Subgroups — SD₃₂×D₈₉ #19152020

Order 5696.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#15667957	C₂	1	1	yes	maximal, characteristic, complemented
4	#15667956	C₂	1	1	yes	maximal, characteristic, complemented
5	#15667955	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₃₂×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×D₈₉	—	2	1	no	—
9	D₄×D₈₉	—	2	1	no	—
10	Dic₃₅₆	C₂²	1	1	yes	characteristic, complemented
11	#13083564	—	2	1	no	—
12	D₇₁₂	C₂²	1	1	yes	characteristic
13	#13083559	—	2	1	no	—
14	C₈×D₈₉	C₂²	1	1	yes	characteristic
15	#13083549	C₂²	1	1	yes	characteristic, complemented
16	Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
17	D₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₈₉	—	4	1	no	—
20	Q₈×C₈₉	—	2	1	no	—
21	D₄×C₈₉	—	2	1	no	—
22	C₂²⋊D₈₉	—	4	1	no	—
23	D₃₅₆	—	2	1	no	—
24	C₄×D₈₉	—	4	1	no	—
25	C₄×D₈₉	D₄	1	1	yes	characteristic
26	Dic₁₇₈	—	2	1	no	—
27	Dic₁₇₈	—	4	1	no	—
28	C₈×C₈₉	C₂³	1	1	yes	characteristic
29	#10623494	D₄	1	1	yes	characteristic
30	C₂²×C₈₉	—	4	1	no	—
31	C₂×D₈₉	—	4	1	no	—
32	C₂×D₈₉	—	8	2	no	—
33	C₂×D₈₉	D₈	1	1	yes	characteristic
34	C₄×C₈₉	—	4	1	no	—
35	C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
36	Dic₈₉	—	4	1	no	—
37	Dic₈₉	D₈	1	1	yes	characteristic
38	C₂×C₈₉	—	8	1	no	—
39	C₂×C₈₉	C₂×D₈	1	1	yes	characteristic
40	D₈₉	—	8	1	no	—
41	D₈₉	SD₃₂	1	2	yes	direct product factor
42	C₈₉	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
43	C₂×SD₃₂	—	89	1	no	maximal, Sylow
44	C₂×Q₁₆	—	89	1	no	—
45	C₂×D₈	—	89	1	no	—
46	SD₃₂	—	89	1	no	—
47	SD₃₂	—	89	1	no	—
48	SD₃₂	—	89	1	no	—
49	SD₃₂	D₈₉	1	1	yes	characteristic, direct product factor
50	C₂×C₁₆	—	89	1	no	—
51	C₂×Q₈	—	178	1	no	—
52	C₂×D₄	—	178	1	no	—
53	Q₁₆	—	89	1	no	—
54	Q₁₆	—	178	1	no	—
55	Q₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
56	D₈	—	89	1	no	—
57	D₈	—	178	1	no	—
58	D₈	C₂×D₈₉	1	1	yes	characteristic
59	C₂×C₈	—	89	1	no	—
60	C₁₆	—	89	1	no	—
61	C₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
62	C₂³	—	356	1	no	—
63	Q₈	—	2	1	no	—
64	Q₈	—	356	1	no	—
65	Q₈	—	178	1	no	—
66	D₄	—	2	1	no	—
67	D₄	—	356	1	no	—
68	D₄	—	178	1	no	—
69	C₂×C₄	—	89	1	no	—
70	C₂×C₄	—	356	1	no	—
71	C₈	—	89	1	no	—
72	C₈	C₂²×D₈₉	1	1	yes	characteristic
73	C₂²	—	4	1	no	—
74	C₂²	—	89	1	no	—
75	C₂²	—	356	1	no	—
76	C₂²	—	712	2	no	—
77	C₄	—	4	1	no	—
78	C₄	—	89	1	no	—
79	C₄	—	356	1	no	—
80	C₄	D₄×D₈₉	1	1	yes	characteristic
81	C₂	—	8	1	no	—
82	C₂	—	89	2	no	—
83	C₂	—	712	1	no	—
84	C₂	D₈×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₈₉
commutator	C₈×C₈₉	C₂³
Frattini	C₈	C₂²×D₈₉
Fitting	SD₃₂×C₈₉	C₂
socle	C₂×C₈₉	C₂×D₈
hypercenter	SD₃₂	D₈₉
hypocenter	C₈₉	C₂×SD₃₂
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ SD₃₂

Complements

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

N	H ≅ G/N	type
1. Q₁₆×D₈₉	C₂	semidirect
3. #15667957	C₂	semidirect
4. #15667956	C₂	semidirect
5. #15667955	C₂	semidirect
6. C₁₆×D₈₉	C₂	semidirect
7. SD₃₂×C₈₉	C₂	semidirect
10. Dic₃₅₆	C₂²	semidirect
15. #13083549	C₂²	semidirect
16. Q₁₆×C₈₉	C₂²	semidirect
18. C₁₆×C₈₉	C₂²	semidirect
41. D₈₉	SD₃₂	direct (N × H)
42. C₈₉	C₂×SD₃₂	semidirect
49. SD₃₂	D₈₉	direct (N × H)
55. Q₁₆	C₂×D₈₉	semidirect
61. C₁₆	C₂×D₈₉	semidirect

Subgroups — SD32×D89 #19152020

Conjugacy classes of subgroups

Complements

Subgroups — SD₃₂×D₈₉ #19152020