Finite Group Databasebeta

← C₂²×C₇⋊D₇ #87663

Subgroups — C₂²×C₇⋊D₇ #87663

Order 392.

160 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, complemented
2	C₂×C₇⋊D₇	C₂	1	6	yes	maximal, direct product factor
3	C₂×C₇²	C₂²	1	3	yes	complemented
4	C₇⋊D₇	C₂²	1	4	yes	direct product factor
5	C₂²×D₇	—	7	8	no	maximal
6	C₇²	C₂³	1	1	yes	characteristic, complemented, Sylow
7	C₂²×C₇	D₇	1	8	yes	complemented
8	C₂×D₇	—	7	48	no	—
9	C₂×C₇	C₂×D₇	1	24	yes	complemented
10	D₇	—	7	32	no	—
11	C₂³	—	49	1	no	Sylow
12	C₇	C₂²×D₇	1	8	yes	complemented
13	C₂²	—	49	6	no	—
14	C₂²	C₇⋊D₇	1	1	yes	characteristic, direct product factor
15	C₂	—	49	4	no	—
16	C₂	C₂×C₇⋊D₇	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂³
Frattini	C₁	G
Fitting, socle	C₂²×C₇²	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇²	C₂	semidirect
2. C₂×C₇⋊D₇	C₂	direct (N × H)
3. C₂×C₇²	C₂²	semidirect
4. C₇⋊D₇	C₂²	direct (N × H)
6. C₇²	C₂³	semidirect
7. C₂²×C₇	D₇	semidirect
9. C₂×C₇	C₂×D₇	semidirect
12. C₇	C₂²×D₇	semidirect
14. C₂²	C₇⋊D₇	direct (N × H)
16. C₂	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
C₂²×C₇²	2
C₂×C₇⋊D₇	2
C₂²×D₇	7