Subgroups — C₁₁×C₃₇×D₃₉ #44540802

Order 31746.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₁₃×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₁₃×C₃₇	—	3	1	no	maximal, Hall
3	C₁₁×C₁₃×C₃₇	D₃	1	1	yes	characteristic, complemented, Hall
4	C₃₇×D₃₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	D₃×C₁₁×C₃₇	—	13	1	no	maximal, Hall
6	C₃×C₁₃×C₃₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₁×C₃₇	D₁₃	1	1	yes	characteristic, complemented, Hall
8	D₁₃×C₃₇	—	3	1	no	Hall
9	C₁₁×D₃₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₁×C₃₇	—	39	1	no	Hall
11	C₁₃×C₃₇	D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₁×C₁₃	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
13	C₁₁×C₃₇	D₃₉	1	1	yes	characteristic, direct product factor, Hall
14	C₁₁×D₁₃	—	3	1	no	Hall
15	D₃×C₃₇	—	13	1	no	Hall
16	C₁₁×C₁₃	D₃×C₃₇	1	1	yes	characteristic, complemented, Hall
17	C₃×C₃₇	C₁₁×D₁₃	1	1	yes	characteristic, complemented, Hall
18	D₃₉	C₁₁×C₃₇	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃₇	—	39	1	no	Hall
20	D₃×C₁₁	—	13	1	no	Hall
21	C₃×C₁₃	C₂×C₁₁×C₃₇	1	1	yes	characteristic, complemented, Hall
22	C₃₇	C₁₁×D₃₉	1	1	yes	characteristic, direct product factor, Sylow
23	C₃×C₁₁	D₁₃×C₃₇	1	1	yes	characteristic, complemented, Hall
24	D₁₃	—	3	1	no	Hall
25	C₂×C₁₁	—	39	1	no	Hall
26	C₁₃	D₃×C₁₁×C₃₇	1	1	yes	characteristic, complemented, Sylow
27	C₁₁	C₃₇×D₃₉	1	1	yes	characteristic, direct product factor, Sylow
28	D₃	—	13	1	no	Hall
29	C₃	C₁₁×D₁₃×C₃₇	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	39	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₃₇	D₃₉
commutator, cosocle, hypocenter	C₃×C₁₃	C₂×C₁₁×C₃₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₃×C₃₇	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₁₁×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×C₁₃×C₃₇	C₂	semidirect
3. C₁₁×C₁₃×C₃₇	D₃	semidirect
4. C₃₇×D₃₉	C₁₁	direct (N × H)
6. C₃×C₁₃×C₃₇	C₂×C₁₁	semidirect
7. C₃×C₁₁×C₃₇	D₁₃	semidirect
9. C₁₁×D₃₉	C₃₇	direct (N × H)
11. C₁₃×C₃₇	D₃×C₁₁	semidirect
12. C₃×C₁₁×C₁₃	C₂×C₃₇	semidirect
13. C₁₁×C₃₇	D₃₉	direct (N × H)
16. C₁₁×C₁₃	D₃×C₃₇	semidirect
17. C₃×C₃₇	C₁₁×D₁₃	semidirect
18. D₃₉	C₁₁×C₃₇	direct (N × H)
21. C₃×C₁₃	C₂×C₁₁×C₃₇	semidirect
22. C₃₇	C₁₁×D₃₉	direct (N × H)
23. C₃×C₁₁	D₁₃×C₃₇	semidirect
26. C₁₃	D₃×C₁₁×C₃₇	semidirect
27. C₁₁	C₃₇×D₃₉	direct (N × H)
29. C₃	C₁₁×D₁₃×C₃₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₁₁×C₁₃×C₃₇	2
C₁₁×D₁₃×C₃₇	3
C₃₇×D₃₉	11
D₃×C₁₁×C₃₇	13
C₁₁×D₃₉	37

Subgroups — C11×C37×D39 #44540802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₃₇×D₃₉ #44540802