Subgroups — C₃⋊(#41⋊C₉) #88620

Order 432.

57 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×#239	C₃	1	1	yes	maximal, characteristic
3	#41⋊C₉	—	3	1	no	maximal
4	C₉×Dic₃	—	4	1	no	maximal
5	C₃²×Q₈	C₂×C₃	1	1	yes	characteristic
6	C₃×D₁₂	—	3	1	no	—
7	C₃×C₄×D₃	—	3	1	no	—
8	Q₈⋊C₉	—	2	1	no	—
9	Q₈⋊C₉	D₃	1	1	yes	characteristic, complemented
10	C₂×C₃×C₉	—	4	1	no	—
11	C₃×#41	—	3	1	no	—
12	#239	C₉	1	1	yes	characteristic, complemented
13	C₂×C₃×D₃	—	3	1	no	—
14	C₃²×C₄	—	3	1	no	—
15	C₃×Dic₃	A₄	1	1	yes	characteristic
16	C₄×C₉	—	12	1	no	—
17	C₃×C₉	—	4	1	no	Sylow
18	C₃×Q₈	—	2	1	no	—
19	C₃×Q₈	C₂×C₉	1	1	yes	characteristic
20	C₃×Q₈	C₃×D₃	1	1	yes	characteristic
21	C₃×D₄	—	9	1	no	—
22	C₂×C₃×C₄	—	9	1	no	—
23	D₁₂	—	3	1	no	—
24	C₄×D₃	—	3	1	no	—
25	C₂×C₃²	C₂×A₄	1	1	yes	characteristic
26	C₃×D₃	—	6	1	no	—
27	C₂×C₉	—	4	1	no	—
28	C₂×C₉	—	8	1	no	—
29	#41	—	3	1	no	Sylow
30	C₂²×C₃	—	9	1	no	—
31	C₂×D₃	—	3	1	no	—
32	C₃×C₄	—	3	1	no	—
33	C₃×C₄	—	3	1	no	—
34	C₃×C₄	—	3	1	no	—
35	C₃×C₄	—	6	1	no	—
36	Dic₃	C₂²⋊C₉	1	1	yes	characteristic
37	C₃²	#41⋊C₃	1	1	yes	characteristic
38	C₉	—	4	1	no	—
39	C₉	—	8	1	no	—
40	Q₈	D₃×C₉	1	1	yes	characteristic
41	D₄	—	9	1	no	—
42	C₂×C₄	—	9	1	no	—
43	C₂×C₃	—	2	1	no	—
44	C₂×C₃	—	18	1	no	—
45	C₂×C₃	C₂×C₂²⋊C₉	1	1	yes	characteristic
46	C₂×C₃	D₃×A₄	1	1	yes	characteristic
47	D₃	—	6	1	no	—
48	C₂²	—	9	1	no	—
49	C₄	—	3	1	no	—
50	C₄	—	3	1	no	—
51	C₃	—	2	1	no	—
52	C₃	#41⋊C₉	1	1	yes	characteristic, complemented
53	C₃	C₃⋊(#41⋊C₃)	1	1	yes	characteristic
54	C₂	—	18	1	no	—
55	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	C₃×#239	C₃
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	semidirect
12. #239	C₉	semidirect
52. C₃	#41⋊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×#239	3
#41⋊C₉	3
C₉×Dic₃	4

Subgroups — C3⋊(#41⋊C9) #88620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(#41⋊C₉) #88620