← #72323002
Subgroups — #72323002
Order 2048.
834 conjugacy classes of subgroups.
The subgroup lattice has 402 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72322983 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72320492 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72286838 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72286459 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #72232000 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C2×#93877 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72231870 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72224639 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #512761 | C4 | 1 | 1 | yes | characteristic |
| 10 | #483760 | — | 2 | 2 | no | — |
| 11 | #483499 | C22 | 1 | 2 | yes | — |
| 12 | #151085 | C4 | 1 | 1 | yes | characteristic |
| 13 | #151085 | C22 | 1 | 1 | yes | characteristic |
| 14 | #151084 | C4 | 1 | 1 | yes | characteristic |
| 15 | #151084 | C22 | 1 | 1 | yes | characteristic |
| 16 | #151083 | C4 | 1 | 2 | yes | — |
| 17 | #151083 | C22 | 1 | 2 | yes | — |
| 18 | #151037 | C4 | 1 | 1 | yes | characteristic |
| 19 | #150062 | C4 | 1 | 2 | yes | — |
| 20 | #149502 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#7330 | C22 | 1 | 1 | yes | characteristic |
| 22 | #122963 | C22 | 1 | 4 | yes | — |
| 23 | #122962 | C22 | 1 | 4 | yes | — |
| 24 | #122961 | — | 2 | 4 | no | — |
| 25 | C2×#7099 | C22 | 1 | 2 | yes | — |
| 26 | #122465 | — | 2 | 2 | no | — |
| 27 | #122214 | C22 | 1 | 1 | yes | characteristic |
| 28 | #93877 | C22 | 1 | 2 | yes | — |
| 29 | #93877 | C22 | 1 | 2 | yes | — |
| 30 | #93758 | C22 | 1 | 4 | yes | — |
| 31 | #93757 | C22 | 1 | 4 | yes | — |
| 32 | #93668 | C22 | 1 | 2 | yes | — |
| 33 | #93668 | C22 | 1 | 2 | yes | — |
| 34 | C2×#2262 | C8 | 1 | 1 | yes | characteristic |
| 35 | #33502 | — | 4 | 2 | no | — |
| 36 | C4×#508 | C2×C4 | 1 | 2 | yes | — |
| 37 | C8×#135 | — | 2 | 2 | no | — |
| 38 | #13654 | C8 | 1 | 1 | yes | characteristic |
| 39 | #13654 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | #13653 | C8 | 1 | 1 | yes | characteristic |
| 41 | #13653 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | #13652 | C8 | 1 | 2 | yes | — |
| 43 | #13652 | C2×C4 | 1 | 2 | yes | — |
| 44 | #13633 | C8 | 1 | 1 | yes | characteristic |
| 45 | #13615 | C8 | 1 | 2 | yes | — |
| 46 | C4×M64 | — | 2 | 1 | no | — |
| 47 | C2×#1397 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | C2×#1397 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | #12062 | — | 2 | 4 | no | — |
