Subgroups — C₃×#23779848 #44525099

Order 30861.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₃²	C₃²⋊(C₁₂₇⋊C₃)
commutator, cosocle	C₃²×C₁₂₇	C₃³
Frattini	C₃²	C₃²×C₁₂₇⋊C₃
Fitting	C₃²×C₉×C₁₂₇	C₃
socle	C₃²×C₁₂₇	H(3,𝔽₃)
hypercenter	C₃²×C₉	C₁₂₇⋊C₃
hypocenter	C₁₂₇	C₃×#732
LCS	G ▷ C₃²×C₁₂₇ ▷ C₃×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₃²⋊(C₁₂₇⋊C₃)	C₃	semidirect
2. #23779848	C₃	direct (N × H)
3. C₃²×C₉×C₁₂₇	C₃	semidirect
6. C₃²⋊(C₁₂₇⋊C₃)	C₃²	semidirect
10. C₃×C₉×C₁₂₇	C₃²	semidirect
20. C₃×C₁₂₇	#732	semidirect
24. C₁₂₇	C₃×#732	semidirect
26. C₃²×C₉	C₁₂₇⋊C₃	semidirect
34. C₃×C₉	C₃×C₁₂₇⋊C₃	semidirect
45. C₃	#23779848	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₃²⋊(C₁₂₇⋊C₃)	3
#23779848	3
C₃²×C₉×C₁₂₇	3
C₃×#732	127

Subgroups — C3×#23779848 #44525099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23779848 #44525099