Subgroups — C₃×#23779850 #44525102

Order 30861.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812184	C₃	1	3	yes	maximal
2	#23779850	C₃	1	9	yes	maximal, direct product factor
3	C₃²×C₉×C₁₂₇	C₃	1	1	yes	maximal, characteristic
4	#16812184	—	3	6	no	—
5	#16812184	C₃²	1	9	yes	—
6	C₃×#11765917	—	3	3	no	—
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	—
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	C₉×C₁₂₇	—	3	3	no	—
16	#11765917	—	3	9	no	—
17	C₃×C₁₂₇	—	3	2	no	—
18	C₃×C₁₂₇	—	3	1	no	—
19	C₃×C₁₂₇	#733	1	3	yes	complemented
20	C₃×C₁₂₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
21	C₃×#733	—	127	1	no	maximal, Sylow
22	C₁₂₇	C₃×#733	1	1	yes	characteristic, complemented, Sylow
23	C₃×3₋¹⁺²	—	127	3	no	—
24	C₃²×C₉	C₁₂₇⋊C₃	1	1	yes	characteristic
25	#733	—	127	9	no	—
26	C₃³	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
27	3₋¹⁺²	—	381	6	no	—
28	3₋¹⁺²	—	127	9	no	—
29	C₃×C₉	—	3	2	no	—
30	C₃×C₉	—	3	1	no	—
31	C₃×C₉	—	381	3	no	—
32	C₃×C₉	C₃×C₁₂₇⋊C₃	1	3	yes	—
33	C₃²	—	3	3	no	—
34	C₃²	C₃²⋊(C₁₂₇⋊C₃)	1	2	yes	—
35	C₃²	C₃²⋊(C₁₂₇⋊C₃)	1	1	yes	characteristic
36	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
37	C₉	—	3	3	no	—
38	C₉	—	381	9	no	—
39	C₃	—	3	2	no	—
40	C₃	—	3	1	no	—
41	C₃	#23779850	1	3	yes	direct product factor
42	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)
prime radical	C₃³×C₁₂₇	C₃²
hypercenter	C₃²×C₉	C₁₂₇⋊C₃
hypocenter	C₁₂₇	C₃×#733
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
2. #23779850	C₃	direct (N × H)
19. C₃×C₁₂₇	#733	semidirect
22. C₁₂₇	C₃×#733	semidirect
41. C₃	#23779850	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×#16812184	3
#23779850	3
C₃²×C₉×C₁₂₇	3
C₃×#733	127

Subgroups — C3×#23779850 #44525102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23779850 #44525102