Subgroups — (C₂×AGL(1,ℤ/9))⋊C₄ #88500

Order 432.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×3₋¹⁺²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×(C₂×D₃)⋊C₄	—	3	1	no	maximal
5	(C₂×D₉)⋊C₄	C₃	1	1	yes	maximal, characteristic, complemented
6	C₂²×3₋¹⁺²	C₂²	1	1	yes	characteristic
7	C₂×AGL(1,ℤ/9)	—	2	1	no	—
8	C₂×AGL(1,ℤ/9)	—	2	1	no	—
9	C₂×AGL(1,ℤ/9)	C₄	1	2	yes	complemented
10	C₄×3₋¹⁺²	—	2	1	no	—
11	3₋¹⁺²⋊C₄	—	2	1	no	—
12	C₂²×C₃×D₃	—	3	1	no	—
13	C₂×C₃²×C₄	D₃	1	1	yes	characteristic
14	C₂×C₃×Dic₃	—	3	1	no	—
15	C₂²×D₉	C₂×C₃	1	1	yes	characteristic
16	C₂×C₄×C₉	—	2	1	no	—
17	C₂×C₄×C₉	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂×Dic₉	C₂×C₃	1	1	yes	characteristic, complemented
19	C₂×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
20	C₂×3₋¹⁺²	D₄	1	1	yes	characteristic
21	C₂×3₋¹⁺²	D₄	1	1	yes	characteristic
22	AGL(1,ℤ/9)	—	2	2	no	—
23	C₃×C₂²⋊C₄	—	9	1	no	—
24	(C₂×D₃)⋊C₄	—	3	1	no	—
25	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
26	C₂×C₃×D₃	—	3	2	no	—
27	C₂×C₃×D₃	—	6	1	no	—
28	C₂×C₃×D₃	—	6	1	no	—
29	C₃²×C₄	—	2	1	no	—
30	C₃×Dic₃	—	6	1	no	—
31	C₂²×C₉	—	2	1	no	—
32	C₂²×C₉	C₂²×C₃	1	1	yes	characteristic
33	C₂×D₉	—	2	1	no	—
34	C₂×D₉	—	2	1	no	—
35	C₂×D₉	C₃×C₄	1	2	yes	complemented
36	C₄×C₉	—	2	2	no	—
37	C₄×C₉	—	2	1	no	—
38	Dic₉	—	2	1	no	—
39	3₋¹⁺²	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
40	C₂³×C₃	—	9	1	no	—
41	C₂²×D₃	—	3	1	no	—
42	C₂×C₃×C₄	—	3	1	no	—
43	C₂×C₃×C₄	—	9	1	no	—
44	C₂×C₃×C₄	C₃×D₃	1	1	yes	characteristic
45	C₂×Dic₃	—	3	1	no	—
46	C₂×C₃²	C₄×D₃	1	1	yes	characteristic
47	C₂×C₃²	D₁₂	1	1	yes	characteristic
48	C₂×C₃²	#67	1	1	yes	characteristic
49	C₃×D₃	—	6	2	no	—
50	C₂×C₉	—	2	1	no	—
51	C₂×C₉	—	2	1	no	—
52	C₂×C₉	—	2	1	no	—
53	C₂×C₉	C₂×C₃×C₄	1	1	yes	characteristic
54	C₂×C₉	C₃×D₄	1	1	yes	characteristic
55	C₂×C₉	C₃×D₄	1	1	yes	characteristic
56	D₉	—	2	2	no	—
57	C₂²⋊C₄	—	9	1	no	Sylow
58	C₂²×C₃	—	3	1	no	—
59	C₂²×C₃	—	9	2	no	—
60	C₂²×C₃	—	18	1	no	—
61	C₂²×C₃	—	18	1	no	—
62	C₂²×C₃	C₂×C₃×D₃	1	1	yes	characteristic
63	C₂×D₃	—	3	2	no	—
64	C₂×D₃	—	6	1	no	—
65	C₂×D₃	—	6	1	no	—
66	C₃×C₄	—	2	1	no	—
67	C₃×C₄	—	6	1	no	—
68	C₃×C₄	—	18	1	no	—
69	Dic₃	—	6	1	no	—
70	C₃²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
71	C₉	—	2	1	no	—
72	C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic, complemented
73	C₂³	—	9	1	no	—
74	C₂×C₄	—	9	1	no	—
75	C₂×C₄	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
76	C₂×C₃	—	3	1	no	—
77	C₂×C₃	—	3	1	no	—
78	C₂×C₃	—	3	1	no	—
79	C₂×C₃	—	18	2	no	—
80	C₂×C₃	C₃×C₄×D₃	1	1	yes	characteristic
81	C₂×C₃	C₃×D₁₂	1	1	yes	characteristic
82	C₂×C₃	C₃×#67	1	1	yes	characteristic
83	D₃	—	6	2	no	—
84	C₂²	—	9	2	no	—
85	C₂²	—	18	1	no	—
86	C₂²	—	18	1	no	—
87	C₂²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	18	1	no	—
90	C₃	—	3	1	no	—
91	C₃	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
92	C₂	—	18	2	no	—
93	C₂	C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
94	C₂	C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
95	C₂	#611⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×AGL(1,ℤ/9)
commutator	C₂×C₉	C₂×C₃×C₄
Frattini, socle	C₂²×C₃	C₂×C₃×D₃
Fitting	C₂×C₄×3₋¹⁺²	C₂
prime radical	C₂²×AGL(1,ℤ/9)	C₂
cosocle	C₂²×C₉	C₂²×C₃
hypercenter	C₂×C₄	AGL(1,ℤ/9)
hypocenter	C₉	C₃×C₂²⋊C₄
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×3₋¹⁺²	C₂	semidirect
3. C₂×3₋¹⁺²⋊C₄	C₂	semidirect
5. (C₂×D₉)⋊C₄	C₃	semidirect
9. C₂×AGL(1,ℤ/9)	C₄	semidirect
17. C₂×C₄×C₉	C₂×C₃	semidirect
18. C₂×Dic₉	C₂×C₃	semidirect
35. C₂×D₉	C₃×C₄	semidirect
39. 3₋¹⁺²	C₂²⋊C₄	semidirect
72. C₉	C₃×C₂²⋊C₄	semidirect
75. C₂×C₄	AGL(1,ℤ/9)	semidirect

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/9)	2
C₂×C₄×3₋¹⁺²	2
C₂×3₋¹⁺²⋊C₄	2
C₃×(C₂×D₃)⋊C₄	3
(C₂×D₉)⋊C₄	3

Subgroups — (C2×AGL(1,ℤ/9))⋊C4 #88500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×AGL(1,ℤ/9))⋊C₄ #88500