← #578×Dic17 #17898572
Subgroups — #578×Dic17 #17898572
Order 4352.
2658 conjugacy classes of subgroups.
The subgroup lattice has 446 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | 2−1+4×Dic17 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #14537660 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #14537652 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #14537628 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #137×Dic17 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #135×Dic17 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×Q16×Dic17 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #14537384 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #14537317 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #131×Dic17 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C2×C17×#578 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C2×#10587634 | C22 | 1 | 1 | yes | characteristic |
| 13 | #11763292 | — | 2 | 6 | no | — |
| 14 | #11763292 | C22 | 1 | 6 | yes | — |
| 15 | #11763292 | C22 | 1 | 2 | yes | — |
| 16 | #11763287 | — | 2 | 2 | no | — |
| 17 | #11763287 | C22 | 1 | 6 | yes | — |
| 18 | #41×Dic17 | — | 2 | 6 | no | — |
| 19 | #41×Dic17 | C22 | 1 | 6 | yes | — |
| 20 | #41×Dic17 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×Q8×Dic17 | — | 2 | 2 | no | — |
| 22 | C2×Q8×Dic17 | C22 | 1 | 6 | yes | — |
| 23 | #11762916 | C22 | 1 | 12 | yes | — |
| 24 | #11762910 | C22 | 1 | 12 | yes | — |
| 25 | Q16×Dic17 | C22 | 1 | 3 | yes | — |
| 26 | Q16×Dic17 | C22 | 1 | 6 | yes | — |
| 27 | Q16×Dic17 | C22 | 1 | 6 | yes | — |
| 28 | Q16×Dic17 | C22 | 1 | 6 | yes | — |
| 29 | Q16×Dic17 | C22 | 1 | 3 | yes | — |
| 30 | SD16×Dic17 | C22 | 1 | 6 | yes | — |
| 31 | SD16×Dic17 | C22 | 1 | 6 | yes | — |
| 32 | D8×Dic17 | C22 | 1 | 1 | yes | characteristic |
| 33 | D8×Dic17 | C22 | 1 | 3 | yes | — |
| 34 | #11762851 | C22 | 1 | 6 | yes | — |
| 35 | #11762847 | C22 | 1 | 3 | yes | — |
| 36 | C2×#10587489 | C22 | 1 | 3 | yes | — |
| 37 | #11762818 | C22 | 1 | 6 | yes | — |
| 38 | #11762810 | C22 | 1 | 6 | yes | — |
| 39 | #11762805 | C22 | 1 | 6 | yes | — |
| 40 | C2×#10587506 | C22 | 1 | 6 | yes | — |
| 41 | #11762767 | C22 | 1 | 3 | yes | — |
| 42 | #11762764 | C22 | 1 | 3 | yes | — |
| 43 | M16×Dic17 | C22 | 1 | 3 | yes | — |
| 44 | C2×C8×Dic17 | C22 | 1 | 3 | yes | — |
| 45 | C2×C17×2−1+4 | C22 | 1 | 2 | yes | — |