| 50 | #12059 | — | 2 | 4 | no | — |
| 51 | C16×SD16 | — | 4 | 4 | no | — |
| 52 | #12045 | C2×C4 | 1 | 2 | yes | — |
| 53 | #12045 | C23 | 1 | 2 | yes | — |
| 54 | #12044 | C2×C4 | 1 | 2 | yes | — |
| 55 | #12044 | C23 | 1 | 2 | yes | — |
| 56 | #12043 | — | 2 | 2 | no | — |
| 57 | #12043 | — | 2 | 2 | no | — |
| 58 | #12008 | C2×C4 | 1 | 2 | yes | — |
| 59 | C2×#1367 | — | 2 | 2 | no | — |
| 60 | #11621 | — | 4 | 2 | no | — |
| 61 | #11591 | — | 2 | 2 | no | — |
| 62 | #11410 | D4 | 1 | 2 | yes | — |
| 63 | C2×#1311 | C23 | 1 | 1 | yes | characteristic |
| 64 | #7463 | C2×C4 | 1 | 2 | yes | — |
| 65 | #7463 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | #7463 | C2×C4 | 1 | 1 | yes | characteristic |
| 67 | #7386 | C2×C4 | 1 | 2 | yes | — |
| 68 | #7386 | C2×C4 | 1 | 2 | yes | — |
| 69 | #7385 | C2×C4 | 1 | 2 | yes | — |
| 70 | #7385 | C2×C4 | 1 | 2 | yes | — |
| 71 | #7332 | — | 2 | 1 | no | — |
| 72 | #7332 | C23 | 1 | 2 | yes | — |
| 73 | #7330 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | #7330 | C2×C4 | 1 | 1 | yes | characteristic |
| 75 | #7330 | C23 | 1 | 1 | yes | characteristic |
| 76 | #7330 | C23 | 1 | 1 | yes | characteristic |
| 77 | #7099 | — | 2 | 2 | no | — |
| 78 | #7099 | C23 | 1 | 4 | yes | — |
| 79 | #7071 | — | 2 | 4 | no | — |
| 80 | #7070 | — | 2 | 4 | no | — |
| 81 | #7053 | D4 | 1 | 2 | yes | — |
| 82 | #7053 | C23 | 1 | 2 | yes | — |
| 83 | C2×#508 | C2×C8 | 1 | 2 | yes | — |
| 84 | C8×#41 | — | 4 | 2 | no | — |
| 85 | C4×#135 | — | 2 | 2 | no | — |
| 86 | #2262 | C16 | 1 | 8 | yes | complemented |
| 87 | C2×Q64 | C2×C8 | 1 | 1 | yes | characteristic |
| 88 | C2×SD64 | C2×C8 | 1 | 2 | yes | — |
| 89 | C2×D32 | C2×C8 | 1 | 1 | yes | characteristic |
| 90 | C2×M64 | — | 4 | 1 | no | — |
| 91 | C22×C32 | — | 2 | 1 | no | — |
| 92 | C22×C32 | C2×C8 | 1 | 1 | yes | characteristic |
| 93 | C22×C32 | C2×C8 | 1 | 1 | yes | characteristic |
| 94 | Q8×C16 | — | 4 | 4 | no | — |
| 95 | C4×Q32 | C2×C8 | 1 | 2 | yes | — |
| 96 | C4×Q32 | C22×C4 | 1 | 2 | yes | — |
| 97 | C4×SD32 | — | 2 | 2 | no | — |
| 98 | C4×SD32 | — | 2 | 2 | no | — |
| 99 | C4×D16 | C2×C8 | 1 | 2 | yes | — |
| 100 | C4×D16 | C22×C4 | 1 | 2 | yes | — |
| 101 | D4×C16 | — | 4 | 4 | no | — |
| 102 | D4×C16 | — | 8 | 4 | no | — |
| 103 | #2162 | — | 2 | 2 | no | — |
| 104 | #2162 | — | 8 | 2 | no | — |
| 105 | #2158 | C2×C8 | 1 | 2 | yes | — |
