Subgroups — C₂×D₃×D₄ #1002

Order 96.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₃	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#67	C₂	1	2	yes	maximal, complemented
4	D₃×D₄	C₂	1	8	yes	maximal, direct product factor
5	C₂×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×D₄	—	3	1	no	maximal, Sylow
8	C₂³×C₃	C₂²	1	2	yes	complemented
9	C₂²×D₃	—	2	8	no	—
10	C₂²×D₃	C₂²	1	1	yes	characteristic
11	C₂²×D₃	C₂²	1	8	yes	complemented
12	C₂²×D₃	C₂²	1	2	yes	complemented
13	C₃×D₄	C₂²	1	4	yes	complemented
14	C₂×C₃×C₄	C₂²	1	1	yes	characteristic, complemented
15	#67	C₂²	1	8	yes	complemented
16	C₂×Dic₃	C₂²	1	1	yes	characteristic, complemented
17	D₁₂	C₂²	1	4	yes	complemented
18	C₄×D₃	C₂²	1	4	yes	complemented
19	C₂⁴	—	3	2	no	—
20	C₂×D₄	—	3	2	no	—
21	C₂×D₄	—	3	8	no	—
22	C₂×D₄	—	3	1	no	—
23	C₂×D₄	D₃	1	1	yes	characteristic, direct product factor
24	C₂²×C₄	—	3	1	no	—
25	C₂²×C₃	—	2	4	no	—
26	C₂²×C₃	C₂³	1	1	yes	characteristic
27	C₂²×C₃	C₂³	1	4	yes	complemented
28	C₂×D₃	—	2	4	no	—
29	C₂×D₃	—	2	16	no	—
30	C₂×D₃	D₄	1	4	yes	direct product factor
31	C₂×D₃	C₂³	1	2	yes	—
32	C₂×D₃	C₂³	1	4	yes	complemented
33	C₃×C₄	C₂³	1	2	yes	complemented
34	Dic₃	C₂³	1	2	yes	complemented
35	C₂³	—	3	1	no	—
36	C₂³	—	3	2	no	—
37	C₂³	—	3	8	no	—
38	C₂³	—	6	8	no	—
39	C₂³	C₂×D₃	1	2	yes	complemented
40	D₄	—	3	8	no	—
41	D₄	—	3	4	no	—
42	D₄	C₂×D₃	1	4	yes	direct product factor
43	C₂×C₄	—	3	1	no	—
44	C₂×C₄	—	3	4	no	—
45	C₂×C₄	C₂×D₃	1	1	yes	characteristic, complemented
46	C₂×C₃	—	2	4	no	—
47	C₂×C₃	C₂×D₄	1	2	yes	complemented
48	C₂×C₃	C₂⁴	1	1	yes	characteristic
49	D₃	—	2	4	no	—
50	D₃	C₂×D₄	1	4	yes	direct product factor
51	C₂²	—	2	4	no	—
52	C₂²	—	3	4	no	—
53	C₂²	—	3	2	no	—
54	C₂²	—	3	4	no	—
55	C₂²	—	6	16	no	—
56	C₂²	—	6	4	no	—
57	C₂²	C₂²×D₃	1	1	yes	characteristic
58	C₂²	C₂²×D₃	1	4	yes	complemented
59	C₄	—	3	2	no	—
60	C₄	C₂²×D₃	1	2	yes	complemented
61	C₃	C₂²×D₄	1	1	yes	characteristic, complemented, Sylow
62	C₂	—	2	4	no	—
63	C₂	—	3	4	no	—
64	C₂	—	6	4	no	—
65	C₂	D₃×D₄	1	2	yes	direct product factor
66	C₂	C₂³×D₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂³×D₃	C₂	semidirect
2. C₂×C₃×D₄	C₂	semidirect
3. C₂×#67	C₂	semidirect
4. D₃×D₄	C₂	direct (N × H)
5. C₂×D₁₂	C₂	semidirect
6. C₂×C₄×D₃	C₂	semidirect
8. C₂³×C₃	C₂²	semidirect
11. C₂²×D₃	C₂²	semidirect
12. C₂²×D₃	C₂²	semidirect
13. C₃×D₄	C₂²	semidirect
14. C₂×C₃×C₄	C₂²	semidirect
15. #67	C₂²	semidirect
16. C₂×Dic₃	C₂²	semidirect
17. D₁₂	C₂²	semidirect
18. C₄×D₃	C₂²	semidirect
23. C₂×D₄	D₃	direct (N × H)
27. C₂²×C₃	C₂³	semidirect
30. C₂×D₃	D₄	direct (N × H)
32. C₂×D₃	C₂³	semidirect
33. C₃×C₄	C₂³	semidirect
34. Dic₃	C₂³	semidirect
39. C₂³	C₂×D₃	semidirect
42. D₄	C₂×D₃	direct (N × H)
45. C₂×C₄	C₂×D₃	semidirect
47. C₂×C₃	C₂×D₄	semidirect
50. D₃	C₂×D₄	direct (N × H)
58. C₂²	C₂²×D₃	semidirect
60. C₄	C₂²×D₃	semidirect
61. C₃	C₂²×D₄	semidirect
65. C₂	D₃×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×D₃	2
C₂×C₃×D₄	2
C₂×#67	2
D₃×D₄	2
C₂×D₁₂	2
C₂×C₄×D₃	2
C₂²×D₄	3

Subgroups — C2×D3×D4 #1002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×D₄ #1002