Subgroups — C₉×C₁₁×C₁₇×C₁₉ #44544263

Order 31977.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₁₇×C₁₉	C₃	1	1	yes	maximal, characteristic
2	C₁₁×C₁₇×C₁₉	C₉	1	1	yes	characteristic, direct product factor, Hall
3	C₉×C₁₇×C₁₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₉×C₁₁×C₁₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₉×C₁₁×C₁₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₁₇×C₁₉	C₃×C₁₁	1	1	yes	characteristic
7	C₃×C₁₁×C₁₉	C₃×C₁₇	1	1	yes	characteristic
8	C₃×C₁₁×C₁₇	C₃×C₁₉	1	1	yes	characteristic
9	C₁₇×C₁₉	C₉×C₁₁	1	1	yes	characteristic, direct product factor, Hall
10	C₁₁×C₁₉	C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
11	C₁₁×C₁₇	C₉×C₁₉	1	1	yes	characteristic, direct product factor, Hall
12	C₉×C₁₉	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
13	C₉×C₁₇	C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Hall
14	C₉×C₁₁	C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₉	C₃×C₁₁×C₁₇	1	1	yes	characteristic
16	C₃×C₁₇	C₃×C₁₁×C₁₉	1	1	yes	characteristic
17	C₃×C₁₁	C₃×C₁₇×C₁₉	1	1	yes	characteristic
18	C₁₉	C₉×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₁₇	C₉×C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₁₁	C₉×C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₉	C₁₁×C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₃	C₃×C₁₁×C₁₇×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₁₁×C₁₇×C₁₉
socle, prime radical	C₃×C₁₁×C₁₇×C₁₉	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×C₁₇×C₁₉	C₉	direct (N × H)
3. C₉×C₁₇×C₁₉	C₁₁	direct (N × H)
4. C₉×C₁₁×C₁₉	C₁₇	direct (N × H)
5. C₉×C₁₁×C₁₇	C₁₉	direct (N × H)
9. C₁₇×C₁₉	C₉×C₁₁	direct (N × H)
10. C₁₁×C₁₉	C₉×C₁₇	direct (N × H)
11. C₁₁×C₁₇	C₉×C₁₉	direct (N × H)
12. C₉×C₁₉	C₁₁×C₁₇	direct (N × H)
13. C₉×C₁₇	C₁₁×C₁₉	direct (N × H)
14. C₉×C₁₁	C₁₇×C₁₉	direct (N × H)
18. C₁₉	C₉×C₁₁×C₁₇	direct (N × H)
19. C₁₇	C₉×C₁₁×C₁₉	direct (N × H)
20. C₁₁	C₉×C₁₇×C₁₉	direct (N × H)
21. C₉	C₁₁×C₁₇×C₁₉	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×C₁₁×C₁₇×C₁₉	3
C₉×C₁₇×C₁₉	11
C₉×C₁₁×C₁₉	17
C₉×C₁₁×C₁₇	19

Subgroups — C9×C11×C17×C19 #44544263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₁₁×C₁₇×C₁₉ #44544263