| 46 | C17×#578 | C4 | 1 | 16 | yes | complemented |
| 47 | C2×C17×#137 | C22 | 1 | 6 | yes | — |
| 48 | C2×C17×#135 | C22 | 1 | 3 | yes | — |
| 49 | C22×Q16×C17 | C22 | 1 | 3 | yes | — |
| 50 | C2×C17×#131 | C22 | 1 | 1 | yes | characteristic |
| 51 | C17×2−1+4 | — | 2 | 8 | no | — |
| 52 | C17×2−1+4 | C2×C4 | 1 | 16 | yes | complemented |
| 53 | C2×#41×C17 | — | 2 | 6 | no | — |
| 54 | C2×#41×C17 | C23 | 1 | 6 | yes | — |
| 55 | C2×#41×C17 | C23 | 1 | 1 | yes | characteristic |
| 56 | C22×Q8×C17 | — | 2 | 2 | no | — |
| 57 | C22×Q8×C17 | C23 | 1 | 6 | yes | — |
| 58 | C17×#137 | C2×C4 | 1 | 48 | yes | complemented |
| 59 | C17×#135 | C2×C4 | 1 | 24 | yes | complemented |
| 60 | C2×Q16×C17 | C2×C4 | 1 | 24 | yes | complemented |
| 61 | C2×Q16×C17 | C23 | 1 | 3 | yes | — |
| 62 | C2×Q16×C17 | C23 | 1 | 6 | yes | — |
| 63 | C2×SD16×C17 | C23 | 1 | 6 | yes | — |
| 64 | C2×D8×C17 | C23 | 1 | 1 | yes | characteristic |
| 65 | C17×#131 | C2×C4 | 1 | 8 | yes | complemented |
| 66 | C2×M16×C17 | C23 | 1 | 3 | yes | — |
| 67 | C22×C8×C17 | C23 | 1 | 3 | yes | — |
| 68 | #10587634 | — | 2 | 4 | no | — |
| 69 | Q8×Dic17 | — | 2 | 6 | no | — |
| 70 | Q8×Dic17 | — | 2 | 6 | no | — |
| 71 | Q8×Dic17 | — | 2 | 6 | no | — |
| 72 | Q8×Dic17 | — | 2 | 6 | no | — |
| 73 | Q8×Dic17 | — | 2 | 2 | no | — |
| 74 | Q8×Dic17 | D4 | 1 | 1 | yes | characteristic |
| 75 | Q8×Dic17 | D4 | 1 | 1 | yes | characteristic |
| 76 | Q8×Dic17 | C23 | 1 | 6 | yes | — |
| 77 | Q8×Dic17 | C23 | 1 | 12 | yes | — |
| 78 | Q8×Dic17 | C23 | 1 | 6 | yes | — |
| 79 | D4×Dic17 | — | 2 | 6 | no | — |
| 80 | D4×Dic17 | — | 2 | 6 | no | — |
| 81 | D4×Dic17 | — | 2 | 6 | no | — |
| 82 | D4×Dic17 | — | 2 | 12 | no | — |
| 83 | D4×Dic17 | D4 | 1 | 3 | yes | — |
| 84 | D4×Dic17 | D4 | 1 | 3 | yes | — |
| 85 | D4×Dic17 | C23 | 1 | 2 | yes | — |
| 86 | D4×Dic17 | C23 | 1 | 6 | yes | — |
| 87 | #10587612 | — | 2 | 6 | no | — |
| 88 | #10587612 | — | 2 | 6 | no | — |
| 89 | #10587612 | — | 2 | 12 | no | — |
| 90 | #10587612 | C23 | 1 | 6 | yes | — |
| 91 | #10587612 | C23 | 1 | 3 | yes | — |
| 92 | C2×C4⋊Dic17 | — | 2 | 6 | no | — |
| 93 | C2×C4⋊Dic17 | — | 2 | 6 | no | — |
| 94 | C2×C4⋊Dic17 | C23 | 1 | 6 | yes | — |
| 95 | C2×C4×Dic17 | — | 2 | 6 | no | — |
| 96 | C2×C4×Dic17 | — | 2 | 6 | no | — |
| 97 | C2×C4×Dic17 | C23 | 1 | 3 | yes | — |
| 98 | C2×#63223 | C23 | 1 | 3 | yes | — |
| 99 | C22×#3622 | C23 | 1 | 3 | yes | — |
