Subgroups — D₄₇×#4294⋊C₂ #44565254

Order 32148.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇⋊(#4294⋊C₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#4294⋊C₂	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄₇×#4294	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₉×D₄₇	C₃	1	1	yes	maximal, characteristic
5	C₄₇×#4294	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₈₉₃	C₂×C₃	1	1	yes	characteristic
7	C₃×D₁₉×C₄₇	C₂×C₃	1	1	yes	characteristic
8	C₃×C₁₉×D₄₇	C₂×C₃	1	1	yes	characteristic
9	D₁₉×D₄₇	C₉	1	1	yes	characteristic, complemented, Hall
10	C₃×C₁₉×C₄₇	C₂²×C₃	1	1	yes	characteristic
11	D₈₉₃	C₂×C₉	1	1	yes	characteristic, complemented
12	C₁₉×D₄₇	C₂×C₉	1	1	yes	characteristic, complemented
13	D₁₉×C₄₇	C₂×C₉	1	1	yes	characteristic, complemented
14	C₂×C₉×D₄₇	—	19	1	no	maximal, Hall
15	C₁₉×C₄₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₉×C₄₇	—	19	1	no	—
17	C₉×D₄₇	—	19	1	no	—
18	C₉×D₄₇	—	19	1	no	—
19	C₂×#4294⋊C₂	—	47	1	no	maximal, Hall
20	C₂×C₃×D₄₇	—	19	1	no	—
21	C₉×C₄₇	—	19	1	no	Hall
22	C₂×#4294	—	47	1	no	—
23	#4294⋊C₂	—	47	1	no	—
24	#4294⋊C₂	D₄₇	1	1	yes	characteristic, direct product factor
25	C₂×C₃×C₄₇	—	19	1	no	—
26	C₃×D₄₇	—	19	1	no	—
27	C₃×D₄₇	D₁₉⋊C₃	1	1	yes	characteristic
28	C₂×C₃×D₁₉	—	47	1	no	—
29	C₂×D₄₇	—	19	1	no	Hall
30	#4294	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
31	C₃×C₄₇	C₂×D₁₉⋊C₃	1	1	yes	characteristic
32	C₂×C₃×C₁₉	—	47	1	no	—
33	C₃×D₁₉	—	47	1	no	—
34	C₃×D₁₉	C₃×D₄₇	1	1	yes	characteristic
35	C₂×C₄₇	—	19	1	no	—
36	D₄₇	—	19	1	no	—
37	D₄₇	#4294⋊C₂	1	1	yes	characteristic, direct product factor
38	C₂×D₁₉	—	47	1	no	Hall
39	C₃×C₁₉	C₂×C₃×D₄₇	1	1	yes	characteristic
40	C₄₇	C₂×#4294⋊C₂	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₁₉	—	47	1	no	—
42	D₁₉	—	47	1	no	—
43	D₁₉	C₉×D₄₇	1	1	yes	characteristic, complemented
44	C₂²×C₉	—	893	1	no	Hall
45	C₁₉	C₂×C₉×D₄₇	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₉	—	19	1	no	—
47	C₂×C₉	—	893	1	no	—
48	C₂×C₉	—	893	1	no	—
49	C₂²×C₃	—	893	1	no	—
50	C₉	—	19	1	no	Sylow
51	C₂×C₃	—	19	1	no	—
52	C₂×C₃	—	47	1	no	—
53	C₂×C₃	—	893	1	no	—
54	C₂²	—	893	1	no	Sylow
55	C₃	D₄₇×D₁₉⋊C₃	1	1	yes	characteristic
56	C₂	—	19	1	no	—
57	C₂	—	47	1	no	—
58	C₂	—	893	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₄₇×D₁₉⋊C₃
commutator, hypocenter	C₁₉×C₄₇	C₂²×C₉
Fitting, socle, cosocle	C₃×C₁₉×C₄₇	C₂²×C₃
prime radical	C₃×D₁₉×D₄₇	C₃
LCS	G ▷ C₁₉×C₄₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₄₇⋊(#4294⋊C₂)	C₂	semidirect
2. C₄₇×#4294⋊C₂	C₂	semidirect
3. D₄₇×#4294	C₂	semidirect
5. C₄₇×#4294	C₂²	semidirect
9. D₁₉×D₄₇	C₉	semidirect
11. D₈₉₃	C₂×C₉	semidirect
12. C₁₉×D₄₇	C₂×C₉	semidirect
13. D₁₉×C₄₇	C₂×C₉	semidirect
15. C₁₉×C₄₇	C₂²×C₉	semidirect
24. #4294⋊C₂	D₄₇	direct (N × H)
30. #4294	C₂×D₄₇	semidirect
37. D₄₇	#4294⋊C₂	direct (N × H)
40. C₄₇	C₂×#4294⋊C₂	semidirect
43. D₁₉	C₉×D₄₇	semidirect
45. C₁₉	C₂×C₉×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇⋊(#4294⋊C₂)	2
C₄₇×#4294⋊C₂	2
D₄₇×#4294	2
C₃×D₁₉×D₄₇	3
C₂×C₉×D₄₇	19
C₂×#4294⋊C₂	47

Subgroups — D47×#4294⋊C2 #44565254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#4294⋊C₂ #44565254