Subgroups — C₂×C₇⋊D₇ #6000

Order 196.

50 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	C₂×D₇	—	7	8	no	maximal
5	C₂×C₇	D₇	1	8	yes	complemented
6	D₇	—	7	16	no	—
7	C₇	C₂×D₇	1	8	yes	complemented
8	C₂²	—	49	1	no	Sylow
9	C₂	—	49	2	no	—
10	C₂	C₇⋊D₇	1	1	yes	characteristic, direct product factor

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

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

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