Subgroups — D₇² #5998

Order 196.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₇	C₂	1	2	yes	maximal, complemented
3	C₇²	C₂²	1	1	yes	characteristic, complemented, Sylow
4	C₂×D₇	—	7	2	no	maximal
5	C₂×C₇	—	7	2	no	—
6	D₇	—	7	2	no	—
7	D₇	—	14	3	no	—
8	D₇	D₇	1	2	yes	direct product factor
9	C₇	—	2	3	no	—
10	C₇	C₂×D₇	1	2	yes	complemented
11	C₂²	—	49	1	no	Sylow
12	C₂	—	7	2	no	—
13	C₂	—	49	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²	C₂²
LCS	G ▷ C₇²
UCS	C₁

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.