← #32033323
Subgroups — #32033323
Order 18176.
1308 conjugacy classes of subgroups.
The subgroup lattice has 394 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#17986271 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22597574 | C2 | 1 | 2 | yes | maximal |
| 3 | #22597034 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #22589605 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22589459 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22589256 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22588378 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #22588264 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C23×Q16×C71 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#14556159 | C22 | 1 | 4 | yes | — |
| 11 | C2×#14556134 | C22 | 1 | 1 | yes | characteristic |
| 12 | #17986510 | C22 | 1 | 1 | yes | characteristic |
| 13 | #17986271 | — | 2 | 8 | no | — |
| 14 | #17986155 | — | 2 | 4 | no | — |
| 15 | #17986138 | — | 2 | 4 | no | — |
| 16 | #17986070 | — | 2 | 2 | no | — |
| 17 | C8×C22⋊D71 | — | 2 | 2 | no | — |
| 18 | C2×#14556064 | C22 | 1 | 2 | yes | — |
| 19 | #17986025 | C22 | 1 | 1 | yes | characteristic |
| 20 | #17986008 | C22 | 1 | 4 | yes | — |
| 21 | C2×#14556047 | C22 | 1 | 4 | yes | — |
| 22 | C2×#14556047 | C22 | 1 | 4 | yes | — |
| 23 | #17985965 | C22 | 1 | 1 | yes | characteristic |
| 24 | #17985963 | C22 | 1 | 1 | yes | characteristic |
| 25 | #17985963 | C22 | 1 | 2 | yes | — |
| 26 | #17985954 | C22 | 1 | 1 | yes | characteristic |
| 27 | #17985764 | C22 | 1 | 2 | yes | — |
| 28 | C23×Q8×C71 | C22 | 1 | 2 | yes | — |
| 29 | C22×Q16×C71 | — | 2 | 8 | no | — |
| 30 | C22×Q16×C71 | — | 2 | 2 | no | — |
| 31 | C22×Q16×C71 | — | 2 | 2 | no | — |
| 32 | C22×Q16×C71 | C22 | 1 | 2 | yes | — |
| 33 | C22×Q16×C71 | C22 | 1 | 2 | yes | — |
| 34 | C23×C8×C71 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×#11765865 | C23 | 1 | 1 | yes | characteristic |
| 36 | #14556159 | — | 2 | 8 | no | — |
| 37 | #14556159 | — | 4 | 4 | no | — |
| 38 | C2×#11765855 | — | 2 | 4 | no | — |
| 39 | C2×#11765852 | — | 2 | 4 | no | — |
| 40 | #14556134 | — | 2 | 4 | no | — |
| 41 | C2×#11765849 | C23 | 1 | 1 | yes | characteristic |
| 42 | C2×#11765849 | C23 | 1 | 1 | yes | characteristic |
| 43 | C2×#11765849 | C23 | 1 | 4 | yes | — |
| 44 | C2×#11765848 | — | 2 | 1 | no | — |
| 45 | C2×C8×D71 | — | 2 | 1 | no | — |
| 46 | #14556111 | — | 2 | 1 | no | — |
