Subgroups — C₂×C₉×D₄₉₇ #31822023

Order 17892.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₄₉₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₉×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₄₉₇	C₃	1	1	yes	maximal, characteristic
4	C₇×C₉×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×D₄₉₇	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₇×C₇₁	C₂×C₃	1	1	yes	characteristic
7	C₂×C₉×D₇₁	—	7	1	no	maximal, Hall
8	C₂×D₄₉₇	C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₇×C₇₁	C₂²×C₃	1	1	yes	characteristic
10	C₂×C₉×C₇₁	D₇	1	1	yes	characteristic, complemented
11	C₉×D₇₁	—	7	2	no	—
12	C₂×C₇×C₇₁	C₂×C₉	1	1	yes	characteristic, complemented
13	D₄₉₇	C₂×C₉	1	2	yes	direct product factor
14	C₂×C₃×D₇₁	—	7	1	no	—
15	C₉×C₇₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	C₇×C₇₁	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₇₁	C₃×D₇	1	1	yes	characteristic
18	C₃×D₇₁	—	7	2	no	—
19	C₂×D₇₁	—	7	1	no	Hall
20	C₂×C₉×D₇	—	71	1	no	maximal, Hall
21	C₃×C₇₁	C₂×C₃×D₇	1	1	yes	characteristic
22	C₂×C₇₁	C₉×D₇	1	1	yes	characteristic, complemented
23	D₇₁	—	7	2	no	—
24	C₂×C₇×C₉	D₇₁	1	1	yes	characteristic, complemented
25	C₉×D₇	—	71	2	no	—
26	C₂×C₃×D₇	—	71	1	no	—
27	C₇₁	C₂×C₉×D₇	1	1	yes	characteristic, complemented, Sylow
28	C₇×C₉	C₂×D₇₁	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₇	C₃×D₇₁	1	1	yes	characteristic
30	C₃×D₇	—	71	2	no	—
31	C₂²×C₉	—	497	1	no	Hall
32	C₂×D₇	—	71	1	no	Hall
33	C₃×C₇	C₂×C₃×D₇₁	1	1	yes	characteristic
34	C₂×C₉	—	497	2	no	—
35	C₂×C₉	D₄₉₇	1	1	yes	characteristic, direct product factor
36	C₂×C₇	C₉×D₇₁	1	1	yes	characteristic, complemented
37	D₇	—	71	2	no	—
38	C₂²×C₃	—	497	1	no	—
39	C₉	C₂×D₄₉₇	1	1	yes	characteristic, direct product factor, Sylow
40	C₇	C₂×C₉×D₇₁	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	497	2	no	—
42	C₂×C₃	C₃×D₄₉₇	1	1	yes	characteristic
43	C₂²	—	497	1	no	Sylow
44	C₃	C₂×C₃×D₄₉₇	1	1	yes	characteristic
45	C₂	—	497	2	no	—
46	C₂	C₉×D₄₉₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₉	D₄₉₇
commutator, hypocenter	C₇×C₇₁	C₂²×C₉
Frattini	C₃	C₂×C₃×D₄₉₇
Fitting	C₂×C₇×C₉×C₇₁	C₂
socle	C₂×C₃×C₇×C₇₁	C₂×C₃
prime radical	C₂×C₃×D₄₉₇	C₃
cosocle	C₃×C₇×C₇₁	C₂²×C₃
LCS	G ▷ C₇×C₇₁
UCS	C₁ ◁ C₂×C₉

Complements

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

N	H ≅ G/N	type
1. C₉×D₄₉₇	C₂	direct (N × H)
2. C₂×C₇×C₉×C₇₁	C₂	semidirect
4. C₇×C₉×C₇₁	C₂²	semidirect
8. C₂×D₄₉₇	C₉	direct (N × H)
10. C₂×C₉×C₇₁	D₇	semidirect
12. C₂×C₇×C₇₁	C₂×C₉	semidirect
13. D₄₉₇	C₂×C₉	direct (N × H)
15. C₉×C₇₁	C₂×D₇	semidirect
16. C₇×C₇₁	C₂²×C₉	semidirect
22. C₂×C₇₁	C₉×D₇	semidirect
24. C₂×C₇×C₉	D₇₁	semidirect
27. C₇₁	C₂×C₉×D₇	semidirect
28. C₇×C₉	C₂×D₇₁	semidirect
35. C₂×C₉	D₄₉₇	direct (N × H)
36. C₂×C₇	C₉×D₇₁	semidirect
39. C₉	C₂×D₄₉₇	direct (N × H)
40. C₇	C₂×C₉×D₇₁	semidirect
46. C₂	C₉×D₄₉₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×D₄₉₇	2
C₂×C₇×C₉×C₇₁	2
C₂×C₃×D₄₉₇	3
C₂×C₉×D₇₁	7
C₂×C₉×D₇	71

Subgroups — C2×C9×D497 #31822023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×D₄₉₇ #31822023