Subgroups — C₉×C₁₉×#5997 #45691666

Order 33516.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₉×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₉×#5997	C₃	1	1	yes	maximal, characteristic
3	C₇²×C₉×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₉×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
5	C₁₉×#5997	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic
7	C₉×D₇×C₁₉	—	14	4	no	—
8	C₁₉×C₇⋊D₇	C₂×C₉	1	1	yes	characteristic
9	C₉×#5997	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₇×C₉×C₁₉	—	2	4	no	—
11	C₇²×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
12	C₉×C₇⋊D₇	C₂×C₁₉	1	1	yes	characteristic
13	C₃×D₇×C₁₉	—	14	4	no	—
14	C₄×C₉×C₁₉	—	49	1	no	maximal, Hall
15	C₃×#5997	C₃×C₁₉	1	1	yes	characteristic
16	C₇²×C₉	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇×C₁₉	—	2	4	no	—
18	C₂×C₉×C₁₉	—	49	1	no	—
19	C₃×C₇⋊D₇	C₂×C₃×C₁₉	1	1	yes	characteristic
20	D₇×C₁₉	—	14	4	no	—
21	C₃×C₄×C₁₉	—	49	1	no	—
22	#5997	C₉×C₁₉	1	1	yes	characteristic, direct product factor, Hall
23	C₉×C₁₉	#5997	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₇²	C₃×C₄×C₁₉	1	1	yes	characteristic
25	C₇×C₁₉	—	2	4	no	—
26	C₉×D₇	—	14	4	no	—
27	C₂×C₃×C₁₉	—	49	1	no	—
28	C₇⋊D₇	C₂×C₉×C₁₉	1	1	yes	characteristic
29	C₄×C₁₉	—	49	1	no	Hall
30	C₇×C₉	—	2	4	no	—
31	C₃×C₁₉	C₃×#5997	1	1	yes	characteristic
32	C₇²	C₄×C₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
33	C₃×D₇	—	14	4	no	—
34	C₂×C₁₉	—	49	1	no	—
35	C₄×C₉	—	49	1	no	Hall
36	C₃×C₇	—	2	4	no	—
37	C₁₉	C₉×#5997	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₉	—	49	1	no	—
39	D₇	—	14	4	no	—
40	C₃×C₄	—	49	1	no	—
41	C₉	C₁₉×#5997	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	—	2	4	no	—
43	C₂×C₃	—	49	1	no	—
44	C₄	—	49	1	no	Sylow
45	C₃	C₃×C₁₉×#5997	1	1	yes	characteristic
46	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₉×C₁₉	#5997
commutator, hypocenter	C₇²	C₄×C₉×C₁₉
Frattini	C₃	C₃×C₁₉×#5997
Fitting	C₇²×C₉×C₁₉	C₄
socle	C₃×C₇²×C₁₉	C₃×C₄
prime radical	C₃×C₁₉×C₇⋊D₇	C₂×C₃
cosocle	C₃×C₇⋊D₇	C₂×C₃×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₉×C₁₉

Complements

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

N	H ≅ G/N	type
3. C₇²×C₉×C₁₉	C₄	semidirect
5. C₁₉×#5997	C₉	direct (N × H)
9. C₉×#5997	C₁₉	direct (N × H)
11. C₇²×C₁₉	C₄×C₉	semidirect
16. C₇²×C₉	C₄×C₁₉	semidirect
22. #5997	C₉×C₁₉	direct (N × H)
23. C₉×C₁₉	#5997	direct (N × H)
32. C₇²	C₄×C₉×C₁₉	semidirect
37. C₁₉	C₉×#5997	direct (N × H)
41. C₉	C₁₉×#5997	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×C₁₉×C₇⋊D₇	2
C₃×C₁₉×#5997	3
C₉×#5997	19
C₄×C₉×C₁₉	49

Subgroups — C9×C19×#5997 #45691666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₁₉×#5997 #45691666