Subgroups — #732×C₁₂₇⋊C₃ #44525097

Order 30861.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	H(3,𝔽₃)×C₁₂₇⋊C₃	C₃	1	3	yes	maximal, complemented
2	C₃×C₉×C₁₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
3	#23779848	C₃	1	2	yes	maximal, complemented
4	#23779847	C₃	1	6	yes	maximal, complemented
5	#732×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₁₂₇⋊C₃	—	3	3	no	—
7	C₃²×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
8	C₃²⋊(C₁₂₇⋊C₃)	—	3	6	no	—
9	C₃²⋊(C₁₂₇⋊C₃)	C₃²	1	6	yes	complemented
10	C₃×#11765917	C₃²	1	2	yes	complemented
11	C₉×C₁₂₇⋊C₃	—	3	2	no	—
12	C₉×C₁₂₇⋊C₃	—	3	1	no	—
13	H(3,𝔽₃)×C₁₂₇	C₃²	1	3	yes	complemented
14	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic, complemented
15	C₃²×C₁₂₇	—	3	3	no	—
16	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
17	C₃×C₁₂₇⋊C₃	—	3	3	no	—
18	C₃×C₁₂₇⋊C₃	—	3	6	no	—
19	C₃×C₁₂₇⋊C₃	—	9	9	no	—
20	C₃×C₁₂₇⋊C₃	H(3,𝔽₃)	1	2	yes	—
21	C₃×C₁₂₇⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
22	C₉×C₁₂₇	—	3	1	no	—
23	#11765917	—	3	2	no	—
24	C₃×C₁₂₇	—	3	1	no	—
25	C₃×C₁₂₇	—	9	3	no	—
26	C₃×C₁₂₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
27	C₁₂₇⋊C₃	—	3	2	no	—
28	C₁₂₇⋊C₃	—	9	6	no	—
29	C₁₂₇⋊C₃	#732	1	3	yes	direct product factor
30	C₃×#732	—	127	1	no	maximal, Sylow
31	C₁₂₇	C₃×#732	1	1	yes	characteristic, complemented, Sylow
32	C₃×H(3,𝔽₃)	—	127	3	no	—
33	C₃²×C₉	—	127	1	no	—
34	#732	—	127	6	no	—
35	#732	—	127	2	no	—
36	#732	C₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor
37	C₃³	—	381	3	no	—
38	C₃³	—	127	1	no	—
39	H(3,𝔽₃)	—	381	6	no	—
40	H(3,𝔽₃)	—	127	6	no	—
41	H(3,𝔽₃)	C₃×C₁₂₇⋊C₃	1	3	yes	complemented
42	C₃×C₉	—	381	2	no	—
43	C₃×C₉	—	381	1	no	—
44	C₃×C₉	—	127	2	no	—
45	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
46	C₃²	—	3	3	no	—
47	C₃²	—	1143	9	no	—
48	C₃²	—	381	3	no	—
49	C₃²	—	381	6	no	—
50	C₃²	—	127	2	no	—
51	C₃²	—	127	1	no	—
52	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
53	C₉	—	3	1	no	—
54	C₉	—	381	2	no	—
55	C₃	—	3	1	no	—
56	C₃	—	9	3	no	—
57	C₃	—	1143	6	no	—
58	C₃	—	381	2	no	—
59	C₃	—	127	3	no	—
60	C₃	H(3,𝔽₃)×C₁₂₇⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃	H(3,𝔽₃)×C₁₂₇⋊C₃
commutator, cosocle	C₃²×C₁₂₇	C₃³
Frattini	C₃²	C₃²×C₁₂₇⋊C₃
Fitting	#732×C₁₂₇	C₃
socle	C₃×C₁₂₇	C₃×H(3,𝔽₃)
hypercenter	#732	C₁₂₇⋊C₃
hypocenter	C₁₂₇	C₃×#732
LCS	G ▷ C₃²×C₁₂₇ ▷ C₃×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃ ◁ C₃² ◁ #732

Complements

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

N	H ≅ G/N	type
1. H(3,𝔽₃)×C₁₂₇⋊C₃	C₃	semidirect
2. C₃×C₉×C₁₂₇⋊C₃	C₃	semidirect
3. #23779848	C₃	semidirect
4. #23779847	C₃	semidirect
5. #732×C₁₂₇	C₃	semidirect
9. C₃²⋊(C₁₂₇⋊C₃)	C₃²	semidirect
10. C₃×#11765917	C₃²	semidirect
13. H(3,𝔽₃)×C₁₂₇	C₃²	semidirect
14. C₃×C₉×C₁₂₇	C₃²	semidirect
29. C₁₂₇⋊C₃	#732	direct (N × H)
31. C₁₂₇	C₃×#732	semidirect
36. #732	C₁₂₇⋊C₃	direct (N × H)
41. H(3,𝔽₃)	C₃×C₁₂₇⋊C₃	semidirect
45. C₃×C₉	C₃×C₁₂₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
H(3,𝔽₃)×C₁₂₇⋊C₃	3
C₃×C₉×C₁₂₇⋊C₃	3
#23779848	3
#23779847	3
#732×C₁₂₇	3
C₃×#732	127

Subgroups — #732×C127⋊C3 #44525097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #732×C₁₂₇⋊C₃ #44525097