| 100 | #10587506 | C23 | 1 | 6 | yes | — |
| 101 | #10587506 | C23 | 1 | 12 | yes | — |
| 102 | #10587506 | C23 | 1 | 6 | yes | — |
| 103 | #10587503 | C23 | 1 | 2 | yes | — |
| 104 | #10587503 | C23 | 1 | 6 | yes | — |
| 105 | #10587489 | C23 | 1 | 3 | yes | — |
| 106 | #10587489 | C23 | 1 | 6 | yes | — |
| 107 | #10587489 | C23 | 1 | 1 | yes | characteristic |
| 108 | #10587488 | C23 | 1 | 6 | yes | — |
| 109 | #10587486 | C23 | 1 | 6 | yes | — |
| 110 | C8×Dic17 | C23 | 1 | 1 | yes | characteristic |
| 111 | C8×Dic17 | C23 | 1 | 3 | yes | — |
| 112 | C8×Dic17 | C23 | 1 | 3 | yes | — |
| 113 | C8×Dic17 | C23 | 1 | 3 | yes | — |
| 114 | #41×C17 | — | 2 | 48 | no | — |
| 115 | #41×C17 | — | 2 | 12 | no | — |
| 116 | #41×C17 | C22×C4 | 1 | 24 | yes | — |
| 117 | #41×C17 | C22×C4 | 1 | 4 | yes | — |
| 118 | #41×C17 | #41 | 1 | 4 | yes | — |
| 119 | C2×Q8×C17 | — | 2 | 16 | no | — |
| 120 | C2×Q8×C17 | — | 2 | 6 | no | — |
| 121 | C2×Q8×C17 | — | 2 | 12 | no | — |
| 122 | C2×Q8×C17 | C22×C4 | 1 | 24 | yes | — |
| 123 | C2×Q8×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C2×Q8×C17 | C24 | 1 | 6 | yes | — |
| 125 | C2×D4×C17 | — | 2 | 6 | no | — |
| 126 | C2×D4×C17 | C2×D4 | 1 | 3 | yes | — |
| 127 | C2×D4×C17 | C24 | 1 | 2 | yes | — |
| 128 | C22×C4×C17 | — | 2 | 6 | no | — |
| 129 | C22×C4×C17 | — | 2 | 6 | no | — |
| 130 | C22×C4×C17 | C24 | 1 | 3 | yes | — |
| 131 | C22×Dic17 | — | 2 | 6 | no | — |
| 132 | C22×Dic17 | — | 2 | 2 | no | — |
| 133 | C22×Dic17 | — | 2 | 6 | no | — |
| 134 | C22×Dic17 | C2×D4 | 1 | 3 | yes | — |
| 135 | C22×Dic17 | C2×D4 | 1 | 3 | yes | — |
| 136 | Q16×C17 | C22×C4 | 1 | 12 | yes | — |
| 137 | Q16×C17 | C22×C4 | 1 | 24 | yes | — |
| 138 | SD16×C17 | C22×C4 | 1 | 24 | yes | — |
| 139 | D8×C17 | C22×C4 | 1 | 4 | yes | — |
| 140 | M16×C17 | C22×C4 | 1 | 12 | yes | — |
| 141 | C2×C8×C17 | C22×C4 | 1 | 12 | yes | — |
| 142 | C2×C8×C17 | C24 | 1 | 1 | yes | characteristic |
| 143 | C2×C8×C17 | C24 | 1 | 3 | yes | — |
| 144 | C22⋊Dic17 | — | 2 | 6 | no | — |
| 145 | C22⋊Dic17 | — | 2 | 2 | no | — |
| 146 | C22⋊Dic17 | — | 2 | 6 | no | — |
| 147 | C22⋊Dic17 | C2×D4 | 1 | 6 | yes | — |
| 148 | C4⋊Dic17 | — | 2 | 6 | no | — |
| 149 | C4⋊Dic17 | — | 2 | 6 | no | — |
| 150 | C4⋊Dic17 | — | 2 | 12 | no | — |
| 151 | C4⋊Dic17 | — | 2 | 6 | no | — |
| 152 | C4⋊Dic17 | C2×D4 | 1 | 3 | yes | — |
| 153 | C4⋊Dic17 | C2×D4 | 1 | 3 | yes | — |
| 154 | C4⋊Dic17 | C24 | 1 | 2 | yes | — |
