Subgroups — C₄₇×Dic₁₇₁ #44565248

Order 32148.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₉×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄₇×Dic₅₇	—	3	1	no	maximal
3	C₉×C₁₉×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₉×C₄₇	D₃	1	1	yes	characteristic
5	C₄₇×Dic₁₉	—	9	1	no	Hall
6	C₃×C₁₉×C₄₇	Dic₃	1	1	yes	characteristic
7	C₂×C₁₉×C₄₇	D₉	1	1	yes	characteristic
8	Dic₉×C₄₇	—	19	1	no	maximal, Hall
9	C₁₉×C₄₇	Dic₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₉×C₄₇	D₁₉	1	1	yes	characteristic
11	Dic₁₇₁	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	Dic₃×C₄₇	—	57	1	no	—
13	C₉×C₄₇	Dic₁₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₉×C₁₉	C₂×C₄₇	1	1	yes	characteristic
15	C₂×C₃×C₄₇	D₅₇	1	1	yes	characteristic
16	Dic₅₇	—	3	1	no	—
17	C₄×C₄₇	—	171	1	no	Hall
18	C₉×C₁₉	C₄×C₄₇	1	1	yes	characteristic, complemented, Hall
19	C₃×C₄₇	Dic₅₇	1	1	yes	characteristic
20	C₂×C₃×C₁₉	D₃×C₄₇	1	1	yes	characteristic
21	C₂×C₄₇	D₁₇₁	1	1	yes	characteristic
22	Dic₁₉	—	9	1	no	Hall
23	C₃×C₁₉	Dic₃×C₄₇	1	1	yes	characteristic
24	C₄₇	Dic₁₇₁	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₁₉	D₉×C₄₇	1	1	yes	characteristic
26	Dic₉	—	19	1	no	Hall
27	C₁₉	Dic₉×C₄₇	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₉	D₁₉×C₄₇	1	1	yes	characteristic
29	Dic₃	—	57	1	no	—
30	C₉	C₄₇×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	C₄₇×D₅₇	1	1	yes	characteristic
32	C₄	—	171	1	no	Sylow
33	C₃	C₄₇×Dic₅₇	1	1	yes	characteristic
34	C₂	C₄₇×D₁₇₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄₇	D₁₇₁
commutator, hypocenter	C₉×C₁₉	C₄×C₄₇
Frattini	C₂×C₃	C₄₇×D₅₇
Fitting	C₂×C₉×C₁₉×C₄₇	C₂
socle, prime radical	C₂×C₃×C₁₉×C₄₇	D₃
cosocle	C₂×C₉×C₁₉	C₂×C₄₇
LCS	G ▷ C₉×C₁₉
UCS	C₁ ◁ C₂×C₄₇

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₉×C₄₇	C₄	semidirect
9. C₁₉×C₄₇	Dic₉	semidirect
11. Dic₁₇₁	C₄₇	direct (N × H)
13. C₉×C₄₇	Dic₁₉	semidirect
18. C₉×C₁₉	C₄×C₄₇	semidirect
24. C₄₇	Dic₁₇₁	direct (N × H)
27. C₁₉	Dic₉×C₄₇	semidirect
30. C₉	C₄₇×Dic₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×C₁₉×C₄₇	2
C₄₇×Dic₅₇	3
Dic₉×C₄₇	19
Dic₁₇₁	47

Subgroups — C47×Dic171 #44565248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×Dic₁₇₁ #44565248