Subgroups — D₉×C₃⋊C₈ #88411

Order 432.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₄	D₃×D₉
commutator, hypocenter	C₃×C₉	C₂×C₈
Frattini	C₃×C₄	D₃²
Fitting, cosocle	C₃×C₄×C₉	C₂²
socle	C₂×C₃²	C₄×D₃
prime radical	C₂×C₃×D₉	C₄
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₉⋊C₈)	C₂	semidirect
3. C₉×C₃⋊C₈	C₂	semidirect
17. C₃×D₉	C₈	semidirect
27. C₃×C₉	C₂×C₈	semidirect
34. C₃⋊C₈	D₉	direct (N × H)
39. D₉	C₃⋊C₈	direct (N × H)
50. C₉	C₂×C₃⋊C₈	semidirect
63. C₃	C₈×D₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×D₉	2
C₃⋊(C₉⋊C₈)	2
C₉×C₃⋊C₈	2
D₃×C₃⋊C₈	3
C₈×D₉	3

Subgroups — D9×C3⋊C8 #88411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×C₃⋊C₈ #88411