| 155 | C4⋊Dic17 | C24 | 1 | 6 | yes | — |
| 156 | C4×Dic17 | — | 2 | 6 | no | — |
| 157 | C4×Dic17 | — | 2 | 6 | no | — |
| 158 | C4×Dic17 | — | 2 | 6 | no | — |
| 159 | C4×Dic17 | — | 2 | 12 | no | — |
| 160 | C4×Dic17 | C2×D4 | 1 | 3 | yes | — |
| 161 | C4×Dic17 | C2×D4 | 1 | 3 | yes | — |
| 162 | C4×Dic17 | C24 | 1 | 1 | yes | characteristic |
| 163 | C4×Dic17 | C24 | 1 | 3 | yes | — |
| 164 | #63223 | — | 2 | 6 | no | — |
| 165 | C2×#3622 | — | 2 | 6 | no | — |
| 166 | C2×#3622 | C24 | 1 | 1 | yes | characteristic |
| 167 | C2×#3622 | C24 | 1 | 3 | yes | — |
| 168 | C4×#578 | — | 17 | 1 | no | maximal, Sylow |
| 169 | C23×C17 | — | 2 | 2 | no | — |
| 170 | C23×C17 | C22×D4 | 1 | 3 | yes | — |
| 171 | Q8×C17 | — | 2 | 24 | no | — |
| 172 | Q8×C17 | — | 2 | 6 | no | — |
| 173 | Q8×C17 | C4×D4 | 1 | 4 | yes | — |
| 174 | Q8×C17 | C23×C4 | 1 | 12 | yes | — |
| 175 | D4×C17 | — | 2 | 24 | no | — |
| 176 | D4×C17 | — | 2 | 2 | no | — |
| 177 | D4×C17 | C4×D4 | 1 | 12 | yes | — |
| 178 | D4×C17 | C23×C4 | 1 | 4 | yes | — |
| 179 | C2×C4×C17 | — | 2 | 24 | no | — |
| 180 | C2×C4×C17 | — | 2 | 6 | no | — |
| 181 | C2×C4×C17 | — | 2 | 24 | no | — |
| 182 | C2×C4×C17 | C23×C4 | 1 | 6 | yes | — |
| 183 | C2×C4×C17 | C22×D4 | 1 | 3 | yes | — |
| 184 | C2×C4×C17 | C2×#41 | 1 | 6 | yes | — |
| 185 | C2×C4×C17 | C25 | 1 | 1 | yes | characteristic |
| 186 | C2×Dic17 | — | 2 | 6 | no | — |
| 187 | C2×Dic17 | — | 2 | 2 | no | — |
| 188 | C2×Dic17 | — | 2 | 6 | no | — |
| 189 | C2×Dic17 | — | 4 | 3 | no | — |
| 190 | C2×Dic17 | — | 4 | 4 | no | — |
| 191 | C2×Dic17 | — | 8 | 6 | no | — |
| 192 | C2×Dic17 | — | 8 | 6 | no | — |
| 193 | C2×Dic17 | C22×D4 | 1 | 3 | yes | — |
| 194 | C2×Dic17 | C22×D4 | 1 | 1 | yes | characteristic |
| 195 | C2×Dic17 | C22×D4 | 1 | 3 | yes | — |
| 196 | C2×Dic17 | C22×D4 | 1 | 1 | yes | characteristic |
| 197 | C8×C17 | C23×C4 | 1 | 2 | yes | — |
| 198 | C8×C17 | C23×C4 | 1 | 6 | yes | — |
| 199 | #3622 | — | 2 | 1 | no | — |
| 200 | #3622 | — | 2 | 3 | no | — |
| 201 | C2×#578 | D17 | 1 | 1 | yes | characteristic |
| 202 | C4×2−1+4 | — | 17 | 2 | no | — |
| 203 | #2951 | — | 17 | 3 | no | — |
| 204 | #2950 | — | 17 | 3 | no | — |
| 205 | #2947 | — | 17 | 6 | no | — |
| 206 | C4×#137 | — | 17 | 6 | no | — |
| 207 | C4×#135 | — | 17 | 3 | no | — |
| 208 | C2×C4×Q16 | — | 17 | 3 | no | — |
| 209 | #2913 | — | 17 | 1 | no | — |
| 210 | #2898 | — | 17 | 2 | no | — |
