Subgroups — C₉×C₁₉×Dic₄₇ #44565243

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	C₃×C₁₉×Dic₄₇	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₉×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₉×C₄₇	C₂×C₃	1	1	yes	characteristic
5	C₁₉×Dic₄₇	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₉×C₄₇	C₃×C₄	1	1	yes	characteristic
7	C₂×C₁₉×C₄₇	C₂×C₉	1	1	yes	characteristic
8	C₉×Dic₄₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₉×C₄₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₉×C₄₇	C₂×C₁₉	1	1	yes	characteristic
11	C₄×C₉×C₁₉	—	47	1	no	maximal, Hall
12	C₃×Dic₄₇	C₃×C₁₉	1	1	yes	characteristic
13	C₉×C₄₇	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₉×C₁₉	D₄₇	1	1	yes	characteristic
15	C₂×C₃×C₄₇	C₂×C₃×C₁₉	1	1	yes	characteristic
16	C₃×C₄×C₁₉	—	47	1	no	—
17	Dic₄₇	C₉×C₁₉	1	1	yes	characteristic, direct product factor, Hall
18	C₉×C₁₉	Dic₄₇	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₄₇	C₃×C₄×C₁₉	1	1	yes	characteristic
20	C₂×C₃×C₁₉	C₃×D₄₇	1	1	yes	characteristic
21	C₂×C₄₇	C₂×C₉×C₁₉	1	1	yes	characteristic
22	C₄×C₁₉	—	47	1	no	Hall
23	C₃×C₁₉	C₃×Dic₄₇	1	1	yes	characteristic
24	C₄₇	C₄×C₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₁₉	C₉×D₄₇	1	1	yes	characteristic
26	C₄×C₉	—	47	1	no	Hall
27	C₁₉	C₉×Dic₄₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₉	C₁₉×D₄₇	1	1	yes	characteristic
29	C₃×C₄	—	47	1	no	—
30	C₉	C₁₉×Dic₄₇	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₃×C₁₉×D₄₇	1	1	yes	characteristic
32	C₄	—	47	1	no	Sylow
33	C₃	C₃×C₁₉×Dic₄₇	1	1	yes	characteristic
34	C₂	C₉×C₁₉×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₉	D₄₇
commutator, hypocenter	C₄₇	C₄×C₉×C₁₉
Frattini	C₂×C₃	C₃×C₁₉×D₄₇
Fitting	C₂×C₉×C₁₉×C₄₇	C₂
socle, prime radical	C₂×C₃×C₁₉×C₄₇	C₂×C₃
cosocle	C₂×C₃×C₄₇	C₂×C₃×C₁₉
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₂×C₉×C₁₉

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₉×C₄₇	C₄	semidirect
5. C₁₉×Dic₄₇	C₉	direct (N × H)
8. C₉×Dic₄₇	C₁₉	direct (N × H)
9. C₁₉×C₄₇	C₄×C₉	semidirect
13. C₉×C₄₇	C₄×C₁₉	semidirect
17. Dic₄₇	C₉×C₁₉	direct (N × H)
18. C₉×C₁₉	Dic₄₇	direct (N × H)
24. C₄₇	C₄×C₉×C₁₉	semidirect
27. C₁₉	C₉×Dic₄₇	direct (N × H)
30. C₉	C₁₉×Dic₄₇	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×C₉×C₁₉×C₄₇	2
C₃×C₁₉×Dic₄₇	3
C₉×Dic₄₇	19
C₄×C₉×C₁₉	47

Subgroups — C9×C19×Dic47 #44565243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₁₉×Dic₄₇ #44565243