Subgroups — C₂×C₄²×#595 #14545209

Order 2176.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×#595	C₂	1	6	yes	maximal
2	C₄²×#595	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄²×D₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂³×#595	C₂²	1	4	yes	—
5	C₂²×C₄×D₁₇	C₂²	1	3	yes	—
6	C₂×C₄×#595	C₄	1	48	yes	direct product factor
7	C₂×C₄×#595	C₂²	1	24	yes	—
8	C₂×C₄²×C₁₇	C₄	1	1	yes	characteristic, complemented
9	C₂×C₄×Dic₁₇	C₄	1	3	yes	complemented
10	C₄²×D₁₇	C₄	1	4	yes	complemented
11	C₄²×D₁₇	C₂²	1	4	yes	—
12	C₂³×D₁₇	C₂³	1	1	yes	characteristic
13	C₂²×#595	C₂×C₄	1	48	yes	—
14	C₂²×#595	C₂³	1	8	yes	—
15	C₂²×C₄×C₁₇	C₂×C₄	1	3	yes	—
16	C₂²×Dic₁₇	C₂×C₄	1	3	yes	—
17	C₂×C₄×D₁₇	C₂×C₄	1	6	yes	—
18	C₂×C₄×D₁₇	C₂×C₄	1	24	yes	—
19	C₂×C₄×D₁₇	C₂³	1	6	yes	—
20	C₄×#595	C₂×C₄	1	96	yes	direct product factor
21	C₄²×C₁₇	C₂×C₄	1	4	yes	complemented
22	C₄×Dic₁₇	C₂×C₄	1	12	yes	complemented
23	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
24	C₂²×D₁₇	C₂²×C₄	1	1	yes	characteristic
25	C₂²×D₁₇	C₂²×C₄	1	12	yes	—
26	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
27	C₂×#595	C₄²	1	64	yes	direct product factor
28	C₂×#595	C₂²×C₄	1	48	yes	—
29	C₂×C₄×C₁₇	C₄²	1	12	yes	complemented
30	C₂×C₄×C₁₇	C₂²×C₄	1	6	yes	—
31	C₂×Dic₁₇	C₄²	1	12	yes	complemented
32	C₂×Dic₁₇	C₂²×C₄	1	6	yes	—
33	C₄×D₁₇	C₄²	1	24	yes	complemented
34	C₄×D₁₇	C₂²×C₄	1	24	yes	—
35	C₂×C₄³	—	17	1	no	maximal, Sylow
36	C₂²×C₁₇	C₂×C₄²	1	6	yes	—
37	C₂²×C₁₇	C₂³×C₄	1	1	yes	characteristic
38	C₂×D₁₇	C₂×C₄²	1	6	yes	—
39	C₂×D₁₇	C₂×C₄²	1	16	yes	—
40	C₂×D₁₇	C₂³×C₄	1	6	yes	—
41	#595	C₂×C₄²	1	32	yes	direct product factor
42	C₄×C₁₇	C₂×C₄²	1	12	yes	complemented
43	Dic₁₇	C₂×C₄²	1	12	yes	complemented
44	C₂²×C₄²	—	17	6	no	—
45	C₂²×C₄²	—	17	1	no	—
46	C₄³	—	17	8	no	—
47	C₂×C₁₇	C₄³	1	4	yes	complemented
48	C₂×C₁₇	C₂²×C₄²	1	3	yes	—
49	D₁₇	C₄³	1	4	yes	complemented
50	D₁₇	C₂²×C₄²	1	4	yes	—
51	C₂³×C₄	—	17	4	no	—
52	C₂³×C₄	—	17	3	no	—
53	C₂×C₄²	—	17	48	no	—
54	C₂×C₄²	—	17	24	no	—
55	C₂×C₄²	—	17	3	no	—
56	C₂×C₄²	—	17	4	no	—
57	C₂×C₄²	—	17	4	no	—
58	C₂×C₄²	#595	1	1	yes	characteristic, direct product factor
