Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
268 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 43 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 | #14545789 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #14544917 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11763922 | — | 2 | 2 | no | — |
| 4 | #11763813 | C4 | 1 | 1 | yes | characteristic |
| 5 | C2×#10587550 | — | 2 | 2 | no | — |
| 6 | C42×#595 | C22 | 1 | 1 | yes | characteristic |
| 7 | #11763360 | C4 | 1 | 1 | yes | characteristic |
| 8 | C2×#63256 | — | 2 | 1 | no | — |
| 9 | C2×C4×#595 | — | 4 | 1 | no | — |
| 10 | C2×C4×#595 | D4 | 1 | 2 | yes | — |
| 11 | C2×#63243 | — | 2 | 1 | no | — |
| 12 | C22⋊#3633 | — | 4 | 2 | no | — |
| 13 | C4⋊#3633 | — | 2 | 4 | no | — |
| 14 | C4×#3633 | — | 4 | 2 | no | — |
| 15 | C17×C4⋊Q8 | C8 | 1 | 1 | yes | characteristic, complemented |
| 16 | #10587633 | — | 2 | 1 | no | — |
| 17 | #10587581 | — | 4 | 1 | no | — |
| 18 | #10587579 | — | 4 | 1 | no | — |
| 19 | #10587560 | C8 | 1 | 1 | yes | characteristic, complemented |
| 20 | C42×D17 | C2×C4 | 1 | 1 | yes | characteristic |
| 21 | #10587550 | — | 4 | 2 | no | — |
| 22 | #10587550 | — | 4 | 2 | no | — |
| 23 | C4⋊#3624 | — | 4 | 1 | no | — |
| 24 | C22×#595 | — | 2 | 2 | no | — |
| 25 | C2×#3633 | — | 4 | 4 | no | — |
| 26 | C2×Q8×C17 | — | 2 | 1 | no | — |
| 27 | #63256 | — | 4 | 2 | no | — |
| 28 | #63256 | — | 4 | 2 | no | — |
| 29 | C2×D68 | — | 2 | 1 | no | — |
| 30 | C2×D68 | — | 4 | 1 | no | — |
| 31 | C2×D68 | — | 4 | 1 | no | — |
| 32 | C2×C4×D17 | — | 2 | 1 | no | — |
| 33 | C2×C4×D17 | — | 4 | 1 | no | — |
| 34 | C2×C4×D17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 35 | C2×#3624 | — | 4 | 1 | no | — |
| 36 | C4×#595 | — | 2 | 2 | no | — |
| 37 | C4×#595 | — | 4 | 4 | no | — |
| 38 | C4×#595 | D8 | 1 | 2 | yes | — |
| 39 | C4×#595 | SD16 | 1 | 2 | yes | — |
| 40 | #63243 | — | 4 | 2 | no | — |
| 41 | C4⋊C4×C17 | — | 4 | 1 | no | — |
| 42 | C42×C17 | C2×C8 | 1 | 1 | yes | characteristic |
| 43 | #63227 | — | 4 | 2 | no | — |
| 44 | C4×Dic17 | — | 2 | 1 | no | — |
| 45 | C4×Dic17 | M16 | 1 | 1 | yes | characteristic |
| 46 | #7106 | — | 17 | 1 | no | maximal, Sylow |
| 47 | C22×D17 | — | 4 | 1 | no | — |
| 48 | C22×D17 | #99 | 1 | 1 | yes | characteristic |
| 49 | C2×#595 | — | 2 | 2 | no | — |
| 50 | C2×#595 | — | 2 | 2 | no | — |
| 51 | C2×#595 | — | 4 | 4 | no | — |