| 47 | #14556107 | D4 | 1 | 2 | yes | — |
| 48 | #14556102 | D4 | 1 | 2 | yes | — |
| 49 | #14556097 | — | 2 | 1 | no | — |
| 50 | C4×C22⋊D71 | — | 2 | 2 | no | — |
| 51 | #14556087 | C23 | 1 | 1 | yes | characteristic |
| 52 | #14556064 | — | 2 | 4 | no | — |
| 53 | Dic71⋊C8 | — | 2 | 2 | no | — |
| 54 | #14556052 | — | 2 | 8 | no | — |
| 55 | #14556047 | — | 2 | 8 | no | — |
| 56 | #14556047 | — | 4 | 4 | no | — |
| 57 | C22⋊(C71⋊C8) | — | 2 | 2 | no | — |
| 58 | C22⋊(C71⋊C8) | — | 2 | 4 | no | — |
| 59 | (C2×D71)⋊C8 | — | 2 | 2 | no | — |
| 60 | #14556038 | — | 2 | 1 | no | — |
| 61 | C8×Dic71 | — | 2 | 1 | no | — |
| 62 | C22×Q8×C71 | — | 2 | 2 | no | — |
| 63 | C22×Q8×C71 | — | 2 | 8 | no | — |
| 64 | C22×Q8×C71 | — | 2 | 4 | no | — |
| 65 | C22×Q8×C71 | — | 2 | 4 | no | — |
| 66 | C22×Q8×C71 | — | 4 | 4 | no | — |
| 67 | C22×Q8×C71 | C23 | 1 | 4 | yes | — |
| 68 | C23×C4×C71 | — | 2 | 2 | no | — |
| 69 | C23×C4×C71 | C23 | 1 | 1 | yes | characteristic |
| 70 | C2×Q16×C71 | — | 2 | 16 | no | — |
| 71 | C2×Q16×C71 | — | 2 | 16 | no | — |
| 72 | C2×Q16×C71 | — | 2 | 8 | no | — |
| 73 | C2×Q16×C71 | — | 2 | 4 | no | — |
| 74 | C2×Q16×C71 | — | 2 | 4 | no | — |
| 75 | C2×Q16×C71 | — | 2 | 2 | no | — |
| 76 | C2×Q16×C71 | — | 2 | 2 | no | — |
| 77 | C2×Q16×C71 | D4 | 1 | 8 | yes | complemented |
| 78 | C22×C8×C71 | — | 2 | 4 | no | — |
| 79 | C22×C8×C71 | D4 | 1 | 2 | yes | — |
| 80 | C22×C8×C71 | D4 | 1 | 2 | yes | — |
| 81 | C22×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 82 | C22×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 83 | #11765865 | — | 2 | 2 | no | — |
| 84 | #11765865 | — | 2 | 2 | no | — |
| 85 | C2×Dic142 | C2×D4 | 1 | 1 | yes | characteristic |
| 86 | C2×D284 | C2×D4 | 1 | 1 | yes | characteristic |
| 87 | C2×C22⋊D71 | — | 2 | 2 | no | — |
| 88 | C2×C22⋊D71 | — | 2 | 1 | no | — |
| 89 | C2×C4×D71 | — | 2 | 1 | no | — |
| 90 | #11765855 | — | 4 | 8 | no | — |
| 91 | #11765852 | — | 4 | 8 | no | — |
| 92 | #11765849 | — | 2 | 2 | no | — |
| 93 | #11765849 | — | 2 | 4 | no | — |
| 94 | #11765849 | — | 2 | 2 | no | — |
| 95 | #11765849 | — | 2 | 4 | no | — |
| 96 | #11765848 | — | 4 | 2 | no | — |
| 97 | C2×C71⋊C8 | — | 2 | 1 | no | — |
| 98 | C2×C71⋊C8 | — | 2 | 4 | no | — |
| 99 | C2×C71⋊C8 | — | 2 | 1 | no | — |
| 100 | C8×D71 | — | 4 | 2 | no | — |
| 101 | C4⋊Dic71 | C2×D4 | 1 | 2 | yes | — |
| 102 | Dic71⋊C4 | — | 2 | 2 | no | — |
