Subgroups — #3697⋊C₃ #88708

Order 432.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
2	#611⋊C₃	C₂	1	2	yes	maximal, complemented
3	C₄⋊AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×AGL(1,ℤ/9)	C₂	1	2	yes	maximal, complemented
5	3₋¹⁺²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#235	—	3	1	no	maximal
7	#3697	C₃	1	1	yes	maximal, characteristic, complemented
8	C₂²×3₋¹⁺²	C₂²	1	1	yes	characteristic
9	C₂×AGL(1,ℤ/9)	C₂²	1	2	yes	—
10	C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
11	C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
12	3₋¹⁺²⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃²×C₄	D₃	1	1	yes	characteristic
14	C₃×#67	—	3	2	no	—
15	C₃×D₁₂	—	3	1	no	—
16	C₃×C₄×D₃	—	3	2	no	—
17	C₃×Dic₆	—	3	1	no	—
18	C₂×C₄×C₉	—	2	1	no	—
19	C₂×C₄×C₉	C₂×C₃	1	1	yes	characteristic, complemented
20	#611	C₂×C₃	1	2	yes	complemented
21	D₃₆	C₂×C₃	1	1	yes	characteristic, complemented
22	C₄×D₉	C₂×C₃	1	2	yes	complemented
23	Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×3₋¹⁺²	—	2	1	no	—
25	C₂×3₋¹⁺²	C₂³	1	1	yes	characteristic
26	AGL(1,ℤ/9)	—	2	2	no	—
27	C₃×#41	—	9	1	no	—
28	#235	—	3	1	no	—
29	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
30	C₂×C₃×D₃	—	3	2	no	—
31	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
32	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
33	C₃×Dic₃	—	3	2	no	—
34	C₂²×C₉	—	2	1	no	—
35	C₂²×C₉	C₂²×C₃	1	1	yes	characteristic
36	C₂×D₉	C₂²×C₃	1	2	yes	—
37	C₄×C₉	—	2	1	no	—
38	C₄×C₉	—	2	1	no	—
39	C₄×C₉	C₂²×C₃	1	1	yes	characteristic
40	C₄×C₉	C₂²×C₃	1	1	yes	characteristic
41	Dic₉	C₂²×C₃	1	2	yes	—
42	3₋¹⁺²	#41	1	1	yes	characteristic, complemented, Sylow
43	C₃×Q₈	—	9	1	no	—
44	C₃×D₄	—	9	1	no	—
45	C₃×D₄	—	9	2	no	—
46	C₂×C₃×C₄	—	3	1	no	—
47	C₂×C₃×C₄	—	9	2	no	—
48	C₂×C₃×C₄	C₃×D₃	1	1	yes	characteristic
49	#67	—	3	2	no	—
50	D₁₂	—	3	1	no	—
51	C₄×D₃	—	3	2	no	—
52	Dic₆	—	3	1	no	—
53	C₂×C₃²	—	2	1	no	—
54	C₂×C₃²	C₂²×D₃	1	1	yes	characteristic
55	C₃×D₃	—	6	2	no	—
56	C₂×C₉	—	2	2	no	—
57	C₂×C₉	—	2	1	no	—
58	C₂×C₉	—	2	1	no	—
59	C₂×C₉	C₂³×C₃	1	1	yes	characteristic
60	D₉	—	2	2	no	—
61	#41	—	9	1	no	Sylow
62	C₂²×C₃	—	3	1	no	—
63	C₂²×C₃	—	9	2	no	—
64	C₂²×C₃	C₂×C₃×D₃	1	1	yes	characteristic
65	C₂×D₃	—	3	2	no	—
66	C₃×C₄	—	3	1	no	—
67	C₃×C₄	—	3	1	no	—
68	C₃×C₄	—	9	2	no	—
69	C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
70	C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
71	Dic₃	—	3	2	no	—
72	C₃²	#235	1	1	yes	characteristic
73	C₉	—	2	1	no	—
74	C₉	C₃×#41	1	1	yes	characteristic, complemented
75	Q₈	—	9	1	no	—
76	D₄	—	9	2	no	—
77	D₄	—	9	1	no	—
78	C₂×C₄	—	9	2	no	—
79	C₂×C₄	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
80	C₂×C₃	—	2	1	no	—
81	C₂×C₃	—	3	1	no	—
82	C₂×C₃	—	6	1	no	—
83	C₂×C₃	—	18	2	no	—
84	C₂×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
85	D₃	—	6	2	no	—
86	C₂²	—	9	2	no	—
87	C₂²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
88	C₄	—	9	2	no	—
89	C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
90	C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
91	C₃	—	3	1	no	—
92	C₃	C₃×#235	1	1	yes	characteristic
93	C₂	—	2	1	no	—
94	C₂	—	18	2	no	—
95	C₂	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×AGL(1,ℤ/9)
commutator, cosocle	C₂×C₉	C₂³×C₃
Frattini, socle	C₂×C₃	C₂²×C₃×D₃
Fitting	C₂×C₄×3₋¹⁺²	C₂
hypercenter	C₂×C₄	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#41
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×3₋¹⁺²	C₂	semidirect
2. #611⋊C₃	C₂	semidirect
3. C₄⋊AGL(1,ℤ/9)	C₂	semidirect
4. C₄×AGL(1,ℤ/9)	C₂	semidirect
5. 3₋¹⁺²⋊Q₈	C₂	semidirect
7. #3697	C₃	semidirect
19. C₂×C₄×C₉	C₂×C₃	semidirect
20. #611	C₂×C₃	semidirect
21. D₃₆	C₂×C₃	semidirect
22. C₄×D₉	C₂×C₃	semidirect
23. Dic₁₈	C₂×C₃	semidirect
42. 3₋¹⁺²	#41	semidirect
74. C₉	C₃×#41	semidirect
79. 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
C₂×C₄×3₋¹⁺²	2
#611⋊C₃	2
C₄⋊AGL(1,ℤ/9)	2
C₄×AGL(1,ℤ/9)	2
3₋¹⁺²⋊Q₈	2
C₃×#235	3
#3697	3

Subgroups — #3697⋊C3 #88708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3697⋊C₃ #88708