← #34031577
Subgroups — #34031577
Order 18688.
1950 conjugacy classes of subgroups.
The subgroup lattice has 684 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22626755 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #22626752 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #22626742 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #22626739 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #22626724 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22626658 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22626651 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #22626616 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #22626610 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C4×#14556679 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C4×D73⋊M16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #22623228 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | C2×#14556679 | C22 | 1 | 4 | yes | — |
| 14 | C2×D73⋊M16 | C22 | 1 | 2 | yes | — |
| 15 | #17989639 | C22 | 1 | 8 | yes | complemented |
| 16 | #17989638 | C22 | 1 | 8 | yes | complemented |
| 17 | #17989621 | C22 | 1 | 8 | yes | — |
| 18 | #17989620 | C22 | 1 | 8 | yes | — |
| 19 | #17989619 | C22 | 1 | 8 | yes | — |
| 20 | #17989617 | C22 | 1 | 8 | yes | — |
| 21 | #17989617 | C22 | 1 | 8 | yes | complemented |
| 22 | #17989617 | C22 | 1 | 8 | yes | complemented |
| 23 | #17989612 | C22 | 1 | 8 | yes | complemented |
| 24 | #17989610 | C22 | 1 | 2 | yes | — |
| 25 | #17989607 | C22 | 1 | 2 | yes | — |
| 26 | #17989606 | C22 | 1 | 4 | yes | complemented |
| 27 | #17989605 | C22 | 1 | 2 | yes | — |
| 28 | #17989605 | C22 | 1 | 4 | yes | complemented |
| 29 | #17989604 | C22 | 1 | 2 | yes | — |
| 30 | #17989594 | C22 | 1 | 4 | yes | — |
| 31 | #17989592 | C22 | 1 | 2 | yes | — |
| 32 | #17989562 | C22 | 1 | 4 | yes | — |
| 33 | #17989558 | C22 | 1 | 2 | yes | — |
| 34 | #17989552 | C22 | 1 | 4 | yes | — |
| 35 | #17989552 | C22 | 1 | 8 | yes | complemented |
| 36 | C4×#11924038 | C22 | 1 | 2 | yes | — |
| 37 | C4×#11924038 | C22 | 1 | 2 | yes | — |
| 38 | C4×#11924038 | C22 | 1 | 2 | yes | — |
| 39 | C4×#11924038 | C22 | 1 | 4 | yes | complemented |
| 40 | C4×#11924037 | C22 | 1 | 2 | yes | — |
| 41 | C4×#11924037 | C22 | 1 | 2 | yes | — |
| 42 | #17989546 | C22 | 1 | 2 | yes | — |
| 43 | C4×#11924036 | C22 | 1 | 1 | yes | characteristic |
| 44 | C4×#11924036 | C22 | 1 | 1 | yes | characteristic |
| 45 | C4×#11924036 | C22 | 1 | 4 | yes | complemented |
| 46 | #17989142 | C4 | 1 | 1 | yes | characteristic |
| 47 | #17989142 | C22 | 1 | 1 | yes | characteristic |
| 48 | #17989138 | C4 | 1 | 1 | yes | characteristic |
| 49 | #17989138 | C22 | 1 | 1 | yes | characteristic |
| 50 | #17989137 | C4 | 1 | 1 | yes | characteristic |
| 51 | #17989124 | C4 | 1 | 2 | yes | — |
| 52 | #17989124 | C4 | 1 | 2 | yes | — |
| 53 | #17989123 | C4 | 1 | 2 | yes | — |
| 54 | #17989123 | C22 | 1 | 2 | yes | — |
| 55 | #17989122 | C4 | 1 | 2 | yes | — |
| 56 | #17989122 | C22 | 1 | 2 | yes | — |
| 57 | #17989100 | C4 | 1 | 2 | yes | — |
| 58 | #17989100 | C22 | 1 | 2 | yes | — |
| 59 | #17989099 | C4 | 1 | 2 | yes | — |
| 60 | C4×#11924029 | C22 | 1 | 2 | yes | — |
| 61 | C4×#11924029 | C22 | 1 | 2 | yes | — |
| 62 | #17989055 | C22 | 1 | 2 | yes | — |
| 63 | C2×C42×D73 | C22 | 1 | 1 | yes | characteristic |
| 64 | #533×C73 | C4 | 1 | 1 | yes | characteristic |
| 65 | #14556679 | — | 2 | 16 | no | — |
| 66 | C2×#11924038 | C23 | 1 | 4 | yes | — |
| 67 | C2×#11924038 | C23 | 1 | 4 | yes | — |
| 68 | C2×#11924038 | C23 | 1 | 8 | yes | — |
| 69 | D73⋊M16 | — | 2 | 8 | no | — |
| 70 | C2×#11924037 | C23 | 1 | 4 | yes | — |
| 71 | C2×#11924036 | C23 | 1 | 2 | yes | — |
| 72 | C2×#11924036 | C23 | 1 | 8 | yes | — |
