Subgroups — D₂₁×D₂₈₁ #37556261

Order 23604.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₉₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₂₁×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×D₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₂₈₁	—	3	1	no	maximal, Hall
5	C₃×C₇×C₂₈₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₉₆₇	—	3	1	no	—
7	C₇×D₂₈₁	D₃	1	1	yes	characteristic, complemented
8	D₇×C₂₈₁	—	3	1	no	—
9	D₃×D₂₈₁	—	7	1	no	maximal, Hall
10	C₇×C₂₈₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₈₄₃	—	7	1	no	—
12	C₃×D₂₈₁	D₇	1	1	yes	characteristic, complemented
13	D₃×C₂₈₁	—	7	1	no	—
14	C₂×D₂₈₁	—	21	1	no	Hall
15	C₃×C₂₈₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₂₈₁	—	21	1	no	—
17	D₂₈₁	—	21	1	no	—
18	D₂₈₁	D₂₁	1	1	yes	characteristic, direct product factor
19	C₂₈₁	C₂×D₂₁	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₂₁	—	281	1	no	maximal, Hall
21	C₂×C₃×C₇	—	281	1	no	—
22	D₂₁	—	281	1	no	—
23	D₂₁	D₂₈₁	1	1	yes	characteristic, direct product factor
24	C₂×D₇	—	843	1	no	Hall
25	C₃×C₇	C₂×D₂₈₁	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇	—	281	1	no	—
27	D₇	—	3	1	no	—
28	D₇	—	843	1	no	—
29	C₂×D₃	—	1967	1	no	Hall
30	C₇	D₃×D₂₈₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	281	1	no	—
32	D₃	—	7	1	no	—
33	D₃	—	1967	1	no	—
34	C₂²	—	5901	1	no	Sylow
35	C₃	D₇×D₂₈₁	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	5901	1	no	—
37	C₂	—	21	1	no	—
38	C₂	—	281	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₂₈₁	C₂²
LCS	G ▷ C₃×C₇×C₂₈₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₅₉₀₁	C₂	semidirect
2. D₂₁×C₂₈₁	C₂	semidirect
3. C₃×C₇×D₂₈₁	C₂	semidirect
5. C₃×C₇×C₂₈₁	C₂²	semidirect
7. C₇×D₂₈₁	D₃	semidirect
10. C₇×C₂₈₁	C₂×D₃	semidirect
12. C₃×D₂₈₁	D₇	semidirect
15. C₃×C₂₈₁	C₂×D₇	semidirect
18. D₂₈₁	D₂₁	direct (N × H)
19. C₂₈₁	C₂×D₂₁	semidirect
23. D₂₁	D₂₈₁	direct (N × H)
25. C₃×C₇	C₂×D₂₈₁	semidirect
30. C₇	D₃×D₂₈₁	semidirect
35. C₃	D₇×D₂₈₁	semidirect

Maximal subgroups

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

subgroup	index
D₅₉₀₁	2
D₂₁×C₂₈₁	2
C₃×C₇×D₂₈₁	2
D₇×D₂₈₁	3
D₃×D₂₈₁	7
C₂×D₂₁	281

Subgroups — D21×D281 #37556261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₁×D₂₈₁ #37556261