Subgroups — C₃³×#41 #89086

Order 432.

560 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃³×D₄	C₂	1	3	yes	maximal, complemented
3	C₂×C₃³×C₄	C₂	1	3	yes	maximal, complemented
4	C₃²×#41	C₃	1	13	yes	maximal, direct product factor
5	C₂²×C₃³	C₂²	1	3	yes	—
6	C₃³×C₄	C₂²	1	3	yes	—
7	C₃³×C₄	C₂²	1	1	yes	characteristic
8	C₃²×Q₈	C₂×C₃	1	13	yes	complemented
9	C₃²×D₄	C₂×C₃	1	39	yes	complemented
10	C₂×C₃²×C₄	C₂×C₃	1	39	yes	complemented
11	C₂×C₃³	—	2	3	no	—
12	C₂×C₃³	C₂³	1	1	yes	characteristic
13	C₃×#41	C₃²	1	13	yes	direct product factor
14	C₂²×C₃²	C₂²×C₃	1	39	yes	—
15	C₃²×C₄	C₂²×C₃	1	39	yes	—
16	C₃²×C₄	C₂²×C₃	1	13	yes	—
17	C₃³	#41	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×Q₈	C₂×C₃²	1	13	yes	complemented
19	C₃×D₄	C₂×C₃²	1	39	yes	complemented
20	C₂×C₃×C₄	C₂×C₃²	1	39	yes	complemented
21	C₂×C₃²	—	2	39	no	—
22	C₂×C₃²	C₂³×C₃	1	13	yes	—
23	#41	C₃³	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²×C₃	C₂²×C₃²	1	39	yes	—
25	C₃×C₄	C₂²×C₃²	1	13	yes	—
26	C₃×C₄	C₂²×C₃²	1	39	yes	—
27	C₃²	C₃×#41	1	13	yes	direct product factor
28	Q₈	C₂×C₃³	1	1	yes	characteristic, complemented
29	D₄	C₂×C₃³	1	3	yes	complemented
30	C₂×C₄	C₂×C₃³	1	3	yes	complemented
31	C₂×C₃	—	2	39	no	—
32	C₂×C₃	C₂³×C₃²	1	13	yes	—
33	C₂²	C₂²×C₃³	1	3	yes	—
34	C₄	C₂²×C₃³	1	1	yes	characteristic
35	C₄	C₂²×C₃³	1	3	yes	—
36	C₃	C₃²×#41	1	13	yes	direct product factor
37	C₂	—	2	3	no	—
38	C₂	C₂³×C₃³	1	1	yes	characteristic

	subgroup	G/H
center	C₃³×C₄	C₂²
commutator, Frattini, cosocle	C₂	C₂³×C₃³
socle	C₂×C₃³	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃³×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃³×Q₈	C₂	semidirect
2. C₃³×D₄	C₂	semidirect
3. C₂×C₃³×C₄	C₂	semidirect
4. C₃²×#41	C₃	direct (N × H)
8. C₃²×Q₈	C₂×C₃	semidirect
9. C₃²×D₄	C₂×C₃	semidirect
10. C₂×C₃²×C₄	C₂×C₃	semidirect
13. C₃×#41	C₃²	direct (N × H)
17. C₃³	#41	direct (N × H)
18. C₃×Q₈	C₂×C₃²	semidirect
19. C₃×D₄	C₂×C₃²	semidirect
20. C₂×C₃×C₄	C₂×C₃²	semidirect
23. #41	C₃³	direct (N × H)
27. C₃²	C₃×#41	direct (N × H)
28. Q₈	C₂×C₃³	semidirect
29. D₄	C₂×C₃³	semidirect
30. C₂×C₄	C₂×C₃³	semidirect
36. C₃	C₃²×#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
C₃³×Q₈	2
C₃³×D₄	2
C₂×C₃³×C₄	2
C₃²×#41	3

Subgroups — C33×#41 #89086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×#41 #89086