Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
644 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 88 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 | #21461262 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | #21461133 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #21460509 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #16840781 | C22 | 1 | 3 | yes | — |
| 5 | #16840707 | C22 | 1 | 1 | yes | characteristic |
| 6 | #16840615 | — | 2 | 3 | no | — |
| 7 | #16840614 | — | 2 | 3 | no | — |
| 8 | #16840612 | — | 2 | 3 | no | — |
| 9 | #16840610 | — | 2 | 3 | no | — |
| 10 | #16840510 | C4 | 1 | 3 | yes | complemented |
| 11 | #16840465 | — | 2 | 3 | no | — |
| 12 | #16840444 | — | 2 | 3 | no | — |
| 13 | #16840368 | — | 2 | 3 | no | — |
| 14 | #16840360 | — | 2 | 3 | no | — |
| 15 | #16840297 | C22 | 1 | 3 | yes | — |
| 16 | C61×#564 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | C4⋊#92420 | — | 2 | 3 | no | — |
| 18 | #14519834 | — | 2 | 3 | no | — |
| 19 | C4×#92420 | — | 2 | 3 | no | — |
| 20 | (C2×#6923)⋊C4 | — | 2 | 3 | no | — |
| 21 | #14519774 | — | 2 | 1 | no | — |
| 22 | #14519772 | — | 2 | 3 | no | — |
| 23 | #14519772 | — | 2 | 3 | no | — |
| 24 | #14519771 | — | 2 | 1 | no | — |
| 25 | #14519767 | — | 2 | 3 | no | — |
| 26 | #14519765 | C2×C4 | 1 | 3 | yes | — |
| 27 | #14519762 | — | 2 | 3 | no | — |
| 28 | #14519762 | — | 2 | 3 | no | — |
| 29 | #14519762 | — | 2 | 3 | no | — |
| 30 | #14519762 | — | 2 | 3 | no | — |
| 31 | #14519762 | — | 2 | 3 | no | — |
| 32 | #14519757 | D4 | 1 | 3 | yes | — |
| 33 | #14519755 | — | 2 | 3 | no | — |
| 34 | #14519755 | — | 2 | 3 | no | — |
| 35 | #14519752 | — | 2 | 3 | no | — |
| 36 | #14519752 | — | 2 | 3 | no | — |
| 37 | #14519752 | — | 2 | 3 | no | — |
| 38 | #14519752 | — | 2 | 3 | no | — |
| 39 | #14519752 | D4 | 1 | 3 | yes | — |
| 40 | #14519742 | D4 | 1 | 3 | yes | — |
| 41 | C4×D244 | — | 2 | 3 | no | — |
| 42 | #14519739 | — | 2 | 3 | no | — |
| 43 | #14519739 | — | 2 | 3 | no | — |
| 44 | #14519739 | D4 | 1 | 3 | yes | — |
| 45 | #14519735 | — | 2 | 3 | no | — |
| 46 | #14519734 | — | 2 | 3 | no | — |
| 47 | C4⋊C4×D61 | — | 2 | 3 | no | — |
| 48 | C42×D61 | C23 | 1 | 1 | yes | characteristic |
| 49 | #125×C61 | — | 2 | 3 | no | — |
| 50 | #125×C61 | — | 2 | 3 | no | — |
| 51 | #125×C61 | C2×C4 | 1 | 3 | yes | — |
| 52 | C22×#6923 | — | 4 | 1 | no | — |
| 53 | C2×D244 | — | 2 | 3 | no | — |
| 54 | C2×D244 | — | 2 | 3 | no | — |
