Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
2414 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 2414 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #379×D61 | C2 | 1 | 3 | yes | maximal |
| 2 | #21443723 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C61×#1304 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C25×D61 | C22 | 1 | 1 | yes | characteristic |
| 5 | C2×C22⋊C4×D61 | — | 2 | 6 | no | — |
| 6 | C2×C22⋊C4×D61 | C4 | 1 | 6 | yes | complemented |
| 7 | #16839618 | C22 | 1 | 3 | yes | — |
| 8 | #16839617 | — | 2 | 6 | no | — |
| 9 | #16839617 | C4 | 1 | 6 | yes | complemented |
| 10 | C61×#379 | C22 | 1 | 3 | yes | — |
| 11 | C24×D61 | — | 4 | 12 | no | — |
| 12 | C24×D61 | C2×C4 | 1 | 3 | yes | — |
| 13 | C24×D61 | C2×C4 | 1 | 3 | yes | — |
| 14 | C24×D61 | D4 | 1 | 6 | yes | — |
| 15 | C24×D61 | Q8 | 1 | 2 | yes | — |
| 16 | C22×C4×D61 | — | 2 | 6 | no | — |
| 17 | C2×C22⋊Dic61 | — | 2 | 6 | no | — |
| 18 | C2×C22⋊Dic61 | C2×C4 | 1 | 6 | yes | complemented |
| 19 | C2×#11758198 | — | 2 | 12 | no | — |
| 20 | C2×#11758198 | — | 2 | 6 | no | — |
| 21 | C22⋊C4×D61 | — | 4 | 24 | no | — |
| 22 | C22⋊C4×D61 | — | 4 | 12 | no | — |
| 23 | C25×C61 | C23 | 1 | 1 | yes | characteristic |
| 24 | C2×C22⋊C4×C61 | — | 2 | 6 | no | — |
| 25 | C2×C22⋊C4×C61 | C2×C4 | 1 | 6 | yes | complemented |
| 26 | C24×C61 | — | 4 | 6 | no | — |
| 27 | C24×C61 | C22×C4 | 1 | 3 | yes | — |
| 28 | C24×C61 | C2×D4 | 1 | 3 | yes | — |
| 29 | C24×C61 | C2×Q8 | 1 | 1 | yes | characteristic |
| 30 | C23×D61 | — | 2 | 12 | no | — |
| 31 | C23×D61 | — | 2 | 24 | no | — |
| 32 | C23×D61 | — | 4 | 12 | no | — |
| 33 | C23×D61 | — | 4 | 12 | no | — |
| 34 | C23×D61 | — | 4 | 12 | no | — |
| 35 | C23×D61 | — | 4 | 12 | no | — |
| 36 | C23×D61 | — | 4 | 6 | no | — |
| 37 | C23×D61 | — | 4 | 12 | no | — |
| 38 | C23×D61 | — | 4 | 64 | no | — |
| 39 | C23×D61 | C42 | 1 | 3 | yes | — |
| 40 | C23×D61 | C42 | 1 | 1 | yes | characteristic |
| 41 | C23×D61 | C22⋊C4 | 1 | 3 | yes | — |
| 42 | C23×D61 | C22⋊C4 | 1 | 6 | yes | — |
| 43 | C23×D61 | C22⋊C4 | 1 | 3 | yes | — |
| 44 | C23×D61 | C4⋊C4 | 1 | 6 | yes | — |
| 45 | C23×D61 | C4⋊C4 | 1 | 6 | yes | — |
| 46 | C22×C4×C61 | — | 2 | 6 | no | — |
| 47 | C22×Dic61 | — | 2 | 6 | no | — |
| 48 | C2×C4×D61 | — | 4 | 24 | no | — |
| 49 | C2×C4×D61 | — | 4 | 12 | no | — |
| 50 | C22⋊C4×C61 | — | 4 | 12 | no | — |
| 51 | C22⋊C4×C61 | — | 4 | 6 | no | — |
| 52 | C22⋊Dic61 | — | 4 | 12 | no | — |
| 53 | C22⋊Dic61 | — | 4 | 6 | no | — |
| 54 | #11758198 | — | 4 | 24 | no | — |
| 55 | #11758198 | — | 4 | 12 | no | — |
