Subgroups — D₃×D₁₇×C₁₅₇ #44545113

Order 32028.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₁₅₇	D₃×D₁₇
commutator, cosocle, hypocenter	C₃×C₁₇	C₂²×C₁₅₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₇×C₁₅₇	C₂²
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₁₅₇

Complements

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

N	H ≅ G/N	type
1. D₅₁×C₁₅₇	C₂	semidirect
2. D₃×C₁₇×C₁₅₇	C₂	semidirect
3. C₃×D₁₇×C₁₅₇	C₂	semidirect
5. C₃×C₁₇×C₁₅₇	C₂²	semidirect
8. D₁₇×C₁₅₇	D₃	direct (N × H)
9. C₁₇×C₁₅₇	C₂×D₃	semidirect
13. D₃×C₁₅₇	D₁₇	direct (N × H)
15. C₃×C₁₅₇	C₂×D₁₇	semidirect
19. D₃×D₁₇	C₁₅₇	direct (N × H)
20. C₁₅₇	D₃×D₁₇	direct (N × H)
21. D₅₁	C₂×C₁₅₇	semidirect
22. C₃×D₁₇	C₂×C₁₅₇	semidirect
23. D₃×C₁₇	C₂×C₁₅₇	semidirect
25. C₃×C₁₇	C₂²×C₁₅₇	semidirect
28. D₁₇	D₃×C₁₅₇	direct (N × H)
29. C₁₇	C₂×D₃×C₁₅₇	semidirect
33. D₃	D₁₇×C₁₅₇	direct (N × H)
35. C₃	C₂×D₁₇×C₁₅₇	semidirect

Maximal subgroups

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

subgroup	index
D₅₁×C₁₅₇	2
D₃×C₁₇×C₁₅₇	2
C₃×D₁₇×C₁₅₇	2
C₂×D₁₇×C₁₅₇	3
C₂×D₃×C₁₅₇	17
D₃×D₁₇	157

Subgroups — D3×D17×C157 #44545113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₁₇×C₁₅₇ #44545113