Subgroups — D₃₂×D₄₃ #19136891

Order 5504.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆×D₄₃	C₂	1	2	yes	maximal, complemented
2	D₁₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582734	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×D₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	D₈×D₄₃	—	2	2	no	—
7	D₆₈₈	C₂²	1	2	yes	complemented
8	#13063266	—	2	2	no	—
9	C₁₆×D₄₃	C₂²	1	1	yes	characteristic
10	C₄₃⋊C₃₂	C₂²	1	1	yes	characteristic, complemented
11	D₁₆×C₄₃	C₂²	1	2	yes	complemented
12	C₃₂×C₄₃	C₂²	1	1	yes	characteristic, complemented
13	D₄×D₄₃	—	4	2	no	—
14	D₈×C₄₃	—	2	2	no	—
15	#10621882	—	4	2	no	—
16	D₃₄₄	—	2	2	no	—
17	C₈×D₄₃	D₄	1	1	yes	characteristic
18	C₁₆×C₄₃	C₂³	1	1	yes	characteristic
19	C₄₃⋊C₁₆	D₄	1	1	yes	characteristic
20	C₂²×D₄₃	—	8	2	no	—
21	D₄×C₄₃	—	4	2	no	—
22	C₂²⋊D₄₃	—	8	2	no	—
23	D₁₇₂	—	4	2	no	—
24	C₄×D₄₃	D₈	1	1	yes	characteristic
25	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
26	C₄₃⋊C₈	D₈	1	1	yes	characteristic
27	C₂²×C₄₃	—	8	2	no	—
28	C₂×D₄₃	—	8	2	no	—
29	C₂×D₄₃	—	16	4	no	—
30	C₂×D₄₃	D₁₆	1	1	yes	characteristic
31	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
32	Dic₄₃	D₁₆	1	1	yes	characteristic
33	C₂×D₃₂	—	43	1	no	maximal, Sylow
34	C₂×C₄₃	—	16	2	no	—
35	C₂×C₄₃	C₂×D₁₆	1	1	yes	characteristic
36	D₄₃	—	16	2	no	—
37	D₄₃	D₃₂	1	2	yes	direct product factor
38	C₂×D₁₆	—	43	2	no	—
39	D₃₂	—	43	2	no	—
40	D₃₂	—	43	1	no	—
41	D₃₂	D₄₃	1	1	yes	characteristic, direct product factor
42	C₂×C₃₂	—	43	1	no	—
43	C₄₃	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₈	—	86	2	no	—
45	D₁₆	—	43	2	no	—
46	D₁₆	—	86	2	no	—
47	D₁₆	C₂×D₄₃	1	2	yes	complemented
48	C₂×C₁₆	—	43	1	no	—
49	C₃₂	—	43	1	no	—
50	C₃₂	C₂×D₄₃	1	1	yes	characteristic, complemented
51	C₂×D₄	—	172	2	no	—
52	D₈	—	2	2	no	—
53	D₈	—	86	2	no	—
54	D₈	—	172	2	no	—
55	C₂×C₈	—	43	1	no	—
56	C₁₆	—	43	1	no	—
57	C₁₆	C₂²×D₄₃	1	1	yes	characteristic
58	C₂³	—	344	2	no	—
59	D₄	—	4	2	no	—
60	D₄	—	344	2	no	—
61	D₄	—	172	2	no	—
62	C₂×C₄	—	43	1	no	—
63	C₈	—	43	1	no	—
64	C₈	D₄×D₄₃	1	1	yes	characteristic
65	C₂²	—	8	2	no	—
66	C₂²	—	43	1	no	—
67	C₂²	—	344	2	no	—
68	C₂²	—	688	4	no	—
69	C₄	—	43	1	no	—
70	C₄	D₈×D₄₃	1	1	yes	characteristic
71	C₂	—	16	2	no	—
72	C₂	—	43	2	no	—
73	C₂	—	688	2	no	—
74	C₂	D₁₆×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₄₃
commutator	C₁₆×C₄₃	C₂³
Frattini	C₁₆	C₂²×D₄₃
Fitting	C₄₃×D₃₂	C₂
socle	C₂×C₄₃	C₂×D₁₆
hypercenter	D₃₂	D₄₃
hypocenter	C₄₃	C₂×D₃₂
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₃₂

Complements

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

N	H ≅ G/N	type
1. D₁₆×D₄₃	C₂	semidirect
2. D₁₃₇₆	C₂	semidirect
3. #14582734	C₂	semidirect
4. C₃₂×D₄₃	C₂	semidirect
5. C₄₃×D₃₂	C₂	semidirect
7. D₆₈₈	C₂²	semidirect
10. C₄₃⋊C₃₂	C₂²	semidirect
11. D₁₆×C₄₃	C₂²	semidirect
12. C₃₂×C₄₃	C₂²	semidirect
37. D₄₃	D₃₂	direct (N × H)
41. D₃₂	D₄₃	direct (N × H)
43. C₄₃	C₂×D₃₂	semidirect
47. D₁₆	C₂×D₄₃	semidirect
50. C₃₂	C₂×D₄₃	semidirect

Subgroups — D32×D43 #19136891

Conjugacy classes of subgroups

Complements

Subgroups — D₃₂×D₄₃ #19136891