← #30647648
Subgroups — #30647648
Order 16256.
452 conjugacy classes of subgroups.
The subgroup lattice has 204 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#16861231 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22550642 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22549999 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #22549994 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | C2×#16861145 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22549894 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #405×C127 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#14523248 | C22 | 1 | 2 | yes | — |
| 9 | #16861231 | C4 | 1 | 2 | yes | complemented |
| 10 | #16861231 | C4 | 1 | 2 | yes | complemented |
| 11 | #16861231 | C22 | 1 | 2 | yes | — |
| 12 | #16861231 | C22 | 1 | 2 | yes | — |
| 13 | C2×Dic508 | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | C2×#14523237 | C4 | 1 | 2 | yes | complemented |
| 15 | C2×D1016 | C4 | 1 | 1 | yes | characteristic, complemented |
| 16 | #16861217 | — | 2 | 4 | no | — |
| 17 | #16861215 | C22 | 1 | 8 | yes | complemented |
| 18 | C2×#14523232 | C22 | 1 | 2 | yes | — |
| 19 | M16×D127 | — | 2 | 4 | no | — |
| 20 | #16861145 | C22 | 1 | 2 | yes | complemented |
| 21 | #16861145 | C22 | 1 | 2 | yes | complemented |
| 22 | #16861137 | C22 | 1 | 8 | yes | complemented |
| 23 | C2×M16×C127 | C22 | 1 | 1 | yes | characteristic |
| 24 | C22×C8×C127 | C22 | 1 | 1 | yes | characteristic |
| 25 | #117×C127 | C22 | 1 | 1 | yes | characteristic |
| 26 | #97×C127 | C22 | 1 | 2 | yes | complemented |
| 27 | C4×C8×C127 | C22 | 1 | 2 | yes | complemented |
| 28 | #14523248 | — | 2 | 2 | no | — |
| 29 | #14523248 | — | 2 | 2 | no | — |
| 30 | #14523248 | C2×C4 | 1 | 4 | yes | — |
| 31 | #14523248 | C23 | 1 | 4 | yes | — |
| 32 | C2×Dic254 | C2×C4 | 1 | 2 | yes | — |
| 33 | C2×D508 | C2×C4 | 1 | 2 | yes | — |
| 34 | C2×C22⋊D127 | — | 2 | 2 | no | — |
| 35 | C2×C4×D127 | — | 2 | 2 | no | — |
| 36 | Dic508 | C2×C4 | 1 | 2 | yes | — |
| 37 | Dic508 | C2×C4 | 1 | 2 | yes | — |
| 38 | #14523237 | C2×C4 | 1 | 4 | yes | — |
| 39 | #14523237 | C2×C4 | 1 | 4 | yes | — |
| 40 | D1016 | C2×C4 | 1 | 2 | yes | — |
| 41 | D1016 | C2×C4 | 1 | 2 | yes | — |
| 42 | #14523232 | — | 2 | 2 | no | — |
| 43 | #14523232 | C23 | 1 | 4 | yes | — |
| 44 | #14523231 | — | 2 | 8 | no | — |
| 45 | C2×C127⋊C8 | — | 2 | 2 | no | — |
| 46 | C8×D127 | — | 2 | 8 | no | — |
| 47 | C22×C4×C127 | C23 | 1 | 1 | yes | characteristic |
| 48 | M16×C127 | D4 | 1 | 2 | yes | — |
| 49 | M16×C127 | D4 | 1 | 2 | yes | — |
| 50 | C2×C8×C127 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C2×C8×C127 | C2×C4 | 1 | 1 | yes | characteristic |
| 52 | C2×C8×C127 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | C2×C8×C127 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | C2×C8×C127 | C23 | 1 | 1 | yes | characteristic |
| 55 | C2×C8×C127 | C23 | 1 | 1 | yes | characteristic |
| 56 | C2×C8×C127 | C23 | 1 | 2 | yes | — |
| 57 | C4⋊C4×C127 | — | 2 | 1 | no | — |
| 58 | C22⋊C4×C127 | — | 2 | 1 | no | — |
| 59 | C42×C127 | C23 | 1 | 2 | yes | — |
| 60 | C22×D127 | — | 2 | 2 | no | — |
| 61 | Dic254 | — | 2 | 2 | no | — |
