← C2×#72227572 #72267945
Subgroups — C2×#72227572 #72267945
Order 3072.
At least 8601 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
The subgroup lattice has 105 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C22×#85563 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C23×#5948 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #72227572 | C2 | 1 | 4 | yes | maximal, direct product factor |
| 4 | C2×#85563 | C22 | 1 | 4 | yes | complemented |
| 5 | C22×#5948 | C4 | 1 | 1 | yes | characteristic, complemented |
| 6 | C22×#5948 | C4 | 1 | 2 | yes | complemented |
| 7 | C22×#5948 | C22 | 1 | 1 | yes | characteristic |
| 8 | C22×#5948 | C22 | 1 | 2 | yes | — |
| 9 | C23×C22⋊SL(2,𝔽3) | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | C25×#41 | D3 | 1 | 1 | yes | characteristic |
| 11 | C2×#5948 | C2×C4 | 1 | 1 | yes | characteristic |
| 12 | C2×#5948 | C2×C4 | 1 | 2 | yes | complemented |
| 13 | C2×#5948 | D4 | 1 | 4 | yes | — |
| 14 | C2×#5948 | C23 | 1 | 1 | yes | characteristic |
| 15 | C22×C22⋊SL(2,𝔽3) | C2×C4 | 1 | 1 | yes | characteristic |
| 16 | C22×C22⋊SL(2,𝔽3) | C2×C4 | 1 | 2 | yes | complemented |
| 17 | C24×#41 | Dic3 | 1 | 1 | yes | characteristic |
| 18 | C24×#41 | Dic3 | 1 | 2 | yes | — |
| 19 | C24×#41 | C2×D3 | 1 | 2 | yes | — |
| 20 | C24×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 21 | C25×Q8 | Dic3 | 1 | 1 | yes | characteristic |
| 22 | #5948 | C22⋊C4 | 1 | 2 | yes | complemented |
| 23 | #5948 | C2×D4 | 1 | 2 | yes | — |
| 24 | C2×C22⋊SL(2,𝔽3) | C22⋊C4 | 1 | 2 | yes | complemented |
| 25 | C2×C22⋊SL(2,𝔽3) | C22×C4 | 1 | 1 | yes | characteristic |
| 26 | C23×#41 | C2×Dic3 | 1 | 2 | yes | — |
| 27 | C23×#41 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 28 | C23×#41 | #67 | 1 | 4 | yes | — |
| 29 | C23×#41 | S4 | 1 | 2 | yes | — |
| 30 | C23×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 31 | C24×Q8 | C2×Dic3 | 1 | 2 | yes | — |
| 32 | C24×Q8 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 33 | C25×C4 | S4 | 1 | 1 | yes | characteristic |
| 34 | C22⋊SL(2,𝔽3) | C2×C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 35 | C26 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 36 | C22×#41 | #217 | 1 | 2 | yes | — |
| 37 | C22×#41 | SL(2,ℤ/4) | 1 | 2 | yes | — |
| 38 | C22×#41 | SL(2,ℤ/4) | 1 | 4 | yes | — |
| 39 | C22×#41 | C2×#67 | 1 | 2 | yes | — |
| 40 | C22×#41 | C2×S4 | 1 | 4 | yes | — |
| 41 | C22×#41 | C2×S4 | 1 | 2 | yes | — |
| 42 | C23×Q8 | #217 | 1 | 2 | yes | — |
| 43 | C23×Q8 | SL(2,ℤ/4) | 1 | 2 | yes | — |
| 44 | C23×Q8 | C22×Dic3 | 1 | 1 | yes | characteristic |
| 45 | C24×C4 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 46 | C24×C4 | SL(2,ℤ/4) | 1 | 2 | yes | — |
| 47 | C24×C4 | C2×S4 | 1 | 2 | yes | — |
| 48 | C24×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 49 | C25 | GU(2,𝔽3) | 1 | 4 | yes | complemented |