| 103 | C22⋊Dic71 | — | 2 | 2 | no | — |
| 104 | C22⋊Dic71 | — | 2 | 1 | no | — |
| 105 | (C2×D71)⋊C4 | — | 2 | 2 | no | — |
| 106 | C4×Dic71 | — | 2 | 1 | no | — |
| 107 | C24×C71 | #41 | 1 | 1 | yes | characteristic |
| 108 | C2×Q8×C71 | — | 2 | 4 | no | — |
| 109 | C2×Q8×C71 | — | 2 | 16 | no | — |
| 110 | C2×Q8×C71 | — | 2 | 4 | no | — |
| 111 | C2×Q8×C71 | — | 2 | 4 | no | — |
| 112 | C2×Q8×C71 | — | 2 | 4 | no | — |
| 113 | C2×Q8×C71 | — | 2 | 4 | no | — |
| 114 | C2×Q8×C71 | — | 4 | 8 | no | — |
| 115 | C2×Q8×C71 | — | 4 | 16 | no | — |
| 116 | C2×Q8×C71 | — | 4 | 8 | no | — |
| 117 | C2×Q8×C71 | — | 4 | 4 | no | — |
| 118 | C2×Q8×C71 | C2×D4 | 1 | 8 | yes | — |
| 119 | C22×C4×C71 | — | 2 | 2 | no | — |
| 120 | C22×C4×C71 | — | 2 | 2 | no | — |
| 121 | C22×C4×C71 | — | 2 | 4 | no | — |
| 122 | C22×C4×C71 | — | 4 | 8 | no | — |
| 123 | C22×C4×C71 | — | 4 | 4 | no | — |
| 124 | C22×C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 125 | C22×C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 126 | C22×C4×C71 | #41 | 1 | 1 | yes | characteristic |
| 127 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 128 | Q16×C71 | — | 2 | 16 | no | — |
| 129 | Q16×C71 | — | 2 | 8 | no | — |
| 130 | Q16×C71 | — | 2 | 8 | no | — |
| 131 | C2×C8×C71 | — | 2 | 2 | no | — |
| 132 | C2×C8×C71 | — | 2 | 4 | no | — |
| 133 | C2×C8×C71 | — | 2 | 4 | no | — |
| 134 | C2×C8×C71 | C2×D4 | 1 | 2 | yes | — |
| 135 | C2×C8×C71 | C2×D4 | 1 | 4 | yes | — |
| 136 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | C23×C71 | — | 2 | 2 | no | — |
| 139 | C23×C71 | — | 2 | 4 | no | — |
| 140 | C23×C71 | #121 | 1 | 2 | yes | — |
| 141 | C23×C71 | C2×#41 | 1 | 1 | yes | characteristic |
| 142 | C22×D71 | — | 2 | 1 | no | — |
| 143 | Q8×C71 | — | 2 | 8 | no | — |
| 144 | Q8×C71 | — | 2 | 8 | no | — |
| 145 | Q8×C71 | — | 4 | 16 | no | — |
| 146 | Q8×C71 | — | 4 | 4 | no | — |
| 147 | Q8×C71 | — | 4 | 4 | no | — |
| 148 | C2×C4×C71 | — | 2 | 2 | no | — |
| 149 | C2×C4×C71 | — | 2 | 2 | no | — |
| 150 | C2×C4×C71 | — | 2 | 2 | no | — |
| 151 | C2×C4×C71 | — | 2 | 4 | no | — |
| 152 | C2×C4×C71 | — | 2 | 8 | no | — |
| 153 | C2×C4×C71 | — | 4 | 16 | no | — |
| 154 | C2×C4×C71 | — | 4 | 4 | no | — |
| 155 | C2×C4×C71 | — | 4 | 4 | no | — |
| 156 | C2×C4×C71 | #121 | 1 | 2 | yes | — |
| 157 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 158 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 159 | C2×C4×C71 | C22×D4 | 1 | 2 | yes | — |