| 73 | C2×#11924036 | C23 | 1 | 2 | yes | — |
| 74 | #14556658 | C23 | 1 | 4 | yes | — |
| 75 | #14556658 | C23 | 1 | 8 | yes | — |
| 76 | #14556658 | C23 | 1 | 4 | yes | — |
| 77 | C4⋊#10596833 | C23 | 1 | 8 | yes | — |
| 78 | #14556648 | C23 | 1 | 4 | yes | — |
| 79 | #14556648 | C23 | 1 | 8 | yes | — |
| 80 | #14556648 | C23 | 1 | 8 | yes | — |
| 81 | C22⋊#10596833 | C23 | 1 | 4 | yes | — |
| 82 | #14556646 | C23 | 1 | 4 | yes | — |
| 83 | #14556646 | C23 | 1 | 8 | yes | — |
| 84 | #14556646 | C23 | 1 | 4 | yes | — |
| 85 | #14556646 | C23 | 1 | 4 | yes | — |
| 86 | C4×#10596833 | C23 | 1 | 8 | yes | — |
| 87 | C4×#10596833 | C23 | 1 | 2 | yes | — |
| 88 | C4×#10596833 | C23 | 1 | 2 | yes | — |
| 89 | C4×#10596833 | C23 | 1 | 2 | yes | — |
| 90 | C4×#10596833 | C23 | 1 | 2 | yes | — |
| 91 | C4×#10596833 | C23 | 1 | 4 | yes | — |
| 92 | C2×#11924029 | C2×C4 | 1 | 2 | yes | — |
| 93 | C2×#11924029 | C23 | 1 | 2 | yes | — |
| 94 | C2×#11924028 | C2×C4 | 1 | 2 | yes | — |
| 95 | C22×C4×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 96 | C22×C4×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 97 | C22×C4×D73 | C23 | 1 | 1 | yes | characteristic |
| 98 | #14556591 | C2×C4 | 1 | 1 | yes | characteristic |
| 99 | #14556588 | C2×C4 | 1 | 1 | yes | characteristic |
| 100 | #14556586 | C2×C4 | 1 | 4 | yes | — |
| 101 | #14556586 | C2×C4 | 1 | 4 | yes | — |
| 102 | #14556582 | C2×C4 | 1 | 2 | yes | — |
| 103 | #14556582 | C2×C4 | 1 | 2 | yes | — |
| 104 | #14556580 | C2×C4 | 1 | 2 | yes | — |
| 105 | #14556580 | C2×C4 | 1 | 2 | yes | — |
| 106 | #14556579 | C2×C4 | 1 | 2 | yes | — |
| 107 | #14556576 | C2×C4 | 1 | 4 | yes | — |
| 108 | #14556576 | C2×C4 | 1 | 4 | yes | — |
| 109 | #14556575 | C2×C4 | 1 | 4 | yes | — |
| 110 | #14556571 | C2×C4 | 1 | 2 | yes | — |
| 111 | #14556571 | C2×C4 | 1 | 2 | yes | — |
| 112 | #14556567 | C2×C4 | 1 | 2 | yes | — |
| 113 | #14556567 | C2×C4 | 1 | 2 | yes | — |
| 114 | #14556566 | C2×C4 | 1 | 2 | yes | — |
| 115 | #14556566 | C2×C4 | 1 | 2 | yes | — |
| 116 | #14556566 | C2×C4 | 1 | 2 | yes | — |
| 117 | #14556566 | C2×C4 | 1 | 2 | yes | — |
| 118 | #14556565 | C2×C4 | 1 | 2 | yes | — |
| 119 | #14556565 | C2×C4 | 1 | 2 | yes | — |
| 120 | #14556561 | C2×C4 | 1 | 4 | yes | — |
| 121 | Q8×Dic73 | C2×C4 | 1 | 2 | yes | — |
| 122 | Q8×Dic73 | C23 | 1 | 2 | yes | — |
| 123 | #14556556 | C2×C4 | 1 | 2 | yes | — |
| 124 | #14556556 | C23 | 1 | 2 | yes | — |
| 125 | C4×D292 | C2×C4 | 1 | 2 | yes | — |
| 126 | C4×D292 | C2×C4 | 1 | 2 | yes | — |
| 127 | C4×D292 | C2×C4 | 1 | 4 | yes | — |
| 128 | C4×D292 | C2×C4 | 1 | 4 | yes | — |
| 129 | #14556553 | C2×C4 | 1 | 2 | yes | — |
| 130 | #14556553 | C2×C4 | 1 | 4 | yes | — |
| 131 | #14556553 | C2×C4 | 1 | 2 | yes | — |
| 132 | #14556553 | C23 | 1 | 2 | yes | — |
| 133 | #14556553 | C23 | 1 | 4 | yes | — |
| 134 | #14556553 | C23 | 1 | 2 | yes | — |
| 135 | #14556551 | C2×C4 | 1 | 4 | yes | — |
| 136 | #14556551 | C23 | 1 | 4 | yes | — |
| 137 | #14556549 | C2×C4 | 1 | 4 | yes | — |
| 138 | #14556549 | C2×C4 | 1 | 2 | yes | — |
| 139 | #14556549 | C23 | 1 | 4 | yes | — |
| 140 | #14556549 | C23 | 1 | 2 | yes | — |
| 141 | #14556548 | C2×C4 | 1 | 4 | yes | — |
| 142 | C2×C4×Dic73 | C2×C4 | 1 | 1 | yes | characteristic |
| 143 | C2×C4×Dic73 | C23 | 1 | 1 | yes | characteristic |
| 144 | C2×C4×Dic73 | C23 | 1 | 1 | yes | characteristic |
| 145 | C42×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 146 | C42×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 147 | C42×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 148 | C42×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 149 | C42×D73 | C23 | 1 | 1 | yes | characteristic |
| 150 | C42×D73 | C23 | 1 | 1 | yes | characteristic |
| 151 | C42×D73 | C23 | 1 | 1 | yes | characteristic |
