Finite Group Databasebeta

← C₂×C₈₁×C₈₉ #72192592

Subgroups — C₂×C₈₁×C₈₉ #72192592

Order 14418.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₇×C₈₉	C₃	1	1	yes	maximal, characteristic
2	C₈₁×C₈₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₇×C₈₉	C₂×C₃	1	1	yes	characteristic
4	C₂×C₉×C₈₉	C₉	1	1	yes	characteristic
5	C₉×C₈₉	C₂×C₉	1	1	yes	characteristic
6	C₂×C₃×C₈₉	C₂₇	1	1	yes	characteristic
7	C₃×C₈₉	C₂×C₂₇	1	1	yes	characteristic
8	C₂×C₈₉	C₈₁	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₈₁	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₈₉	C₂×C₈₁	1	1	yes	characteristic, direct product factor, Sylow
11	C₈₁	C₂×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₂₇	C₃×C₈₉	1	1	yes	characteristic
13	C₂₇	C₂×C₃×C₈₉	1	1	yes	characteristic
14	C₂×C₉	C₉×C₈₉	1	1	yes	characteristic
15	C₉	C₂×C₉×C₈₉	1	1	yes	characteristic
16	C₂×C₃	C₂₇×C₈₉	1	1	yes	characteristic
17	C₃	C₂×C₂₇×C₈₉	1	1	yes	characteristic
18	C₂	C₈₁×C₈₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₇	C₂×C₃×C₈₉
socle, prime radical	C₂×C₃×C₈₉	C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₈₁×C₈₉	C₂	direct (N × H)
8. C₂×C₈₉	C₈₁	direct (N × H)
9. C₂×C₈₁	C₈₉	direct (N × H)
10. C₈₉	C₂×C₈₁	direct (N × H)
11. C₈₁	C₂×C₈₉	direct (N × H)
18. C₂	C₈₁×C₈₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₂₇×C₈₉	3
C₈₁×C₈₉	2
C₂×C₈₁	89