| 160 | C2×C4×C71 | H(5,𝔽2) | 1 | 2 | yes | — |
| 161 | C22⋊D71 | — | 4 | 2 | no | — |
| 162 | C22⋊D71 | — | 4 | 4 | no | — |
| 163 | C2×Dic71 | — | 2 | 2 | no | — |
| 164 | C2×Dic71 | — | 2 | 1 | no | — |
| 165 | D284 | — | 2 | 2 | no | — |
| 166 | C4×D71 | — | 4 | 1 | no | — |
| 167 | C4×D71 | — | 4 | 1 | no | — |
| 168 | Dic142 | — | 2 | 2 | no | — |
| 169 | C8×C71 | — | 2 | 2 | no | — |
| 170 | C8×C71 | #120 | 1 | 2 | yes | — |
| 171 | C8×C71 | #120 | 1 | 2 | yes | — |
| 172 | C71⋊C8 | — | 4 | 1 | no | — |
| 173 | C71⋊C8 | — | 4 | 1 | no | — |
| 174 | C71⋊C8 | — | 4 | 4 | no | — |
| 175 | C22×C71 | — | 2 | 8 | no | — |
| 176 | C22×C71 | — | 2 | 2 | no | — |
| 177 | C22×C71 | — | 2 | 2 | no | — |
| 178 | C22×C71 | — | 2 | 2 | no | — |
| 179 | C22×C71 | #473 | 1 | 4 | yes | complemented |
| 180 | C22×C71 | C2×#121 | 1 | 1 | yes | characteristic |
| 181 | C22×C71 | #546 | 1 | 2 | yes | — |
| 182 | C2×D71 | — | 4 | 1 | no | — |
| 183 | C2×D71 | — | 4 | 2 | no | — |
| 184 | C4×C71 | — | 2 | 2 | no | — |
| 185 | C4×C71 | — | 4 | 8 | no | — |
| 186 | C4×C71 | C2×#120 | 1 | 1 | yes | characteristic |
| 187 | C4×C71 | #535 | 1 | 1 | yes | characteristic |
| 188 | C4×C71 | D42 | 1 | 2 | yes | — |
| 189 | Dic71 | — | 4 | 1 | no | — |
| 190 | Dic71 | — | 4 | 2 | no | — |
| 191 | #24282 | — | 71 | 1 | no | maximal, Sylow |
| 192 | C2×C71 | — | 2 | 2 | no | — |
| 193 | C2×C71 | — | 2 | 4 | no | — |
| 194 | C2×C71 | #2408 | 1 | 1 | yes | characteristic |
| 195 | C2×C71 | C2×#473 | 1 | 2 | yes | — |
| 196 | D71 | — | 8 | 1 | no | — |
| 197 | C23×Q16 | D71 | 1 | 1 | yes | characteristic, complemented |
| 198 | C2×#473 | — | 71 | 2 | no | — |
| 199 | #3004 | — | 71 | 2 | no | — |
| 200 | #2929 | — | 71 | 1 | no | — |
| 201 | #2047 | — | 71 | 2 | no | — |
| 202 | #2020 | — | 71 | 2 | no | — |
| 203 | #1979 | — | 71 | 2 | no | — |
| 204 | #1810 | — | 71 | 1 | no | — |
| 205 | #1784 | — | 71 | 2 | no | — |
| 206 | C71 | #24282 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 207 | C23×Q8 | C2×D71 | 1 | 2 | yes | — |
| 208 | C2×#137 | — | 71 | 4 | no | — |
| 209 | C22×Q16 | — | 2 | 8 | no | — |
| 210 | C22×Q16 | — | 2 | 2 | no | — |
| 211 | C22×Q16 | — | 2 | 2 | no | — |
| 212 | C22×Q16 | C2×D71 | 1 | 2 | yes | — |
| 213 | C22×Q16 | C2×D71 | 1 | 2 | yes | — |
| 214 | C2×#131 | — | 71 | 1 | no | — |
| 215 | C23×C8 | C2×D71 | 1 | 1 | yes | characteristic |
