Subgroups — D₃×D₆₆₁⋊C₃ #37558310

Order 23796.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₆₆₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊(D₆₆₁⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₆₆₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₆₆₁	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×D₆₆₁⋊C₃	—	3	1	no	maximal
6	C₃×C₆₆₁⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₁₉₈₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×D₆₆₁	C₂×C₃	1	1	yes	characteristic, complemented
9	D₃×C₆₆₁	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₆₆₁⋊C₃	—	3	1	no	—
11	D₆₆₁⋊C₃	—	2	1	no	—
12	D₆₆₁⋊C₃	—	3	1	no	—
13	D₆₆₁⋊C₃	D₃	1	1	yes	characteristic, direct product factor
14	C₂×D₆₆₁	—	3	1	no	Hall
15	C₃×C₆₆₁	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₆₆₁⋊C₃	—	2	1	no	—
17	C₆₆₁⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
18	C₂×C₆₆₁	—	3	1	no	—
19	D₆₆₁	—	3	1	no	—
20	D₆₆₁	C₃×D₃	1	1	yes	characteristic, complemented
21	C₆₆₁	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃×D₃	—	661	1	no	maximal, Hall
23	C₂×C₃²	—	661	1	no	—
24	C₃×D₃	—	1322	1	no	—
25	C₃×D₃	—	661	1	no	—
26	C₂²×C₃	—	1983	1	no	—
27	C₂×D₃	—	661	1	no	—
28	C₃²	—	1322	1	no	Sylow
29	C₂×C₃	—	1322	1	no	—
30	C₂×C₃	—	3966	1	no	—
31	C₂×C₃	—	661	1	no	—
32	C₂×C₃	—	661	1	no	—
33	C₂×C₃	—	1983	1	no	—
34	D₃	—	661	1	no	—
35	D₃	D₆₆₁⋊C₃	1	1	yes	characteristic, direct product factor
36	C₂²	—	1983	1	no	Sylow
37	C₃	—	1322	1	no	—
38	C₃	—	2644	1	no	—
39	C₃	C₂×D₆₆₁⋊C₃	1	1	yes	characteristic, complemented
40	C₂	—	3	1	no	—
41	C₂	—	661	1	no	—
42	C₂	—	1983	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₆₆₁	C₂²×C₃
LCS	G ▷ C₃×C₆₆₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₃×C₆₆₁⋊C₃	C₂	semidirect
2. C₃⋊(D₆₆₁⋊C₃)	C₂	semidirect
3. C₃×D₆₆₁⋊C₃	C₂	semidirect
4. D₃×D₆₆₁	C₃	semidirect
6. C₃×C₆₆₁⋊C₃	C₂²	semidirect
7. D₁₉₈₃	C₂×C₃	semidirect
8. C₃×D₆₆₁	C₂×C₃	semidirect
9. D₃×C₆₆₁	C₂×C₃	semidirect
13. D₆₆₁⋊C₃	D₃	direct (N × H)
15. C₃×C₆₆₁	C₂²×C₃	semidirect
17. C₆₆₁⋊C₃	C₂×D₃	semidirect
20. D₆₆₁	C₃×D₃	semidirect
21. C₆₆₁	C₂×C₃×D₃	semidirect
35. D₃	D₆₆₁⋊C₃	direct (N × H)
39. C₃	C₂×D₆₆₁⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
D₃×C₆₆₁⋊C₃	2
C₃⋊(D₆₆₁⋊C₃)	2
C₃×D₆₆₁⋊C₃	2
D₃×D₆₆₁	3
C₂×D₆₆₁⋊C₃	3
C₂×C₃×D₃	661

Subgroups — D3×D661⋊C3 #37558310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₆₆₁⋊C₃ #37558310