Subgroups — C₂×3₋¹⁺²⋊C₈ #88495

Order 432.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₄	AGL(1,ℤ/9)
commutator, hypocenter	C₉	C₂×C₃×C₈
Frattini	C₃×C₄	C₂×C₃×D₃
Fitting	C₂×C₄×3₋¹⁺²	C₂
socle	C₂²×C₃	C₃×Dic₃
prime radical	C₂²×C₃²	Dic₃
cosocle	C₄×C₉	C₂²×C₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. 3₋¹⁺²⋊C₈	C₂	direct (N × H)
4. C₂×C₉⋊C₈	C₃	semidirect
12. C₉⋊C₈	C₂×C₃	semidirect
13. C₂×3₋¹⁺²	C₈	semidirect
26. 3₋¹⁺²	C₂×C₈	semidirect
35. C₂×C₉	C₃×C₈	semidirect
46. C₉	C₂×C₃×C₈	semidirect
58. C₂	3₋¹⁺²⋊C₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×3₋¹⁺²	2
3₋¹⁺²⋊C₈	2
C₂×C₃×C₃⋊C₈	3
C₂×C₉⋊C₈	3

Subgroups — C2×3−1+2⋊C8 #88495

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×3₋¹⁺²⋊C₈ #88495