| 62 | Dic254 | C22×C4 | 1 | 4 | yes | — |
| 63 | D508 | — | 2 | 2 | no | — |
| 64 | D508 | C22×C4 | 1 | 4 | yes | — |
| 65 | C22⋊D127 | — | 2 | 4 | no | — |
| 66 | C22⋊D127 | — | 2 | 4 | no | — |
| 67 | C2×Dic127 | — | 2 | 2 | no | — |
| 68 | C4×D127 | — | 2 | 4 | no | — |
| 69 | C4×D127 | — | 2 | 4 | no | — |
| 70 | C127⋊C8 | — | 2 | 4 | no | — |
| 71 | C23×C127 | #41 | 1 | 1 | yes | characteristic |
| 72 | C2×C4×C127 | — | 2 | 2 | no | — |
| 73 | C2×C4×C127 | C22×C4 | 1 | 1 | yes | characteristic |
| 74 | C2×C4×C127 | C22×C4 | 1 | 1 | yes | characteristic |
| 75 | C2×C4×C127 | C2×D4 | 1 | 1 | yes | characteristic |
| 76 | C2×C4×C127 | C2×D4 | 1 | 1 | yes | characteristic |
| 77 | C2×C4×C127 | #41 | 1 | 1 | yes | characteristic |
| 78 | C2×C4×C127 | C24 | 1 | 1 | yes | characteristic |
| 79 | C8×C127 | C22×C4 | 1 | 1 | yes | characteristic |
| 80 | C8×C127 | C22×C4 | 1 | 1 | yes | characteristic |
| 81 | C8×C127 | C22×C4 | 1 | 1 | yes | characteristic |
| 82 | C8×C127 | C22×C4 | 1 | 1 | yes | characteristic |
| 83 | C8×C127 | C2×D4 | 1 | 4 | yes | — |
| 84 | C22×C127 | — | 4 | 1 | no | — |
| 85 | C22×C127 | C4×D4 | 1 | 1 | yes | characteristic |
| 86 | C22×C127 | C4×D4 | 1 | 1 | yes | characteristic |
| 87 | C22×C127 | C2×#41 | 1 | 1 | yes | characteristic |
| 88 | C2×D127 | — | 2 | 4 | no | — |
| 89 | C2×D127 | — | 8 | 2 | no | — |
| 90 | C4×C127 | — | 4 | 2 | no | — |
| 91 | C4×C127 | C4×D4 | 1 | 1 | yes | characteristic |
| 92 | C4×C127 | C4×D4 | 1 | 1 | yes | characteristic |
| 93 | C4×C127 | C23×C4 | 1 | 1 | yes | characteristic |
| 94 | C4×C127 | C22×D4 | 1 | 1 | yes | characteristic |
| 95 | Dic127 | — | 2 | 4 | no | — |
| 96 | C2×C127 | — | 2 | 1 | no | — |
| 97 | C2×C127 | — | 2 | 1 | no | — |
| 98 | C2×C127 | — | 2 | 1 | no | — |
| 99 | C2×C127 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 100 | D127 | — | 4 | 4 | no | — |
| 101 | #2957 | — | 127 | 1 | no | maximal, Sylow |
| 102 | C127 | #2957 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 103 | C2×#135 | — | 127 | 1 | no | — |
| 104 | #568 | — | 127 | 2 | no | — |
| 105 | #444 | — | 127 | 4 | no | — |
| 106 | #443 | — | 127 | 4 | no | — |
| 107 | C2×#108 | — | 127 | 1 | no | — |
| 108 | #421 | — | 127 | 2 | no | — |
| 109 | #405 | D127 | 1 | 1 | yes | characteristic, complemented |
| 110 | C2×#41 | — | 127 | 2 | no | — |
| 111 | #135 | — | 127 | 2 | no | — |
| 112 | #135 | — | 127 | 2 | no | — |
| 113 | #135 | — | 127 | 2 | no | — |
| 114 | #135 | — | 127 | 2 | no | — |
| 115 | C2×Q16 | — | 127 | 1 | no | — |
| 116 | C2×SD16 | — | 127 | 2 | no | — |
| 117 | C2×D8 | — | 127 | 1 | no | — |
| 118 | #131 | — | 127 | 8 | no | — |
| 119 | #131 | — | 254 | 4 | no | — |
| 120 | C2×M16 | — | 127 | 2 | no | — |
| 121 | C2×M16 | — | 254 | 4 | no | — |
| 122 | C2×M16 | C2×D127 | 1 | 1 | yes | characteristic |
| 123 | C22×C8 | C2×D127 | 1 | 1 | yes | characteristic |
| 124 | #117 | C2×D127 | 1 | 1 | yes | characteristic |
| 125 | #108 | — | 127 | 2 | no | — |
| 126 | #108 | — | 127 | 2 | no | — |
| 127 | #104 | — | 127 | 8 | no | — |
| 128 | #97 | C2×D127 | 1 | 2 | yes | complemented |
| 129 | C4×C8 | C2×D127 | 1 | 2 | yes | complemented |
| 130 | #41 | — | 127 | 4 | no | — |
| 131 | #41 | — | 127 | 4 | no | — |
