Subgroups — C₁₉×C₃⋊(C₃⋊#5997) #45692726

Order 33516.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₉×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₃⋊#5997	—	3	4	no	maximal
3	C₃²×C₇²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₉×C₇⋊D₇	D₃	1	4	yes	—
5	C₁₉×#5997	—	9	1	no	Hall
6	C₃×C₇²×C₁₉	Dic₃	1	4	yes	complemented
7	C₃²×D₇×C₁₉	—	14	4	no	—
8	C₁₉×C₇⋊D₇	C₃⋊D₃	1	1	yes	characteristic
9	C₃⋊(C₃⋊#5997)	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃²×C₇×C₁₉	—	2	4	no	—
11	C₇²×C₁₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₇⋊D₇	C₂×C₁₉	1	1	yes	characteristic
13	C₃×D₇×C₁₉	—	14	16	no	—
14	C₁₉×C₃⋊Dic₃	—	49	1	no	maximal, Hall
15	C₃⋊#5997	—	3	4	no	—
16	C₃²×C₇²	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇×C₁₉	—	2	16	no	—
18	C₂×C₃²×C₁₉	—	49	1	no	—
19	C₃×C₇⋊D₇	D₃×C₁₉	1	4	yes	—
20	D₇×C₁₉	—	14	4	no	—
21	Dic₃×C₁₉	—	147	4	no	—
22	#5997	—	9	1	no	Hall
23	C₃²×C₁₉	#5997	1	1	yes	characteristic, complemented, Hall
24	C₃×C₇²	Dic₃×C₁₉	1	4	yes	complemented
25	C₇×C₁₉	—	2	4	no	—
26	C₃²×D₇	—	14	4	no	—
27	C₂×C₃×C₁₉	—	49	4	no	—
28	C₇⋊D₇	C₃⋊D₃×C₁₉	1	1	yes	characteristic
29	C₄×C₁₉	—	441	1	no	Hall
30	C₃²×C₇	—	2	4	no	—
31	C₃×C₁₉	C₃⋊#5997	1	4	yes	complemented
32	C₇²	C₁₉×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
33	C₃×D₇	—	14	16	no	—
34	C₂×C₁₉	—	49	1	no	—
35	C₃⋊Dic₃	—	49	1	no	Hall
36	C₃×C₇	—	2	16	no	—
37	C₁₉	C₃⋊(C₃⋊#5997)	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₃²	—	49	1	no	—
39	D₇	—	14	4	no	—
40	Dic₃	—	147	4	no	—
41	C₃²	C₁₉×#5997	1	1	yes	characteristic, complemented, Sylow
42	C₇	—	2	4	no	—
43	C₂×C₃	—	49	4	no	—
44	C₄	—	441	1	no	Sylow
45	C₃	C₁₉×C₃⋊#5997	1	4	yes	complemented
46	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊(C₃⋊#5997)
commutator, hypocenter	C₃²×C₇²	C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₉	C₄
prime radical	C₃²×C₁₉×C₇⋊D₇	C₂
cosocle	C₃²×C₇⋊D₇	C₂×C₁₉
LCS	G ▷ C₃²×C₇²
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
3. C₃²×C₇²×C₁₉	C₄	semidirect
6. C₃×C₇²×C₁₉	Dic₃	semidirect
9. C₃⋊(C₃⋊#5997)	C₁₉	direct (N × H)
11. C₇²×C₁₉	C₃⋊Dic₃	semidirect
16. C₃²×C₇²	C₄×C₁₉	semidirect
23. C₃²×C₁₉	#5997	semidirect
24. C₃×C₇²	Dic₃×C₁₉	semidirect
31. C₃×C₁₉	C₃⋊#5997	semidirect
32. C₇²	C₁₉×C₃⋊Dic₃	semidirect
37. C₁₉	C₃⋊(C₃⋊#5997)	direct (N × H)
41. C₃²	C₁₉×#5997	semidirect
45. C₃	C₁₉×C₃⋊#5997	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₁₉×C₇⋊D₇	2
C₁₉×C₃⋊#5997	3
C₃⋊(C₃⋊#5997)	19
C₁₉×C₃⋊Dic₃	49

Subgroups — C19×C3⋊(C3⋊#5997) #45692726

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₃⋊(C₃⋊#5997) #45692726