Subgroups — C₇×C₃⋊Dic₃×C₁₂₇ #44544762

Order 32004.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₃×C₁₂₇	—	3	4	no	maximal
3	C₃²×C₇×C₁₂₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₁₂₇	D₃	1	4	yes	—
5	C₃⋊Dic₃×C₁₂₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₄×C₇×C₁₂₇	—	9	1	no	Hall
7	C₃×C₇×C₁₂₇	Dic₃	1	4	yes	complemented
8	C₂×C₃²×C₁₂₇	C₂×C₇	1	1	yes	characteristic
9	C₂×C₇×C₁₂₇	C₃⋊D₃	1	1	yes	characteristic
10	Dic₃×C₁₂₇	—	3	4	no	—
11	C₃²×C₁₂₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₂₇	C₃⋊Dic₃	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₁₂₇	D₃×C₇	1	4	yes	—
14	C₄×C₁₂₇	—	9	1	no	Hall
15	C₃×C₁₂₇	C₇×Dic₃	1	4	yes	complemented
16	C₂×C₁₂₇	C₇×C₃⋊D₃	1	1	yes	characteristic
17	C₇×C₃⋊Dic₃	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₁₂₇	C₇×C₃⋊Dic₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃²×C₇	C₂×C₁₂₇	1	1	yes	characteristic
20	C₇×Dic₃	—	3	4	no	—
21	C₃²×C₇	C₄×C₁₂₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇	D₃×C₁₂₇	1	4	yes	—
23	C₃⋊Dic₃	C₇×C₁₂₇	1	1	yes	characteristic, direct product factor, Hall
24	C₄×C₇	—	9	1	no	Hall
25	C₃×C₇	Dic₃×C₁₂₇	1	4	yes	complemented
26	C₂×C₃²	C₂×C₇×C₁₂₇	1	1	yes	characteristic
27	C₂×C₇	C₃⋊D₃×C₁₂₇	1	1	yes	characteristic
28	Dic₃	—	3	4	no	—
29	C₃²	C₄×C₇×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
30	C₇	C₃⋊Dic₃×C₁₂₇	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	D₃×C₇×C₁₂₇	1	4	yes	—
32	C₄	—	9	1	no	Sylow
33	C₃	C₇×Dic₃×C₁₂₇	1	4	yes	complemented
34	C₂	C₇×C₃⋊D₃×C₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₂₇	C₃⋊D₃
commutator, hypocenter	C₃²	C₄×C₇×C₁₂₇
Frattini	C₂	C₇×C₃⋊D₃×C₁₂₇
Fitting, socle, prime radical	C₂×C₃²×C₇×C₁₂₇	C₂
cosocle	C₂×C₃²	C₂×C₇×C₁₂₇
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₇×C₁₂₇

Complements

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

N	H ≅ G/N	type
3. C₃²×C₇×C₁₂₇	C₄	semidirect
5. C₃⋊Dic₃×C₁₂₇	C₇	direct (N × H)
7. C₃×C₇×C₁₂₇	Dic₃	semidirect
11. C₃²×C₁₂₇	C₄×C₇	semidirect
12. C₇×C₁₂₇	C₃⋊Dic₃	direct (N × H)
15. C₃×C₁₂₇	C₇×Dic₃	semidirect
17. C₇×C₃⋊Dic₃	C₁₂₇	direct (N × H)
18. C₁₂₇	C₇×C₃⋊Dic₃	direct (N × H)
21. C₃²×C₇	C₄×C₁₂₇	semidirect
23. C₃⋊Dic₃	C₇×C₁₂₇	direct (N × H)
25. C₃×C₇	Dic₃×C₁₂₇	semidirect
29. C₃²	C₄×C₇×C₁₂₇	semidirect
30. C₇	C₃⋊Dic₃×C₁₂₇	direct (N × H)
33. C₃	C₇×Dic₃×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₇×C₁₂₇	2
C₇×Dic₃×C₁₂₇	3
C₃⋊Dic₃×C₁₂₇	7
C₇×C₃⋊Dic₃	127

Subgroups — C7×C3⋊Dic3×C127 #44544762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₃⋊Dic₃×C₁₂₇ #44544762