← #33056535
Subgroups — #33056535
Order 18688.
666 conjugacy classes of subgroups.
The subgroup lattice has 384 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22618866 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22618643 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22608834 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | SD16⋊#10596831 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #22608690 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22608386 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #22608382 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×#17988308 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C73×#3167 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C2×#14556598 | — | 2 | 1 | no | — |
| 11 | #17988718 | — | 2 | 1 | no | — |
| 12 | #17988718 | C22 | 1 | 2 | yes | — |
| 13 | Q8×#10596831 | — | 2 | 1 | no | — |
| 14 | Q8×#10596831 | C22 | 1 | 2 | yes | — |
| 15 | #17988665 | — | 2 | 1 | no | — |
| 16 | #17988665 | C22 | 1 | 2 | yes | — |
| 17 | D4×#10596831 | — | 2 | 1 | no | — |
| 18 | D4×#10596831 | C22 | 1 | 2 | yes | — |
| 19 | #17988614 | — | 2 | 1 | no | — |
| 20 | #17988611 | C22 | 1 | 1 | yes | characteristic |
| 21 | #17988611 | C22 | 1 | 1 | yes | characteristic |
| 22 | #17988554 | — | 2 | 1 | no | — |
| 23 | #17988543 | — | 2 | 1 | no | — |
| 24 | C2×C4×#10596831 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×C4×#10596831 | C22 | 1 | 1 | yes | characteristic |
| 26 | #17988340 | C22 | 1 | 4 | yes | — |
| 27 | Q8⋊#10596831 | C22 | 1 | 4 | yes | — |
| 28 | D4⋊#10596831 | C22 | 1 | 4 | yes | — |
| 29 | #17988308 | C22 | 1 | 2 | yes | — |
| 30 | #17988308 | C22 | 1 | 2 | yes | — |
| 31 | #533×C73 | C22 | 1 | 1 | yes | characteristic |
| 32 | #532×C73 | C22 | 1 | 1 | yes | characteristic |
| 33 | #498×C73 | C4 | 1 | 1 | yes | characteristic |
| 34 | #492×C73 | C4 | 1 | 1 | yes | characteristic |
| 35 | #487×C73 | C4 | 1 | 1 | yes | characteristic |
| 36 | #486×C73 | C4 | 1 | 1 | yes | characteristic |
| 37 | #465×C73 | C4 | 1 | 4 | yes | — |
| 38 | C4×SD16×C73 | C22 | 1 | 4 | yes | — |
| 39 | C2×C4×C8×C73 | C22 | 1 | 1 | yes | characteristic |
| 40 | #14556598 | — | 4 | 4 | no | — |
| 41 | C2×#11924012 | — | 2 | 2 | no | — |
| 42 | C2×#11924012 | — | 2 | 1 | no | — |
| 43 | C2×#11924012 | — | 2 | 1 | no | — |
| 44 | C22×#10596831 | — | 2 | 2 | no | — |
| 45 | C22×#10596831 | — | 2 | 1 | no | — |
| 46 | C22×#10596831 | D4 | 1 | 1 | yes | characteristic |
