Subgroups — C₃⋊Dic₃×C₁₂₇⋊C₇ #44544721

Order 32004.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₂₇⋊C₇	C₂	1	1	yes	maximal, characteristic
2	Dic₃×C₁₂₇⋊C₇	—	3	4	no	maximal
3	C₃²×C₁₂₇⋊C₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₂₇⋊C₇	D₃	1	4	yes	—
5	C₃⋊Dic₃×C₁₂₇	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₄×C₁₂₇⋊C₇	—	9	1	no	Hall
7	C₃×C₁₂₇⋊C₇	Dic₃	1	4	yes	complemented
8	C₂×C₃²×C₁₂₇	C₂×C₇	1	1	yes	characteristic
9	C₂×C₁₂₇⋊C₇	C₃⋊D₃	1	1	yes	characteristic
10	Dic₃×C₁₂₇	—	3	4	no	—
11	C₃²×C₁₂₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₁₂₇⋊C₇	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	—	127	1	no	maximal, Hall
18	C₁₂₇	C₇×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃²×C₇	—	127	1	no	—
20	C₇×Dic₃	—	381	4	no	—
21	C₃²×C₇	—	127	1	no	Hall
22	C₂×C₃×C₇	—	127	4	no	—
23	C₃⋊Dic₃	C₁₂₇⋊C₇	1	1	yes	characteristic, direct product factor, Hall
24	C₄×C₇	—	1143	1	no	Hall
25	C₃×C₇	—	127	4	no	—
26	C₂×C₃²	C₂×C₁₂₇⋊C₇	1	1	yes	characteristic
27	C₂×C₇	—	127	1	no	—
28	Dic₃	—	3	4	no	—
29	C₃²	C₄×C₁₂₇⋊C₇	1	1	yes	characteristic, complemented, Sylow
30	C₇	—	127	1	no	Sylow
31	C₂×C₃	D₃×C₁₂₇⋊C₇	1	4	yes	—
32	C₄	—	9	1	no	Sylow
33	C₃	Dic₃×C₁₂₇⋊C₇	1	4	yes	complemented
34	C₂	C₃⋊D₃×C₁₂₇⋊C₇	1	1	yes	characteristic

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

Complements

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

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

Maximal subgroups

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

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

Subgroups — C3⋊Dic3×C127⋊C7 #44544721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊Dic₃×C₁₂₇⋊C₇ #44544721