← #33078003
Subgroups — #33078003
Order 18688.
556 conjugacy classes of subgroups.
The subgroup lattice has 370 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | Q8×Dic292 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22622669 | C2 | 1 | 2 | yes | maximal |
| 3 | #22622362 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #22609541 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22609514 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22609330 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #22609325 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #22609154 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #22609105 | C2 | 1 | 2 | yes | maximal |
| 10 | #22608829 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C8×SD16×C73 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | Q8×Dic146 | C22 | 1 | 2 | yes | — |
| 13 | #17989307 | C22 | 1 | 2 | yes | — |
| 14 | #17988992 | — | 2 | 1 | no | — |
| 15 | #17988992 | C22 | 1 | 1 | yes | characteristic |
| 16 | #17988992 | C22 | 1 | 1 | yes | characteristic |
| 17 | #17988945 | — | 2 | 2 | no | — |
| 18 | #17988938 | C22 | 1 | 2 | yes | — |
| 19 | #17988938 | C22 | 1 | 2 | yes | — |
| 20 | #17988929 | — | 2 | 2 | no | — |
| 21 | #17988883 | — | 2 | 2 | no | — |
| 22 | #17988883 | C22 | 1 | 2 | yes | — |
| 23 | #17988877 | C22 | 1 | 2 | yes | — |
| 24 | #17988873 | C22 | 1 | 2 | yes | — |
| 25 | #17988871 | — | 2 | 2 | no | — |
| 26 | #17988828 | — | 2 | 1 | no | — |
| 27 | #17988807 | — | 2 | 2 | no | — |
| 28 | #17988797 | C22 | 1 | 2 | yes | — |
| 29 | #17988717 | C22 | 1 | 2 | yes | — |
| 30 | #17988691 | — | 2 | 2 | no | — |
| 31 | C4×Dic292 | — | 2 | 1 | no | — |
| 32 | C4×Dic292 | C22 | 1 | 1 | yes | characteristic |
| 33 | #17988625 | — | 2 | 1 | no | — |
| 34 | #17988340 | C22 | 1 | 1 | yes | characteristic |
| 35 | #17988335 | C22 | 1 | 2 | yes | — |
| 36 | #17988332 | C22 | 1 | 2 | yes | — |
| 37 | #17988319 | C22 | 1 | 2 | yes | — |
| 38 | C8×Q8×C73 | C22 | 1 | 1 | yes | characteristic |
| 39 | C4×SD16×C73 | C22 | 1 | 1 | yes | characteristic |
| 40 | C8×D4×C73 | C22 | 1 | 1 | yes | characteristic |
| 41 | #334×C73 | C22 | 1 | 1 | yes | characteristic |
| 42 | Q8⋊C8×C73 | C22 | 1 | 1 | yes | characteristic |
| 43 | D4⋊C8×C73 | C22 | 1 | 1 | yes | characteristic |
| 44 | C82×C73 | C22 | 1 | 1 | yes | characteristic |
| 45 | C2×Dic292 | D4 | 1 | 1 | yes | characteristic |
| 46 | C2×#11924018 | — | 2 | 2 | no | — |
| 47 | #14556591 | — | 2 | 2 | no | — |
| 48 | #14556591 | C23 | 1 | 2 | yes | — |
| 49 | #14556591 | C23 | 1 | 2 | yes | — |
| 50 | #14556590 | — | 2 | 2 | no | — |
| 51 | #14556590 | — | 4 | 2 | no | — |
| 52 | #14556584 | — | 4 | 2 | no | — |
