Finite Group Databasebeta

← C₂×C₇×D₇ #5999

Subgroups — C₂×C₇×D₇ #5999

Order 196.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₇	C₂	1	2	yes	maximal, direct product factor
3	C₇²	C₂²	1	1	yes	characteristic, complemented, Sylow
4	C₂²×C₇	—	7	1	no	maximal
5	C₂×D₇	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₇	—	2	3	no	—
7	C₂×C₇	—	7	2	no	—
8	C₂×C₇	D₇	1	1	yes	characteristic, direct product factor
9	C₂×C₇	C₂×C₇	1	1	yes	characteristic, complemented
10	D₇	C₂×C₇	1	2	yes	direct product factor
11	C₇	—	2	3	no	—
12	C₇	C₂×D₇	1	1	yes	characteristic, direct product factor
13	C₇	C₂²×C₇	1	1	yes	characteristic, complemented
14	C₂²	—	7	1	no	Sylow
15	C₂	—	7	2	no	—
16	C₂	C₇×D₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	D₇
commutator, cosocle, hypocenter	C₇	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₇²	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₂×C₇²	C₂	semidirect
2. C₇×D₇	C₂	direct (N × H)
3. C₇²	C₂²	semidirect
5. C₂×D₇	C₇	direct (N × H)
8. C₂×C₇	D₇	direct (N × H)
9. C₂×C₇	C₂×C₇	semidirect
10. D₇	C₂×C₇	direct (N × H)
12. C₇	C₂×D₇	direct (N × H)
13. C₇	C₂²×C₇	semidirect
16. C₂	C₇×D₇	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×C₇²	2
C₇×D₇	2
C₂²×C₇	7
C₂×D₇	7