| 52 | #3633 | — | 8 | 4 | no | — |
| 53 | Q8×C17 | — | 4 | 2 | no | — |
| 54 | C2×C4×C17 | — | 2 | 1 | no | — |
| 55 | C2×C4×C17 | — | 4 | 1 | no | — |
| 56 | C2×C4×C17 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 57 | C2×Dic17 | — | 2 | 1 | no | — |
| 58 | C2×Dic17 | #100 | 1 | 1 | yes | characteristic |
| 59 | D68 | — | 4 | 2 | no | — |
| 60 | D68 | — | 8 | 2 | no | — |
| 61 | D68 | — | 8 | 2 | no | — |
| 62 | C4×D17 | — | 4 | 2 | no | — |
| 63 | C4×D17 | — | 8 | 1 | no | — |
| 64 | C4×D17 | — | 8 | 1 | no | — |
| 65 | C4×D17 | #102 | 1 | 2 | yes | — |
| 66 | C4×D17 | #104 | 1 | 2 | yes | — |
| 67 | #3624 | — | 8 | 1 | no | — |
| 68 | #1962 | — | 17 | 1 | no | — |
| 69 | #1276 | — | 17 | 2 | no | — |
| 70 | C22×C17 | #323 | 1 | 1 | yes | characteristic |
| 71 | C2×D17 | — | 4 | 1 | no | — |
| 72 | C2×D17 | — | 8 | 2 | no | — |
| 73 | C2×D17 | — | 8 | 1 | no | — |
| 74 | C2×D17 | #327 | 1 | 2 | yes | — |
| 75 | #595 | — | 2 | 4 | no | — |
| 76 | #595 | — | 4 | 2 | no | — |
| 77 | C4×C17 | — | 2 | 2 | no | — |
| 78 | C4×C17 | — | 8 | 1 | no | — |
| 79 | C4×C17 | D4⋊C8 | 1 | 2 | yes | — |
| 80 | Dic17 | — | 4 | 1 | no | — |
| 81 | Dic17 | #329 | 1 | 1 | yes | characteristic |
| 82 | Dic17 | #331 | 1 | 1 | yes | characteristic |
| 83 | #532 | — | 17 | 1 | no | — |
| 84 | #431 | — | 34 | 2 | no | — |
| 85 | #423 | — | 17 | 1 | no | — |
| 86 | C2×#104 | — | 34 | 2 | no | — |
| 87 | C43 | — | 17 | 1 | no | — |
| 88 | C2×C17 | — | 2 | 1 | no | — |
| 89 | C2×C17 | #1270 | 1 | 1 | yes | characteristic |
| 90 | D17 | — | 2 | 2 | no | — |
| 91 | D17 | — | 16 | 1 | no | — |
| 92 | C2×#41 | — | 34 | 1 | no | — |
| 93 | C2×M16 | — | 34 | 1 | no | — |
| 94 | C4⋊Q8 | #3633 | 1 | 1 | yes | characteristic, complemented |
| 95 | #127 | — | 17 | 1 | no | — |
| 96 | #124 | — | 34 | 1 | no | — |
| 97 | #121 | — | 68 | 1 | no | — |
| 98 | C4×D4 | — | 68 | 1 | no | — |
| 99 | C2×C42 | — | 17 | 2 | no | — |
| 100 | C2×C42 | — | 17 | 1 | no | — |
| 101 | C2×C42 | — | 68 | 1 | no | — |
| 102 | C4⋊C8 | — | 34 | 4 | no | — |
| 103 | C4⋊C8 | — | 68 | 1 | no | — |
| 104 | #104 | — | 68 | 2 | no | — |
| 105 | #104 | — | 68 | 2 | no | — |
| 106 | C22⋊C8 | — | 68 | 2 | no | — |
| 107 | C4×C8 | — | 68 | 2 | no | — |
| 108 | C17 | #7106 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 109 | #41 | — | 68 | 2 | no | — |
| 110 | #41 | — | 68 | 2 | no | — |
| 111 | C2×Q8 | — | 2 | 1 | no | — |
| 112 | C2×D4 | — | 34 | 1 | no | — |