| 53 | #14556578 | — | 2 | 2 | no | — |
| 54 | #14556570 | — | 2 | 2 | no | — |
| 55 | Q8×Dic73 | — | 2 | 2 | no | — |
| 56 | C4×Dic146 | — | 2 | 2 | no | — |
| 57 | C4×Dic146 | C23 | 1 | 2 | yes | — |
| 58 | #14556556 | — | 2 | 2 | no | — |
| 59 | #14556550 | — | 2 | 2 | no | — |
| 60 | #14556525 | — | 2 | 2 | no | — |
| 61 | #14556525 | — | 2 | 1 | no | — |
| 62 | #14556525 | — | 2 | 1 | no | — |
| 63 | #14556525 | — | 2 | 1 | no | — |
| 64 | #14556525 | — | 2 | 1 | no | — |
| 65 | #14556525 | D4 | 1 | 1 | yes | characteristic |
| 66 | #14556523 | — | 2 | 2 | no | — |
| 67 | #14556522 | — | 2 | 2 | no | — |
| 68 | C4⋊#10596831 | C23 | 1 | 2 | yes | — |
| 69 | #14556520 | — | 2 | 2 | no | — |
| 70 | #14556516 | — | 2 | 2 | no | — |
| 71 | #14556516 | — | 2 | 2 | no | — |
| 72 | #14556516 | — | 2 | 2 | no | — |
| 73 | #14556516 | — | 2 | 2 | no | — |
| 74 | #14556516 | — | 4 | 2 | no | — |
| 75 | #14556516 | D4 | 1 | 2 | yes | — |
| 76 | #14556514 | — | 2 | 2 | no | — |
| 77 | #14556512 | — | 2 | 2 | no | — |
| 78 | #14556501 | — | 2 | 2 | no | — |
| 79 | C2×SD16×C73 | D4 | 1 | 1 | yes | characteristic |
| 80 | C22×C8×C73 | — | 2 | 1 | no | — |
| 81 | C4×Q8×C73 | C23 | 1 | 1 | yes | characteristic |
| 82 | C4×D4×C73 | C23 | 1 | 1 | yes | characteristic |
| 83 | #106×C73 | D4 | 1 | 1 | yes | characteristic |
| 84 | C4⋊C8×C73 | — | 2 | 1 | no | — |
| 85 | C4⋊C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 86 | C4⋊C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 87 | #103×C73 | D4 | 1 | 1 | yes | characteristic |
| 88 | #102×C73 | D4 | 1 | 1 | yes | characteristic |
| 89 | C22⋊C8×C73 | — | 2 | 1 | no | — |
| 90 | C4×C8×C73 | — | 2 | 1 | no | — |
| 91 | C4×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 92 | C4×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 93 | C4×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×Dic146 | — | 2 | 2 | no | — |
| 95 | C2×Dic146 | — | 2 | 2 | no | — |
| 96 | C2×Dic146 | — | 4 | 2 | no | — |
| 97 | C2×Dic146 | C2×D4 | 1 | 2 | yes | — |
| 98 | Dic292 | — | 2 | 2 | no | — |
| 99 | #11924018 | — | 4 | 4 | no | — |
| 100 | C2×#10596831 | — | 2 | 2 | no | — |
| 101 | C4⋊Dic73 | — | 2 | 2 | no | — |
| 102 | C4⋊Dic73 | — | 2 | 2 | no | — |
| 103 | C4⋊Dic73 | — | 2 | 2 | no | — |
| 104 | C4⋊Dic73 | — | 2 | 2 | no | — |
| 105 | C4⋊Dic73 | — | 4 | 2 | no | — |
| 106 | C4⋊Dic73 | C2×D4 | 1 | 2 | yes | — |
| 107 | #11924007 | — | 2 | 2 | no | — |
| 108 | #11924007 | — | 4 | 2 | no | — |
| 109 | #11924007 | — | 4 | 2 | no | — |
| 110 | C22⋊Dic73 | — | 4 | 2 | no | — |
| 111 | C22⋊Dic73 | — | 4 | 2 | no | — |
| 112 | C4×Dic73 | — | 2 | 2 | no | — |
| 113 | C4×Dic73 | — | 4 | 2 | no | — |
