Subgroups — #3699⋊C₃ #88716

Order 432.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
2	#611⋊C₃	C₂	1	2	yes	maximal, complemented
3	C₂×3₋¹⁺²⋊C₄	C₂	1	2	yes	maximal, complemented
4	C₄×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
5	3₋¹⁺²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#237	—	3	1	no	maximal
7	#3699	C₃	1	1	yes	maximal, characteristic, complemented
8	C₂²×3₋¹⁺²	C₂²	1	2	yes	—
9	C₂×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
10	C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
11	3₋¹⁺²⋊C₄	C₂²	1	2	yes	—
12	3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
13	C₃²×D₄	D₃	1	1	yes	characteristic
14	C₃×#67	—	3	2	no	—
15	C₂×C₃×Dic₃	—	3	2	no	—
16	C₃×C₄×D₃	—	3	1	no	—
17	C₃×Dic₆	—	3	1	no	—
18	D₄×C₉	—	2	1	no	—
19	D₄×C₉	C₂×C₃	1	1	yes	characteristic, complemented
20	#611	C₂×C₃	1	2	yes	complemented
21	C₂×Dic₉	C₂×C₃	1	2	yes	complemented
22	C₄×D₉	C₂×C₃	1	1	yes	characteristic, complemented
23	Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×3₋¹⁺²	—	2	2	no	—
25	C₂×3₋¹⁺²	C₂³	1	1	yes	characteristic
26	AGL(1,ℤ/9)	—	2	1	no	—
27	C₃×#41	—	9	1	no	—
28	#237	—	3	1	no	—
29	C₂²×C₃²	C₂×D₃	1	2	yes	—
30	C₂×C₃×D₃	—	3	1	no	—
31	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
32	C₃×Dic₃	—	3	2	no	—
33	C₃×Dic₃	—	3	1	no	—
34	C₂²×C₉	—	2	2	no	—
35	C₂²×C₉	C₂²×C₃	1	2	yes	—
36	C₂×D₉	C₂²×C₃	1	1	yes	characteristic
37	C₄×C₉	—	2	1	no	—
38	C₄×C₉	C₂²×C₃	1	1	yes	characteristic
39	Dic₉	C₂²×C₃	1	2	yes	—
40	Dic₉	C₂²×C₃	1	1	yes	characteristic
41	3₋¹⁺²	#41	1	1	yes	characteristic, complemented, Sylow
42	C₃×Q₈	—	9	1	no	—
43	C₃×D₄	—	3	1	no	—
44	C₃×D₄	—	9	2	no	—
45	C₃×D₄	C₃×D₃	1	1	yes	characteristic
46	C₂×C₃×C₄	—	9	1	no	—
47	C₂×C₃×C₄	—	9	2	no	—
48	#67	—	3	2	no	—
49	C₂×Dic₃	—	3	2	no	—
50	C₄×D₃	—	3	1	no	—
51	Dic₆	—	3	1	no	—
52	C₂×C₃²	—	2	2	no	—
53	C₂×C₃²	C₂²×D₃	1	1	yes	characteristic
54	C₃×D₃	—	6	1	no	—
55	C₂×C₉	—	2	2	no	—
56	C₂×C₉	—	2	1	no	—
57	C₂×C₉	—	4	2	no	—
58	C₂×C₉	C₂³×C₃	1	1	yes	characteristic
59	D₉	—	2	1	no	—
60	#41	—	9	1	no	Sylow
61	C₂²×C₃	—	3	2	no	—
62	C₂²×C₃	—	9	1	no	—
63	C₂²×C₃	C₂×C₃×D₃	1	2	yes	—
64	C₂×D₃	—	3	1	no	—
65	C₃×C₄	—	3	1	no	—
66	C₃×C₄	—	9	1	no	—
67	C₃×C₄	—	9	2	no	—
68	C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
69	Dic₃	—	3	2	no	—
70	Dic₃	—	3	1	no	—
71	C₃²	#237	1	1	yes	characteristic
72	C₉	—	2	1	no	—
73	C₉	C₃×#41	1	1	yes	characteristic, complemented
74	Q₈	—	9	1	no	—
75	D₄	—	9	2	no	—
76	D₄	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
77	C₂×C₄	—	9	2	no	—
78	C₂×C₄	—	9	1	no	—
79	C₂×C₃	—	2	2	no	—
80	C₂×C₃	—	3	1	no	—
81	C₂×C₃	—	6	2	no	—
82	C₂×C₃	—	18	1	no	—
83	C₂×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
84	D₃	—	6	1	no	—
85	C₂²	—	9	1	no	—
86	C₂²	C₂×AGL(1,ℤ/9)	1	2	yes	—
87	C₄	—	9	1	no	—
88	C₄	—	9	2	no	—
89	C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
90	C₃	—	3	1	no	—
91	C₃	C₃×#237	1	1	yes	characteristic
92	C₂	—	2	2	no	—
93	C₂	—	18	1	no	—
94	C₂	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×AGL(1,ℤ/9)
commutator, cosocle	C₂×C₉	C₂³×C₃
Frattini, socle	C₂×C₃	C₂²×C₃×D₃
Fitting	D₄×3₋¹⁺²	C₂
hypercenter	D₄	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#41
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. D₄×3₋¹⁺²	C₂	semidirect
2. #611⋊C₃	C₂	semidirect
3. C₂×3₋¹⁺²⋊C₄	C₂	semidirect
4. C₄×AGL(1,ℤ/9)	C₂	semidirect
5. 3₋¹⁺²⋊Q₈	C₂	semidirect
7. #3699	C₃	semidirect
19. D₄×C₉	C₂×C₃	semidirect
20. #611	C₂×C₃	semidirect
21. C₂×Dic₉	C₂×C₃	semidirect
22. C₄×D₉	C₂×C₃	semidirect
23. Dic₁₈	C₂×C₃	semidirect
41. 3₋¹⁺²	#41	semidirect
73. C₉	C₃×#41	semidirect
76. D₄	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
D₄×3₋¹⁺²	2
#611⋊C₃	2
C₂×3₋¹⁺²⋊C₄	2
C₄×AGL(1,ℤ/9)	2
3₋¹⁺²⋊Q₈	2
C₃×#237	3
#3699	3

Subgroups — #3699⋊C3 #88716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3699⋊C₃ #88716