| 56 | C23×C61 | — | 2 | 6 | no | — |
| 57 | C23×C61 | — | 2 | 12 | no | — |
| 58 | C23×C61 | — | 4 | 6 | no | — |
| 59 | C23×C61 | — | 4 | 3 | no | — |
| 60 | C23×C61 | — | 4 | 3 | no | — |
| 61 | C23×C61 | — | 4 | 16 | no | — |
| 62 | C23×C61 | C2×C42 | 1 | 1 | yes | characteristic |
| 63 | C23×C61 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 64 | C23×C61 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 65 | C22×D61 | — | 2 | 6 | no | — |
| 66 | C22×D61 | — | 2 | 12 | no | — |
| 67 | C22×D61 | — | 2 | 12 | no | — |
| 68 | C22×D61 | — | 2 | 12 | no | — |
| 69 | C22×D61 | — | 2 | 12 | no | — |
| 70 | C22×D61 | — | 2 | 12 | no | — |
| 71 | C22×D61 | — | 2 | 12 | no | — |
| 72 | C22×D61 | — | 2 | 12 | no | — |
| 73 | C22×D61 | — | 4 | 3 | no | — |
| 74 | C22×D61 | — | 4 | 3 | no | — |
| 75 | C22×D61 | — | 4 | 6 | no | — |
| 76 | C22×D61 | — | 4 | 6 | no | — |
| 77 | C22×D61 | — | 4 | 6 | no | — |
| 78 | C22×D61 | — | 4 | 6 | no | — |
| 79 | C22×D61 | — | 4 | 6 | no | — |
| 80 | C22×D61 | — | 4 | 48 | no | — |
| 81 | C22×D61 | — | 4 | 96 | no | — |
| 82 | C22×D61 | — | 4 | 32 | no | — |
| 83 | C22×D61 | — | 4 | 48 | no | — |
| 84 | C22×D61 | #95 | 1 | 2 | yes | — |
| 85 | C22×D61 | #95 | 1 | 6 | yes | — |
| 86 | C22×D61 | #99 | 1 | 12 | yes | — |
| 87 | C2×C4×C61 | — | 4 | 12 | no | — |
| 88 | C2×C4×C61 | — | 4 | 6 | no | — |
| 89 | C2×Dic61 | — | 4 | 12 | no | — |
| 90 | C2×Dic61 | — | 4 | 6 | no | — |
| 91 | C4×D61 | — | 8 | 24 | no | — |
| 92 | #8101 | — | 61 | 1 | no | maximal, Sylow |
| 93 | C22×C61 | — | 2 | 6 | no | — |
| 94 | C22×C61 | — | 2 | 3 | no | — |
| 95 | C22×C61 | — | 2 | 3 | no | — |
| 96 | C22×C61 | — | 2 | 6 | no | — |
| 97 | C22×C61 | — | 4 | 12 | no | — |
| 98 | C22×C61 | — | 4 | 12 | no | — |
| 99 | C22×C61 | — | 4 | 4 | no | — |
| 100 | C22×C61 | C2×#95 | 1 | 1 | yes | characteristic |
| 101 | C22×C61 | C2×#99 | 1 | 6 | yes | — |
| 102 | C2×D61 | — | 2 | 24 | no | — |
| 103 | C2×D61 | — | 2 | 6 | no | — |
| 104 | C2×D61 | — | 2 | 6 | no | — |
| 105 | C2×D61 | — | 2 | 6 | no | — |
| 106 | C2×D61 | — | 4 | 12 | no | — |
| 107 | C2×D61 | — | 4 | 12 | no | — |
| 108 | C2×D61 | — | 4 | 24 | no | — |
| 109 | C2×D61 | — | 4 | 24 | no | — |
| 110 | C2×D61 | — | 4 | 24 | no | — |
| 111 | C2×D61 | — | 4 | 4 | no | — |
| 112 | C2×D61 | #342 | 1 | 12 | yes | — |
| 113 | C4×C61 | — | 8 | 6 | no | — |
| 114 | Dic61 | — | 8 | 6 | no | — |
| 115 | C2×#379 | — | 61 | 3 | no | — |
| 116 | #1304 | — | 61 | 3 | no | — |
| 117 | #1304 | D61 | 1 | 1 | yes | characteristic, complemented |
| 118 | C2×C61 | — | 2 | 6 | no | — |
| 119 | C2×C61 | — | 4 | 1 | no | — |
