Subgroups — C₂×C₃×D₂₁ #7004

Order 252.

44 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	C₃×D₂₁	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×D₇	—	3	1	no	maximal
5	C₃²×C₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₇	—	2	1	no	—
7	C₂×C₃×C₇	D₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₇	C₂×C₃	1	1	yes	characteristic, complemented
9	D₂₁	C₂×C₃	1	2	yes	direct product factor
10	C₃×D₇	—	3	2	no	—
11	C₂×C₃×D₃	—	7	1	no	maximal, Hall
12	C₂×D₇	—	3	1	no	Hall
13	C₃×C₇	—	2	1	no	—
14	C₃×C₇	C₂×D₃	1	1	yes	characteristic, complemented
15	C₃×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₂×C₃²	D₇	1	1	yes	characteristic, complemented
17	C₃×D₃	—	7	2	no	—
18	C₂×C₇	C₃×D₃	1	1	yes	characteristic, complemented
19	D₇	—	3	2	no	—
20	C₂²×C₃	—	21	1	no	—
21	C₂×D₃	—	7	1	no	—
22	C₃²	C₂×D₇	1	1	yes	characteristic, complemented, Sylow
23	C₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃	—	2	1	no	—
25	C₂×C₃	—	21	2	no	—
26	C₂×C₃	C₃×D₇	1	1	yes	characteristic, complemented
27	C₂×C₃	D₂₁	1	1	yes	characteristic, direct product factor
28	D₃	—	7	2	no	—
29	C₂²	—	21	1	no	Sylow
30	C₃	—	2	1	no	—
31	C₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented
32	C₃	C₂×D₂₁	1	1	yes	characteristic, direct product factor
33	C₂	—	21	2	no	—
34	C₂	C₃×D₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₃

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.