Subgroups — C₂³×C₄×#595 #14545754

Order 2176.

3000 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×#595	C₂	1	2	yes	maximal
2	C₂²×C₄×#595	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₄×D₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂⁴×D₁₇	C₂²	1	1	yes	characteristic
5	C₂³×#595	C₄	1	32	yes	direct product factor
6	C₂³×#595	C₂²	1	28	yes	—
7	C₂³×C₄×C₁₇	C₄	1	1	yes	characteristic, complemented
8	C₂³×Dic₁₇	C₄	1	1	yes	characteristic, complemented
9	C₂²×C₄×D₁₇	C₄	1	14	yes	complemented
10	C₂²×C₄×D₁₇	C₂²	1	14	yes	—
11	C₂×C₄×#595	C₂²	1	112	yes	direct product factor
12	C₂⁴×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₂³×D₁₇	C₂×C₄	1	7	yes	—
14	C₂³×D₁₇	C₂×C₄	1	16	yes	—
15	C₂³×D₁₇	C₂³	1	7	yes	—
16	C₂²×#595	C₂×C₄	1	224	yes	direct product factor
17	C₂²×#595	C₂³	1	56	yes	—
18	C₂²×C₄×C₁₇	C₂×C₄	1	14	yes	complemented
19	C₂²×Dic₁₇	C₂×C₄	1	14	yes	complemented
20	C₂×C₄×D₁₇	C₂×C₄	1	84	yes	complemented
21	C₂×C₄×D₁₇	C₂³	1	28	yes	—
22	C₄×#595	C₂³	1	64	yes	direct product factor
23	C₂³×C₁₇	C₄²	1	8	yes	complemented
24	C₂³×C₁₇	C₂²×C₄	1	7	yes	—
25	C₂²×D₁₇	C₄²	1	56	yes	complemented
26	C₂²×D₁₇	C₂²×C₄	1	21	yes	—
27	C₂²×D₁₇	C₂²×C₄	1	56	yes	—
28	C₂²×D₁₇	C₂⁴	1	7	yes	—
29	C₂×#595	C₂²×C₄	1	224	yes	direct product factor
30	C₂×#595	C₂⁴	1	16	yes	—
31	C₂×C₄×C₁₇	C₂²×C₄	1	28	yes	complemented
32	C₂×Dic₁₇	C₂²×C₄	1	28	yes	complemented
33	C₄×D₁₇	C₂²×C₄	1	56	yes	complemented
34	C₄×D₁₇	C₂⁴	1	8	yes	—
35	C₂³×C₄²	—	17	1	no	maximal, Sylow
36	C₂²×C₁₇	C₂×C₄²	1	28	yes	complemented
37	C₂²×C₁₇	C₂³×C₄	1	7	yes	—
38	C₂×D₁₇	C₂×C₄²	1	84	yes	complemented
39	C₂×D₁₇	C₂³×C₄	1	28	yes	—
40	C₂×D₁₇	C₂³×C₄	1	7	yes	—
41	C₂×D₁₇	C₂⁵	1	1	yes	characteristic
42	#595	C₂³×C₄	1	32	yes	direct product factor
43	C₄×C₁₇	C₂³×C₄	1	8	yes	complemented
44	Dic₁₇	C₂³×C₄	1	8	yes	complemented
45	C₂⁴×C₄	—	17	2	no	—
46	C₂⁴×C₄	—	17	1	no	—
47	C₂²×C₄²	—	17	28	no	—
48	C₂×C₁₇	C₂²×C₄²	1	14	yes	complemented
49	C₂×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
50	D₁₇	C₂²×C₄²	1	14	yes	complemented
51	D₁₇	C₂⁴×C₄	1	2	yes	—
52	C₂⁵	—	17	1	no	—
53	C₂³×C₄	—	17	32	no	—
54	C₂³×C₄	—	17	28	no	—
55	C₂³×C₄	—	17	1	no	—
56	C₂³×C₄	—	17	14	no	—
57	C₂³×C₄	—	17	14	no	—
58	C₂³×C₄	#595	1	1	yes	characteristic, direct product factor
59	C₂×C₄²	—	17	112	no	—
60	C₁₇	C₂³×C₄²	1	1	yes	characteristic, complemented, Sylow
61	C₂⁴	—	17	16	no	—
62	C₂⁴	—	17	7	no	—
