← #34005658
Subgroups — #34005658
Order 18688.
514 conjugacy classes of subgroups.
The subgroup lattice has 424 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | Q8×C4⋊#64408 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22626042 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22625867 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #22625800 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #22624810 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #22624766 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | Q8⋊C8×D73 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×Q8×#64408 | — | 2 | 1 | no | — |
| 9 | C2×#14556660 | — | 2 | 2 | no | — |
| 10 | C2×#14556660 | — | 2 | 1 | no | — |
| 11 | #17989588 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#14556654 | — | 2 | 1 | no | — |
| 13 | #17989538 | — | 2 | 2 | no | — |
| 14 | #17989538 | — | 2 | 1 | no | — |
| 15 | #17989533 | — | 2 | 1 | no | — |
| 16 | #17989533 | C22 | 1 | 1 | yes | characteristic |
| 17 | #17989533 | C22 | 1 | 1 | yes | characteristic |
| 18 | C4×C4⋊#64408 | — | 2 | 1 | no | — |
| 19 | C4×C4⋊#64408 | C22 | 1 | 1 | yes | characteristic |
| 20 | #17989461 | — | 2 | 1 | no | — |
| 21 | #17989460 | — | 2 | 1 | no | — |
| 22 | C4×Q8×D73 | C22 | 1 | 1 | yes | characteristic |
| 23 | C4⋊C8×D73 | C22 | 1 | 1 | yes | characteristic |
| 24 | C4×C8×D73 | C22 | 1 | 1 | yes | characteristic |
| 25 | #17988319 | C4 | 1 | 1 | yes | characteristic, complemented |
| 26 | Q8⋊#10596831 | C4 | 1 | 1 | yes | characteristic, complemented |
| 27 | #17988317 | C4 | 1 | 1 | yes | characteristic, complemented |
| 28 | Q8⋊C8×C73 | C4 | 1 | 1 | yes | characteristic, complemented |
| 29 | C2×#11924036 | — | 2 | 1 | no | — |
| 30 | Q8×#64408 | — | 4 | 2 | no | — |
| 31 | Q8×#64408 | — | 4 | 2 | no | — |
| 32 | C2×C4⋊#64408 | — | 2 | 2 | no | — |
| 33 | C2×C4⋊#64408 | — | 2 | 2 | no | — |
| 34 | C2×C4⋊#64408 | — | 2 | 1 | no | — |
| 35 | C2×C4⋊#64408 | — | 2 | 1 | no | — |
| 36 | C2×C4⋊#64408 | — | 2 | 1 | no | — |
| 37 | C2×C4⋊#64408 | — | 2 | 1 | no | — |
| 38 | C2×C4⋊#64408 | — | 2 | 1 | no | — |
| 39 | C2×C4⋊#64408 | D4 | 1 | 1 | yes | characteristic |
| 40 | C2×C4⋊#64408 | D4 | 1 | 1 | yes | characteristic |
| 41 | C2×C4⋊#64408 | D4 | 1 | 2 | yes | — |
| 42 | C2×C4×#64408 | — | 2 | 2 | no | — |
| 43 | C2×C4×#64408 | — | 2 | 1 | no | — |
| 44 | #14556660 | — | 4 | 4 | no | — |
| 45 | #14556660 | — | 4 | 2 | no | — |
| 46 | #14556658 | — | 2 | 1 | no | — |
| 47 | C4⋊#10596833 | — | 2 | 1 | no | — |
| 48 | #14556654 | — | 4 | 2 | no | — |
| 49 | (C2×#64408)⋊C4 | — | 2 | 2 | no | — |
| 50 | (C2×#64408)⋊C4 | — | 2 | 1 | no | — |