| 114 | C4×Dic73 | — | 4 | 2 | no | — |
| 115 | C2×Q8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C2×D4×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 117 | C22×C4×C73 | — | 2 | 1 | no | — |
| 118 | SD16×C73 | — | 2 | 2 | no | — |
| 119 | C2×C8×C73 | — | 2 | 1 | no | — |
| 120 | C2×C8×C73 | — | 2 | 1 | no | — |
| 121 | C2×C8×C73 | — | 2 | 1 | no | — |
| 122 | C2×C8×C73 | — | 4 | 2 | no | — |
| 123 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 126 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 128 | C4⋊C4×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C4⋊C4×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C22⋊C4×C73 | — | 2 | 1 | no | — |
| 131 | C42×C73 | — | 2 | 1 | no | — |
| 132 | C42×C73 | C24 | 1 | 1 | yes | characteristic |
| 133 | C23×C73 | — | 2 | 1 | no | — |
| 134 | Q8×C73 | — | 2 | 1 | no | — |
| 135 | Q8×C73 | #135 | 1 | 2 | yes | — |
| 136 | D4×C73 | — | 2 | 1 | no | — |
| 137 | D4×C73 | — | 2 | 1 | no | — |
| 138 | C2×C4×C73 | — | 2 | 1 | no | — |
| 139 | C2×C4×C73 | — | 2 | 1 | no | — |
| 140 | C2×C4×C73 | — | 2 | 1 | no | — |
| 141 | C2×C4×C73 | — | 4 | 1 | no | — |
| 142 | C2×C4×C73 | — | 4 | 1 | no | — |
| 143 | C2×C4×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 144 | C2×C4×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 145 | C2×C4×C73 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 146 | C2×Dic73 | — | 2 | 2 | no | — |
| 147 | C2×Dic73 | — | 2 | 2 | no | — |
| 148 | C2×Dic73 | — | 4 | 2 | no | — |
| 149 | C2×Dic73 | — | 4 | 2 | no | — |
| 150 | Dic146 | — | 2 | 2 | no | — |
| 151 | Dic146 | — | 2 | 2 | no | — |
| 152 | Dic146 | — | 4 | 2 | no | — |
| 153 | Dic146 | — | 4 | 2 | no | — |
| 154 | Dic146 | — | 8 | 2 | no | — |
| 155 | Dic146 | — | 16 | 2 | no | — |
| 156 | C8×C73 | — | 2 | 1 | no | — |
| 157 | C8×C73 | — | 2 | 1 | no | — |
| 158 | C8×C73 | — | 2 | 1 | no | — |
| 159 | C8×C73 | — | 4 | 1 | no | — |
| 160 | C8×C73 | — | 4 | 1 | no | — |
| 161 | C8×C73 | — | 4 | 1 | no | — |
| 162 | C8×C73 | #137 | 1 | 2 | yes | — |
| 163 | #10596831 | — | 4 | 2 | no | — |
| 164 | C22×C73 | — | 4 | 1 | no | — |
| 165 | C22×C73 | — | 4 | 1 | no | — |
| 166 | C22×C73 | — | 4 | 1 | no | — |
| 167 | C22×C73 | D42 | 1 | 1 | yes | characteristic |
| 168 | C4×C73 | — | 2 | 2 | no | — |
| 169 | C4×C73 | — | 2 | 1 | no | — |
| 170 | C4×C73 | — | 4 | 1 | no | — |
| 171 | C4×C73 | — | 4 | 1 | no | — |
| 172 | C4×C73 | C2×#135 | 1 | 1 | yes | characteristic |
| 173 | C4×C73 | C2×#137 | 1 | 1 | yes | characteristic |
| 174 | C4×C73 | #578 | 1 | 1 | yes | characteristic |
| 175 | C4×C73 | #578 | 1 | 1 | yes | characteristic |
| 176 | Dic73 | — | 4 | 2 | no | — |
| 177 | Dic73 | — | 4 | 2 | no | — |
