Subgroups — C₃×C₂²⋊#14581888 #44544912

Order 32004.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#14581888	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₇×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#14581888	—	4	1	no	maximal, Hall
4	C₂×C₃×C₇×C₁₂₇	—	3	1	no	—
5	C₃×C₂²⋊(C₁₂₇⋊C₃)	—	7	1	no	maximal, Hall
6	C₂²×C₇×C₁₂₇	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇×C₁₂₇	A₄	1	1	yes	characteristic, complemented
8	#14581888	—	4	3	no	—
9	C₂×C₇×C₁₂₇	—	3	1	no	—
10	C₂²×C₃×C₁₂₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
11	C₂²⋊(C₁₂₇⋊C₃)	—	7	3	no	—
12	C₃×C₁₂₇⋊C₃	—	28	1	no	Hall
13	C₇×C₁₂₇	C₃×A₄	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₁₂₇	—	3	1	no	—
15	C₂²×C₁₂₇	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
16	C₃×C₁₂₇	C₂²⋊ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
17	C₁₂₇⋊C₃	—	28	3	no	—
18	C₂×C₁₂₇	—	3	1	no	—
19	C₃×C₂²⋊ΓL(1,𝔽₈)	—	127	1	no	maximal, Hall
20	C₁₂₇	C₃×C₂²⋊ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
21	C₂²×C₃×C₇	C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
22	C₂²⋊ΓL(1,𝔽₈)	—	127	3	no	—
23	C₃×ΓL(1,𝔽₈)	—	508	1	no	Hall
24	C₂×C₃×C₇	—	3	1	no	—
25	C₃×A₄	—	889	1	no	Hall
26	C₂²×C₇	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic, complemented, Hall
27	C₃×C₇	C₂²⋊(C₁₂₇⋊C₃)	1	1	yes	characteristic, complemented
28	ΓL(1,𝔽₈)	—	508	3	no	—
29	C₂×C₇	—	3	1	no	—
30	C₂²×C₃	#14581888	1	1	yes	characteristic, complemented
31	A₄	—	889	3	no	—
32	C₃²	—	3556	1	no	Sylow
33	C₇	C₃×C₂²⋊(C₁₂₇⋊C₃)	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃	—	3	1	no	—
35	C₂²	C₃×#14581888	1	1	yes	characteristic, complemented, Sylow
36	C₃	—	3556	3	no	—
37	C₃	C₂²⋊#14581888	1	1	yes	characteristic, direct product factor
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₂²⋊#14581888
commutator, cosocle, hypocenter	C₂²×C₇×C₁₂₇	C₃²
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₇×C₁₂₇	C₃
LCS	G ▷ C₂²×C₇×C₁₂₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₂²⋊#14581888	C₃	direct (N × H)
2. C₂²×C₃×C₇×C₁₂₇	C₃	semidirect
6. C₂²×C₇×C₁₂₇	C₃²	semidirect
7. C₃×C₇×C₁₂₇	A₄	semidirect
10. C₂²×C₃×C₁₂₇	ΓL(1,𝔽₈)	semidirect
13. C₇×C₁₂₇	C₃×A₄	semidirect
15. C₂²×C₁₂₇	C₃×ΓL(1,𝔽₈)	semidirect
16. C₃×C₁₂₇	C₂²⋊ΓL(1,𝔽₈)	semidirect
20. C₁₂₇	C₃×C₂²⋊ΓL(1,𝔽₈)	semidirect
21. C₂²×C₃×C₇	C₁₂₇⋊C₃	semidirect
26. C₂²×C₇	C₃×C₁₂₇⋊C₃	semidirect
27. C₃×C₇	C₂²⋊(C₁₂₇⋊C₃)	semidirect
30. C₂²×C₃	#14581888	semidirect
33. C₇	C₃×C₂²⋊(C₁₂₇⋊C₃)	semidirect
35. C₂²	C₃×#14581888	semidirect
37. C₃	C₂²⋊#14581888	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²⋊#14581888	3
C₂²×C₃×C₇×C₁₂₇	3
C₃×#14581888	4
C₃×C₂²⋊(C₁₂₇⋊C₃)	7
C₃×C₂²⋊ΓL(1,𝔽₈)	127

Subgroups — C3×C22⋊#14581888 #44544912

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂²⋊#14581888 #44544912