Subgroups — C₉⋊(#733⋊C₂) #13091007

Order 1458.

238 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#733	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊(#733⋊C₂)	—	3	1	no	maximal
3	#92299	—	3	3	no	maximal
4	C₃×C₉⋊D₉	—	3	1	no	maximal
5	(3₋¹⁺²⋊C₉)⋊C₂	—	3	6	no	maximal
6	#92209	—	3	2	no	maximal
7	C₃×#733	D₃	1	1	yes	characteristic
8	C₉×3₋¹⁺²	D₃	1	3	yes	—
9	C₃×C₉²	D₃	1	1	yes	characteristic
10	3₋¹⁺²⋊C₉	D₃	1	6	yes	—
11	#6868	D₃	1	2	yes	—
12	C₃⋊AGL(1,ℤ/9)	—	9	3	no	—
13	C₃×C₃⋊D₉	—	9	1	no	—
14	C₃×C₃⋊D₉	—	9	2	no	—
15	C₃×C₃⋊D₉	—	9	1	no	—
16	#733⋊C₂	—	9	9	no	—
17	C₉⋊D₉	—	3	1	no	—
18	C₉⋊D₉	—	3	3	no	—
19	#4169	—	9	6	no	—
20	C₃×3₋¹⁺²	C₃⋊D₃	1	3	yes	—
21	C₃²×C₉	C₃⋊D₃	1	1	yes	characteristic
22	C₃²×C₉	C₃⋊D₃	1	2	yes	—
23	C₃²×C₉	C₃⋊D₃	1	1	yes	characteristic
24	#733	D₉	1	9	yes	complemented
25	C₉⋊C₉	—	6	3	no	—
26	C₃²⋊C₉	C₃⋊D₃	1	6	yes	—
27	C₉²	—	3	1	no	—
28	C₉²	—	3	3	no	—
29	C₉²	—	6	1	no	—
30	C₃×C₃⋊D₃	—	27	1	no	—
31	C₃⋊D₉	—	9	1	no	—
32	C₃⋊D₉	—	9	2	no	—
33	C₃⋊D₉	—	9	3	no	—
34	C₃⋊D₉	—	9	1	no	—
35	C₃⋊D₉	—	9	6	no	—
36	AGL(1,ℤ/9)	—	27	9	no	—
37	C₃×D₉	—	27	6	no	—
38	C₃×D₉	—	27	3	no	—
39	C₃×D₉	—	27	3	no	—
40	C₃³	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
41	3₋¹⁺²	—	6	3	no	—
42	3₋¹⁺²	C₃⋊D₉	1	9	yes	—
43	C₃×C₉	—	2	1	no	—
44	C₃×C₉	—	3	1	no	—
45	C₃×C₉	—	3	2	no	—
46	C₃×C₉	—	3	3	no	—
47	C₃×C₉	—	3	6	no	—
48	C₃×C₉	—	3	3	no	—
49	C₃×C₉	—	3	6	no	—
50	C₃×C₉	—	6	1	no	—
51	C₃×C₉	C₃⋊D₉	1	3	yes	—
52	C₃×C₉	#272	1	1	yes	characteristic
53	C₃⋊D₃	—	27	1	no	—
54	C₃×D₃	—	81	1	no	—
55	C₃×D₃	—	81	2	no	—
56	C₃×D₃	—	81	1	no	—
57	D₉	—	27	3	no	—
58	D₉	—	27	6	no	—
59	D₉	—	27	9	no	—
60	D₉	—	27	3	no	—
61	D₉	—	81	6	no	—
62	C₃²	—	2	1	no	—
63	C₃²	—	3	1	no	—
64	C₃²	—	3	2	no	—
65	C₃²	C₃⋊(C₃⋊D₉)	1	1	yes	characteristic
66	C₃²	C₃⋊#272	1	1	yes	characteristic
67	C₉	—	3	3	no	—
68	C₉	—	3	9	no	—
69	C₉	—	3	6	no	—
70	C₉	—	6	1	no	—
71	C₉	—	9	6	no	—
72	C₉	#733⋊C₂	1	3	yes	complemented
73	C₂×C₃	—	243	1	no	—
74	D₃	—	81	1	no	—
75	D₃	—	81	1	no	—
76	D₃	—	81	2	no	—
77	C₃	—	3	1	no	—
78	C₃	—	6	1	no	—
79	C₃	C₉⋊#272	1	1	yes	characteristic
80	C₃	C₃⋊(#733⋊C₂)	1	1	yes	characteristic
81	C₃	#92344	1	2	yes	—
82	C₂	—	243	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×#733	C₂
Frattini	C₃³	C₃⋊(C₃⋊D₃)
socle	C₃²	C₃⋊#272
LCS	G ▷ C₉×#733
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₉×#733	C₂	semidirect
24. #733	D₉	semidirect
72. C₉	#733⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
C₉×#733	2
C₃⋊(#733⋊C₂)	3
#92299	3
C₃×C₉⋊D₉	3
(3₋¹⁺²⋊C₉)⋊C₂	3
#92209	3

Subgroups — C9⋊(#733⋊C2) #13091007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉⋊(#733⋊C₂) #13091007