Subgroups — C₃×D₃×D₇ #6994

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

	subgroup	G/H
center, hypercenter	C₃	D₃×D₇
commutator, cosocle, hypocenter	C₃×C₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×D₂₁	C₂	semidirect
2. C₃×D₃×C₇	C₂	semidirect
3. C₃²×D₇	C₂	semidirect
5. D₃×D₇	C₃	direct (N × H)
6. C₃²×C₇	C₂²	semidirect
8. D₂₁	C₂×C₃	semidirect
11. C₃×D₇	D₃	direct (N × H)
12. C₃×D₇	C₂×C₃	semidirect
13. D₃×C₇	C₂×C₃	semidirect
17. C₃×C₇	C₂×D₃	semidirect
18. C₃×C₇	C₂²×C₃	semidirect
21. C₃×D₃	D₇	direct (N × H)
24. D₇	C₃×D₃	direct (N × H)
27. C₃²	C₂×D₇	semidirect
28. C₇	C₂×C₃×D₃	semidirect
35. D₃	C₃×D₇	direct (N × H)
38. C₃	D₃×D₇	direct (N × H)
39. C₃	C₂×C₃×D₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×D₂₁	2
C₃×D₃×C₇	2
C₃²×D₇	2
C₂×C₃×D₇	3
D₃×D₇	3
C₂×C₃×D₃	7

Subgroups — C3×D3×D7 #6994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×D₇ #6994