| 51 | C2×Q8×D73 | D4 | 1 | 1 | yes | characteristic |
| 52 | C2×C8×D73 | — | 2 | 1 | no | — |
| 53 | C2×C8×D73 | — | 2 | 1 | no | — |
| 54 | Q8×Dic73 | Q8 | 1 | 1 | yes | characteristic |
| 55 | C4×Dic146 | — | 2 | 1 | no | — |
| 56 | C4×Dic146 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | #14556556 | — | 2 | 1 | no | — |
| 58 | #14556556 | Q8 | 1 | 1 | yes | characteristic |
| 59 | C4⋊C4×D73 | — | 2 | 1 | no | — |
| 60 | C4⋊C4×D73 | D4 | 1 | 1 | yes | characteristic |
| 61 | C42×D73 | — | 2 | 1 | no | — |
| 62 | C42×D73 | C23 | 1 | 1 | yes | characteristic |
| 63 | C4⋊#10596831 | C2×C4 | 1 | 1 | yes | characteristic |
| 64 | #14556520 | — | 2 | 1 | no | — |
| 65 | C4×#10596831 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | C8×Dic73 | — | 2 | 1 | no | — |
| 67 | C4×Q8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 68 | C4⋊C8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 69 | C4×C8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 70 | C22×#64408 | — | 2 | 1 | no | — |
| 71 | C22×#64408 | — | 2 | 1 | no | — |
| 72 | C22×#64408 | — | 2 | 2 | no | — |
| 73 | C22×#64408 | — | 4 | 1 | no | — |
| 74 | #11924036 | — | 4 | 1 | no | — |
| 75 | #11924036 | — | 4 | 1 | no | — |
| 76 | C2×#10596833 | — | 4 | 1 | no | — |
| 77 | C4⋊#64408 | — | 2 | 1 | no | — |
| 78 | C4⋊#64408 | — | 2 | 1 | no | — |
| 79 | C4⋊#64408 | — | 2 | 1 | no | — |
| 80 | C4⋊#64408 | — | 4 | 2 | no | — |
| 81 | C4⋊#64408 | — | 4 | 4 | no | — |
| 82 | C4⋊#64408 | — | 4 | 2 | no | — |
| 83 | C4⋊#64408 | — | 4 | 1 | no | — |
| 84 | C4⋊#64408 | — | 4 | 1 | no | — |
| 85 | C4⋊#64408 | — | 4 | 1 | no | — |
| 86 | C4⋊#64408 | — | 4 | 1 | no | — |
| 87 | C4⋊#64408 | — | 4 | 1 | no | — |
| 88 | C4⋊#64408 | — | 4 | 1 | no | — |
| 89 | C4⋊#64408 | — | 4 | 1 | no | — |
| 90 | C4⋊#64408 | — | 4 | 1 | no | — |
| 91 | C4⋊#64408 | — | 8 | 2 | no | — |
| 92 | C4⋊#64408 | Q16 | 1 | 2 | yes | — |
| 93 | C4×#64408 | — | 4 | 4 | no | — |
| 94 | C4×#64408 | — | 4 | 1 | no | — |
| 95 | C4×#64408 | — | 4 | 1 | no | — |
| 96 | C2×Dic146 | — | 2 | 1 | no | — |
| 97 | C2×Dic146 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 98 | Q8×D73 | — | 2 | 1 | no | — |
| 99 | Q8×D73 | — | 2 | 1 | no | — |
| 100 | Q8×D73 | D8 | 1 | 2 | yes | — |
| 101 | Q8×D73 | Q16 | 1 | 2 | yes | — |
| 102 | C2×C4×D73 | — | 2 | 1 | no | — |
| 103 | C2×C4×D73 | — | 2 | 1 | no | — |
| 104 | C2×C4×D73 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | C2×C4×D73 | C2×D4 | 1 | 1 | yes | characteristic |
| 106 | C2×C4×D73 | C2×D4 | 1 | 1 | yes | characteristic |
| 107 | C2×#10596831 | — | 2 | 1 | no | — |
| 108 | C2×#10596831 | — | 2 | 1 | no | — |
| 109 | C8×D73 | — | 2 | 2 | no | — |
| 110 | C8×D73 | — | 2 | 2 | no | — |