| 211 | C4×#131 | — | 17 | 1 | no | — |
| 212 | C22×C17 | — | 2 | 3 | no | — |
| 213 | C22×C17 | — | 2 | 3 | no | — |
| 214 | C22×C17 | — | 2 | 4 | no | — |
| 215 | C22×C17 | — | 4 | 2 | no | — |
| 216 | C22×C17 | — | 4 | 2 | no | — |
| 217 | C22×C17 | C2×C4×D4 | 1 | 6 | yes | — |
| 218 | C22×C17 | C23×D4 | 1 | 1 | yes | characteristic |
| 219 | C4×C17 | — | 2 | 12 | no | — |
| 220 | C4×C17 | C2×C4×D4 | 1 | 6 | yes | — |
| 221 | C4×C17 | C24×C4 | 1 | 1 | yes | characteristic |
| 222 | C4×C17 | C22×#41 | 1 | 1 | yes | characteristic |
| 223 | Dic17 | — | 2 | 1 | no | — |
| 224 | Dic17 | — | 2 | 3 | no | — |
| 225 | Dic17 | — | 2 | 3 | no | — |
| 226 | Dic17 | — | 4 | 6 | no | — |
| 227 | Dic17 | — | 4 | 2 | no | — |
| 228 | Dic17 | #578 | 1 | 2 | yes | direct product factor |
| 229 | C2×2−1+4 | C2×D17 | 1 | 2 | yes | — |
| 230 | #578 | Dic17 | 1 | 16 | yes | direct product factor |
| 231 | C2×#137 | C2×D17 | 1 | 6 | yes | — |
| 232 | C2×#135 | C2×D17 | 1 | 3 | yes | — |
| 233 | C22×Q16 | C2×D17 | 1 | 3 | yes | — |
| 234 | C2×#131 | — | 17 | 1 | no | — |
| 235 | C2×#131 | C2×D17 | 1 | 1 | yes | characteristic |
| 236 | #520 | — | 17 | 2 | no | — |
| 237 | #520 | — | 17 | 6 | no | — |
| 238 | #520 | — | 34 | 6 | no | — |
| 239 | #519 | — | 17 | 6 | no | — |
| 240 | #519 | — | 34 | 2 | no | — |
| 241 | C4×#41 | — | 17 | 1 | no | — |
| 242 | C4×#41 | — | 17 | 6 | no | — |
| 243 | C4×#41 | — | 34 | 6 | no | — |
| 244 | C2×C4×Q8 | — | 17 | 6 | no | — |
| 245 | C2×C4×Q8 | — | 34 | 2 | no | — |
| 246 | #441 | — | 17 | 12 | no | — |
| 247 | #440 | — | 17 | 12 | no | — |
| 248 | C4×Q16 | — | 17 | 3 | no | — |
| 249 | C4×Q16 | — | 17 | 6 | no | — |
| 250 | C4×Q16 | — | 17 | 6 | no | — |
| 251 | C4×Q16 | — | 17 | 6 | no | — |
| 252 | C4×Q16 | — | 17 | 3 | no | — |
| 253 | C4×SD16 | — | 17 | 6 | no | — |
| 254 | C4×SD16 | — | 17 | 6 | no | — |
| 255 | C4×D8 | — | 17 | 1 | no | — |
| 256 | C4×D8 | — | 17 | 3 | no | — |
| 257 | #428 | — | 17 | 6 | no | — |
| 258 | #427 | — | 17 | 3 | no | — |
| 259 | C2×#107 | — | 17 | 3 | no | — |
| 260 | #419 | — | 17 | 6 | no | — |
| 261 | #417 | — | 17 | 6 | no | — |
| 262 | #416 | — | 17 | 6 | no | — |
| 263 | C2×#103 | — | 17 | 6 | no | — |
| 264 | #405 | — | 17 | 3 | no | — |
| 265 | #405 | — | 17 | 3 | no | — |
| 266 | C4×M16 | — | 17 | 3 | no | — |
| 267 | C2×C4×C8 | — | 17 | 3 | no | — |
| 268 | C2×C17 | — | 2 | 6 | no | — |
