Subgroups — #87639

Order 392.

47 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇²
commutator, hypocenter	C₇²	C₂×C₄
Fitting, socle, cosocle	C₂×C₇²	C₂²
prime radical	C₂×C₇⋊D₇	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.