Subgroups — C₈×Dic₂₀₆ #20267916

Order 6592.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₂₀₆	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₁₀₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	Dic₁₀₃⋊C₈	C₂	1	2	yes	maximal
4	C₈×Dic₁₀₃	C₂	1	2	yes	maximal
5	C₄×C₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₀₆	C₄	1	1	yes	characteristic
7	C₂×C₁₀₃⋊C₈	C₂²	1	2	yes	—
8	C₄⋊Dic₁₀₃	C₄	1	1	yes	characteristic
9	Dic₁₀₃⋊C₄	C₄	1	2	yes	—
10	C₄×Dic₁₀₃	C₂²	1	2	yes	—
11	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
13	C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
17	C₂×Dic₁₀₃	C₂×C₄	1	2	yes	—
18	C₂×Dic₁₀₃	C₂×C₄	1	2	yes	—
19	Dic₂₀₆	C₈	1	4	yes	direct product factor
20	C₈×C₁₀₃	—	2	1	no	—
21	C₈×C₁₀₃	Q₈	1	2	yes	complemented
22	C₁₀₃⋊C₈	—	2	2	no	—
23	C₂²×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₁₀₃	—	2	1	no	—
25	C₄×C₁₀₃	C₂×C₈	1	2	yes	—
26	C₄×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
27	C₄×C₁₀₃	#41	1	1	yes	characteristic
28	Dic₁₀₃	—	2	2	no	—
29	Dic₁₀₃	C₂×C₈	1	4	yes	—
30	C₂×C₁₀₃	C₄×Q₈	1	1	yes	characteristic
31	C₂×C₁₀₃	C₂²×C₈	1	1	yes	characteristic
32	C₂×C₁₀₃	#131	1	1	yes	characteristic
33	C₁₀₃	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
34	C₈×Q₈	—	103	1	no	maximal, Sylow
35	C₄×Q₈	—	103	1	no	—
36	C₄⋊C₈	—	103	2	no	—
37	C₄⋊C₈	—	103	1	no	—
38	C₄×C₈	—	103	2	no	—
39	C₄×C₈	D₁₀₃	1	1	yes	characteristic
40	C₂×Q₈	—	103	1	no	—
41	C₂×C₈	—	103	2	no	—
42	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
43	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
44	C₄⋊C₄	—	103	2	no	—
45	C₄⋊C₄	—	103	1	no	—
46	C₄²	—	103	2	no	—
47	C₄²	C₂×D₁₀₃	1	1	yes	characteristic
48	Q₈	—	103	4	no	—
49	C₂×C₄	—	103	2	no	—
50	C₂×C₄	—	103	2	no	—
51	C₂×C₄	C₄×D₁₀₃	1	1	yes	characteristic
52	C₂×C₄	C₄×D₁₀₃	1	1	yes	characteristic
53	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
54	C₈	—	2	1	no	—
55	C₈	—	206	2	no	—
56	C₈	Dic₂₀₆	1	2	yes	direct product factor
57	C₂²	C₂×C₄×D₁₀₃	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	103	4	no	—
60	C₄	—	206	2	no	—
61	C₄	C₈×D₁₀₃	1	2	yes	—
62	C₄	C₂×Dic₂₀₆	1	1	yes	characteristic
63	C₄	#13110105	1	1	yes	characteristic
64	C₂	C₄×Dic₂₀₆	1	1	yes	characteristic
65	C₂	C₂×C₈×D₁₀₃	1	1	yes	characteristic
66	C₂	#15693027	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₁₀₃
commutator	C₂×C₁₀₃	C₂²×C₈
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	C₄×C₈×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂²×C₄
hypercenter	C₄×C₈	D₁₀₃
hypocenter	C₁₀₃	C₈×Q₈
LCS	G ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
19. Dic₂₀₆	C₈	direct (N × H)
21. C₈×C₁₀₃	Q₈	semidirect
33. C₁₀₃	C₈×Q₈	semidirect
56. C₈	Dic₂₀₆	direct (N × H)

Subgroups — C8×Dic206 #20267916

Conjugacy classes of subgroups

Complements

Subgroups — C₈×Dic₂₀₆ #20267916