63	C₂⁴	—	17	7	no	—
64	C₂⁴	C₂×#595	1	1	yes	characteristic
65	C₂²×C₄	—	17	224	no	—
66	C₂²×C₄	—	17	56	no	—
67	C₂²×C₄	—	17	14	no	—
68	C₂²×C₄	—	17	84	no	—
69	C₂²×C₄	—	17	28	no	—
70	C₂²×C₄	C₂×#595	1	14	yes	direct product factor
71	C₄²	—	17	64	no	—
72	C₂³	—	17	56	no	—
73	C₂³	—	17	56	no	—
74	C₂³	—	17	7	no	—
75	C₂³	—	17	21	no	—
76	C₂³	C₄×#595	1	8	yes	direct product factor
77	C₂³	C₂²×#595	1	7	yes	—
78	C₂×C₄	—	17	16	no	—
79	C₂×C₄	—	17	224	no	—
80	C₂×C₄	—	17	28	no	—
81	C₂×C₄	—	17	8	no	—
82	C₂×C₄	—	17	56	no	—
83	C₂×C₄	C₂²×#595	1	28	yes	direct product factor
84	C₂²	—	17	28	no	—
85	C₂²	—	17	84	no	—
86	C₂²	—	17	1	no	—
87	C₂²	—	17	7	no	—
88	C₂²	C₂×C₄×#595	1	28	yes	direct product factor
89	C₂²	C₂³×#595	1	7	yes	—
90	C₄	—	17	32	no	—
91	C₄	—	17	8	no	—
92	C₄	C₂³×#595	1	8	yes	direct product factor
93	C₂	—	17	2	no	—
94	C₂	—	17	14	no	—
95	C₂	C₂²×C₄×#595	1	14	yes	direct product factor
96	C₂	C₂⁴×#595	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₄	#595
commutator, hypocenter	C₁₇	C₂³×C₄²
Frattini	C₂	C₂⁴×#595
Fitting	C₂³×C₄×C₁₇	C₄
socle	C₂⁴×C₁₇	C₂×C₄
prime radical	C₂⁴×D₁₇	C₂²
cosocle	C₂×D₁₇	C₂⁵
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×#595	C₂	direct (N × H)
5. C₂³×#595	C₄	direct (N × H)
7. C₂³×C₄×C₁₇	C₄	semidirect
8. C₂³×Dic₁₇	C₄	semidirect
9. C₂²×C₄×D₁₇	C₄	semidirect
11. C₂×C₄×#595	C₂²	direct (N × H)
16. C₂²×#595	C₂×C₄	direct (N × H)
18. C₂²×C₄×C₁₇	C₂×C₄	semidirect
19. C₂²×Dic₁₇	C₂×C₄	semidirect
20. C₂×C₄×D₁₇	C₂×C₄	semidirect
22. C₄×#595	C₂³	direct (N × H)
23. C₂³×C₁₇	C₄²	semidirect
25. C₂²×D₁₇	C₄²	semidirect
29. C₂×#595	C₂²×C₄	direct (N × H)
31. C₂×C₄×C₁₇	C₂²×C₄	semidirect
32. C₂×Dic₁₇	C₂²×C₄	semidirect
33. C₄×D₁₇	C₂²×C₄	semidirect
36. C₂²×C₁₇	C₂×C₄²	semidirect
38. C₂×D₁₇	C₂×C₄²	semidirect
42. #595	C₂³×C₄	direct (N × H)
43. C₄×C₁₇	C₂³×C₄	semidirect
44. Dic₁₇	C₂³×C₄	semidirect
48. C₂×C₁₇	C₂²×C₄²	semidirect
50. D₁₇	C₂²×C₄²	semidirect
58. C₂³×C₄	#595	direct (N × H)
60. C₁₇	C₂³×C₄²	semidirect
70. C₂²×C₄	C₂×#595	direct (N × H)
76. C₂³	C₄×#595	direct (N × H)
83. C₂×C₄	C₂²×#595	direct (N × H)
88. C₂²	C₂×C₄×#595	direct (N × H)
92. C₄	C₂³×#595	direct (N × H)
95. C₂	C₂²×C₄×#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
C₂⁴×#595	2
C₂²×C₄×#595	2
C₂³×C₄×D₁₇	2
C₂³×C₄²	17

Subgroups — C23×C4×#595 #14545754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄×#595 #14545754