Subgroups — C₂×C₇₁×D₆₃ #31822026

Order 17892.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×D₆₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₉×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₁×C₇₁	—	3	1	no	maximal
4	C₇×C₉×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₂₁×C₇₁	—	3	2	no	—
6	C₂×C₃×C₇×C₇₁	D₃	1	1	yes	characteristic
7	C₂×D₉×C₇₁	—	7	1	no	maximal, Hall
8	C₂×D₇×C₇₁	—	9	1	no	Hall
9	C₃×C₇×C₇₁	C₂×D₃	1	1	yes	characteristic
10	C₂×C₉×C₇₁	D₇	1	1	yes	characteristic, complemented
11	D₉×C₇₁	—	7	2	no	—
12	C₂×C₇×C₇₁	D₉	1	1	yes	characteristic, complemented
13	D₇×C₇₁	—	9	2	no	—
14	C₂×D₃×C₇₁	—	21	1	no	—
15	C₉×C₇₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	C₇×C₇₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₇₁	D₂₁	1	1	yes	characteristic
18	D₃×C₇₁	—	21	2	no	—
19	C₂²×C₇₁	—	63	1	no	Hall
20	C₂×D₆₃	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₃×C₇₁	C₂×D₂₁	1	1	yes	characteristic
22	C₂×C₇₁	—	63	2	no	—
23	C₂×C₇₁	D₆₃	1	1	yes	characteristic, direct product factor
24	C₂×C₇×C₉	C₂×C₇₁	1	1	yes	characteristic, complemented
25	D₆₃	C₂×C₇₁	1	2	yes	direct product factor
26	C₂×D₂₁	—	3	1	no	—
27	C₇₁	C₂×D₆₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₇×C₉	C₂²×C₇₁	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₇	D₃×C₇₁	1	1	yes	characteristic
30	D₂₁	—	3	2	no	—
31	C₂×D₉	—	7	1	no	Hall
32	C₂×D₇	—	9	1	no	Hall
33	C₃×C₇	C₂×D₃×C₇₁	1	1	yes	characteristic
34	C₂×C₉	D₇×C₇₁	1	1	yes	characteristic, complemented
35	D₉	—	7	2	no	—
36	C₂×C₇	D₉×C₇₁	1	1	yes	characteristic, complemented
37	D₇	—	9	2	no	—
38	C₂×D₃	—	21	1	no	—
39	C₉	C₂×D₇×C₇₁	1	1	yes	characteristic, complemented, Sylow
40	C₇	C₂×D₉×C₇₁	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₂₁×C₇₁	1	1	yes	characteristic
42	D₃	—	21	2	no	—
43	C₂²	—	63	1	no	Sylow
44	C₃	C₂×D₂₁×C₇₁	1	1	yes	characteristic
45	C₂	—	63	2	no	—
46	C₂	C₇₁×D₆₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇₁	D₆₃
commutator, cosocle, hypocenter	C₇×C₉	C₂²×C₇₁
Frattini	C₃	C₂×D₂₁×C₇₁
Fitting	C₂×C₇×C₉×C₇₁	C₂
socle	C₂×C₃×C₇×C₇₁	D₃
LCS	G ▷ C₇×C₉
UCS	C₁ ◁ C₂×C₇₁

Complements

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

N	H ≅ G/N	type
1. C₇₁×D₆₃	C₂	direct (N × H)
2. C₂×C₇×C₉×C₇₁	C₂	semidirect
4. C₇×C₉×C₇₁	C₂²	semidirect
10. C₂×C₉×C₇₁	D₇	semidirect
12. C₂×C₇×C₇₁	D₉	semidirect
15. C₉×C₇₁	C₂×D₇	semidirect
16. C₇×C₇₁	C₂×D₉	semidirect
20. C₂×D₆₃	C₇₁	direct (N × H)
23. C₂×C₇₁	D₆₃	direct (N × H)
24. C₂×C₇×C₉	C₂×C₇₁	semidirect
25. D₆₃	C₂×C₇₁	direct (N × H)
27. C₇₁	C₂×D₆₃	direct (N × H)
28. C₇×C₉	C₂²×C₇₁	semidirect
34. C₂×C₉	D₇×C₇₁	semidirect
36. C₂×C₇	D₉×C₇₁	semidirect
39. C₉	C₂×D₇×C₇₁	semidirect
40. C₇	C₂×D₉×C₇₁	semidirect
46. C₂	C₇₁×D₆₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₁×D₆₃	2
C₂×C₇×C₉×C₇₁	2
C₂×D₂₁×C₇₁	3
C₂×D₉×C₇₁	7
C₂×D₆₃	71

Subgroups — C2×C71×D63 #31822026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₁×D₆₃ #31822026