| 120 | C2×C61 | — | 4 | 3 | no | — |
| 121 | C2×C61 | C2×#342 | 1 | 3 | yes | — |
| 122 | D61 | — | 2 | 12 | no | — |
| 123 | D61 | — | 4 | 2 | no | — |
| 124 | C26 | — | 61 | 1 | no | — |
| 125 | C22×C22⋊C4 | — | 61 | 6 | no | — |
| 126 | C22×C22⋊C4 | — | 122 | 6 | no | — |
| 127 | #379 | — | 61 | 3 | no | — |
| 128 | #379 | — | 61 | 6 | no | — |
| 129 | #379 | — | 122 | 6 | no | — |
| 130 | #379 | C2×D61 | 1 | 3 | yes | — |
| 131 | C61 | #8101 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 132 | C25 | — | 61 | 3 | no | — |
| 133 | C25 | — | 61 | 6 | no | — |
| 134 | C25 | — | 61 | 3 | no | — |
| 135 | C25 | — | 61 | 2 | no | — |
| 136 | C25 | — | 244 | 12 | no | — |
| 137 | C25 | C22×D61 | 1 | 1 | yes | characteristic |
| 138 | C23×C4 | — | 122 | 6 | no | — |
| 139 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 140 | C2×C22⋊C4 | — | 61 | 6 | no | — |
| 141 | C2×C22⋊C4 | — | 122 | 6 | no | — |
| 142 | C2×C22⋊C4 | — | 122 | 12 | no | — |
| 143 | C2×C22⋊C4 | — | 122 | 6 | no | — |
| 144 | C2×C22⋊C4 | — | 244 | 24 | no | — |
| 145 | C2×C22⋊C4 | — | 244 | 12 | no | — |
| 146 | C2×C22⋊C4 | C4×D61 | 1 | 6 | yes | complemented |
| 147 | C24 | — | 4 | 6 | no | — |
| 148 | C24 | — | 61 | 3 | no | — |
| 149 | C24 | — | 61 | 3 | no | — |
| 150 | C24 | — | 61 | 3 | no | — |
| 151 | C24 | — | 61 | 6 | no | — |
| 152 | C24 | — | 61 | 6 | no | — |
| 153 | C24 | — | 61 | 6 | no | — |
| 154 | C24 | — | 61 | 1 | no | — |
| 155 | C24 | — | 122 | 12 | no | — |
| 156 | C24 | — | 122 | 24 | no | — |
| 157 | C24 | — | 244 | 6 | no | — |
| 158 | C24 | — | 244 | 12 | no | — |
| 159 | C24 | — | 244 | 12 | no | — |
| 160 | C24 | — | 244 | 12 | no | — |
| 161 | C24 | — | 244 | 12 | no | — |
| 162 | C24 | — | 244 | 12 | no | — |
| 163 | C24 | — | 244 | 64 | no | — |
| 164 | C24 | C2×C4×D61 | 1 | 3 | yes | — |
| 165 | C24 | D4×D61 | 1 | 3 | yes | — |
| 166 | C24 | Q8×D61 | 1 | 1 | yes | characteristic |
| 167 | C22×C4 | — | 2 | 6 | no | — |
| 168 | C22×C4 | — | 122 | 6 | no | — |
| 169 | C22×C4 | — | 244 | 24 | no | — |
| 170 | C22×C4 | — | 244 | 12 | no | — |
| 171 | C22⋊C4 | — | 4 | 12 | no | — |
| 172 | C22⋊C4 | — | 4 | 6 | no | — |
| 173 | C22⋊C4 | — | 244 | 12 | no | — |
| 174 | C22⋊C4 | — | 244 | 24 | no | — |
| 175 | C22⋊C4 | — | 244 | 12 | no | — |
| 176 | C22⋊C4 | — | 244 | 6 | no | — |
| 177 | C23 | — | 2 | 6 | no | — |
| 178 | C23 | — | 2 | 12 | no | — |
| 179 | C23 | — | 4 | 6 | no | — |
| 180 | C23 | — | 4 | 3 | no | — |
| 181 | C23 | — | 4 | 3 | no | — |
| 182 | C23 | — | 4 | 16 | no | — |
| 183 | C23 | — | 61 | 6 | no | — |
| 184 | C23 | — | 61 | 12 | no | — |