| 269 | C2×C17 | — | 4 | 4 | no | — |
| 270 | C2×C17 | C22×C4×D4 | 1 | 1 | yes | characteristic |
| 271 | C2×C17 | C2×#578 | 1 | 1 | yes | characteristic |
| 272 | C2×C17 | #3584 | 1 | 1 | yes | characteristic |
| 273 | 2−1+4 | — | 2 | 8 | no | — |
| 274 | 2−1+4 | C2×Dic17 | 1 | 16 | yes | complemented |
| 275 | C2×#41 | — | 2 | 6 | no | — |
| 276 | C2×#41 | C22×D17 | 1 | 6 | yes | — |
| 277 | C2×#41 | C22×D17 | 1 | 1 | yes | characteristic |
| 278 | C22×Q8 | — | 2 | 2 | no | — |
| 279 | C22×Q8 | C22×D17 | 1 | 6 | yes | — |
| 280 | #137 | C2×Dic17 | 1 | 48 | yes | complemented |
| 281 | #135 | C2×Dic17 | 1 | 24 | yes | complemented |
| 282 | C2×Q16 | C2×Dic17 | 1 | 24 | yes | complemented |
| 283 | C2×Q16 | C22×D17 | 1 | 3 | yes | — |
| 284 | C2×Q16 | C22×D17 | 1 | 6 | yes | — |
| 285 | C2×SD16 | C22×D17 | 1 | 6 | yes | — |
| 286 | C2×D8 | C22×D17 | 1 | 1 | yes | characteristic |
| 287 | #131 | — | 34 | 4 | no | — |
| 288 | #131 | C2×Dic17 | 1 | 8 | yes | complemented |
| 289 | C2×M16 | — | 17 | 3 | no | — |
| 290 | C2×M16 | C22×D17 | 1 | 3 | yes | — |
| 291 | C22×C8 | — | 17 | 3 | no | — |
| 292 | C22×C8 | C22×D17 | 1 | 3 | yes | — |
| 293 | C4×Q8 | — | 17 | 1 | no | — |
| 294 | C4×Q8 | — | 17 | 1 | no | — |
| 295 | C4×Q8 | — | 17 | 6 | no | — |
| 296 | C4×Q8 | — | 17 | 12 | no | — |
| 297 | C4×Q8 | — | 17 | 6 | no | — |
| 298 | C4×Q8 | — | 34 | 6 | no | — |
| 299 | C4×Q8 | — | 34 | 6 | no | — |
| 300 | C4×Q8 | — | 34 | 6 | no | — |
| 301 | C4×Q8 | — | 34 | 6 | no | — |
| 302 | C4×Q8 | — | 34 | 2 | no | — |
| 303 | C4×D4 | — | 17 | 3 | no | — |
| 304 | C4×D4 | — | 17 | 3 | no | — |
| 305 | C4×D4 | — | 17 | 2 | no | — |
| 306 | C4×D4 | — | 17 | 6 | no | — |
| 307 | C4×D4 | — | 34 | 12 | no | — |
| 308 | C4×D4 | — | 34 | 6 | no | — |
| 309 | C4×D4 | — | 34 | 6 | no | — |
| 310 | C4×D4 | — | 34 | 6 | no | — |
| 311 | #117 | — | 17 | 3 | no | — |
| 312 | #117 | — | 17 | 6 | no | — |
| 313 | #117 | — | 34 | 6 | no | — |
| 314 | #117 | — | 34 | 12 | no | — |
| 315 | #117 | — | 34 | 6 | no | — |
| 316 | C2×C4⋊C4 | — | 17 | 6 | no | — |
| 317 | C2×C4⋊C4 | — | 34 | 6 | no | — |
| 318 | C2×C4⋊C4 | — | 34 | 6 | no | — |
| 319 | C2×C42 | — | 17 | 3 | no | — |
| 320 | C2×C42 | — | 34 | 6 | no | — |
| 321 | C2×C42 | — | 34 | 6 | no | — |
| 322 | #107 | — | 17 | 3 | no | — |
| 323 | #107 | — | 17 | 6 | no | — |
| 324 | #107 | — | 17 | 1 | no | — |
| 325 | #106 | — | 17 | 6 | no | — |