| 106 | C2×C4⋊C16 | — | 4 | 2 | no | — |
| 107 | C2×C4⋊C16 | — | 8 | 2 | no | — |
| 108 | #2138 | — | 2 | 2 | no | — |
| 109 | C2×C4×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 110 | C2×C4×C16 | #41 | 1 | 1 | yes | characteristic |
| 111 | C8×Q16 | — | 2 | 2 | no | — |
| 112 | C8×Q16 | — | 2 | 2 | no | — |
| 113 | C8×SD16 | — | 4 | 2 | no | — |
| 114 | C8×SD16 | — | 4 | 2 | no | — |
| 115 | C8×D8 | — | 2 | 2 | no | — |
| 116 | C8×D8 | — | 2 | 2 | no | — |
| 117 | #1564 | — | 2 | 2 | no | — |
| 118 | #1476 | — | 4 | 2 | no | — |
| 119 | C2×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | #1424 | C2×C8 | 1 | 1 | yes | characteristic |
| 121 | #1424 | C2×C8 | 1 | 1 | yes | characteristic |
| 122 | #1423 | C2×C8 | 1 | 2 | yes | — |
| 123 | #1416 | C2×C8 | 1 | 2 | yes | — |
| 124 | #1416 | C2×C8 | 1 | 2 | yes | — |
| 125 | #1415 | C2×C8 | 1 | 2 | yes | — |
| 126 | #1415 | C2×C8 | 1 | 2 | yes | — |
| 127 | #1397 | — | 2 | 1 | no | — |
| 128 | #1397 | — | 2 | 2 | no | — |
| 129 | #1397 | C2×C8 | 1 | 1 | yes | characteristic |
| 130 | #1397 | C2×C8 | 1 | 1 | yes | characteristic |
| 131 | #1397 | C22×C4 | 1 | 1 | yes | characteristic |
| 132 | #1397 | C22×C4 | 1 | 1 | yes | characteristic |
| 133 | #1397 | C22×C4 | 1 | 1 | yes | characteristic |
| 134 | #1397 | C22×C4 | 1 | 1 | yes | characteristic |
| 135 | C4×C32 | — | 4 | 1 | no | — |
| 136 | #1372 | C22×C4 | 1 | 2 | yes | — |
| 137 | #1372 | C22×C4 | 1 | 2 | yes | — |
| 138 | #1371 | — | 2 | 2 | no | — |
| 139 | #1367 | — | 2 | 4 | no | — |
| 140 | #1367 | — | 4 | 2 | no | — |
| 141 | Q8⋊C16 | — | 4 | 4 | no | — |
| 142 | #1332 | — | 2 | 2 | no | — |
| 143 | #1332 | — | 2 | 2 | no | — |
| 144 | #1331 | — | 2 | 2 | no | — |
| 145 | #1331 | — | 2 | 2 | no | — |
| 146 | D4⋊C16 | — | 4 | 4 | no | — |
| 147 | #1312 | C2×D4 | 1 | 4 | yes | — |
| 148 | #1311 | C22×C4 | 1 | 1 | yes | characteristic |
| 149 | #1311 | C2×D4 | 1 | 1 | yes | characteristic |
| 150 | #1311 | #41 | 1 | 1 | yes | characteristic |
| 151 | #1311 | C24 | 1 | 1 | yes | characteristic |
| 152 | C8×C16 | — | 2 | 2 | no | — |
| 153 | C2×#135 | — | 2 | 2 | no | — |
| 154 | C4×#41 | — | 4 | 2 | no | — |
| 155 | #508 | — | 2 | 4 | no | — |
| 156 | #508 | C2×C16 | 1 | 8 | yes | complemented |
| 157 | C2×Q32 | C22×C8 | 1 | 2 | yes | — |
| 158 | C2×SD32 | — | 2 | 2 | no | — |
| 159 | C2×D16 | C22×C8 | 1 | 2 | yes | — |
| 160 | C22×C16 | — | 2 | 1 | no | — |
| 161 | C22×C16 | — | 8 | 4 | no | — |
| 162 | C22×C16 | — | 8 | 2 | no | — |
