Subgroups — C₄²×#3633 #14545916

Order 2176.

408 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#3633	C₂	1	6	yes	maximal
2	C₄²×#595	C₂	1	1	yes	maximal, characteristic
3	C₂²×#3633	C₂²	1	4	yes	—
4	C₂×C₄×#595	C₄	1	3	yes	—
5	C₂×C₄×#595	C₂²	1	3	yes	—
6	C₄×#3633	C₄	1	24	yes	direct product factor
7	C₄²×D₁₇	C₄	1	1	yes	characteristic
8	C₂²×#595	C₂×C₄	1	3	yes	—
9	C₂²×#595	C₂³	1	1	yes	characteristic
10	C₂×#3633	C₂×C₄	1	24	yes	—
11	C₂×C₄×D₁₇	C₂×C₄	1	3	yes	—
12	C₄×#595	C₈	1	12	yes	complemented
13	C₄×#595	C₂×C₄	1	12	yes	—
14	C₄²×C₁₇	C₈	1	1	yes	characteristic, complemented
15	C₄×Dic₁₇	C₈	1	3	yes	complemented
16	C₂²×D₁₇	C₂²×C₄	1	1	yes	characteristic
17	C₂×#595	C₄²	1	6	yes	—
18	C₂×#595	C₂×C₈	1	12	yes	—
19	C₂×#595	C₂²×C₄	1	6	yes	—
20	#3633	C₄²	1	16	yes	direct product factor
21	C₂×C₄×C₁₇	C₂×C₈	1	3	yes	—
22	C₂×Dic₁₇	C₂×C₈	1	3	yes	—
23	C₄×D₁₇	C₄²	1	6	yes	—
24	C₄×D₁₇	C₂×C₈	1	6	yes	—
25	C₄²×C₈	—	17	1	no	maximal, Sylow
26	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
27	C₂×D₁₇	C₂×C₄²	1	3	yes	—
28	C₂×D₁₇	C₂²×C₈	1	3	yes	—
29	#595	C₄×C₈	1	12	yes	complemented
30	#595	C₂×C₄²	1	4	yes	—
31	C₄×C₁₇	C₄×C₈	1	6	yes	complemented
32	Dic₁₇	C₄×C₈	1	6	yes	complemented
33	C₂×C₄×C₈	—	17	6	no	—
34	C₄³	—	17	1	no	—
35	C₂×C₁₇	C₂×C₄×C₈	1	3	yes	—
36	D₁₇	C₄³	1	1	yes	characteristic
37	D₁₇	C₂×C₄×C₈	1	3	yes	—
38	C₂²×C₈	—	17	4	no	—
39	C₂×C₄²	—	17	3	no	—
40	C₂×C₄²	—	17	3	no	—
41	C₂×C₄²	—	17	1	no	—
42	C₄×C₈	—	17	24	no	—
43	C₁₇	C₄²×C₈	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₄	—	17	3	no	—
45	C₂²×C₄	—	17	1	no	—
46	C₂²×C₄	—	17	3	no	—
47	C₂×C₈	—	17	24	no	—
48	C₄²	—	17	12	no	—
49	C₄²	—	17	12	no	—
50	C₄²	—	17	3	no	—
51	C₄²	#3633	1	1	yes	characteristic, direct product factor
52	C₂³	—	17	1	no	—
53	C₂×C₄	—	17	6	no	—
54	C₂×C₄	—	17	6	no	—
55	C₂×C₄	—	17	12	no	—
56	C₂×C₄	—	17	3	no	—
57	C₂×C₄	—	17	6	no	—
58	C₂×C₄	—	17	6	no	—
59	C₂×C₄	C₂×#3633	1	3	yes	—
60	C₈	—	17	16	no	—
61	C₂²	—	17	3	no	—
62	C₂²	—	17	3	no	—
63	C₂²	C₂²×#3633	1	1	yes	characteristic
64	C₄	—	17	4	no	—
65	C₄	—	17	12	no	—
66	C₄	—	17	6	no	—
67	C₄	C₄×#3633	1	6	yes	direct product factor
68	C₂	—	17	1	no	—
69	C₂	—	17	3	no	—
70	C₂	C₂×C₄×#3633	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₄²	#3633
commutator, hypocenter	C₁₇	C₄²×C₈
Frattini	C₂²	C₂²×#3633
Fitting	C₄²×C₁₇	C₈
socle	C₂²×C₁₇	C₂²×C₈
prime radical	C₂²×D₁₇	C₂²×C₄
cosocle	C₂²×#595	C₂³
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₄²

Complements

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

N	H ≅ G/N	type
6. C₄×#3633	C₄	direct (N × H)
12. C₄×#595	C₈	semidirect
14. C₄²×C₁₇	C₈	semidirect
15. C₄×Dic₁₇	C₈	semidirect
20. #3633	C₄²	direct (N × H)
29. #595	C₄×C₈	semidirect
31. C₄×C₁₇	C₄×C₈	semidirect
32. Dic₁₇	C₄×C₈	semidirect
43. C₁₇	C₄²×C₈	semidirect
51. C₄²	#3633	direct (N × H)
67. C₄	C₄×#3633	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×#3633	2
C₄²×#595	2
C₄²×C₈	17

Subgroups — C42×#3633 #14545916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×#3633 #14545916