← #17954180
Subgroups — #17954180
Order 4352.
514 conjugacy classes of subgroups.
The subgroup lattice has 430 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #14545699 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #14544953 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #14544086 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #14544075 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #14543630 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #14543617 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #137×Dic17 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | Q8×#3624 | — | 2 | 1 | no | — |
| 9 | D4×#3624 | — | 2 | 1 | no | — |
| 10 | D4×#3624 | — | 2 | 2 | no | — |
| 11 | #11763825 | — | 2 | 1 | no | — |
| 12 | #11763825 | C22 | 1 | 1 | yes | characteristic |
| 13 | #11763825 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C4⋊#3624 | — | 2 | 1 | no | — |
| 15 | C2×C4⋊#3624 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C4×#3624 | C22 | 1 | 1 | yes | characteristic |
| 17 | #11763675 | — | 2 | 2 | no | — |
| 18 | Q8⋊#3624 | — | 2 | 1 | no | — |
| 19 | Q8⋊#3624 | — | 2 | 1 | no | — |
| 20 | Q8⋊#3624 | — | 2 | 1 | no | — |
| 21 | D4⋊#3624 | — | 2 | 1 | no | — |
| 22 | #41×Dic17 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×Q8×Dic17 | C22 | 1 | 1 | yes | characteristic |
| 24 | #11762916 | — | 2 | 1 | no | — |
| 25 | #11762910 | — | 2 | 1 | no | — |
| 26 | Q16×Dic17 | — | 2 | 1 | no | — |
| 27 | SD16×Dic17 | — | 2 | 1 | no | — |
| 28 | #11762851 | C4 | 1 | 1 | yes | characteristic |
| 29 | #11762818 | C4 | 1 | 1 | yes | characteristic |
| 30 | #11762810 | C4 | 1 | 1 | yes | characteristic |
| 31 | M16×Dic17 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×C17×#137 | C4 | 1 | 1 | yes | characteristic |
| 33 | C2×#41×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C22×Q8×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C22×#3624 | — | 2 | 1 | no | — |
| 36 | C22×#3624 | — | 2 | 2 | no | — |
| 37 | C22×#3624 | D4 | 1 | 2 | yes | — |
| 38 | C17×#137 | — | 2 | 2 | no | — |
| 39 | C17×#137 | C8 | 1 | 4 | yes | complemented |
| 40 | C2×Q16×C17 | — | 2 | 1 | no | — |
| 41 | C2×SD16×C17 | — | 2 | 1 | no | — |
| 42 | C2×M16×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | Q8×Dic17 | — | 2 | 1 | no | — |
| 44 | Q8×Dic17 | — | 2 | 1 | no | — |
| 45 | Q8×Dic17 | — | 2 | 1 | no | — |
| 46 | Q8×Dic17 | — | 2 | 1 | no | — |
| 47 | Q8×Dic17 | D4 | 1 | 1 | yes | characteristic |
| 48 | Q8×Dic17 | D4 | 1 | 1 | yes | characteristic |
| 49 | D4×Dic17 | — | 2 | 1 | no | — |
| 50 | D4×Dic17 | — | 2 | 1 | no | — |
| 51 | D4×Dic17 | D4 | 1 | 1 | yes | characteristic |
