Subgroups — C₂×D₇² #87661

Order 392.

79 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, complemented
2	C₂×C₇×D₇	C₂	1	2	yes	maximal, complemented
3	D₇²	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₇²	C₂²	1	1	yes	characteristic, complemented
5	C₇⋊D₇	C₂²	1	2	yes	complemented
6	C₇×D₇	C₂²	1	4	yes	complemented
7	C₂²×D₇	—	7	2	no	maximal
8	C₇²	C₂³	1	1	yes	characteristic, complemented, Sylow
9	C₂²×C₇	—	7	2	no	—
10	C₂×D₇	—	7	2	no	—
11	C₂×D₇	—	7	8	no	—
12	C₂×D₇	—	14	3	no	—
13	C₂×D₇	D₇	1	2	yes	direct product factor
14	C₂×C₇	—	2	3	no	—
15	C₂×C₇	—	7	4	no	—
16	C₂×C₇	C₂×D₇	1	2	yes	complemented
17	D₇	—	7	4	no	—
18	D₇	—	14	6	no	—
19	D₇	C₂×D₇	1	4	yes	direct product factor
20	C₂³	—	49	1	no	Sylow
21	C₇	—	2	3	no	—
22	C₇	C₂²×D₇	1	2	yes	complemented
23	C₂²	—	7	2	no	—
24	C₂²	—	49	4	no	—
25	C₂²	—	49	1	no	—
26	C₂	—	7	4	no	—
27	C₂	—	49	2	no	—
28	C₂	D₇²	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₇²
commutator, cosocle, hypocenter	C₇²	C₂³
Frattini	C₁	G
Fitting, socle	C₂×C₇²	C₂²
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.