| 163 | C22×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 164 | C22×C16 | #131 | 1 | 1 | yes | characteristic |
| 165 | C8×Q8 | — | 4 | 2 | no | — |
| 166 | C8×Q8 | — | 4 | 2 | no | — |
| 167 | C4×Q16 | — | 2 | 2 | no | — |
| 168 | C4×Q16 | — | 2 | 2 | no | — |
| 169 | C4×SD16 | — | 4 | 2 | no | — |
| 170 | C4×SD16 | — | 4 | 2 | no | — |
| 171 | C4×D8 | — | 2 | 2 | no | — |
| 172 | C4×D8 | — | 2 | 2 | no | — |
| 173 | C8×D4 | — | 4 | 2 | no | — |
| 174 | C8×D4 | — | 4 | 2 | no | — |
| 175 | C8×D4 | — | 8 | 2 | no | — |
| 176 | C8×D4 | — | 8 | 2 | no | — |
| 177 | #431 | — | 4 | 2 | no | — |
| 178 | #431 | — | 8 | 2 | no | — |
| 179 | #427 | — | 2 | 2 | no | — |
| 180 | #416 | — | 4 | 2 | no | — |
| 181 | C2×C4×C8 | — | 8 | 2 | no | — |
| 182 | C2×C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 183 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 184 | Q64 | C2×C16 | 1 | 4 | yes | complemented |
| 185 | SD64 | C2×C16 | 1 | 8 | yes | complemented |
| 186 | D32 | C2×C16 | 1 | 4 | yes | complemented |
| 187 | M64 | — | 8 | 2 | no | — |
| 188 | C2×C32 | — | 2 | 2 | no | — |
| 189 | C2×C32 | — | 2 | 1 | no | — |
| 190 | C2×C32 | — | 2 | 1 | no | — |
| 191 | C2×C32 | — | 4 | 2 | no | — |
| 192 | C2×C32 | — | 4 | 2 | no | — |
| 193 | C2×C32 | C2×C16 | 1 | 4 | yes | complemented |
| 194 | C2×C32 | C22×C8 | 1 | 1 | yes | characteristic |
| 195 | C2×C32 | C22×C8 | 1 | 1 | yes | characteristic |
| 196 | C2×C32 | C22×C8 | 1 | 1 | yes | characteristic |
| 197 | C2×C32 | C22×C8 | 1 | 1 | yes | characteristic |
| 198 | #367 | — | 2 | 2 | no | — |
| 199 | #366 | C22×C8 | 1 | 2 | yes | — |
| 200 | #366 | C22×C8 | 1 | 2 | yes | — |
| 201 | C4⋊C16 | — | 4 | 2 | no | — |
| 202 | C4⋊C16 | — | 4 | 4 | no | — |
| 203 | C4⋊C16 | — | 8 | 2 | no | — |
| 204 | C4⋊C16 | — | 8 | 4 | no | — |
| 205 | #358 | — | 2 | 2 | no | — |
| 206 | #358 | — | 2 | 2 | no | — |
| 207 | #357 | — | 2 | 2 | no | — |
| 208 | #357 | — | 2 | 2 | no | — |
| 209 | C22⋊C16 | — | 4 | 2 | no | — |
| 210 | C22⋊C16 | — | 8 | 4 | no | — |
| 211 | C4×C16 | — | 2 | 4 | no | — |
| 212 | C4×C16 | — | 2 | 1 | no | — |
| 213 | C4×C16 | — | 8 | 4 | no | — |
| 214 | C4×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 215 | C4×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 216 | C4×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 217 | C4×C16 | #131 | 1 | 1 | yes | characteristic |
| 218 | C4×C16 | C23×C4 | 1 | 1 | yes | characteristic |
| 219 | C4×C16 | C2×#41 | 1 | 1 | yes | characteristic |
