Subgroups — #87640

Order 392.

41 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₇	C₂	1	2	yes	maximal, complemented
2	C₇⋊Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇²	C₂²	1	1	yes	characteristic
4	C₇×D₇	—	2	2	no	—
5	C₂²⋊D₇	—	7	2	no	maximal
6	C₇²	D₄	1	1	yes	characteristic, complemented, Sylow
7	C₂²×C₇	—	7	2	no	—
8	C₂×D₇	D₇	1	2	yes	complemented
9	Dic₇	—	7	2	no	—
10	Dic₇	—	14	3	no	—
11	C₂×C₇	—	2	3	no	—
12	C₂×C₇	—	14	2	no	—
13	C₂×C₇	C₂×D₇	1	2	yes	—
14	D₇	—	2	2	no	—
15	D₄	—	49	1	no	Sylow
16	C₇	—	2	3	no	—
17	C₇	C₂²⋊D₇	1	2	yes	complemented
18	C₂²	—	7	2	no	—
19	C₄	—	49	1	no	—
20	C₂	—	14	2	no	—
21	C₂	D₇²	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇²
commutator, Fitting, socle, cosocle	C₂×C₇²	C₂²
hypocenter	C₇²	D₄
LCS	G ▷ C₂×C₇² ▷ 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.