| 132 | #41 | — | 254 | 2 | no | — |
| 133 | #41 | — | 254 | 2 | no | — |
| 134 | C2×Q8 | — | 127 | 2 | no | — |
| 135 | C2×D4 | — | 127 | 2 | no | — |
| 136 | C2×D4 | — | 254 | 2 | no | — |
| 137 | C22×C4 | — | 254 | 2 | no | — |
| 138 | C22×C4 | C22×D127 | 1 | 1 | yes | characteristic |
| 139 | Q16 | — | 127 | 2 | no | — |
| 140 | Q16 | — | 127 | 2 | no | — |
| 141 | SD16 | — | 127 | 4 | no | — |
| 142 | SD16 | — | 127 | 4 | no | — |
| 143 | D8 | — | 127 | 2 | no | — |
| 144 | D8 | — | 127 | 2 | no | — |
| 145 | M16 | — | 127 | 4 | no | — |
| 146 | M16 | — | 254 | 2 | no | — |
| 147 | M16 | — | 254 | 8 | no | — |
| 148 | M16 | D508 | 1 | 2 | yes | — |
| 149 | M16 | D508 | 1 | 2 | yes | — |
| 150 | C2×C8 | — | 254 | 2 | no | — |
| 151 | C2×C8 | — | 254 | 8 | no | — |
| 152 | C2×C8 | C4×D127 | 1 | 1 | yes | characteristic |
| 153 | C2×C8 | C4×D127 | 1 | 1 | yes | characteristic |
| 154 | C2×C8 | C4×D127 | 1 | 1 | yes | characteristic |
| 155 | C2×C8 | C4×D127 | 1 | 1 | yes | characteristic |
| 156 | C2×C8 | C22×D127 | 1 | 1 | yes | characteristic |
| 157 | C2×C8 | C22×D127 | 1 | 1 | yes | characteristic |
| 158 | C2×C8 | C22×D127 | 1 | 2 | yes | — |
| 159 | C4⋊C4 | — | 2 | 1 | no | — |
| 160 | C22⋊C4 | — | 2 | 1 | no | — |
| 161 | C42 | C22×D127 | 1 | 2 | yes | — |
| 162 | C23 | — | 254 | 2 | no | — |
| 163 | C23 | #14523248 | 1 | 1 | yes | characteristic |
| 164 | Q8 | — | 127 | 4 | no | — |
| 165 | Q8 | — | 254 | 2 | no | — |
| 166 | D4 | — | 127 | 4 | no | — |
| 167 | D4 | — | 254 | 4 | no | — |
| 168 | D4 | — | 254 | 4 | no | — |
| 169 | D4 | — | 254 | 2 | no | — |
| 170 | C2×C4 | — | 2 | 2 | no | — |
| 171 | C2×C4 | — | 254 | 2 | no | — |
| 172 | C2×C4 | — | 254 | 4 | no | — |
| 173 | C2×C4 | — | 254 | 4 | no | — |
| 174 | C2×C4 | C2×C4×D127 | 1 | 1 | yes | characteristic |
| 175 | C2×C4 | C2×C4×D127 | 1 | 1 | yes | characteristic |
| 176 | C2×C4 | C2×D508 | 1 | 1 | yes | characteristic |
| 177 | C2×C4 | C2×D508 | 1 | 1 | yes | characteristic |
| 178 | C2×C4 | #14523248 | 1 | 1 | yes | characteristic |
| 179 | C2×C4 | C23×D127 | 1 | 1 | yes | characteristic |
| 180 | C8 | — | 254 | 4 | no | — |
| 181 | C8 | C2×C4×D127 | 1 | 1 | yes | characteristic |
| 182 | C8 | C2×C4×D127 | 1 | 1 | yes | characteristic |
| 183 | C8 | C2×C4×D127 | 1 | 1 | yes | characteristic |
| 184 | C8 | C2×C4×D127 | 1 | 1 | yes | characteristic |
| 185 | C8 | C2×D508 | 1 | 4 | yes | — |
| 186 | C22 | — | 4 | 1 | no | — |
| 187 | C22 | — | 1016 | 2 | no | — |
| 188 | C22 | — | 254 | 4 | no | — |
| 189 | C22 | C4×D508 | 1 | 1 | yes | characteristic |
| 190 | C22 | C4×D508 | 1 | 1 | yes | characteristic |
| 191 | C22 | C2×#14523248 | 1 | 1 | yes | characteristic |
| 192 | C4 | — | 4 | 2 | no | — |
| 193 | C4 | — | 254 | 4 | no | — |
| 194 | C4 | C4×D508 | 1 | 1 | yes | characteristic |
| 195 | C4 | C4×D508 | 1 | 1 | yes | characteristic |
| 196 | C4 | C22×C4×D127 | 1 | 1 | yes | characteristic |
| 197 | C4 | C22×D508 | 1 | 1 | yes | characteristic |
| 198 | C2 | — | 2 | 1 | no | — |
| 199 | C2 | — | 2 | 1 | no | — |
| 200 | C2 | — | 2 | 1 | no | — |
| 201 | C2 | — | 508 | 4 | no | — |
| 202 | C2 | C2×C4×D508 | 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