Subgroups — #44525131

Order 30861.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779859	C₃	1	3	yes	maximal, complemented
2	C₃×#16812183	C₃	1	1	yes	maximal, characteristic, complemented
3	#23779850	C₃	1	2	yes	maximal, complemented
4	#23779844	C₃	1	3	yes	maximal, complemented
5	#23779841	C₃	1	3	yes	maximal, complemented
6	#732×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃²×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
8	#16812184	—	3	6	no	—
9	#16812184	C₃²	1	6	yes	—
10	#16812183	—	3	3	no	—
11	C₃×#11765917	—	3	3	no	—
12	C₃×#11765917	C₃²	1	1	yes	characteristic
13	C₃×#11765917	C₃²	1	1	yes	characteristic
14	H(3,𝔽₃)×C₁₂₇	C₃²	1	3	yes	—
15	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
16	C₃²×C₁₂₇	—	3	3	no	—
17	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
18	C₃×C₁₂₇⋊C₃	—	3	1	no	—
19	C₃×C₁₂₇⋊C₃	—	9	1	no	—
20	C₉×C₁₂₇	—	3	1	no	—
21	#11765917	—	3	6	no	—
22	#11765917	—	3	1	no	—
23	#11765917	H(3,𝔽₃)	1	3	yes	—
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	—	9	1	no	—
28	#6913	—	127	1	no	maximal, Sylow
29	C₁₂₇	#6913	1	1	yes	characteristic, complemented, Sylow
30	#737	—	127	3	no	—
31	C₃×3₋¹⁺²	—	127	1	no	—
32	#733	—	127	2	no	—
33	#732	C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
34	#731	—	127	3	no	—
35	AΣL(1,𝔽₂₇)	—	127	3	no	—
36	C₃³	—	127	1	no	—
37	3₋¹⁺²	—	381	3	no	—
38	3₋¹⁺²	—	381	6	no	—
39	3₋¹⁺²	—	127	6	no	—
40	H(3,𝔽₃)	C₃×C₁₂₇⋊C₃	1	3	yes	—
41	C₃×C₉	—	381	3	no	—
42	C₃×C₉	—	127	1	no	—
43	C₃×C₉	—	127	1	no	—
44	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
45	C₃²	—	3	3	no	—
46	C₃²	—	1143	1	no	—
47	C₃²	—	381	1	no	—
48	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
49	C₉	—	3	1	no	—
50	C₉	—	381	6	no	—
51	C₉	—	381	1	no	—
52	C₉	—	127	3	no	—
53	C₃	—	3	1	no	—
54	C₃	—	9	3	no	—
55	C₃	—	1143	1	no	—
56	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	#6913
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. #23779859	C₃	semidirect
2. C₃×#16812183	C₃	semidirect
3. #23779850	C₃	semidirect
4. #23779844	C₃	semidirect
5. #23779841	C₃	semidirect
6. #732×C₁₂₇	C₃	semidirect
29. C₁₂₇	#6913	semidirect
33. #732	C₁₂₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#23779859	3
C₃×#16812183	3
#23779850	3
#23779844	3
#23779841	3
#732×C₁₂₇	3
#6913	127