| 111 | C8×D73 | — | 4 | 1 | no | — |
| 112 | C8×D73 | — | 4 | 1 | no | — |
| 113 | C4⋊Dic73 | — | 2 | 1 | no | — |
| 114 | C4⋊Dic73 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 115 | #11924007 | — | 2 | 1 | no | — |
| 116 | #11924007 | — | 2 | 1 | no | — |
| 117 | #11924007 | — | 2 | 1 | no | — |
| 118 | C4×Dic73 | — | 2 | 1 | no | — |
| 119 | C4×Dic73 | — | 2 | 1 | no | — |
| 120 | C4×Dic73 | — | 2 | 1 | no | — |
| 121 | C4×Dic73 | C2×Q8 | 1 | 1 | yes | characteristic |
| 122 | C4×Dic73 | #41 | 1 | 1 | yes | characteristic |
| 123 | C4×Dic73 | #41 | 1 | 1 | yes | characteristic |
| 124 | C2×Q8×C73 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 125 | C2×C8×C73 | — | 2 | 1 | no | — |
| 126 | C2×C8×C73 | — | 2 | 1 | no | — |
| 127 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 128 | C4⋊C4×C73 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 129 | C42×C73 | — | 2 | 1 | no | — |
| 130 | C42×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 131 | C22×D73 | #120 | 1 | 1 | yes | characteristic |
| 132 | C2×#64408 | — | 2 | 2 | no | — |
| 133 | C2×#64408 | — | 4 | 1 | no | — |
| 134 | C2×#64408 | — | 4 | 1 | no | — |
| 135 | C2×#64408 | — | 4 | 2 | no | — |
| 136 | C2×#64408 | — | 4 | 1 | no | — |
| 137 | C2×#64408 | — | 4 | 1 | no | — |
| 138 | C2×#64408 | — | 4 | 2 | no | — |
| 139 | C2×#64408 | — | 4 | 2 | no | — |
| 140 | C2×#64408 | — | 4 | 1 | no | — |
| 141 | C2×#64408 | — | 8 | 1 | no | — |
| 142 | C2×#64408 | — | 8 | 1 | no | — |
| 143 | C2×#64408 | — | 8 | 1 | no | — |
| 144 | Q8×C73 | — | 2 | 1 | no | — |
| 145 | Q8×C73 | #107 | 1 | 2 | yes | complemented |
| 146 | C2×C4×C73 | — | 2 | 1 | no | — |
| 147 | C2×C4×C73 | — | 2 | 1 | no | — |
| 148 | C2×C4×C73 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 149 | C2×C4×C73 | C4×D4 | 1 | 1 | yes | characteristic |
| 150 | C2×C4×C73 | C4×D4 | 1 | 1 | yes | characteristic |
| 151 | C2×Dic73 | — | 2 | 1 | no | — |
| 152 | C2×Dic73 | — | 2 | 1 | no | — |
| 153 | C2×Dic73 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 154 | C2×Dic73 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 155 | C2×Dic73 | #123 | 1 | 1 | yes | characteristic |
| 156 | C4×D73 | — | 2 | 2 | no | — |
| 157 | C4×D73 | — | 2 | 2 | no | — |
| 158 | C4×D73 | — | 2 | 1 | no | — |
| 159 | C4×D73 | — | 2 | 1 | no | — |
| 160 | C4×D73 | — | 4 | 1 | no | — |
| 161 | C4×D73 | — | 4 | 1 | no | — |
| 162 | C4×D73 | C2×D8 | 1 | 1 | yes | characteristic |
| 163 | C4×D73 | C2×Q16 | 1 | 1 | yes | characteristic |
| 164 | C4×D73 | C2×Q16 | 1 | 1 | yes | characteristic |
| 165 | C4×D73 | #135 | 1 | 1 | yes | characteristic |
