Subgroups — C₃×C₉×D₈ #88568

Order 432.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₄×C₉	C₂	1	2	yes	maximal, complemented
2	C₃×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₈	C₃	1	1	yes	maximal, characteristic
4	C₉×D₈	C₃	1	3	yes	maximal, direct product factor
5	C₂²×C₃×C₉	—	2	2	no	—
6	C₃×C₄×C₉	C₂²	1	1	yes	characteristic
7	C₃²×D₄	C₂×C₃	1	2	yes	—
8	C₃²×C₈	C₂×C₃	1	1	yes	characteristic
9	D₄×C₉	C₂×C₃	1	6	yes	complemented
10	C₈×C₉	C₂×C₃	1	3	yes	complemented
11	C₂×C₃×C₉	—	4	2	no	—
12	C₂×C₃×C₉	D₄	1	1	yes	characteristic
13	C₃×D₈	C₉	1	3	yes	direct product factor
14	C₃×D₈	C₃²	1	1	yes	characteristic
15	C₂²×C₃²	—	2	2	no	—
16	C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
17	C₂²×C₉	—	2	6	no	—
18	C₄×C₉	C₂²×C₃	1	3	yes	—
19	C₃×C₉	D₈	1	1	yes	characteristic, direct product factor, Sylow
20	C₃×D₄	C₂×C₉	1	6	yes	complemented
21	C₃×D₄	C₂×C₃²	1	2	yes	—
22	C₃×C₈	C₂×C₉	1	3	yes	complemented
23	C₃×C₈	C₂×C₃²	1	1	yes	characteristic
24	C₂×C₃²	—	4	2	no	—
25	C₂×C₃²	C₃×D₄	1	1	yes	characteristic
26	C₂×C₉	—	4	6	no	—
27	C₂×C₉	C₃×D₄	1	3	yes	—
28	D₈	C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²×C₃	—	2	6	no	—
30	C₂²×C₃	—	2	2	no	—
31	C₃×C₄	C₂²×C₉	1	3	yes	—
32	C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
33	C₃²	C₃×D₈	1	1	yes	characteristic
34	C₉	C₃×D₈	1	3	yes	direct product factor
35	D₄	C₂×C₃×C₉	1	2	yes	complemented
36	C₈	C₂×C₃×C₉	1	1	yes	characteristic, complemented
37	C₂×C₃	—	4	6	no	—
38	C₂×C₃	—	4	2	no	—
39	C₂×C₃	D₄×C₉	1	3	yes	—
40	C₂×C₃	C₃²×D₄	1	1	yes	characteristic
41	C₂²	—	2	2	no	—
42	C₄	C₂²×C₃×C₉	1	1	yes	characteristic
43	C₃	C₉×D₈	1	3	yes	direct product factor
44	C₃	C₃²×D₈	1	1	yes	characteristic
45	C₂	—	4	2	no	—
46	C₂	C₃×D₄×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₉	D₄
commutator	C₄	C₂²×C₃×C₉
Frattini, cosocle	C₃×C₄	C₂²×C₃²
socle	C₂×C₃²	C₃×D₄
prime radical	C₃²×D₈	C₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₉ ◁ C₃×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×D₄×C₉	C₂	semidirect
2. C₃×C₈×C₉	C₂	semidirect
4. C₉×D₈	C₃	direct (N × H)
9. D₄×C₉	C₂×C₃	semidirect
10. C₈×C₉	C₂×C₃	semidirect
13. C₃×D₈	C₉	direct (N × H)
19. C₃×C₉	D₈	direct (N × H)
20. C₃×D₄	C₂×C₉	semidirect
22. C₃×C₈	C₂×C₉	semidirect
28. D₈	C₃×C₉	direct (N × H)
34. C₉	C₃×D₈	direct (N × H)
35. D₄	C₂×C₃×C₉	semidirect
36. C₈	C₂×C₃×C₉	semidirect
43. C₃	C₉×D₈	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×D₄×C₉	2
C₃×C₈×C₉	2
C₃²×D₈	3
C₉×D₈	3

Subgroups — C3×C9×D8 #88568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×D₈ #88568