Subgroups — C₃×Q₈×D₉ #88717

Order 432.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×D₉	C₂	1	3	yes	maximal
3	C₃×Dic₁₈	C₂	1	3	yes	maximal, complemented
4	C₃×D₃×Q₈	—	3	1	no	maximal
5	Q₈×D₉	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃×D₉	C₂²	1	1	yes	characteristic
7	C₃×C₄×C₉	C₂²	1	3	yes	—
8	C₃×Dic₉	C₂²	1	3	yes	—
9	C₃²×Q₈	D₃	1	1	yes	characteristic
10	C₃×C₄×D₃	—	3	3	no	—
11	C₃×Dic₆	—	3	3	no	—
12	Q₈×C₉	—	2	1	no	—
13	Q₈×C₉	C₂×C₃	1	1	yes	characteristic, complemented
14	C₄×D₉	C₂×C₃	1	3	yes	—
15	Dic₁₈	C₂×C₃	1	3	yes	complemented
16	C₂×C₃×C₉	C₂³	1	1	yes	characteristic
17	C₃×D₉	Q₈	1	2	yes	direct product factor
18	C₂×C₃×Q₈	—	9	1	no	—
19	D₃×Q₈	—	3	1	no	—
20	C₂×C₃×D₃	—	3	1	no	—
21	C₃²×C₄	C₂×D₃	1	3	yes	—
22	C₃×Dic₃	—	3	3	no	—
23	C₂×D₉	C₂²×C₃	1	1	yes	characteristic
24	C₄×C₉	—	2	3	no	—
25	C₄×C₉	C₂²×C₃	1	3	yes	—
26	Dic₉	C₂²×C₃	1	3	yes	—
27	C₃×C₉	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
28	C₃×Q₈	—	2	1	no	—
29	C₃×Q₈	—	9	3	no	—
30	C₃×Q₈	D₉	1	1	yes	characteristic, direct product factor
31	C₃×Q₈	C₃×D₃	1	1	yes	characteristic
32	C₂×C₃×C₄	—	9	3	no	—
33	C₄×D₃	—	3	3	no	—
34	Dic₆	—	3	3	no	—
35	C₂×C₃²	C₂²×D₃	1	1	yes	characteristic
36	C₃×D₃	—	3	2	no	—
37	C₂×C₉	—	2	1	no	—
38	C₂×C₉	C₂³×C₃	1	1	yes	characteristic
39	D₉	C₃×Q₈	1	2	yes	direct product factor
40	C₂×Q₈	—	9	1	no	Sylow
41	C₂²×C₃	—	9	1	no	—
42	C₂×D₃	—	3	1	no	—
43	C₃×C₄	—	2	3	no	—
44	C₃×C₄	—	9	3	no	—
45	C₃×C₄	C₂×D₉	1	3	yes	—
46	C₃×C₄	C₂×C₃×D₃	1	3	yes	—
47	Dic₃	—	3	3	no	—
48	C₃²	D₃×Q₈	1	1	yes	characteristic
49	C₉	—	2	1	no	—
50	C₉	C₂×C₃×Q₈	1	1	yes	characteristic, complemented
51	Q₈	—	9	3	no	—
52	Q₈	C₃×D₉	1	1	yes	characteristic, direct product factor
53	C₂×C₄	—	9	3	no	—
54	C₂×C₃	—	2	1	no	—
55	C₂×C₃	—	9	2	no	—
56	C₂×C₃	C₂²×D₉	1	1	yes	characteristic
57	C₂×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
58	D₃	—	3	2	no	—
59	C₂²	—	9	1	no	—
60	C₄	—	9	3	no	—
61	C₄	C₂×C₃×D₉	1	3	yes	—
62	C₃	—	2	1	no	—
63	C₃	Q₈×D₉	1	1	yes	characteristic, direct product factor
64	C₃	C₃×D₃×Q₈	1	1	yes	characteristic
65	C₂	—	9	2	no	—
66	C₂	C₂²×C₃×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²×D₉
commutator, cosocle	C₂×C₉	C₂³×C₃
Frattini	C₂×C₃	C₂²×C₃×D₃
Fitting	C₃×Q₈×C₉	C₂
socle	C₂×C₃²	C₂²×D₃
prime radical	C₂×C₃×D₉	C₂²
hypercenter	C₃×Q₈	D₉
hypocenter	C₉	C₂×C₃×Q₈
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃ ◁ C₃×Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×Q₈×C₉	C₂	semidirect
3. C₃×Dic₁₈	C₂	semidirect
5. Q₈×D₉	C₃	direct (N × H)
13. Q₈×C₉	C₂×C₃	semidirect
15. Dic₁₈	C₂×C₃	semidirect
17. C₃×D₉	Q₈	direct (N × H)
27. C₃×C₉	C₂×Q₈	semidirect
30. C₃×Q₈	D₉	direct (N × H)
39. D₉	C₃×Q₈	direct (N × H)
50. C₉	C₂×C₃×Q₈	semidirect
52. Q₈	C₃×D₉	direct (N × H)
63. C₃	Q₈×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
C₃×Q₈×C₉	2
C₃×C₄×D₉	2
C₃×Dic₁₈	2
C₃×D₃×Q₈	3
Q₈×D₉	3

Subgroups — C3×Q8×D9 #88717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Q₈×D₉ #88717