| 178 | Dic73 | — | 8 | 2 | no | — |
| 179 | Dic73 | — | 8 | 2 | no | — |
| 180 | #19940 | — | 73 | 1 | no | maximal, Sylow |
| 181 | C2×C73 | — | 8 | 1 | no | — |
| 182 | C2×C73 | #3276 | 1 | 1 | yes | characteristic |
| 183 | C2×C73 | #3285 | 1 | 1 | yes | characteristic |
| 184 | C2×C73 | #3290 | 1 | 1 | yes | characteristic |
| 185 | Q8×Q16 | — | 73 | 1 | no | — |
| 186 | #3369 | — | 73 | 2 | no | — |
| 187 | #3342 | — | 73 | 1 | no | — |
| 188 | #1710 | — | 73 | 1 | no | — |
| 189 | #1704 | — | 73 | 2 | no | — |
| 190 | #1675 | — | 73 | 1 | no | — |
| 191 | #1674 | — | 73 | 1 | no | — |
| 192 | #1645 | — | 73 | 2 | no | — |
| 193 | #1638 | — | 73 | 2 | no | — |
| 194 | #1591 | — | 73 | 1 | no | — |
| 195 | C8×SD16 | D73 | 1 | 1 | yes | characteristic |
| 196 | C73 | #19940 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 197 | Q82 | — | 73 | 2 | no | — |
| 198 | #556 | — | 73 | 2 | no | — |
| 199 | #500 | — | 73 | 1 | no | — |
| 200 | #500 | — | 73 | 1 | no | — |
| 201 | #500 | — | 146 | 1 | no | — |
| 202 | #489 | — | 146 | 2 | no | — |
| 203 | #487 | — | 73 | 2 | no | — |
| 204 | #487 | — | 73 | 2 | no | — |
| 205 | #485 | — | 146 | 2 | no | — |
| 206 | #477 | — | 73 | 2 | no | — |
| 207 | #477 | — | 146 | 2 | no | — |
| 208 | #476 | — | 73 | 2 | no | — |
| 209 | #475 | — | 73 | 2 | no | — |
| 210 | #475 | — | 146 | 2 | no | — |
| 211 | #467 | — | 146 | 1 | no | — |
| 212 | #464 | — | 146 | 2 | no | — |
| 213 | #462 | — | 73 | 2 | no | — |
| 214 | #446 | — | 73 | 2 | no | — |
| 215 | C8×Q8 | C2×D73 | 1 | 1 | yes | characteristic |
| 216 | #441 | — | 146 | 2 | no | — |
| 217 | C4×Q16 | — | 73 | 1 | no | — |
| 218 | C4×Q16 | — | 146 | 1 | no | — |
| 219 | C4×SD16 | C2×D73 | 1 | 1 | yes | characteristic |
| 220 | C8×D4 | C2×D73 | 1 | 1 | yes | characteristic |
| 221 | #427 | — | 146 | 1 | no | — |
| 222 | #335 | — | 73 | 1 | no | — |
| 223 | #334 | C2×D73 | 1 | 1 | yes | characteristic |
| 224 | #333 | — | 73 | 2 | no | — |
| 225 | #332 | — | 73 | 2 | no | — |
| 226 | Q8⋊C8 | — | 73 | 2 | no | — |
| 227 | Q8⋊C8 | C2×D73 | 1 | 1 | yes | characteristic |
| 228 | D4⋊C8 | C2×D73 | 1 | 1 | yes | characteristic |
| 229 | C82 | C2×D73 | 1 | 1 | yes | characteristic |
| 230 | C2×Q16 | — | 73 | 1 | no | — |
| 231 | C2×Q16 | — | 146 | 2 | no | — |
| 232 | C2×SD16 | D292 | 1 | 1 | yes | characteristic |
| 233 | C22×C8 | — | 2 | 1 | no | — |
| 234 | C4⋊Q8 | — | 292 | 2 | no | — |
| 235 | C4⋊Q8 | — | 73 | 2 | no | — |
| 236 | C4⋊Q8 | — | 73 | 2 | no | — |
| 237 | C4⋊Q8 | — | 146 | 2 | no | — |
| 238 | C4⋊Q8 | — | 146 | 2 | no | — |
| 239 | #126 | — | 292 | 2 | no | — |
| 240 | #124 | — | 146 | 2 | no | — |
