Subgroups — C₂×C₃²×D₇ #7002

Order 252.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×D₇	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×D₇	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇	C₂×C₃	1	4	yes	complemented
6	C₃×D₇	C₂×C₃	1	8	yes	direct product factor
7	C₂²×C₃²	—	7	1	no	maximal, Hall
8	C₂×D₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₇	C₂²×C₃	1	4	yes	complemented
10	C₂×C₃²	—	7	2	no	—
11	C₂×C₃²	D₇	1	1	yes	characteristic, direct product factor
12	C₂×C₇	C₂×C₃²	1	1	yes	characteristic, complemented
13	D₇	C₂×C₃²	1	2	yes	direct product factor
14	C₂²×C₃	—	7	4	no	—
15	C₃²	C₂×D₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₇	C₂²×C₃²	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃	—	7	8	no	—
18	C₂×C₃	C₃×D₇	1	4	yes	direct product factor
19	C₂²	—	7	1	no	Sylow
20	C₃	C₂×C₃×D₇	1	4	yes	direct product factor
21	C₂	—	7	2	no	—
22	C₂	C₃²×D₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₇
commutator, cosocle, hypocenter	C₇	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃²

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.