| 152 | C42×D73 | C23 | 1 | 1 | yes | characteristic |
| 153 | C42×D73 | C23 | 1 | 4 | yes | — |
| 154 | C4⋊Q8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 155 | C4⋊Q8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 156 | #125×C73 | C2×C4 | 1 | 2 | yes | — |
| 157 | C22⋊Q8×C73 | C2×C4 | 1 | 2 | yes | — |
| 158 | C22⋊Q8×C73 | C2×C4 | 1 | 2 | yes | — |
| 159 | C4×Q8×C73 | C2×C4 | 1 | 2 | yes | — |
| 160 | C4×Q8×C73 | C2×C4 | 1 | 2 | yes | — |
| 161 | #117×C73 | C2×C4 | 1 | 2 | yes | — |
| 162 | C2×C42×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 163 | #11924038 | — | 2 | 8 | no | — |
| 164 | #11924038 | — | 2 | 8 | no | — |
| 165 | #11924038 | — | 2 | 16 | no | — |
| 166 | #11924037 | — | 2 | 8 | no | — |
| 167 | #11924036 | — | 2 | 4 | no | — |
| 168 | #11924036 | — | 2 | 16 | no | — |
| 169 | #11924036 | #41 | 1 | 8 | yes | complemented |
| 170 | C2×#10596833 | C24 | 1 | 4 | yes | — |
| 171 | C2×#10596833 | C24 | 1 | 8 | yes | — |
| 172 | C2×#10596833 | C24 | 1 | 4 | yes | — |
| 173 | C23×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 174 | #11924029 | — | 2 | 8 | no | — |
| 175 | #11924029 | — | 4 | 4 | no | — |
| 176 | #11924028 | — | 4 | 4 | no | — |
| 177 | C2×Dic146 | C22×C4 | 1 | 2 | yes | — |
| 178 | C2×D292 | C22×C4 | 1 | 4 | yes | — |
| 179 | C2×D292 | C22×C4 | 1 | 2 | yes | — |
| 180 | C2×D292 | C22×C4 | 1 | 2 | yes | — |
| 181 | C2×D292 | C22×C4 | 1 | 4 | yes | — |
| 182 | C2×D292 | C22×C4 | 1 | 2 | yes | — |
| 183 | C2×C22⋊D73 | C22×C4 | 1 | 4 | yes | — |
| 184 | C22×Dic73 | C22×C4 | 1 | 1 | yes | characteristic |
| 185 | C22×Dic73 | C22×C4 | 1 | 1 | yes | characteristic |
| 186 | C22×Dic73 | C24 | 1 | 1 | yes | characteristic |
| 187 | C2×C4×D73 | — | 2 | 4 | no | — |
| 188 | C2×C4×D73 | — | 4 | 2 | no | — |
| 189 | C2×C4×D73 | — | 4 | 2 | no | — |
| 190 | C2×C4×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 191 | C2×C4×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 192 | C2×C4×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 193 | C2×C4×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 194 | C2×C4×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 195 | C2×C4×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 196 | C2×C4×D73 | C22×C4 | 1 | 4 | yes | — |
| 197 | C2×C4×D73 | C22×C4 | 1 | 4 | yes | — |
| 198 | C2×C4×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 199 | C2×C4×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 200 | C2×C4×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 201 | C2×C4×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 202 | C2×C4×D73 | C24 | 1 | 4 | yes | — |
| 203 | C2×C4×D73 | C24 | 1 | 1 | yes | characteristic |
| 204 | C2×C4×D73 | C24 | 1 | 1 | yes | characteristic |
| 205 | C4⋊Dic73 | C22×C4 | 1 | 2 | yes | — |
| 206 | C4⋊Dic73 | C22×C4 | 1 | 4 | yes | — |
| 207 | C4⋊Dic73 | C22×C4 | 1 | 2 | yes | — |
| 208 | C4⋊Dic73 | C22×C4 | 1 | 4 | yes | — |
| 209 | #11924007 | C22×C4 | 1 | 4 | yes | — |
| 210 | #11924007 | C22×C4 | 1 | 4 | yes | — |
| 211 | #11924005 | C22×C4 | 1 | 4 | yes | — |
| 212 | #11924005 | C22×C4 | 1 | 4 | yes | — |
| 213 | #11924005 | C22×C4 | 1 | 4 | yes | — |
| 214 | #11924005 | C22×C4 | 1 | 4 | yes | — |
| 215 | #11924005 | C22×C4 | 1 | 4 | yes | — |
| 216 | #11924005 | C22×C4 | 1 | 4 | yes | — |
| 217 | #11924005 | C22×C4 | 1 | 4 | yes | — |
| 218 | #11924005 | C22×C4 | 1 | 4 | yes | — |
| 219 | C4×Dic73 | C22×C4 | 1 | 1 | yes | characteristic |
| 220 | C4×Dic73 | C22×C4 | 1 | 1 | yes | characteristic |
| 221 | C4×Dic73 | C22×C4 | 1 | 1 | yes | characteristic |
| 222 | C4×Dic73 | C22×C4 | 1 | 1 | yes | characteristic |
| 223 | C4×Dic73 | C22×C4 | 1 | 1 | yes | characteristic |
| 224 | C4×Dic73 | C22×C4 | 1 | 1 | yes | characteristic |
| 225 | C4×Dic73 | C22×C4 | 1 | 1 | yes | characteristic |
