Subgroups — C₃⋊#92209 #13090902

Order 1458.

347 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6868	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×C₃⋊(C₃⋊D₉)	—	3	1	no	maximal
3	C₃⋊#4169	—	3	3	no	maximal
4	#92209	—	3	9	no	maximal
5	C₃³×C₉	D₃	1	1	yes	characteristic
6	C₃×C₃²⋊C₉	D₃	1	3	yes	—
7	#6868	D₃	1	9	yes	complemented
8	C₃×C₃⋊(C₃⋊D₃)	—	9	1	no	—
9	C₃⋊(C₃⋊D₉)	—	3	1	no	—
10	C₃⋊(C₃⋊D₉)	—	3	3	no	—
11	C₃×C₃⋊D₉	—	9	9	no	—
12	C₃×C₃⋊D₉	—	9	3	no	—
13	#4169	—	9	9	no	—
14	C₃⁴	C₃⋊D₃	1	1	yes	characteristic
15	C₃²×C₉	—	3	1	no	—
16	C₃²×C₉	—	3	3	no	—
17	C₃²×C₉	—	6	3	no	—
18	C₃²×C₉	—	6	1	no	—
19	C₃²×C₉	D₉	1	9	yes	complemented
20	C₃²×C₉	C₃⋊D₃	1	3	yes	—
21	C₃²⋊C₉	—	6	3	no	—
22	C₃²⋊C₉	C₃⋊D₃	1	9	yes	—
23	C₃⋊(C₃⋊D₃)	—	9	1	no	—
24	C₃×C₃⋊D₃	—	27	3	no	—
25	C₃×C₃⋊D₃	—	27	6	no	—
26	C₃×C₃⋊D₃	—	27	3	no	—
27	C₃×C₃⋊D₃	—	27	1	no	—
28	C₃⋊D₉	—	9	9	no	—
29	C₃⋊D₉	—	9	3	no	—
30	C₃⋊D₉	—	9	9	no	—
31	C₃⋊D₉	—	27	9	no	—
32	C₃×D₉	—	27	9	no	—
33	C₃³	—	2	3	no	—
34	C₃³	—	2	1	no	—
35	C₃³	—	3	3	no	—
36	C₃³	—	3	6	no	—
37	C₃³	C₃⋊D₉	1	3	yes	—
38	C₃³	#272	1	1	yes	characteristic
39	C₃³	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
40	C₃×C₉	—	3	9	no	—
41	C₃×C₉	—	3	3	no	—
42	C₃×C₉	—	3	9	no	—
43	C₃×C₉	—	6	9	no	—
44	C₃×C₉	—	6	3	no	—
45	C₃×C₉	—	9	9	no	—
46	C₃×C₉	C₃⋊D₉	1	9	yes	complemented
47	C₃⋊D₃	—	27	3	no	—
48	C₃⋊D₃	—	27	3	no	—
49	C₃⋊D₃	—	27	6	no	—
50	C₃⋊D₃	—	27	1	no	—
51	C₃×D₃	—	81	9	no	—
52	C₃×D₃	—	81	1	no	—
53	C₃×D₃	—	81	2	no	—
54	C₃×D₃	—	81	1	no	—
55	D₉	—	27	9	no	—
56	D₉	—	81	9	no	—
57	C₃²	—	2	3	no	—
58	C₃²	—	2	1	no	—
59	C₃²	—	3	9	no	—
60	C₃²	—	3	1	no	—
61	C₃²	—	3	2	no	—
62	C₃²	—	6	9	no	—
63	C₃²	—	6	1	no	—
64	C₃²	—	6	2	no	—
65	C₃²	#4181	1	3	yes	—
66	C₃²	#4185	1	3	yes	—
67	C₃²	#733⋊C₂	1	6	yes	—
68	C₃²	C₃⋊(C₃⋊D₉)	1	1	yes	characteristic
69	C₃²	C₃⋊#272	1	1	yes	characteristic
70	C₉	—	3	9	no	—
71	C₉	—	9	9	no	—
72	C₂×C₃	—	243	1	no	—
73	D₃	—	81	9	no	—
74	D₃	—	81	1	no	—
75	D₃	—	81	1	no	—
76	D₃	—	81	2	no	—
77	C₃	—	3	1	no	—
78	C₃	—	6	3	no	—
79	C₃	—	6	1	no	—
80	C₃	#92209	1	9	yes	complemented
81	C₃	C₃⋊#4181	1	1	yes	characteristic
82	C₃	C₃⋊#4185	1	1	yes	characteristic
83	C₃	C₃⋊(#733⋊C₂)	1	2	yes	—
84	C₂	—	243	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×#6868	C₂
Frattini	C₃³	C₃⋊(C₃⋊D₃)
socle	C₃³	#272
LCS	G ▷ C₃×#6868
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×#6868	C₂	semidirect
7. #6868	D₃	semidirect
19. C₃²×C₉	D₉	semidirect
46. C₃×C₉	C₃⋊D₉	semidirect
80. C₃	#92209	semidirect

Maximal subgroups

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

subgroup	index
C₃×#6868	2
C₃×C₃⋊(C₃⋊D₉)	3
C₃⋊#4169	3
#92209	3

Subgroups — C3⋊#92209 #13090902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#92209 #13090902