Subgroups — C₃×#24922587 #44544729

Order 32004.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#14581888	C₂	1	1	yes	maximal, characteristic
2	#24922587	C₃	1	3	yes	maximal, direct product factor
3	C₃×Dic₈₈₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×#14581888	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×#14581888	C₂×C₃	1	3	yes	—
6	C₂×C₃×C₇×C₁₂₇	C₂×C₃	1	1	yes	characteristic
7	C₃×(C₁₂₇⋊C₃)⋊C₄	—	7	1	no	maximal, Hall
8	Dic₈₈₉	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×C₁₂₇	C₃×C₄	1	1	yes	characteristic, complemented
10	#14581888	C₃×C₄	1	3	yes	complemented
11	C₂×C₃×C₁₂₇⋊C₃	—	7	1	no	—
12	C₂×C₇×C₁₂₇	C₂×C₃²	1	1	yes	characteristic
13	C₃×Dic₁₂₇	—	7	1	no	—
14	(C₁₂₇⋊C₃)⋊C₄	—	7	3	no	—
15	C₃×C₁₂₇⋊C₃	—	7	1	no	Hall
16	C₇×C₁₂₇	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₂₇	AGL(1,𝔽₇)	1	1	yes	characteristic
18	C₂×C₁₂₇⋊C₃	—	7	3	no	—
19	Dic₁₂₇	—	7	1	no	Hall
20	C₃×C₁₂₇	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic, complemented
21	C₁₂₇⋊C₃	—	7	3	no	—
22	C₂×C₁₂₇	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic
23	C₃×ΓL(1,𝔽₈)⋊C₄	—	127	1	no	maximal, Hall
24	C₁₂₇	C₃×ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃×ΓL(1,𝔽₈)	—	127	1	no	—
26	C₃×Dic₇	—	127	1	no	—
27	ΓL(1,𝔽₈)⋊C₄	—	127	3	no	—
28	C₃×ΓL(1,𝔽₈)	—	127	1	no	Hall
29	C₂×C₃×C₇	D₁₂₇⋊C₃	1	1	yes	characteristic
30	C₂×ΓL(1,𝔽₈)	—	127	3	no	—
31	C₃²×C₄	—	889	1	no	Hall
32	Dic₇	—	127	1	no	Hall
33	C₃×C₇	(C₁₂₇⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
34	ΓL(1,𝔽₈)	—	127	3	no	—
35	C₂×C₃²	—	889	1	no	—
36	C₂×C₇	C₃×D₁₂₇⋊C₃	1	1	yes	characteristic
37	C₃×C₄	—	889	3	no	—
38	C₃×C₄	—	889	1	no	—
39	C₃²	—	889	1	no	Sylow
40	C₇	C₃×(C₁₂₇⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	889	3	no	—
42	C₂×C₃	#19128632	1	1	yes	characteristic
43	C₄	—	889	1	no	Sylow
44	C₃	—	889	3	no	—
45	C₃	#24922587	1	1	yes	characteristic, direct product factor
46	C₂	C₃×#19128632	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	#19128632
commutator, hypocenter	C₇×C₁₂₇	C₃²×C₄
Frattini	C₂	C₃×#19128632
Fitting, socle	C₂×C₃×C₇×C₁₂₇	C₂×C₃
prime radical	C₂×C₃×#14581888	C₂
cosocle	C₂×C₇×C₁₂₇	C₂×C₃²
LCS	G ▷ C₇×C₁₂₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. #24922587	C₃	direct (N × H)
3. C₃×Dic₈₈₉	C₃	semidirect
4. C₃×#14581888	C₄	semidirect
8. Dic₈₈₉	C₃²	semidirect
9. C₃×C₇×C₁₂₇	C₃×C₄	semidirect
10. #14581888	C₃×C₄	semidirect
16. C₇×C₁₂₇	C₃²×C₄	semidirect
20. C₃×C₁₂₇	ΓL(1,𝔽₈)⋊C₄	semidirect
24. C₁₂₇	C₃×ΓL(1,𝔽₈)⋊C₄	semidirect
33. C₃×C₇	(C₁₂₇⋊C₃)⋊C₄	semidirect
40. C₇	C₃×(C₁₂₇⋊C₃)⋊C₄	semidirect
45. C₃	#24922587	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#14581888	2
#24922587	3
C₃×Dic₈₈₉	3
C₃×(C₁₂₇⋊C₃)⋊C₄	7
C₃×ΓL(1,𝔽₈)⋊C₄	127

Subgroups — C3×#24922587 #44544729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#24922587 #44544729