Subgroups — D₃×Q₈⋊C₉ #88621

Order 432.

65 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×D₃×Q₈	C₃	1	1	yes	maximal, characteristic
3	C₂×Q₈⋊C₉	—	3	1	no	maximal
4	C₂×D₃×C₉	—	4	1	no	maximal
5	C₃²×Q₈	C₂×C₃	1	1	yes	characteristic
6	C₃×C₄×D₃	—	3	1	no	—
7	C₃×Dic₆	—	3	1	no	—
8	Q₈⋊C₉	—	2	1	no	—
9	Q₈⋊C₉	D₃	1	1	yes	characteristic, direct product factor
10	C₂×C₃×C₉	—	4	1	no	—
11	D₃×C₉	—	4	2	no	—
12	C₂×C₃×Q₈	—	3	1	no	—
13	D₃×Q₈	C₉	1	1	yes	characteristic, complemented
14	C₂×C₃×D₃	A₄	1	1	yes	characteristic
15	C₃²×C₄	—	3	1	no	—
16	C₃×Dic₃	—	3	1	no	—
17	C₂²×C₉	—	12	1	no	—
18	C₃×C₉	—	4	1	no	Sylow
19	C₃×Q₈	—	2	1	no	—
20	C₃×Q₈	—	9	1	no	—
21	C₃×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
22	C₃×Q₈	C₃×D₃	1	1	yes	characteristic
23	C₂×C₃×C₄	—	9	1	no	—
24	C₄×D₃	—	3	1	no	—
25	Dic₆	—	3	1	no	—
26	C₂×C₃²	C₂×A₄	1	1	yes	characteristic
27	C₃×D₃	SL(2,𝔽₃)	1	2	yes	—
28	C₂×C₉	—	4	1	no	—
29	C₂×C₉	—	8	1	no	—
30	C₂×C₉	—	12	2	no	—
31	C₂×Q₈	—	3	1	no	Sylow
32	C₂²×C₃	—	3	1	no	—
33	C₂×D₃	C₂²⋊C₉	1	1	yes	characteristic
34	C₃×C₄	—	3	1	no	—
35	C₃×C₄	—	3	1	no	—
36	C₃×C₄	—	6	1	no	—
37	C₃×C₄	—	9	1	no	—
38	Dic₃	—	3	1	no	—
39	C₃²	C₂×SL(2,𝔽₃)	1	1	yes	characteristic
40	C₉	—	4	1	no	—
41	C₉	—	8	1	no	—
42	Q₈	—	9	1	no	—
43	Q₈	D₃×C₉	1	1	yes	characteristic, complemented
44	C₂×C₄	—	9	1	no	—
45	C₂×C₃	—	2	1	no	—
46	C₂×C₃	—	3	2	no	—
47	C₂×C₃	C₂×C₂²⋊C₉	1	1	yes	characteristic
48	C₂×C₃	D₃×A₄	1	1	yes	characteristic
49	D₃	Q₈⋊C₉	1	2	yes	direct product factor
50	C₂²	—	3	1	no	—
51	C₄	—	3	1	no	—
52	C₄	—	9	1	no	—
53	C₃	—	2	1	no	—
54	C₃	C₂×Q₈⋊C₉	1	1	yes	characteristic, complemented
55	C₃	D₃×SL(2,𝔽₃)	1	1	yes	characteristic
56	C₂	—	3	2	no	—
57	C₂	D₃×C₂²⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	D₃×A₄
commutator, hypocenter	C₃×Q₈	C₂×C₉
Fitting, cosocle	C₃²×Q₈	C₂×C₃
socle	C₂×C₃²	C₂×A₄
prime radical	C₂×C₃×D₃	A₄
LCS	G ▷ C₃×Q₈
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×Q₈⋊C₉	C₂	semidirect
9. Q₈⋊C₉	D₃	direct (N × H)
13. D₃×Q₈	C₉	semidirect
21. C₃×Q₈	C₂×C₉	semidirect
43. Q₈	D₃×C₉	semidirect
49. D₃	Q₈⋊C₉	direct (N × H)
54. C₃	C₂×Q₈⋊C₉	semidirect

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×D₃×Q₈	3
C₂×Q₈⋊C₉	3
C₂×D₃×C₉	4

Subgroups — D3×Q8⋊C9 #88621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×Q₈⋊C₉ #88621