| 216 | #525 | — | 71 | 1 | no | — |
| 217 | #473 | — | 142 | 8 | no | — |
| 218 | #451 | — | 142 | 4 | no | — |
| 219 | #448 | — | 142 | 4 | no | — |
| 220 | #435 | — | 142 | 2 | no | — |
| 221 | C8×D4 | — | 142 | 2 | no | — |
| 222 | C2×#108 | — | 71 | 2 | no | — |
| 223 | #424 | — | 71 | 1 | no | — |
| 224 | #419 | — | 71 | 4 | no | — |
| 225 | C2×#101 | — | 71 | 4 | no | — |
| 226 | C2×#101 | — | 71 | 4 | no | — |
| 227 | #408 | — | 71 | 1 | no | — |
| 228 | #407 | — | 71 | 2 | no | — |
| 229 | #407 | — | 71 | 1 | no | — |
| 230 | #405 | — | 71 | 1 | no | — |
| 231 | #341 | — | 71 | 2 | no | — |
| 232 | C2×#41 | — | 71 | 1 | no | — |
| 233 | C22×Q8 | — | 2 | 2 | no | — |
| 234 | C22×Q8 | — | 2 | 8 | no | — |
| 235 | C22×Q8 | — | 2 | 4 | no | — |
| 236 | C22×Q8 | — | 2 | 4 | no | — |
| 237 | C22×Q8 | — | 4 | 4 | no | — |
| 238 | C22×Q8 | C22×D71 | 1 | 4 | yes | — |
| 239 | C23×C4 | — | 2 | 2 | no | — |
| 240 | C23×C4 | C22×D71 | 1 | 1 | yes | characteristic |
| 241 | #137 | — | 284 | 4 | no | — |
| 242 | #137 | — | 142 | 8 | no | — |
| 243 | C2×Q16 | — | 2 | 16 | no | — |
| 244 | C2×Q16 | — | 2 | 16 | no | — |
| 245 | C2×Q16 | — | 2 | 8 | no | — |
| 246 | C2×Q16 | — | 2 | 4 | no | — |
| 247 | C2×Q16 | — | 2 | 2 | no | — |
| 248 | C2×Q16 | — | 2 | 2 | no | — |
| 249 | C2×Q16 | — | 2 | 4 | no | — |
| 250 | C2×Q16 | — | 142 | 4 | no | — |
| 251 | C2×Q16 | C22⋊D71 | 1 | 8 | yes | complemented |
| 252 | C2×SD16 | — | 142 | 4 | no | — |
| 253 | #131 | — | 142 | 4 | no | — |
| 254 | C2×M16 | — | 71 | 1 | no | — |
| 255 | C2×M16 | — | 71 | 4 | no | — |
| 256 | C2×M16 | — | 71 | 1 | no | — |
| 257 | C2×M16 | — | 142 | 1 | no | — |
| 258 | C22×C8 | — | 2 | 4 | no | — |
| 259 | C22×C8 | — | 142 | 1 | no | — |
| 260 | C22×C8 | C22⋊D71 | 1 | 2 | yes | — |
| 261 | C22×C8 | C22⋊D71 | 1 | 2 | yes | — |
| 262 | C22×C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 263 | C22×C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 264 | #123 | — | 142 | 1 | no | — |
| 265 | C22⋊Q8 | — | 71 | 2 | no | — |
| 266 | #121 | — | 71 | 2 | no | — |
| 267 | #120 | — | 142 | 1 | no | — |
| 268 | C4×D4 | — | 142 | 2 | no | — |
| 269 | #117 | — | 71 | 1 | no | — |
| 270 | #108 | — | 142 | 4 | no | — |
| 271 | C4⋊C8 | — | 142 | 2 | no | — |
| 272 | #103 | — | 142 | 8 | no | — |
| 273 | #101 | — | 284 | 4 | no | — |
| 274 | #101 | — | 142 | 8 | no | — |
| 275 | C22⋊C8 | — | 142 | 4 | no | — |
