Subgroups — C₈²×#595 #17950260

Order 4352.

750 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×#595	C₂	1	3	yes	maximal
2	C₈×#63242	C₂	1	3	yes	maximal
3	C₈²×D₁₇	C₂	1	1	yes	maximal, characteristic
4	C₄×#63242	C₂²	1	3	yes	—
5	C₂×C₈×#595	C₄	1	12	yes	—
6	C₄²×#595	C₂²	1	1	yes	characteristic
7	C₈×#3624	C₄	1	12	yes	complemented
8	C₄×C₈×D₁₇	C₂²	1	3	yes	—
9	C₈×#3622	C₄	1	3	yes	complemented
10	C₈²×C₁₇	C₄	1	1	yes	characteristic, complemented
11	C₂×C₄×#595	C₂×C₄	1	6	yes	—
12	C₂×#63242	C₂×C₄	1	6	yes	—
13	C₂×C₈×D₁₇	C₂×C₄	1	6	yes	—
14	C₄²×D₁₇	C₂³	1	1	yes	characteristic
15	C₄×#3624	C₂×C₄	1	12	yes	—
16	C₈×#595	C₈	1	48	yes	direct product factor
17	C₄×C₈×C₁₇	C₂×C₄	1	3	yes	—
18	C₈×Dic₁₇	C₂×C₄	1	6	yes	—
19	C₄×#3622	C₂×C₄	1	3	yes	—
20	C₂²×#595	C₄²	1	4	yes	—
21	C₂×C₄×D₁₇	C₂²×C₄	1	3	yes	—
22	C₂×#3624	C₄²	1	12	yes	—
23	C₄×#595	C₂×C₈	1	24	yes	—
24	#63242	C₂×C₈	1	24	yes	—
25	C₂×C₈×C₁₇	C₄²	1	6	yes	—
26	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
27	C₄×Dic₁₇	C₂²×C₄	1	3	yes	—
28	C₂×#3622	C₄²	1	6	yes	—
29	C₈×D₁₇	C₂×C₈	1	24	yes	—
30	C₄×C₈²	—	17	1	no	maximal, Sylow
31	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
32	C₂×#595	C₄×C₈	1	24	yes	—
33	C₂×C₄×C₁₇	C₂×C₄²	1	3	yes	—
34	C₂×Dic₁₇	C₂×C₄²	1	3	yes	—
35	C₄×D₁₇	C₂²×C₈	1	12	yes	—
36	#3624	C₄×C₈	1	24	yes	complemented
37	C₈×C₁₇	C₄×C₈	1	12	yes	complemented
38	#3622	C₄×C₈	1	12	yes	complemented
39	C₄²×C₈	—	17	3	no	—
40	C₂×C₈²	—	17	3	no	—
41	C₂×C₈²	—	17	1	no	—
42	C₂²×C₁₇	C₄³	1	1	yes	characteristic
43	C₂×D₁₇	C₂×C₄×C₈	1	6	yes	—
44	#595	C₈²	1	16	yes	direct product factor
45	C₄×C₁₇	C₂×C₄×C₈	1	6	yes	—
46	Dic₁₇	C₂×C₄×C₈	1	6	yes	—
47	C₂×C₄×C₈	—	17	12	no	—
48	C₂×C₄×C₈	—	17	3	no	—
49	C₂×C₄×C₈	—	17	3	no	—
50	C₄³	—	17	1	no	—
51	C₈²	—	17	12	no	—
52	C₈²	—	17	3	no	—
53	C₈²	#595	1	1	yes	characteristic, direct product factor
54	C₂×C₁₇	C₄²×C₈	1	3	yes	—
55	D₁₇	C₂×C₈²	1	4	yes	—
56	C₂²×C₈	—	17	6	no	—
57	C₂²×C₈	—	17	6	no	—
58	C₂×C₄²	—	17	6	no	—
59	C₂×C₄²	—	17	1	no	—
60	C₄×C₈	—	17	12	no	—
61	C₄×C₈	—	17	48	no	—
62	C₄×C₈	—	17	6	no	—
63	C₄×C₈	—	17	3	no	—
64	C₄×C₈	C₂×#595	1	3	yes	—
65	C₁₇	C₄×C₈²	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₄	—	17	4	no	—
67	C₂²×C₄	—	17	3	no	—
68	C₂×C₈	—	17	24	no	—
69	C₂×C₈	—	17	12	no	—
70	C₂×C₈	—	17	6	no	—
71	C₂×C₈	—	17	24	no	—
72	C₂×C₈	C₄×#595	1	6	yes	—
73	C₄²	—	17	24	no	—
74	C₄²	—	17	3	no	—
75	C₄²	C₂²×#595	1	1	yes	characteristic
76	C₂³	—	17	1	no	—
77	C₂×C₄	—	17	24	no	—
78	C₂×C₄	—	17	3	no	—
79	C₂×C₄	—	17	12	no	—
80	C₂×C₄	C₂×C₄×#595	1	3	yes	—
81	C₈	—	17	24	no	—
82	C₈	—	17	12	no	—
83	C₈	C₈×#595	1	12	yes	direct product factor
84	C₂²	—	17	6	no	—
85	C₂²	C₄²×#595	1	1	yes	characteristic
86	C₄	—	17	16	no	—
87	C₄	—	17	6	no	—
88	C₄	C₂×C₈×#595	1	6	yes	—
89	C₂	—	17	4	no	—
90	C₂	C₄×C₈×#595	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₈²	#595
commutator, hypocenter	C₁₇	C₄×C₈²
Frattini	C₄²	C₂²×#595
Fitting	C₈²×C₁₇	C₄
socle	C₂²×C₁₇	C₄³
prime radical	C₂²×D₁₇	C₂×C₄²
cosocle	C₄²×D₁₇	C₂³
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₈²

Complements

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

N	H ≅ G/N	type
7. C₈×#3624	C₄	semidirect
9. C₈×#3622	C₄	semidirect
10. C₈²×C₁₇	C₄	semidirect
16. C₈×#595	C₈	direct (N × H)
36. #3624	C₄×C₈	semidirect
37. C₈×C₁₇	C₄×C₈	semidirect
38. #3622	C₄×C₈	semidirect
44. #595	C₈²	direct (N × H)
53. C₈²	#595	direct (N × H)
65. C₁₇	C₄×C₈²	semidirect
83. C₈	C₈×#595	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₈×#595	2
C₈×#63242	2
C₈²×D₁₇	2
C₄×C₈²	17

Subgroups — C82×#595 #17950260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈²×#595 #17950260