Subgroups — C₂³×D₁₂ #5953

Order 192.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₃	C₂	1	2	yes	maximal, complemented
2	C₂³×C₃×C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₁₂	C₂	1	28	yes	maximal, direct product factor
4	C₂³×D₄	—	3	1	no	maximal, Sylow
5	C₂⁴×C₃	C₂²	1	1	yes	characteristic
6	C₂³×D₃	—	2	16	no	—
7	C₂³×D₃	C₂²	1	28	yes	complemented
8	C₂²×C₃×C₄	C₂²	1	14	yes	complemented
9	C₂×D₁₂	C₂²	1	112	yes	direct product factor
10	C₂⁵	—	3	2	no	—
11	C₂²×D₄	—	3	28	no	—
12	C₂³×C₄	D₃	1	1	yes	characteristic, complemented
13	C₂³×C₃	D₄	1	8	yes	complemented
14	C₂³×C₃	C₂³	1	7	yes	—
15	C₂²×D₃	—	2	112	no	—
16	C₂²×D₃	C₂³	1	56	yes	complemented
17	C₂×C₃×C₄	C₂³	1	28	yes	complemented
18	D₁₂	C₂³	1	64	yes	direct product factor
19	C₂⁴	—	3	28	no	—
20	C₂⁴	—	6	16	no	—
21	C₂⁴	C₂×D₃	1	1	yes	characteristic
22	C₂×D₄	—	3	112	no	—
23	C₂²×C₄	C₂×D₃	1	14	yes	complemented
24	C₂²×C₃	C₂×D₄	1	28	yes	complemented
25	C₂²×C₃	C₂⁴	1	7	yes	—
26	C₂×D₃	—	2	112	no	—
27	C₂×D₃	C₂⁴	1	16	yes	complemented
28	C₃×C₄	C₂⁴	1	8	yes	complemented
29	C₂³	—	3	56	no	—
30	C₂³	—	6	112	no	—
31	C₂³	D₁₂	1	8	yes	direct product factor
32	C₂³	C₂²×D₃	1	7	yes	—
33	D₄	—	3	64	no	—
34	C₂×C₄	C₂²×D₃	1	28	yes	complemented
35	C₂×C₃	C₂²×D₄	1	14	yes	complemented
36	C₂×C₃	C₂⁵	1	1	yes	characteristic
37	D₃	—	2	16	no	—
38	C₂²	—	3	16	no	—
39	C₂²	—	6	112	no	—
40	C₂²	C₂×D₁₂	1	28	yes	direct product factor
41	C₂²	C₂³×D₃	1	7	yes	—
42	C₄	C₂³×D₃	1	8	yes	complemented
43	C₃	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
44	C₂	—	6	16	no	—
45	C₂	C₂²×D₁₂	1	14	yes	direct product factor
46	C₂	C₂⁴×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₃
commutator, cosocle	C₂×C₃	C₂⁵
Frattini	C₂	C₂⁴×D₃
Fitting	C₂³×C₃×C₄	C₂
socle	C₂⁴×C₃	C₂²
hypercenter	C₂³×C₄	D₃
hypocenter	C₃	C₂³×D₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₃	C₂	semidirect
2. C₂³×C₃×C₄	C₂	semidirect
3. C₂²×D₁₂	C₂	direct (N × H)
7. C₂³×D₃	C₂²	semidirect
8. C₂²×C₃×C₄	C₂²	semidirect
9. C₂×D₁₂	C₂²	direct (N × H)
12. C₂³×C₄	D₃	semidirect
13. C₂³×C₃	D₄	semidirect
16. C₂²×D₃	C₂³	semidirect
17. C₂×C₃×C₄	C₂³	semidirect
18. D₁₂	C₂³	direct (N × H)
23. C₂²×C₄	C₂×D₃	semidirect
24. C₂²×C₃	C₂×D₄	semidirect
27. C₂×D₃	C₂⁴	semidirect
28. C₃×C₄	C₂⁴	semidirect
31. C₂³	D₁₂	direct (N × H)
34. C₂×C₄	C₂²×D₃	semidirect
35. C₂×C₃	C₂²×D₄	semidirect
40. C₂²	C₂×D₁₂	direct (N × H)
42. C₄	C₂³×D₃	semidirect
43. C₃	C₂³×D₄	semidirect
45. C₂	C₂²×D₁₂	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
C₂²×D₁₂	2
C₂³×D₄	3

Subgroups — C23×D12 #5953

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×D₁₂ #5953