Subgroups — D₃₇×D₂₁₃ #44538626

Order 31524.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₈₈₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×D₂₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇₁×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₇×D₇₁	—	3	1	no	maximal, Hall
5	C₃×C₃₇×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₆₂₇	—	3	1	no	—
7	C₃₇×D₇₁	—	3	1	no	—
8	C₇₁×D₃₇	D₃	1	1	yes	characteristic, complemented
9	C₃₇×C₇₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₂₁₃	—	37	1	no	maximal, Hall
11	D₃×D₃₇	—	71	1	no	maximal, Hall
12	C₂×C₃×C₇₁	—	37	1	no	—
13	D₂₁₃	—	37	1	no	—
14	D₂₁₃	D₃₇	1	1	yes	characteristic, direct product factor
15	C₂×D₇₁	—	111	1	no	Hall
16	D₁₁₁	—	71	1	no	—
17	C₃×D₃₇	D₇₁	1	1	yes	characteristic, complemented
18	D₃×C₃₇	—	71	1	no	—
19	C₃×C₇₁	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
20	C₂×D₃₇	—	213	1	no	Hall
21	C₂×C₇₁	—	37	1	no	—
22	D₇₁	—	3	1	no	—
23	D₇₁	—	111	1	no	—
24	C₃×C₃₇	C₂×D₇₁	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃₇	—	213	1	no	—
26	D₃₇	—	213	1	no	—
27	D₃₇	D₂₁₃	1	1	yes	characteristic, direct product factor
28	C₇₁	D₃×D₃₇	1	1	yes	characteristic, complemented, Sylow
29	C₃₇	C₂×D₂₁₃	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	2627	1	no	Hall
31	C₂×C₃	—	37	1	no	—
32	D₃	—	2627	1	no	—
33	D₃	—	71	1	no	—
34	C₂²	—	7881	1	no	Sylow
35	C₃	D₃₇×D₇₁	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	37	1	no	—
37	C₂	—	7881	1	no	—
38	C₂	—	213	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. D₇₈₈₁	C₂	semidirect
2. C₃₇×D₂₁₃	C₂	semidirect
3. C₃×C₇₁×D₃₇	C₂	semidirect
5. C₃×C₃₇×C₇₁	C₂²	semidirect
8. C₇₁×D₃₇	D₃	semidirect
9. C₃₇×C₇₁	C₂×D₃	semidirect
14. D₂₁₃	D₃₇	direct (N × H)
17. C₃×D₃₇	D₇₁	semidirect
19. C₃×C₇₁	C₂×D₃₇	semidirect
24. C₃×C₃₇	C₂×D₇₁	semidirect
27. D₃₇	D₂₁₃	direct (N × H)
28. C₇₁	D₃×D₃₇	semidirect
29. C₃₇	C₂×D₂₁₃	semidirect
35. C₃	D₃₇×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
D₇₈₈₁	2
C₃₇×D₂₁₃	2
C₃×C₇₁×D₃₇	2
D₃₇×D₇₁	3
C₂×D₂₁₃	37
D₃×D₃₇	71

Subgroups — D37×D213 #44538626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₇×D₂₁₃ #44538626