| 166 | C4×D73 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 167 | C4×D73 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 168 | C4×D73 | #137 | 1 | 1 | yes | characteristic |
| 169 | C4×D73 | #137 | 1 | 1 | yes | characteristic |
| 170 | Dic146 | — | 2 | 1 | no | — |
| 171 | Dic146 | — | 2 | 2 | no | — |
| 172 | Dic146 | — | 2 | 2 | no | — |
| 173 | Dic146 | #107 | 1 | 2 | yes | complemented |
| 174 | #10596833 | — | 8 | 1 | no | — |
| 175 | C8×C73 | — | 2 | 2 | no | — |
| 176 | C8×C73 | — | 4 | 1 | no | — |
| 177 | #10596831 | — | 2 | 2 | no | — |
| 178 | #10596831 | — | 4 | 1 | no | — |
| 179 | C22×C73 | #385 | 1 | 1 | yes | characteristic |
| 180 | C2×D73 | #447 | 1 | 1 | yes | characteristic |
| 181 | C2×D73 | #449 | 1 | 1 | yes | characteristic |
| 182 | C2×D73 | #451 | 1 | 1 | yes | characteristic |
| 183 | C2×D73 | #451 | 1 | 1 | yes | characteristic |
| 184 | C2×D73 | #453 | 1 | 1 | yes | characteristic |
| 185 | C2×D73 | #456 | 1 | 1 | yes | characteristic |
| 186 | #64408 | — | 4 | 2 | no | — |
| 187 | #64408 | — | 8 | 1 | no | — |
| 188 | #64408 | — | 8 | 2 | no | — |
| 189 | #64408 | — | 16 | 1 | no | — |
| 190 | C4×C73 | — | 2 | 2 | no | — |
| 191 | C4×C73 | — | 2 | 1 | no | — |
| 192 | C4×C73 | — | 4 | 1 | no | — |
| 193 | C4×C73 | C2×#107 | 1 | 1 | yes | characteristic |
| 194 | C4×C73 | #428 | 1 | 1 | yes | characteristic |
| 195 | C4×C73 | C4×Q16 | 1 | 1 | yes | characteristic |
| 196 | C4×C73 | #440 | 1 | 1 | yes | characteristic |
| 197 | Dic73 | — | 2 | 2 | no | — |
| 198 | Dic73 | — | 2 | 1 | no | — |
| 199 | Dic73 | — | 4 | 1 | no | — |
| 200 | Dic73 | #477 | 1 | 1 | yes | characteristic |
| 201 | Dic73 | #479 | 1 | 1 | yes | characteristic |
| 202 | Dic73 | #480 | 1 | 1 | yes | characteristic |
| 203 | Dic73 | #484 | 1 | 1 | yes | characteristic |
| 204 | #8884 | — | 73 | 1 | no | maximal, Sylow |
| 205 | C2×C73 | #1852 | 1 | 1 | yes | characteristic |
| 206 | C2×C73 | #1859 | 1 | 1 | yes | characteristic |
| 207 | C2×C73 | #1863 | 1 | 1 | yes | characteristic |
| 208 | D73 | #1621 | 1 | 1 | yes | characteristic |
| 209 | D73 | #1633 | 1 | 1 | yes | characteristic |
| 210 | D73 | #1648 | 1 | 1 | yes | characteristic |
| 211 | D73 | #1649 | 1 | 1 | yes | characteristic |
| 212 | Q8×C4⋊C4 | — | 73 | 1 | no | — |
| 213 | #1947 | — | 73 | 1 | no | — |
| 214 | #1845 | — | 73 | 1 | no | — |
| 215 | #1803 | — | 73 | 1 | no | — |
| 216 | C2×Q8⋊C8 | — | 73 | 1 | no | — |
| 217 | #1296 | — | 73 | 1 | no | — |
| 218 | #1279 | — | 73 | 1 | no | — |
| 219 | C73 | #8884 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 220 | C2×C4×Q8 | — | 73 | 1 | no | — |
| 221 | C2×C4×Q8 | — | 146 | 1 | no | — |
| 222 | C2×#107 | — | 146 | 2 | no | — |
