Subgroups — C₄²×#3624 #14544436

Order 2176.

408 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#3624	C₂	1	6	yes	maximal
2	C₄²×Dic₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×#3624	C₂²	1	4	yes	—
4	C₂×C₄²×C₁₇	C₄	1	1	yes	characteristic
5	C₂×C₄×Dic₁₇	C₄	1	3	yes	—
6	C₂×C₄×Dic₁₇	C₂²	1	3	yes	—
7	C₄×#3624	C₄	1	24	yes	direct product factor
8	C₂²×C₄×C₁₇	C₂×C₄	1	3	yes	—
9	C₂²×Dic₁₇	C₂×C₄	1	3	yes	—
10	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
11	C₂×#3624	C₂×C₄	1	24	yes	—
12	C₄²×C₁₇	C₈	1	4	yes	complemented
13	C₄×Dic₁₇	C₈	1	12	yes	complemented
14	C₄×Dic₁₇	C₂×C₄	1	12	yes	—
15	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₇	C₄²	1	6	yes	—
17	C₂×C₄×C₁₇	C₂×C₈	1	6	yes	—
18	C₂×C₄×C₁₇	C₂×C₈	1	6	yes	—
19	C₂×Dic₁₇	C₄²	1	6	yes	—
20	C₂×Dic₁₇	C₂×C₈	1	12	yes	—
21	C₂×Dic₁₇	C₂²×C₄	1	6	yes	—
22	#3624	C₄²	1	16	yes	direct product factor
23	C₄²×C₈	—	17	1	no	maximal, Sylow
24	C₂²×C₁₇	C₂×C₄²	1	3	yes	—
25	C₂²×C₁₇	C₂²×C₈	1	3	yes	—
26	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
27	C₄×C₁₇	C₄×C₈	1	12	yes	complemented
28	Dic₁₇	C₄×C₈	1	12	yes	complemented
29	Dic₁₇	C₂×C₄²	1	4	yes	—
30	C₂×C₄×C₈	—	17	6	no	—
31	C₄³	—	17	1	no	—
32	C₂×C₁₇	C₄³	1	1	yes	characteristic
33	C₂×C₁₇	C₂×C₄×C₈	1	3	yes	—
34	C₂×C₁₇	C₂×C₄×C₈	1	3	yes	—
35	C₂²×C₈	—	17	4	no	—
36	C₂×C₄²	—	17	3	no	—
37	C₂×C₄²	—	17	3	no	—
38	C₂×C₄²	#595	1	1	yes	characteristic
39	C₄×C₈	—	17	24	no	—
40	C₁₇	C₄²×C₈	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₄	—	17	3	no	—
42	C₂²×C₄	—	17	1	no	—
43	C₂²×C₄	C₂×#595	1	3	yes	—
44	C₂×C₈	—	17	24	no	—
45	C₄²	—	17	12	no	—
46	C₄²	—	17	12	no	—
47	C₄²	#3624	1	4	yes	direct product factor
48	C₂³	C₂²×#595	1	1	yes	characteristic
49	C₂×C₄	—	17	12	no	—
50	C₂×C₄	—	17	6	no	—
51	C₂×C₄	—	17	6	no	—
52	C₂×C₄	#63242	1	6	yes	—
53	C₂×C₄	C₄×#595	1	6	yes	—
54	C₂×C₄	C₂×#3624	1	6	yes	—
55	C₈	—	17	16	no	—
56	C₂²	C₂×#63242	1	3	yes	—
57	C₂²	C₂×C₄×#595	1	3	yes	—
58	C₂²	C₂²×#3624	1	1	yes	characteristic
59	C₄	—	17	4	no	—
60	C₄	—	17	12	no	—
61	C₄	C₄×#3624	1	12	yes	direct product factor
62	C₂	C₄²×#595	1	1	yes	characteristic
63	C₂	C₂×C₄×#3624	1	3	yes	—
64	C₂	C₄×#63242	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₄²	#595
commutator, hypocenter	C₁₇	C₄²×C₈
Frattini	C₂³	C₂²×#595
Fitting	C₂×C₄²×C₁₇	C₄
socle, prime radical	C₂³×C₁₇	C₂²×C₄
cosocle	C₂²×Dic₁₇	C₂³
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
7. C₄×#3624	C₄	direct (N × H)
12. C₄²×C₁₇	C₈	semidirect
13. C₄×Dic₁₇	C₈	semidirect
22. #3624	C₄²	direct (N × H)
27. C₄×C₁₇	C₄×C₈	semidirect
28. Dic₁₇	C₄×C₈	semidirect
40. C₁₇	C₄²×C₈	semidirect
47. C₄²	#3624	direct (N × H)
61. C₄	C₄×#3624	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×#3624	2
C₄²×Dic₁₇	2
C₄²×C₈	17

Subgroups — C42×#3624 #14544436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×#3624 #14544436