Subgroups — C₂×C₄²×D₃ #5471

Order 192.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₃	C₂	1	3	yes	maximal
2	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×Dic₃	C₂	1	3	yes	maximal, complemented
4	C₄²×D₃	C₂	1	8	yes	maximal, direct product factor
5	C₂²×C₄²	—	3	1	no	maximal, Sylow
6	C₂³×D₃	C₂²	1	1	yes	characteristic
7	C₂²×C₃×C₄	C₂²	1	3	yes	—
8	C₂²×Dic₃	C₂²	1	3	yes	—
9	C₂×C₄×D₃	C₄	1	24	yes	direct product factor
10	C₂×C₄×D₃	C₂²	1	12	yes	—
11	C₃×C₄²	C₂²	1	4	yes	complemented
12	C₄×Dic₃	C₂²	1	12	yes	complemented
13	C₂³×C₄	—	3	3	no	—
14	C₂×C₄²	—	3	3	no	—
15	C₂×C₄²	—	3	8	no	—
16	C₂×C₄²	D₃	1	1	yes	characteristic, direct product factor
17	C₂³×C₃	C₂³	1	1	yes	characteristic
18	C₂²×D₃	C₂×C₄	1	12	yes	—
19	C₂²×D₃	C₂³	1	2	yes	—
20	C₂×C₃×C₄	C₂×C₄	1	12	yes	complemented
21	C₂×C₃×C₄	C₂³	1	6	yes	—
22	C₂×Dic₃	C₂×C₄	1	12	yes	complemented
23	C₂×Dic₃	C₂³	1	6	yes	—
24	C₄×D₃	C₂×C₄	1	48	yes	direct product factor
25	C₂⁴	—	3	1	no	—
26	C₂²×C₄	—	3	3	no	—
27	C₂²×C₄	—	3	24	no	—
28	C₂²×C₄	—	3	12	no	—
29	C₂²×C₄	C₂×D₃	1	3	yes	—
30	C₄²	—	3	12	no	—
31	C₄²	C₂×D₃	1	4	yes	direct product factor
32	C₂²×C₃	C₂²×C₄	1	6	yes	—
33	C₂²×C₃	C₂⁴	1	1	yes	characteristic
34	C₂×D₃	C₄²	1	16	yes	direct product factor
35	C₂×D₃	C₂²×C₄	1	12	yes	—
36	C₃×C₄	C₂²×C₄	1	12	yes	complemented
37	Dic₃	C₂²×C₄	1	12	yes	complemented
38	C₂³	—	3	12	no	—
39	C₂³	—	3	2	no	—
40	C₂³	C₂²×D₃	1	1	yes	characteristic
41	C₂×C₄	—	3	12	no	—
42	C₂×C₄	—	3	6	no	—
43	C₂×C₄	—	3	48	no	—
44	C₂×C₄	C₄×D₃	1	12	yes	direct product factor
45	C₂×C₄	C₂²×D₃	1	6	yes	—
46	C₂×C₃	C₂×C₄²	1	4	yes	complemented
47	C₂×C₃	C₂³×C₄	1	3	yes	—
48	D₃	C₂×C₄²	1	8	yes	direct product factor
49	C₂²	—	3	16	no	—
50	C₂²	—	3	12	no	—
51	C₂²	C₂×C₄×D₃	1	6	yes	—
52	C₂²	C₂³×D₃	1	1	yes	characteristic
53	C₄	—	3	12	no	—
54	C₄	C₂×C₄×D₃	1	12	yes	direct product factor
55	C₃	C₂²×C₄²	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	3	8	no	—
57	C₂	C₄²×D₃	1	4	yes	direct product factor
58	C₂	C₂²×C₄×D₃	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₄²	D₃
commutator, hypocenter	C₃	C₂²×C₄²
Frattini	C₂²	C₂³×D₃
Fitting	C₂×C₃×C₄²	C₂
socle	C₂³×C₃	C₂³
prime radical	C₂³×D₃	C₂²
cosocle	C₂²×C₃	C₂⁴
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄²	C₂	semidirect
3. C₂×C₄×Dic₃	C₂	semidirect
4. C₄²×D₃	C₂	direct (N × H)
9. C₂×C₄×D₃	C₄	direct (N × H)
11. C₃×C₄²	C₂²	semidirect
12. C₄×Dic₃	C₂²	semidirect
16. C₂×C₄²	D₃	direct (N × H)
20. C₂×C₃×C₄	C₂×C₄	semidirect
22. C₂×Dic₃	C₂×C₄	semidirect
24. C₄×D₃	C₂×C₄	direct (N × H)
31. C₄²	C₂×D₃	direct (N × H)
34. C₂×D₃	C₄²	direct (N × H)
36. C₃×C₄	C₂²×C₄	semidirect
37. Dic₃	C₂²×C₄	semidirect
44. C₂×C₄	C₄×D₃	direct (N × H)
46. C₂×C₃	C₂×C₄²	semidirect
48. D₃	C₂×C₄²	direct (N × H)
54. C₄	C₂×C₄×D₃	direct (N × H)
55. C₃	C₂²×C₄²	semidirect
57. C₂	C₄²×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
C₂²×C₄×D₃	2
C₂×C₃×C₄²	2
C₂×C₄×Dic₃	2
C₄²×D₃	2
C₂²×C₄²	3

Subgroups — C2×C42×D3 #5471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄²×D₃ #5471