Subgroups — C₂×(C₇⋊C₉)⋊D₁₂₇ #44544669

Order 32004.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₇⋊C₉)⋊D₁₂₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇⋊C₉×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₈₈₉	C₃	1	1	yes	maximal, characteristic
4	C₇⋊C₉×C₁₂₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×D₈₈₉	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₇×C₁₂₇	C₂×C₃	1	1	yes	characteristic
7	C₂×C₉×D₁₂₇	—	7	1	no	maximal, Hall
8	C₂×D₈₈₉	C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×C₁₂₇	C₂²×C₃	1	1	yes	characteristic
10	C₉×D₁₂₇	—	7	2	no	—
11	C₂×C₉×C₁₂₇	—	7	1	no	—
12	C₂×C₇×C₁₂₇	C₂×C₉	1	1	yes	characteristic, complemented
13	D₈₈₉	C₂×C₉	1	2	yes	complemented
14	C₂×C₃×D₁₂₇	—	7	1	no	—
15	C₉×C₁₂₇	—	7	1	no	Hall
16	C₇×C₁₂₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₂₇	AGL(1,𝔽₇)	1	1	yes	characteristic
18	C₃×D₁₂₇	—	7	2	no	—
19	C₂×D₁₂₇	—	7	1	no	Hall
20	C₃×C₁₂₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
21	C₂×C₁₂₇	D₇⋊C₉	1	1	yes	characteristic, complemented
22	D₁₂₇	—	7	2	no	—
23	C₂×D₇⋊C₉	—	127	1	no	maximal, Hall
24	C₁₂₇	C₂×D₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₇⋊C₉	D₁₂₇	1	1	yes	characteristic, complemented
26	D₇⋊C₉	—	127	2	no	—
27	C₂×C₃×D₇	—	127	1	no	—
28	C₇⋊C₉	C₂×D₁₂₇	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₇	C₃×D₁₂₇	1	1	yes	characteristic
30	C₃×D₇	—	127	2	no	—
31	C₂²×C₉	—	889	1	no	Hall
32	C₂×D₇	—	127	1	no	Hall
33	C₃×C₇	C₂×C₃×D₁₂₇	1	1	yes	characteristic
34	C₂×C₉	—	7	1	no	—
35	C₂×C₉	—	889	2	no	—
36	C₂×C₇	C₉×D₁₂₇	1	1	yes	characteristic, complemented
37	D₇	—	127	2	no	—
38	C₂²×C₃	—	889	1	no	—
39	C₉	—	7	1	no	Sylow
40	C₇	C₂×C₉×D₁₂₇	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	889	2	no	—
42	C₂×C₃	ΓL(1,𝔽₈)⋊D₁₂₇	1	1	yes	characteristic
43	C₂²	—	889	1	no	Sylow
44	C₃	C₂×ΓL(1,𝔽₈)⋊D₁₂₇	1	1	yes	characteristic
45	C₂	—	889	2	no	—
46	C₂	(C₇⋊C₉)⋊D₁₂₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	ΓL(1,𝔽₈)⋊D₁₂₇
commutator, hypocenter	C₇×C₁₂₇	C₂²×C₉
Frattini	C₃	C₂×ΓL(1,𝔽₈)⋊D₁₂₇
Fitting, socle	C₂×C₃×C₇×C₁₂₇	C₂×C₃
prime radical	C₂×C₃×D₈₈₉	C₃
cosocle	C₃×C₇×C₁₂₇	C₂²×C₃
LCS	G ▷ C₇×C₁₂₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. (C₇⋊C₉)⋊D₁₂₇	C₂	direct (N × H)
2. C₂×C₇⋊C₉×C₁₂₇	C₂	semidirect
4. C₇⋊C₉×C₁₂₇	C₂²	semidirect
8. C₂×D₈₈₉	C₉	semidirect
12. C₂×C₇×C₁₂₇	C₂×C₉	semidirect
13. D₈₈₉	C₂×C₉	semidirect
16. C₇×C₁₂₇	C₂²×C₉	semidirect
21. C₂×C₁₂₇	D₇⋊C₉	semidirect
24. C₁₂₇	C₂×D₇⋊C₉	semidirect
25. C₂×C₇⋊C₉	D₁₂₇	semidirect
28. C₇⋊C₉	C₂×D₁₂₇	semidirect
36. C₂×C₇	C₉×D₁₂₇	semidirect
40. C₇	C₂×C₉×D₁₂₇	semidirect
46. C₂	(C₇⋊C₉)⋊D₁₂₇	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⋊C₉)⋊D₁₂₇	2
C₂×C₇⋊C₉×C₁₂₇	2
C₂×C₃×D₈₈₉	3
C₂×C₉×D₁₂₇	7
C₂×D₇⋊C₉	127

Subgroups — C2×(C7⋊C9)⋊D127 #44544669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×(C₇⋊C₉)⋊D₁₂₇ #44544669