Subgroups — C₂×C₃×C₉⋊C₈ #88477

Order 432.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₉⋊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, direct product factor
5	C₂²×C₃×C₉	C₄	1	1	yes	characteristic
6	C₃×C₄×C₉	C₄	1	1	yes	characteristic
7	C₃×C₄×C₉	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	direct product factor
13	C₂×C₃×C₉	C₈	1	2	yes	complemented
14	C₂×C₃×C₉	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	C₃×C₉	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃×C₄	—	2	1	no	—
28	C₂×C₃×C₄	D₉	1	1	yes	characteristic
29	C₂×C₃×C₄	C₃×D₃	1	1	yes	characteristic
30	C₃×C₈	—	9	2	no	—
31	C₃⋊C₈	—	3	2	no	—
32	C₂×C₃²	C₃⋊C₈	1	2	yes	—
33	C₂×C₃²	C₂×Dic₃	1	1	yes	characteristic
34	C₂×C₉	—	2	2	no	—
35	C₂×C₉	—	2	1	no	—
36	C₂×C₉	C₃×C₈	1	2	yes	complemented
37	C₂×C₉	C₂×C₃×C₄	1	1	yes	characteristic
38	C₂×C₈	—	9	1	no	Sylow
39	C₂²×C₃	—	2	1	no	—
40	C₂²×C₃	Dic₉	1	1	yes	characteristic
41	C₂²×C₃	C₃×Dic₃	1	1	yes	characteristic
42	C₃×C₄	—	2	1	no	—
43	C₃×C₄	—	2	1	no	—
44	C₃×C₄	Dic₉	1	1	yes	characteristic
45	C₃×C₄	C₂×D₉	1	1	yes	characteristic
46	C₃×C₄	C₃×Dic₃	1	1	yes	characteristic
47	C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
48	C₃²	C₂×C₃⋊C₈	1	1	yes	characteristic
49	C₉	—	2	1	no	—
50	C₉	C₂×C₃×C₈	1	1	yes	characteristic, complemented
51	C₂×C₄	C₃×D₉	1	1	yes	characteristic
52	C₈	—	9	2	no	—
53	C₂×C₃	—	2	2	no	—
54	C₂×C₃	—	2	1	no	—
55	C₂×C₃	C₉⋊C₈	1	2	yes	direct product factor
56	C₂×C₃	C₂×Dic₉	1	1	yes	characteristic
57	C₂×C₃	C₃×C₃⋊C₈	1	2	yes	—
58	C₂×C₃	C₂×C₃×Dic₃	1	1	yes	characteristic
59	C₂²	C₃×Dic₉	1	1	yes	characteristic
60	C₄	C₃×Dic₉	1	1	yes	characteristic
61	C₄	C₂×C₃×D₉	1	1	yes	characteristic
62	C₃	—	2	1	no	—
63	C₃	C₂×C₉⋊C₈	1	1	yes	characteristic, direct product factor
64	C₃	C₂×C₃×C₃⋊C₈	1	1	yes	characteristic
65	C₂	C₃×C₉⋊C₈	1	2	yes	direct product factor
66	C₂	C₂×C₃×Dic₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₄	D₉
commutator, hypocenter	C₉	C₂×C₃×C₈
Frattini	C₃×C₄	C₂×C₃×D₃
Fitting	C₂×C₃×C₄×C₉	C₂
socle, prime radical	C₂²×C₃²	Dic₃
cosocle	C₄×C₉	C₂²×C₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₃×C₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₉⋊C₈	C₂	direct (N × H)
4. C₂×C₉⋊C₈	C₃	direct (N × H)
12. C₉⋊C₈	C₂×C₃	direct (N × H)
13. C₂×C₃×C₉	C₈	semidirect
26. C₃×C₉	C₂×C₈	semidirect
36. C₂×C₉	C₃×C₈	semidirect
50. C₉	C₂×C₃×C₈	semidirect
55. C₂×C₃	C₉⋊C₈	direct (N × H)
63. C₃	C₂×C₉⋊C₈	direct (N × H)
65. C₂	C₃×C₉⋊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×C₃×C₄×C₉	2
C₃×C₉⋊C₈	2
C₂×C₃×C₃⋊C₈	3
C₂×C₉⋊C₈	3

Subgroups — C2×C3×C9⋊C8 #88477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₉⋊C₈ #88477