Subgroups — C₂³×C₃⋊D₉ #88913

Order 432.

670 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃⋊D₉	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₃⋊D₃	—	3	1	no	maximal
4	C₂³×D₉	—	3	3	no	maximal
5	C₂²×C₃×C₉	C₂²	1	7	yes	complemented
6	C₂×C₃⋊D₉	C₂²	1	28	yes	direct product factor
7	C₂³×C₃²	D₃	1	1	yes	characteristic
8	C₂²×C₃⋊D₃	—	3	14	no	—
9	C₂³×C₉	D₃	1	3	yes	complemented
10	C₂²×D₉	—	3	42	no	—
11	C₂×C₃×C₉	C₂³	1	7	yes	complemented
12	C₃⋊D₉	C₂³	1	8	yes	direct product factor
13	C₂³×D₃	—	9	3	no	—
14	C₂³×D₃	—	9	1	no	—
15	C₂²×C₃²	C₂×D₃	1	7	yes	—
16	C₂×C₃⋊D₃	—	3	28	no	—
17	C₂²×C₉	C₂×D₃	1	21	yes	complemented
18	C₂×D₉	—	3	84	no	—
19	C₃×C₉	C₂⁴	1	1	yes	characteristic, complemented, Sylow
20	C₂³×C₃	D₉	1	3	yes	complemented
21	C₂³×C₃	C₃⋊D₃	1	1	yes	characteristic
22	C₂²×D₃	—	9	42	no	—
23	C₂²×D₃	—	9	14	no	—
24	C₂×C₃²	C₂²×D₃	1	7	yes	—
25	C₃⋊D₃	—	3	8	no	—
26	C₂×C₉	C₂²×D₃	1	21	yes	complemented
27	D₉	—	3	24	no	—
28	C₂⁴	—	27	1	no	Sylow
29	C₂²×C₃	C₂×D₉	1	21	yes	complemented
30	C₂²×C₃	C₂×C₃⋊D₃	1	7	yes	—
31	C₂×D₃	—	9	84	no	—
32	C₂×D₃	—	9	28	no	—
33	C₃²	C₂³×D₃	1	1	yes	characteristic
34	C₉	C₂³×D₃	1	3	yes	complemented
35	C₂³	—	27	14	no	—
36	C₂³	C₃⋊D₉	1	1	yes	characteristic, direct product factor
37	C₂×C₃	C₂²×D₉	1	21	yes	complemented
38	C₂×C₃	C₂²×C₃⋊D₃	1	7	yes	—
39	D₃	—	9	8	no	—
40	D₃	—	9	24	no	—
41	C₂²	—	27	28	no	—
42	C₂²	C₂×C₃⋊D₉	1	7	yes	direct product factor
43	C₃	C₂³×D₉	1	3	yes	complemented
44	C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
45	C₂	—	27	8	no	—
46	C₂	C₂²×C₃⋊D₉	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³	C₃⋊D₉
commutator, cosocle, hypocenter	C₃×C₉	C₂⁴
Frattini	C₃	C₂³×C₃⋊D₃
Fitting	C₂³×C₃×C₉	C₂
socle	C₂³×C₃²	D₃
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₉	C₂	semidirect
2. C₂²×C₃⋊D₉	C₂	direct (N × H)
5. C₂²×C₃×C₉	C₂²	semidirect
6. C₂×C₃⋊D₉	C₂²	direct (N × H)
9. C₂³×C₉	D₃	semidirect
11. C₂×C₃×C₉	C₂³	semidirect
12. C₃⋊D₉	C₂³	direct (N × H)
17. C₂²×C₉	C₂×D₃	semidirect
19. C₃×C₉	C₂⁴	semidirect
20. C₂³×C₃	D₉	semidirect
26. C₂×C₉	C₂²×D₃	semidirect
29. C₂²×C₃	C₂×D₉	semidirect
34. C₉	C₂³×D₃	semidirect
36. C₂³	C₃⋊D₉	direct (N × H)
37. C₂×C₃	C₂²×D₉	semidirect
42. C₂²	C₂×C₃⋊D₉	direct (N × H)
43. C₃	C₂³×D₉	semidirect
46. C₂	C₂²×C₃⋊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
C₂³×C₃×C₉	2
C₂²×C₃⋊D₉	2
C₂³×C₃⋊D₃	3
C₂³×D₉	3

Subgroups — C23×C3⋊D9 #88913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃⋊D₉ #88913