| 52 | D4×Dic17 | D4 | 1 | 1 | yes | characteristic |
| 53 | #10587612 | — | 2 | 1 | no | — |
| 54 | #10587612 | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | C2×C4⋊Dic17 | — | 2 | 1 | no | — |
| 56 | C2×C4⋊Dic17 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | C2×C4×Dic17 | — | 2 | 1 | no | — |
| 58 | C2×C4×Dic17 | — | 2 | 1 | no | — |
| 59 | C2×C4×Dic17 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×#63223 | C2×C4 | 1 | 1 | yes | characteristic |
| 61 | C22⋊#3624 | — | 2 | 2 | no | — |
| 62 | C22⋊#3624 | — | 2 | 1 | no | — |
| 63 | C22⋊#3624 | — | 2 | 1 | no | — |
| 64 | C4⋊#3624 | — | 2 | 2 | no | — |
| 65 | C4⋊#3624 | — | 2 | 1 | no | — |
| 66 | C4⋊#3624 | — | 2 | 1 | no | — |
| 67 | C4⋊#3624 | — | 2 | 1 | no | — |
| 68 | C4⋊#3624 | D4 | 1 | 1 | yes | characteristic |
| 69 | C4⋊#3624 | D4 | 1 | 1 | yes | characteristic |
| 70 | C4×#3624 | — | 2 | 2 | no | — |
| 71 | C4×#3624 | — | 2 | 1 | no | — |
| 72 | C4×#3624 | — | 2 | 1 | no | — |
| 73 | C4×#3624 | — | 2 | 1 | no | — |
| 74 | C4×#3624 | — | 2 | 1 | no | — |
| 75 | #10587506 | — | 2 | 1 | no | — |
| 76 | #10587506 | — | 2 | 1 | no | — |
| 77 | #10587506 | — | 2 | 1 | no | — |
| 78 | #10587503 | — | 2 | 1 | no | — |
| 79 | #10587489 | — | 2 | 1 | no | — |
| 80 | #10587488 | — | 2 | 1 | no | — |
| 81 | #10587486 | — | 2 | 1 | no | — |
| 82 | C8×Dic17 | — | 2 | 1 | no | — |
| 83 | #41×C17 | — | 2 | 1 | no | — |
| 84 | #41×C17 | — | 2 | 1 | no | — |
| 85 | #41×C17 | C2×C8 | 1 | 2 | yes | — |
| 86 | #41×C17 | M16 | 1 | 2 | yes | — |
| 87 | C2×Q8×C17 | — | 2 | 1 | no | — |
| 88 | C2×Q8×C17 | — | 2 | 1 | no | — |
| 89 | C2×Q8×C17 | — | 2 | 1 | no | — |
| 90 | C2×Q8×C17 | — | 2 | 1 | no | — |
| 91 | C2×Q8×C17 | — | 2 | 1 | no | — |
| 92 | C2×Q8×C17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 93 | C2×Q8×C17 | C2×C8 | 1 | 2 | yes | complemented |
| 94 | C2×D4×C17 | — | 2 | 1 | no | — |
| 95 | C2×D4×C17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 96 | C22×C4×C17 | — | 2 | 1 | no | — |
| 97 | C22×C4×C17 | — | 2 | 1 | no | — |
| 98 | C22×C4×C17 | C22×C4 | 1 | 1 | yes | characteristic |
| 99 | C22×Dic17 | — | 2 | 1 | no | — |
| 100 | C22×Dic17 | — | 2 | 1 | no | — |
| 101 | C22×Dic17 | — | 2 | 1 | no | — |
| 102 | C22×Dic17 | C2×D4 | 1 | 1 | yes | characteristic |
| 103 | C22×Dic17 | #41 | 1 | 1 | yes | characteristic |
| 104 | C2×#3624 | — | 2 | 2 | no | — |
| 105 | C2×#3624 | — | 2 | 1 | no | — |
| 106 | C2×#3624 | — | 2 | 2 | no | — |
| 107 | C2×#3624 | — | 2 | 1 | no | — |
| 108 | C2×#3624 | — | 4 | 1 | no | — |
| 109 | C2×#3624 | — | 4 | 1 | no | — |
| 110 | C2×#3624 | — | 4 | 2 | no | — |
| 111 | C2×#3624 | — | 4 | 1 | no | — |
