Subgroups — #44525125

Order 30861.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812184	C₃	1	2	yes	maximal
2	C₃×#16812184	C₃	1	1	yes	maximal, characteristic
3	#23779849	C₃	1	9	yes	maximal, complemented
4	C₃×3₋¹⁺²×C₁₂₇	C₃	1	1	yes	maximal, characteristic
5	#16812184	—	3	2	no	—
6	#16812184	—	3	2	no	—
7	#16812184	—	3	1	no	—
8	#16812184	—	3	2	no	—
9	#16812184	C₃²	1	6	yes	—
10	C₃×#11765917	—	3	2	no	—
11	C₃×#11765917	C₃²	1	3	yes	—
12	C₃³×C₁₂₇	C₃²	1	1	yes	characteristic
13	3₋¹⁺²×C₁₂₇	—	3	2	no	—
14	3₋¹⁺²×C₁₂₇	C₃²	1	3	yes	—
15	C₃×C₉×C₁₂₇	—	3	1	no	—
16	C₃²×C₁₂₇	—	9	1	no	—
17	C₃²×C₁₂₇	H(3,𝔽₃)	1	1	yes	characteristic
18	C₃²×C₁₂₇	H(3,𝔽₃)	1	2	yes	—
19	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
20	C₉×C₁₂₇	—	3	3	no	—
21	#11765917	—	3	6	no	—
22	#11765917	—	3	3	no	—
23	C₃×C₁₂₇	—	3	1	no	—
24	C₃×C₁₂₇	—	3	2	no	—
25	C₃×C₁₂₇	—	3	1	no	—
26	C₃×C₁₂₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
27	#6912	—	127	1	no	maximal, Sylow
28	C₁₂₇	#6912	1	1	yes	characteristic, complemented, Sylow
29	C₃×3₋¹⁺²	—	127	2	no	—
30	C₃×3₋¹⁺²	—	127	1	no	—
31	C₃×3₋¹⁺²	C₁₂₇⋊C₃	1	1	yes	characteristic
32	#733	—	127	9	no	—
33	C₃³	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
34	3₋¹⁺²	—	3	2	no	—
35	3₋¹⁺²	—	381	2	no	—
36	3₋¹⁺²	—	381	2	no	—
37	3₋¹⁺²	—	381	1	no	—
38	3₋¹⁺²	—	381	2	no	—
39	3₋¹⁺²	—	127	6	no	—
40	3₋¹⁺²	C₃×C₁₂₇⋊C₃	1	3	yes	—
41	C₃×C₉	—	3	1	no	—
42	C₃×C₉	—	381	2	no	—
43	C₃×C₉	—	127	3	no	—
44	C₃²	—	9	1	no	—
45	C₃²	C₃²⋊(C₁₂₇⋊C₃)	1	1	yes	characteristic
46	C₃²	C₃²⋊(C₁₂₇⋊C₃)	1	2	yes	—
47	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
48	C₉	—	3	3	no	—
49	C₉	—	381	6	no	—
50	C₉	—	381	3	no	—
51	C₃	—	3	1	no	—
52	C₃	—	3	2	no	—
53	C₃	—	3	1	no	—
54	C₃	C₃×C₃²⋊(C₁₂₇⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×C₃²⋊(C₁₂₇⋊C₃)
commutator, cosocle	C₃²×C₁₂₇	C₃³
Frattini	C₃²	C₃²×C₁₂₇⋊C₃
Fitting	C₃×3₋¹⁺²×C₁₂₇	C₃
socle	C₃×C₁₂₇	C₃×H(3,𝔽₃)
prime radical	C₃³×C₁₂₇	C₃²
hypercenter	C₃×3₋¹⁺²	C₁₂₇⋊C₃
hypocenter	C₁₂₇	#6912
LCS	G ▷ C₃²×C₁₂₇ ▷ C₃×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
3. #23779849	C₃	semidirect
28. C₁₂₇	#6912	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16812184	3
#23779849	3
C₃×3₋¹⁺²×C₁₂₇	3
#6912	127