Subgroups — C₂×C₃³×D₄ #89084

Order 432.

756 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃³	C₂	1	2	yes	maximal, complemented
2	C₃³×D₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃³×C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃²×D₄	C₃	1	13	yes	maximal, direct product factor
5	C₂²×C₃³	—	2	4	no	—
6	C₂²×C₃³	C₂²	1	1	yes	characteristic
7	C₂²×C₃³	C₂²	1	4	yes	complemented
8	C₃³×C₄	C₂²	1	2	yes	complemented
9	C₂³×C₃²	C₂×C₃	1	26	yes	complemented
10	C₃²×D₄	C₂×C₃	1	52	yes	direct product factor
11	C₂×C₃²×C₄	C₂×C₃	1	13	yes	complemented
12	C₂×C₃³	—	2	4	no	—
13	C₂×C₃³	D₄	1	2	yes	direct product factor
14	C₂×C₃³	C₂³	1	1	yes	characteristic
15	C₂×C₃×D₄	C₃²	1	13	yes	direct product factor
16	C₂²×C₃²	—	2	52	no	—
17	C₂²×C₃²	C₂²×C₃	1	13	yes	—
18	C₂²×C₃²	C₂²×C₃	1	52	yes	complemented
19	C₃²×C₄	C₂²×C₃	1	26	yes	complemented
20	C₃³	C₂×D₄	1	1	yes	characteristic, direct product factor, Sylow
21	C₂³×C₃	C₂×C₃²	1	26	yes	complemented
22	C₃×D₄	C₂×C₃²	1	52	yes	direct product factor
23	C₂×C₃×C₄	C₂×C₃²	1	13	yes	complemented
24	C₂×C₃²	—	2	52	no	—
25	C₂×C₃²	C₃×D₄	1	26	yes	direct product factor
26	C₂×C₃²	C₂³×C₃	1	13	yes	—
27	C₂×D₄	C₃³	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²×C₃	—	2	52	no	—
29	C₂²×C₃	C₂²×C₃²	1	13	yes	—
30	C₂²×C₃	C₂²×C₃²	1	52	yes	complemented
31	C₃×C₄	C₂²×C₃²	1	26	yes	complemented
32	C₃²	C₂×C₃×D₄	1	13	yes	direct product factor
33	C₂³	C₂×C₃³	1	2	yes	complemented
34	D₄	C₂×C₃³	1	4	yes	direct product factor
35	C₂×C₄	C₂×C₃³	1	1	yes	characteristic, complemented
36	C₂×C₃	—	2	52	no	—
37	C₂×C₃	C₃²×D₄	1	26	yes	direct product factor
38	C₂×C₃	C₂³×C₃²	1	13	yes	—
39	C₂²	—	2	4	no	—
40	C₂²	C₂²×C₃³	1	1	yes	characteristic
41	C₂²	C₂²×C₃³	1	4	yes	complemented
42	C₄	C₂²×C₃³	1	2	yes	complemented
43	C₃	C₂×C₃²×D₄	1	13	yes	direct product factor
44	C₂	—	2	4	no	—
45	C₂	C₃³×D₄	1	2	yes	direct product factor
46	C₂	C₂³×C₃³	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃³	C₂	semidirect
2. C₃³×D₄	C₂	direct (N × H)
3. C₂×C₃³×C₄	C₂	semidirect
4. C₂×C₃²×D₄	C₃	direct (N × H)
7. C₂²×C₃³	C₂²	semidirect
8. C₃³×C₄	C₂²	semidirect
9. C₂³×C₃²	C₂×C₃	semidirect
10. C₃²×D₄	C₂×C₃	direct (N × H)
11. C₂×C₃²×C₄	C₂×C₃	semidirect
13. C₂×C₃³	D₄	direct (N × H)
15. C₂×C₃×D₄	C₃²	direct (N × H)
18. C₂²×C₃²	C₂²×C₃	semidirect
19. C₃²×C₄	C₂²×C₃	semidirect
20. C₃³	C₂×D₄	direct (N × H)
21. C₂³×C₃	C₂×C₃²	semidirect
22. C₃×D₄	C₂×C₃²	direct (N × H)
23. C₂×C₃×C₄	C₂×C₃²	semidirect
25. C₂×C₃²	C₃×D₄	direct (N × H)
27. C₂×D₄	C₃³	direct (N × H)
30. C₂²×C₃	C₂²×C₃²	semidirect
31. C₃×C₄	C₂²×C₃²	semidirect
32. C₃²	C₂×C₃×D₄	direct (N × H)
33. C₂³	C₂×C₃³	semidirect
34. D₄	C₂×C₃³	direct (N × H)
35. C₂×C₄	C₂×C₃³	semidirect
37. C₂×C₃	C₃²×D₄	direct (N × H)
41. C₂²	C₂²×C₃³	semidirect
42. C₄	C₂²×C₃³	semidirect
43. C₃	C₂×C₃²×D₄	direct (N × H)
45. C₂	C₃³×D₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃³	2
C₃³×D₄	2
C₂×C₃³×C₄	2
C₂×C₃²×D₄	3

Subgroups — C2×C33×D4 #89084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃³×D₄ #89084