Subgroups — C₂³×C₄×D₃ #5952

Order 192.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₃×C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₃	C₂	1	28	yes	maximal, direct product factor
5	C₂⁴×C₄	—	3	1	no	maximal, Sylow
6	C₂⁴×C₃	C₂²	1	1	yes	characteristic
7	C₂³×D₃	C₄	1	16	yes	direct product factor
8	C₂³×D₃	C₂²	1	14	yes	—
9	C₂²×C₃×C₄	C₂²	1	14	yes	complemented
10	C₂²×Dic₃	C₂²	1	14	yes	complemented
11	C₂×C₄×D₃	C₂²	1	112	yes	direct product factor
12	C₂⁵	—	3	1	no	—
13	C₂³×C₄	—	3	1	no	—
14	C₂³×C₄	—	3	28	no	—
15	C₂³×C₄	D₃	1	1	yes	characteristic, direct product factor
16	C₂³×C₃	C₂×C₄	1	8	yes	complemented
17	C₂³×C₃	C₂³	1	7	yes	—
18	C₂²×D₃	C₂×C₄	1	112	yes	direct product factor
19	C₂²×D₃	C₂³	1	28	yes	—
20	C₂×C₃×C₄	C₂³	1	28	yes	complemented
21	C₂×Dic₃	C₂³	1	28	yes	complemented
22	C₄×D₃	C₂³	1	64	yes	direct product factor
23	C₂⁴	—	3	16	no	—
24	C₂⁴	—	3	14	no	—
25	C₂⁴	C₂×D₃	1	1	yes	characteristic
26	C₂²×C₄	—	3	14	no	—
27	C₂²×C₄	—	3	112	no	—
28	C₂²×C₄	C₂×D₃	1	14	yes	direct product factor
29	C₂²×C₃	C₂²×C₄	1	28	yes	complemented
30	C₂²×C₃	C₂⁴	1	7	yes	—
31	C₂×D₃	C₂²×C₄	1	112	yes	direct product factor
32	C₂×D₃	C₂⁴	1	8	yes	—
33	C₃×C₄	C₂⁴	1	8	yes	complemented
34	Dic₃	C₂⁴	1	8	yes	complemented
35	C₂³	—	3	112	no	—
36	C₂³	—	3	28	no	—
37	C₂³	C₄×D₃	1	8	yes	direct product factor
38	C₂³	C₂²×D₃	1	7	yes	—
39	C₂×C₄	—	3	28	no	—
40	C₂×C₄	—	3	64	no	—
41	C₂×C₄	C₂²×D₃	1	28	yes	direct product factor
42	C₂×C₃	C₂³×C₄	1	14	yes	complemented
43	C₂×C₃	C₂⁵	1	1	yes	characteristic
44	D₃	C₂³×C₄	1	16	yes	direct product factor
45	C₂²	—	3	112	no	—
46	C₂²	—	3	8	no	—
47	C₂²	C₂×C₄×D₃	1	28	yes	direct product factor
48	C₂²	C₂³×D₃	1	7	yes	—
49	C₄	—	3	8	no	—
50	C₄	C₂³×D₃	1	8	yes	direct product factor
51	C₃	C₂⁴×C₄	1	1	yes	characteristic, complemented, Sylow
52	C₂	—	3	16	no	—
53	C₂	C₂²×C₄×D₃	1	14	yes	direct product factor
54	C₂	C₂⁴×D₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₄	D₃
commutator, hypocenter	C₃	C₂⁴×C₄
Frattini	C₂	C₂⁴×D₃
Fitting	C₂³×C₃×C₄	C₂
socle	C₂⁴×C₃	C₂²
prime radical	C₂⁴×D₃	C₂
cosocle	C₂×C₃	C₂⁵
LCS	G ▷ C₃
UCS	C₁ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₃×C₄	C₂	semidirect
3. C₂³×Dic₃	C₂	semidirect
4. C₂²×C₄×D₃	C₂	direct (N × H)
7. C₂³×D₃	C₄	direct (N × H)
9. C₂²×C₃×C₄	C₂²	semidirect
10. C₂²×Dic₃	C₂²	semidirect
11. C₂×C₄×D₃	C₂²	direct (N × H)
15. C₂³×C₄	D₃	direct (N × H)
16. C₂³×C₃	C₂×C₄	semidirect
18. C₂²×D₃	C₂×C₄	direct (N × H)
20. C₂×C₃×C₄	C₂³	semidirect
21. C₂×Dic₃	C₂³	semidirect
22. C₄×D₃	C₂³	direct (N × H)
28. C₂²×C₄	C₂×D₃	direct (N × H)
29. C₂²×C₃	C₂²×C₄	semidirect
31. C₂×D₃	C₂²×C₄	direct (N × H)
33. C₃×C₄	C₂⁴	semidirect
34. Dic₃	C₂⁴	semidirect
37. C₂³	C₄×D₃	direct (N × H)
41. C₂×C₄	C₂²×D₃	direct (N × H)
42. C₂×C₃	C₂³×C₄	semidirect
44. D₃	C₂³×C₄	direct (N × H)
47. C₂²	C₂×C₄×D₃	direct (N × H)
50. C₄	C₂³×D₃	direct (N × H)
51. C₃	C₂⁴×C₄	semidirect
53. C₂	C₂²×C₄×D₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₃	2
C₂³×C₃×C₄	2
C₂³×Dic₃	2
C₂²×C₄×D₃	2
C₂⁴×C₄	3

Subgroups — C23×C4×D3 #5952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄×D₃ #5952