Subgroups — C₂×C₃×C₁₇×D₁₆₃ #45685293

Order 33252.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×D₁₆₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₇×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×D₁₆₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₇×C₁₆₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₇×C₁₆₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₁₇×D₁₆₃	C₂×C₃	1	2	yes	direct product factor
7	C₁₇×C₁₆₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×D₁₆₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₁₆₃	C₂×C₁₇	1	1	yes	characteristic, complemented
10	C₃×D₁₆₃	C₂×C₁₇	1	2	yes	direct product factor
11	C₂×D₁₆₃	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₁₆₃	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₆₃	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
14	D₁₆₃	C₂×C₃×C₁₇	1	2	yes	direct product factor
15	C₂²×C₃×C₁₇	—	163	1	no	maximal, Hall
16	C₁₆₃	C₂²×C₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃×C₁₇	—	163	2	no	—
18	C₂×C₃×C₁₇	D₁₆₃	1	1	yes	characteristic, direct product factor
19	C₂²×C₁₇	—	163	1	no	Hall
20	C₃×C₁₇	C₂×D₁₆₃	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₁₇	—	163	2	no	—
22	C₂×C₁₇	C₃×D₁₆₃	1	1	yes	characteristic, direct product factor
23	C₁₇	C₂×C₃×D₁₆₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²×C₃	—	163	1	no	Hall
25	C₂×C₃	—	163	2	no	—
26	C₂×C₃	C₁₇×D₁₆₃	1	1	yes	characteristic, direct product factor
27	C₂²	—	163	1	no	Sylow
28	C₃	C₂×C₁₇×D₁₆₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	163	2	no	—
30	C₂	C₃×C₁₇×D₁₆₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₇	D₁₆₃
commutator, cosocle, hypocenter	C₁₆₃	C₂²×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₇×C₁₆₃	C₂
LCS	G ▷ C₁₆₃
UCS	C₁ ◁ C₂×C₃×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₇×D₁₆₃	C₂	direct (N × H)
2. C₂×C₃×C₁₇×C₁₆₃	C₂	semidirect
3. C₂×C₁₇×D₁₆₃	C₃	direct (N × H)
4. C₃×C₁₇×C₁₆₃	C₂²	semidirect
5. C₂×C₁₇×C₁₆₃	C₂×C₃	semidirect
6. C₁₇×D₁₆₃	C₂×C₃	direct (N × H)
7. C₁₇×C₁₆₃	C₂²×C₃	semidirect
8. C₂×C₃×D₁₆₃	C₁₇	direct (N × H)
9. C₂×C₃×C₁₆₃	C₂×C₁₇	semidirect
10. C₃×D₁₆₃	C₂×C₁₇	direct (N × H)
11. C₂×D₁₆₃	C₃×C₁₇	direct (N × H)
12. C₃×C₁₆₃	C₂²×C₁₇	semidirect
13. C₂×C₁₆₃	C₂×C₃×C₁₇	semidirect
14. D₁₆₃	C₂×C₃×C₁₇	direct (N × H)
16. C₁₆₃	C₂²×C₃×C₁₇	semidirect
18. C₂×C₃×C₁₇	D₁₆₃	direct (N × H)
20. C₃×C₁₇	C₂×D₁₆₃	direct (N × H)
22. C₂×C₁₇	C₃×D₁₆₃	direct (N × H)
23. C₁₇	C₂×C₃×D₁₆₃	direct (N × H)
26. C₂×C₃	C₁₇×D₁₆₃	direct (N × H)
28. C₃	C₂×C₁₇×D₁₆₃	direct (N × H)
30. C₂	C₃×C₁₇×D₁₆₃	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×D₁₆₃	2
C₂×C₃×C₁₇×C₁₆₃	2
C₂×C₁₇×D₁₆₃	3
C₂×C₃×D₁₆₃	17
C₂²×C₃×C₁₇	163

Subgroups — C2×C3×C17×D163 #45685293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₇×D₁₆₃ #45685293