| 241 | C22⋊Q8 | — | 146 | 2 | no | — |
| 242 | C4×Q8 | — | 73 | 2 | no | — |
| 243 | C4×Q8 | — | 146 | 2 | no | — |
| 244 | C4×Q8 | — | 146 | 2 | no | — |
| 245 | C4×Q8 | — | 146 | 2 | no | — |
| 246 | C4×Q8 | C22×D73 | 1 | 1 | yes | characteristic |
| 247 | C4×D4 | C22×D73 | 1 | 1 | yes | characteristic |
| 248 | #117 | — | 146 | 2 | no | — |
| 249 | #107 | — | 73 | 1 | no | — |
| 250 | #107 | — | 146 | 2 | no | — |
| 251 | #107 | — | 146 | 1 | no | — |
| 252 | #107 | — | 146 | 1 | no | — |
| 253 | #107 | — | 146 | 1 | no | — |
| 254 | #107 | — | 146 | 1 | no | — |
| 255 | #106 | — | 146 | 2 | no | — |
| 256 | #106 | — | 146 | 2 | no | — |
| 257 | #106 | D292 | 1 | 1 | yes | characteristic |
| 258 | C4⋊C8 | — | 2 | 1 | no | — |
| 259 | C4⋊C8 | — | 73 | 2 | no | — |
| 260 | C4⋊C8 | — | 146 | 2 | no | — |
| 261 | C4⋊C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 262 | C4⋊C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 263 | #103 | — | 292 | 2 | no | — |
| 264 | #103 | — | 73 | 2 | no | — |
| 265 | #103 | — | 146 | 2 | no | — |
| 266 | #103 | — | 146 | 2 | no | — |
| 267 | #103 | — | 146 | 2 | no | — |
| 268 | #103 | — | 146 | 2 | no | — |
| 269 | #103 | — | 146 | 2 | no | — |
| 270 | #103 | D292 | 1 | 1 | yes | characteristic |
| 271 | #102 | — | 146 | 2 | no | — |
| 272 | #102 | D292 | 1 | 1 | yes | characteristic |
| 273 | C22⋊C8 | — | 2 | 1 | no | — |
| 274 | #97 | — | 146 | 2 | no | — |
| 275 | C4×C8 | — | 2 | 1 | no | — |
| 276 | C4×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 277 | C4×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 278 | C4×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 279 | C2×Q8 | — | 292 | 2 | no | — |
| 280 | C2×Q8 | — | 73 | 2 | no | — |
| 281 | C2×Q8 | — | 146 | 2 | no | — |
| 282 | C2×Q8 | — | 146 | 2 | no | — |
| 283 | C2×Q8 | C2×D292 | 1 | 1 | yes | characteristic |
| 284 | C2×D4 | C2×D292 | 1 | 1 | yes | characteristic |
| 285 | C22×C4 | — | 2 | 1 | no | — |
| 286 | Q16 | — | 292 | 4 | no | — |
| 287 | Q16 | — | 146 | 2 | no | — |
| 288 | SD16 | — | 2 | 2 | no | — |
| 289 | C2×C8 | — | 2 | 1 | no | — |
| 290 | C2×C8 | — | 2 | 1 | no | — |
| 291 | C2×C8 | — | 2 | 1 | no | — |
| 292 | C2×C8 | — | 4 | 2 | no | — |
| 293 | C2×C8 | — | 146 | 2 | no | — |
| 294 | C2×C8 | D4×D73 | 1 | 1 | yes | characteristic |
| 295 | C2×C8 | D4×D73 | 1 | 1 | yes | characteristic |
| 296 | C2×C8 | C2×D292 | 1 | 1 | yes | characteristic |
| 297 | C2×C8 | C2×D292 | 1 | 1 | yes | characteristic |
| 298 | C4⋊C4 | — | 2 | 1 | no | — |
| 299 | C4⋊C4 | — | 292 | 2 | no | — |
| 300 | C4⋊C4 | — | 292 | 2 | no | — |
| 301 | C4⋊C4 | — | 292 | 2 | no | — |
| 302 | C4⋊C4 | — | 73 | 2 | no | — |
| 303 | C4⋊C4 | — | 146 | 2 | no | — |
