Finite Group Databasebeta

← C₂×C₄×C₇² #87653

Subgroups — C₂×C₄×C₇² #87653

Order 392.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇²	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇²	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇²	C₄	1	2	yes	direct product factor
4	C₂×C₇²	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₇	C₇	1	8	yes	maximal, direct product factor
6	C₇²	C₂×C₄	1	1	yes	characteristic, direct product factor, Sylow
7	C₂²×C₇	C₂×C₇	1	8	yes	—
8	C₄×C₇	C₂×C₇	1	16	yes	direct product factor
9	C₂×C₇	C₄×C₇	1	16	yes	direct product factor
10	C₂×C₇	C₂²×C₇	1	8	yes	—
11	C₂×C₄	C₇²	1	1	yes	characteristic, direct product factor, Sylow
12	C₇	C₂×C₄×C₇	1	8	yes	direct product factor
13	C₂²	C₂×C₇²	1	1	yes	characteristic
14	C₄	C₂×C₇²	1	2	yes	direct product factor
15	C₂	C₄×C₇²	1	2	yes	direct product factor
16	C₂	C₂²×C₇²	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₇²
socle, prime radical	C₂²×C₇²	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₇²	C₂	direct (N × H)
3. C₂×C₇²	C₄	direct (N × H)
5. C₂×C₄×C₇	C₇	direct (N × H)
6. C₇²	C₂×C₄	direct (N × H)
8. C₄×C₇	C₂×C₇	direct (N × H)
9. C₂×C₇	C₄×C₇	direct (N × H)
11. C₂×C₄	C₇²	direct (N × H)
12. C₇	C₂×C₄×C₇	direct (N × H)
14. C₄	C₂×C₇²	direct (N × H)
15. C₂	C₄×C₇²	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₇²	2
C₄×C₇²	2
C₂×C₄×C₇	7