← #36368334
Subgroups — #36368334
Order 22144.
1424 conjugacy classes of subgroups.
The subgroup lattice has 258 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #26012327 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #26012306 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #26012302 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #26012299 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #26012294 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #26012289 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | C2×#19149699 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | C2×#19149686 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #585×C173 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #19149727 | — | 2 | 1 | no | — |
| 11 | #19149726 | C22 | 1 | 4 | yes | complemented |
| 12 | #19149725 | C22 | 1 | 4 | yes | complemented |
| 13 | #19149724 | — | 2 | 3 | no | — |
| 14 | C2×#14583826 | C22 | 1 | 6 | yes | complemented |
| 15 | #41×D173 | — | 2 | 4 | no | — |
| 16 | #19149710 | C22 | 1 | 12 | yes | complemented |
| 17 | #19149709 | C22 | 1 | 12 | yes | complemented |
| 18 | #19149705 | C22 | 1 | 12 | yes | complemented |
| 19 | #19149704 | C22 | 1 | 12 | yes | complemented |
| 20 | #19149699 | C22 | 1 | 4 | yes | complemented |
| 21 | #19149699 | C22 | 1 | 12 | yes | complemented |
| 22 | #19149699 | C22 | 1 | 12 | yes | complemented |
| 23 | #19149699 | C22 | 1 | 12 | yes | complemented |
| 24 | C2×#14583816 | C22 | 1 | 6 | yes | complemented |
| 25 | C2×#14583814 | C22 | 1 | 6 | yes | complemented |
| 26 | C2×#14583813 | C22 | 1 | 6 | yes | complemented |
| 27 | C2×#14583811 | C22 | 1 | 6 | yes | complemented |
| 28 | #19149686 | C22 | 1 | 4 | yes | complemented |
| 29 | #19149686 | C22 | 1 | 4 | yes | complemented |
| 30 | C2×#14583810 | C22 | 1 | 3 | yes | complemented |
| 31 | C22×#13063436 | C22 | 1 | 3 | yes | complemented |
| 32 | 2−1+4×C173 | — | 2 | 1 | no | — |
| 33 | 2−1+4×C173 | C22 | 1 | 4 | yes | complemented |
| 34 | H(5,𝔽2)×C173 | — | 2 | 3 | no | — |
| 35 | H(5,𝔽2)×C173 | C22 | 1 | 4 | yes | complemented |
| 36 | C2×#41×C173 | — | 2 | 4 | no | — |
| 37 | C2×#41×C173 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×#41×C173 | C22 | 1 | 6 | yes | complemented |
| 39 | #14583827 | — | 2 | 4 | no | — |
| 40 | #14583826 | — | 2 | 6 | no | — |
| 41 | #14583826 | — | 2 | 6 | no | — |
| 42 | #14583826 | C23 | 1 | 4 | yes | — |
| 43 | #14583826 | C23 | 1 | 12 | yes | — |
| 44 | #14583825 | — | 2 | 12 | no | — |
| 45 | C2×Dic346 | C23 | 1 | 6 | yes | — |
| 46 | Q8×D173 | — | 2 | 4 | no | — |
| 47 | C2×D692 | C23 | 1 | 6 | yes | — |
| 48 | C2×C22⋊D173 | — | 2 | 6 | no | — |
| 49 | D4×D173 | — | 2 | 12 | no | — |
| 50 | C2×C4×D173 | — | 2 | 6 | no | — |
| 51 | #14583816 | C23 | 1 | 4 | yes | — |
| 52 | #14583816 | C23 | 1 | 12 | yes | — |