| 47 | C22×#10596831 | D4 | 1 | 1 | yes | characteristic |
| 48 | C4⋊#10596831 | — | 2 | 2 | no | — |
| 49 | C4⋊#10596831 | — | 2 | 2 | no | — |
| 50 | C4⋊#10596831 | — | 2 | 1 | no | — |
| 51 | C4⋊#10596831 | — | 2 | 1 | no | — |
| 52 | C4⋊#10596831 | C23 | 1 | 2 | yes | — |
| 53 | C4⋊#10596831 | C23 | 1 | 2 | yes | — |
| 54 | C22⋊#10596831 | — | 2 | 2 | no | — |
| 55 | C22⋊#10596831 | — | 2 | 2 | no | — |
| 56 | #14556502 | — | 2 | 2 | no | — |
| 57 | C4×#10596831 | — | 2 | 2 | no | — |
| 58 | C4×#10596831 | — | 2 | 1 | no | — |
| 59 | C4×#10596831 | D4 | 1 | 1 | yes | characteristic |
| 60 | C4×#10596831 | D4 | 1 | 1 | yes | characteristic |
| 61 | C4×#10596831 | C23 | 1 | 2 | yes | — |
| 62 | C4×#10596831 | C23 | 1 | 1 | yes | characteristic |
| 63 | C4×#10596831 | C23 | 1 | 1 | yes | characteristic |
| 64 | C2×#41×C73 | — | 2 | 1 | no | — |
| 65 | C2×SD16×C73 | C2×C4 | 1 | 4 | yes | — |
| 66 | C22×C8×C73 | C2×C4 | 1 | 2 | yes | — |
| 67 | C4⋊Q8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 68 | C4⋊Q8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 69 | C4⋊Q8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 70 | #127×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 71 | #125×C73 | — | 2 | 1 | no | — |
| 72 | #124×C73 | — | 2 | 1 | no | — |
| 73 | C22⋊Q8×C73 | — | 2 | 1 | no | — |
| 74 | C22⋊Q8×C73 | C2×C4 | 1 | 2 | yes | — |
| 75 | #121×C73 | — | 2 | 1 | no | — |
| 76 | #121×C73 | C2×C4 | 1 | 2 | yes | — |
| 77 | C4×Q8×C73 | — | 2 | 1 | no | — |
| 78 | C4×Q8×C73 | C23 | 1 | 2 | yes | — |
| 79 | C4×D4×C73 | — | 2 | 1 | no | — |
| 80 | C4×D4×C73 | C23 | 1 | 2 | yes | — |
| 81 | #117×C73 | — | 2 | 1 | no | — |
| 82 | C2×C42×C73 | C23 | 1 | 1 | yes | characteristic |
| 83 | #106×C73 | C2×C4 | 1 | 4 | yes | — |
| 84 | #103×C73 | C2×C4 | 1 | 4 | yes | — |
| 85 | #102×C73 | C2×C4 | 1 | 4 | yes | — |
| 86 | C4×C8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 87 | C4×C8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 88 | C4×C8×C73 | C23 | 1 | 2 | yes | — |
| 89 | #11924012 | — | 4 | 4 | no | — |
| 90 | #11924012 | — | 4 | 2 | no | — |
| 91 | #11924012 | — | 4 | 2 | no | — |
| 92 | C2×#10596831 | — | 2 | 2 | no | — |
| 93 | C2×#10596831 | — | 2 | 2 | no | — |
| 94 | C2×#10596831 | — | 2 | 2 | no | — |
| 95 | C2×#10596831 | — | 2 | 2 | no | — |
| 96 | C2×#10596831 | — | 2 | 2 | no | — |
| 97 | C2×#10596831 | — | 4 | 4 | no | — |
| 98 | C2×#10596831 | — | 4 | 2 | no | — |
| 99 | C2×#10596831 | C2×D4 | 1 | 1 | yes | characteristic |