| 326 | #103 | — | 17 | 6 | no | — |
| 327 | #103 | — | 17 | 12 | no | — |
| 328 | #103 | — | 17 | 6 | no | — |
| 329 | #102 | — | 17 | 2 | no | — |
| 330 | #102 | — | 17 | 6 | no | — |
| 331 | #97 | — | 17 | 6 | no | — |
| 332 | C4×C8 | — | 17 | 1 | no | — |
| 333 | C4×C8 | — | 17 | 3 | no | — |
| 334 | C4×C8 | — | 17 | 3 | no | — |
| 335 | C4×C8 | — | 17 | 3 | no | — |
| 336 | C17 | C4×#578 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 337 | #41 | — | 2 | 48 | no | — |
| 338 | #41 | — | 2 | 12 | no | — |
| 339 | #41 | #63254 | 1 | 4 | yes | — |
| 340 | #41 | C22×Dic17 | 1 | 24 | yes | — |
| 341 | #41 | C22×Dic17 | 1 | 4 | yes | — |
| 342 | C2×Q8 | — | 2 | 16 | no | — |
| 343 | C2×Q8 | — | 2 | 6 | no | — |
| 344 | C2×Q8 | — | 2 | 12 | no | — |
| 345 | C2×Q8 | D4×D17 | 1 | 1 | yes | characteristic |
| 346 | C2×Q8 | C22×Dic17 | 1 | 24 | yes | — |
| 347 | C2×Q8 | C23×D17 | 1 | 6 | yes | — |
| 348 | C2×D4 | — | 2 | 6 | no | — |
| 349 | C2×D4 | D4×D17 | 1 | 3 | yes | — |
| 350 | C2×D4 | C23×D17 | 1 | 2 | yes | — |
| 351 | C22×C4 | — | 2 | 6 | no | — |
| 352 | C22×C4 | — | 2 | 6 | no | — |
| 353 | C22×C4 | — | 17 | 3 | no | — |
| 354 | C22×C4 | — | 17 | 3 | no | — |
| 355 | C22×C4 | — | 34 | 2 | no | — |
| 356 | C22×C4 | — | 34 | 6 | no | — |
| 357 | C22×C4 | — | 34 | 6 | no | — |
| 358 | C22×C4 | C23×D17 | 1 | 3 | yes | — |
| 359 | Q16 | C22×Dic17 | 1 | 12 | yes | — |
| 360 | Q16 | C22×Dic17 | 1 | 24 | yes | — |
| 361 | SD16 | C22×Dic17 | 1 | 24 | yes | — |
| 362 | D8 | C22×Dic17 | 1 | 4 | yes | — |
| 363 | M16 | — | 34 | 6 | no | — |
| 364 | M16 | C22×Dic17 | 1 | 12 | yes | — |
| 365 | C2×C8 | — | 17 | 1 | no | — |
| 366 | C2×C8 | — | 17 | 3 | no | — |
| 367 | C2×C8 | — | 34 | 6 | no | — |
| 368 | C2×C8 | C22×Dic17 | 1 | 12 | yes | — |
| 369 | C2×C8 | C23×D17 | 1 | 1 | yes | characteristic |
| 370 | C2×C8 | C23×D17 | 1 | 3 | yes | — |
| 371 | C4⋊C4 | — | 17 | 3 | no | — |
| 372 | C4⋊C4 | — | 17 | 3 | no | — |
| 373 | C4⋊C4 | — | 17 | 2 | no | — |
| 374 | C4⋊C4 | — | 17 | 6 | no | — |
| 375 | C4⋊C4 | — | 34 | 6 | no | — |
| 376 | C4⋊C4 | — | 34 | 12 | no | — |
| 377 | C4⋊C4 | — | 34 | 6 | no | — |
| 378 | C4⋊C4 | — | 34 | 6 | no | — |
| 379 | C22⋊C4 | — | 17 | 6 | no | — |
| 380 | C22⋊C4 | — | 34 | 2 | no | — |
| 381 | C22⋊C4 | — | 34 | 6 | no | — |
| 382 | C22⋊C4 | — | 34 | 6 | no | — |
| 383 | C42 | — | 17 | 3 | no | — |
| 384 | C42 | — | 17 | 3 | no | — |