| 220 | #335 | — | 2 | 2 | no | — |
| 221 | #335 | — | 2 | 2 | no | — |
| 222 | #334 | — | 4 | 2 | no | — |
| 223 | Q8⋊C8 | — | 4 | 2 | no | — |
| 224 | Q8⋊C8 | — | 4 | 2 | no | — |
| 225 | D4⋊C8 | — | 4 | 2 | no | — |
| 226 | D4⋊C8 | — | 4 | 2 | no | — |
| 227 | C82 | C4×D4 | 1 | 1 | yes | characteristic |
| 228 | C82 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 229 | C82 | C22×D4 | 1 | 1 | yes | characteristic |
| 230 | C2×#41 | — | 4 | 2 | no | — |
| 231 | #135 | — | 2 | 8 | no | — |
| 232 | #135 | — | 4 | 4 | no | — |
| 233 | C2×Q16 | — | 2 | 2 | no | — |
| 234 | C2×SD16 | — | 4 | 2 | no | — |
| 235 | C2×D8 | — | 2 | 2 | no | — |
| 236 | C22×C8 | — | 2 | 2 | no | — |
| 237 | C22×C8 | — | 8 | 2 | no | — |
| 238 | C22×C8 | — | 8 | 2 | no | — |
| 239 | C22×C8 | C8×D4 | 1 | 1 | yes | characteristic |
| 240 | C22×C8 | #444 | 1 | 1 | yes | characteristic |
| 241 | C4×Q8 | — | 4 | 2 | no | — |
| 242 | C4×Q8 | — | 4 | 2 | no | — |
| 243 | C4×D4 | — | 4 | 2 | no | — |
| 244 | C4×D4 | — | 4 | 2 | no | — |
| 245 | C4×D4 | — | 8 | 2 | no | — |
| 246 | C4×D4 | — | 8 | 2 | no | — |
| 247 | #117 | — | 4 | 2 | no | — |
| 248 | #117 | — | 8 | 2 | no | — |
| 249 | C2×C42 | — | 8 | 2 | no | — |
| 250 | C2×C42 | #442 | 1 | 1 | yes | characteristic |
| 251 | Q32 | — | 2 | 2 | no | — |
| 252 | Q32 | C22×C16 | 1 | 4 | yes | — |
| 253 | SD32 | — | 2 | 8 | no | — |
| 254 | D16 | — | 2 | 2 | no | — |
| 255 | D16 | C22×C16 | 1 | 4 | yes | — |
| 256 | C2×C16 | — | 2 | 2 | no | — |
| 257 | C2×C16 | — | 2 | 1 | no | — |
| 258 | C2×C16 | — | 2 | 1 | no | — |
| 259 | C2×C16 | — | 4 | 2 | no | — |
| 260 | C2×C16 | — | 4 | 4 | no | — |
| 261 | C2×C16 | — | 8 | 4 | no | — |
| 262 | C2×C16 | — | 32 | 4 | no | — |
| 263 | C2×C16 | — | 32 | 2 | no | — |
| 264 | C2×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 265 | C2×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 266 | C2×C16 | C22×C16 | 1 | 2 | yes | — |
| 267 | C2×C16 | #504 | 1 | 2 | yes | — |
| 268 | C2×C16 | C23×C8 | 1 | 1 | yes | characteristic |
| 269 | C2×C16 | C2×#131 | 1 | 1 | yes | characteristic |
| 270 | #107 | — | 2 | 2 | no | — |
| 271 | #107 | — | 2 | 2 | no | — |
| 272 | #106 | — | 4 | 2 | no | — |
| 273 | C4⋊C8 | — | 4 | 2 | no | — |
| 274 | C4⋊C8 | — | 4 | 2 | no | — |
| 275 | C4⋊C8 | — | 8 | 2 | no | — |
| 276 | C4⋊C8 | — | 8 | 2 | no | — |
| 277 | #103 | — | 4 | 2 | no | — |
| 278 | #103 | — | 4 | 2 | no | — |
| 279 | #102 | — | 4 | 2 | no | — |