| 100 | C2×#10596831 | C2×D4 | 1 | 1 | yes | characteristic |
| 101 | C2×#10596831 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | C2×#10596831 | C2×D4 | 1 | 1 | yes | characteristic |
| 103 | #41×C73 | — | 4 | 2 | no | — |
| 104 | #41×C73 | — | 4 | 2 | no | — |
| 105 | C2×Q8×C73 | — | 2 | 1 | no | — |
| 106 | C2×Q8×C73 | — | 2 | 1 | no | — |
| 107 | C2×Q8×C73 | C22×C4 | 1 | 2 | yes | — |
| 108 | C2×D4×C73 | — | 2 | 2 | no | — |
| 109 | C2×D4×C73 | — | 2 | 1 | no | — |
| 110 | C2×D4×C73 | — | 2 | 1 | no | — |
| 111 | C2×D4×C73 | C22×C4 | 1 | 2 | yes | — |
| 112 | C22×C4×C73 | — | 2 | 2 | no | — |
| 113 | C22×C4×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 114 | C22×C4×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C22×C4×C73 | #41 | 1 | 1 | yes | characteristic |
| 116 | SD16×C73 | — | 2 | 8 | no | — |
| 117 | C2×C8×C73 | — | 2 | 4 | no | — |
| 118 | C2×C8×C73 | C22×C4 | 1 | 2 | yes | — |
| 119 | C2×C8×C73 | C22×C4 | 1 | 2 | yes | — |
| 120 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 121 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 122 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 123 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 124 | C4⋊C4×C73 | — | 2 | 2 | no | — |
| 125 | C4⋊C4×C73 | — | 2 | 2 | no | — |
| 126 | C4⋊C4×C73 | C22×C4 | 1 | 2 | yes | — |
| 127 | C4⋊C4×C73 | C22×C4 | 1 | 2 | yes | — |
| 128 | C22⋊C4×C73 | — | 2 | 2 | no | — |
| 129 | C22⋊C4×C73 | — | 2 | 2 | no | — |
| 130 | C22⋊C4×C73 | — | 2 | 2 | no | — |
| 131 | C42×C73 | — | 2 | 2 | no | — |
| 132 | C42×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 133 | C42×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 134 | C42×C73 | #41 | 1 | 1 | yes | characteristic |
| 135 | C42×C73 | C24 | 1 | 1 | yes | characteristic |
| 136 | C23×C73 | — | 2 | 2 | no | — |
| 137 | C23×C73 | C4×D4 | 1 | 1 | yes | characteristic |
| 138 | Q8×C73 | — | 2 | 4 | no | — |
| 139 | Q8×C73 | — | 4 | 2 | no | — |
| 140 | Q8×C73 | — | 4 | 2 | no | — |
| 141 | D4×C73 | — | 2 | 4 | no | — |
| 142 | D4×C73 | — | 4 | 4 | no | — |
| 143 | D4×C73 | — | 4 | 2 | no | — |
| 144 | D4×C73 | — | 4 | 2 | no | — |
| 145 | C2×C4×C73 | — | 2 | 2 | no | — |
| 146 | C2×C4×C73 | — | 2 | 2 | no | — |
| 147 | C2×C4×C73 | — | 2 | 2 | no | — |
| 148 | C2×C4×C73 | — | 2 | 2 | no | — |
| 149 | C2×C4×C73 | — | 2 | 2 | no | — |
| 150 | C2×C4×C73 | — | 4 | 2 | no | — |
| 151 | C2×C4×C73 | — | 4 | 2 | no | — |
| 152 | C2×C4×C73 | C4×D4 | 1 | 1 | yes | characteristic |