| 112 | C2×#3624 | — | 8 | 2 | no | — |
| 113 | Q16×C17 | — | 2 | 4 | no | — |
| 114 | SD16×C17 | — | 2 | 4 | no | — |
| 115 | M16×C17 | — | 2 | 1 | no | — |
| 116 | M16×C17 | C2×C8 | 1 | 2 | yes | complemented |
| 117 | C2×C8×C17 | — | 2 | 1 | no | — |
| 118 | C22⋊Dic17 | — | 2 | 1 | no | — |
| 119 | C22⋊Dic17 | — | 2 | 1 | no | — |
| 120 | C22⋊Dic17 | — | 2 | 1 | no | — |
| 121 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 122 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 123 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 124 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 125 | C4⋊Dic17 | — | 4 | 1 | no | — |
| 126 | C4⋊Dic17 | — | 4 | 1 | no | — |
| 127 | C4⋊Dic17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 128 | C4⋊Dic17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 129 | C4×Dic17 | — | 2 | 1 | no | — |
| 130 | C4×Dic17 | — | 2 | 1 | no | — |
| 131 | C4×Dic17 | — | 2 | 1 | no | — |
| 132 | C4×Dic17 | — | 4 | 1 | no | — |
| 133 | C4×Dic17 | — | 4 | 1 | no | — |
| 134 | C4×Dic17 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | C4×Dic17 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | C4×Dic17 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C4×Dic17 | #41 | 1 | 1 | yes | characteristic |
| 138 | #63223 | — | 2 | 1 | no | — |
| 139 | #63223 | — | 2 | 1 | no | — |
| 140 | C2×#3622 | — | 2 | 1 | no | — |
| 141 | #8953 | — | 17 | 1 | no | maximal, Sylow |
| 142 | C23×C17 | — | 2 | 1 | no | — |
| 143 | C23×C17 | C4×D4 | 1 | 1 | yes | characteristic |
| 144 | Q8×C17 | — | 2 | 1 | no | — |
| 145 | Q8×C17 | — | 2 | 2 | no | — |
| 146 | Q8×C17 | — | 2 | 2 | no | — |
| 147 | Q8×C17 | — | 4 | 1 | no | — |
| 148 | Q8×C17 | — | 4 | 1 | no | — |
| 149 | Q8×C17 | C22⋊C8 | 1 | 2 | yes | — |
| 150 | D4×C17 | — | 2 | 2 | no | — |
| 151 | D4×C17 | — | 2 | 2 | no | — |
| 152 | D4×C17 | — | 2 | 1 | no | — |
| 153 | D4×C17 | C22⋊C8 | 1 | 2 | yes | — |
| 154 | C2×C4×C17 | — | 2 | 1 | no | — |
| 155 | C2×C4×C17 | — | 2 | 2 | no | — |
| 156 | C2×C4×C17 | — | 2 | 2 | no | — |
| 157 | C2×C4×C17 | — | 2 | 2 | no | — |
| 158 | C2×C4×C17 | — | 4 | 1 | no | — |
| 159 | C2×C4×C17 | — | 4 | 1 | no | — |
| 160 | C2×C4×C17 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 161 | C2×C4×C17 | C4×D4 | 1 | 1 | yes | characteristic |
| 162 | C2×C4×C17 | C22×C8 | 1 | 1 | yes | characteristic |
| 163 | C2×C4×C17 | C2×M16 | 1 | 1 | yes | characteristic |
| 164 | C2×C4×C17 | #131 | 1 | 1 | yes | characteristic |
| 165 | C2×C4×C17 | #131 | 1 | 1 | yes | characteristic |
| 166 | C2×Dic17 | — | 2 | 1 | no | — |
| 167 | C2×Dic17 | — | 2 | 1 | no | — |
| 168 | C2×Dic17 | — | 2 | 1 | no | — |
