Subgroups — C₃×C₁₁×C₁₇×C₁₉⋊C₃ #44544267

Order 31977.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₇×C₁₉⋊C₃	C₃	1	3	yes	maximal, direct product factor
2	C₃×C₁₁×C₁₇×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₁₇×C₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₇×C₁₉⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₁×C₁₉⋊C₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃²×C₁₁×C₁₇	—	19	1	no	maximal, Hall
7	C₃×C₁₇×C₁₉	C₃×C₁₁	1	1	yes	characteristic, complemented
8	C₁₇×C₁₉⋊C₃	C₃×C₁₁	1	3	yes	direct product factor
9	C₃×C₁₁×C₁₉	C₃×C₁₇	1	1	yes	characteristic, complemented
10	C₁₁×C₁₉⋊C₃	C₃×C₁₇	1	3	yes	direct product factor
11	C₃×C₁₁×C₁₇	—	19	3	no	—
12	C₃×C₁₁×C₁₇	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
13	C₁₇×C₁₉	C₃²×C₁₁	1	1	yes	characteristic, complemented, Hall
14	C₁₁×C₁₉	C₃²×C₁₇	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₁₇	C₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₉⋊C₃	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
17	C₃²×C₁₇	—	19	1	no	Hall
18	C₃²×C₁₁	—	19	1	no	Hall
19	C₃×C₁₉	C₃×C₁₁×C₁₇	1	1	yes	characteristic, complemented
20	C₁₉⋊C₃	C₃×C₁₁×C₁₇	1	3	yes	direct product factor
21	C₃×C₁₇	—	19	3	no	—
22	C₃×C₁₇	C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
23	C₃×C₁₁	—	19	3	no	—
24	C₃×C₁₁	C₁₇×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
25	C₁₉	C₃²×C₁₁×C₁₇	1	1	yes	characteristic, complemented, Sylow
26	C₁₇	C₃×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₁₁	C₃×C₁₇×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₃²	—	19	1	no	Sylow
29	C₃	—	19	3	no	—
30	C₃	C₁₁×C₁₇×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₃×C₁₁×C₁₇	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₃²×C₁₁×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₇×C₁₉	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃×C₁₁×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₇×C₁₉⋊C₃	C₃	direct (N × H)
2. C₃×C₁₁×C₁₇×C₁₉	C₃	semidirect
3. C₁₁×C₁₇×C₁₉	C₃²	semidirect
4. C₃×C₁₇×C₁₉⋊C₃	C₁₁	direct (N × H)
5. C₃×C₁₁×C₁₉⋊C₃	C₁₇	direct (N × H)
7. C₃×C₁₇×C₁₉	C₃×C₁₁	semidirect
8. C₁₇×C₁₉⋊C₃	C₃×C₁₁	direct (N × H)
9. C₃×C₁₁×C₁₉	C₃×C₁₇	semidirect
10. C₁₁×C₁₉⋊C₃	C₃×C₁₇	direct (N × H)
12. C₃×C₁₁×C₁₇	C₁₉⋊C₃	direct (N × H)
13. C₁₇×C₁₉	C₃²×C₁₁	semidirect
14. C₁₁×C₁₉	C₃²×C₁₇	semidirect
15. C₁₁×C₁₇	C₃×C₁₉⋊C₃	direct (N × H)
16. C₃×C₁₉⋊C₃	C₁₁×C₁₇	direct (N × H)
19. C₃×C₁₉	C₃×C₁₁×C₁₇	semidirect
20. C₁₉⋊C₃	C₃×C₁₁×C₁₇	direct (N × H)
22. C₃×C₁₇	C₁₁×C₁₉⋊C₃	direct (N × H)
24. C₃×C₁₁	C₁₇×C₁₉⋊C₃	direct (N × H)
25. C₁₉	C₃²×C₁₁×C₁₇	semidirect
26. C₁₇	C₃×C₁₁×C₁₉⋊C₃	direct (N × H)
27. C₁₁	C₃×C₁₇×C₁₉⋊C₃	direct (N × H)
30. C₃	C₁₁×C₁₇×C₁₉⋊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
C₁₁×C₁₇×C₁₉⋊C₃	3
C₃×C₁₁×C₁₇×C₁₉	3
C₃×C₁₇×C₁₉⋊C₃	11
C₃×C₁₁×C₁₉⋊C₃	17
C₃²×C₁₁×C₁₇	19

Subgroups — C3×C11×C17×C19⋊C3 #44544267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁×C₁₇×C₁₉⋊C₃ #44544267