| 153 | C2×C4×C73 | C4×D4 | 1 | 1 | yes | characteristic |
| 154 | C2×C4×C73 | C4×D4 | 1 | 1 | yes | characteristic |
| 155 | C2×C4×C73 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 156 | C2×C4×C73 | #137 | 1 | 2 | yes | — |
| 157 | C2×C4×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 158 | C2×C4×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 159 | C2×C4×C73 | C2×#41 | 1 | 1 | yes | characteristic |
| 160 | C8×C73 | — | 2 | 2 | no | — |
| 161 | C8×C73 | #131 | 1 | 4 | yes | complemented |
| 162 | #10596831 | — | 2 | 1 | no | — |
| 163 | #10596831 | — | 2 | 1 | no | — |
| 164 | #10596831 | — | 2 | 1 | no | — |
| 165 | #10596831 | — | 2 | 1 | no | — |
| 166 | #10596831 | — | 4 | 2 | no | — |
| 167 | #10596831 | — | 4 | 2 | no | — |
| 168 | #10596831 | — | 4 | 2 | no | — |
| 169 | C22×C73 | — | 2 | 1 | no | — |
| 170 | C22×C73 | — | 2 | 1 | no | — |
| 171 | C22×C73 | — | 4 | 2 | no | — |
| 172 | C22×C73 | — | 4 | 2 | no | — |
| 173 | C22×C73 | — | 4 | 2 | no | — |
| 174 | C22×C73 | #440 | 1 | 2 | yes | — |
| 175 | C22×C73 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 176 | C4×C73 | — | 2 | 1 | no | — |
| 177 | C4×C73 | — | 2 | 1 | no | — |
| 178 | C4×C73 | — | 4 | 2 | no | — |
| 179 | C4×C73 | — | 4 | 2 | no | — |
| 180 | C4×C73 | — | 4 | 2 | no | — |
| 181 | C4×C73 | #440 | 1 | 2 | yes | — |
| 182 | C4×C73 | #444 | 1 | 2 | yes | — |
| 183 | C4×C73 | C2×#131 | 1 | 2 | yes | — |
| 184 | C4×C73 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 185 | C4×C73 | C2×#137 | 1 | 1 | yes | characteristic |
| 186 | #17960 | — | 73 | 1 | no | maximal, Sylow |
| 187 | C2×C73 | — | 2 | 2 | no | — |
| 188 | C2×C73 | — | 8 | 2 | no | — |
| 189 | C2×C73 | #2931 | 1 | 1 | yes | characteristic |
| 190 | C2×C73 | C2×#440 | 1 | 1 | yes | characteristic |
| 191 | C2×C73 | C2×#444 | 1 | 1 | yes | characteristic |
| 192 | #3167 | D73 | 1 | 1 | yes | characteristic |
| 193 | #2960 | — | 73 | 1 | no | — |
| 194 | #2931 | — | 73 | 1 | no | — |
| 195 | #1592 | — | 73 | 4 | no | — |
| 196 | SD16⋊C8 | — | 73 | 4 | no | — |
| 197 | #1567 | — | 73 | 1 | no | — |
| 198 | #1493 | — | 73 | 1 | no | — |
| 199 | #1492 | — | 73 | 1 | no | — |
| 200 | C2×#322 | — | 73 | 1 | no | — |
| 201 | C73 | #17960 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 202 | C2×#131 | — | 146 | 1 | no | — |
| 203 | #533 | C2×D73 | 1 | 1 | yes | characteristic |
| 204 | #532 | C2×D73 | 1 | 1 | yes | characteristic |
| 205 | #498 | Dic73 | 1 | 1 | yes | characteristic |
