Subgroups — C₃×C₉×#41 #88762

Order 432.

200 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×D₄×C₉	C₂	1	3	yes	maximal, complemented
3	C₂×C₃×C₄×C₉	C₂	1	3	yes	maximal, complemented
4	C₃²×#41	C₃	1	1	yes	maximal, characteristic
5	C₉×#41	C₃	1	3	yes	maximal, direct product factor
6	C₂²×C₃×C₉	C₂²	1	3	yes	—
7	C₃×C₄×C₉	C₂²	1	3	yes	—
8	C₃×C₄×C₉	C₂²	1	1	yes	characteristic
9	C₃²×Q₈	C₂×C₃	1	1	yes	characteristic
10	C₃²×D₄	C₂×C₃	1	3	yes	—
11	C₂×C₃²×C₄	C₂×C₃	1	3	yes	—
12	Q₈×C₉	C₂×C₃	1	3	yes	complemented
13	D₄×C₉	C₂×C₃	1	9	yes	complemented
14	C₂×C₄×C₉	C₂×C₃	1	9	yes	complemented
15	C₂×C₃×C₉	—	2	3	no	—
16	C₂×C₃×C₉	C₂³	1	1	yes	characteristic
17	C₃×#41	C₉	1	3	yes	direct product factor
18	C₃×#41	C₃²	1	1	yes	characteristic
19	C₂²×C₃²	C₂²×C₃	1	3	yes	—
20	C₃²×C₄	C₂²×C₃	1	3	yes	—
21	C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
22	C₂²×C₉	C₂²×C₃	1	9	yes	—
23	C₄×C₉	C₂²×C₃	1	9	yes	—
24	C₄×C₉	C₂²×C₃	1	3	yes	—
25	C₃×C₉	#41	1	1	yes	characteristic, direct product factor, Sylow
26	C₃×Q₈	C₂×C₉	1	3	yes	complemented
27	C₃×Q₈	C₂×C₃²	1	1	yes	characteristic
28	C₃×D₄	C₂×C₉	1	9	yes	complemented
29	C₃×D₄	C₂×C₃²	1	3	yes	—
30	C₂×C₃×C₄	C₂×C₉	1	9	yes	complemented
31	C₂×C₃×C₄	C₂×C₃²	1	3	yes	—
32	C₂×C₃²	—	2	3	no	—
33	C₂×C₃²	C₂³×C₃	1	1	yes	characteristic
34	C₂×C₉	—	2	9	no	—
35	C₂×C₉	C₂³×C₃	1	3	yes	—
36	#41	C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
37	C₂²×C₃	C₂²×C₉	1	9	yes	—
38	C₂²×C₃	C₂²×C₃²	1	3	yes	—
39	C₃×C₄	C₂²×C₉	1	3	yes	—
40	C₃×C₄	C₂²×C₉	1	9	yes	—
41	C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
42	C₃×C₄	C₂²×C₃²	1	3	yes	—
43	C₃²	C₃×#41	1	1	yes	characteristic
44	C₉	C₃×#41	1	3	yes	direct product factor
45	Q₈	C₂×C₃×C₉	1	1	yes	characteristic, complemented
46	D₄	C₂×C₃×C₉	1	3	yes	complemented
47	C₂×C₄	C₂×C₃×C₉	1	3	yes	complemented
48	C₂×C₃	—	2	9	no	—
49	C₂×C₃	—	2	3	no	—
50	C₂×C₃	C₂³×C₉	1	3	yes	—
51	C₂×C₃	C₂³×C₃²	1	1	yes	characteristic
52	C₂²	C₂²×C₃×C₉	1	3	yes	—
53	C₄	C₂²×C₃×C₉	1	1	yes	characteristic
54	C₄	C₂²×C₃×C₉	1	3	yes	—
55	C₃	C₉×#41	1	3	yes	direct product factor
56	C₃	C₃²×#41	1	1	yes	characteristic
57	C₂	—	2	3	no	—
58	C₂	C₂³×C₃×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄×C₉	C₂²
commutator	C₂	C₂³×C₃×C₉
Frattini, cosocle	C₂×C₃	C₂³×C₃²
socle	C₂×C₃²	C₂³×C₃
prime radical	C₃²×#41	C₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×Q₈×C₉	C₂	semidirect
2. C₃×D₄×C₉	C₂	semidirect
3. C₂×C₃×C₄×C₉	C₂	semidirect
5. C₉×#41	C₃	direct (N × H)
12. Q₈×C₉	C₂×C₃	semidirect
13. D₄×C₉	C₂×C₃	semidirect
14. C₂×C₄×C₉	C₂×C₃	semidirect
17. C₃×#41	C₉	direct (N × H)
25. C₃×C₉	#41	direct (N × H)
26. C₃×Q₈	C₂×C₉	semidirect
28. C₃×D₄	C₂×C₉	semidirect
30. C₂×C₃×C₄	C₂×C₉	semidirect
36. #41	C₃×C₉	direct (N × H)
44. C₉	C₃×#41	direct (N × H)
45. Q₈	C₂×C₃×C₉	semidirect
46. D₄	C₂×C₃×C₉	semidirect
47. C₂×C₄	C₂×C₃×C₉	semidirect
55. C₃	C₉×#41	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×D₄×C₉	2
C₂×C₃×C₄×C₉	2
C₃²×#41	3
C₉×#41	3

Subgroups — C3×C9×#41 #88762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×#41 #88762