Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
244 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 32 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 | #14543873 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14543707 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #14529887 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11763788 | — | 2 | 1 | no | — |
| 5 | C22⋊#63216 | — | 2 | 1 | no | — |
| 6 | #11763607 | — | 2 | 1 | no | — |
| 7 | #11762777 | C22 | 1 | 1 | yes | characteristic |
| 8 | #11762776 | — | 2 | 1 | no | — |
| 9 | #11762567 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | C17×#575 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×#41×C17 | — | 2 | 1 | no | — |
| 12 | C2×#63252 | D4 | 1 | 1 | yes | characteristic |
| 13 | #10587677 | — | 4 | 1 | no | — |
| 14 | C17×#137 | — | 4 | 1 | no | — |
| 15 | C17×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 16 | C17×#135 | — | 4 | 1 | no | — |
| 17 | C2×M16×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 18 | #10587637 | — | 4 | 1 | no | — |
| 19 | #10587636 | — | 4 | 2 | no | — |
| 20 | #10587635 | — | 4 | 1 | no | — |
| 21 | #10587628 | — | 4 | 1 | no | — |
| 22 | #10587618 | — | 4 | 1 | no | — |
| 23 | C2×#63223 | — | 2 | 1 | no | — |
| 24 | C22×#3622 | D4 | 1 | 1 | yes | characteristic |
| 25 | #10587551 | — | 2 | 2 | no | — |
| 26 | #10587539 | — | 4 | 1 | no | — |
| 27 | C2×#63216 | — | 4 | 1 | no | — |
| 28 | C22⋊#3622 | — | 4 | 2 | no | — |
| 29 | #10587491 | — | 4 | 1 | no | — |
| 30 | #41×C17 | — | 4 | 1 | no | — |
| 31 | #41×C17 | — | 4 | 1 | no | — |
| 32 | #41×C17 | — | 4 | 1 | no | — |
| 33 | #41×C17 | — | 4 | 1 | no | — |
| 34 | C2×Q8×C17 | — | 2 | 1 | no | — |
| 35 | C2×D4×C17 | — | 2 | 1 | no | — |
| 36 | C2×D4×C17 | — | 4 | 1 | no | — |
| 37 | C22×C4×C17 | — | 4 | 1 | no | — |
| 38 | C22×C4×C17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 39 | C2×C22⋊D17 | — | 2 | 1 | no | — |
| 40 | #63252 | — | 4 | 1 | no | — |
| 41 | #63252 | — | 4 | 1 | no | — |
| 42 | C2×D68 | D8 | 1 | 1 | yes | characteristic |
| 43 | C2×C4×D17 | — | 2 | 1 | no | — |
| 44 | C2×Dic34 | SD16 | 1 | 1 | yes | characteristic |
| 45 | C22⋊#595 | — | 4 | 2 | no | — |
| 46 | C4⋊#595 | — | 8 | 1 | no | — |
| 47 | C4×#595 | — | 8 | 1 | no | — |
| 48 | Q16×C17 | — | 4 | 1 | no | — |
| 49 | SD16×C17 | — | 4 | 2 | no | — |
| 50 | D8×C17 | — | 4 | 1 | no | — |
| 51 | M16×C17 | — | 4 | 1 | no | — |
| 52 | C2×C8×C17 | — | 2 | 1 | no | — |
| 53 | #63231 | — | 4 | 2 | no | — |
| 54 | #63230 | — | 4 | 2 | no | — |
| 55 | #63229 | — | 4 | 2 | no | — |
| 56 | #63228 | — | 4 | 2 | no | — |
| 57 | #63223 | — | 4 | 1 | no | — |
| 58 | #63223 | — | 4 | 1 | no | — |
| 59 | C2×#3622 | — | 2 | 2 | no | — |
| 60 | C2×#3622 | — | 2 | 1 | no | — |
| 61 | C2×#3622 | — | 4 | 1 | no | — |
| 62 | #63216 | — | 8 | 1 | no | — |
| 63 | #7406 | — | 17 | 1 | no | maximal, Sylow |
| 64 | C23×C17 | — | 4 | 1 | no | — |
| 65 | C23×C17 | #104 | 1 | 1 | yes | characteristic |
| 66 | C22×D17 | — | 2 | 1 | no | — |
| 67 | C2×#595 | — | 8 | 2 | no | — |
