Subgroups — C₂×C₈×#3624 #14543975

Order 2176.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂²×C₈	#595
commutator, hypocenter	C₁₇	C₂×C₈²
Frattini	C₂×C₄	C₂²×#595
Fitting	C₂²×C₈×C₁₇	C₄
socle, prime radical	C₂³×C₁₇	C₄²
cosocle	C₄×Dic₁₇	C₂³
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₈×#3624	C₂	direct (N × H)
14. C₂×#3624	C₈	direct (N × H)
16. C₂×C₈×C₁₇	C₈	semidirect
21. C₂×#3622	C₈	semidirect
31. #3624	C₂×C₈	direct (N × H)
32. C₈×C₁₇	C₂×C₈	semidirect
33. #3622	C₂×C₈	semidirect
46. C₂×C₁₇	C₈²	semidirect
57. C₁₇	C₂×C₈²	semidirect
64. C₂×C₈	#3624	direct (N × H)
79. C₈	C₂×#3624	direct (N × H)
88. C₂	C₈×#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
C₈×#3624	2
C₂×C₈×Dic₁₇	2
C₂×C₈²	17

Subgroups — C2×C8×#3624 #14543975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×#3624 #14543975