| 280 | #102 | — | 4 | 2 | no | — |
| 281 | C22⋊C8 | — | 8 | 2 | no | — |
| 282 | C22⋊C8 | — | 8 | 2 | no | — |
| 283 | C22⋊C8 | — | 8 | 2 | no | — |
| 284 | C4×C8 | — | 2 | 2 | no | — |
| 285 | C4×C8 | — | 8 | 2 | no | — |
| 286 | C4×C8 | — | 8 | 2 | no | — |
| 287 | C4×C8 | — | 8 | 2 | no | — |
| 288 | C4×C8 | C8×D4 | 1 | 1 | yes | characteristic |
| 289 | C4×C8 | #442 | 1 | 2 | yes | — |
| 290 | C4×C8 | #442 | 1 | 1 | yes | characteristic |
| 291 | C4×C8 | #444 | 1 | 1 | yes | characteristic |
| 292 | C4×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 293 | C4×C8 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 294 | C32 | — | 2 | 1 | no | — |
| 295 | C32 | — | 2 | 1 | no | — |
| 296 | C32 | — | 4 | 1 | no | — |
| 297 | C32 | — | 4 | 1 | no | — |
| 298 | C32 | — | 8 | 2 | no | — |
| 299 | C32 | C22×C16 | 1 | 2 | yes | — |
| 300 | C32 | C22×C16 | 1 | 2 | yes | — |
| 301 | #41 | — | 4 | 8 | no | — |
| 302 | #41 | — | 8 | 4 | no | — |
| 303 | C2×Q8 | — | 4 | 2 | no | — |
| 304 | C2×D4 | — | 4 | 2 | no | — |
| 305 | C2×D4 | — | 8 | 2 | no | — |
| 306 | C22×C4 | — | 8 | 2 | no | — |
| 307 | C22×C4 | — | 8 | 2 | no | — |
| 308 | C22×C4 | — | 8 | 2 | no | — |
| 309 | C22×C4 | #1580 | 1 | 1 | yes | characteristic |
| 310 | C22×C4 | AGL(1,ℤ/16) | 1 | 2 | yes | — |
| 311 | Q16 | — | 2 | 4 | no | — |
| 312 | Q16 | — | 4 | 2 | no | — |
| 313 | SD16 | — | 4 | 8 | no | — |
| 314 | D8 | — | 2 | 4 | no | — |
| 315 | D8 | — | 4 | 2 | no | — |
| 316 | C2×C8 | — | 2 | 2 | no | — |
| 317 | C2×C8 | — | 2 | 2 | no | — |
| 318 | C2×C8 | — | 2 | 2 | no | — |
| 319 | C2×C8 | — | 8 | 2 | no | — |
| 320 | C2×C8 | — | 8 | 2 | no | — |
| 321 | C2×C8 | — | 8 | 2 | no | — |
| 322 | C2×C8 | — | 16 | 2 | no | — |
| 323 | C2×C8 | — | 16 | 2 | no | — |
| 324 | C2×C8 | — | 32 | 2 | no | — |
| 325 | C2×C8 | #1580 | 1 | 1 | yes | characteristic |
| 326 | C2×C8 | #1580 | 1 | 1 | yes | characteristic |
| 327 | C2×C8 | D4×C16 | 1 | 2 | yes | — |
| 328 | C2×C8 | #2171 | 1 | 2 | yes | — |
| 329 | C2×C8 | C2×C8×D4 | 1 | 1 | yes | characteristic |
| 330 | C2×C8 | C2×#444 | 1 | 1 | yes | characteristic |
| 331 | C4⋊C4 | — | 4 | 2 | no | — |
| 332 | C4⋊C4 | — | 4 | 2 | no | — |
| 333 | C4⋊C4 | — | 8 | 2 | no | — |
| 334 | C4⋊C4 | — | 8 | 2 | no | — |
| 335 | C22⋊C4 | — | 8 | 2 | no | — |
| 336 | C22⋊C4 | — | 8 | 2 | no | — |
| 337 | C22⋊C4 | — | 8 | 2 | no | — |
| 338 | C42 | — | 8 | 2 | no | — |
| 339 | C42 | — | 8 | 2 | no | — |
| 340 | C42 | — | 8 | 2 | no | — |