| 68 | Q8×C17 | — | 4 | 1 | no | — |
| 69 | Q8×C17 | — | 4 | 1 | no | — |
| 70 | D4×C17 | — | 4 | 1 | no | — |
| 71 | D4×C17 | — | 4 | 1 | no | — |
| 72 | D4×C17 | — | 8 | 1 | no | — |
| 73 | D4×C17 | — | 8 | 1 | no | — |
| 74 | C2×C4×C17 | — | 2 | 1 | no | — |
| 75 | C2×C4×C17 | — | 2 | 1 | no | — |
| 76 | C2×C4×C17 | — | 4 | 1 | no | — |
| 77 | C2×C4×C17 | — | 8 | 1 | no | — |
| 78 | C2×C4×C17 | — | 8 | 1 | no | — |
| 79 | C2×C4×C17 | #99 | 1 | 1 | yes | characteristic |
| 80 | C2×C4×C17 | #102 | 1 | 1 | yes | characteristic |
| 81 | C22⋊D17 | — | 8 | 1 | no | — |
| 82 | C2×Dic17 | — | 2 | 1 | no | — |
| 83 | D68 | — | 4 | 1 | no | — |
| 84 | C4×D17 | — | 4 | 1 | no | — |
| 85 | C4×D17 | — | 4 | 1 | no | — |
| 86 | Dic34 | — | 4 | 1 | no | — |
| 87 | C8×C17 | — | 4 | 1 | no | — |
| 88 | #3622 | — | 4 | 2 | no | — |
| 89 | #3622 | — | 4 | 1 | no | — |
| 90 | #2017 | — | 17 | 1 | no | — |
| 91 | #1391 | — | 17 | 1 | no | — |
| 92 | #1315 | — | 17 | 1 | no | — |
| 93 | C22×C17 | — | 2 | 1 | no | — |
| 94 | C22×C17 | — | 4 | 1 | no | — |
| 95 | C22×C17 | — | 8 | 2 | no | — |
| 96 | C22×C17 | — | 8 | 1 | no | — |
| 97 | C22×C17 | #327 | 1 | 1 | yes | characteristic |
| 98 | C2×D17 | — | 4 | 1 | no | — |
| 99 | C2×D17 | — | 8 | 1 | no | — |
| 100 | #595 | — | 16 | 2 | no | — |
| 101 | C4×C17 | — | 2 | 1 | no | — |
| 102 | C4×C17 | — | 8 | 1 | no | — |
| 103 | C4×C17 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 104 | C4×C17 | #353 | 1 | 1 | yes | characteristic |
| 105 | Dic17 | — | 4 | 1 | no | — |
| 106 | #575 | — | 34 | 1 | no | — |
| 107 | #575 | #595 | 1 | 1 | yes | characteristic, complemented |
| 108 | #410 | — | 34 | 1 | no | — |
| 109 | #408 | — | 17 | 1 | no | — |
| 110 | #408 | — | 34 | 1 | no | — |
| 111 | C22⋊C16 | — | 34 | 1 | no | — |
| 112 | #338 | — | 17 | 1 | no | — |
| 113 | C2×C17 | — | 2 | 1 | no | — |
| 114 | C2×C17 | — | 4 | 1 | no | — |
| 115 | C2×C17 | — | 16 | 1 | no | — |
| 116 | C2×C17 | #1343 | 1 | 1 | yes | characteristic |
| 117 | D17 | — | 8 | 1 | no | — |
| 118 | C2×#41 | — | 2 | 1 | no | — |
| 119 | C2×#41 | — | 17 | 1 | no | — |
| 120 | #137 | — | 4 | 1 | no | — |
| 121 | #137 | — | 68 | 1 | no | — |
| 122 | #137 | — | 68 | 1 | no | — |
| 123 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 124 | AGL(1,ℤ/8) | — | 68 | 1 | no | — |
| 125 | AGL(1,ℤ/8) | — | 68 | 1 | no | — |
| 126 | #135 | — | 4 | 1 | no | — |
| 127 | #135 | — | 68 | 2 | no | — |
| 128 | C2×M16 | — | 34 | 1 | no | — |
| 129 | C2×M16 | C2×#595 | 1 | 1 | yes | characteristic |
| 130 | C22×C8 | — | 17 | 1 | no | — |
| 131 | #117 | — | 68 | 1 | no | — |
| 132 | C2×C16 | — | 68 | 1 | no | — |
| 133 | #99 | — | 34 | 2 | no | — |
| 134 | #99 | — | 68 | 1 | no | — |
| 135 | C22⋊C8 | — | 68 | 1 | no | — |
| 136 | C22⋊C8 | — | 68 | 2 | no | — |
| 137 | C17 | #7406 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 138 | #41 | — | 4 | 1 | no | — |
| 139 | #41 | — | 4 | 1 | no | — |
| 140 | #41 | — | 4 | 1 | no | — |
| 141 | #41 | — | 4 | 1 | no | — |
| 142 | #41 | — | 68 | 1 | no | — |
| 143 | #41 | — | 68 | 1 | no | — |
