Subgroups — C₂×C₃×C₁₇×C₁₀₃⋊C₃ #44538569

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, direct product factor, Hall
2	C₂×C₁₇×C₁₀₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₂×C₃×C₁₇×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	direct product factor
6	C₂×C₁₇×C₁₀₃	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₀₃⋊C₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₁₀₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₀₃⋊C₃	C₂×C₁₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₁₀₃	C₃×C₁₇	1	1	yes	characteristic, complemented
11	C₂×C₁₀₃⋊C₃	C₃×C₁₇	1	3	yes	direct product factor
12	C₃×C₁₀₃	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
13	C₁₀₃⋊C₃	C₂×C₃×C₁₇	1	3	yes	direct product factor
14	C₂×C₃²×C₁₇	—	103	1	no	maximal, Hall
15	C₂×C₁₀₃	C₃²×C₁₇	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₁₇	—	103	1	no	Hall
17	C₁₀₃	C₂×C₃²×C₁₇	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃×C₁₇	—	103	3	no	—
19	C₂×C₃×C₁₇	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, direct product factor
22	C₂×C₁₇	C₃×C₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃²	—	103	1	no	Hall
24	C₁₇	C₂×C₃×C₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₃²	—	103	1	no	Sylow
26	C₂×C₃	—	103	3	no	—
27	C₂×C₃	C₁₇×C₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor
28	C₃	—	103	3	no	—
29	C₃	C₂×C₁₇×C₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor
30	C₂	C₃×C₁₇×C₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₇×C₁₀₃⋊C₃	C₂	direct (N × H)
2. C₂×C₁₇×C₁₀₃⋊C₃	C₃	direct (N × H)
3. C₂×C₃×C₁₇×C₁₀₃	C₃	semidirect
4. C₃×C₁₇×C₁₀₃	C₂×C₃	semidirect
5. C₁₇×C₁₀₃⋊C₃	C₂×C₃	direct (N × H)
6. C₂×C₁₇×C₁₀₃	C₃²	semidirect
7. C₂×C₃×C₁₀₃⋊C₃	C₁₇	direct (N × H)
8. C₁₇×C₁₀₃	C₂×C₃²	semidirect
9. C₃×C₁₀₃⋊C₃	C₂×C₁₇	direct (N × H)
10. C₂×C₃×C₁₀₃	C₃×C₁₇	semidirect
11. C₂×C₁₀₃⋊C₃	C₃×C₁₇	direct (N × H)
12. C₃×C₁₀₃	C₂×C₃×C₁₇	semidirect
13. C₁₀₃⋊C₃	C₂×C₃×C₁₇	direct (N × H)
15. C₂×C₁₀₃	C₃²×C₁₇	semidirect
17. C₁₀₃	C₂×C₃²×C₁₇	semidirect
19. C₂×C₃×C₁₇	C₁₀₃⋊C₃	direct (N × H)
21. C₃×C₁₇	C₂×C₁₀₃⋊C₃	direct (N × H)
22. C₂×C₁₇	C₃×C₁₀₃⋊C₃	direct (N × H)
24. C₁₇	C₂×C₃×C₁₀₃⋊C₃	direct (N × H)
27. C₂×C₃	C₁₇×C₁₀₃⋊C₃	direct (N × H)
29. C₃	C₂×C₁₇×C₁₀₃⋊C₃	direct (N × H)
30. C₂	C₃×C₁₇×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
C₂×C₁₇×C₁₀₃⋊C₃	3
C₂×C₃×C₁₇×C₁₀₃	3
C₂×C₃×C₁₀₃⋊C₃	17
C₂×C₃²×C₁₇	103

Subgroups — C2×C3×C17×C103⋊C3 #44538569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₇×C₁₀₃⋊C₃ #44538569