| 341 | C42 | #1580 | 1 | 1 | yes | characteristic |
| 342 | C42 | AGL(1,ℤ/16) | 1 | 2 | yes | — |
| 343 | C42 | C2×#442 | 1 | 1 | yes | characteristic |
| 344 | C16 | — | 2 | 1 | no | — |
| 345 | C16 | — | 2 | 1 | no | — |
| 346 | C16 | — | 4 | 1 | no | — |
| 347 | C16 | — | 4 | 1 | no | — |
| 348 | C16 | — | 8 | 4 | no | — |
| 349 | C16 | — | 16 | 4 | no | — |
| 350 | C16 | D4×C16 | 1 | 2 | yes | — |
| 351 | C16 | C23×C16 | 1 | 1 | yes | characteristic |
| 352 | C16 | C2×#504 | 1 | 1 | yes | characteristic |
| 353 | C23 | — | 8 | 2 | no | — |
| 354 | C23 | #12067 | 1 | 1 | yes | characteristic |
| 355 | Q8 | — | 4 | 4 | no | — |
| 356 | Q8 | — | 8 | 2 | no | — |
| 357 | D4 | — | 4 | 4 | no | — |
| 358 | D4 | — | 8 | 8 | no | — |
| 359 | D4 | — | 8 | 2 | no | — |
| 360 | C2×C4 | — | 4 | 2 | no | — |
| 361 | C2×C4 | — | 8 | 2 | no | — |
| 362 | C2×C4 | — | 8 | 8 | no | — |
| 363 | C2×C4 | — | 8 | 2 | no | — |
| 364 | C2×C4 | — | 8 | 2 | no | — |
| 365 | C2×C4 | — | 16 | 2 | no | — |
| 366 | C2×C4 | — | 16 | 2 | no | — |
| 367 | C2×C4 | — | 32 | 2 | no | — |
| 368 | C2×C4 | #12062 | 1 | 2 | yes | — |
| 369 | C2×C4 | #12067 | 1 | 2 | yes | — |
| 370 | C2×C4 | #12067 | 1 | 1 | yes | characteristic |
| 371 | C2×C4 | #12068 | 1 | 2 | yes | — |
| 372 | C2×C4 | C2×#1580 | 1 | 1 | yes | characteristic |
| 373 | C2×C4 | C2×AGL(1,ℤ/16) | 1 | 2 | yes | — |
| 374 | C8 | — | 2 | 1 | no | — |
| 375 | C8 | — | 2 | 1 | no | — |
| 376 | C8 | — | 4 | 2 | no | — |
| 377 | C8 | — | 4 | 2 | no | — |
| 378 | C8 | — | 16 | 2 | no | — |
| 379 | C8 | — | 16 | 2 | no | — |
| 380 | C8 | #12062 | 1 | 2 | yes | — |
| 381 | C8 | C2×D4×C16 | 1 | 1 | yes | characteristic |
| 382 | C8 | C2×#2171 | 1 | 1 | yes | characteristic |
| 383 | C22 | — | 2 | 2 | no | — |
| 384 | C22 | — | 8 | 4 | no | — |
| 385 | C22 | — | 16 | 2 | no | — |
| 386 | C22 | — | 16 | 2 | no | — |
| 387 | C22 | #122963 | 1 | 2 | yes | — |
| 388 | C22 | C2×#12067 | 1 | 1 | yes | characteristic |
| 389 | C4 | — | 2 | 2 | no | — |
| 390 | C4 | — | 2 | 2 | no | — |
| 391 | C4 | — | 8 | 4 | no | — |
| 392 | C4 | — | 16 | 2 | no | — |
| 393 | C4 | — | 16 | 2 | no | — |
| 394 | C4 | #122963 | 1 | 2 | yes | — |
| 395 | C4 | C2×#12062 | 1 | 1 | yes | characteristic |
| 396 | C4 | C2×#12068 | 1 | 1 | yes | characteristic |
| 397 | C2 | — | 2 | 2 | no | — |
| 398 | C2 | — | 16 | 4 | no | — |
| 399 | C2 | #72225055 | 1 | 2 | yes | — |
| 400 | C2 | C2×#122963 | 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