| 185 | C23 | — | 61 | 2 | no | — |
| 186 | C23 | — | 122 | 12 | no | — |
| 187 | C23 | — | 122 | 12 | no | — |
| 188 | C23 | — | 122 | 12 | no | — |
| 189 | C23 | — | 122 | 12 | no | — |
| 190 | C23 | — | 122 | 12 | no | — |
| 191 | C23 | — | 122 | 12 | no | — |
| 192 | C23 | — | 122 | 6 | no | — |
| 193 | C23 | — | 122 | 12 | no | — |
| 194 | C23 | — | 244 | 6 | no | — |
| 195 | C23 | — | 244 | 6 | no | — |
| 196 | C23 | — | 244 | 3 | no | — |
| 197 | C23 | — | 244 | 3 | no | — |
| 198 | C23 | — | 244 | 6 | no | — |
| 199 | C23 | — | 244 | 6 | no | — |
| 200 | C23 | — | 244 | 6 | no | — |
| 201 | C23 | — | 244 | 96 | no | — |
| 202 | C23 | — | 244 | 48 | no | — |
| 203 | C23 | — | 244 | 48 | no | — |
| 204 | C23 | — | 244 | 32 | no | — |
| 205 | C23 | C42×D61 | 1 | 1 | yes | characteristic |
| 206 | C23 | C22⋊C4×D61 | 1 | 3 | yes | — |
| 207 | C23 | C4⋊C4×D61 | 1 | 3 | yes | — |
| 208 | C2×C4 | — | 4 | 12 | no | — |
| 209 | C2×C4 | — | 4 | 6 | no | — |
| 210 | C2×C4 | — | 488 | 24 | no | — |
| 211 | C2×C4 | — | 244 | 12 | no | — |
| 212 | C2×C4 | — | 244 | 6 | no | — |
| 213 | C22 | — | 2 | 6 | no | — |
| 214 | C22 | — | 2 | 3 | no | — |
| 215 | C22 | — | 2 | 3 | no | — |
| 216 | C22 | — | 2 | 6 | no | — |
| 217 | C22 | — | 4 | 12 | no | — |
| 218 | C22 | — | 4 | 12 | no | — |
| 219 | C22 | — | 4 | 4 | no | — |
| 220 | C22 | — | 61 | 12 | no | — |
| 221 | C22 | — | 122 | 24 | no | — |
| 222 | C22 | — | 122 | 6 | no | — |
| 223 | C22 | — | 122 | 6 | no | — |
| 224 | C22 | — | 122 | 6 | no | — |
| 225 | C22 | — | 244 | 12 | no | — |
| 226 | C22 | — | 244 | 24 | no | — |
| 227 | C22 | — | 244 | 12 | no | — |
| 228 | C22 | — | 244 | 24 | no | — |
| 229 | C22 | — | 244 | 24 | no | — |
| 230 | C22 | — | 244 | 4 | no | — |
| 231 | C22 | #95×D61 | 1 | 1 | yes | characteristic |
| 232 | C22 | #99×D61 | 1 | 6 | yes | — |
| 233 | C4 | — | 8 | 6 | no | — |
| 234 | C4 | — | 488 | 6 | no | — |
| 235 | C2 | — | 2 | 6 | no | — |
| 236 | C2 | — | 4 | 1 | no | — |
| 237 | C2 | — | 4 | 3 | no | — |
| 238 | C2 | — | 122 | 12 | no | — |
| 239 | C2 | — | 244 | 2 | no | — |
| 240 | C2 | #342×D61 | 1 | 3 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #21443723 | C2 | semidirect |
| 3. C61×#1304 | C2 | semidirect |
| 6. C2×C22⋊C4×D61 | C4 | semidirect |
| 9. #16839617 | C4 | semidirect |
| 18. C2×C22⋊Dic61 | C2×C4 | semidirect |
| 25. C2×C22⋊C4×C61 | C2×C4 | semidirect |
| 117. #1304 | D61 | semidirect |
| 131. C61 | #8101 | semidirect |
| 146. C2×C22⋊C4 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #379×D61 | 2 |
| #21443723 | 2 |
| C61×#1304 | 2 |
| #8101 | 61 |