| 304 | C4⋊C4 | — | 146 | 2 | no | — |
| 305 | C4⋊C4 | — | 146 | 2 | no | — |
| 306 | C4⋊C4 | — | 146 | 2 | no | — |
| 307 | C4⋊C4 | — | 146 | 2 | no | — |
| 308 | C4⋊C4 | C2×D292 | 1 | 1 | yes | characteristic |
| 309 | C4⋊C4 | C2×D292 | 1 | 1 | yes | characteristic |
| 310 | C22⋊C4 | — | 2 | 1 | no | — |
| 311 | C22⋊C4 | — | 292 | 2 | no | — |
| 312 | C22⋊C4 | — | 292 | 2 | no | — |
| 313 | C42 | — | 2 | 1 | no | — |
| 314 | C42 | — | 292 | 2 | no | — |
| 315 | C42 | — | 292 | 2 | no | — |
| 316 | C42 | — | 146 | 2 | no | — |
| 317 | C42 | C23×D73 | 1 | 1 | yes | characteristic |
| 318 | C23 | — | 2 | 1 | no | — |
| 319 | Q8 | — | 2 | 1 | no | — |
| 320 | Q8 | — | 292 | 2 | no | — |
| 321 | Q8 | — | 292 | 2 | no | — |
| 322 | Q8 | — | 584 | 2 | no | — |
| 323 | Q8 | — | 1168 | 2 | no | — |
| 324 | Q8 | — | 146 | 2 | no | — |
| 325 | Q8 | — | 146 | 2 | no | — |
| 326 | Q8 | #14556613 | 1 | 2 | yes | — |
| 327 | D4 | — | 2 | 1 | no | — |
| 328 | D4 | — | 2 | 1 | no | — |
| 329 | C2×C4 | — | 2 | 1 | no | — |
| 330 | C2×C4 | — | 2 | 1 | no | — |
| 331 | C2×C4 | — | 2 | 1 | no | — |
| 332 | C2×C4 | — | 4 | 1 | no | — |
| 333 | C2×C4 | — | 4 | 1 | no | — |
| 334 | C2×C4 | — | 292 | 2 | no | — |
| 335 | C2×C4 | — | 292 | 2 | no | — |
| 336 | C2×C4 | — | 146 | 2 | no | — |
| 337 | C2×C4 | — | 146 | 2 | no | — |
| 338 | C2×C4 | C2×D4×D73 | 1 | 1 | yes | characteristic |
| 339 | C2×C4 | C22×D292 | 1 | 1 | yes | characteristic |
| 340 | C2×C4 | #14556637 | 1 | 1 | yes | characteristic |
| 341 | C8 | — | 2 | 1 | no | — |
| 342 | C8 | — | 2 | 1 | no | — |
| 343 | C8 | — | 2 | 1 | no | — |
| 344 | C8 | — | 4 | 1 | no | — |
| 345 | C8 | — | 4 | 1 | no | — |
| 346 | C8 | — | 4 | 1 | no | — |
| 347 | C8 | — | 292 | 2 | no | — |
| 348 | C8 | #14556620 | 1 | 2 | yes | — |
| 349 | C22 | — | 4 | 1 | no | — |
| 350 | C22 | — | 4 | 1 | no | — |
| 351 | C22 | — | 4 | 1 | no | — |
| 352 | C22 | D4×D292 | 1 | 1 | yes | characteristic |
| 353 | C4 | — | 2 | 1 | no | — |
| 354 | C4 | — | 2 | 2 | no | — |
| 355 | C4 | — | 4 | 1 | no | — |
| 356 | C4 | — | 4 | 1 | no | — |
| 357 | C4 | — | 292 | 2 | no | — |
| 358 | C4 | — | 292 | 2 | no | — |
| 359 | C4 | — | 584 | 2 | no | — |
| 360 | C4 | — | 584 | 2 | no | — |
| 361 | C4 | C2×#14556613 | 1 | 1 | yes | characteristic |
| 362 | C4 | C2×#14556620 | 1 | 1 | yes | characteristic |
| 363 | C4 | #17989401 | 1 | 1 | yes | characteristic |
| 364 | C4 | #17989404 | 1 | 1 | yes | characteristic |
| 365 | C2 | — | 8 | 1 | no | — |
| 366 | C2 | #22621578 | 1 | 1 | yes | characteristic |
| 367 | C2 | #22621674 | 1 | 1 | yes | characteristic |
| 368 | C2 | #22621718 | 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