| 385 | C42 | — | 17 | 1 | no | — |
| 386 | C42 | — | 17 | 3 | no | — |
| 387 | C42 | — | 34 | 6 | no | — |
| 388 | C42 | — | 34 | 12 | no | — |
| 389 | C42 | — | 34 | 6 | no | — |
| 390 | C42 | — | 34 | 6 | no | — |
| 391 | C23 | — | 2 | 2 | no | — |
| 392 | C23 | C2×D4×D17 | 1 | 3 | yes | — |
| 393 | Q8 | — | 2 | 24 | no | — |
| 394 | Q8 | — | 2 | 6 | no | — |
| 395 | Q8 | D4×Dic17 | 1 | 4 | yes | — |
| 396 | Q8 | C23×Dic17 | 1 | 12 | yes | — |
| 397 | D4 | — | 2 | 24 | no | — |
| 398 | D4 | — | 2 | 2 | no | — |
| 399 | D4 | D4×Dic17 | 1 | 12 | yes | — |
| 400 | D4 | C23×Dic17 | 1 | 4 | yes | — |
| 401 | C2×C4 | — | 2 | 24 | no | — |
| 402 | C2×C4 | — | 2 | 6 | no | — |
| 403 | C2×C4 | — | 2 | 24 | no | — |
| 404 | C2×C4 | — | 17 | 1 | no | — |
| 405 | C2×C4 | — | 17 | 1 | no | — |
| 406 | C2×C4 | — | 17 | 3 | no | — |
| 407 | C2×C4 | — | 17 | 3 | no | — |
| 408 | C2×C4 | — | 34 | 6 | no | — |
| 409 | C2×C4 | — | 34 | 2 | no | — |
| 410 | C2×C4 | — | 34 | 6 | no | — |
| 411 | C2×C4 | — | 68 | 4 | no | — |
| 412 | C2×C4 | — | 68 | 3 | no | — |
| 413 | C2×C4 | — | 136 | 6 | no | — |
| 414 | C2×C4 | — | 136 | 6 | no | — |
| 415 | C2×C4 | C2×D4×D17 | 1 | 3 | yes | — |
| 416 | C2×C4 | C2×#63254 | 1 | 6 | yes | — |
| 417 | C2×C4 | C23×Dic17 | 1 | 6 | yes | — |
| 418 | C2×C4 | C24×D17 | 1 | 1 | yes | characteristic |
| 419 | C8 | — | 34 | 1 | no | — |
| 420 | C8 | — | 34 | 3 | no | — |
| 421 | C8 | C23×Dic17 | 1 | 2 | yes | — |
| 422 | C8 | C23×Dic17 | 1 | 6 | yes | — |
| 423 | C22 | — | 2 | 3 | no | — |
| 424 | C22 | — | 2 | 3 | no | — |
| 425 | C22 | — | 2 | 4 | no | — |
| 426 | C22 | — | 4 | 2 | no | — |
| 427 | C22 | — | 4 | 2 | no | — |
| 428 | C22 | C2×D4×Dic17 | 1 | 6 | yes | — |
| 429 | C22 | C22×D4×D17 | 1 | 1 | yes | characteristic |
| 430 | C4 | — | 2 | 12 | no | — |
| 431 | C4 | — | 17 | 2 | no | — |
| 432 | C4 | — | 34 | 3 | no | — |
| 433 | C4 | — | 34 | 1 | no | — |
| 434 | C4 | — | 34 | 3 | no | — |
| 435 | C4 | — | 68 | 2 | no | — |
| 436 | C4 | — | 68 | 6 | no | — |
| 437 | C4 | C2×D4×Dic17 | 1 | 6 | yes | — |
| 438 | C4 | C24×Dic17 | 1 | 1 | yes | characteristic |
| 439 | C4 | C22×#63254 | 1 | 1 | yes | characteristic |
| 440 | C2 | — | 2 | 6 | no | — |
| 441 | C2 | — | 4 | 4 | no | — |
| 442 | C2 | C22×D4×Dic17 | 1 | 1 | yes | characteristic |
| 443 | C2 | D17×#578 | 1 | 1 | yes | characteristic |
| 444 | C2 | #14543554 | 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