Subgroups — D₁₆×D₈₉ #19152017

Order 5696.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈×D₈₉	C₂	1	2	yes	maximal, complemented
2	D₁₄₂₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#15667953	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×D₈₉	—	2	2	no	—
7	D₇₁₂	C₂²	1	2	yes	complemented
8	#13083559	—	2	2	no	—
9	C₈×D₈₉	C₂²	1	1	yes	characteristic
10	#13083549	C₂²	1	1	yes	characteristic, complemented
11	D₈×C₈₉	C₂²	1	2	yes	complemented
12	C₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
13	C₂²×D₈₉	—	4	2	no	—
14	D₄×C₈₉	—	2	2	no	—
15	C₂²⋊D₈₉	—	4	2	no	—
16	D₃₅₆	—	2	2	no	—
17	C₄×D₈₉	D₄	1	1	yes	characteristic
18	C₈×C₈₉	C₂³	1	1	yes	characteristic
19	#10623494	D₄	1	1	yes	characteristic
20	C₂²×C₈₉	—	4	2	no	—
21	C₂×D₈₉	—	4	2	no	—
22	C₂×D₈₉	—	8	4	no	—
23	C₂×D₈₉	D₈	1	1	yes	characteristic
24	C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
25	Dic₈₉	D₈	1	1	yes	characteristic
26	C₂×C₈₉	—	8	2	no	—
27	C₂×C₈₉	C₂×D₈	1	1	yes	characteristic
28	D₈₉	—	8	2	no	—
29	D₈₉	D₁₆	1	2	yes	direct product factor
30	C₈₉	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
31	C₂×D₁₆	—	89	1	no	maximal, Sylow
32	C₂×D₈	—	89	2	no	—
33	D₁₆	—	89	2	no	—
34	D₁₆	—	89	1	no	—
35	D₁₆	D₈₉	1	1	yes	characteristic, direct product factor
36	C₂×C₁₆	—	89	1	no	—
37	C₂×D₄	—	178	2	no	—
38	D₈	—	89	2	no	—
39	D₈	—	178	2	no	—
40	D₈	C₂×D₈₉	1	2	yes	complemented
41	C₂×C₈	—	89	1	no	—
42	C₁₆	—	89	1	no	—
43	C₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
44	C₂³	—	356	2	no	—
45	D₄	—	2	2	no	—
46	D₄	—	356	2	no	—
47	D₄	—	178	2	no	—
48	C₂×C₄	—	89	1	no	—
49	C₈	—	89	1	no	—
50	C₈	C₂²×D₈₉	1	1	yes	characteristic
51	C₂²	—	4	2	no	—
52	C₂²	—	89	1	no	—
53	C₂²	—	356	2	no	—
54	C₂²	—	712	4	no	—
55	C₄	—	89	1	no	—
56	C₄	D₄×D₈₉	1	1	yes	characteristic
57	C₂	—	8	2	no	—
58	C₂	—	89	2	no	—
59	C₂	—	712	2	no	—
60	C₂	D₈×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₈₉
commutator	C₈×C₈₉	C₂³
Frattini	C₈	C₂²×D₈₉
Fitting	D₁₆×C₈₉	C₂
socle	C₂×C₈₉	C₂×D₈
hypercenter	D₁₆	D₈₉
hypocenter	C₈₉	C₂×D₁₆
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. D₈×D₈₉	C₂	semidirect
2. D₁₄₂₄	C₂	semidirect
3. #15667953	C₂	semidirect
4. C₁₆×D₈₉	C₂	semidirect
5. D₁₆×C₈₉	C₂	semidirect
7. D₇₁₂	C₂²	semidirect
10. #13083549	C₂²	semidirect
11. D₈×C₈₉	C₂²	semidirect
12. C₁₆×C₈₉	C₂²	semidirect
29. D₈₉	D₁₆	direct (N × H)
30. C₈₉	C₂×D₁₆	semidirect
35. D₁₆	D₈₉	direct (N × H)
40. D₈	C₂×D₈₉	semidirect
43. C₁₆	C₂×D₈₉	semidirect

Subgroups — D16×D89 #19152017

Conjugacy classes of subgroups

Complements

Subgroups — D₁₆×D₈₉ #19152017