| 226 | C4×Dic73 | C22×C4 | 1 | 1 | yes | characteristic |
| 227 | C4×Dic73 | C22×C4 | 1 | 4 | yes | — |
| 228 | C4×Dic73 | C24 | 1 | 1 | yes | characteristic |
| 229 | C4×Dic73 | C24 | 1 | 1 | yes | characteristic |
| 230 | C4×Dic73 | C24 | 1 | 1 | yes | characteristic |
| 231 | C4×Dic73 | C24 | 1 | 1 | yes | characteristic |
| 232 | C4×Dic73 | C24 | 1 | 4 | yes | — |
| 233 | C2×Q8×C73 | C22×C4 | 1 | 2 | yes | — |
| 234 | C2×Q8×C73 | C22×C4 | 1 | 2 | yes | — |
| 235 | C22×C4×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 236 | C22×C4×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 237 | C22×C4×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 238 | C4⋊C4×C73 | C22×C4 | 1 | 2 | yes | — |
| 239 | C4⋊C4×C73 | C22×C4 | 1 | 2 | yes | — |
| 240 | C4⋊C4×C73 | C22×C4 | 1 | 4 | yes | — |
| 241 | C4⋊C4×C73 | C22×C4 | 1 | 4 | yes | — |
| 242 | C4⋊C4×C73 | C22×C4 | 1 | 2 | yes | — |
| 243 | C4⋊C4×C73 | C22×C4 | 1 | 2 | yes | — |
| 244 | C22⋊C4×C73 | C22×C4 | 1 | 4 | yes | — |
| 245 | C42×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 246 | C42×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 247 | C42×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 248 | C42×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 249 | C42×C73 | C22×C4 | 1 | 4 | yes | — |
| 250 | C23×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 251 | C22×D73 | — | 2 | 2 | no | — |
| 252 | C22×D73 | — | 4 | 1 | no | — |
| 253 | C22×D73 | — | 4 | 1 | no | — |
| 254 | C22×D73 | C23×C4 | 1 | 4 | yes | — |
| 255 | C22×D73 | C23×C4 | 1 | 1 | yes | characteristic |
| 256 | C22×D73 | C23×C4 | 1 | 1 | yes | characteristic |
| 257 | Q8×C73 | — | 2 | 4 | no | — |
| 258 | Q8×C73 | — | 4 | 2 | no | — |
| 259 | C2×C4×C73 | — | 2 | 2 | no | — |
| 260 | C2×C4×C73 | — | 2 | 2 | no | — |
| 261 | C2×C4×C73 | — | 4 | 1 | no | — |
| 262 | C2×C4×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 263 | C2×C4×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 264 | C2×C4×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 265 | C2×C4×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 266 | C2×C4×C73 | C23×C4 | 1 | 4 | yes | — |
| 267 | C2×C4×C73 | C23×C4 | 1 | 4 | yes | — |
| 268 | C2×C4×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 269 | C2×C4×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 270 | C22⋊D73 | — | 4 | 4 | no | — |
| 271 | C2×Dic73 | — | 2 | 2 | no | — |
| 272 | C2×Dic73 | — | 2 | 2 | no | — |
| 273 | C2×Dic73 | — | 4 | 1 | no | — |
| 274 | C2×Dic73 | C23×C4 | 1 | 1 | yes | characteristic |
| 275 | C2×Dic73 | C23×C4 | 1 | 1 | yes | characteristic |
| 276 | C2×Dic73 | C23×C4 | 1 | 1 | yes | characteristic |
| 277 | C2×Dic73 | C23×C4 | 1 | 1 | yes | characteristic |
| 278 | C2×Dic73 | C23×C4 | 1 | 4 | yes | — |
| 279 | C2×Dic73 | C23×C4 | 1 | 1 | yes | characteristic |
| 280 | C2×Dic73 | C25 | 1 | 1 | yes | characteristic |
| 281 | D292 | — | 2 | 8 | no | — |
| 282 | D292 | — | 2 | 4 | no | — |
| 283 | D292 | — | 4 | 2 | no | — |
| 284 | D292 | — | 4 | 2 | no | — |
| 285 | D292 | — | 4 | 4 | no | — |
| 286 | C4×D73 | — | 2 | 2 | no | — |
| 287 | C4×D73 | — | 2 | 2 | no | — |
| 288 | C4×D73 | — | 2 | 2 | no | — |
| 289 | C4×D73 | — | 2 | 2 | no | — |
| 290 | C4×D73 | — | 2 | 8 | no | — |
| 291 | C4×D73 | — | 2 | 2 | no | — |
| 292 | C4×D73 | — | 2 | 2 | no | — |
| 293 | C4×D73 | — | 2 | 8 | no | — |
| 294 | C4×D73 | — | 2 | 2 | no | — |
| 295 | C4×D73 | — | 2 | 8 | no | — |
| 296 | C4×D73 | — | 4 | 1 | no | — |
| 297 | C4×D73 | — | 4 | 1 | no | — |
| 298 | C4×D73 | — | 4 | 1 | no | — |
| 299 | C4×D73 | — | 4 | 1 | no | — |
| 300 | C4×D73 | C2×#41 | 1 | 4 | yes | — |
| 301 | Dic146 | — | 4 | 2 | no | — |
| 302 | #10596833 | — | 2 | 4 | no | — |
| 303 | #10596833 | — | 2 | 8 | no | — |