| 53 | #14583814 | C23 | 1 | 4 | yes | — |
| 54 | #14583814 | C23 | 1 | 12 | yes | — |
| 55 | #14583813 | C23 | 1 | 4 | yes | — |
| 56 | #14583813 | C23 | 1 | 12 | yes | — |
| 57 | #14583811 | C23 | 1 | 4 | yes | — |
| 58 | #14583811 | C23 | 1 | 12 | yes | — |
| 59 | #14583810 | C23 | 1 | 12 | yes | — |
| 60 | C2×#13063436 | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×#13063436 | C23 | 1 | 3 | yes | — |
| 62 | C2×#13063436 | C23 | 1 | 6 | yes | — |
| 63 | C2×#13063436 | C23 | 1 | 6 | yes | — |
| 64 | #41×C173 | — | 2 | 4 | no | — |
| 65 | #41×C173 | — | 2 | 12 | no | — |
| 66 | #41×C173 | — | 2 | 6 | no | — |
| 67 | #41×C173 | — | 2 | 6 | no | — |
| 68 | #41×C173 | D4 | 1 | 4 | yes | — |
| 69 | #41×C173 | C23 | 1 | 4 | yes | — |
| 70 | #41×C173 | C23 | 1 | 12 | yes | — |
| 71 | #41×C173 | C23 | 1 | 4 | yes | — |
| 72 | C2×Q8×C173 | — | 2 | 4 | no | — |
| 73 | C2×Q8×C173 | D4 | 1 | 1 | yes | characteristic |
| 74 | C2×Q8×C173 | C23 | 1 | 6 | yes | — |
| 75 | C2×D4×C173 | — | 2 | 6 | no | — |
| 76 | C2×D4×C173 | — | 2 | 12 | no | — |
| 77 | C2×D4×C173 | D4 | 1 | 3 | yes | — |
| 78 | C2×D4×C173 | C23 | 1 | 6 | yes | — |
| 79 | C22×C4×C173 | — | 2 | 6 | no | — |
| 80 | C22×C4×C173 | C23 | 1 | 3 | yes | — |
| 81 | C22×D173 | — | 2 | 6 | no | — |
| 82 | Dic346 | — | 2 | 6 | no | — |
| 83 | Dic346 | C24 | 1 | 4 | yes | — |
| 84 | D692 | — | 2 | 6 | no | — |
| 85 | D692 | C24 | 1 | 4 | yes | — |
| 86 | C22⋊D173 | — | 2 | 12 | no | — |
| 87 | C22⋊D173 | — | 2 | 4 | no | — |
| 88 | C2×Dic173 | — | 2 | 6 | no | — |
| 89 | C4×D173 | — | 2 | 4 | no | — |
| 90 | C4×D173 | — | 2 | 12 | no | — |
| 91 | #13063436 | C24 | 1 | 1 | yes | characteristic |
| 92 | #13063436 | C24 | 1 | 1 | yes | characteristic |
| 93 | #13063436 | C24 | 1 | 6 | yes | — |
| 94 | C23×C173 | — | 2 | 6 | no | — |
| 95 | C23×C173 | C2×D4 | 1 | 3 | yes | — |
| 96 | Q8×C173 | — | 2 | 6 | no | — |
| 97 | Q8×C173 | C2×D4 | 1 | 4 | yes | — |
| 98 | Q8×C173 | C24 | 1 | 4 | yes | — |
| 99 | D4×C173 | — | 2 | 12 | no | — |
| 100 | D4×C173 | — | 2 | 4 | no | — |
| 101 | D4×C173 | — | 2 | 6 | no | — |
| 102 | D4×C173 | C2×D4 | 1 | 12 | yes | — |
| 103 | D4×C173 | C24 | 1 | 4 | yes | — |
| 104 | C2×C4×C173 | — | 2 | 6 | no | — |
| 105 | C2×C4×C173 | — | 2 | 4 | no | — |
| 106 | C2×C4×C173 | — | 2 | 12 | no | — |
| 107 | C2×C4×C173 | C2×D4 | 1 | 6 | yes | — |
| 108 | C2×C4×C173 | C2×D4 | 1 | 3 | yes | — |
| 109 | C2×C4×C173 | C24 | 1 | 1 | yes | characteristic |
| 110 | C2×C4×C173 | C24 | 1 | 6 | yes | — |
| 111 | C22×C173 | — | 2 | 4 | no | — |
| 112 | C22×C173 | — | 4 | 3 | no | — |
| 113 | C22×C173 | — | 8 | 6 | no | — |
| 114 | C22×C173 | C22×D4 | 1 | 6 | yes | — |
| 115 | C22×C173 | C22×D4 | 1 | 1 | yes | characteristic |
| 116 | C2×D173 | — | 2 | 4 | no | — |
| 117 | C2×D173 | — | 8 | 6 | no | — |
| 118 | C4×C173 | — | 2 | 4 | no | — |
