Subgroups — C₄×C₃⋊(C₉⋊D₉) #14517720

Order 1944.

1008 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊(C₉⋊D₉)	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₉²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₉⋊Dic₉)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₃⋊(C₃⋊D₉)	—	3	4	no	maximal
5	C₄×C₉⋊D₉	—	3	9	no	maximal
6	C₂×C₃×C₉²	C₂²	1	1	yes	characteristic
7	C₃⋊(C₉⋊D₉)	C₄	1	2	yes	direct product factor
8	C₂×C₃⋊(C₃⋊D₉)	—	3	4	no	—
9	C₃²×C₄×C₉	D₃	1	4	yes	—
10	C₃⋊(C₃⋊Dic₉)	—	3	4	no	—
11	C₂×C₉⋊D₉	—	3	9	no	—
12	C₄×C₉²	D₃	1	9	yes	complemented
13	C₉⋊Dic₉	—	3	9	no	—
14	C₃×C₉²	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
15	C₄×C₃⋊(C₃⋊D₃)	—	9	1	no	—
16	C₄×C₃⋊D₉	—	9	36	no	—
17	C₄×C₃⋊D₉	—	9	12	no	—
18	C₂×C₃²×C₉	C₂×D₃	1	4	yes	—
19	C₃⋊(C₃⋊D₉)	—	3	8	no	—
20	C₂×C₉²	C₂×D₃	1	9	yes	—
21	C₉⋊D₉	—	3	18	no	—
22	C₂×C₃⋊(C₃⋊D₃)	—	9	1	no	—
23	C₃³×C₄	C₃⋊D₃	1	1	yes	characteristic
24	C₃⋊(C₃⋊Dic₃)	—	9	1	no	—
25	C₂×C₃⋊D₉	—	9	36	no	—
26	C₂×C₃⋊D₉	—	9	12	no	—
27	C₃×C₄×C₉	D₉	1	36	yes	complemented
28	C₃×C₄×C₉	C₃⋊D₃	1	12	yes	—
29	C₃⋊Dic₉	—	9	36	no	—
30	C₃⋊Dic₉	—	9	12	no	—
31	C₃²×C₉	C₄×D₃	1	4	yes	—
32	C₉²	C₄×D₃	1	9	yes	complemented
33	C₄×C₃⋊D₃	—	27	12	no	—
34	C₄×C₃⋊D₃	—	27	1	no	—
35	C₄×D₉	—	27	36	no	—
36	C₂×C₃³	C₂×C₃⋊D₃	1	1	yes	characteristic
37	C₃⋊(C₃⋊D₃)	—	9	2	no	—
38	C₂×C₃×C₉	C₂×D₉	1	36	yes	—
39	C₂×C₃×C₉	C₂×C₃⋊D₃	1	12	yes	—
40	C₃⋊D₉	—	9	72	no	—
41	C₃⋊D₉	—	9	24	no	—
42	C₂×C₃⋊D₃	—	27	12	no	—
43	C₂×C₃⋊D₃	—	27	1	no	—
44	C₃²×C₄	C₃⋊D₉	1	12	yes	—
45	C₃²×C₄	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
46	C₃⋊Dic₃	—	27	12	no	—
47	C₃⋊Dic₃	—	27	1	no	—
48	C₂×D₉	—	27	36	no	—
49	C₄×C₉	C₃⋊D₉	1	36	yes	complemented
50	Dic₉	—	27	36	no	—
51	C₃³	C₄×C₃⋊D₃	1	1	yes	characteristic
52	C₃×C₉	C₄×D₉	1	36	yes	complemented
53	C₃×C₉	C₄×C₃⋊D₃	1	12	yes	—
54	C₄×D₃	—	81	9	no	—
55	C₄×D₃	—	81	4	no	—
56	C₂×C₃²	C₂×C₃⋊D₉	1	12	yes	—
57	C₂×C₃²	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
58	C₃⋊D₃	—	27	24	no	—
59	C₃⋊D₃	—	27	2	no	—
60	C₂×C₉	C₂×C₃⋊D₉	1	36	yes	—
61	D₉	—	27	72	no	—
62	C₂×D₃	—	81	9	no	—
63	C₂×D₃	—	81	4	no	—
64	C₃×C₄	C₉⋊D₉	1	9	yes	complemented
65	C₃×C₄	C₃⋊(C₃⋊D₉)	1	4	yes	—
66	Dic₃	—	81	9	no	—
67	Dic₃	—	81	4	no	—
68	C₃²	C₄×C₃⋊D₉	1	12	yes	—
69	C₃²	C₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
70	C₉	C₄×C₃⋊D₉	1	36	yes	complemented
71	C₂×C₄	—	243	1	no	Sylow
72	C₂×C₃	C₂×C₉⋊D₉	1	9	yes	—
73	C₂×C₃	C₂×C₃⋊(C₃⋊D₉)	1	4	yes	—
74	D₃	—	81	18	no	—
75	D₃	—	81	8	no	—
76	C₂²	—	243	1	no	—
77	C₄	—	243	1	no	—
78	C₄	C₃⋊(C₉⋊D₉)	1	1	yes	characteristic, direct product factor
79	C₃	C₄×C₉⋊D₉	1	9	yes	complemented
80	C₃	C₄×C₃⋊(C₃⋊D₉)	1	4	yes	—
81	C₂	—	243	2	no	—
82	C₂	C₂×C₃⋊(C₉⋊D₉)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	C₃⋊(C₉⋊D₉)
commutator, hypocenter	C₃×C₉²	C₂×C₄
Frattini	C₂×C₃²	C₂×C₃⋊(C₃⋊D₃)
Fitting	C₃×C₄×C₉²	C₂
socle	C₂×C₃³	C₂×C₃⋊D₃
prime radical	C₂×C₃⋊(C₉⋊D₉)	C₂
cosocle	C₂×C₃×C₉²	C₂²
LCS	G ▷ C₃×C₉²
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₉²	C₂	semidirect
3. C₃⋊(C₉⋊Dic₉)	C₂	semidirect
7. C₃⋊(C₉⋊D₉)	C₄	direct (N × H)
12. C₄×C₉²	D₃	semidirect
14. C₃×C₉²	C₂×C₄	semidirect
27. C₃×C₄×C₉	D₉	semidirect
32. C₉²	C₄×D₃	semidirect
49. C₄×C₉	C₃⋊D₉	semidirect
52. C₃×C₉	C₄×D₉	semidirect
64. C₃×C₄	C₉⋊D₉	semidirect
70. C₉	C₄×C₃⋊D₉	semidirect
78. C₄	C₃⋊(C₉⋊D₉)	direct (N × H)
79. C₃	C₄×C₉⋊D₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃⋊(C₉⋊D₉)	2
C₃×C₄×C₉²	2
C₃⋊(C₉⋊Dic₉)	2
C₄×C₃⋊(C₃⋊D₉)	3
C₄×C₉⋊D₉	3

Subgroups — C4×C3⋊(C9⋊D9) #14517720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₃⋊(C₉⋊D₉) #14517720