| 169 | C2×Dic17 | — | 2 | 1 | no | — |
| 170 | C2×Dic17 | — | 4 | 1 | no | — |
| 171 | C2×Dic17 | — | 4 | 1 | no | — |
| 172 | C2×Dic17 | — | 4 | 1 | no | — |
| 173 | C2×Dic17 | — | 4 | 2 | no | — |
| 174 | C2×Dic17 | — | 4 | 1 | no | — |
| 175 | C2×Dic17 | — | 8 | 1 | no | — |
| 176 | C2×Dic17 | #120 | 1 | 1 | yes | characteristic |
| 177 | C2×Dic17 | #121 | 1 | 1 | yes | characteristic |
| 178 | C2×Dic17 | #121 | 1 | 1 | yes | characteristic |
| 179 | C2×Dic17 | #123 | 1 | 1 | yes | characteristic |
| 180 | #3624 | — | 4 | 2 | no | — |
| 181 | #3624 | — | 4 | 2 | no | — |
| 182 | #3624 | — | 4 | 1 | no | — |
| 183 | #3624 | — | 4 | 1 | no | — |
| 184 | #3624 | — | 8 | 1 | no | — |
| 185 | C8×C17 | — | 2 | 2 | no | — |
| 186 | #3622 | — | 4 | 1 | no | — |
| 187 | #2988 | — | 17 | 1 | no | — |
| 188 | C4×#137 | — | 17 | 1 | no | — |
| 189 | #1984 | — | 17 | 1 | no | — |
| 190 | #1479 | — | 17 | 1 | no | — |
| 191 | #1476 | — | 17 | 1 | no | — |
| 192 | #1283 | — | 17 | 1 | no | — |
| 193 | #1278 | — | 17 | 1 | no | — |
| 194 | C22×C17 | — | 2 | 1 | no | — |
| 195 | C22×C17 | — | 2 | 1 | no | — |
| 196 | C22×C17 | — | 2 | 2 | no | — |
| 197 | C22×C17 | — | 4 | 1 | no | — |
| 198 | C22×C17 | — | 4 | 1 | no | — |
| 199 | C22×C17 | #386 | 1 | 1 | yes | characteristic |
| 200 | C22×C17 | C8×D4 | 1 | 1 | yes | characteristic |
| 201 | C22×C17 | #435 | 1 | 1 | yes | characteristic |
| 202 | C4×C17 | — | 2 | 2 | no | — |
| 203 | C4×C17 | — | 4 | 2 | no | — |
| 204 | C4×C17 | C2×C22⋊C8 | 1 | 1 | yes | characteristic |
| 205 | C4×C17 | #408 | 1 | 1 | yes | characteristic |
| 206 | C4×C17 | C8×D4 | 1 | 1 | yes | characteristic |
| 207 | C4×C17 | #435 | 1 | 1 | yes | characteristic |
| 208 | Dic17 | — | 2 | 1 | no | — |
| 209 | Dic17 | — | 2 | 1 | no | — |
| 210 | Dic17 | — | 2 | 1 | no | — |
| 211 | Dic17 | — | 4 | 1 | no | — |
| 212 | Dic17 | — | 4 | 1 | no | — |
| 213 | Dic17 | — | 8 | 1 | no | — |
| 214 | Dic17 | #455 | 1 | 1 | yes | characteristic |
| 215 | Dic17 | #456 | 1 | 1 | yes | characteristic |
| 216 | C2×#137 | #595 | 1 | 1 | yes | characteristic |
| 217 | C4×#41 | — | 17 | 1 | no | — |
| 218 | C2×C4×Q8 | — | 17 | 1 | no | — |
| 219 | C8×Q8 | — | 34 | 1 | no | — |
| 220 | #441 | — | 34 | 1 | no | — |
| 221 | #440 | — | 34 | 1 | no | — |
| 222 | C4×Q16 | — | 34 | 1 | no | — |
| 223 | C4×SD16 | — | 34 | 1 | no | — |
| 224 | C8×D4 | — | 34 | 1 | no | — |
| 225 | C8×D4 | — | 34 | 2 | no | — |
| 226 | #431 | — | 17 | 1 | no | — |
| 227 | #431 | — | 17 | 1 | no | — |
| 228 | #431 | — | 34 | 1 | no | — |
| 229 | #428 | — | 17 | 1 | no | — |
| 230 | C2×C4⋊C8 | — | 17 | 1 | no | — |
| 231 | C2×C4⋊C8 | — | 34 | 1 | no | — |