| 113 | C2×D4 | — | 68 | 1 | no | — |
| 114 | C2×D4 | — | 68 | 1 | no | — |
| 115 | C22×C4 | — | 17 | 1 | no | — |
| 116 | C22×C4 | — | 34 | 1 | no | — |
| 117 | C22×C4 | — | 34 | 2 | no | — |
| 118 | C22×C4 | — | 68 | 1 | no | — |
| 119 | M16 | — | 68 | 2 | no | — |
| 120 | C2×C8 | — | 68 | 1 | no | — |
| 121 | C2×C8 | — | 68 | 4 | no | — |
| 122 | C4⋊C4 | — | 4 | 1 | no | — |
| 123 | C22⋊C4 | — | 68 | 2 | no | — |
| 124 | C42 | — | 17 | 2 | no | — |
| 125 | C42 | — | 17 | 2 | no | — |
| 126 | C42 | — | 17 | 1 | no | — |
| 127 | C42 | — | 34 | 1 | no | — |
| 128 | C42 | — | 34 | 2 | no | — |
| 129 | C42 | — | 68 | 4 | no | — |
| 130 | C42 | C2×#3633 | 1 | 1 | yes | characteristic |
| 131 | C23 | — | 17 | 1 | no | — |
| 132 | C23 | — | 68 | 1 | no | — |
| 133 | Q8 | — | 4 | 2 | no | — |
| 134 | D4 | — | 68 | 2 | no | — |
| 135 | D4 | — | 136 | 2 | no | — |
| 136 | D4 | — | 136 | 2 | no | — |
| 137 | C2×C4 | — | 2 | 1 | no | — |
| 138 | C2×C4 | — | 4 | 1 | no | — |
| 139 | C2×C4 | — | 17 | 1 | no | — |
| 140 | C2×C4 | — | 17 | 2 | no | — |
| 141 | C2×C4 | — | 17 | 2 | no | — |
| 142 | C2×C4 | — | 34 | 2 | no | — |
| 143 | C2×C4 | — | 34 | 2 | no | — |
| 144 | C2×C4 | — | 34 | 1 | no | — |
| 145 | C2×C4 | — | 68 | 2 | no | — |
| 146 | C2×C4 | — | 68 | 4 | no | — |
| 147 | C2×C4 | — | 136 | 1 | no | — |
| 148 | C2×C4 | — | 136 | 1 | no | — |
| 149 | C2×C4 | C22⋊#3633 | 1 | 1 | yes | characteristic |
| 150 | C8 | — | 136 | 1 | no | — |
| 151 | C8 | — | 136 | 4 | no | — |
| 152 | C22 | — | 17 | 2 | no | — |
| 153 | C22 | — | 68 | 1 | no | — |
| 154 | C22 | — | 136 | 2 | no | — |
| 155 | C22 | — | 136 | 1 | no | — |
| 156 | C22 | #11763894 | 1 | 1 | yes | characteristic |
| 157 | C4 | — | 2 | 2 | no | — |
| 158 | C4 | — | 8 | 1 | no | — |
| 159 | C4 | — | 17 | 1 | no | — |
| 160 | C4 | — | 17 | 1 | no | — |
| 161 | C4 | — | 34 | 4 | no | — |
| 162 | C4 | — | 68 | 1 | no | — |
| 163 | C4 | — | 68 | 2 | no | — |
| 164 | C4 | D4⋊#3633 | 1 | 2 | yes | — |
| 165 | C2 | — | 2 | 1 | no | — |
| 166 | C2 | — | 272 | 1 | no | — |
| 167 | C2 | — | 34 | 2 | no | — |
| 168 | C2 | #14545783 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14545789 | C2 | semidirect |
| 15. C17×C4⋊Q8 | C8 | semidirect |
| 19. #10587560 | C8 | semidirect |
| 94. C4⋊Q8 | #3633 | semidirect |
| 108. C17 | #7106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545789 | 2 |
| #14544917 | 2 |
| #7106 | 17 |