Subgroups — #88414

Order 432.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃⋊D₉	C₂	1	1	yes	maximal, characteristic
2	C₉×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#3712	—	3	1	no	maximal
5	#3663	—	3	1	no	maximal
6	C₂×C₃⋊D₉	C₄	1	1	yes	characteristic
7	C₃×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₃⋊Dic₉	C₄	1	1	yes	characteristic
9	C₄×C₃⋊D₃	—	3	1	no	—
10	C₃×C₃⋊C₈	—	3	1	no	—
11	C₃×C₃⋊C₈	D₃	1	1	yes	characteristic
12	C₄×D₉	—	3	1	no	—
13	C₄×D₉	—	6	1	no	—
14	C₈×C₉	—	3	1	no	—
15	C₉⋊C₈	D₃	1	1	yes	characteristic, complemented
16	C₂×C₃×C₉	C₂×C₄	1	1	yes	characteristic
17	C₃⋊D₉	—	2	1	no	—
18	ΓL(1,𝔽₂₅)	—	9	1	no	—
19	ΓL(1,𝔽₂₅)	—	9	1	no	—
20	C₂×C₃⋊D₃	—	3	1	no	—
21	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
22	C₃⋊Dic₃	—	3	1	no	—
23	C₂×D₉	—	3	1	no	—
24	C₂×D₉	—	6	1	no	—
25	C₄×C₉	—	2	1	no	—
26	C₄×C₉	C₂×D₃	1	1	yes	characteristic
27	Dic₉	—	3	1	no	—
28	Dic₉	—	6	1	no	—
29	C₃×C₉	M₁₆	1	1	yes	characteristic, complemented, Sylow
30	C₄×D₃	—	9	1	no	—
31	C₄×D₃	—	9	1	no	—
32	C₄×D₃	—	18	1	no	—
33	C₃×C₈	—	3	1	no	—
34	C₃×C₈	—	9	1	no	—
35	C₃⋊C₈	—	3	1	no	—
36	C₃⋊C₈	D₉	1	1	yes	characteristic, complemented
37	C₂×C₃²	C₄×D₃	1	1	yes	characteristic
38	C₃⋊D₃	—	6	1	no	—
39	C₂×C₉	—	2	1	no	—
40	C₂×C₉	C₄×D₃	1	1	yes	characteristic
41	D₉	—	6	2	no	—
42	D₉	—	6	1	no	—
43	M₁₆	—	27	1	no	Sylow
44	C₂×D₃	—	9	1	no	—
45	C₂×D₃	—	9	1	no	—
46	C₂×D₃	—	18	1	no	—
47	C₃×C₄	—	2	1	no	—
48	C₃×C₄	C₂×D₉	1	1	yes	characteristic
49	C₃×C₄	D₃²	1	1	yes	characteristic
50	Dic₃	—	9	1	no	—
51	Dic₃	—	9	1	no	—
52	Dic₃	—	18	1	no	—
53	C₃²	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
54	C₉	—	2	1	no	—
55	C₉	ΓL(1,𝔽₂₅)	1	1	yes	characteristic, complemented
56	C₂×C₄	—	27	1	no	—
57	C₈	—	3	1	no	—
58	C₈	—	9	1	no	—
59	C₂×C₃	—	2	1	no	—
60	C₂×C₃	C₄×D₉	1	1	yes	characteristic
61	C₂×C₃	#624	1	1	yes	characteristic
62	D₃	—	18	2	no	—
63	D₃	—	18	1	no	—
64	D₃	—	18	1	no	—
65	C₂²	—	27	1	no	—
66	C₄	—	27	1	no	—
67	C₄	D₃×D₉	1	1	yes	characteristic
68	C₃	—	2	1	no	—
69	C₃	#3663	1	1	yes	characteristic, complemented
70	C₃	#3712	1	1	yes	characteristic
71	C₂	—	54	1	no	—
72	C₂	(C₃⋊D₉)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	D₃×D₉
commutator	C₂×C₃×C₉	C₂×C₄
Frattini	C₃×C₄	D₃²
Fitting, cosocle	C₃×C₄×C₉	C₂²
socle	C₂×C₃²	C₄×D₃
prime radical	C₂×C₃⋊D₉	C₄
hypocenter	C₃×C₉	M₁₆
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₉×C₃⋊C₈	C₂	semidirect
3. C₃×C₉⋊C₈	C₂	semidirect
15. C₉⋊C₈	D₃	semidirect
29. C₃×C₉	M₁₆	semidirect
36. C₃⋊C₈	D₉	semidirect
55. C₉	ΓL(1,𝔽₂₅)	semidirect
69. C₃	#3663	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₃⋊D₉	2
C₉×C₃⋊C₈	2
C₃×C₉⋊C₈	2
#3712	3
#3663	3