Subgroups — C₂×C₃₇⋊C₃×D₇₁ #44538617

Order 31524.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇⋊C₃×D₇₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇₁×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×D₇₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇₁×C₃₇⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃₇×C₇₁	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃₇×D₇₁	C₂×C₃	1	2	yes	complemented
7	C₃₇×C₇₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×D₇₁	—	37	1	no	maximal, Hall
9	C₂²×C₃₇⋊C₃	—	71	1	no	maximal, Hall
10	C₂×C₃×C₇₁	—	37	1	no	—
11	C₃×D₇₁	—	37	2	no	—
12	C₂×D₇₁	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃₇⋊C₃	—	71	2	no	—
14	C₂×C₃₇⋊C₃	D₇₁	1	1	yes	characteristic, direct product factor
15	C₃×C₇₁	—	37	1	no	Hall
16	C₂²×C₃₇	—	71	1	no	Hall
17	C₂×C₇₁	C₂×C₃₇⋊C₃	1	1	yes	characteristic, complemented
18	D₇₁	C₂×C₃₇⋊C₃	1	2	yes	direct product factor
19	C₃₇⋊C₃	C₂×D₇₁	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃₇	—	71	2	no	—
21	C₂×C₃₇	C₃×D₇₁	1	1	yes	characteristic, complemented
22	C₇₁	C₂²×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₃₇	C₂×C₃×D₇₁	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	2627	1	no	Hall
25	C₂×C₃	—	37	1	no	—
26	C₂×C₃	—	2627	2	no	—
27	C₂²	—	71	1	no	Sylow
28	C₃	—	37	1	no	Sylow
29	C₂	—	71	2	no	—
30	C₂	C₃₇⋊C₃×D₇₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃₇⋊C₃×D₇₁
commutator, cosocle, hypocenter	C₃₇×C₇₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃₇×C₇₁	C₂×C₃
LCS	G ▷ C₃₇×C₇₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₃₇⋊C₃×D₇₁	C₂	direct (N × H)
2. C₂×C₇₁×C₃₇⋊C₃	C₂	semidirect
3. C₂×C₃₇×D₇₁	C₃	semidirect
4. C₇₁×C₃₇⋊C₃	C₂²	semidirect
5. C₂×C₃₇×C₇₁	C₂×C₃	semidirect
6. C₃₇×D₇₁	C₂×C₃	semidirect
7. C₃₇×C₇₁	C₂²×C₃	semidirect
12. C₂×D₇₁	C₃₇⋊C₃	direct (N × H)
14. C₂×C₃₇⋊C₃	D₇₁	direct (N × H)
17. C₂×C₇₁	C₂×C₃₇⋊C₃	semidirect
18. D₇₁	C₂×C₃₇⋊C₃	direct (N × H)
19. C₃₇⋊C₃	C₂×D₇₁	direct (N × H)
21. C₂×C₃₇	C₃×D₇₁	semidirect
22. C₇₁	C₂²×C₃₇⋊C₃	semidirect
23. C₃₇	C₂×C₃×D₇₁	semidirect
30. C₂	C₃₇⋊C₃×D₇₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₇⋊C₃×D₇₁	2
C₂×C₇₁×C₃₇⋊C₃	2
C₂×C₃₇×D₇₁	3
C₂×C₃×D₇₁	37
C₂²×C₃₇⋊C₃	71

Subgroups — C2×C37⋊C3×D71 #44538617

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₇⋊C₃×D₇₁ #44538617