| 119 | C4×C173 | C22×D4 | 1 | 6 | yes | — |
| 120 | C4×C173 | C22×D4 | 1 | 1 | yes | characteristic |
| 121 | C4×C173 | C25 | 1 | 1 | yes | characteristic |
| 122 | Dic173 | — | 2 | 4 | no | — |
| 123 | C2×C173 | — | 2 | 6 | no | — |
| 124 | C2×C173 | — | 2 | 1 | no | — |
| 125 | C2×C173 | — | 4 | 4 | no | — |
| 126 | C2×C173 | C23×D4 | 1 | 1 | yes | characteristic |
| 127 | D173 | — | 4 | 4 | no | — |
| 128 | C173 | #3584 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 129 | #3584 | — | 173 | 1 | no | maximal, Sylow |
| 130 | #585 | — | 173 | 1 | no | — |
| 131 | #585 | D173 | 1 | 1 | yes | characteristic, complemented |
| 132 | #578 | — | 173 | 4 | no | — |
| 133 | #577 | — | 173 | 4 | no | — |
| 134 | #577 | — | 173 | 4 | no | — |
| 135 | #576 | — | 173 | 4 | no | — |
| 136 | #575 | — | 173 | 6 | no | — |
| 137 | C2×#135 | — | 173 | 6 | no | — |
| 138 | C2×#131 | — | 173 | 1 | no | — |
| 139 | 2−1+4 | — | 2 | 1 | no | — |
| 140 | 2−1+4 | — | 346 | 1 | no | — |
| 141 | 2−1+4 | — | 173 | 4 | no | — |
| 142 | 2−1+4 | C2×D173 | 1 | 4 | yes | complemented |
| 143 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 144 | H(5,𝔽2) | — | 346 | 3 | no | — |
| 145 | H(5,𝔽2) | — | 173 | 4 | no | — |
| 146 | H(5,𝔽2) | C2×D173 | 1 | 4 | yes | complemented |
| 147 | C2×#41 | — | 2 | 4 | no | — |
| 148 | C2×#41 | — | 346 | 4 | no | — |
| 149 | C2×#41 | — | 173 | 6 | no | — |
| 150 | C2×#41 | C2×D173 | 1 | 1 | yes | characteristic |
| 151 | C2×#41 | C2×D173 | 1 | 6 | yes | complemented |
| 152 | #137 | — | 173 | 12 | no | — |
| 153 | #137 | — | 173 | 12 | no | — |
| 154 | AGL(1,ℤ/8) | — | 173 | 12 | no | — |
| 155 | AGL(1,ℤ/8) | — | 173 | 12 | no | — |
| 156 | #135 | — | 173 | 4 | no | — |
| 157 | #135 | — | 173 | 12 | no | — |
| 158 | #135 | — | 173 | 12 | no | — |
| 159 | #135 | — | 173 | 12 | no | — |
| 160 | C2×Q16 | — | 173 | 6 | no | — |
| 161 | C2×SD16 | — | 173 | 6 | no | — |
| 162 | C2×SD16 | — | 173 | 6 | no | — |
| 163 | C2×D8 | — | 173 | 6 | no | — |
| 164 | #131 | — | 173 | 4 | no | — |
| 165 | #131 | — | 173 | 4 | no | — |
| 166 | C2×M16 | — | 173 | 3 | no | — |
| 167 | C22×C8 | — | 173 | 3 | no | — |
| 168 | #41 | — | 2 | 4 | no | — |
| 169 | #41 | — | 2 | 12 | no | — |
| 170 | #41 | — | 2 | 6 | no | — |
| 171 | #41 | — | 2 | 6 | no | — |
| 172 | #41 | — | 346 | 4 | no | — |
| 173 | #41 | — | 346 | 12 | no | — |
| 174 | #41 | — | 346 | 6 | no | — |
| 175 | #41 | — | 346 | 6 | no | — |
| 176 | #41 | — | 173 | 4 | no | — |
| 177 | #41 | — | 173 | 12 | no | — |
| 178 | #41 | C22⋊D173 | 1 | 4 | yes | — |
| 179 | #41 | C22×D173 | 1 | 4 | yes | — |
| 180 | #41 | C22×D173 | 1 | 12 | yes | — |
| 181 | #41 | C22×D173 | 1 | 4 | yes | — |
| 182 | C2×Q8 | — | 2 | 4 | no | — |
| 183 | C2×Q8 | — | 346 | 4 | no | — |
| 184 | C2×Q8 | — | 173 | 6 | no | — |
| 185 | C2×Q8 | C22⋊D173 | 1 | 1 | yes | characteristic |