| 50 | C25 | C2×SL(2,ℤ/4) | 1 | 2 | yes | — |
| 51 | C25 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 52 | C2×#41 | C2×SL(2,ℤ/4) | 1 | 4 | yes | — |
| 53 | C2×#41 | C2×SL(2,ℤ/4) | 1 | 2 | yes | — |
| 54 | C2×#41 | GL(2,ℤ/4) | 1 | 8 | yes | — |
| 55 | C2×#41 | C22×S4 | 1 | 2 | yes | — |
| 56 | C22×Q8 | C2×#217 | 1 | 1 | yes | characteristic |
| 57 | C22×Q8 | C2×SL(2,ℤ/4) | 1 | 4 | yes | — |
| 58 | C22×Q8 | C2×SL(2,ℤ/4) | 1 | 2 | yes | — |
| 59 | C23×C4 | C2×SL(2,ℤ/4) | 1 | 2 | yes | — |
| 60 | C23×C4 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 61 | C23×C4 | GL(2,ℤ/4) | 1 | 4 | yes | — |
| 62 | C23×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 63 | C23×C4 | #1020 | 1 | 1 | yes | characteristic |
| 64 | C24 | C2×GU(2,𝔽3) | 1 | 2 | yes | — |
| 65 | C24 | C2×GU(2,𝔽3) | 1 | 4 | yes | complemented |
| 66 | C24 | #5423 | 1 | 2 | yes | — |
| 67 | C24 | #5432 | 1 | 2 | yes | — |
| 68 | C24 | C22×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 69 | C24 | #5936 | 1 | 1 | yes | characteristic |
| 70 | #41 | #5432 | 1 | 4 | yes | — |
| 71 | #41 | C2×GL(2,ℤ/4) | 1 | 4 | yes | — |
| 72 | C2×Q8 | #5432 | 1 | 4 | yes | — |
| 73 | C2×Q8 | C22×SL(2,ℤ/4) | 1 | 2 | yes | — |
| 74 | C22×C4 | #5432 | 1 | 2 | yes | — |
| 75 | C22×C4 | C2×GL(2,ℤ/4) | 1 | 2 | yes | — |
| 76 | C22×C4 | #5936 | 1 | 1 | yes | characteristic |
| 77 | C22×C4 | #5936 | 1 | 2 | yes | — |
| 78 | C22×C4 | C2×#1020 | 1 | 2 | yes | — |
| 79 | C22×C4 | C2×#1020 | 1 | 1 | yes | characteristic |
| 80 | C23 | #73149 | 1 | 4 | yes | complemented |
| 81 | C23 | C2×#5423 | 1 | 1 | yes | characteristic |
| 82 | C23 | C22×GU(2,𝔽3) | 1 | 1 | yes | characteristic |
| 83 | C23 | C2×#5432 | 1 | 1 | yes | characteristic |
| 84 | C23 | #85563 | 1 | 4 | yes | complemented |
| 85 | C23 | C2×#5936 | 1 | 2 | yes | — |
| 86 | C23 | C2×#5936 | 1 | 1 | yes | characteristic |
| 87 | Q8 | C2×#5432 | 1 | 2 | yes | — |
| 88 | C2×C4 | C2×#5936 | 1 | 2 | yes | — |
| 89 | C2×C4 | C2×#5936 | 1 | 1 | yes | characteristic |
| 90 | C2×C4 | #87524 | 1 | 4 | yes | — |
| 91 | C2×C4 | C22×#1020 | 1 | 1 | yes | characteristic |
| 92 | C22 | C2×#73149 | 1 | 1 | yes | characteristic, complemented |
| 93 | C22 | #11715569 | 1 | 2 | yes | — |
| 94 | C22 | C2×#85563 | 1 | 2 | yes | — |
| 95 | C22 | C2×#85563 | 1 | 4 | yes | complemented |
| 96 | C22 | #11715655 | 1 | 2 | yes | — |
| 97 | C22 | C22×#5936 | 1 | 1 | yes | characteristic |
| 98 | C4 | #11715569 | 1 | 2 | yes | — |
| 99 | C4 | C2×#87524 | 1 | 2 | yes | — |
| 100 | C2 | #72227572 | 1 | 4 | yes | direct product factor |
| 101 | C2 | C2×#11715569 | 1 | 1 | yes | characteristic |
| 102 | C2 | C22×#85563 | 1 | 1 | yes | characteristic |
| 103 | C2 | C2×#11715655 | 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