Subgroups — #88742

Order 432.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#6233	C₂	1	2	yes	maximal, complemented
3	C₂×C₃⋊Dic₉	C₂	1	2	yes	maximal, complemented
4	C₄×C₃⋊D₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#6226	C₂	1	1	yes	maximal, characteristic, complemented
6	#3830	—	3	1	no	maximal
7	#3699	—	3	3	no	maximal
8	C₂²×C₃×C₉	C₂²	1	2	yes	—
9	C₂×C₃⋊D₉	C₂²	1	1	yes	characteristic
10	C₃×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₃⋊Dic₉	C₂²	1	2	yes	—
12	C₃⋊Dic₉	C₂²	1	1	yes	characteristic
13	C₃²×D₄	D₃	1	1	yes	characteristic
14	#638	—	3	2	no	—
15	C₂×C₃⋊Dic₃	—	3	2	no	—
16	C₄×C₃⋊D₃	—	3	1	no	—
17	#634	—	3	1	no	—
18	D₄×C₉	D₃	1	3	yes	complemented
19	#611	—	3	6	no	—
20	C₂×Dic₉	—	3	6	no	—
21	C₄×D₉	—	3	3	no	—
22	Dic₁₈	—	3	3	no	—
23	C₂×C₃×C₉	—	2	2	no	—
24	C₂×C₃×C₉	C₂³	1	1	yes	characteristic
25	C₃⋊D₉	—	2	1	no	—
26	#237	—	9	3	no	—
27	#237	—	9	1	no	—
28	C₂²×C₃²	C₂×D₃	1	2	yes	—
29	C₂×C₃⋊D₃	—	3	1	no	—
30	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
31	C₃⋊Dic₃	—	3	2	no	—
32	C₃⋊Dic₃	—	3	1	no	—
33	C₂²×C₉	C₂×D₃	1	6	yes	—
34	C₂×D₉	—	3	3	no	—
35	C₄×C₉	C₂×D₃	1	3	yes	—
36	Dic₉	—	3	6	no	—
37	Dic₉	—	3	3	no	—
38	C₃×C₉	#41	1	1	yes	characteristic, complemented, Sylow
39	C₃×D₄	D₉	1	3	yes	complemented
40	C₃×D₄	C₃⋊D₃	1	1	yes	characteristic
41	#67	—	9	6	no	—
42	#67	—	9	2	no	—
43	C₂×Dic₃	—	9	6	no	—
44	C₂×Dic₃	—	9	2	no	—
45	C₄×D₃	—	9	3	no	—
46	C₄×D₃	—	9	1	no	—
47	Dic₆	—	9	3	no	—
48	Dic₆	—	9	1	no	—
49	C₂×C₃²	—	2	2	no	—
50	C₂×C₃²	C₂²×D₃	1	1	yes	characteristic
51	C₃⋊D₃	—	6	1	no	—
52	C₂×C₉	—	2	6	no	—
53	C₂×C₉	C₂²×D₃	1	3	yes	—
54	D₉	—	6	3	no	—
55	#41	—	27	1	no	Sylow
56	C₂²×C₃	C₂×D₉	1	6	yes	—
57	C₂²×C₃	C₂×C₃⋊D₃	1	2	yes	—
58	C₂×D₃	—	9	3	no	—
59	C₂×D₃	—	9	1	no	—
60	C₃×C₄	C₂×D₉	1	3	yes	—
61	C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
62	Dic₃	—	9	6	no	—
63	Dic₃	—	9	3	no	—
64	Dic₃	—	9	2	no	—
65	Dic₃	—	9	1	no	—
66	C₃²	#237	1	1	yes	characteristic
67	C₉	#237	1	3	yes	complemented
68	Q₈	—	27	1	no	—
69	D₄	—	27	2	no	—
70	D₄	C₃⋊D₉	1	1	yes	characteristic, complemented
71	C₂×C₄	—	27	2	no	—
72	C₂×C₄	—	27	1	no	—
73	C₂×C₃	—	2	6	no	—
74	C₂×C₃	—	2	2	no	—
75	C₂×C₃	C₂²×D₉	1	3	yes	—
76	C₂×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
77	D₃	—	18	3	no	—
78	D₃	—	18	1	no	—
79	C₂²	—	27	1	no	—
80	C₂²	C₂×C₃⋊D₉	1	2	yes	—
81	C₄	—	27	1	no	—
82	C₄	—	27	2	no	—
83	C₄	C₂×C₃⋊D₉	1	1	yes	characteristic
84	C₃	#3699	1	3	yes	complemented
85	C₃	#3830	1	1	yes	characteristic
86	C₂	—	2	2	no	—
87	C₂	—	54	1	no	—
88	C₂	C₂²×C₃⋊D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×C₃⋊D₉
commutator, cosocle	C₂×C₃×C₉	C₂³
Frattini	C₂×C₃	C₂²×C₃⋊D₃
Fitting	C₃×D₄×C₉	C₂
socle	C₂×C₃²	C₂²×D₃
hypercenter	D₄	C₃⋊D₉
hypocenter	C₃×C₉	#41
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₃×D₄×C₉	C₂	semidirect
2. #6233	C₂	semidirect
3. C₂×C₃⋊Dic₉	C₂	semidirect
4. C₄×C₃⋊D₉	C₂	semidirect
5. #6226	C₂	semidirect
18. D₄×C₉	D₃	semidirect
38. C₃×C₉	#41	semidirect
39. C₃×D₄	D₉	semidirect
67. C₉	#237	semidirect
70. D₄	C₃⋊D₉	semidirect
84. C₃	#3699	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₄×C₉	2
#6233	2
C₂×C₃⋊Dic₉	2
C₄×C₃⋊D₉	2
#6226	2
#3830	3
#3699	3