| 206 | #492 | Dic73 | 1 | 1 | yes | characteristic |
| 207 | #487 | Dic73 | 1 | 1 | yes | characteristic |
| 208 | #486 | Dic73 | 1 | 1 | yes | characteristic |
| 209 | #465 | Dic73 | 1 | 4 | yes | — |
| 210 | #446 | — | 73 | 2 | no | — |
| 211 | #446 | — | 146 | 1 | no | — |
| 212 | C8×Q8 | — | 73 | 2 | no | — |
| 213 | C8×Q8 | — | 146 | 1 | no | — |
| 214 | C4×SD16 | C2×D73 | 1 | 4 | yes | — |
| 215 | #436 | — | 73 | 2 | no | — |
| 216 | #436 | — | 146 | 1 | no | — |
| 217 | C8×D4 | — | 73 | 2 | no | — |
| 218 | C8×D4 | — | 146 | 1 | no | — |
| 219 | #424 | — | 146 | 1 | no | — |
| 220 | #423 | — | 73 | 1 | no | — |
| 221 | #423 | — | 73 | 1 | no | — |
| 222 | #408 | — | 146 | 1 | no | — |
| 223 | #405 | — | 146 | 1 | no | — |
| 224 | C2×C4×C8 | — | 73 | 1 | no | — |
| 225 | C2×C4×C8 | — | 73 | 1 | no | — |
| 226 | C2×C4×C8 | C2×D73 | 1 | 1 | yes | characteristic |
| 227 | #335 | — | 73 | 4 | no | — |
| 228 | Q8⋊C8 | — | 73 | 4 | no | — |
| 229 | D4⋊C8 | — | 73 | 4 | no | — |
| 230 | #322 | — | 73 | 2 | no | — |
| 231 | #322 | — | 73 | 2 | no | — |
| 232 | C2×#41 | — | 2 | 1 | no | — |
| 233 | C2×SD16 | C2×Dic73 | 1 | 4 | yes | — |
| 234 | #131 | — | 292 | 4 | no | — |
| 235 | C2×M16 | — | 146 | 2 | no | — |
| 236 | C2×M16 | — | 146 | 1 | no | — |
| 237 | C2×M16 | — | 146 | 1 | no | — |
| 238 | C22×C8 | — | 73 | 1 | no | — |
| 239 | C22×C8 | — | 73 | 1 | no | — |
| 240 | C22×C8 | — | 146 | 2 | no | — |
| 241 | C22×C8 | — | 146 | 1 | no | — |
| 242 | C22×C8 | C2×Dic73 | 1 | 2 | yes | — |
| 243 | C4⋊Q8 | C2×Dic73 | 1 | 1 | yes | characteristic |
| 244 | C4⋊Q8 | C2×Dic73 | 1 | 1 | yes | characteristic |
| 245 | C4⋊Q8 | C2×Dic73 | 1 | 1 | yes | characteristic |
| 246 | #127 | C2×Dic73 | 1 | 1 | yes | characteristic |
| 247 | #125 | — | 2 | 1 | no | — |
| 248 | #124 | — | 2 | 1 | no | — |
| 249 | C22⋊Q8 | — | 2 | 1 | no | — |
| 250 | C22⋊Q8 | C2×Dic73 | 1 | 2 | yes | — |
| 251 | #121 | — | 2 | 1 | no | — |
| 252 | #121 | C2×Dic73 | 1 | 2 | yes | — |
| 253 | C4×Q8 | — | 2 | 1 | no | — |
| 254 | C4×Q8 | C22×D73 | 1 | 2 | yes | — |
| 255 | C4×D4 | — | 2 | 1 | no | — |
| 256 | C4×D4 | C22×D73 | 1 | 2 | yes | — |
| 257 | #117 | — | 2 | 1 | no | — |
| 258 | C2×C42 | C22×D73 | 1 | 1 | yes | characteristic |
| 259 | #106 | C2×Dic73 | 1 | 4 | yes | — |
| 260 | C4⋊C8 | — | 73 | 2 | no | — |
| 261 | C4⋊C8 | — | 73 | 2 | no | — |
| 262 | C4⋊C8 | — | 146 | 2 | no | — |
| 263 | C4⋊C8 | — | 146 | 2 | no | — |
| 264 | C4⋊C8 | — | 146 | 1 | no | — |