| 304 | #10596833 | C2×#41 | 1 | 8 | yes | — |
| 305 | C22×C73 | — | 2 | 1 | no | — |
| 306 | C22×C73 | — | 2 | 1 | no | — |
| 307 | C22×C73 | — | 2 | 1 | no | — |
| 308 | C22×C73 | C24×C4 | 1 | 1 | yes | characteristic |
| 309 | C2×D73 | — | 2 | 1 | no | — |
| 310 | C2×D73 | — | 2 | 1 | no | — |
| 311 | C2×D73 | — | 2 | 1 | no | — |
| 312 | C2×D73 | — | 2 | 4 | no | — |
| 313 | C2×D73 | — | 2 | 1 | no | — |
| 314 | C2×D73 | — | 2 | 1 | no | — |
| 315 | C2×D73 | — | 2 | 4 | no | — |
| 316 | C2×D73 | — | 2 | 4 | no | — |
| 317 | C2×D73 | — | 4 | 4 | no | — |
| 318 | C2×D73 | C4×#41 | 1 | 2 | yes | — |
| 319 | C4×C73 | — | 2 | 1 | no | — |
| 320 | C4×C73 | — | 2 | 4 | no | — |
| 321 | C4×C73 | — | 2 | 1 | no | — |
| 322 | C4×C73 | — | 2 | 1 | no | — |
| 323 | C4×C73 | — | 2 | 1 | no | — |
| 324 | C4×C73 | — | 2 | 4 | no | — |
| 325 | C4×C73 | C4×#41 | 1 | 2 | yes | — |
| 326 | C4×C73 | #568 | 1 | 2 | yes | — |
| 327 | Dic73 | — | 2 | 1 | no | — |
| 328 | Dic73 | — | 2 | 4 | no | — |
| 329 | Dic73 | — | 2 | 1 | no | — |
| 330 | Dic73 | — | 2 | 1 | no | — |
| 331 | Dic73 | — | 2 | 1 | no | — |
| 332 | Dic73 | #568 | 1 | 2 | yes | — |
| 333 | Dic73 | C22×#41 | 1 | 2 | yes | — |
| 334 | #60205 | — | 73 | 1 | no | maximal, Sylow |
| 335 | C2×C73 | — | 4 | 1 | no | — |
| 336 | C2×C73 | C2×C4×#41 | 1 | 1 | yes | characteristic |
| 337 | C2×C73 | C2×#568 | 1 | 1 | yes | characteristic |
| 338 | C2×C73 | C2×#568 | 1 | 1 | yes | characteristic |
| 339 | D73 | — | 2 | 2 | no | — |
| 340 | D73 | — | 4 | 4 | no | — |
| 341 | D73 | — | 4 | 1 | no | — |
| 342 | #3444 | — | 73 | 1 | no | — |
| 343 | #2967 | — | 73 | 4 | no | — |
| 344 | #2967 | — | 73 | 4 | no | — |
| 345 | #2965 | — | 73 | 4 | no | — |
| 346 | #2965 | — | 73 | 4 | no | — |
| 347 | #2961 | — | 73 | 2 | no | — |
| 348 | #2932 | — | 73 | 2 | no | — |
| 349 | #2930 | — | 73 | 4 | no | — |
| 350 | #2922 | — | 73 | 2 | no | — |
| 351 | #2920 | — | 73 | 1 | no | — |
| 352 | C4×#131 | — | 73 | 2 | no | — |
| 353 | C2×C4×M16 | — | 73 | 1 | no | — |
| 354 | C73 | #60205 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 355 | C2×#131 | — | 73 | 4 | no | — |
| 356 | C22×M16 | — | 73 | 2 | no | — |
| 357 | #533 | — | 73 | 1 | no | — |
| 358 | #533 | — | 73 | 1 | no | — |
| 359 | #533 | #64408 | 1 | 1 | yes | characteristic |
| 360 | #532 | — | 73 | 1 | no | — |
| 361 | #532 | — | 73 | 1 | no | — |
| 362 | #532 | — | 73 | 1 | no | — |
| 363 | #529 | — | 73 | 2 | no | — |
| 364 | #529 | — | 73 | 2 | no | — |
| 365 | #529 | — | 73 | 2 | no | — |
| 366 | #529 | — | 73 | 2 | no | — |
| 367 | #529 | — | 73 | 2 | no | — |
| 368 | #529 | — | 73 | 2 | no | — |
| 369 | #525 | — | 73 | 2 | no | — |
| 370 | #525 | — | 73 | 2 | no | — |
| 371 | #525 | — | 73 | 2 | no | — |
| 372 | C4×#41 | — | 73 | 2 | no | — |
| 373 | C4×#41 | — | 73 | 2 | no | — |
| 374 | C4×#41 | — | 73 | 2 | no | — |
| 375 | C22×C42 | — | 73 | 1 | no | — |
| 376 | #446 | — | 73 | 8 | no | — |
| 377 | #446 | — | 73 | 8 | no | — |
| 378 | #436 | — | 73 | 8 | no | — |
| 379 | #436 | — | 73 | 8 | no | — |
| 380 | #435 | — | 73 | 8 | no | — |
| 381 | #435 | — | 73 | 8 | no | — |
| 382 | #435 | — | 73 | 8 | no | — |
| 383 | #435 | — | 73 | 8 | no | — |
| 384 | #433 | — | 73 | 8 | no | — |
| 385 | #432 | — | 73 | 2 | no | — |
| 386 | #432 | — | 73 | 2 | no | — |
| 387 | #431 | — | 73 | 2 | no | — |
| 388 | #431 | — | 73 | 2 | no | — |
| 389 | #431 | — | 73 | 4 | no | — |
| 390 | #431 | — | 73 | 4 | no | — |
| 391 | #424 | — | 73 | 4 | no | — |
| 392 | #423 | — | 73 | 2 | no | — |
| 393 | #408 | — | 73 | 4 | no | — |
| 394 | #407 | — | 73 | 2 | no | — |
| 395 | #405 | — | 73 | 4 | no | — |
| 396 | #405 | — | 73 | 8 | no | — |
| 397 | C4×M16 | — | 73 | 2 | no | — |
| 398 | C4×M16 | — | 73 | 2 | no | — |
