Subgroups — C₃×C₇×D₄ #4270

Order 168.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₇	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₄	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₇	—	2	2	no	—
5	C₂×C₃×C₇	C₂²	1	1	yes	characteristic
6	C₂²×C₇	C₂×C₃	1	2	yes	complemented
7	C₄×C₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×D₄	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₇	D₄	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₇	—	2	2	no	—
11	C₂×C₇	C₂²×C₃	1	1	yes	characteristic
12	C₂²×C₃	C₂×C₇	1	2	yes	complemented
13	C₃×C₄	C₂×C₇	1	1	yes	characteristic, complemented
14	D₄	C₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
15	C₇	C₃×D₄	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃	—	2	2	no	—
17	C₂×C₃	C₂²×C₇	1	1	yes	characteristic
18	C₂²	C₂×C₃×C₇	1	2	yes	complemented
19	C₄	C₂×C₃×C₇	1	1	yes	characteristic, complemented
20	C₃	C₇×D₄	1	1	yes	characteristic, direct product factor, Sylow
21	C₂	—	2	2	no	—
22	C₂	C₂²×C₃×C₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃×C₇	C₂²
commutator, Frattini, cosocle	C₂	C₂²×C₃×C₇
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₇ ◁ G

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.