Subgroups — Dic₉×#168 #13083721

Order 1440.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉⋊#168	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×Dic₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₉×#168	C₂	1	1	yes	maximal, characteristic
4	Dic₃×#168	—	3	1	no	maximal
5	C₂×C₄×C₅×C₉	C₂²	1	1	yes	characteristic
6	C₂×C₅×Dic₉	C₄	1	2	yes	—
7	C₉⋊#168	C₄	1	2	yes	complemented
8	C₉×#168	C₄	1	2	yes	complemented
9	C₈×Dic₉	—	5	1	no	maximal, Hall
10	C₂×C₃⋊#168	—	3	1	no	—
11	C₄×C₅×Dic₃	—	3	1	no	—
12	C₂×C₃×#168	D₃	1	1	yes	characteristic
13	C₂²×C₅×C₉	C₂×C₄	1	1	yes	characteristic
14	C₄×C₅×C₉	C₂×C₄	1	1	yes	characteristic
15	C₄×C₅×C₉	C₂×C₄	1	1	yes	characteristic
16	C₅×Dic₉	C₈	1	4	yes	complemented
17	C₄×#168	—	9	1	no	Hall
18	C₂×C₈×C₉	—	5	1	no	—
19	C₄×Dic₉	D₅	1	1	yes	characteristic
20	C₂×C₉⋊C₈	—	5	1	no	—
21	C₂×C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic
22	C₂×C₅×Dic₃	—	3	2	no	—
23	C₃⋊#168	—	3	2	no	—
24	C₃×#168	Dic₃	1	2	yes	—
25	C₈×Dic₃	—	15	1	no	—
26	C₂×C₅×C₉	C₄²	1	1	yes	characteristic
27	C₂×C₅×C₉	C₂×C₈	1	2	yes	—
28	C₄²×C₅	—	9	1	no	—
29	C₂×#168	—	9	1	no	—
30	C₂×#168	D₉	1	1	yes	characteristic
31	C₂×C₄×C₉	C₂×D₅	1	1	yes	characteristic
32	C₂×Dic₉	Dic₅	1	2	yes	—
33	C₈×C₉	—	5	2	no	—
34	C₉⋊C₈	—	5	2	no	—
35	C₂²×C₃×C₅	C₄×D₃	1	1	yes	characteristic
36	C₃×C₄×C₅	C₄×D₃	1	1	yes	characteristic
37	C₃×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
38	C₅×Dic₃	—	3	4	no	—
39	C₂×C₃×C₈	—	5	1	no	—
40	C₄×Dic₃	—	3	1	no	—
41	C₂×C₃⋊C₈	—	15	1	no	—
42	C₅×C₉	C₄×C₈	1	1	yes	characteristic, complemented, Hall
43	C₂×C₄×C₅	—	9	2	no	—
44	C₂×C₄×C₅	C₂×D₉	1	1	yes	characteristic
45	#168	—	9	2	no	—
46	#168	Dic₉	1	2	yes	direct product factor
47	C₂²×C₉	C₂×Dic₅	1	1	yes	characteristic
48	C₄×C₉	C₄×D₅	1	1	yes	characteristic
49	C₄×C₉	C₄×D₅	1	1	yes	characteristic
50	Dic₉	#168	1	4	yes	direct product factor
51	C₄×C₈	—	45	1	no	Sylow
52	C₂×C₃×C₅	D₃×C₈	1	2	yes	—
53	C₂×C₃×C₅	C₄×Dic₃	1	1	yes	characteristic
54	C₂×C₃×C₄	D₃×D₅	1	1	yes	characteristic
55	C₂×Dic₃	—	3	2	no	—
56	C₃×C₈	—	5	2	no	—
57	C₃⋊C₈	—	15	2	no	—
58	C₂²×C₅	C₄×D₉	1	1	yes	characteristic
59	C₄×C₅	—	9	4	no	—
60	C₄×C₅	C₄×D₉	1	1	yes	characteristic
61	C₄×C₅	C₂×Dic₉	1	1	yes	characteristic
62	C₂×C₉	C₂×#168	1	2	yes	—
63	C₂×C₉	C₄×Dic₅	1	1	yes	characteristic
64	C₂×C₈	—	5	1	no	—
65	C₂×C₈	—	45	1	no	—
66	C₄²	—	9	1	no	—
67	C₃×C₅	C₈×Dic₃	1	1	yes	characteristic
68	C₂²×C₃	D₃×Dic₅	1	1	yes	characteristic
69	C₃×C₄	D₅×Dic₃	1	1	yes	characteristic
70	C₃×C₄	#1200	1	1	yes	characteristic
71	Dic₃	—	3	4	no	—
72	C₂×C₅	C₈×D₉	1	2	yes	—
73	C₂×C₅	C₄×Dic₉	1	1	yes	characteristic
74	C₉	C₄×#168	1	1	yes	characteristic, complemented, Sylow
75	C₂×C₄	—	9	2	no	—
76	C₂×C₄	D₅×D₉	1	1	yes	characteristic
77	C₈	—	5	2	no	—
78	C₈	—	45	2	no	—
79	C₂×C₃	D₃×#168	1	2	yes	—
80	C₂×C₃	Dic₃×Dic₅	1	1	yes	characteristic
81	C₅	C₈×Dic₉	1	1	yes	characteristic, complemented, Sylow
82	C₂²	D₉×Dic₅	1	1	yes	characteristic
83	C₄	—	9	4	no	—
84	C₄	#67079	1	1	yes	characteristic
85	C₄	D₅×Dic₉	1	1	yes	characteristic
86	C₃	Dic₃×#168	1	1	yes	characteristic
87	C₂	D₉×#168	1	2	yes	—
88	C₂	Dic₅×Dic₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₅×D₉
commutator, hypocenter	C₅×C₉	C₄×C₈
Frattini	C₂×C₃×C₄	D₃×D₅
Fitting, cosocle	C₂×C₄×C₅×C₉	C₂²
socle, prime radical	C₂²×C₃×C₅	C₄×D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
7. C₉⋊#168	C₄	semidirect
8. C₉×#168	C₄	semidirect
16. C₅×Dic₉	C₈	semidirect
42. C₅×C₉	C₄×C₈	semidirect
46. #168	Dic₉	direct (N × H)
50. Dic₉	#168	direct (N × H)
74. C₉	C₄×#168	semidirect
81. C₅	C₈×Dic₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉⋊#168	2
C₄×C₅×Dic₉	2
C₂×C₉×#168	2
Dic₃×#168	3
C₈×Dic₉	5

Subgroups — Dic9×#168 #13083721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₉×#168 #13083721