Subgroups — C₂×D₃×D₇ #4280

Order 168.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₇	C₂	1	4	yes	maximal, direct product factor
5	C₂²×D₇	—	3	1	no	maximal, Hall
6	C₂×C₃×C₇	C₂²	1	1	yes	characteristic, complemented
7	D₂₁	C₂²	1	2	yes	complemented
8	C₃×D₇	C₂²	1	2	yes	complemented
9	D₃×C₇	C₂²	1	2	yes	complemented
10	C₂²×C₇	—	3	1	no	—
11	C₂×D₇	—	3	1	no	—
12	C₂×D₇	—	3	4	no	—
13	C₂×D₇	D₃	1	1	yes	characteristic, direct product factor
14	C₂²×D₃	—	7	1	no	maximal, Hall
15	C₃×C₇	C₂³	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇	—	3	2	no	—
17	C₂×C₇	C₂×D₃	1	1	yes	characteristic, complemented
18	D₇	—	3	2	no	—
19	D₇	C₂×D₃	1	2	yes	direct product factor
20	C₂²×C₃	—	7	1	no	—
21	C₂×D₃	—	7	1	no	—
22	C₂×D₃	—	7	4	no	—
23	C₂×D₃	D₇	1	1	yes	characteristic, direct product factor
24	C₂³	—	21	1	no	Sylow
25	C₇	C₂²×D₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃	—	7	2	no	—
27	C₂×C₃	C₂×D₇	1	1	yes	characteristic, complemented
28	D₃	—	7	2	no	—
29	D₃	C₂×D₇	1	2	yes	direct product factor
30	C₂²	—	3	1	no	—
31	C₂²	—	7	1	no	—
32	C₂²	—	21	4	no	—
33	C₂²	—	21	1	no	—
34	C₃	C₂²×D₇	1	1	yes	characteristic, complemented, Sylow
35	C₂	—	3	2	no	—
36	C₂	—	7	2	no	—
37	C₂	—	21	2	no	—
38	C₂	D₃×D₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₃×D₇
commutator, cosocle, hypocenter	C₃×C₇	C₂³
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇	C₂²
LCS	G ▷ C₃×C₇
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.