| 144 | C2×Q8 | — | 2 | 1 | no | — |
| 145 | C2×Q8 | — | 17 | 1 | no | — |
| 146 | C2×D4 | — | 2 | 1 | no | — |
| 147 | C2×D4 | — | 4 | 1 | no | — |
| 148 | C2×D4 | — | 17 | 1 | no | — |
| 149 | C2×D4 | — | 34 | 1 | no | — |
| 150 | C22×C4 | — | 4 | 1 | no | — |
| 151 | C22×C4 | — | 34 | 1 | no | — |
| 152 | C22×C4 | C22⋊#595 | 1 | 1 | yes | characteristic |
| 153 | Q16 | — | 4 | 1 | no | — |
| 154 | Q16 | — | 68 | 2 | no | — |
| 155 | SD16 | — | 4 | 2 | no | — |
| 156 | SD16 | — | 68 | 2 | no | — |
| 157 | SD16 | — | 68 | 2 | no | — |
| 158 | D8 | — | 4 | 1 | no | — |
| 159 | D8 | — | 68 | 2 | no | — |
| 160 | M16 | — | 4 | 1 | no | — |
| 161 | M16 | — | 68 | 1 | no | — |
| 162 | M16 | — | 68 | 1 | no | — |
| 163 | C2×C8 | — | 2 | 1 | no | — |
| 164 | C2×C8 | — | 34 | 2 | no | — |
| 165 | C2×C8 | — | 34 | 1 | no | — |
| 166 | C2×C8 | — | 68 | 1 | no | — |
| 167 | C4⋊C4 | — | 136 | 1 | no | — |
| 168 | C22⋊C4 | — | 68 | 2 | no | — |
| 169 | C42 | — | 136 | 1 | no | — |
| 170 | C16 | — | 136 | 1 | no | — |
| 171 | C23 | — | 4 | 1 | no | — |
| 172 | C23 | — | 34 | 1 | no | — |
| 173 | C23 | #10587548 | 1 | 1 | yes | characteristic |
| 174 | Q8 | — | 4 | 1 | no | — |
| 175 | Q8 | — | 4 | 1 | no | — |
| 176 | Q8 | — | 68 | 1 | no | — |
| 177 | D4 | — | 4 | 1 | no | — |
| 178 | D4 | — | 4 | 1 | no | — |
| 179 | D4 | — | 8 | 1 | no | — |
| 180 | D4 | — | 8 | 1 | no | — |
| 181 | D4 | — | 68 | 1 | no | — |
| 182 | D4 | — | 136 | 1 | no | — |
| 183 | C2×C4 | — | 2 | 1 | no | — |
| 184 | C2×C4 | — | 2 | 1 | no | — |
| 185 | C2×C4 | — | 4 | 1 | no | — |
| 186 | C2×C4 | — | 8 | 1 | no | — |
| 187 | C2×C4 | — | 8 | 1 | no | — |
| 188 | C2×C4 | — | 34 | 1 | no | — |
| 189 | C2×C4 | — | 68 | 1 | no | — |
| 190 | C2×C4 | — | 68 | 1 | no | — |
| 191 | C2×C4 | — | 136 | 2 | no | — |
| 192 | C2×C4 | #10587547 | 1 | 1 | yes | characteristic |
| 193 | C2×C4 | #10587551 | 1 | 1 | yes | characteristic |
| 194 | C8 | — | 4 | 1 | no | — |
| 195 | C8 | — | 68 | 2 | no | — |
| 196 | C8 | — | 68 | 1 | no | — |
| 197 | C22 | — | 2 | 1 | no | — |
| 198 | C22 | — | 4 | 1 | no | — |
| 199 | C22 | — | 8 | 2 | no | — |
| 200 | C22 | — | 8 | 1 | no | — |
| 201 | C22 | — | 68 | 1 | no | — |
| 202 | C22 | — | 136 | 1 | no | — |
| 203 | C22 | #11763660 | 1 | 1 | yes | characteristic |
| 204 | C4 | — | 2 | 1 | no | — |
| 205 | C4 | — | 8 | 1 | no | — |
| 206 | C4 | — | 272 | 2 | no | — |
| 207 | C4 | — | 68 | 1 | no | — |
| 208 | C4 | #11763709 | 1 | 1 | yes | characteristic |
| 209 | C4 | #11763713 | 1 | 1 | yes | characteristic |
| 210 | C2 | — | 2 | 1 | no | — |
| 211 | C2 | — | 4 | 1 | no | — |
| 212 | C2 | — | 16 | 1 | no | — |
| 213 | C2 | — | 136 | 1 | no | — |
| 214 | C2 | #14543762 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14543873 | C2 | semidirect |
| 2. #14543707 | C2 | semidirect |
| 9. #11762567 | C4 | semidirect |
| 10. C17×#575 | C4 | semidirect |
| 107. #575 | #595 | semidirect |
| 137. C17 | #7406 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14543873 | 2 |
| #14543707 | 2 |
| #14529887 | 2 |
| #7406 | 17 |