Subgroups — D₃₂×D₈₉ #26022548

Order 11392.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆×D₈₉	C₂	1	2	yes	maximal, complemented
2	D₂₈₄₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#19151433	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃₂×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	D₈×D₈₉	—	2	2	no	—
7	D₁₄₂₄	C₂²	1	2	yes	complemented
8	#15667953	—	2	2	no	—
9	C₁₆×D₈₉	C₂²	1	1	yes	characteristic
10	#15667918	C₂²	1	1	yes	characteristic, complemented
11	D₁₆×C₈₉	C₂²	1	2	yes	complemented
12	C₃₂×C₈₉	C₂²	1	1	yes	characteristic, complemented
13	D₄×D₈₉	—	4	2	no	—
14	D₇₁₂	—	2	2	no	—
15	#13083559	—	4	2	no	—
16	C₈×D₈₉	D₄	1	1	yes	characteristic
17	#13083549	D₄	1	1	yes	characteristic
18	D₈×C₈₉	—	2	2	no	—
19	C₁₆×C₈₉	C₂³	1	1	yes	characteristic
20	C₂²×D₈₉	—	8	2	no	—
21	D₄×C₈₉	—	4	2	no	—
22	C₂²⋊D₈₉	—	8	2	no	—
23	D₃₅₆	—	4	2	no	—
24	C₄×D₈₉	D₈	1	1	yes	characteristic
25	C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
26	#10623494	D₈	1	1	yes	characteristic
27	C₂²×C₈₉	—	8	2	no	—
28	C₂×D₈₉	—	8	2	no	—
29	C₂×D₈₉	—	16	4	no	—
30	C₂×D₈₉	D₁₆	1	1	yes	characteristic
31	C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
32	Dic₈₉	D₁₆	1	1	yes	characteristic
33	C₂×C₈₉	—	16	2	no	—
34	C₂×C₈₉	C₂×D₁₆	1	1	yes	characteristic
35	D₈₉	—	16	2	no	—
36	D₈₉	D₃₂	1	2	yes	direct product factor
37	C₂×D₃₂	—	89	1	no	maximal, Sylow
38	C₈₉	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₁₆	—	89	2	no	—
40	D₃₂	—	89	2	no	—
41	D₃₂	—	89	1	no	—
42	D₃₂	D₈₉	1	1	yes	characteristic, direct product factor
43	C₂×C₃₂	—	89	1	no	—
44	C₂×D₈	—	178	2	no	—
45	D₁₆	—	89	2	no	—
46	D₁₆	—	178	2	no	—
47	D₁₆	C₂×D₈₉	1	2	yes	complemented
48	C₂×C₁₆	—	89	1	no	—
49	C₃₂	—	89	1	no	—
50	C₃₂	C₂×D₈₉	1	1	yes	characteristic, complemented
51	C₂×D₄	—	356	2	no	—
52	D₈	—	2	2	no	—
53	D₈	—	356	2	no	—
54	D₈	—	178	2	no	—
55	C₂×C₈	—	89	1	no	—
56	C₁₆	—	89	1	no	—
57	C₁₆	C₂²×D₈₉	1	1	yes	characteristic
58	C₂³	—	712	2	no	—
59	D₄	—	4	2	no	—
60	D₄	—	356	2	no	—
61	D₄	—	712	2	no	—
62	C₂×C₄	—	89	1	no	—
63	C₈	—	89	1	no	—
64	C₈	D₄×D₈₉	1	1	yes	characteristic
65	C₂²	—	8	2	no	—
66	C₂²	—	89	1	no	—
67	C₂²	—	1424	4	no	—
68	C₂²	—	712	2	no	—
69	C₄	—	89	1	no	—
70	C₄	D₈×D₈₉	1	1	yes	characteristic
71	C₂	—	16	2	no	—
72	C₂	—	89	2	no	—
73	C₂	—	1424	2	no	—
74	C₂	D₁₆×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₈₉
commutator, cosocle	C₁₆×C₈₉	C₂³
Frattini	C₁₆	C₂²×D₈₉
Fitting	D₃₂×C₈₉	C₂
socle	C₂×C₈₉	C₂×D₁₆
hypercenter	D₃₂	D₈₉
hypocenter	C₈₉	C₂×D₃₂
LCS	G ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
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×D₈₉	C₂	semidirect
2. D₂₈₄₈	C₂	semidirect
3. #19151433	C₂	semidirect
4. C₃₂×D₈₉	C₂	semidirect
5. D₃₂×C₈₉	C₂	semidirect
7. D₁₄₂₄	C₂²	semidirect
10. #15667918	C₂²	semidirect
11. D₁₆×C₈₉	C₂²	semidirect
12. C₃₂×C₈₉	C₂²	semidirect
36. D₈₉	D₃₂	direct (N × H)
38. C₈₉	C₂×D₃₂	semidirect
42. D₃₂	D₈₉	direct (N × H)
47. D₁₆	C₂×D₈₉	semidirect
50. C₃₂	C₂×D₈₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₁₆×D₈₉	2
D₂₈₄₈	2
#19151433	2
C₃₂×D₈₉	2
D₃₂×C₈₉	2
C₂×D₃₂	89

Subgroups — D32×D89 #26022548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₂×D₈₉ #26022548