Subgroups — C₂×C₁₁×C₃₇×C₁₃⋊C₃ #44540790

Order 31746.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₃₇×C₁₃⋊C₃	C₂	direct (N × H)
2. C₂×C₁₁×C₁₃×C₃₇	C₃	semidirect
3. C₁₁×C₁₃×C₃₇	C₂×C₃	semidirect
4. C₂×C₃₇×C₁₃⋊C₃	C₁₁	direct (N × H)
6. C₃₇×C₁₃⋊C₃	C₂×C₁₁	direct (N × H)
8. C₂×C₁₃×C₃₇	C₃×C₁₁	semidirect
9. C₂×C₁₁×C₁₃⋊C₃	C₃₇	direct (N × H)
10. C₂×C₁₁×C₃₇	C₁₃⋊C₃	direct (N × H)
11. C₁₃×C₃₇	C₂×C₃×C₁₁	semidirect
12. C₁₁×C₁₃⋊C₃	C₂×C₃₇	direct (N × H)
13. C₁₁×C₃₇	C₂×C₁₃⋊C₃	direct (N × H)
14. C₂×C₁₁×C₁₃	C₃×C₃₇	semidirect
16. C₁₁×C₁₃	C₂×C₃×C₃₇	semidirect
18. C₂×C₁₃⋊C₃	C₁₁×C₃₇	direct (N × H)
19. C₂×C₃₇	C₁₁×C₁₃⋊C₃	direct (N × H)
21. C₁₃⋊C₃	C₂×C₁₁×C₃₇	direct (N × H)
22. C₃₇	C₂×C₁₁×C₁₃⋊C₃	direct (N × H)
24. C₂×C₁₃	C₃×C₁₁×C₃₇	semidirect
25. C₂×C₁₁	C₃₇×C₁₃⋊C₃	direct (N × H)
26. C₁₃	C₂×C₃×C₁₁×C₃₇	semidirect
27. C₁₁	C₂×C₃₇×C₁₃⋊C₃	direct (N × H)
30. C₂	C₁₁×C₃₇×C₁₃⋊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×C₃₇×C₁₃⋊C₃	2
C₂×C₁₁×C₁₃×C₃₇	3
C₂×C₃₇×C₁₃⋊C₃	11
C₂×C₃×C₁₁×C₃₇	13
C₂×C₁₁×C₁₃⋊C₃	37

Subgroups — C2×C11×C37×C13⋊C3 #44540790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×C₃₇×C₁₃⋊C₃ #44540790