Subgroups — C₉×C₁₇×#5997 #44472589

Order 29988.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₇×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₇×#5997	C₃	1	1	yes	maximal, characteristic
3	C₇²×C₉×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₇×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
5	C₁₇×#5997	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₇²×C₁₇	C₃×C₄	1	1	yes	characteristic
7	C₉×D₇×C₁₇	—	14	4	no	—
8	C₉×#5997	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₇×C₇⋊D₇	C₂×C₉	1	1	yes	characteristic
10	C₇×C₉×C₁₇	—	2	4	no	—
11	C₉×C₇⋊D₇	C₂×C₁₇	1	1	yes	characteristic
12	C₇²×C₁₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	C₃×D₇×C₁₇	—	14	4	no	—
14	C₄×C₉×C₁₇	—	49	1	no	maximal, Hall
15	C₃×#5997	C₃×C₁₇	1	1	yes	characteristic
16	C₇²×C₉	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇×C₁₇	—	2	4	no	—
18	C₂×C₉×C₁₇	—	49	1	no	—
19	C₃×C₇⋊D₇	C₂×C₃×C₁₇	1	1	yes	characteristic
20	D₇×C₁₇	—	14	4	no	—
21	C₃×C₄×C₁₇	—	49	1	no	—
22	#5997	C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
23	C₉×C₁₇	#5997	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₇²	C₃×C₄×C₁₇	1	1	yes	characteristic
25	C₉×D₇	—	14	4	no	—
26	C₇×C₁₇	—	2	4	no	—
27	C₂×C₃×C₁₇	—	49	1	no	—
28	C₇⋊D₇	C₂×C₉×C₁₇	1	1	yes	characteristic
29	C₄×C₁₇	—	49	1	no	Hall
30	C₇×C₉	—	2	4	no	—
31	C₃×C₁₇	C₃×#5997	1	1	yes	characteristic
32	C₇²	C₄×C₉×C₁₇	1	1	yes	characteristic, complemented, Sylow
33	C₃×D₇	—	14	4	no	—
34	C₄×C₉	—	49	1	no	Hall
35	C₂×C₁₇	—	49	1	no	—
36	C₃×C₇	—	2	4	no	—
37	C₂×C₉	—	49	1	no	—
38	C₁₇	C₉×#5997	1	1	yes	characteristic, direct product factor, Sylow
39	D₇	—	14	4	no	—
40	C₃×C₄	—	49	1	no	—
41	C₉	C₁₇×#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×C₁₇×#5997	1	1	yes	characteristic
46	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₉×C₁₇	#5997
commutator, hypocenter	C₇²	C₄×C₉×C₁₇
Frattini	C₃	C₃×C₁₇×#5997
Fitting	C₇²×C₉×C₁₇	C₄
socle	C₃×C₇²×C₁₇	C₃×C₄
prime radical	C₃×C₁₇×C₇⋊D₇	C₂×C₃
cosocle	C₃×C₇⋊D₇	C₂×C₃×C₁₇
LCS	G ▷ C₇²
UCS	C₁ ◁ C₉×C₁₇

Complements

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

N	H ≅ G/N	type
3. C₇²×C₉×C₁₇	C₄	semidirect
5. C₁₇×#5997	C₉	direct (N × H)
8. C₉×#5997	C₁₇	direct (N × H)
12. C₇²×C₁₇	C₄×C₉	semidirect
16. C₇²×C₉	C₄×C₁₇	semidirect
22. #5997	C₉×C₁₇	direct (N × H)
23. C₉×C₁₇	#5997	direct (N × H)
32. C₇²	C₄×C₉×C₁₇	semidirect
38. C₁₇	C₉×#5997	direct (N × H)
41. C₉	C₁₇×#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×C₁₇×C₇⋊D₇	2
C₃×C₁₇×#5997	3
C₉×#5997	17
C₄×C₉×C₁₇	49

Subgroups — C9×C17×#5997 #44472589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₁₇×#5997 #44472589