Subgroups — C₇×D₇ #1028

Order 98.

11 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₂×C₇	—	7	1	no	maximal
3	D₇	C₇	1	1	yes	maximal, characteristic, direct product factor
4	C₇	—	2	3	no	—
5	C₇	D₇	1	1	yes	characteristic, direct product factor
6	C₇	C₂×C₇	1	1	yes	characteristic, complemented
7	C₂	—	7	1	no	Sylow

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

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.