| 223 | C2×#107 | — | 146 | 1 | no | — |
| 224 | C2×C4⋊C8 | — | 73 | 1 | no | — |
| 225 | C2×C4⋊C8 | — | 73 | 1 | no | — |
| 226 | C2×#103 | — | 146 | 1 | no | — |
| 227 | C2×C4×C8 | — | 73 | 1 | no | — |
| 228 | #389 | — | 146 | 2 | no | — |
| 229 | #389 | — | 146 | 1 | no | — |
| 230 | #384 | — | 73 | 1 | no | — |
| 231 | #384 | — | 73 | 1 | no | — |
| 232 | #384 | — | 146 | 1 | no | — |
| 233 | C4×C4⋊C4 | — | 73 | 1 | no | — |
| 234 | C4×C4⋊C4 | — | 146 | 1 | no | — |
| 235 | #340 | — | 146 | 1 | no | — |
| 236 | #340 | — | 146 | 1 | no | — |
| 237 | Q8⋊C8 | — | 73 | 1 | no | — |
| 238 | Q8⋊C8 | — | 73 | 1 | no | — |
| 239 | Q8⋊C8 | — | 73 | 1 | no | — |
| 240 | Q8⋊C8 | #64408 | 1 | 1 | yes | characteristic, complemented |
| 241 | C22×Q8 | — | 73 | 1 | no | — |
| 242 | C22×C8 | — | 146 | 1 | no | — |
| 243 | C22×C8 | — | 146 | 1 | no | — |
| 244 | C22×C8 | — | 146 | 1 | no | — |
| 245 | C4×Q8 | — | 292 | 2 | no | — |
| 246 | C4×Q8 | — | 292 | 2 | no | — |
| 247 | C4×Q8 | — | 73 | 1 | no | — |
| 248 | C4×Q8 | — | 73 | 1 | no | — |
| 249 | C4×Q8 | — | 73 | 1 | no | — |
| 250 | C4×Q8 | — | 146 | 1 | no | — |
| 251 | C4×Q8 | — | 146 | 1 | no | — |
| 252 | C4×Q8 | C2×#64408 | 1 | 1 | yes | characteristic |
| 253 | C2×C4⋊C4 | — | 73 | 2 | no | — |
| 254 | C2×C4⋊C4 | — | 73 | 1 | no | — |
| 255 | C2×C4⋊C4 | — | 73 | 1 | no | — |
| 256 | C2×C4⋊C4 | — | 73 | 1 | no | — |
| 257 | C2×C4⋊C4 | — | 146 | 1 | no | — |
| 258 | C2×C4⋊C4 | — | 146 | 1 | no | — |
| 259 | C2×C4⋊C4 | — | 146 | 1 | no | — |
| 260 | C2×C4⋊C4 | — | 146 | 1 | no | — |
| 261 | C2×C4⋊C4 | — | 146 | 1 | no | — |
| 262 | C2×C4⋊C4 | — | 146 | 1 | no | — |
| 263 | C2×C4⋊C4 | — | 146 | 2 | no | — |
| 264 | C2×C4⋊C4 | — | 146 | 2 | no | — |
| 265 | C2×C42 | — | 73 | 1 | no | — |
| 266 | C2×C42 | — | 146 | 1 | no | — |
| 267 | C2×C42 | — | 146 | 1 | no | — |
| 268 | C2×C42 | — | 146 | 2 | no | — |
| 269 | #107 | — | 292 | 4 | no | — |
| 270 | #107 | — | 292 | 2 | no | — |
| 271 | C4⋊C8 | — | 73 | 1 | no | — |
| 272 | C4⋊C8 | — | 146 | 1 | no | — |
| 273 | C4⋊C8 | — | 146 | 1 | no | — |
| 274 | C4⋊C8 | — | 146 | 1 | no | — |
| 275 | C4⋊C8 | C2×#64408 | 1 | 1 | yes | characteristic |
| 276 | #103 | — | 292 | 2 | no | — |
| 277 | C4×C8 | — | 73 | 1 | no | — |
| 278 | C4×C8 | — | 146 | 1 | no | — |
| 279 | C4×C8 | C2×#64408 | 1 | 1 | yes | characteristic |
| 280 | #95 | — | 146 | 1 | no | — |
| 281 | #95 | — | 146 | 2 | no | — |
| 282 | C2×Q8 | — | 73 | 2 | no | — |
| 283 | C2×Q8 | — | 73 | 2 | no | — |
| 284 | C2×Q8 | — | 73 | 1 | no | — |
| 285 | C2×Q8 | — | 146 | 1 | no | — |
| 286 | C2×Q8 | — | 146 | 1 | no | — |
| 287 | C2×Q8 | — | 146 | 1 | no | — |
| 288 | C2×Q8 | C4⋊#64408 | 1 | 1 | yes | characteristic |
