Subgroups — C₇×C₂²⋊C₉×C₁₂₇ #44544686

Order 32004.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₇×C₁₂₇	C₃	1	1	yes	maximal, characteristic
2	C₇×C₉×C₁₂₇	—	4	1	no	maximal, Hall
3	C₂×C₃×C₇×C₁₂₇	—	3	1	no	—
4	C₂²⋊C₉×C₁₂₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₇×C₁₂₇	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₇×C₁₂₇	A₄	1	1	yes	characteristic
7	C₂×C₇×C₁₂₇	—	3	1	no	—
8	C₂²×C₃×C₁₂₇	C₃×C₇	1	1	yes	characteristic
9	C₉×C₁₂₇	—	4	1	no	Hall
10	C₇×C₁₂₇	C₂²⋊C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₁₂₇	—	3	1	no	—
12	C₂²×C₁₂₇	C₇×C₉	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₂₇	C₇×A₄	1	1	yes	characteristic
14	C₂×C₁₂₇	—	3	1	no	—
15	C₇×C₂²⋊C₉	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₁₂₇	C₇×C₂²⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₂²×C₃×C₇	C₃×C₁₂₇	1	1	yes	characteristic
18	C₇×C₉	—	4	1	no	Hall
19	C₂×C₃×C₇	—	3	1	no	—
20	C₂²⋊C₉	C₇×C₁₂₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂²×C₇	C₉×C₁₂₇	1	1	yes	characteristic, complemented, Hall
22	C₃×C₇	A₄×C₁₂₇	1	1	yes	characteristic
23	C₂×C₇	—	3	1	no	—
24	C₂²×C₃	C₃×C₇×C₁₂₇	1	1	yes	characteristic
25	C₉	—	4	1	no	Sylow
26	C₇	C₂²⋊C₉×C₁₂₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	—	3	1	no	—
28	C₂²	C₇×C₉×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₇×A₄×C₁₂₇	1	1	yes	characteristic
30	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₇×C₁₂₇	A₄
commutator, hypocenter	C₂²	C₇×C₉×C₁₂₇
Frattini	C₃	C₇×A₄×C₁₂₇
Fitting, socle, prime radical	C₂²×C₃×C₇×C₁₂₇	C₃
cosocle	C₂²×C₃	C₃×C₇×C₁₂₇
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₇×C₁₂₇

Complements

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

N	H ≅ G/N	type
4. C₂²⋊C₉×C₁₂₇	C₇	direct (N × H)
5. C₂²×C₇×C₁₂₇	C₉	semidirect
10. C₇×C₁₂₇	C₂²⋊C₉	direct (N × H)
12. C₂²×C₁₂₇	C₇×C₉	semidirect
15. C₇×C₂²⋊C₉	C₁₂₇	direct (N × H)
16. C₁₂₇	C₇×C₂²⋊C₉	direct (N × H)
20. C₂²⋊C₉	C₇×C₁₂₇	direct (N × H)
21. C₂²×C₇	C₉×C₁₂₇	semidirect
26. C₇	C₂²⋊C₉×C₁₂₇	direct (N × H)
28. C₂²	C₇×C₉×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₇×C₁₂₇	3
C₇×C₉×C₁₂₇	4
C₂²⋊C₉×C₁₂₇	7
C₇×C₂²⋊C₉	127

Subgroups — C7×C22⋊C9×C127 #44544686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₂²⋊C₉×C₁₂₇ #44544686