Subgroups — C₃×C₁₉×C₂²⋊(C₄₉⋊C₃) #45691444

Order 33516.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₂²⋊(C₄₉⋊C₃)	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₁₉×C₄₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₉×C₄₉⋊C₃	—	4	1	no	maximal, Hall
4	C₂×C₃×C₁₉×C₄₉	—	3	1	no	—
5	C₃×C₁₉×C₂²⋊ΓL(1,𝔽₈)	—	7	1	no	maximal
6	C₂²×C₁₉×C₄₉	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₁₉×C₄₉⋊C₃	—	4	3	no	—
8	C₃×C₁₉×C₄₉	A₄	1	1	yes	characteristic, complemented
9	C₂×C₁₉×C₄₉	—	3	1	no	—
10	C₃×C₂²⋊(C₄₉⋊C₃)	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₇×C₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
12	C₁₉×C₂²⋊ΓL(1,𝔽₈)	—	7	3	no	—
13	C₃×C₁₉×ΓL(1,𝔽₈)	—	28	1	no	—
14	C₁₉×C₄₉	C₃×A₄	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₇×C₁₉	—	3	1	no	—
16	C₃×A₄×C₁₉	—	49	1	no	Hall
17	C₂²×C₃×C₄₉	C₃×C₁₉	1	1	yes	characteristic, complemented
18	C₂²⋊(C₄₉⋊C₃)	C₃×C₁₉	1	3	yes	direct product factor
19	C₂²×C₇×C₁₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
20	C₃×C₄₉⋊C₃	—	4	1	no	Hall
21	C₃×C₇×C₁₉	C₂²⋊ΓL(1,𝔽₈)	1	1	yes	characteristic
22	C₁₉×ΓL(1,𝔽₈)	—	28	3	no	—
23	C₂×C₃×C₄₉	—	3	1	no	—
24	C₂×C₇×C₁₉	—	3	1	no	—
25	C₃×C₂²⋊ΓL(1,𝔽₈)	—	7	1	no	—
26	C₂²×C₃×C₁₉	C₄₉⋊C₃	1	1	yes	characteristic, complemented
27	A₄×C₁₉	—	49	3	no	—
28	C₂²×C₄₉	C₃²×C₁₉	1	1	yes	characteristic, complemented, Hall
29	C₃²×C₁₉	—	196	1	no	Hall
30	C₃×C₄₉	A₄×C₁₉	1	1	yes	characteristic, complemented
31	C₄₉⋊C₃	—	4	3	no	—
32	C₇×C₁₉	C₃×C₂²⋊ΓL(1,𝔽₈)	1	1	yes	characteristic
33	C₂×C₃×C₁₉	—	3	1	no	—
34	C₂×C₄₉	—	3	1	no	—
35	C₂²×C₃×C₇	C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
36	C₂²⋊ΓL(1,𝔽₈)	—	7	3	no	—
37	C₂²×C₁₉	C₃×C₄₉⋊C₃	1	1	yes	characteristic, complemented, Hall
38	C₃×ΓL(1,𝔽₈)	—	28	1	no	—
39	C₃×C₁₉	—	196	3	no	—
40	C₃×C₁₉	C₂²⋊(C₄₉⋊C₃)	1	1	yes	characteristic, direct product factor
41	C₄₉	C₃×A₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃×C₇	—	3	1	no	—
43	C₂×C₁₉	—	3	1	no	—
44	C₃×A₄	—	49	1	no	Hall
45	C₂²×C₇	C₃×C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
46	C₃×C₇	C₁₉×C₂²⋊ΓL(1,𝔽₈)	1	1	yes	characteristic
47	ΓL(1,𝔽₈)	—	28	3	no	—
48	C₁₉	C₃×C₂²⋊(C₄₉⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
49	C₂×C₇	—	3	1	no	—
50	C₂²×C₃	C₁₉×C₄₉⋊C₃	1	1	yes	characteristic, complemented
51	A₄	—	49	3	no	—
52	C₃²	—	196	1	no	Sylow
53	C₇	C₃×C₁₉×C₂²⋊ΓL(1,𝔽₈)	1	1	yes	characteristic
54	C₂×C₃	—	3	1	no	—
55	C₂²	C₃×C₁₉×C₄₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
56	C₃	—	196	3	no	—
57	C₃	C₁₉×C₂²⋊(C₄₉⋊C₃)	1	1	yes	characteristic, direct product factor
58	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₉	C₂²⋊(C₄₉⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₄₉	C₃²×C₁₉
Frattini	C₇	C₃×C₁₉×C₂²⋊ΓL(1,𝔽₈)
Fitting	C₂²×C₃×C₁₉×C₄₉	C₃
socle	C₂²×C₃×C₇×C₁₉	ΓL(1,𝔽₈)
LCS	G ▷ C₂²×C₄₉
UCS	C₁ ◁ C₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×C₂²⋊(C₄₉⋊C₃)	C₃	direct (N × H)
2. C₂²×C₃×C₁₉×C₄₉	C₃	semidirect
6. C₂²×C₁₉×C₄₉	C₃²	semidirect
8. C₃×C₁₉×C₄₉	A₄	semidirect
10. C₃×C₂²⋊(C₄₉⋊C₃)	C₁₉	direct (N × H)
14. C₁₉×C₄₉	C₃×A₄	semidirect
17. C₂²×C₃×C₄₉	C₃×C₁₉	semidirect
18. C₂²⋊(C₄₉⋊C₃)	C₃×C₁₉	direct (N × H)
26. C₂²×C₃×C₁₉	C₄₉⋊C₃	semidirect
28. C₂²×C₄₉	C₃²×C₁₉	semidirect
30. C₃×C₄₉	A₄×C₁₉	semidirect
37. C₂²×C₁₉	C₃×C₄₉⋊C₃	semidirect
40. C₃×C₁₉	C₂²⋊(C₄₉⋊C₃)	direct (N × H)
41. C₄₉	C₃×A₄×C₁₉	semidirect
48. C₁₉	C₃×C₂²⋊(C₄₉⋊C₃)	direct (N × H)
50. C₂²×C₃	C₁₉×C₄₉⋊C₃	semidirect
55. C₂²	C₃×C₁₉×C₄₉⋊C₃	semidirect
57. C₃	C₁₉×C₂²⋊(C₄₉⋊C₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×C₂²⋊(C₄₉⋊C₃)	3
C₂²×C₃×C₁₉×C₄₉	3
C₃×C₁₉×C₄₉⋊C₃	4
C₃×C₁₉×C₂²⋊ΓL(1,𝔽₈)	7
C₃×C₂²⋊(C₄₉⋊C₃)	19

Subgroups — C3×C19×C22⋊(C49⋊C3) #45691444

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉×C₂²⋊(C₄₉⋊C₃) #45691444