| 289 | C22×C4 | — | 292 | 1 | no | — |
| 290 | C22×C4 | — | 73 | 1 | no | — |
| 291 | C22×C4 | — | 73 | 1 | no | — |
| 292 | C22×C4 | — | 73 | 1 | no | — |
| 293 | C22×C4 | — | 146 | 1 | no | — |
| 294 | C22×C4 | — | 146 | 1 | no | — |
| 295 | C22×C4 | — | 146 | 2 | no | — |
| 296 | C22×C4 | — | 146 | 1 | no | — |
| 297 | C22×C4 | — | 146 | 1 | no | — |
| 298 | C2×C8 | — | 2 | 1 | no | — |
| 299 | C2×C8 | — | 2 | 1 | no | — |
| 300 | C2×C8 | — | 292 | 1 | no | — |
| 301 | C2×C8 | — | 292 | 1 | no | — |
| 302 | C2×C8 | — | 292 | 1 | no | — |
| 303 | C2×C8 | — | 292 | 1 | no | — |
| 304 | C2×C8 | — | 292 | 1 | no | — |
| 305 | C2×C8 | — | 146 | 2 | no | — |
| 306 | C2×C8 | — | 146 | 2 | no | — |
| 307 | C2×C8 | — | 146 | 1 | no | — |
| 308 | C2×C8 | — | 146 | 1 | no | — |
| 309 | C4⋊C4 | — | 2 | 1 | no | — |
| 310 | C4⋊C4 | — | 292 | 1 | no | — |
| 311 | C4⋊C4 | — | 292 | 1 | no | — |
| 312 | C4⋊C4 | — | 292 | 1 | no | — |
| 313 | C4⋊C4 | — | 292 | 1 | no | — |
| 314 | C4⋊C4 | — | 292 | 4 | no | — |
| 315 | C4⋊C4 | — | 292 | 2 | no | — |
| 316 | C4⋊C4 | — | 292 | 1 | no | — |
| 317 | C4⋊C4 | — | 292 | 1 | no | — |
| 318 | C4⋊C4 | — | 292 | 1 | no | — |
| 319 | C4⋊C4 | — | 292 | 1 | no | — |
| 320 | C4⋊C4 | — | 292 | 2 | no | — |
| 321 | C4⋊C4 | — | 584 | 2 | no | — |
| 322 | C4⋊C4 | — | 73 | 2 | no | — |
| 323 | C4⋊C4 | — | 73 | 1 | no | — |
| 324 | C4⋊C4 | — | 146 | 1 | no | — |
| 325 | C4⋊C4 | — | 146 | 1 | no | — |
| 326 | C4⋊C4 | — | 146 | 1 | no | — |
| 327 | C4⋊C4 | — | 146 | 1 | no | — |
| 328 | C4⋊C4 | — | 146 | 1 | no | — |
| 329 | C4⋊C4 | — | 146 | 1 | no | — |
| 330 | C4⋊C4 | — | 146 | 1 | no | — |
| 331 | C4⋊C4 | C4⋊#64408 | 1 | 1 | yes | characteristic |
| 332 | C42 | — | 2 | 1 | no | — |
| 333 | C42 | — | 292 | 1 | no | — |
| 334 | C42 | — | 292 | 1 | no | — |
| 335 | C42 | — | 292 | 4 | no | — |
| 336 | C42 | — | 73 | 1 | no | — |
| 337 | C42 | — | 73 | 1 | no | — |
| 338 | C42 | — | 73 | 1 | no | — |
| 339 | C42 | — | 146 | 1 | no | — |
| 340 | C42 | — | 146 | 1 | no | — |
| 341 | C42 | — | 146 | 1 | no | — |
| 342 | C42 | C22×#64408 | 1 | 1 | yes | characteristic |
| 343 | C23 | — | 73 | 1 | no | — |
| 344 | Q8 | — | 2 | 1 | no | — |
| 345 | Q8 | — | 73 | 2 | no | — |
| 346 | Q8 | — | 146 | 2 | no | — |
| 347 | Q8 | — | 146 | 2 | no | — |
| 348 | Q8 | — | 146 | 1 | no | — |
| 349 | Q8 | #14556660 | 1 | 2 | yes | complemented |
| 350 | C2×C4 | — | 2 | 1 | no | — |
| 351 | C2×C4 | — | 2 | 1 | no | — |
| 352 | C2×C4 | — | 292 | 1 | no | — |
| 353 | C2×C4 | — | 292 | 1 | no | — |
| 354 | C2×C4 | — | 292 | 1 | no | — |
| 355 | C2×C4 | — | 292 | 1 | no | — |
| 356 | C2×C4 | — | 292 | 1 | no | — |