| 265 | C4⋊C8 | — | 146 | 1 | no | — |
| 266 | #103 | C2×Dic73 | 1 | 4 | yes | — |
| 267 | #102 | C2×Dic73 | 1 | 4 | yes | — |
| 268 | C22⋊C8 | — | 146 | 2 | no | — |
| 269 | C22⋊C8 | — | 146 | 2 | no | — |
| 270 | #97 | — | 146 | 2 | no | — |
| 271 | C4×C8 | — | 73 | 1 | no | — |
| 272 | C4×C8 | — | 73 | 1 | no | — |
| 273 | C4×C8 | — | 73 | 1 | no | — |
| 274 | C4×C8 | — | 73 | 1 | no | — |
| 275 | C4×C8 | — | 73 | 2 | no | — |
| 276 | C4×C8 | — | 146 | 2 | no | — |
| 277 | C4×C8 | — | 146 | 1 | no | — |
| 278 | C4×C8 | C2×Dic73 | 1 | 1 | yes | characteristic |
| 279 | C4×C8 | C2×Dic73 | 1 | 1 | yes | characteristic |
| 280 | C4×C8 | C22×D73 | 1 | 2 | yes | — |
| 281 | #41 | — | 4 | 2 | no | — |
| 282 | #41 | — | 4 | 2 | no | — |
| 283 | C2×Q8 | — | 2 | 1 | no | — |
| 284 | C2×Q8 | — | 2 | 1 | no | — |
| 285 | C2×Q8 | C22×Dic73 | 1 | 2 | yes | — |
| 286 | C2×D4 | — | 2 | 2 | no | — |
| 287 | C2×D4 | — | 2 | 1 | no | — |
| 288 | C2×D4 | — | 2 | 1 | no | — |
| 289 | C2×D4 | C22×Dic73 | 1 | 2 | yes | — |
| 290 | C22×C4 | — | 2 | 2 | no | — |
| 291 | C22×C4 | C22×Dic73 | 1 | 1 | yes | characteristic |
| 292 | C22×C4 | D4×D73 | 1 | 1 | yes | characteristic |
| 293 | C22×C4 | #11924027 | 1 | 1 | yes | characteristic |
| 294 | SD16 | — | 2 | 8 | no | — |
| 295 | M16 | — | 292 | 2 | no | — |
| 296 | M16 | — | 292 | 2 | no | — |
| 297 | M16 | — | 292 | 4 | no | — |
| 298 | C2×C8 | — | 2 | 4 | no | — |
| 299 | C2×C8 | — | 292 | 2 | no | — |
| 300 | C2×C8 | — | 292 | 4 | no | — |
| 301 | C2×C8 | — | 73 | 1 | no | — |
| 302 | C2×C8 | — | 73 | 1 | no | — |
| 303 | C2×C8 | — | 73 | 1 | no | — |
| 304 | C2×C8 | — | 73 | 1 | no | — |
| 305 | C2×C8 | — | 146 | 2 | no | — |
| 306 | C2×C8 | — | 146 | 2 | no | — |
| 307 | C2×C8 | — | 146 | 2 | no | — |
| 308 | C2×C8 | — | 146 | 2 | no | — |
| 309 | C2×C8 | — | 146 | 2 | no | — |
| 310 | C2×C8 | C22×Dic73 | 1 | 2 | yes | — |
| 311 | C2×C8 | C22×Dic73 | 1 | 2 | yes | — |
| 312 | C4⋊C4 | — | 2 | 1 | no | — |
| 313 | C4⋊C4 | — | 2 | 1 | no | — |
| 314 | C4⋊C4 | — | 2 | 1 | no | — |
| 315 | C4⋊C4 | — | 2 | 1 | no | — |
| 316 | C4⋊C4 | — | 2 | 2 | no | — |
| 317 | C4⋊C4 | — | 2 | 2 | no | — |
| 318 | C4⋊C4 | C22×Dic73 | 1 | 2 | yes | — |
| 319 | C4⋊C4 | C22×Dic73 | 1 | 2 | yes | — |
| 320 | C22⋊C4 | — | 2 | 2 | no | — |
| 321 | C22⋊C4 | — | 2 | 2 | no | — |
| 322 | C22⋊C4 | — | 2 | 2 | no | — |
| 323 | C42 | — | 2 | 2 | no | — |
| 324 | C42 | C22×Dic73 | 1 | 1 | yes | characteristic |
