Subgroups — C₈×D₁₇₅₆ #43243671

Order 28096.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄₃₉	C₂	1	2	yes	maximal, complemented
2	C₄×D₁₇₅₆	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₄₃₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₄₃₉)⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₄₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₇₅₆	C₄	1	1	yes	characteristic
7	C₂×C₄×D₄₃₉	C₂²	1	2	yes	—
8	C₂×C₄₃₉⋊C₈	C₂²	1	2	yes	—
9	C₈×D₄₃₉	—	2	4	no	—
10	C₄⋊Dic₄₃₉	C₄	1	1	yes	characteristic
11	(C₂×D₄₃₉)⋊C₄	C₄	1	2	yes	—
12	C₂×C₈×C₄₃₉	C₂²	1	1	yes	characteristic
13	C₂×C₈×C₄₃₉	C₂²	1	1	yes	characteristic
14	C₄²×C₄₃₉	C₂²	1	1	yes	characteristic
15	C₂²×D₄₃₉	C₂×C₄	1	2	yes	—
16	D₁₇₅₆	C₈	1	4	yes	direct product factor
17	C₂×Dic₄₃₉	C₂×C₄	1	2	yes	—
18	C₄×D₄₃₉	—	2	2	no	—
19	C₄×D₄₃₉	—	2	2	no	—
20	C₄₃₉⋊C₈	—	2	2	no	—
21	C₂×C₄×C₄₃₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₄₃₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×C₄₃₉	C₂³	1	1	yes	characteristic
24	C₈×C₄₃₉	—	2	1	no	—
25	C₈×C₄₃₉	D₄	1	2	yes	complemented
26	C₂²×C₄₃₉	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₄₃₉	—	2	2	no	—
28	C₂×D₄₃₉	—	2	2	no	—
29	C₂×D₄₃₉	C₂×C₈	1	4	yes	complemented
30	C₄×C₄₃₉	—	2	1	no	—
31	C₄×C₄₃₉	C₂×C₈	1	2	yes	complemented
32	C₄×C₄₃₉	C₂×D₄	1	1	yes	characteristic
33	C₄×C₄₃₉	#41	1	1	yes	characteristic
34	Dic₄₃₉	—	2	2	no	—
35	C₂×C₄₃₉	C₄×D₄	1	1	yes	characteristic
36	C₂×C₄₃₉	C₂²×C₈	1	1	yes	characteristic
37	C₂×C₄₃₉	#131	1	1	yes	characteristic
38	D₄₃₉	—	2	4	no	—
39	C₄₃₉	C₈×D₄	1	1	yes	characteristic, complemented, Sylow
40	C₈×D₄	—	439	1	no	maximal, Sylow
41	C₂²×C₈	—	439	2	no	—
42	C₄×D₄	—	439	1	no	—
43	C₄⋊C₈	—	439	1	no	—
44	C₂²⋊C₈	—	439	2	no	—
45	C₄×C₈	D₄₃₉	1	1	yes	characteristic, complemented
46	C₂×D₄	—	439	1	no	—
47	C₂²×C₄	—	439	2	no	—
48	C₂×C₈	—	878	4	no	—
49	C₂×C₈	—	439	2	no	—
50	C₂×C₈	C₂×D₄₃₉	1	1	yes	characteristic
51	C₂×C₈	C₂×D₄₃₉	1	1	yes	characteristic
52	C₄⋊C₄	—	439	1	no	—
53	C₂²⋊C₄	—	439	2	no	—
54	C₄²	C₂×D₄₃₉	1	1	yes	characteristic
55	C₂³	—	439	2	no	—
56	D₄	—	439	4	no	—
57	C₂×C₄	—	878	2	no	—
58	C₂×C₄	—	878	2	no	—
59	C₂×C₄	—	439	2	no	—
60	C₂×C₄	C₄×D₄₃₉	1	1	yes	characteristic
61	C₂×C₄	C₄×D₄₃₉	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₄₃₉	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	878	2	no	—
65	C₈	D₁₇₅₆	1	2	yes	direct product factor
66	C₂²	—	878	2	no	—
67	C₂²	—	878	2	no	—
68	C₂²	—	439	4	no	—
69	C₂²	C₂×C₄×D₄₃₉	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	878	2	no	—
72	C₄	C₈×D₄₃₉	1	2	yes	complemented
73	C₄	C₂×D₁₇₅₆	1	1	yes	characteristic
74	C₄	#20296329	1	1	yes	characteristic
75	C₂	—	878	4	no	—
76	C₂	C₄×D₁₇₅₆	1	1	yes	characteristic
77	C₂	C₂×C₈×D₄₃₉	1	1	yes	characteristic
78	C₂	#28380749	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₄₃₉
commutator	C₂×C₄₃₉	C₂²×C₈
Frattini	C₂×C₄	C₂²×D₄₃₉
Fitting	C₄×C₈×C₄₃₉	C₂
socle	C₂²×C₄₃₉	C₂²×C₄
prime radical	C₂×D₁₇₅₆	C₄
cosocle	C₂×C₄×C₄₃₉	C₂³
hypercenter	C₄×C₈	D₄₃₉
hypocenter	C₄₃₉	C₈×D₄
LCS	G ▷ C₂×C₄₃₉ ▷ C₄₃₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×D₄₃₉	C₂	semidirect
3. C₄⋊(C₄₃₉⋊C₈)	C₂	semidirect
4. (C₂×D₄₃₉)⋊C₈	C₂	semidirect
5. C₄×C₈×C₄₃₉	C₂	semidirect
16. D₁₇₅₆	C₈	direct (N × H)
25. C₈×C₄₃₉	D₄	semidirect
29. C₂×D₄₃₉	C₂×C₈	semidirect
31. C₄×C₄₃₉	C₂×C₈	semidirect
39. C₄₃₉	C₈×D₄	semidirect
45. C₄×C₈	D₄₃₉	semidirect
65. C₈	D₁₇₅₆	direct (N × H)
72. C₄	C₈×D₄₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₄₃₉	2
C₄×D₁₇₅₆	2
C₄⋊(C₄₃₉⋊C₈)	2
(C₂×D₄₃₉)⋊C₈	2
C₄×C₈×C₄₃₉	2
C₈×D₄	439

Subgroups — C8×D1756 #43243671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×D₁₇₅₆ #43243671