| 399 | C4×M16 | — | 73 | 2 | no | — |
| 400 | C4×M16 | — | 73 | 2 | no | — |
| 401 | C4×M16 | — | 73 | 2 | no | — |
| 402 | C4×M16 | — | 73 | 4 | no | — |
| 403 | C2×#97 | — | 73 | 2 | no | — |
| 404 | C2×C4×C8 | — | 73 | 1 | no | — |
| 405 | C2×C4×C8 | — | 73 | 1 | no | — |
| 406 | C2×C4×C8 | — | 73 | 4 | no | — |
| 407 | C2×#41 | — | 73 | 2 | no | — |
| 408 | C2×#41 | — | 73 | 2 | no | — |
| 409 | C2×#41 | — | 73 | 2 | no | — |
| 410 | C23×C4 | — | 73 | 1 | no | — |
| 411 | C23×C4 | — | 73 | 1 | no | — |
| 412 | C23×C4 | — | 73 | 1 | no | — |
| 413 | #131 | — | 146 | 16 | no | — |
| 414 | C2×M16 | — | 73 | 4 | no | — |
| 415 | C2×M16 | — | 73 | 4 | no | — |
| 416 | C2×M16 | — | 73 | 4 | no | — |
| 417 | C2×M16 | — | 73 | 8 | no | — |
| 418 | C2×M16 | — | 146 | 8 | no | — |
| 419 | C22×C8 | — | 73 | 2 | no | — |
| 420 | C22×C8 | — | 73 | 2 | no | — |
| 421 | C22×C8 | — | 73 | 8 | no | — |
| 422 | C4⋊Q8 | — | 73 | 1 | no | — |
| 423 | C4⋊Q8 | C2×#64408 | 1 | 1 | yes | characteristic |
| 424 | C4⋊Q8 | C2×#64408 | 1 | 1 | yes | characteristic |
| 425 | #127 | — | 73 | 1 | no | — |
| 426 | #126 | — | 73 | 4 | no | — |
| 427 | #126 | — | 73 | 4 | no | — |
| 428 | #125 | — | 73 | 2 | no | — |
| 429 | #125 | — | 73 | 2 | no | — |
| 430 | #125 | C2×#64408 | 1 | 2 | yes | — |
| 431 | #124 | — | 73 | 2 | no | — |
| 432 | #124 | — | 73 | 2 | no | — |
| 433 | #124 | — | 73 | 2 | no | — |
| 434 | #123 | — | 73 | 4 | no | — |
| 435 | #123 | — | 73 | 4 | no | — |
| 436 | #123 | — | 73 | 4 | no | — |
| 437 | C22⋊Q8 | — | 73 | 2 | no | — |
| 438 | C22⋊Q8 | — | 73 | 2 | no | — |
| 439 | C22⋊Q8 | — | 73 | 2 | no | — |
| 440 | C22⋊Q8 | — | 73 | 2 | no | — |
| 441 | C22⋊Q8 | C2×#64408 | 1 | 2 | yes | — |
| 442 | C22⋊Q8 | C2×#64408 | 1 | 2 | yes | — |
| 443 | #121 | — | 73 | 2 | no | — |
| 444 | #121 | — | 73 | 2 | no | — |
| 445 | #121 | — | 73 | 2 | no | — |
| 446 | #121 | — | 73 | 2 | no | — |
| 447 | #121 | — | 73 | 2 | no | — |
| 448 | #121 | — | 73 | 2 | no | — |
| 449 | #120 | — | 73 | 4 | no | — |
| 450 | C4×Q8 | — | 73 | 2 | no | — |
| 451 | C4×Q8 | — | 73 | 2 | no | — |
| 452 | C4×Q8 | — | 73 | 2 | no | — |
| 453 | C4×Q8 | — | 73 | 2 | no | — |
| 454 | C4×Q8 | C2×#64408 | 1 | 2 | yes | — |
| 455 | C4×Q8 | C2×#64408 | 1 | 2 | yes | — |
| 456 | C4×D4 | — | 73 | 4 | no | — |
| 457 | C4×D4 | — | 73 | 4 | no | — |
| 458 | C4×D4 | — | 73 | 2 | no | — |
| 459 | C4×D4 | — | 73 | 2 | no | — |
| 460 | C4×D4 | — | 73 | 2 | no | — |
| 461 | C4×D4 | — | 73 | 2 | no | — |
| 462 | C4×D4 | — | 73 | 4 | no | — |
| 463 | C4×D4 | — | 73 | 4 | no | — |
| 464 | C4×D4 | — | 73 | 4 | no | — |
| 465 | C4×D4 | — | 73 | 4 | no | — |
| 466 | C4×D4 | — | 73 | 2 | no | — |
| 467 | C4×D4 | — | 73 | 2 | no | — |
| 468 | #117 | — | 73 | 2 | no | — |
| 469 | #117 | — | 73 | 2 | no | — |
| 470 | #117 | — | 73 | 4 | no | — |
| 471 | #117 | — | 73 | 4 | no | — |
| 472 | #117 | — | 73 | 4 | no | — |
| 473 | #117 | C2×#64408 | 1 | 2 | yes | — |
| 474 | C2×C42 | — | 73 | 1 | no | — |
| 475 | C2×C42 | — | 73 | 1 | no | — |
| 476 | C2×C42 | — | 73 | 1 | no | — |
| 477 | C2×C42 | — | 73 | 4 | no | — |
| 478 | C2×C42 | — | 73 | 1 | no | — |
| 479 | C2×C42 | — | 73 | 1 | no | — |
| 480 | C2×C42 | — | 73 | 1 | no | — |
| 481 | C2×C42 | — | 73 | 1 | no | — |
| 482 | C2×C42 | — | 73 | 1 | no | — |
| 483 | C2×C42 | — | 73 | 1 | no | — |
| 484 | C2×C42 | — | 73 | 1 | no | — |
| 485 | C2×C42 | — | 73 | 1 | no | — |
| 486 | C2×C42 | C2×#64408 | 1 | 1 | yes | characteristic |
| 487 | C4⋊C8 | — | 73 | 4 | no | — |
| 488 | C4⋊C8 | — | 73 | 4 | no | — |
| 489 | C4⋊C8 | — | 73 | 8 | no | — |
| 490 | C4⋊C8 | — | 73 | 8 | no | — |
| 491 | C22⋊C8 | — | 73 | 4 | no | — |
| 492 | C22⋊C8 | — | 73 | 4 | no | — |
| 493 | C22⋊C8 | — | 73 | 8 | no | — |
| 494 | C22⋊C8 | — | 73 | 8 | no | — |
