Subgroups — D₃×D₁₀₄₇ #27160276

Order 12564.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₁₀₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₀₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×C₃₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₀₄₇	—	3	1	no	maximal
5	D₃×D₃₄₉	—	3	1	no	maximal
6	C₃²×C₃₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₃₄₉	—	3	1	no	—
8	D₁₀₄₇	—	3	1	no	—
9	D₁₀₄₇	—	3	1	no	—
10	D₁₀₄₇	—	6	1	no	—
11	D₁₀₄₇	D₃	1	1	yes	characteristic, direct product factor
12	C₃×D₃₄₉	—	3	1	no	—
13	D₃×C₃₄₉	D₃	1	1	yes	characteristic, complemented
14	C₂×D₃₄₉	—	9	1	no	Hall
15	C₃×C₃₄₉	—	2	1	no	—
16	C₃×C₃₄₉	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₃₄₉	C₂×D₃	1	1	yes	characteristic, complemented
18	C₂×C₃₄₉	—	3	1	no	—
19	D₃₄₉	—	3	1	no	—
20	D₃₄₉	—	9	1	no	—
21	C₃₄₉	D₃²	1	1	yes	characteristic, complemented, Sylow
22	D₃²	—	349	1	no	maximal, Hall
23	C₃⋊D₃	—	349	1	no	—
24	C₃×D₃	—	349	1	no	—
25	C₃×D₃	D₃₄₉	1	1	yes	characteristic, complemented
26	C₂×D₃	—	1047	1	no	—
27	C₂×D₃	—	1047	1	no	—
28	C₃²	C₂×D₃₄₉	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	3	1	no	—
30	C₂×C₃	—	1047	1	no	—
31	D₃	—	1047	1	no	—
32	D₃	—	1047	1	no	—
33	D₃	—	2094	1	no	—
34	D₃	—	349	1	no	—
35	D₃	D₁₀₄₇	1	1	yes	characteristic, direct product factor
36	C₂²	—	3141	1	no	Sylow
37	C₃	—	2	1	no	—
38	C₃	D₃×D₃₄₉	1	1	yes	characteristic, complemented
39	C₃	C₂×D₁₀₄₇	1	1	yes	characteristic, complemented
40	C₂	—	3	1	no	—
41	C₂	—	1047	1	no	—
42	C₂	—	3141	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₃₄₉	C₂²
LCS	G ▷ C₃²×C₃₄₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₁₀₄₇	C₂	semidirect
2. C₃×D₁₀₄₇	C₂	semidirect
3. C₃×D₃×C₃₄₉	C₂	semidirect
6. C₃²×C₃₄₉	C₂²	semidirect
11. D₁₀₄₇	D₃	direct (N × H)
13. D₃×C₃₄₉	D₃	semidirect
16. C₃×C₃₄₉	C₂×D₃	semidirect
17. C₃×C₃₄₉	C₂×D₃	semidirect
21. C₃₄₉	D₃²	semidirect
25. C₃×D₃	D₃₄₉	semidirect
28. C₃²	C₂×D₃₄₉	semidirect
35. D₃	D₁₀₄₇	direct (N × H)
38. C₃	D₃×D₃₄₉	semidirect
39. C₃	C₂×D₁₀₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₁₀₄₇	2
C₃×D₁₀₄₇	2
C₃×D₃×C₃₄₉	2
C₂×D₁₀₄₇	3
D₃×D₃₄₉	3
D₃²	349

Subgroups — D3×D1047 #27160276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₁₀₄₇ #27160276