Subgroups — C₂×C₇×D₂₇₁⋊C₃ #36384635

Order 22764.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₂₇₁⋊C₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₂₇₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₂₇₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇×C₂₇₁⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₂₇₁	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇×D₂₇₁	C₂×C₃	1	2	yes	complemented
7	C₂×D₂₇₁⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₂₇₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₂₇₁⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
10	D₂₇₁⋊C₃	C₂×C₇	1	2	yes	direct product factor
11	C₂×D₂₇₁	C₃×C₇	1	1	yes	characteristic, complemented, Hall
12	C₂₇₁⋊C₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₂₇₁	C₂×C₃×C₇	1	1	yes	characteristic, complemented
14	D₂₇₁	C₂×C₃×C₇	1	2	yes	complemented
15	C₂₇₁	C₂²×C₃×C₇	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₃×C₇	—	271	1	no	maximal, Hall
17	C₂×C₃×C₇	—	271	2	no	—
18	C₂×C₃×C₇	—	271	1	no	—
19	C₂²×C₇	—	271	1	no	Hall
20	C₃×C₇	—	271	1	no	Hall
21	C₂×C₇	—	271	2	no	—
22	C₂×C₇	D₂₇₁⋊C₃	1	1	yes	characteristic, direct product factor
23	C₂²×C₃	—	271	1	no	Hall
24	C₇	C₂×D₂₇₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₃	—	271	2	no	—
26	C₂×C₃	—	271	1	no	—
27	C₂²	—	271	1	no	Sylow
28	C₃	—	271	1	no	Sylow
29	C₂	—	271	2	no	—
30	C₂	C₇×D₂₇₁⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	D₂₇₁⋊C₃
commutator, cosocle, hypocenter	C₂₇₁	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₂₇₁	C₂×C₃
LCS	G ▷ C₂₇₁
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₂₇₁⋊C₃	C₂	direct (N × H)
2. C₂×C₇×C₂₇₁⋊C₃	C₂	semidirect
3. C₂×C₇×D₂₇₁	C₃	semidirect
4. C₇×C₂₇₁⋊C₃	C₂²	semidirect
5. C₂×C₇×C₂₇₁	C₂×C₃	semidirect
6. C₇×D₂₇₁	C₂×C₃	semidirect
7. C₂×D₂₇₁⋊C₃	C₇	direct (N × H)
8. C₇×C₂₇₁	C₂²×C₃	semidirect
9. C₂×C₂₇₁⋊C₃	C₂×C₇	semidirect
10. D₂₇₁⋊C₃	C₂×C₇	direct (N × H)
11. C₂×D₂₇₁	C₃×C₇	semidirect
12. C₂₇₁⋊C₃	C₂²×C₇	semidirect
13. C₂×C₂₇₁	C₂×C₃×C₇	semidirect
14. D₂₇₁	C₂×C₃×C₇	semidirect
15. C₂₇₁	C₂²×C₃×C₇	semidirect
22. C₂×C₇	D₂₇₁⋊C₃	direct (N × H)
24. C₇	C₂×D₂₇₁⋊C₃	direct (N × H)
30. C₂	C₇×D₂₇₁⋊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
C₇×D₂₇₁⋊C₃	2
C₂×C₇×C₂₇₁⋊C₃	2
C₂×C₇×D₂₇₁	3
C₂×D₂₇₁⋊C₃	7
C₂²×C₃×C₇	271

Subgroups — C2×C7×D271⋊C3 #36384635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₂₇₁⋊C₃ #36384635