23×C4 | — | 71 | 12 | no | — |
| 287 | C23×C4 | C22×D71 | 1 | 3 | yes | — |
| 288 | #131 | — | 71 | 64 | no | — |
| 289 | #131 | — | 71 | 192 | no | — |
| 290 | #131 | — | 71 | 64 | no | — |
| 291 | #131 | — | 71 | 192 | no | — |
| 292 | #131 | — | 71 | 64 | no | — |
| 293 | #131 | C22×D71 | 1 | 64 | yes | complemented |
| 294 | C2×M16 | — | 71 | 24 | no | — |
| 295 | C2×M16 | — | 71 | 4 | no | — |
| 296 | C2×M16 | — | 71 | 12 | no | — |
| 297 | C2×M16 | — | 71 | 24 | no | — |
| 298 | C2×M16 | — | 71 | 64 | no | — |
| 299 | C2×M16 | — | 71 | 192 | no | — |
| 300 | C2×M16 | — | 71 | 96 | no | — |
| 301 | C2×M16 | C22×D71 | 1 | 24 | yes | — |
| 302 | C2×M16 | C22×D71 | 1 | 4 | yes | — |
| 303 | C2×M16 | C22×D71 | 1 | 24 | yes | complemented |
| 304 | C2×M16 | C22×D71 | 1 | 12 | yes | complemented |
| 305 | C22×C8 | — | 71 | 12 | no | — |
| 306 | C22×C8 | — | 71 | 96 | no | — |
| 307 | C22×C8 | C22×D71 | 1 | 12 | yes | complemented |
| 308 | C24 | — | 71 | 12 | no | — |
| 309 | C24 | C2×C4×D71 | 1 | 3 | yes | — |
| 310 | #41 | — | 71 | 64 | no | — |
| 311 | #41 | — | 71 | 192 | no | — |
| 312 | #41 | — | 71 | 48 | no | — |
| 313 | #41 | — | 71 | 8 | no | — |
| 314 | #41 | — | 71 | 8 | no | — |
| 315 | #41 | — | 71 | 48 | no | — |
| 316 | #41 | — | 71 | 48 | no | — |
| 317 | #41 | — | 71 | 48 | no | — |
| 318 | #41 | — | 71 | 48 | no | — |
| 319 | #41 | — | 71 | 8 | no | — |
| 320 | #41 | — | 71 | 48 | no | — |
| 321 | #41 | — | 71 | 8 | no | — |
| 322 | #41 | C2×C4×D71 | 1 | 16 | yes | — |
| 323 | #41 | C2×C4×D71 | 1 | 16 | yes | — |
| 324 | #41 | C2×C4×D71 | 1 | 16 | yes | — |
| 325 | #41 | C23×D71 | 1 | 16 | yes | — |
| 326 | C2×Q8 | — | 71 | 64 | no | — |
| 327 | C2×Q8 | — | 71 | 12 | no | — |
| 328 | C2×Q8 | — | 71 | 4 | no | — |
| 329 | C2×Q8 | — | 71 | 24 | no | — |
| 330 | C2×Q8 | — | 71 | 24 | no | — |
| 331 | C2×Q8 | C2×C4×D71 | 1 | 4 | yes | — |
| 332 | C2×Q8 | C2×C4×D71 | 1 | 4 | yes | — |
| 333 | C2×Q8 | C2×C4×D71 | 1 | 4 | yes | — |
| 334 | C2×D4 | — | 71 | 24 | no | — |
| 335 | C2×D4 | — | 71 | 8 | no | — |
| 336 | C2×D4 | — | 71 | 48 | no | — |
| 337 | C2×D4 | — | 71 | 48 | no | — |
| 338 | C2×D4 | — | 71 | 192 | no | — |
| 339 | C2×D4 | — | 71 | 12 | no | — |
| 340 | C2×D4 | — | 71 | 4 | no | — |
| 341 | C2×D4 | — | 71 | 24 | no | — |
| 342 | C2×D4 | — | 71 | 24 | no | — |
| 343 | C2×D4 | C2×C4×D71 | 1 | 12 | yes | — |
| 344 | C2×D4 | C2×C4×D71 | 1 | 12 | yes | — |
| 345 | C2×D4 | C2×C4×D71 | 1 | 12 | yes | — |
| 346 | C22×C4 | — | 71 | 12 | no | — |
| 347 | C22×C4 | — | 71 | 24 | no | — |
| 348 | C22×C4 | — | 71 | 48 | no | — |
| 349 | C22×C4 | — | 71 | 48 | no | — |
| 350 | C22×C4 | — | 71 | 8 | no | — |
| 351 | C22×C4 | C2×C4×D71 | 1 | 6 | yes | — |
| 352 | C22×C4 | C2×C4×D71 | 1 | 3 | yes | — |
| 353 | C22×C4 | C2×C4×D71 | 1 | 6 | yes | — |
| 354 | C22×C4 | C2×C4×D71 | 1 | 6 | yes | — |
| 355 | C22×C4 | C23×D71 | 1 | 6 | yes | — |
| 356 | C22×C4 | C23×D71 | 1 | 6 | yes | — |
| 357 | C22×C4 | C23×D71 | 1 | 6 | yes | — |
| 358 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 359 | M16 | — | 71 | 8 | no | — |
| 360 | M16 | — | 71 | 48 | no | — |
| 361 | M16 | — | 71 | 8 | no | — |
