Subgroups — D₃×#41 #1008

Order 96.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	#239	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#237	C₂	1	3	yes	maximal, complemented
5	D₃×D₄	C₂	1	3	yes	maximal, complemented
6	#235	C₂	1	3	yes	maximal, complemented
7	C₂×C₄×D₃	C₂	1	3	yes	maximal, complemented
8	C₂×#41	—	3	1	no	maximal, Sylow
9	C₂²×D₃	C₂²	1	3	yes	—
10	C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
11	C₃×D₄	C₂²	1	3	yes	complemented
12	C₂×C₃×C₄	C₂²	1	3	yes	complemented
13	#67	C₂²	1	6	yes	complemented
14	C₂×Dic₃	C₂²	1	3	yes	complemented
15	D₁₂	C₂²	1	3	yes	complemented
16	C₄×D₃	C₂²	1	1	yes	characteristic
17	C₄×D₃	C₂²	1	3	yes	—
18	C₄×D₃	C₂²	1	3	yes	complemented
19	C₄×D₃	C₂²	1	3	yes	complemented
20	Dic₆	C₂²	1	3	yes	complemented
21	#41	—	3	1	no	—
22	#41	—	3	3	no	—
23	#41	—	3	3	no	—
24	#41	D₃	1	1	yes	characteristic, direct product factor
25	C₂×Q₈	—	3	1	no	—
26	C₂×D₄	—	3	3	no	—
27	C₂²×C₄	—	3	3	no	—
28	C₂²×C₃	C₂³	1	3	yes	—
29	C₂×D₃	—	2	6	no	—
30	C₂×D₃	C₂³	1	3	yes	—
31	C₂×D₃	C₂³	1	1	yes	characteristic
32	C₃×C₄	C₂³	1	3	yes	—
33	C₃×C₄	C₂³	1	1	yes	characteristic
34	Dic₃	C₂³	1	3	yes	—
35	Dic₃	C₂³	1	1	yes	characteristic
36	C₂³	—	3	3	no	—
37	Q₈	—	3	3	no	—
38	Q₈	C₂×D₃	1	1	yes	characteristic, complemented
39	D₄	—	3	6	no	—
40	D₄	—	3	3	no	—
41	D₄	C₂×D₃	1	3	yes	complemented
42	C₂×C₄	—	3	3	no	—
43	C₂×C₄	—	3	3	no	—
44	C₂×C₄	—	3	3	no	—
45	C₂×C₄	—	3	1	no	—
46	C₂×C₄	—	3	3	no	—
47	C₂×C₄	C₂×D₃	1	3	yes	complemented
48	C₂×C₃	—	2	3	no	—
49	C₂×C₃	C₂⁴	1	1	yes	characteristic
50	D₃	—	2	3	no	—
51	D₃	#41	1	2	yes	direct product factor
52	C₂²	—	3	1	no	—
53	C₂²	—	3	3	no	—
54	C₂²	—	6	6	no	—
55	C₂²	C₂²×D₃	1	3	yes	—
56	C₄	—	3	1	no	—
57	C₄	—	3	3	no	—
58	C₄	C₂²×D₃	1	3	yes	—
59	C₄	C₂²×D₃	1	1	yes	characteristic
60	C₃	C₂×#41	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	2	3	no	—
62	C₂	—	3	2	no	—
63	C₂	—	6	3	no	—
64	C₂	C₂³×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₃
commutator, socle, cosocle	C₂×C₃	C₂⁴
Frattini	C₂	C₂³×D₃
Fitting	C₃×#41	C₂
hypercenter	#41	D₃
hypocenter	C₃	C₂×#41
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. C₃×#41	C₂	semidirect
2. #239	C₂	semidirect
3. D₃×Q₈	C₂	semidirect
4. #237	C₂	semidirect
5. D₃×D₄	C₂	semidirect
6. #235	C₂	semidirect
7. C₂×C₄×D₃	C₂	semidirect
10. C₃×Q₈	C₂²	semidirect
11. C₃×D₄	C₂²	semidirect
12. C₂×C₃×C₄	C₂²	semidirect
13. #67	C₂²	semidirect
14. C₂×Dic₃	C₂²	semidirect
15. D₁₂	C₂²	semidirect
18. C₄×D₃	C₂²	semidirect
19. C₄×D₃	C₂²	semidirect
20. Dic₆	C₂²	semidirect
24. #41	D₃	direct (N × H)
38. Q₈	C₂×D₃	semidirect
41. D₄	C₂×D₃	semidirect
47. C₂×C₄	C₂×D₃	semidirect
51. D₃	#41	direct (N × H)
60. C₃	C₂×#41	semidirect

Maximal subgroups

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

subgroup	index
C₃×#41	2
#239	2
D₃×Q₈	2
#237	2
D₃×D₄	2
#235	2
C₂×C₄×D₃	2
C₂×#41	3

Subgroups — D3×#41 #1008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#41 #1008