Subgroups — D₃×D₂₆₆₉ #44545115

Order 32028.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₀₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₇×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₆₆₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₆₆₉	—	3	1	no	maximal, Hall
5	C₃×C₁₇×C₁₅₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₇×C₁₅₇	—	3	1	no	—
7	D₂₆₆₉	—	3	1	no	—
8	D₂₆₆₉	D₃	1	1	yes	characteristic, direct product factor
9	C₁₇×C₁₅₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×D₁₅₇	—	17	1	no	maximal, Hall
11	D₄₇₁	—	17	1	no	—
12	C₃×D₁₅₇	—	17	1	no	—
13	D₃×C₁₅₇	D₁₇	1	1	yes	characteristic, complemented
14	C₂×D₁₅₇	—	51	1	no	Hall
15	C₃×C₁₅₇	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₅₇	—	3	1	no	—
17	D₁₅₇	—	17	1	no	—
18	D₁₅₇	—	51	1	no	—
19	D₃×D₁₇	—	157	1	no	maximal, Hall
20	C₁₅₇	D₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
21	D₅₁	—	157	1	no	—
22	C₃×D₁₇	—	157	1	no	—
23	D₃×C₁₇	D₁₅₇	1	1	yes	characteristic, complemented
24	C₂×D₁₇	—	471	1	no	Hall
25	C₃×C₁₇	C₂×D₁₅₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₇	—	3	1	no	—
27	D₁₇	—	157	1	no	—
28	D₁₇	—	471	1	no	—
29	C₁₇	D₃×D₁₅₇	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	2669	1	no	Hall
31	C₂×C₃	—	2669	1	no	—
32	D₃	—	2669	1	no	—
33	D₃	D₂₆₆₉	1	1	yes	characteristic, direct product factor
34	C₂²	—	8007	1	no	Sylow
35	C₃	C₂×D₂₆₆₉	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	8007	1	no	—
38	C₂	—	2669	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₇×C₁₅₇	C₂²
LCS	G ▷ C₃×C₁₇×C₁₅₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₈₀₀₇	C₂	semidirect
2. D₃×C₁₇×C₁₅₇	C₂	semidirect
3. C₃×D₂₆₆₉	C₂	semidirect
5. C₃×C₁₇×C₁₅₇	C₂²	semidirect
8. D₂₆₆₉	D₃	direct (N × H)
9. C₁₇×C₁₅₇	C₂×D₃	semidirect
13. D₃×C₁₅₇	D₁₇	semidirect
15. C₃×C₁₅₇	C₂×D₁₇	semidirect
20. C₁₅₇	D₃×D₁₇	semidirect
23. D₃×C₁₇	D₁₅₇	semidirect
25. C₃×C₁₇	C₂×D₁₅₇	semidirect
29. C₁₇	D₃×D₁₅₇	semidirect
33. D₃	D₂₆₆₉	direct (N × H)
35. C₃	C₂×D₂₆₆₉	semidirect

Maximal subgroups

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

subgroup	index
D₈₀₀₇	2
D₃×C₁₇×C₁₅₇	2
C₃×D₂₆₆₉	2
C₂×D₂₆₆₉	3
D₃×D₁₅₇	17
D₃×D₁₇	157

Subgroups — D3×D2669 #44545115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₂₆₆₉ #44545115