| 276 | C22⋊C8 | — | 142 | 2 | no | — |
| 277 | C22⋊C8 | — | 142 | 2 | no | — |
| 278 | #97 | — | 142 | 1 | no | — |
| 279 | C4×C8 | — | 142 | 1 | no | — |
| 280 | C24 | #11765864 | 1 | 1 | yes | characteristic |
| 281 | #41 | — | 142 | 2 | no | — |
| 282 | #41 | — | 142 | 2 | no | — |
| 283 | C2×Q8 | — | 2 | 4 | no | — |
| 284 | C2×Q8 | — | 2 | 16 | no | — |
| 285 | C2×Q8 | — | 2 | 4 | no | — |
| 286 | C2×Q8 | — | 2 | 4 | no | — |
| 287 | C2×Q8 | — | 2 | 4 | no | — |
| 288 | C2×Q8 | — | 2 | 4 | no | — |
| 289 | C2×Q8 | — | 4 | 8 | no | — |
| 290 | C2×Q8 | — | 4 | 16 | no | — |
| 291 | C2×Q8 | — | 4 | 8 | no | — |
| 292 | C2×Q8 | — | 4 | 4 | no | — |
| 293 | C2×Q8 | — | 71 | 1 | no | — |
| 294 | C2×Q8 | C2×C22⋊D71 | 1 | 8 | yes | — |
| 295 | C2×D4 | — | 71 | 1 | no | — |
| 296 | C2×D4 | — | 142 | 1 | no | — |
| 297 | C2×D4 | — | 142 | 2 | no | — |
| 298 | C22×C4 | — | 2 | 2 | no | — |
| 299 | C22×C4 | — | 2 | 2 | no | — |
| 300 | C22×C4 | — | 2 | 4 | no | — |
| 301 | C22×C4 | — | 4 | 8 | no | — |
| 302 | C22×C4 | — | 4 | 4 | no | — |
| 303 | C22×C4 | — | 142 | 1 | no | — |
| 304 | C22×C4 | D4×D71 | 1 | 2 | yes | — |
| 305 | C22×C4 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 306 | C22×C4 | #11765864 | 1 | 1 | yes | characteristic |
| 307 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 308 | Q16 | — | 2 | 16 | no | — |
| 309 | Q16 | — | 2 | 8 | no | — |
| 310 | Q16 | — | 2 | 8 | no | — |
| 311 | Q16 | — | 284 | 8 | no | — |
| 312 | SD16 | — | 284 | 8 | no | — |
| 313 | M16 | — | 284 | 2 | no | — |
| 314 | M16 | — | 142 | 2 | no | — |
| 315 | M16 | — | 142 | 4 | no | — |
| 316 | M16 | — | 142 | 2 | no | — |
| 317 | M16 | — | 142 | 4 | no | — |
| 318 | C2×C8 | — | 2 | 2 | no | — |
| 319 | C2×C8 | — | 2 | 4 | no | — |
| 320 | C2×C8 | — | 2 | 4 | no | — |
| 321 | C2×C8 | — | 284 | 2 | no | — |
| 322 | C2×C8 | — | 142 | 4 | no | — |
| 323 | C2×C8 | — | 142 | 1 | no | — |
| 324 | C2×C8 | — | 142 | 1 | no | — |
| 325 | C2×C8 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 326 | C2×C8 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 327 | C2×C8 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 328 | C2×C8 | C2×C22⋊D71 | 1 | 4 | yes | — |
| 329 | C4⋊C4 | — | 71 | 2 | no | — |
| 330 | C4⋊C4 | — | 142 | 2 | no | — |
| 331 | C22⋊C4 | — | 142 | 1 | no | — |
| 332 | C22⋊C4 | — | 142 | 2 | no | — |
| 333 | C22⋊C4 | — | 142 | 2 | no | — |