| 55 | C2×D244 | — | 2 | 3 | no | — |
| 56 | C2×D244 | C22⋊C4 | 1 | 3 | yes | — |
| 57 | C2×C4×D61 | — | 2 | 3 | no | — |
| 58 | C2×C4×D61 | — | 2 | 3 | no | — |
| 59 | C2×C4×D61 | — | 2 | 3 | no | — |
| 60 | C2×C4×D61 | C2×D4 | 1 | 3 | yes | — |
| 61 | C2×Dic122 | C22⋊C4 | 1 | 3 | yes | — |
| 62 | C2×#92420 | — | 4 | 3 | no | — |
| 63 | C4⋊C4×C61 | — | 2 | 3 | no | — |
| 64 | C4⋊C4×C61 | — | 2 | 3 | no | — |
| 65 | C4⋊C4×C61 | — | 2 | 3 | no | — |
| 66 | C4⋊C4×C61 | — | 2 | 3 | no | — |
| 67 | C4⋊C4×C61 | C22⋊C4 | 1 | 3 | yes | — |
| 68 | C4⋊C4×C61 | C22⋊C4 | 1 | 3 | yes | — |
| 69 | C42×C61 | — | 2 | 1 | no | — |
| 70 | C42×C61 | — | 2 | 1 | no | — |
| 71 | C42×C61 | C22×C4 | 1 | 1 | yes | characteristic |
| 72 | #11758198 | — | 2 | 3 | no | — |
| 73 | #11758198 | — | 2 | 3 | no | — |
| 74 | #11758198 | — | 2 | 3 | no | — |
| 75 | #11758198 | — | 2 | 3 | no | — |
| 76 | #11758198 | — | 2 | 3 | no | — |
| 77 | #11758198 | — | 2 | 3 | no | — |
| 78 | #11758198 | — | 2 | 3 | no | — |
| 79 | C4⋊Dic61 | — | 2 | 3 | no | — |
| 80 | #11758196 | — | 2 | 3 | no | — |
| 81 | #11758196 | — | 2 | 3 | no | — |
| 82 | #11758196 | — | 2 | 3 | no | — |
| 83 | C4×Dic61 | — | 2 | 3 | no | — |
| 84 | C4×Dic61 | C2×D4 | 1 | 3 | yes | — |
| 85 | C22×D61 | — | 2 | 3 | no | — |
| 86 | C22×D61 | #120 | 1 | 1 | yes | characteristic |
| 87 | C2×#6923 | — | 8 | 3 | no | — |
| 88 | C2×C4×C61 | — | 2 | 3 | no | — |
| 89 | C2×C4×C61 | — | 2 | 3 | no | — |
| 90 | C2×C4×C61 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 91 | C2×Dic61 | — | 2 | 3 | no | — |
| 92 | C2×Dic61 | #120 | 1 | 3 | yes | — |
| 93 | D244 | — | 4 | 3 | no | — |
| 94 | D244 | — | 8 | 3 | no | — |
| 95 | D244 | — | 8 | 3 | no | — |
| 96 | D244 | — | 8 | 3 | no | — |
| 97 | C4×D61 | — | 4 | 3 | no | — |
| 98 | C4×D61 | — | 8 | 3 | no | — |
| 99 | C4×D61 | — | 8 | 3 | no | — |
| 100 | C4×D61 | — | 8 | 3 | no | — |
| 101 | Dic122 | — | 4 | 3 | no | — |
| 102 | #92420 | — | 8 | 3 | no | — |
| 103 | #8515 | — | 61 | 1 | no | maximal, Sylow |
| 104 | C22×C61 | #379 | 1 | 1 | yes | characteristic |
| 105 | C2×D61 | — | 2 | 3 | no | — |
| 106 | C2×D61 | — | 4 | 3 | no | — |
| 107 | C2×D61 | — | 4 | 3 | no | — |
| 108 | C2×D61 | — | 4 | 3 | no | — |
| 109 | #6923 | — | 16 | 1 | no | — |
| 110 | C4×C61 | — | 2 | 3 | no | — |
| 111 | C4×C61 | — | 4 | 3 | no | — |
| 112 | C4×C61 | — | 4 | 3 | no | — |
| 113 | Dic61 | — | 2 | 3 | no | — |
| 114 | Dic61 | — | 4 | 3 | no | — |
| 115 | #3567 | — | 61 | 1 | no | — |
