Subgroups — D₇⋊C₉×C₂₈₉ #49138708

Order 36414.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊C₉×C₂₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₇×C₂₈₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇×C₂₈₉	C₂×C₃	1	1	yes	characteristic
4	C₂×C₉×C₂₈₉	—	7	1	no	maximal, Hall
5	D₇×C₂₈₉	C₉	1	1	yes	characteristic, complemented, Hall
6	C₉×C₂₈₉	—	7	1	no	Hall
7	C₁₇×D₇⋊C₉	C₁₇	1	1	yes	maximal, characteristic
8	C₇×C₂₈₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₂₈₉	—	7	1	no	—
10	C₁₇×C₇⋊C₉	C₂×C₁₇	1	1	yes	characteristic
11	C₃×C₂₈₉	AGL(1,𝔽₇)	1	1	yes	characteristic
12	C₃×D₇×C₁₇	C₃×C₁₇	1	1	yes	characteristic
13	C₂×C₂₈₉	—	7	1	no	Hall
14	C₃×C₇×C₁₇	C₂×C₃×C₁₇	1	1	yes	characteristic
15	C₂×C₉×C₁₇	—	7	1	no	—
16	C₂₈₉	D₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
17	D₇×C₁₇	C₉×C₁₇	1	1	yes	characteristic
18	C₉×C₁₇	—	7	1	no	—
19	D₇⋊C₉	C₂₈₉	1	1	yes	characteristic, direct product factor, Hall
20	C₇×C₁₇	C₂×C₉×C₁₇	1	1	yes	characteristic
21	C₂×C₃×C₁₇	—	7	1	no	—
22	C₇⋊C₉	C₂×C₂₈₉	1	1	yes	characteristic, complemented, Hall
23	C₃×C₁₇	C₁₇×AGL(1,𝔽₇)	1	1	yes	characteristic
24	C₃×D₇	C₃×C₂₈₉	1	1	yes	characteristic
25	C₂×C₁₇	—	7	1	no	—
26	C₃×C₇	C₂×C₃×C₂₈₉	1	1	yes	characteristic
27	C₂×C₉	—	7	1	no	Hall
28	C₁₇	C₁₇×D₇⋊C₉	1	1	yes	characteristic
29	D₇	C₉×C₂₈₉	1	1	yes	characteristic, complemented, Hall
30	C₉	—	7	1	no	Sylow
31	C₇	C₂×C₉×C₂₈₉	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃	—	7	1	no	—
33	C₃	AGL(1,𝔽₇)×C₂₈₉	1	1	yes	characteristic
34	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₂₈₉	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂×C₉×C₂₈₉
Frattini	C₃×C₁₇	C₁₇×AGL(1,𝔽₇)
Fitting	C₃×C₇×C₂₈₉	C₂×C₃
socle, cosocle	C₃×C₇×C₁₇	C₂×C₃×C₁₇
prime radical	C₃×D₇×C₁₇	C₃×C₁₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₂₈₉

Complements

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

N	H ≅ G/N	type
1. C₇⋊C₉×C₂₈₉	C₂	semidirect
5. D₇×C₂₈₉	C₉	semidirect
8. C₇×C₂₈₉	C₂×C₉	semidirect
16. C₂₈₉	D₇⋊C₉	direct (N × H)
19. D₇⋊C₉	C₂₈₉	direct (N × H)
22. C₇⋊C₉	C₂×C₂₈₉	semidirect
29. D₇	C₉×C₂₈₉	semidirect
31. C₇	C₂×C₉×C₂₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₇⋊C₉×C₂₈₉	2
C₃×D₇×C₂₈₉	3
C₂×C₉×C₂₈₉	7
C₁₇×D₇⋊C₉	17

Subgroups — D7⋊C9×C289 #49138708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇⋊C₉×C₂₈₉ #49138708