Subgroups — C₃×C₉⋊(Q₈⋊C₉) #14517226

Order 1944.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×Q₈×C₉	C₃	1	1	yes	maximal, characteristic
2	C₃²×Q₈⋊C₉	C₃	1	3	yes	maximal
3	C₉⋊(Q₈⋊C₉)	C₃	1	9	yes	maximal, direct product factor
4	C₂×C₃×C₉⋊C₉	—	4	1	no	maximal
5	C₃²×C₄×C₉	—	3	1	no	—
6	C₃×C₉⋊C₉	—	4	1	no	Sylow
7	C₃³×Q₈	C₃²	1	1	yes	characteristic
8	C₃×Q₈×C₉	C₉	1	9	yes	complemented
9	C₃×Q₈×C₉	C₃²	1	3	yes	—
10	C₃×Q₈⋊C₉	—	3	9	no	—
11	C₃×Q₈⋊C₉	C₃²	1	9	yes	—
12	C₂×C₃²×C₉	—	4	3	no	—
13	C₂×C₃²×C₉	A₄	1	1	yes	characteristic
14	C₂×C₉⋊C₉	—	4	9	no	—
15	C₃³×C₄	—	3	1	no	—
16	C₃×C₄×C₉	—	3	9	no	—
17	C₃×C₄×C₉	—	3	3	no	—
18	C₃²×C₉	—	4	3	no	—
19	C₃²×C₉	SL(2,𝔽₃)	1	1	yes	characteristic
20	C₉⋊C₉	—	4	9	no	—
21	C₃²×Q₈	C₃×C₉	1	3	yes	—
22	C₃²×Q₈	3₋¹⁺²	1	9	yes	—
23	C₃²×Q₈	C₃³	1	1	yes	characteristic
24	Q₈×C₉	C₃×C₉	1	9	yes	complemented
25	Q₈⋊C₉	—	3	9	no	—
26	C₂×C₃³	C₃×A₄	1	1	yes	characteristic
27	C₂×C₃×C₉	—	4	9	no	—
28	C₂×C₃×C₉	—	12	9	no	—
29	C₂×C₃×C₉	C₂²⋊C₉	1	9	yes	—
30	C₂×C₃×C₉	C₃×A₄	1	3	yes	—
31	C₃²×C₄	—	3	9	no	—
32	C₃²×C₄	—	3	3	no	—
33	C₃²×C₄	—	3	1	no	—
34	C₄×C₉	—	3	9	no	—
35	C₃³	C₃×SL(2,𝔽₃)	1	1	yes	characteristic
36	C₃×C₉	—	4	9	no	—
37	C₃×C₉	—	12	9	no	—
38	C₃×C₉	Q₈⋊C₉	1	9	yes	complemented
39	C₃×C₉	C₃×SL(2,𝔽₃)	1	3	yes	—
40	C₃×Q₈	C₉⋊C₉	1	9	yes	complemented
41	C₃×Q₈	C₃²×C₉	1	1	yes	characteristic
42	C₃×Q₈	C₃×3₋¹⁺²	1	3	yes	—
43	C₂×C₃²	C₉⋊A₄	1	9	yes	—
44	C₂×C₃²	C₃×C₂²⋊C₉	1	3	yes	—
45	C₂×C₃²	C₃²×A₄	1	1	yes	characteristic
46	C₂×C₉	—	12	9	no	—
47	C₂×C₉	C₃×C₂²⋊C₉	1	9	yes	—
48	C₃×C₄	—	3	9	no	—
49	C₃×C₄	—	3	3	no	—
50	C₃×C₄	—	3	1	no	—
51	C₃²	C₉⋊SL(2,𝔽₃)	1	9	yes	—
52	C₃²	C₃×Q₈⋊C₉	1	3	yes	—
53	C₃²	C₃²×SL(2,𝔽₃)	1	1	yes	characteristic
54	C₉	—	12	9	no	—
55	C₉	C₃×Q₈⋊C₉	1	9	yes	complemented
56	Q₈	C₃×C₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	C₉⋊(C₂²⋊C₉)	1	9	yes	—
58	C₂×C₃	C₃×C₉⋊A₄	1	3	yes	—
59	C₂×C₃	C₃²×C₂²⋊C₉	1	1	yes	characteristic
60	C₄	—	3	1	no	—
61	C₃	C₉⋊(Q₈⋊C₉)	1	9	yes	direct product factor
62	C₃	C₃×C₉⋊SL(2,𝔽₃)	1	3	yes	—
63	C₃	C₃²×Q₈⋊C₉	1	1	yes	characteristic
64	C₂	C₃×C₉⋊(C₂²⋊C₉)	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂×C₃³	C₃×A₄
commutator	C₃×Q₈	C₃²×C₉
Frattini	C₂×C₃²	C₃²×A₄
Fitting	C₃²×Q₈×C₉	C₃
cosocle	C₃²×Q₈	C₃³
hypercenter	C₂×C₃²×C₉	A₄
hypocenter	Q₈	C₃×C₉⋊C₉
LCS	G ▷ C₃×Q₈ ▷ Q₈
UCS	C₁ ◁ C₂×C₃³ ◁ C₂×C₃²×C₉

Complements

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

N	H ≅ G/N	type
3. C₉⋊(Q₈⋊C₉)	C₃	direct (N × H)
8. C₃×Q₈×C₉	C₉	semidirect
24. Q₈×C₉	C₃×C₉	semidirect
38. C₃×C₉	Q₈⋊C₉	semidirect
40. C₃×Q₈	C₉⋊C₉	semidirect
55. C₉	C₃×Q₈⋊C₉	semidirect
56. Q₈	C₃×C₉⋊C₉	semidirect
61. C₃	C₉⋊(Q₈⋊C₉)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×Q₈×C₉	3
C₃²×Q₈⋊C₉	3
C₉⋊(Q₈⋊C₉)	3
C₂×C₃×C₉⋊C₉	4

Subgroups — C3×C9⋊(Q8⋊C9) #14517226

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉⋊(Q₈⋊C₉) #14517226