Subgroups — D₃×D₂₁ #6997

Order 252.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×C₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₁	—	3	1	no	maximal
5	D₃×D₇	—	3	1	no	maximal
6	C₃²×C₇	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₇	—	3	1	no	—
8	D₂₁	—	3	1	no	—
9	D₂₁	—	3	1	no	—
10	D₂₁	—	6	1	no	—
11	D₂₁	D₃	1	1	yes	characteristic, direct product factor
12	C₃×D₇	—	3	1	no	—
13	D₃×C₇	D₃	1	1	yes	characteristic, complemented
14	D₃²	—	7	1	no	maximal, Hall
15	C₂×D₇	—	9	1	no	Hall
16	C₃×C₇	—	2	1	no	—
17	C₃×C₇	C₂×D₃	1	1	yes	characteristic, complemented
18	C₃×C₇	C₂×D₃	1	1	yes	characteristic, complemented
19	C₃⋊D₃	—	7	1	no	—
20	C₃×D₃	—	7	1	no	—
21	C₃×D₃	D₇	1	1	yes	characteristic, complemented
22	C₂×C₇	—	3	1	no	—
23	D₇	—	3	1	no	—
24	D₇	—	9	1	no	—
25	C₂×D₃	—	21	1	no	—
26	C₂×D₃	—	21	1	no	—
27	C₃²	C₂×D₇	1	1	yes	characteristic, complemented, Sylow
28	C₇	D₃²	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	3	1	no	—
30	C₂×C₃	—	21	1	no	—
31	D₃	—	7	1	no	—
32	D₃	—	21	1	no	—
33	D₃	—	21	1	no	—
34	D₃	—	42	1	no	—
35	D₃	D₂₁	1	1	yes	characteristic, direct product factor
36	C₂²	—	63	1	no	Sylow
37	C₃	—	2	1	no	—
38	C₃	D₃×D₇	1	1	yes	characteristic, complemented
39	C₃	C₂×D₂₁	1	1	yes	characteristic, complemented
40	C₂	—	3	1	no	—
41	C₂	—	21	1	no	—
42	C₂	—	63	1	no	—

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

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.