Subgroups — C₃×D₁₇×C₁₀₃⋊C₃ #44538564

Order 31518.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×C₁₀₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₇×C₁₀₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×D₁₇×C₁₀₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₇×C₁₀₃	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₇×C₁₀₃⋊C₃	C₂×C₃	1	3	yes	complemented
6	D₁₇×C₁₀₃	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₀₃⋊C₃	—	17	1	no	maximal, Hall
8	C₁₇×C₁₀₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₀₃⋊C₃	D₁₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₁₀₃	—	17	1	no	—
11	C₂×C₁₀₃⋊C₃	—	17	3	no	—
12	C₃×C₁₀₃	C₃×D₁₇	1	1	yes	characteristic, complemented
13	C₁₀₃⋊C₃	C₃×D₁₇	1	3	yes	direct product factor
14	C₃²×D₁₇	—	103	1	no	maximal, Hall
15	C₂×C₁₀₃	—	17	1	no	Hall
16	C₃²×C₁₇	—	103	1	no	Hall
17	C₁₀₃	C₃²×D₁₇	1	1	yes	characteristic, complemented, Sylow
18	C₃×D₁₇	—	103	3	no	—
19	C₃×D₁₇	C₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor
20	C₃×C₁₇	—	103	3	no	—
21	C₃×C₁₇	C₂×C₁₀₃⋊C₃	1	1	yes	characteristic, complemented
22	D₁₇	C₃×C₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃²	—	1751	1	no	Hall
24	C₁₇	C₂×C₃×C₁₀₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₃²	—	103	1	no	Sylow
26	C₂×C₃	—	17	1	no	—
27	C₂×C₃	—	1751	3	no	—
28	C₃	—	103	3	no	—
29	C₃	D₁₇×C₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor
30	C₂	—	17	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₁₇×C₁₀₃⋊C₃
commutator, cosocle, hypocenter	C₁₇×C₁₀₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₁₇×C₁₀₃	C₂×C₃
LCS	G ▷ C₁₇×C₁₀₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₇×C₁₀₃⋊C₃	C₂	semidirect
2. D₁₇×C₁₀₃⋊C₃	C₃	direct (N × H)
3. C₃×D₁₇×C₁₀₃	C₃	semidirect
4. C₃×C₁₇×C₁₀₃	C₂×C₃	semidirect
5. C₁₇×C₁₀₃⋊C₃	C₂×C₃	semidirect
6. D₁₇×C₁₀₃	C₃²	semidirect
8. C₁₇×C₁₀₃	C₂×C₃²	semidirect
9. C₃×C₁₀₃⋊C₃	D₁₇	direct (N × H)
12. C₃×C₁₀₃	C₃×D₁₇	semidirect
13. C₁₀₃⋊C₃	C₃×D₁₇	direct (N × H)
17. C₁₀₃	C₃²×D₁₇	semidirect
19. C₃×D₁₇	C₁₀₃⋊C₃	direct (N × H)
21. C₃×C₁₇	C₂×C₁₀₃⋊C₃	semidirect
22. D₁₇	C₃×C₁₀₃⋊C₃	direct (N × H)
24. C₁₇	C₂×C₃×C₁₀₃⋊C₃	semidirect
29. C₃	D₁₇×C₁₀₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₇×C₁₀₃⋊C₃	2
D₁₇×C₁₀₃⋊C₃	3
C₃×D₁₇×C₁₀₃	3
C₂×C₃×C₁₀₃⋊C₃	17
C₃²×D₁₇	103

Subgroups — C3×D17×C103⋊C3 #44538564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₁₇×C₁₀₃⋊C₃ #44538564