| 116 | #1521 | — | 61 | 3 | no | — |
| 117 | #1482 | — | 61 | 3 | no | — |
| 118 | C2×C61 | #1794 | 1 | 3 | yes | — |
| 119 | D61 | — | 4 | 1 | no | — |
| 120 | D61 | — | 8 | 3 | no | — |
| 121 | #564 | #6923 | 1 | 1 | yes | characteristic, complemented |
| 122 | #562 | — | 61 | 3 | no | — |
| 123 | #553 | — | 122 | 3 | no | — |
| 124 | #552 | — | 122 | 3 | no | — |
| 125 | #540 | — | 122 | 3 | no | — |
| 126 | #539 | — | 122 | 3 | no | — |
| 127 | #529 | — | 61 | 3 | no | — |
| 128 | #431 | — | 61 | 3 | no | — |
| 129 | #383 | — | 61 | 1 | no | — |
| 130 | #328 | — | 122 | 3 | no | — |
| 131 | #327 | — | 122 | 3 | no | — |
| 132 | Q8⋊C8 | — | 122 | 3 | no | — |
| 133 | D4⋊C8 | — | 122 | 3 | no | — |
| 134 | C61 | #8515 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 135 | #127 | — | 122 | 1 | no | — |
| 136 | #126 | — | 122 | 1 | no | — |
| 137 | #126 | — | 122 | 3 | no | — |
| 138 | #126 | — | 122 | 3 | no | — |
| 139 | #125 | — | 2 | 3 | no | — |
| 140 | #125 | — | 2 | 3 | no | — |
| 141 | #125 | — | 122 | 3 | no | — |
| 142 | #125 | C2×#6923 | 1 | 3 | yes | — |
| 143 | #124 | — | 61 | 3 | no | — |
| 144 | #123 | — | 122 | 3 | no | — |
| 145 | #123 | — | 122 | 3 | no | — |
| 146 | #123 | — | 122 | 3 | no | — |
| 147 | #123 | — | 122 | 3 | no | — |
| 148 | #123 | — | 122 | 3 | no | — |
| 149 | C22⋊Q8 | — | 61 | 3 | no | — |
| 150 | C22⋊Q8 | — | 122 | 3 | no | — |
| 151 | C22⋊Q8 | — | 122 | 3 | no | — |
| 152 | #121 | — | 61 | 3 | no | — |
| 153 | #121 | — | 122 | 3 | no | — |
| 154 | #121 | — | 122 | 3 | no | — |
| 155 | #121 | — | 122 | 3 | no | — |
| 156 | #121 | — | 122 | 3 | no | — |
| 157 | C4×Q8 | — | 61 | 3 | no | — |
| 158 | C4×D4 | — | 61 | 3 | no | — |
| 159 | C4×D4 | — | 122 | 3 | no | — |
| 160 | C4×D4 | — | 122 | 3 | no | — |
| 161 | C4×D4 | — | 122 | 3 | no | — |
| 162 | #117 | — | 122 | 3 | no | — |
| 163 | #117 | — | 122 | 3 | no | — |
| 164 | C2×C4⋊C4 | — | 122 | 3 | no | — |
| 165 | C2×C42 | — | 61 | 1 | no | — |
| 166 | C4⋊C8 | — | 122 | 3 | no | — |
| 167 | C22⋊C8 | — | 122 | 3 | no | — |
| 168 | C4×C8 | — | 122 | 3 | no | — |
| 169 | #95 | — | 122 | 3 | no | — |
| 170 | C2×Q8 | — | 61 | 3 | no | — |
| 171 | C2×D4 | — | 61 | 3 | no | — |
| 172 | C2×D4 | — | 122 | 3 | no | — |
| 173 | C2×D4 | — | 122 | 3 | no | — |
| 174 | C2×D4 | — | 122 | 3 | no | — |
| 175 | C22×C4 | — | 61 | 3 | no | — |
| 176 | C22×C4 | — | 122 | 3 | no | — |
| 177 | C22×C4 | — | 122 | 3 | no | — |
| 178 | C22×C4 | — | 122 | 3 | no | — |
| 179 | C22×C4 | — | 244 | 1 | no | — |
