Subgroups — D₃×#127 #5714

Order 192.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×D₄	C₂	1	6	yes	maximal, complemented
2	C₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	#940	C₂	1	6	yes	maximal, complemented
4	#874	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄²×D₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#127	—	3	1	no	maximal, Sylow
7	C₂³×D₃	C₂²	1	4	yes	—
8	C₂×C₃×D₄	C₂²	1	6	yes	complemented
9	C₂×#67	C₂²	1	12	yes	complemented
10	D₃×D₄	—	2	24	no	—
11	C₂×D₁₂	C₂²	1	6	yes	complemented
12	C₂×C₄×D₃	C₂²	1	3	yes	—
13	C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
14	C₄×Dic₃	C₂²	1	3	yes	complemented
15	C₂²×D₄	—	3	6	no	—
16	#127	—	3	6	no	—
17	#127	—	3	1	no	—
18	#127	D₃	1	1	yes	characteristic, direct product factor
19	C₂×C₄²	—	3	1	no	—
20	C₂³×C₃	C₂³	1	4	yes	—
21	C₂²×D₃	—	2	24	no	—
22	C₂²×D₃	C₂³	1	4	yes	—
23	C₂²×D₃	C₂³	1	1	yes	characteristic
24	C₃×D₄	—	2	12	no	—
25	C₂×C₃×C₄	C₂³	1	3	yes	—
26	#67	—	2	24	no	—
27	C₂×Dic₃	C₂³	1	3	yes	—
28	D₁₂	—	2	12	no	—
29	C₄×D₃	D₄	1	12	yes	complemented
30	C₂⁴	—	3	4	no	—
31	C₂×D₄	—	3	12	no	—
32	C₂×D₄	—	3	6	no	—
33	C₂×D₄	—	6	24	no	—
34	C₂×D₄	C₂×D₃	1	6	yes	complemented
35	C₂²×C₄	—	3	3	no	—
36	C₄²	—	3	3	no	—
37	C₄²	C₂×D₃	1	1	yes	characteristic, complemented
38	C₂²×C₃	—	2	12	no	—
39	C₂²×C₃	C₂⁴	1	1	yes	characteristic
40	C₂×D₃	—	2	12	no	—
41	C₂×D₃	—	4	16	no	—
42	C₂×D₃	C₂×D₄	1	6	yes	—
43	C₃×C₄	C₂×D₄	1	6	yes	complemented
44	Dic₃	C₂×D₄	1	6	yes	complemented
45	C₂³	—	3	1	no	—
46	C₂³	—	3	4	no	—
47	C₂³	—	6	24	no	—
48	C₂³	C₂²×D₃	1	4	yes	—
49	D₄	—	2	12	no	—
50	D₄	—	6	24	no	—
51	D₄	—	6	12	no	—
52	C₂×C₄	—	3	3	no	—
53	C₂×C₄	—	3	12	no	—
54	C₂×C₄	C₂²×D₃	1	3	yes	—
55	C₂×C₃	—	4	4	no	—
56	C₂×C₃	C₂²×D₄	1	3	yes	—
57	D₃	—	4	4	no	—
58	D₃	#127	1	4	yes	direct product factor
59	C₂²	—	2	12	no	—
60	C₂²	—	3	6	no	—
61	C₂²	—	6	12	no	—
62	C₂²	—	12	16	no	—
63	C₂²	C₂³×D₃	1	1	yes	characteristic
64	C₄	—	3	6	no	—
65	C₄	D₃×D₄	1	6	yes	complemented
66	C₃	C₂×#127	1	1	yes	characteristic, complemented, Sylow
67	C₂	—	3	4	no	—
68	C₂	—	4	4	no	—
69	C₂	—	12	4	no	—
70	C₂	C₂×D₃×D₄	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁴
Fitting	C₃×#127	C₂
hypercenter	#127	D₃
hypocenter	C₃	C₂×#127
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₂×D₃×D₄	C₂	semidirect
2. C₃×#127	C₂	semidirect
3. #940	C₂	semidirect
4. #874	C₂	semidirect
5. C₄²×D₃	C₂	semidirect
8. C₂×C₃×D₄	C₂²	semidirect
9. C₂×#67	C₂²	semidirect
11. C₂×D₁₂	C₂²	semidirect
13. C₃×C₄²	C₂²	semidirect
14. C₄×Dic₃	C₂²	semidirect
18. #127	D₃	direct (N × H)
29. C₄×D₃	D₄	semidirect
34. C₂×D₄	C₂×D₃	semidirect
37. C₄²	C₂×D₃	semidirect
43. C₃×C₄	C₂×D₄	semidirect
44. Dic₃	C₂×D₄	semidirect
58. D₃	#127	direct (N × H)
65. C₄	D₃×D₄	semidirect
66. C₃	C₂×#127	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×D₄	2
C₃×#127	2
#940	2
#874	2
C₄²×D₃	2
C₂×#127	3

Subgroups — D3×#127 #5714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#127 #5714