Subgroups — C₃×C₇×Dic₂₂₁ #32915413

Order 18564.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₂₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₁₃×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic
5	C₃×Dic₂₂₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₃×C₁₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇×Dic₁₇	—	13	1	no	maximal, Hall
8	C₂×C₃×C₁₃×C₁₇	C₂×C₇	1	1	yes	characteristic
9	C₃×C₇×Dic₁₃	—	17	1	no	maximal, Hall
10	Dic₂₂₁	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₇×C₁₇	D₁₃	1	1	yes	characteristic
12	C₃×C₁₃×C₁₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₇×C₁₃	D₁₇	1	1	yes	characteristic
14	C₇×Dic₁₇	—	13	1	no	Hall
15	C₂×C₁₃×C₁₇	C₂×C₃×C₇	1	1	yes	characteristic
16	C₇×Dic₁₃	—	17	1	no	Hall
17	C₃×C₇×C₁₇	Dic₁₃	1	1	yes	characteristic, complemented, Hall
18	C₃×C₇×C₁₃	Dic₁₇	1	1	yes	characteristic, complemented, Hall
19	C₂×C₇×C₁₇	C₃×D₁₃	1	1	yes	characteristic
20	C₁₃×C₁₇	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Hall
21	C₃×Dic₁₇	—	13	1	no	Hall
22	C₂×C₇×C₁₃	C₃×D₁₇	1	1	yes	characteristic
23	C₃×Dic₁₃	—	17	1	no	Hall
24	C₇×C₁₇	C₃×Dic₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₁₇	C₇×D₁₃	1	1	yes	characteristic
26	C₇×C₁₃	C₃×Dic₁₇	1	1	yes	characteristic, complemented, Hall
27	C₃×C₄×C₇	—	221	1	no	Hall
28	C₂×C₃×C₁₃	C₇×D₁₇	1	1	yes	characteristic
29	Dic₁₇	—	13	1	no	Hall
30	Dic₁₃	—	17	1	no	Hall
31	C₃×C₁₇	C₇×Dic₁₃	1	1	yes	characteristic, complemented, Hall
32	C₂×C₃×C₇	D₂₂₁	1	1	yes	characteristic
33	C₃×C₁₃	C₇×Dic₁₇	1	1	yes	characteristic, complemented, Hall
34	C₂×C₁₇	C₃×C₇×D₁₃	1	1	yes	characteristic
35	C₄×C₇	—	221	1	no	Hall
36	C₂×C₁₃	C₃×C₇×D₁₇	1	1	yes	characteristic
37	C₃×C₇	Dic₂₂₁	1	1	yes	characteristic, direct product factor, Hall
38	C₁₇	C₃×C₇×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₇	C₃×D₂₂₁	1	1	yes	characteristic
40	C₁₃	C₃×C₇×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₄	—	221	1	no	Hall
42	C₇	C₃×Dic₂₂₁	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	C₇×D₂₂₁	1	1	yes	characteristic
44	C₄	—	221	1	no	Sylow
45	C₃	C₇×Dic₂₂₁	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×C₇×D₂₂₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇	D₂₂₁
commutator, hypocenter	C₁₃×C₁₇	C₃×C₄×C₇
Frattini	C₂	C₃×C₇×D₂₂₁
Fitting, socle, prime radical	C₂×C₃×C₇×C₁₃×C₁₇	C₂
cosocle	C₂×C₁₃×C₁₇	C₂×C₃×C₇
LCS	G ▷ C₁₃×C₁₇
UCS	C₁ ◁ C₂×C₃×C₇

Complements

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

N	H ≅ G/N	type
2. C₇×Dic₂₂₁	C₃	direct (N × H)
3. C₃×C₇×C₁₃×C₁₇	C₄	semidirect
5. C₃×Dic₂₂₁	C₇	direct (N × H)
6. C₇×C₁₃×C₁₇	C₃×C₄	semidirect
10. Dic₂₂₁	C₃×C₇	direct (N × H)
12. C₃×C₁₃×C₁₇	C₄×C₇	semidirect
17. C₃×C₇×C₁₇	Dic₁₃	semidirect
18. C₃×C₇×C₁₃	Dic₁₇	semidirect
20. C₁₃×C₁₇	C₃×C₄×C₇	semidirect
24. C₇×C₁₇	C₃×Dic₁₃	semidirect
26. C₇×C₁₃	C₃×Dic₁₇	semidirect
31. C₃×C₁₇	C₇×Dic₁₃	semidirect
33. C₃×C₁₃	C₇×Dic₁₇	semidirect
37. C₃×C₇	Dic₂₂₁	direct (N × H)
38. C₁₇	C₃×C₇×Dic₁₃	semidirect
40. C₁₃	C₃×C₇×Dic₁₇	semidirect
42. C₇	C₃×Dic₂₂₁	direct (N × H)
45. C₃	C₇×Dic₂₂₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇×C₁₃×C₁₇	2
C₇×Dic₂₂₁	3
C₃×Dic₂₂₁	7
C₃×C₇×Dic₁₇	13
C₃×C₇×Dic₁₃	17

Subgroups — C3×C7×Dic221 #32915413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×Dic₂₂₁ #32915413