| 232 | #419 | — | 17 | 1 | no | — |
| 233 | #417 | — | 17 | 1 | no | — |
| 234 | C4×M16 | — | 17 | 1 | no | — |
| 235 | C2×C4×C8 | — | 17 | 1 | no | — |
| 236 | #336 | — | 34 | 2 | no | — |
| 237 | Q8⋊C8 | — | 34 | 1 | no | — |
| 238 | Q8⋊C8 | — | 34 | 1 | no | — |
| 239 | Q8⋊C8 | — | 34 | 1 | no | — |
| 240 | D4⋊C8 | — | 34 | 1 | no | — |
| 241 | C2×C17 | — | 2 | 1 | no | — |
| 242 | C2×C17 | — | 2 | 1 | no | — |
| 243 | C2×C17 | — | 4 | 2 | no | — |
| 244 | C2×C17 | #1869 | 1 | 1 | yes | characteristic |
| 245 | C2×C17 | #1881 | 1 | 1 | yes | characteristic |
| 246 | C2×C17 | #1882 | 1 | 1 | yes | characteristic |
| 247 | C2×#41 | C2×#595 | 1 | 1 | yes | characteristic |
| 248 | C22×Q8 | C2×#595 | 1 | 1 | yes | characteristic |
| 249 | #137 | — | 2 | 2 | no | — |
| 250 | #137 | #3624 | 1 | 4 | yes | complemented |
| 251 | C2×Q16 | — | 2 | 1 | no | — |
| 252 | C2×SD16 | — | 2 | 1 | no | — |
| 253 | C2×M16 | — | 17 | 1 | no | — |
| 254 | C2×M16 | C2×#595 | 1 | 1 | yes | characteristic |
| 255 | C22×C8 | — | 17 | 2 | no | — |
| 256 | C22×C8 | — | 34 | 1 | no | — |
| 257 | C22×C8 | — | 34 | 2 | no | — |
| 258 | C4×Q8 | — | 17 | 1 | no | — |
| 259 | C4×Q8 | — | 17 | 1 | no | — |
| 260 | C4×Q8 | — | 34 | 1 | no | — |
| 261 | C4×Q8 | — | 34 | 1 | no | — |
| 262 | C4×Q8 | — | 34 | 1 | no | — |
| 263 | C4×Q8 | — | 34 | 1 | no | — |
| 264 | C4×D4 | — | 17 | 1 | no | — |
| 265 | C4×D4 | — | 17 | 1 | no | — |
| 266 | C4×D4 | — | 34 | 1 | no | — |
| 267 | C4×D4 | — | 34 | 1 | no | — |
| 268 | #117 | — | 17 | 1 | no | — |
| 269 | #117 | — | 34 | 1 | no | — |
| 270 | C2×C4⋊C4 | — | 17 | 1 | no | — |
| 271 | C2×C4⋊C4 | — | 34 | 1 | no | — |
| 272 | C2×C42 | — | 17 | 1 | no | — |
| 273 | C2×C42 | — | 34 | 1 | no | — |
| 274 | C2×C42 | — | 34 | 1 | no | — |
| 275 | #107 | — | 34 | 1 | no | — |
| 276 | #106 | — | 34 | 1 | no | — |
| 277 | C4⋊C8 | — | 17 | 1 | no | — |
| 278 | C4⋊C8 | — | 17 | 1 | no | — |
| 279 | C4⋊C8 | — | 34 | 1 | no | — |
| 280 | C4⋊C8 | — | 34 | 1 | no | — |
| 281 | C4⋊C8 | — | 34 | 1 | no | — |
| 282 | C4⋊C8 | — | 34 | 2 | no | — |
| 283 | #103 | — | 34 | 1 | no | — |
| 284 | #103 | — | 34 | 1 | no | — |
| 285 | #103 | — | 34 | 1 | no | — |
| 286 | #102 | — | 34 | 1 | no | — |
| 287 | C22⋊C8 | — | 34 | 1 | no | — |
| 288 | C22⋊C8 | — | 34 | 2 | no | — |
| 289 | C22⋊C8 | — | 34 | 1 | no | — |
| 290 | #97 | — | 34 | 1 | no | — |
| 291 | C4×C8 | — | 34 | 1 | no | — |
| 292 | C4×C8 | — | 34 | 1 | no | — |
| 293 | C4×C8 | — | 34 | 1 | no | — |
| 294 | C4×C8 | — | 34 | 1 | no | — |
| 295 | C4×C8 | — | 34 | 1 | no | — |
| 296 | C4×C8 | — | 34 | 2 | no | — |
