Subgroups — #595×#89205 #44472548

Order 29988.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₇×#89205	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇²×#595	C₃	1	1	yes	maximal, characteristic
3	C₁₇×#89205	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇²×D₁₇	C₂×C₃	1	1	yes	characteristic
5	C₇⋊C₉×#595	—	7	2	no	maximal
6	C₇²×#595	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇²×C₁₇	C₃×C₄	1	1	yes	characteristic
8	D₁₇×C₇⋊C₉	—	7	2	no	—
9	C₄×#89205	—	17	1	no	maximal, Hall
10	C₇²×D₁₇	C₂×C₉	1	1	yes	characteristic
11	C₃×C₇×#595	—	3	2	no	—
12	C₃×C₇×#595	ΓL(1,𝔽₈)	1	2	yes	—
13	C₁₇×C₇⋊C₉	—	7	2	no	—
14	C₂×#89205	—	17	1	no	—
15	C₇²×C₁₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇×D₁₇	—	3	2	no	—
17	C₃×C₇×D₁₇	C₂×ΓL(1,𝔽₈)	1	2	yes	—
18	C₉×#595	—	49	1	no	Hall
19	C₃×C₄×C₇²	—	17	1	no	—
20	C₇×#595	—	3	2	no	—
21	C₇×#595	C₇⋊C₉	1	2	yes	complemented
22	#89205	#595	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₇×C₁₇	—	3	2	no	—
24	C₃×C₇×C₁₇	C₄×ΓL(1,𝔽₈)	1	2	yes	—
25	C₉×D₁₇	—	49	1	no	—
26	C₂×C₃×C₇²	—	17	1	no	—
27	C₄×C₇⋊C₉	—	119	2	no	—
28	C₇×D₁₇	—	3	2	no	—
29	C₇×D₁₇	C₂×C₇⋊C₉	1	2	yes	—
30	C₃×#595	#3862	1	1	yes	characteristic
31	C₄×C₇²	—	17	1	no	Hall
32	C₉×C₁₇	—	49	1	no	Hall
33	C₃×C₇²	C₃×#595	1	1	yes	characteristic
34	C₂×C₇⋊C₉	—	119	2	no	—
35	C₇×C₁₇	—	3	2	no	—
36	C₇×C₁₇	C₄×C₇⋊C₉	1	2	yes	complemented
37	C₃×D₁₇	C₂×#3862	1	1	yes	characteristic
38	C₂×C₇²	—	17	1	no	—
39	C₃×C₄×C₇	—	17	2	no	—
40	C₃×C₄×C₇	—	51	2	no	—
41	#595	#89205	1	1	yes	characteristic, direct product factor, Hall
42	C₇⋊C₉	—	7	2	no	—
43	C₃×C₁₇	C₄×#3862	1	1	yes	characteristic
44	C₇²	C₉×#595	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₃×C₇	—	17	2	no	—
46	C₂×C₃×C₇	—	51	2	no	—
47	C₄×C₉	—	833	1	no	Hall
48	D₁₇	C₂×#89205	1	1	yes	characteristic
49	C₄×C₇	—	17	2	no	—
50	C₄×C₇	—	51	2	no	—
51	C₃×C₇	—	3	2	no	—
52	C₃×C₇	ΓL(1,𝔽₈)×#595	1	2	yes	—
53	C₂×C₉	—	833	1	no	—
54	C₁₇	C₄×#89205	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₇	—	17	2	no	—
56	C₂×C₇	—	51	2	no	—
57	C₃×C₄	—	17	1	no	—
58	C₉	—	49	1	no	Sylow
59	C₇	—	3	2	no	—
60	C₇	C₇⋊C₉×#595	1	2	yes	complemented
61	C₂×C₃	—	17	1	no	—
62	C₄	—	17	1	no	Sylow
63	C₃	#595×#3862	1	1	yes	characteristic
64	C₂	—	17	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	#595×#3862
commutator, hypocenter	C₇²×C₁₇	C₄×C₉
Fitting, socle	C₃×C₇²×C₁₇	C₃×C₄
prime radical, cosocle	C₃×C₇²×D₁₇	C₂×C₃
LCS	G ▷ C₇²×C₁₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
3. C₁₇×#89205	C₄	semidirect
6. C₇²×#595	C₉	semidirect
15. C₇²×C₁₇	C₄×C₉	semidirect
21. C₇×#595	C₇⋊C₉	semidirect
22. #89205	#595	direct (N × H)
36. C₇×C₁₇	C₄×C₇⋊C₉	semidirect
41. #595	#89205	direct (N × H)
44. C₇²	C₉×#595	semidirect
54. C₁₇	C₄×#89205	semidirect
60. C₇	C₇⋊C₉×#595	semidirect

Maximal subgroups

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

subgroup	index
D₁₇×#89205	2
C₃×C₇²×#595	3
C₇⋊C₉×#595	7
C₄×#89205	17