Subgroups — D₇₂⋊C₃ #88476

Order 432.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊AGL(1,ℤ/9)	C₂	1	2	yes	maximal, complemented
2	C₈×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₄	—	3	1	no	maximal
4	D₇₂	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×AGL(1,ℤ/9)	—	2	2	no	—
6	C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
7	C₃×D₁₂	—	3	2	no	—
8	C₃²×C₈	D₃	1	1	yes	characteristic
9	D₃₆	C₂×C₃	1	2	yes	complemented
10	C₈×C₉	—	2	1	no	—
11	C₈×C₉	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×3₋¹⁺²	D₄	1	1	yes	characteristic
13	AGL(1,ℤ/9)	—	4	2	no	—
14	C₃×D₈	—	9	1	no	—
15	D₂₄	—	3	1	no	—
16	C₂×C₃×D₃	—	6	2	no	—
17	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
18	C₂×D₉	—	2	2	no	—
19	C₄×C₉	—	2	1	no	—
20	C₄×C₉	C₂²×C₃	1	1	yes	characteristic
21	3₋¹⁺²	D₈	1	1	yes	characteristic, complemented, Sylow
22	C₃×D₄	—	9	2	no	—
23	D₁₂	—	3	2	no	—
24	C₃×C₈	—	3	1	no	—
25	C₃×C₈	C₃×D₃	1	1	yes	characteristic
26	C₂×C₃²	D₁₂	1	1	yes	characteristic
27	C₃×D₃	—	12	2	no	—
28	C₂×C₉	—	2	1	no	—
29	C₂×C₉	C₃×D₄	1	1	yes	characteristic
30	D₉	—	4	2	no	—
31	D₈	—	9	1	no	Sylow
32	C₂²×C₃	—	18	2	no	—
33	C₂×D₃	—	6	2	no	—
34	C₃×C₄	—	3	1	no	—
35	C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
36	C₃²	D₂₄	1	1	yes	characteristic
37	C₉	—	2	1	no	—
38	C₉	C₃×D₈	1	1	yes	characteristic, complemented
39	D₄	—	9	2	no	—
40	C₈	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
41	C₂×C₃	—	3	1	no	—
42	C₂×C₃	—	36	2	no	—
43	C₂×C₃	C₃×D₁₂	1	1	yes	characteristic
44	D₃	—	12	2	no	—
45	C₂²	—	18	2	no	—
46	C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
47	C₃	—	3	1	no	—
48	C₃	C₃×D₂₄	1	1	yes	characteristic
49	C₂	—	36	2	no	—
50	C₂	C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₄⋊AGL(1,ℤ/9)
commutator, cosocle	C₄×C₉	C₂²×C₃
Frattini	C₃×C₄	C₂×C₃×D₃
Fitting	C₈×3₋¹⁺²	C₂
socle	C₂×C₃	C₃×D₁₂
hypercenter	C₈	AGL(1,ℤ/9)
hypocenter	C₉	C₃×D₈
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
1. C₄⋊AGL(1,ℤ/9)	C₂	semidirect
2. C₈×3₋¹⁺²	C₂	semidirect
4. D₇₂	C₃	semidirect
9. D₃₆	C₂×C₃	semidirect
11. C₈×C₉	C₂×C₃	semidirect
21. 3₋¹⁺²	D₈	semidirect
38. C₉	C₃×D₈	semidirect
40. C₈	AGL(1,ℤ/9)	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊AGL(1,ℤ/9)	2
C₈×3₋¹⁺²	2
C₃×D₂₄	3
D₇₂	3

Subgroups — D72⋊C3 #88476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇₂⋊C₃ #88476