| 495 | #97 | — | 73 | 4 | no | — |
| 496 | #97 | — | 73 | 4 | no | — |
| 497 | #97 | — | 73 | 4 | no | — |
| 498 | #97 | — | 73 | 8 | no | — |
| 499 | C4×C8 | — | 73 | 2 | no | — |
| 500 | C4×C8 | — | 73 | 2 | no | — |
| 501 | C4×C8 | — | 73 | 2 | no | — |
| 502 | C4×C8 | — | 73 | 4 | no | — |
| 503 | C4×C8 | — | 73 | 2 | no | — |
| 504 | C4×C8 | — | 73 | 8 | no | — |
| 505 | C24 | — | 73 | 1 | no | — |
| 506 | #41 | — | 292 | 4 | no | — |
| 507 | #41 | — | 292 | 4 | no | — |
| 508 | #41 | — | 146 | 8 | no | — |
| 509 | C2×Q8 | — | 73 | 2 | no | — |
| 510 | C2×Q8 | C22×#64408 | 1 | 2 | yes | — |
| 511 | C2×Q8 | C22×#64408 | 1 | 2 | yes | — |
| 512 | C2×D4 | — | 73 | 4 | no | — |
| 513 | C2×D4 | — | 73 | 4 | no | — |
| 514 | C2×D4 | — | 73 | 2 | no | — |
| 515 | C2×D4 | — | 73 | 2 | no | — |
| 516 | C2×D4 | — | 73 | 4 | no | — |
| 517 | C2×D4 | — | 73 | 2 | no | — |
| 518 | C22×C4 | — | 292 | 2 | no | — |
| 519 | C22×C4 | — | 292 | 2 | no | — |
| 520 | C22×C4 | — | 73 | 1 | no | — |
| 521 | C22×C4 | — | 73 | 1 | no | — |
| 522 | C22×C4 | — | 73 | 1 | no | — |
| 523 | C22×C4 | — | 73 | 1 | no | — |
| 524 | C22×C4 | — | 73 | 1 | no | — |
| 525 | C22×C4 | — | 73 | 1 | no | — |
| 526 | C22×C4 | — | 73 | 1 | no | — |
| 527 | C22×C4 | — | 73 | 1 | no | — |
| 528 | C22×C4 | — | 73 | 1 | no | — |
| 529 | C22×C4 | — | 73 | 1 | no | — |
| 530 | C22×C4 | — | 73 | 1 | no | — |
| 531 | C22×C4 | — | 73 | 1 | no | — |
| 532 | C22×C4 | — | 73 | 4 | no | — |
| 533 | C22×C4 | — | 73 | 1 | no | — |
| 534 | C22×C4 | — | 73 | 4 | no | — |
| 535 | C22×C4 | — | 73 | 1 | no | — |
| 536 | C22×C4 | — | 73 | 1 | no | — |
| 537 | C22×C4 | — | 73 | 4 | no | — |
| 538 | C22×C4 | — | 146 | 4 | no | — |
| 539 | C22×C4 | C22×#64408 | 1 | 1 | yes | characteristic |
| 540 | C22×C4 | C22×#64408 | 1 | 1 | yes | characteristic |
| 541 | C22×C4 | C22×#64408 | 1 | 1 | yes | characteristic |
| 542 | M16 | — | 146 | 8 | no | — |
| 543 | M16 | — | 146 | 8 | no | — |
| 544 | M16 | — | 146 | 16 | no | — |
| 545 | M16 | — | 146 | 8 | no | — |
| 546 | C2×C8 | — | 73 | 4 | no | — |
| 547 | C2×C8 | — | 73 | 8 | no | — |
| 548 | C2×C8 | — | 73 | 4 | no | — |
| 549 | C2×C8 | — | 73 | 8 | no | — |
| 550 | C2×C8 | — | 146 | 16 | no | — |
| 551 | C2×C8 | — | 146 | 4 | no | — |
| 552 | C4⋊C4 | — | 73 | 4 | no | — |
| 553 | C4⋊C4 | — | 73 | 4 | no | — |
| 554 | C4⋊C4 | — | 73 | 2 | no | — |
| 555 | C4⋊C4 | — | 73 | 2 | no | — |
| 556 | C4⋊C4 | — | 73 | 4 | no | — |
| 557 | C4⋊C4 | — | 73 | 4 | no | — |
| 558 | C4⋊C4 | C22×#64408 | 1 | 2 | yes | — |
| 559 | C4⋊C4 | C22×#64408 | 1 | 2 | yes | — |
| 560 | C4⋊C4 | C22×#64408 | 1 | 4 | yes | — |
| 561 | C4⋊C4 | C22×#64408 | 1 | 4 | yes | — |
| 562 | C4⋊C4 | C22×#64408 | 1 | 2 | yes | — |
| 563 | C4⋊C4 | C22×#64408 | 1 | 2 | yes | — |
| 564 | C22⋊C4 | — | 73 | 4 | no | — |
| 565 | C22⋊C4 | — | 73 | 4 | no | — |
| 566 | C22⋊C4 | — | 73 | 4 | no | — |
| 567 | C22⋊C4 | — | 73 | 4 | no | — |
| 568 | C22⋊C4 | — | 73 | 4 | no | — |
| 569 | C22⋊C4 | — | 73 | 4 | no | — |
| 570 | C22⋊C4 | — | 73 | 4 | no | — |
| 571 | C22⋊C4 | — | 73 | 4 | no | — |
| 572 | C22⋊C4 | C22×#64408 | 1 | 4 | yes | — |
| 573 | C42 | — | 73 | 1 | no | — |
| 574 | C42 | — | 73 | 1 | no | — |
| 575 | C42 | — | 73 | 1 | no | — |
| 576 | C42 | — | 73 | 1 | no | — |
| 577 | C42 | — | 73 | 1 | no | — |
| 578 | C42 | — | 73 | 1 | no | — |
| 579 | C42 | — | 73 | 1 | no | — |
| 580 | C42 | — | 73 | 4 | no | — |
| 581 | C42 | — | 73 | 1 | no | — |
| 582 | C42 | — | 73 | 4 | no | — |
| 583 | C42 | — | 73 | 1 | no | — |
| 584 | C42 | — | 73 | 1 | no | — |
| 585 | C42 | — | 73 | 1 | no | — |
| 586 | C42 | — | 73 | 1 | no | — |
| 587 | C42 | C22×#64408 | 1 | 1 | yes | characteristic |
| 588 | C42 | C22×#64408 | 1 | 1 | yes | characteristic |
