Subgroups — C₃×C₇×D₃₂₃ #27214483

Order 13566.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₃₂₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₃₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₇×C₁₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₃×C₇×D₁₉	—	17	1	no	maximal, Hall
7	C₃×C₇×D₁₇	—	19	1	no	maximal, Hall
8	D₃₂₃	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₇×C₁₉	D₁₇	1	1	yes	characteristic, complemented, Hall
10	C₃×C₇×C₁₇	D₁₉	1	1	yes	characteristic, complemented, Hall
11	C₁₇×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×D₁₉	—	17	1	no	Hall
13	C₇×D₁₇	—	19	1	no	Hall
14	C₇×C₁₉	C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
15	C₇×C₁₇	C₃×D₁₉	1	1	yes	characteristic, complemented, Hall
16	C₃×D₁₉	—	17	1	no	Hall
17	C₃×D₁₇	—	19	1	no	Hall
18	C₃×C₁₉	C₇×D₁₇	1	1	yes	characteristic, complemented, Hall
19	C₃×C₁₇	C₇×D₁₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₇	—	323	1	no	Hall
21	D₁₉	—	17	1	no	Hall
22	D₁₇	—	19	1	no	Hall
23	C₃×C₇	D₃₂₃	1	1	yes	characteristic, direct product factor, Hall
24	C₁₉	C₃×C₇×D₁₇	1	1	yes	characteristic, complemented, Sylow
25	C₁₇	C₃×C₇×D₁₉	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₇	—	323	1	no	Hall
27	C₇	C₃×D₃₂₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	323	1	no	Hall
29	C₃	C₇×D₃₂₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	323	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇	D₃₂₃
commutator, cosocle, hypocenter	C₁₇×C₁₉	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₇×C₁₉	C₂
LCS	G ▷ C₁₇×C₁₉
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₇×C₁₉	C₂	semidirect
2. C₇×D₃₂₃	C₃	direct (N × H)
3. C₇×C₁₇×C₁₉	C₂×C₃	semidirect
4. C₃×D₃₂₃	C₇	direct (N × H)
5. C₃×C₁₇×C₁₉	C₂×C₇	semidirect
8. D₃₂₃	C₃×C₇	direct (N × H)
9. C₃×C₇×C₁₉	D₁₇	semidirect
10. C₃×C₇×C₁₇	D₁₉	semidirect
11. C₁₇×C₁₉	C₂×C₃×C₇	semidirect
14. C₇×C₁₉	C₃×D₁₇	semidirect
15. C₇×C₁₇	C₃×D₁₉	semidirect
18. C₃×C₁₉	C₇×D₁₇	semidirect
19. C₃×C₁₇	C₇×D₁₉	semidirect
23. C₃×C₇	D₃₂₃	direct (N × H)
24. C₁₉	C₃×C₇×D₁₇	semidirect
25. C₁₇	C₃×C₇×D₁₉	semidirect
27. C₇	C₃×D₃₂₃	direct (N × H)
29. C₃	C₇×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×C₇×C₁₇×C₁₉	2
C₇×D₃₂₃	3
C₃×D₃₂₃	7
C₃×C₇×D₁₉	17
C₃×C₇×D₁₇	19

Subgroups — C3×C7×D323 #27214483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×D₃₂₃ #27214483