| 357 | C2×C4 | — | 292 | 2 | no | — |
| 358 | C2×C4 | — | 292 | 2 | no | — |
| 359 | C2×C4 | — | 292 | 2 | no | — |
| 360 | C2×C4 | — | 292 | 1 | no | — |
| 361 | C2×C4 | — | 292 | 1 | no | — |
| 362 | C2×C4 | — | 584 | 1 | no | — |
| 363 | C2×C4 | — | 584 | 1 | no | — |
| 364 | C2×C4 | — | 584 | 1 | no | — |
| 365 | C2×C4 | — | 73 | 1 | no | — |
| 366 | C2×C4 | — | 73 | 1 | no | — |
| 367 | C2×C4 | — | 73 | 1 | no | — |
| 368 | C2×C4 | — | 73 | 1 | no | — |
| 369 | C2×C4 | — | 73 | 1 | no | — |
| 370 | C2×C4 | — | 73 | 1 | no | — |
| 371 | C2×C4 | — | 73 | 1 | no | — |
| 372 | C2×C4 | — | 73 | 1 | no | — |
| 373 | C2×C4 | — | 73 | 1 | no | — |
| 374 | C2×C4 | — | 73 | 1 | no | — |
| 375 | C2×C4 | — | 73 | 1 | no | — |
| 376 | C2×C4 | — | 146 | 2 | no | — |
| 377 | C2×C4 | — | 146 | 1 | no | — |
| 378 | C2×C4 | — | 146 | 1 | no | — |
| 379 | C2×C4 | — | 146 | 2 | no | — |
| 380 | C2×C4 | — | 146 | 2 | no | — |
| 381 | C2×C4 | — | 146 | 1 | no | — |
| 382 | C2×C4 | — | 146 | 1 | no | — |
| 383 | C2×C4 | C2×C4⋊#64408 | 1 | 1 | yes | characteristic |
| 384 | C2×C4 | D4×#64408 | 1 | 1 | yes | characteristic |
| 385 | C2×C4 | D4×#64408 | 1 | 1 | yes | characteristic |
| 386 | C8 | — | 2 | 2 | no | — |
| 387 | C8 | — | 4 | 1 | no | — |
| 388 | C8 | — | 292 | 1 | no | — |
| 389 | C8 | — | 584 | 1 | no | — |
| 390 | C8 | — | 146 | 2 | no | — |
| 391 | C22 | — | 73 | 1 | no | — |
| 392 | C22 | — | 73 | 1 | no | — |
| 393 | C22 | — | 73 | 1 | no | — |
| 394 | C22 | — | 73 | 1 | no | — |
| 395 | C22 | — | 73 | 1 | no | — |
| 396 | C22 | — | 73 | 1 | no | — |
| 397 | C22 | #17989534 | 1 | 1 | yes | characteristic |
| 398 | C4 | — | 2 | 2 | no | — |
| 399 | C4 | — | 2 | 1 | no | — |
| 400 | C4 | — | 4 | 1 | no | — |
| 401 | C4 | — | 292 | 2 | no | — |
| 402 | C4 | — | 292 | 1 | no | — |
| 403 | C4 | — | 584 | 2 | no | — |
| 404 | C4 | — | 584 | 1 | no | — |
| 405 | C4 | — | 73 | 1 | no | — |
| 406 | C4 | — | 73 | 1 | no | — |
| 407 | C4 | — | 73 | 1 | no | — |
| 408 | C4 | — | 73 | 1 | no | — |
| 409 | C4 | — | 1168 | 1 | no | — |
| 410 | C4 | — | 146 | 2 | no | — |
| 411 | C4 | — | 146 | 1 | no | — |
| 412 | C4 | C2×#14556660 | 1 | 1 | yes | characteristic |
| 413 | C4 | #17989598 | 1 | 1 | yes | characteristic |
| 414 | C4 | Q16×#64408 | 1 | 1 | yes | characteristic |
| 415 | C4 | #17989626 | 1 | 1 | yes | characteristic |
| 416 | C2 | — | 73 | 1 | no | — |
| 417 | C2 | — | 73 | 1 | no | — |
| 418 | C2 | — | 73 | 1 | no | — |
| 419 | C2 | — | 73 | 1 | no | — |
| 420 | C2 | #22625880 | 1 | 1 | yes | characteristic |
| 421 | C2 | #22625890 | 1 | 1 | yes | characteristic |
| 422 | C2 | #22625895 | 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