| 186 | C2×Q8 | C22×D173 | 1 | 6 | yes | — |
| 187 | C2×D4 | — | 2 | 6 | no | — |
| 188 | C2×D4 | — | 2 | 12 | no | — |
| 189 | C2×D4 | — | 346 | 6 | no | — |
| 190 | C2×D4 | — | 346 | 12 | no | — |
| 191 | C2×D4 | — | 173 | 6 | no | — |
| 192 | C2×D4 | C22⋊D173 | 1 | 3 | yes | — |
| 193 | C2×D4 | C22×D173 | 1 | 6 | yes | — |
| 194 | C22×C4 | — | 2 | 6 | no | — |
| 195 | C22×C4 | — | 346 | 6 | no | — |
| 196 | C22×C4 | C22×D173 | 1 | 3 | yes | — |
| 197 | Q16 | — | 173 | 4 | no | — |
| 198 | Q16 | — | 173 | 12 | no | — |
| 199 | SD16 | — | 173 | 4 | no | — |
| 200 | SD16 | — | 173 | 12 | no | — |
| 201 | SD16 | — | 173 | 4 | no | — |
| 202 | SD16 | — | 173 | 12 | no | — |
| 203 | D8 | — | 173 | 4 | no | — |
| 204 | D8 | — | 173 | 12 | no | — |
| 205 | M16 | — | 173 | 12 | no | — |
| 206 | C2×C8 | — | 173 | 1 | no | — |
| 207 | C2×C8 | — | 173 | 3 | no | — |
| 208 | C2×C8 | — | 173 | 6 | no | — |
| 209 | C2×C8 | — | 173 | 6 | no | — |
| 210 | C23 | — | 2 | 6 | no | — |
| 211 | C23 | — | 346 | 6 | no | — |
| 212 | C23 | C2×C22⋊D173 | 1 | 3 | yes | — |
| 213 | Q8 | — | 2 | 6 | no | — |
| 214 | Q8 | — | 346 | 6 | no | — |
| 215 | Q8 | — | 173 | 4 | no | — |
| 216 | Q8 | C2×C22⋊D173 | 1 | 4 | yes | — |
| 217 | Q8 | C23×D173 | 1 | 4 | yes | — |
| 218 | D4 | — | 2 | 12 | no | — |
| 219 | D4 | — | 2 | 4 | no | — |
| 220 | D4 | — | 2 | 6 | no | — |
| 221 | D4 | — | 346 | 12 | no | — |
| 222 | D4 | — | 346 | 4 | no | — |
| 223 | D4 | — | 346 | 6 | no | — |
| 224 | D4 | — | 173 | 4 | no | — |
| 225 | D4 | C2×C22⋊D173 | 1 | 12 | yes | — |
| 226 | D4 | C23×D173 | 1 | 4 | yes | — |
| 227 | C2×C4 | — | 2 | 6 | no | — |
| 228 | C2×C4 | — | 2 | 12 | no | — |
| 229 | C2×C4 | — | 2 | 4 | no | — |
| 230 | C2×C4 | — | 346 | 6 | no | — |
| 231 | C2×C4 | — | 346 | 12 | no | — |
| 232 | C2×C4 | — | 346 | 4 | no | — |
| 233 | C2×C4 | C2×C22⋊D173 | 1 | 3 | yes | — |
| 234 | C2×C4 | C2×C22⋊D173 | 1 | 6 | yes | — |
| 235 | C2×C4 | C23×D173 | 1 | 6 | yes | — |
| 236 | C2×C4 | C23×D173 | 1 | 1 | yes | characteristic |
| 237 | C8 | — | 173 | 1 | no | — |
| 238 | C8 | — | 173 | 1 | no | — |
| 239 | C8 | — | 173 | 6 | no | — |
| 240 | C22 | — | 2 | 4 | no | — |
| 241 | C22 | — | 4 | 3 | no | — |
| 242 | C22 | — | 8 | 6 | no | — |
| 243 | C22 | — | 346 | 4 | no | — |
| 244 | C22 | — | 1384 | 6 | no | — |
| 245 | C22 | C22×C22⋊D173 | 1 | 6 | yes | — |
| 246 | C22 | C22×C22⋊D173 | 1 | 1 | yes | characteristic |
| 247 | C4 | — | 2 | 4 | no | — |
| 248 | C4 | — | 346 | 4 | no | — |
| 249 | C4 | C22×C22⋊D173 | 1 | 6 | yes | — |
| 250 | C4 | C22×C22⋊D173 | 1 | 1 | yes | characteristic |
| 251 | C4 | C24×D173 | 1 | 1 | yes | characteristic |
| 252 | C2 | — | 2 | 1 | no | — |
| 253 | C2 | — | 2 | 6 | no | — |
| 254 | C2 | — | 4 | 4 | no | — |
| 255 | C2 | — | 692 | 4 | no | — |
| 256 | C2 | C23×C22⋊D173 | 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