Subgroups — C₂²×C₄₇×#4296 #44565313

Order 32148.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#4296	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₄₇×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₄₇×#4296	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₄₇×C₁₉⋊C₃	C₂×C₃	1	3	yes	—
5	C₂²×C₁₉×C₄₇	C₉	1	1	yes	characteristic, complemented, Hall
6	C₄₇×C₁₉⋊C₃	C₂²×C₃	1	1	yes	characteristic
7	C₂×C₁₉×C₄₇	C₂×C₉	1	3	yes	complemented
8	C₂²×C₉×C₄₇	—	19	1	no	maximal, Hall
9	C₁₉×C₄₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₉×C₄₇	—	19	3	no	—
11	C₂²×#4296	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₃×C₄₇	—	19	1	no	—
13	C₉×C₄₇	—	19	1	no	Hall
14	C₂×#4296	C₂×C₄₇	1	3	yes	direct product factor
15	C₂×C₃×C₄₇	—	19	3	no	—
16	C₂²×C₁₉⋊C₃	C₃×C₄₇	1	1	yes	characteristic
17	C₂²×C₄₇	#4296	1	1	yes	characteristic, direct product factor, Hall
18	#4296	C₂²×C₄₇	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₄₇	—	19	1	no	—
20	C₂×C₁₉⋊C₃	C₂×C₃×C₄₇	1	3	yes	—
21	C₂×C₄₇	C₂×#4296	1	3	yes	direct product factor
22	C₂²×C₁₉	C₉×C₄₇	1	1	yes	characteristic, complemented, Hall
23	C₁₉⋊C₃	C₂²×C₃×C₄₇	1	1	yes	characteristic
24	C₄₇	C₂²×#4296	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₁₉	C₂×C₉×C₄₇	1	3	yes	complemented
26	C₂²×C₉	—	19	1	no	Hall
27	C₁₉	C₂²×C₉×C₄₇	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₉	—	19	3	no	—
29	C₂²×C₃	—	19	1	no	—
30	C₉	—	19	1	no	Sylow
31	C₂×C₃	—	19	3	no	—
32	C₂²	C₄₇×#4296	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	—	19	1	no	—
34	C₂	C₂×C₄₇×#4296	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₄₇	#4296
commutator, hypocenter	C₁₉	C₂²×C₉×C₄₇
Frattini	C₁	G
Fitting, socle	C₂²×C₁₉×C₄₇	C₉
prime radical	C₂²×C₄₇×C₁₉⋊C₃	C₃
cosocle	C₁₉⋊C₃	C₂²×C₃×C₄₇
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄₇

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇×#4296	C₂	direct (N × H)
3. C₄₇×#4296	C₂²	direct (N × H)
5. C₂²×C₁₉×C₄₇	C₉	semidirect
7. C₂×C₁₉×C₄₇	C₂×C₉	semidirect
9. C₁₉×C₄₇	C₂²×C₉	semidirect
11. C₂²×#4296	C₄₇	direct (N × H)
14. C₂×#4296	C₂×C₄₇	direct (N × H)
17. C₂²×C₄₇	#4296	direct (N × H)
18. #4296	C₂²×C₄₇	direct (N × H)
21. C₂×C₄₇	C₂×#4296	direct (N × H)
22. C₂²×C₁₉	C₉×C₄₇	semidirect
24. C₄₇	C₂²×#4296	direct (N × H)
25. C₂×C₁₉	C₂×C₉×C₄₇	semidirect
27. C₁₉	C₂²×C₉×C₄₇	semidirect
32. C₂²	C₄₇×#4296	direct (N × H)
34. C₂	C₂×C₄₇×#4296	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×C₄₇×#4296	2
C₂²×C₄₇×C₁₉⋊C₃	3
C₂²×C₉×C₄₇	19
C₂²×#4296	47

Subgroups — C22×C47×#4296 #44565313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄₇×#4296 #44565313