Subgroups — C₃×C₈×D₉ #88458

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×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₃×C₈	—	3	1	no	maximal
5	C₈×D₉	C₃	1	1	yes	maximal, characteristic, direct product factor
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	C₃²×C₈	D₃	1	1	yes	characteristic
11	C₃×C₃⋊C₈	—	3	1	no	—
12	C₄×D₉	C₂×C₃	1	1	yes	characteristic
13	C₈×C₉	—	2	1	no	—
14	C₈×C₉	C₂×C₃	1	1	yes	characteristic, complemented
15	C₉⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
16	C₂×C₃×C₉	C₂×C₄	1	1	yes	characteristic
17	C₃×D₉	C₈	1	2	yes	direct product factor
18	C₂×C₃×C₈	—	9	1	no	—
19	D₃×C₈	—	3	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	C₃×C₄	1	1	yes	characteristic
24	C₄×C₉	—	2	1	no	—
25	C₄×C₉	C₂²×C₃	1	1	yes	characteristic
26	Dic₉	C₃×C₄	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	—	2	1	no	—
31	C₃×C₈	—	9	1	no	—
32	C₃×C₈	D₉	1	1	yes	characteristic, direct product factor
33	C₃×C₈	C₃×D₃	1	1	yes	characteristic
34	C₃⋊C₈	—	3	1	no	—
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×C₃×C₄	1	1	yes	characteristic
39	D₉	C₃×C₈	1	2	yes	direct product factor
40	C₂×C₈	—	9	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	C₂×C₃×D₃	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	—	9	1	no	—
53	C₈	C₃×D₉	1	1	yes	characteristic, direct product factor
54	C₂×C₃	—	2	1	no	—
55	C₂×C₃	—	9	2	no	—
56	C₂×C₃	C₄×D₉	1	1	yes	characteristic
57	C₂×C₃	C₃×C₄×D₃	1	1	yes	characteristic
58	D₃	—	3	2	no	—
59	C₂²	—	9	1	no	—
60	C₄	—	9	1	no	—
61	C₄	C₂×C₃×D₉	1	1	yes	characteristic
62	C₃	—	2	1	no	—
63	C₃	C₈×D₉	1	1	yes	characteristic, direct product factor
64	C₃	C₃×D₃×C₈	1	1	yes	characteristic
65	C₂	—	9	2	no	—
66	C₂	C₃×C₄×D₉	1	1	yes	characteristic

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

Complements

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

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

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×C₈×C₉	2
C₃×C₉⋊C₈	2
C₃×D₃×C₈	3
C₈×D₉	3

Subgroups — C3×C8×D9 #88458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈×D₉ #88458