| 180 | C2×C8 | — | 244 | 3 | no | — |
| 181 | C4⋊C4 | — | 2 | 3 | no | — |
| 182 | C4⋊C4 | — | 2 | 3 | no | — |
| 183 | C4⋊C4 | — | 2 | 3 | no | — |
| 184 | C4⋊C4 | — | 2 | 3 | no | — |
| 185 | C4⋊C4 | — | 122 | 3 | no | — |
| 186 | C4⋊C4 | — | 122 | 3 | no | — |
| 187 | C4⋊C4 | — | 122 | 3 | no | — |
| 188 | C4⋊C4 | — | 122 | 3 | no | — |
| 189 | C4⋊C4 | C22⋊#6923 | 1 | 3 | yes | — |
| 190 | C4⋊C4 | C22⋊#6923 | 1 | 3 | yes | — |
| 191 | C22⋊C4 | — | 122 | 3 | no | — |
| 192 | C22⋊C4 | — | 122 | 3 | no | — |
| 193 | C22⋊C4 | — | 122 | 3 | no | — |
| 194 | C22⋊C4 | — | 122 | 3 | no | — |
| 195 | C22⋊C4 | — | 122 | 3 | no | — |
| 196 | C22⋊C4 | — | 122 | 3 | no | — |
| 197 | C22⋊C4 | — | 122 | 3 | no | — |
| 198 | C42 | — | 2 | 1 | no | — |
| 199 | C42 | — | 2 | 1 | no | — |
| 200 | C42 | — | 61 | 3 | no | — |
| 201 | C42 | — | 122 | 3 | no | — |
| 202 | C42 | C22×#6923 | 1 | 1 | yes | characteristic |
| 203 | C23 | — | 61 | 1 | no | — |
| 204 | C23 | — | 122 | 3 | no | — |
| 205 | Q8 | — | 244 | 3 | no | — |
| 206 | D4 | — | 488 | 3 | no | — |
| 207 | D4 | — | 488 | 3 | no | — |
| 208 | D4 | — | 488 | 3 | no | — |
| 209 | D4 | — | 244 | 3 | no | — |
| 210 | C2×C4 | — | 2 | 3 | no | — |
| 211 | C2×C4 | — | 2 | 3 | no | — |
| 212 | C2×C4 | — | 61 | 3 | no | — |
| 213 | C2×C4 | — | 122 | 3 | no | — |
| 214 | C2×C4 | — | 488 | 3 | no | — |
| 215 | C2×C4 | — | 488 | 3 | no | — |
| 216 | C2×C4 | — | 488 | 3 | no | — |
| 217 | C2×C4 | — | 488 | 3 | no | — |
| 218 | C2×C4 | — | 244 | 3 | no | — |
| 219 | C2×C4 | C2×C22⋊#6923 | 1 | 3 | yes | — |
| 220 | C8 | — | 488 | 3 | no | — |
| 221 | C22 | — | 122 | 3 | no | — |
| 222 | C22 | — | 244 | 3 | no | — |
| 223 | C22 | — | 244 | 3 | no | — |
| 224 | C22 | — | 244 | 3 | no | — |
| 225 | C22 | #16840703 | 1 | 1 | yes | characteristic |
| 226 | C4 | — | 2 | 3 | no | — |
| 227 | C4 | — | 4 | 3 | no | — |
| 228 | C4 | — | 4 | 3 | no | — |
| 229 | C4 | — | 122 | 3 | no | — |
| 230 | C4 | — | 976 | 1 | no | — |
| 231 | C4 | — | 244 | 3 | no | — |
| 232 | C2 | — | 488 | 3 | no | — |
| 233 | C2 | — | 244 | 1 | no | — |
| 234 | C2 | #21461668 | 1 | 3 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21461262 | C2 | semidirect |
| 2. #21461133 | C2 | semidirect |
| 10. #16840510 | C4 | semidirect |
| 16. C61×#564 | C4 | semidirect |
| 121. #564 | #6923 | semidirect |
| 134. C61 | #8515 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461262 | 2 |
| #21461133 | 2 |
| #21460509 | 2 |
| #8515 | 61 |