| 589 | C42 | C22×#64408 | 1 | 1 | yes | characteristic |
| 590 | C42 | C22×#64408 | 1 | 1 | yes | characteristic |
| 591 | C42 | C22×#64408 | 1 | 4 | yes | — |
| 592 | C23 | — | 292 | 1 | no | — |
| 593 | C23 | — | 292 | 1 | no | — |
| 594 | C23 | — | 73 | 1 | no | — |
| 595 | C23 | — | 73 | 4 | no | — |
| 596 | C23 | — | 73 | 1 | no | — |
| 597 | C23 | — | 146 | 2 | no | — |
| 598 | C23 | C23×#64408 | 1 | 1 | yes | characteristic |
| 599 | Q8 | — | 2 | 4 | no | — |
| 600 | Q8 | — | 4 | 2 | no | — |
| 601 | Q8 | — | 292 | 2 | no | — |
| 602 | D4 | — | 292 | 2 | no | — |
| 603 | D4 | — | 292 | 4 | no | — |
| 604 | D4 | — | 292 | 2 | no | — |
| 605 | D4 | — | 292 | 4 | no | — |
| 606 | D4 | — | 146 | 8 | no | — |
| 607 | D4 | — | 146 | 4 | no | — |
| 608 | C2×C4 | — | 2 | 2 | no | — |
| 609 | C2×C4 | — | 2 | 2 | no | — |
| 610 | C2×C4 | — | 4 | 1 | no | — |
| 611 | C2×C4 | — | 292 | 1 | no | — |
| 612 | C2×C4 | — | 292 | 1 | no | — |
| 613 | C2×C4 | — | 292 | 1 | no | — |
| 614 | C2×C4 | — | 292 | 1 | no | — |
| 615 | C2×C4 | — | 292 | 1 | no | — |
| 616 | C2×C4 | — | 73 | 1 | no | — |
| 617 | C2×C4 | — | 73 | 1 | no | — |
| 618 | C2×C4 | — | 73 | 4 | no | — |
| 619 | C2×C4 | — | 73 | 1 | no | — |
| 620 | C2×C4 | — | 73 | 1 | no | — |
| 621 | C2×C4 | — | 73 | 1 | no | — |
| 622 | C2×C4 | — | 73 | 1 | no | — |
| 623 | C2×C4 | — | 73 | 4 | no | — |
| 624 | C2×C4 | — | 146 | 8 | no | — |
| 625 | C2×C4 | — | 146 | 2 | no | — |
| 626 | C2×C4 | — | 146 | 2 | no | — |
| 627 | C2×C4 | — | 146 | 2 | no | — |
| 628 | C2×C4 | — | 146 | 8 | no | — |
| 629 | C2×C4 | — | 146 | 2 | no | — |
| 630 | C2×C4 | — | 146 | 2 | no | — |
| 631 | C2×C4 | — | 146 | 2 | no | — |
| 632 | C2×C4 | — | 146 | 2 | no | — |
| 633 | C2×C4 | — | 146 | 2 | no | — |
| 634 | C2×C4 | — | 146 | 2 | no | — |
| 635 | C2×C4 | — | 146 | 8 | no | — |
| 636 | C2×C4 | C23×#64408 | 1 | 1 | yes | characteristic |
| 637 | C2×C4 | C23×#64408 | 1 | 1 | yes | characteristic |
| 638 | C2×C4 | C23×#64408 | 1 | 1 | yes | characteristic |
| 639 | C2×C4 | C23×#64408 | 1 | 1 | yes | characteristic |
| 640 | C2×C4 | C23×#64408 | 1 | 4 | yes | — |
| 641 | C2×C4 | C23×#64408 | 1 | 4 | yes | — |
| 642 | C2×C4 | C23×#64408 | 1 | 1 | yes | characteristic |
| 643 | C2×C4 | C23×#64408 | 1 | 1 | yes | characteristic |
| 644 | C8 | — | 73 | 8 | no | — |
| 645 | C8 | — | 146 | 8 | no | — |
| 646 | C8 | — | 146 | 4 | no | — |
| 647 | C22 | — | 2 | 1 | no | — |
| 648 | C22 | — | 2 | 1 | no | — |
| 649 | C22 | — | 2 | 1 | no | — |
| 650 | C22 | — | 292 | 4 | no | — |
| 651 | C22 | — | 73 | 2 | no | — |
| 652 | C22 | — | 146 | 1 | no | — |
| 653 | C22 | — | 146 | 4 | no | — |
| 654 | C22 | — | 146 | 1 | no | — |
| 655 | C22 | — | 146 | 4 | no | — |
| 656 | C22 | — | 146 | 1 | no | — |
| 657 | C22 | — | 146 | 4 | no | — |
| 658 | C22 | — | 146 | 1 | no | — |
| 659 | C22 | — | 146 | 1 | no | — |
| 660 | C22 | C24×#64408 | 1 | 1 | yes | characteristic |
| 661 | C4 | — | 2 | 1 | no | — |
| 662 | C4 | — | 2 | 4 | no | — |
| 663 | C4 | — | 2 | 1 | no | — |
| 664 | C4 | — | 2 | 1 | no | — |
| 665 | C4 | — | 2 | 4 | no | — |
| 666 | C4 | — | 2 | 1 | no | — |
| 667 | C4 | — | 73 | 2 | no | — |
| 668 | C4 | — | 73 | 2 | no | — |
| 669 | C4 | — | 146 | 1 | no | — |
| 670 | C4 | — | 146 | 1 | no | — |
| 671 | C4 | — | 146 | 1 | no | — |
| 672 | C4 | — | 146 | 1 | no | — |
| 673 | C4 | — | 146 | 4 | no | — |
| 674 | C4 | #41×#64408 | 1 | 2 | yes | — |
| 675 | C4 | #17989667 | 1 | 2 | yes | — |
| 676 | C2 | — | 4 | 1 | no | — |
| 677 | C2 | — | 292 | 1 | no | — |
| 678 | C2 | — | 292 | 4 | no | — |
| 679 | C2 | — | 146 | 2 | no | — |
| 680 | C2 | C2×#41×#64408 | 1 | 1 | yes | characteristic |
| 681 | C2 | D73⋊#568 | 1 | 1 | yes | characteristic |
| 682 | C2 | C2×#17989667 | 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