| 334 | C42 | — | 142 | 1 | no | — |
| 335 | C23 | — | 2 | 2 | no | — |
| 336 | C23 | — | 2 | 4 | no | — |
| 337 | C23 | — | 142 | 1 | no | — |
| 338 | C23 | #14556099 | 1 | 2 | yes | — |
| 339 | C23 | C2×#11765864 | 1 | 1 | yes | characteristic |
| 340 | Q8 | — | 2 | 8 | no | — |
| 341 | Q8 | — | 2 | 8 | no | — |
| 342 | Q8 | — | 4 | 16 | no | — |
| 343 | Q8 | — | 4 | 4 | no | — |
| 344 | Q8 | — | 4 | 4 | no | — |
| 345 | Q8 | — | 142 | 2 | no | — |
| 346 | D4 | — | 284 | 2 | no | — |
| 347 | D4 | — | 284 | 4 | no | — |
| 348 | D4 | — | 142 | 2 | no | — |
| 349 | C2×C4 | — | 2 | 2 | no | — |
| 350 | C2×C4 | — | 2 | 2 | no | — |
| 351 | C2×C4 | — | 2 | 4 | no | — |
| 352 | C2×C4 | — | 2 | 2 | no | — |
| 353 | C2×C4 | — | 2 | 8 | no | — |
| 354 | C2×C4 | — | 4 | 16 | no | — |
| 355 | C2×C4 | — | 4 | 4 | no | — |
| 356 | C2×C4 | — | 4 | 4 | no | — |
| 357 | C2×C4 | — | 284 | 1 | no | — |
| 358 | C2×C4 | — | 284 | 1 | no | — |
| 359 | C2×C4 | — | 142 | 2 | no | — |
| 360 | C2×C4 | — | 142 | 1 | no | — |
| 361 | C2×C4 | #14556099 | 1 | 2 | yes | — |
| 362 | C2×C4 | C2×D4×D71 | 1 | 1 | yes | characteristic |
| 363 | C2×C4 | C22×C22⋊D71 | 1 | 1 | yes | characteristic |
| 364 | C2×C4 | C22×C22⋊D71 | 1 | 2 | yes | — |
| 365 | C2×C4 | #14556173 | 1 | 2 | yes | — |
| 366 | C8 | — | 2 | 2 | no | — |
| 367 | C8 | — | 284 | 1 | no | — |
| 368 | C8 | — | 284 | 4 | no | — |
| 369 | C8 | — | 284 | 1 | no | — |
| 370 | C8 | #14556097 | 1 | 2 | yes | — |
| 371 | C8 | #14556097 | 1 | 2 | yes | — |
| 372 | C22 | — | 2 | 8 | no | — |
| 373 | C22 | — | 2 | 2 | no | — |
| 374 | C22 | — | 2 | 2 | no | — |
| 375 | C22 | — | 2 | 2 | no | — |
| 376 | C22 | — | 284 | 2 | no | — |
| 377 | C22 | — | 284 | 1 | no | — |
| 378 | C22 | #17986271 | 1 | 4 | yes | complemented |
| 379 | C22 | C2×#14556099 | 1 | 1 | yes | characteristic |
| 380 | C22 | #17986643 | 1 | 2 | yes | — |
| 381 | C4 | — | 2 | 2 | no | — |
| 382 | C4 | — | 4 | 8 | no | — |
| 383 | C4 | — | 284 | 2 | no | — |
| 384 | C4 | — | 284 | 1 | no | — |
| 385 | C4 | C2×#14556097 | 1 | 1 | yes | characteristic |
| 386 | C4 | #17986566 | 1 | 1 | yes | characteristic |
| 387 | C4 | D4×C22⋊D71 | 1 | 2 | yes | — |
| 388 | C2 | — | 2 | 2 | no | — |
| 389 | C2 | — | 2 | 4 | no | — |
| 390 | C2 | — | 568 | 1 | no | — |
| 391 | C2 | #22591690 | 1 | 1 | yes | characteristic |
| 392 | C2 | C2×#17986271 | 1 | 2 | yes | — |
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