Subgroups — C₄⋊(C₄₃⋊C₃₂) #19132791

Order 5504.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃⋊C₃₂	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄₃⋊C₃₂	—	2	2	no	—
4	C₂×C₁₆×C₄₃	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₄₃	C₄	1	1	yes	characteristic
7	C₂×C₈×C₄₃	C₈	1	1	yes	characteristic
8	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₄₃	C₈	1	1	yes	characteristic
10	C₁₆×C₄₃	—	2	1	no	—
11	C₁₆×C₄₃	D₄	1	1	yes	characteristic
12	C₁₆×C₄₃	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₄₃	C₁₆	1	1	yes	characteristic
14	C₂×C₄×C₄₃	C₁₆	1	1	yes	characteristic
15	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
16	C₈×C₄₃	—	2	1	no	—
17	C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₄₃	M₁₆	1	1	yes	characteristic
19	C₂²×C₄₃	C₂×C₁₆	1	1	yes	characteristic
20	C₄×C₄₃	—	2	1	no	—
21	C₄×C₄₃	C₃₂	1	2	yes	complemented
22	C₄×C₄₃	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₄₃	M₃₂	1	1	yes	characteristic
24	C₄⋊C₃₂	—	43	1	no	maximal, Sylow
25	C₂×C₄₃	C₄⋊C₁₆	1	1	yes	characteristic
26	C₂×C₄₃	C₂×C₃₂	1	1	yes	characteristic
27	C₂×C₄₃	M₆₄	1	1	yes	characteristic
28	C₂×C₃₂	—	43	2	no	—
29	C₄×C₁₆	D₄₃	1	1	yes	characteristic
30	C₄₃	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₁₆	Dic₄₃	1	1	yes	characteristic
32	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
33	C₄×C₈	Dic₄₃	1	1	yes	characteristic
34	C₃₂	—	86	2	no	—
35	C₂×C₈	C₄₃⋊C₈	1	1	yes	characteristic
36	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
37	C₄²	C₄₃⋊C₈	1	1	yes	characteristic
38	C₁₆	—	2	1	no	—
39	C₁₆	Dic₈₆	1	1	yes	characteristic
40	C₁₆	D₁₇₂	1	1	yes	characteristic
41	C₂×C₄	C₄₃⋊C₁₆	1	1	yes	characteristic
42	C₂×C₄	C₄₃⋊C₁₆	1	1	yes	characteristic
43	C₂×C₄	C₂×C₄₃⋊C₈	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	#10621877	1	1	yes	characteristic
46	C₈	C₄⋊Dic₄₃	1	1	yes	characteristic
47	C₂²	C₂×C₄₃⋊C₁₆	1	1	yes	characteristic
48	C₄	—	2	1	no	—
49	C₄	C₄₃⋊C₃₂	1	2	yes	complemented
50	C₄	C₄⋊(C₄₃⋊C₈)	1	1	yes	characteristic
51	C₄	#13063265	1	1	yes	characteristic
52	C₂	C₄⋊(C₄₃⋊C₁₆)	1	1	yes	characteristic
53	C₂	C₂×C₄₃⋊C₃₂	1	1	yes	characteristic
54	C₂	#14582733	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₄₃
commutator	C₂×C₄₃	C₂×C₃₂
Fitting	C₄×C₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₁₆
hypercenter	C₄×C₁₆	D₄₃
hypocenter	C₄₃	C₄⋊C₃₂
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
21. C₄×C₄₃	C₃₂	semidirect
30. C₄₃	C₄⋊C₃₂	semidirect
49. C₄	C₄₃⋊C₃₂	semidirect

Subgroups — C4⋊(C43⋊C32) #19132791

Conjugacy classes of subgroups

Complements

Subgroups — C₄⋊(C₄₃⋊C₃₂) #19132791