59	C₁₇	C₂×C₄³	1	1	yes	characteristic, complemented, Sylow
60	C₂⁴	—	17	1	no	—
61	C₂²×C₄	—	17	48	no	—
62	C₂²×C₄	—	17	8	no	—
63	C₂²×C₄	—	17	3	no	—
64	C₂²×C₄	—	17	24	no	—
65	C₂²×C₄	—	17	6	no	—
66	C₂²×C₄	—	17	6	no	—
67	C₂²×C₄	C₂×#595	1	3	yes	—
68	C₄²	—	17	96	no	—
69	C₄²	—	17	12	no	—
70	C₄²	C₂×#595	1	4	yes	direct product factor
71	C₂³	—	17	12	no	—
72	C₂³	—	17	1	no	—
73	C₂³	—	17	1	no	—
74	C₂³	C₂²×#595	1	1	yes	characteristic
75	C₂×C₄	—	17	48	no	—
76	C₂×C₄	—	17	64	no	—
77	C₂×C₄	—	17	12	no	—
78	C₂×C₄	—	17	6	no	—
79	C₂×C₄	—	17	24	no	—
80	C₂×C₄	—	17	24	no	—
81	C₂×C₄	C₄×#595	1	12	yes	direct product factor
82	C₂×C₄	C₂²×#595	1	6	yes	—
83	C₂²	—	17	16	no	—
84	C₂²	—	17	6	no	—
85	C₂²	—	17	6	no	—
86	C₂²	C₂×C₄×#595	1	6	yes	—
87	C₂²	C₂³×#595	1	1	yes	characteristic
88	C₄	—	17	32	no	—
89	C₄	—	17	12	no	—
90	C₄	C₂×C₄×#595	1	12	yes	direct product factor
91	C₂	—	17	4	no	—
92	C₂	—	17	4	no	—
93	C₂	C₄²×#595	1	4	yes	direct product factor
94	C₂	C₂²×C₄×#595	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₄²	#595
commutator, hypocenter	C₁₇	C₂×C₄³
Frattini	C₂²	C₂³×#595
Fitting	C₂×C₄²×C₁₇	C₄
socle	C₂³×C₁₇	C₂²×C₄
prime radical	C₂³×D₁₇	C₂³
cosocle	C₂²×D₁₇	C₂⁴
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₄²×#595	C₂	direct (N × H)
6. C₂×C₄×#595	C₄	direct (N × H)
8. C₂×C₄²×C₁₇	C₄	semidirect
9. C₂×C₄×Dic₁₇	C₄	semidirect
10. C₄²×D₁₇	C₄	semidirect
20. C₄×#595	C₂×C₄	direct (N × H)
21. C₄²×C₁₇	C₂×C₄	semidirect
22. C₄×Dic₁₇	C₂×C₄	semidirect
27. C₂×#595	C₄²	direct (N × H)
29. C₂×C₄×C₁₇	C₄²	semidirect
31. C₂×Dic₁₇	C₄²	semidirect
33. C₄×D₁₇	C₄²	semidirect
41. #595	C₂×C₄²	direct (N × H)
42. C₄×C₁₇	C₂×C₄²	semidirect
43. Dic₁₇	C₂×C₄²	semidirect
47. C₂×C₁₇	C₄³	semidirect
49. D₁₇	C₄³	semidirect
58. C₂×C₄²	#595	direct (N × H)
59. C₁₇	C₂×C₄³	semidirect
70. C₄²	C₂×#595	direct (N × H)
81. C₂×C₄	C₄×#595	direct (N × H)
90. C₄	C₂×C₄×#595	direct (N × H)
93. C₂	C₄²×#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
C₂²×C₄×#595	2
C₄²×#595	2
C₂×C₄²×D₁₇	2
C₂×C₄³	17

Subgroups — C2×C42×#595 #14545209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄²×#595 #14545209