Finite Group Databasebeta

← C₂×C₈×C₂₂₂₁ #48001072

Subgroups — C₂×C₈×C₂₂₂₁ #48001072

Order 35536.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₂₂₂₁	C₂	1	1	yes	maximal, characteristic
2	C₈×C₂₂₂₁	C₂	1	2	yes	maximal, direct product factor
3	C₂²×C₂₂₂₁	C₄	1	1	yes	characteristic
4	C₄×C₂₂₂₁	C₄	1	1	yes	characteristic
5	C₄×C₂₂₂₁	C₂²	1	1	yes	characteristic
6	C₂×C₂₂₂₁	C₈	1	2	yes	direct product factor
7	C₂×C₂₂₂₁	C₂×C₄	1	1	yes	characteristic
8	C₂₂₂₁	C₂×C₈	1	1	yes	characteristic, direct product factor, Sylow
9	C₂×C₈	C₂₂₂₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂×C₄	C₂×C₂₂₂₁	1	1	yes	characteristic
11	C₈	C₂×C₂₂₂₁	1	2	yes	direct product factor
12	C₂²	C₄×C₂₂₂₁	1	1	yes	characteristic
13	C₄	C₄×C₂₂₂₁	1	1	yes	characteristic
14	C₄	C₂²×C₂₂₂₁	1	1	yes	characteristic
15	C₂	C₈×C₂₂₂₁	1	2	yes	direct product factor
16	C₂	C₂×C₄×C₂₂₂₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₂₂₂₁
socle, prime radical	C₂²×C₂₂₂₁	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈×C₂₂₂₁	C₂	direct (N × H)
6. C₂×C₂₂₂₁	C₈	direct (N × H)
8. C₂₂₂₁	C₂×C₈	direct (N × H)
9. C₂×C₈	C₂₂₂₁	direct (N × H)
11. C₈	C₂×C₂₂₂₁	direct (N × H)
15. C₂	C₈×C₂₂₂₁	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×C₄×C₂₂₂₁	2
C₈×C₂₂₂₁	2
C₂×C₈	2221