| 362 | M16 | — | 71 | 128 | no | — |
| 363 | M16 | C23×D71 | 1 | 8 | yes | — |
| 364 | M16 | C23×D71 | 1 | 48 | yes | — |
| 365 | M16 | C23×D71 | 1 | 8 | yes | — |
| 366 | C2×C8 | — | 71 | 8 | no | — |
| 367 | C2×C8 | — | 71 | 48 | no | — |
| 368 | C2×C8 | — | 71 | 128 | no | — |
| 369 | C2×C8 | C23×D71 | 1 | 48 | yes | — |
| 370 | C2×C8 | C23×D71 | 1 | 8 | yes | — |
| 371 | C23 | — | 8 | 3 | no | — |
| 372 | C23 | — | 568 | 12 | no | — |
| 373 | C23 | — | 71 | 8 | no | — |
| 374 | C23 | — | 71 | 48 | no | — |
| 375 | C23 | C22×C4×D71 | 1 | 6 | yes | — |
| 376 | C23 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 377 | C23 | C22×C4×D71 | 1 | 6 | yes | — |
| 378 | C23 | C22×C4×D71 | 1 | 6 | yes | — |
| 379 | Q8 | — | 71 | 48 | no | — |
| 380 | Q8 | — | 71 | 8 | no | — |
| 381 | Q8 | — | 71 | 8 | no | — |
| 382 | Q8 | C22×C4×D71 | 1 | 16 | yes | — |
| 383 | D4 | — | 71 | 96 | no | — |
| 384 | D4 | — | 71 | 16 | no | — |
| 385 | D4 | — | 71 | 16 | no | — |
| 386 | D4 | — | 71 | 48 | no | — |
| 387 | D4 | — | 71 | 8 | no | — |
| 388 | D4 | — | 71 | 8 | no | — |
| 389 | D4 | C22×C4×D71 | 1 | 48 | yes | — |
| 390 | C2×C4 | — | 71 | 8 | no | — |
| 391 | C2×C4 | — | 71 | 48 | no | — |
| 392 | C2×C4 | — | 71 | 16 | no | — |
| 393 | C2×C4 | — | 71 | 96 | no | — |
| 394 | C2×C4 | — | 71 | 16 | no | — |
| 395 | C2×C4 | C22×C4×D71 | 1 | 6 | yes | — |
| 396 | C2×C4 | C22×C4×D71 | 1 | 12 | yes | — |
| 397 | C2×C4 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 398 | C2×C4 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 399 | C2×C4 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 400 | C2×C4 | C22×C4×D71 | 1 | 12 | yes | — |
| 401 | C2×C4 | C22×C4×D71 | 1 | 12 | yes | — |
| 402 | C2×C4 | C22×C4×D71 | 1 | 6 | yes | — |
| 403 | C2×C4 | C22×C4×D71 | 1 | 6 | yes | — |
| 404 | C2×C4 | C24×D71 | 1 | 1 | yes | characteristic |
| 405 | C2×C4 | C24×D71 | 1 | 12 | yes | — |
| 406 | C2×C4 | C24×D71 | 1 | 1 | yes | characteristic |
| 407 | C2×C4 | C24×D71 | 1 | 1 | yes | characteristic |
| 408 | C8 | — | 71 | 16 | no | — |
| 409 | C8 | C24×D71 | 1 | 16 | yes | — |
| 410 | C22 | — | 4 | 1 | no | — |
| 411 | C22 | — | 4 | 6 | no | — |
| 412 | C22 | — | 4 | 6 | no | — |
| 413 | C22 | — | 4 | 6 | no | — |
| 414 | C22 | — | 284 | 8 | no | — |
| 415 | C22 | — | 284 | 48 | no | — |
| 416 | C22 | — | 71 | 16 | no | — |
| 417 | C22 | C23×C4×D71 | 1 | 1 | yes | characteristic |
| 418 | C22 | C23×C4×D71 | 1 | 12 | yes | — |
| 419 | C22 | C23×C4×D71 | 1 | 1 | yes | characteristic |
| 420 | C22 | C23×C4×D71 | 1 | 1 | yes | characteristic |
| 421 | C4 | — | 71 | 16 | no | — |
| 422 | C4 | C23×C4×D71 | 1 | 1 | yes | characteristic |
| 423 | C4 | C23×C4×D71 | 1 | 12 | yes | — |
| 424 | C4 | C23×C4×D71 | 1 | 1 | yes | characteristic |
| 425 | C4 | C23×C4×D71 | 1 | 1 | yes | characteristic |
| 426 | C4 | C25×D71 | 1 | 1 | yes | characteristic |
| 427 | C2 | — | 2 | 1 | no | — |
| 428 | C2 | — | 2 | 1 | no | — |
| 429 | C2 | — | 2 | 1 | no | — |
| 430 | C2 | — | 2 | 12 | no | — |
| 431 | C2 | — | 142 | 16 | no | — |
| 432 | C2 | C24×C4×D71 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta