Subgroups — C₄×D₈₅₆ #20292711

Order 6848.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈₅₆	C₂	1	1	yes	maximal, characteristic
2	C₄×D₄₂₈	C₂	1	2	yes	maximal, complemented
3	#16812043	C₂	1	1	yes	maximal, characteristic, complemented
4	#16812031	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄₂₈	C₂²	1	2	yes	—
7	C₂×C₄×D₁₀₇	—	2	2	no	—
8	D₈₅₆	C₄	1	4	yes	direct product factor
9	C₄⋊Dic₁₀₇	C₂²	1	2	yes	—
10	(C₂×D₁₀₇)⋊C₄	—	2	2	no	—
11	C₂×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
13	C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
14	C₂²×D₁₀₇	—	2	2	no	—
15	C₂×C₄×C₁₀₇	D₄	1	1	yes	characteristic
16	C₂×C₄×C₁₀₇	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
18	C₂×Dic₁₀₇	—	2	2	no	—
19	D₄₂₈	—	2	2	no	—
20	D₄₂₈	C₂×C₄	1	4	yes	complemented
21	C₄×D₁₀₇	—	4	4	no	—
22	C₈×C₁₀₇	—	2	1	no	—
23	C₈×C₁₀₇	C₂×C₄	1	2	yes	complemented
24	C₂²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
25	C₂×D₁₀₇	—	2	4	no	—
26	C₂×D₁₀₇	—	4	2	no	—
27	C₂×D₁₀₇	—	4	2	no	—
28	C₄×C₁₀₇	—	2	1	no	—
29	C₄×C₁₀₇	D₈	1	2	yes	complemented
30	C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₁₀₇	#41	1	1	yes	characteristic
32	Dic₁₀₇	—	4	2	no	—
33	C₂×C₁₀₇	C₄×D₄	1	1	yes	characteristic
34	C₂×C₁₀₇	C₂×D₈	1	1	yes	characteristic
35	C₂×C₁₀₇	#135	1	1	yes	characteristic
36	D₁₀₇	—	4	4	no	—
37	C₁₀₇	C₄×D₈	1	1	yes	characteristic, complemented, Sylow
38	C₄×D₈	—	107	1	no	maximal, Sylow
39	C₂×D₈	—	107	1	no	—
40	C₄×D₄	—	107	2	no	—
41	#107	—	107	1	no	—
42	#102	—	107	2	no	—
43	C₄×C₈	D₁₀₇	1	1	yes	characteristic, complemented
44	C₂×D₄	—	107	2	no	—
45	C₂²×C₄	—	214	2	no	—
46	D₈	—	107	4	no	—
47	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
48	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
49	C₄⋊C₄	—	107	2	no	—
50	C₂²⋊C₄	—	214	2	no	—
51	C₄²	C₂×D₁₀₇	1	1	yes	characteristic
52	C₂³	—	214	2	no	—
53	D₄	—	107	4	no	—
54	D₄	—	214	2	no	—
55	C₂×C₄	—	428	4	no	—
56	C₂×C₄	—	214	2	no	—
57	C₂×C₄	D₄₂₈	1	1	yes	characteristic
58	C₂×C₄	D₄₂₈	1	1	yes	characteristic
59	C₂×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
60	C₈	—	2	1	no	—
61	C₈	C₄×D₁₀₇	1	2	yes	complemented
62	C₂²	—	428	2	no	—
63	C₂²	—	428	2	no	—
64	C₂²	—	214	4	no	—
65	C₂²	C₂×D₄₂₈	1	1	yes	characteristic
66	C₄	—	2	1	no	—
67	C₄	—	428	2	no	—
68	C₄	D₈₅₆	1	2	yes	direct product factor
69	C₄	C₂×C₄×D₁₀₇	1	1	yes	characteristic
70	C₄	#13133818	1	1	yes	characteristic
71	C₂	—	428	4	no	—
72	C₂	C₄×D₄₂₈	1	1	yes	characteristic
73	C₂	C₂×D₈₅₆	1	1	yes	characteristic
74	C₂	#16812131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄₂₈
commutator	C₄×C₁₀₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₇
Fitting	C₄×C₈×C₁₀₇	C₂
socle	C₂²×C₁₀₇	C₂×D₄
hypercenter	C₄×C₈	D₁₀₇
hypocenter	C₁₀₇	C₄×D₈
LCS	G ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₄×D₄₂₈	C₂	semidirect
3. #16812043	C₂	semidirect
4. #16812031	C₂	semidirect
5. C₄×C₈×C₁₀₇	C₂	semidirect
8. D₈₅₆	C₄	direct (N × H)
20. D₄₂₈	C₂×C₄	semidirect
23. C₈×C₁₀₇	C₂×C₄	semidirect
29. C₄×C₁₀₇	D₈	semidirect
37. C₁₀₇	C₄×D₈	semidirect
43. C₄×C₈	D₁₀₇	semidirect
61. C₈	C₄×D₁₀₇	semidirect
68. C₄	D₈₅₆	direct (N × H)

Subgroups — C4×D856 #20292711

Conjugacy classes of subgroups

Complements

Subgroups — C₄×D₈₅₆ #20292711