| 297 | C17 | #8953 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 298 | #41 | — | 2 | 1 | no | — |
| 299 | #41 | — | 2 | 1 | no | — |
| 300 | #41 | C2×#3624 | 1 | 2 | yes | — |
| 301 | #41 | #63247 | 1 | 2 | yes | — |
| 302 | C2×Q8 | — | 2 | 1 | no | — |
| 303 | C2×Q8 | — | 2 | 1 | no | — |
| 304 | C2×Q8 | — | 2 | 1 | no | — |
| 305 | C2×Q8 | — | 2 | 1 | no | — |
| 306 | C2×Q8 | — | 2 | 1 | no | — |
| 307 | C2×Q8 | C2×#3624 | 1 | 2 | yes | complemented |
| 308 | C2×Q8 | C22⋊#595 | 1 | 1 | yes | characteristic |
| 309 | C2×D4 | — | 2 | 1 | no | — |
| 310 | C2×D4 | C22⋊#595 | 1 | 1 | yes | characteristic |
| 311 | C22×C4 | — | 2 | 1 | no | — |
| 312 | C22×C4 | — | 2 | 1 | no | — |
| 313 | C22×C4 | — | 17 | 1 | no | — |
| 314 | C22×C4 | — | 17 | 1 | no | — |
| 315 | C22×C4 | — | 34 | 1 | no | — |
| 316 | C22×C4 | — | 34 | 1 | no | — |
| 317 | C22×C4 | — | 34 | 1 | no | — |
| 318 | C22×C4 | C22×#595 | 1 | 1 | yes | characteristic |
| 319 | Q16 | — | 2 | 4 | no | — |
| 320 | SD16 | — | 2 | 4 | no | — |
| 321 | M16 | — | 2 | 1 | no | — |
| 322 | M16 | — | 34 | 1 | no | — |
| 323 | M16 | — | 34 | 1 | no | — |
| 324 | M16 | C2×#3624 | 1 | 2 | yes | complemented |
| 325 | C2×C8 | — | 2 | 1 | no | — |
| 326 | C2×C8 | — | 34 | 1 | no | — |
| 327 | C2×C8 | — | 34 | 1 | no | — |
| 328 | C2×C8 | — | 34 | 2 | no | — |
| 329 | C2×C8 | — | 34 | 2 | no | — |
| 330 | C2×C8 | — | 34 | 1 | no | — |
| 331 | C2×C8 | — | 68 | 1 | no | — |
| 332 | C2×C8 | — | 68 | 1 | no | — |
| 333 | C2×C8 | — | 68 | 2 | no | — |
| 334 | C2×C8 | — | 68 | 1 | no | — |
| 335 | C2×C8 | — | 136 | 2 | no | — |
| 336 | C4⋊C4 | — | 17 | 1 | no | — |
| 337 | C4⋊C4 | — | 17 | 1 | no | — |
| 338 | C4⋊C4 | — | 34 | 1 | no | — |
| 339 | C4⋊C4 | — | 34 | 1 | no | — |
| 340 | C4⋊C4 | — | 34 | 1 | no | — |
| 341 | C4⋊C4 | — | 34 | 1 | no | — |
| 342 | C4⋊C4 | — | 68 | 1 | no | — |
| 343 | C4⋊C4 | — | 68 | 1 | no | — |
| 344 | C22⋊C4 | — | 34 | 1 | no | — |
| 345 | C22⋊C4 | — | 34 | 1 | no | — |
| 346 | C22⋊C4 | — | 34 | 1 | no | — |
| 347 | C42 | — | 17 | 1 | no | — |
| 348 | C42 | — | 17 | 1 | no | — |
| 349 | C42 | — | 17 | 1 | no | — |
| 350 | C42 | — | 17 | 1 | no | — |
| 351 | C42 | — | 34 | 1 | no | — |
| 352 | C42 | — | 34 | 1 | no | — |
| 353 | C42 | — | 34 | 1 | no | — |
| 354 | C42 | — | 68 | 1 | no | — |
| 355 | C42 | — | 68 | 1 | no | — |
| 356 | C23 | — | 2 | 1 | no | — |
| 357 | C23 | D4×#595 | 1 | 1 | yes | characteristic |
| 358 | Q8 | — | 2 | 1 | no | — |
| 359 | Q8 | — | 2 | 2 | no | — |
| 360 | Q8 | — | 2 | 2 | no | — |
| 361 | Q8 | — | 4 | 1 | no | — |
| 362 | Q8 | — | 4 | 1 | no | — |
| 363 | Q8 | C22⋊#3624 | 1 | 2 | yes | — |
| 364 | D4 | — | 2 | 2 | no | — |
| 365 | D4 | — | 2 | 2 | no | — |
