Subgroups — C₂×D₄₉ #5992

Order 196.

15 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄₉	C₂	1	2	yes	maximal, direct product factor
3	C₄₉	C₂²	1	1	yes	characteristic, complemented, Sylow
4	C₂×D₇	—	7	1	no	maximal
5	C₂×C₇	D₇	1	1	yes	characteristic
6	D₇	—	7	2	no	—
7	C₇	C₂×D₇	1	1	yes	characteristic
8	C₂²	—	49	1	no	Sylow
9	C₂	—	49	2	no	—
10	C₂	D₄₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₄₉
commutator, cosocle, hypocenter	C₄₉	C₂²
Frattini	C₇	C₂×D₇
Fitting	C₂×C₄₉	C₂
socle	C₂×C₇	D₇
LCS	G ▷ C₄₉
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.