| 325 | C42 | D4×D73 | 1 | 1 | yes | characteristic |
| 326 | C42 | #11924027 | 1 | 1 | yes | characteristic |
| 327 | C42 | C23×D73 | 1 | 1 | yes | characteristic |
| 328 | C23 | — | 2 | 2 | no | — |
| 329 | C23 | D4×Dic73 | 1 | 1 | yes | characteristic |
| 330 | Q8 | — | 2 | 4 | no | — |
| 331 | Q8 | — | 4 | 2 | no | — |
| 332 | Q8 | — | 4 | 2 | no | — |
| 333 | D4 | — | 2 | 4 | no | — |
| 334 | D4 | — | 4 | 4 | no | — |
| 335 | D4 | — | 4 | 2 | no | — |
| 336 | D4 | — | 4 | 2 | no | — |
| 337 | C2×C4 | — | 2 | 2 | no | — |
| 338 | C2×C4 | — | 2 | 2 | no | — |
| 339 | C2×C4 | — | 2 | 2 | no | — |
| 340 | C2×C4 | — | 2 | 2 | no | — |
| 341 | C2×C4 | — | 2 | 2 | no | — |
| 342 | C2×C4 | — | 4 | 2 | no | — |
| 343 | C2×C4 | — | 4 | 2 | no | — |
| 344 | C2×C4 | D4×Dic73 | 1 | 1 | yes | characteristic |
| 345 | C2×C4 | D4×Dic73 | 1 | 1 | yes | characteristic |
| 346 | C2×C4 | D4×Dic73 | 1 | 1 | yes | characteristic |
| 347 | C2×C4 | #14556618 | 1 | 2 | yes | — |
| 348 | C2×C4 | #14556620 | 1 | 2 | yes | — |
| 349 | C2×C4 | C23×Dic73 | 1 | 1 | yes | characteristic |
| 350 | C2×C4 | C2×D4×D73 | 1 | 1 | yes | characteristic |
| 351 | C2×C4 | C2×#11924027 | 1 | 1 | yes | characteristic |
| 352 | C8 | — | 2 | 2 | no | — |
| 353 | C8 | — | 292 | 2 | no | — |
| 354 | C8 | — | 292 | 2 | no | — |
| 355 | C8 | — | 292 | 2 | no | — |
| 356 | C8 | — | 146 | 1 | no | — |
| 357 | C8 | — | 146 | 1 | no | — |
| 358 | C8 | — | 146 | 1 | no | — |
| 359 | C8 | — | 146 | 1 | no | — |
| 360 | C8 | #14556598 | 1 | 4 | yes | complemented |
| 361 | C22 | — | 2 | 1 | no | — |
| 362 | C22 | — | 2 | 1 | no | — |
| 363 | C22 | — | 4 | 2 | no | — |
| 364 | C22 | — | 4 | 2 | no | — |
| 365 | C22 | — | 4 | 2 | no | — |
| 366 | C22 | #17988688 | 1 | 2 | yes | — |
| 367 | C22 | C2×D4×Dic73 | 1 | 1 | yes | characteristic |
| 368 | C4 | — | 2 | 1 | no | — |
| 369 | C4 | — | 2 | 1 | no | — |
| 370 | C4 | — | 4 | 2 | no | — |
| 371 | C4 | — | 4 | 2 | no | — |
| 372 | C4 | — | 4 | 2 | no | — |
| 373 | C4 | #17988688 | 1 | 2 | yes | — |
| 374 | C4 | #17988709 | 1 | 2 | yes | — |
| 375 | C4 | C2×#14556598 | 1 | 2 | yes | — |
| 376 | C4 | C2×#14556618 | 1 | 1 | yes | characteristic |
| 377 | C4 | C2×#14556620 | 1 | 1 | yes | characteristic |
| 378 | C2 | — | 2 | 2 | no | — |
| 379 | C2 | — | 8 | 2 | no | — |
| 380 | C2 | #22618643 | 1 | 1 | yes | characteristic |
| 381 | C2 | C2×#17988688 | 1 | 1 | yes | characteristic |
| 382 | C2 | C2×#17988709 | 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