| 366 | D4 | — | 2 | 1 | no | — |
| 367 | D4 | C22⋊#3624 | 1 | 2 | yes | — |
| 368 | C2×C4 | — | 2 | 1 | no | — |
| 369 | C2×C4 | — | 2 | 2 | no | — |
| 370 | C2×C4 | — | 2 | 2 | no | — |
| 371 | C2×C4 | — | 2 | 2 | no | — |
| 372 | C2×C4 | — | 4 | 1 | no | — |
| 373 | C2×C4 | — | 4 | 1 | no | — |
| 374 | C2×C4 | — | 17 | 1 | no | — |
| 375 | C2×C4 | — | 17 | 1 | no | — |
| 376 | C2×C4 | — | 17 | 1 | no | — |
| 377 | C2×C4 | — | 17 | 1 | no | — |
| 378 | C2×C4 | — | 34 | 1 | no | — |
| 379 | C2×C4 | — | 34 | 1 | no | — |
| 380 | C2×C4 | — | 34 | 1 | no | — |
| 381 | C2×C4 | — | 34 | 1 | no | — |
| 382 | C2×C4 | — | 68 | 1 | no | — |
| 383 | C2×C4 | — | 68 | 1 | no | — |
| 384 | C2×C4 | — | 68 | 1 | no | — |
| 385 | C2×C4 | — | 68 | 2 | no | — |
| 386 | C2×C4 | — | 68 | 1 | no | — |
| 387 | C2×C4 | — | 136 | 1 | no | — |
| 388 | C2×C4 | #10587678 | 1 | 1 | yes | characteristic |
| 389 | C2×C4 | #10587678 | 1 | 1 | yes | characteristic |
| 390 | C2×C4 | D4×#595 | 1 | 1 | yes | characteristic |
| 391 | C2×C4 | C22×#3624 | 1 | 1 | yes | characteristic |
| 392 | C2×C4 | C2×#63247 | 1 | 1 | yes | characteristic |
| 393 | C2×C4 | C2×C22⋊#595 | 1 | 1 | yes | characteristic |
| 394 | C8 | — | 2 | 2 | no | — |
| 395 | C8 | — | 68 | 2 | no | — |
| 396 | C8 | — | 68 | 1 | no | — |
| 397 | C8 | — | 68 | 1 | no | — |
| 398 | C8 | — | 68 | 2 | no | — |
| 399 | C8 | — | 68 | 1 | no | — |
| 400 | C8 | — | 136 | 1 | no | — |
| 401 | C22 | — | 2 | 1 | no | — |
| 402 | C22 | — | 2 | 1 | no | — |
| 403 | C22 | — | 2 | 2 | no | — |
| 404 | C22 | — | 4 | 1 | no | — |
| 405 | C22 | — | 4 | 1 | no | — |
| 406 | C22 | #11763757 | 1 | 1 | yes | characteristic |
| 407 | C22 | D4×#3624 | 1 | 1 | yes | characteristic |
| 408 | C22 | #11763840 | 1 | 1 | yes | characteristic |
| 409 | C4 | — | 2 | 2 | no | — |
| 410 | C4 | — | 4 | 2 | no | — |
| 411 | C4 | — | 17 | 1 | no | — |
| 412 | C4 | — | 17 | 1 | no | — |
| 413 | C4 | — | 34 | 1 | no | — |
| 414 | C4 | — | 34 | 1 | no | — |
| 415 | C4 | — | 34 | 1 | no | — |
| 416 | C4 | — | 68 | 1 | no | — |
| 417 | C4 | — | 68 | 1 | no | — |
| 418 | C4 | — | 136 | 1 | no | — |
| 419 | C4 | C2×C22⋊#3624 | 1 | 1 | yes | characteristic |
| 420 | C4 | #11763782 | 1 | 1 | yes | characteristic |
| 421 | C4 | D4×#3624 | 1 | 1 | yes | characteristic |
| 422 | C4 | #11763840 | 1 | 1 | yes | characteristic |
| 423 | C2 | — | 2 | 1 | no | — |
| 424 | C2 | — | 2 | 1 | no | — |
| 425 | C2 | — | 4 | 2 | no | — |
| 426 | C2 | #14544757 | 1 | 1 | yes | characteristic |
| 427 | C2 | #14544781 | 1 | 1 | yes | characteristic |
| 428 | C2 | #14544783 | 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