Subgroups — C₃×C₁₇×D₃₂₃ #45681982

Order 32946.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×D₃₂₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₃₂₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor
5	C₃×C₁₇×D₁₉	—	17	1	no	maximal
6	C₃×C₁₇×D₁₇	—	19	1	no	maximal, Hall
7	C₃×C₁₇×C₁₉	—	2	8	no	—
8	C₃×C₁₇×C₁₉	D₁₇	1	1	yes	characteristic, complemented
9	C₃×C₁₇×C₁₉	C₂×C₁₇	1	1	yes	characteristic, complemented
10	C₃×C₁₇²	D₁₉	1	1	yes	characteristic, complemented, Hall
11	D₃₂₃	C₃×C₁₇	1	1	yes	characteristic, direct product factor
12	C₁₇×D₁₉	—	17	1	no	—
13	C₁₇×D₁₇	—	19	1	no	Hall
14	C₁₇×C₁₉	—	2	8	no	—
15	C₁₇×C₁₉	C₃×D₁₇	1	1	yes	characteristic, complemented
16	C₁₇×C₁₉	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
17	C₁₇²	C₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
18	C₃×D₁₉	—	17	1	no	Hall
19	C₂×C₃×C₁₇	—	323	1	no	—
20	C₃×D₁₇	—	19	1	no	—
21	C₃×C₁₉	C₁₇×D₁₇	1	1	yes	characteristic, complemented, Hall
22	C₃×C₁₇	—	2	8	no	—
23	C₃×C₁₇	C₁₇×D₁₉	1	1	yes	characteristic, complemented
24	C₃×C₁₇	D₃₂₃	1	1	yes	characteristic, direct product factor
25	D₁₉	—	17	1	no	Hall
26	C₂×C₁₇	—	323	1	no	—
27	D₁₇	—	19	1	no	—
28	C₁₉	C₃×C₁₇×D₁₇	1	1	yes	characteristic, complemented, Sylow
29	C₁₇	—	2	8	no	—
30	C₁₇	C₃×C₁₇×D₁₉	1	1	yes	characteristic, complemented
31	C₁₇	C₃×D₃₂₃	1	1	yes	characteristic, direct product factor
32	C₂×C₃	—	323	1	no	Hall
33	C₃	C₁₇×D₃₂₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	323	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₇	D₃₂₃
commutator, cosocle, hypocenter	C₁₇×C₁₉	C₂×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₇²×C₁₉	C₂
LCS	G ▷ C₁₇×C₁₉
UCS	C₁ ◁ C₃×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₇²×C₁₉	C₂	semidirect
2. C₁₇×D₃₂₃	C₃	direct (N × H)
3. C₁₇²×C₁₉	C₂×C₃	semidirect
4. C₃×D₃₂₃	C₁₇	direct (N × H)
8. C₃×C₁₇×C₁₉	D₁₇	semidirect
9. C₃×C₁₇×C₁₉	C₂×C₁₇	semidirect
10. C₃×C₁₇²	D₁₉	semidirect
11. D₃₂₃	C₃×C₁₇	direct (N × H)
15. C₁₇×C₁₉	C₃×D₁₇	semidirect
16. C₁₇×C₁₉	C₂×C₃×C₁₇	semidirect
17. C₁₇²	C₃×D₁₉	semidirect
21. C₃×C₁₉	C₁₇×D₁₇	semidirect
23. C₃×C₁₇	C₁₇×D₁₉	semidirect
24. C₃×C₁₇	D₃₂₃	direct (N × H)
28. C₁₉	C₃×C₁₇×D₁₇	semidirect
30. C₁₇	C₃×C₁₇×D₁₉	semidirect
31. C₁₇	C₃×D₃₂₃	direct (N × H)
33. C₃	C₁₇×D₃₂₃	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×C₁₇²×C₁₉	2
C₁₇×D₃₂₃	3
C₃×D₃₂₃	17
C₃×C₁₇×D₁₉	17
C₃×C₁₇×D₁₇	19

Subgroups — C3×C17×D323 #45681982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₇×D₃₂₃ #45681982