Subgroups — C₂²×#92314 #14518521

Order 1944.

796 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6900	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#92314	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃⋊AGL(1,ℤ/9)	—	3	4	no	maximal
4	C₂²×C₉⋊D₉	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×#6900	C₂²	1	3	yes	complemented
6	#92314	C₂²	1	4	yes	direct product factor
7	C₂²×C₃×3₋¹⁺²	D₃	1	4	yes	—
8	C₂×C₃⋊AGL(1,ℤ/9)	—	3	24	no	—
9	C₂²×C₉⋊C₉	—	2	4	no	—
10	C₂²×C₉²	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₉⋊D₉	C₂×C₃	1	6	yes	complemented
12	#6900	C₂³	1	1	yes	characteristic, complemented, Sylow
13	C₂²×C₃×C₃⋊D₃	—	9	1	no	—
14	C₂²×C₃⋊D₉	—	3	4	no	—
15	C₂²×AGL(1,ℤ/9)	—	9	12	no	—
16	C₂×C₃×3₋¹⁺²	C₂×D₃	1	12	yes	—
17	C₃⋊AGL(1,ℤ/9)	—	3	16	no	—
18	C₂×C₉⋊C₉	—	2	12	no	—
19	C₂×C₉²	C₂²×C₃	1	3	yes	complemented
20	C₉⋊D₉	C₂²×C₃	1	4	yes	complemented
21	C₂²×C₃³	C₃⋊D₃	1	1	yes	characteristic
22	C₂×C₃×C₃⋊D₃	—	9	6	no	—
23	C₂²×3₋¹⁺²	—	3	12	no	—
24	C₂²×C₃×C₉	—	2	4	no	—
25	C₂²×C₃×C₉	C₃×D₃	1	4	yes	—
26	C₂×C₃⋊D₉	—	3	24	no	—
27	C₂×AGL(1,ℤ/9)	—	9	72	no	—
28	C₃×3₋¹⁺²	C₂²×D₃	1	4	yes	—
29	C₉⋊C₉	—	2	4	no	—
30	C₉²	C₂³×C₃	1	1	yes	characteristic, complemented
31	C₂²×C₃⋊D₃	—	9	1	no	—
32	C₂²×C₃×D₃	—	27	4	no	—
33	C₂²×D₉	—	9	12	no	—
34	C₂×C₃³	C₂×C₃⋊D₃	1	3	yes	—
35	C₃×C₃⋊D₃	—	9	4	no	—
36	C₂×3₋¹⁺²	—	3	36	no	—
37	C₂×C₃×C₉	—	2	12	no	—
38	C₂×C₃×C₉	C₂×C₃×D₃	1	12	yes	—
39	C₃⋊D₉	—	3	16	no	—
40	AGL(1,ℤ/9)	—	9	48	no	—
41	C₂²×C₃²	—	3	4	no	—
42	C₂²×C₃²	C₃×C₃⋊D₃	1	1	yes	characteristic
43	C₂×C₃⋊D₃	—	9	6	no	—
44	C₂×C₃×D₃	—	27	24	no	—
45	C₂²×C₉	—	6	4	no	—
46	C₂²×C₉	AGL(1,ℤ/9)	1	12	yes	complemented
47	C₂×D₉	—	9	72	no	—
48	C₃³	C₂²×C₃⋊D₃	1	1	yes	characteristic
49	3₋¹⁺²	—	3	12	no	—
50	C₃×C₉	—	2	4	no	—
51	C₃×C₉	C₂²×C₃×D₃	1	4	yes	—
52	C₂³×C₃	—	81	1	no	—
53	C₂²×D₃	—	27	4	no	—
54	C₂×C₃²	—	3	12	no	—
55	C₂×C₃²	C₂×C₃×C₃⋊D₃	1	3	yes	—
56	C₃⋊D₃	—	9	4	no	—
57	C₃×D₃	—	27	16	no	—
58	C₂×C₉	—	6	12	no	—
59	C₂×C₉	C₂×AGL(1,ℤ/9)	1	36	yes	complemented
60	D₉	—	9	48	no	—
61	C₂²×C₃	—	9	1	no	—
62	C₂²×C₃	—	81	6	no	—
63	C₂²×C₃	C₃⋊AGL(1,ℤ/9)	1	4	yes	—
64	C₂×D₃	—	27	24	no	—
65	C₃²	—	3	4	no	—
66	C₃²	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
67	C₉	—	6	4	no	—
68	C₉	C₂²×AGL(1,ℤ/9)	1	12	yes	complemented
69	C₂³	—	81	1	no	Sylow
70	C₂×C₃	—	9	3	no	—
71	C₂×C₃	—	81	4	no	—
72	C₂×C₃	C₂×C₃⋊AGL(1,ℤ/9)	1	12	yes	—
73	D₃	—	27	16	no	—
74	C₂²	—	81	6	no	—
75	C₂²	#92314	1	1	yes	characteristic, direct product factor
76	C₃	—	9	1	no	—
77	C₃	C₂²×C₃⋊AGL(1,ℤ/9)	1	4	yes	—
78	C₂	—	81	4	no	—
79	C₂	C₂×#92314	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	#92314
commutator, cosocle, hypocenter	C₉²	C₂³×C₃
Frattini	C₃²	C₂²×C₃×C₃⋊D₃
Fitting	C₂²×#6900	C₂
socle	C₂²×C₃²	C₃×C₃⋊D₃
LCS	G ▷ C₉²
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×#6900	C₂	semidirect
2. C₂×#92314	C₂	direct (N × H)
4. C₂²×C₉⋊D₉	C₃	semidirect
5. C₂×#6900	C₂²	semidirect
6. #92314	C₂²	direct (N × H)
10. C₂²×C₉²	C₂×C₃	semidirect
11. C₂×C₉⋊D₉	C₂×C₃	semidirect
12. #6900	C₂³	semidirect
19. C₂×C₉²	C₂²×C₃	semidirect
20. C₉⋊D₉	C₂²×C₃	semidirect
30. C₉²	C₂³×C₃	semidirect
46. C₂²×C₉	AGL(1,ℤ/9)	semidirect
59. C₂×C₉	C₂×AGL(1,ℤ/9)	semidirect
68. C₉	C₂²×AGL(1,ℤ/9)	semidirect
75. C₂²	#92314	direct (N × H)
79. C₂	C₂×#92314	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#6900	2
C₂×#92314	2
C₂²×C₃⋊AGL(1,ℤ/9)	3
C₂²×C₉⋊D₉	3

Subgroups — C22×#92314 #14518521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#92314 #14518521