Subgroups — #44524921

Order 30861.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²⋊#11765917	C₃	1	1	yes	maximal, characteristic
2	C₃²⋊#11765917	C₃	1	2	yes	maximal
3	C₃×3₋¹⁺²×C₁₂₇	C₃	1	1	yes	maximal, characteristic
4	C₃×#11765917	—	3	1	no	—
5	C₃×#11765917	—	3	2	no	—
6	C₃³×C₁₂₇	C₃²	1	1	yes	characteristic
7	3₋¹⁺²×C₁₂₇	—	3	3	no	—
8	C₃×C₉×C₁₂₇	—	3	1	no	—
9	C₃²×C₁₂₇	—	3	1	no	—
10	C₃²×C₁₂₇	—	3	2	no	—
11	C₃²×C₁₂₇	—	3	1	no	—
12	C₃²×C₁₂₇	H(3,𝔽₃)	1	1	yes	characteristic
13	C₉×C₁₂₇	—	3	3	no	—
14	#11765917	—	9	1	no	—
15	#11765917	—	9	2	no	—
16	C₃×C₁₂₇	—	9	1	no	—
17	C₃×C₁₂₇	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
18	C₃×C₁₂₇	#731	1	2	yes	—
19	C₃×C₁₂₇	#733	1	1	yes	characteristic
20	#6858	—	127	1	no	maximal, Sylow
21	C₁₂₇	#6858	1	1	yes	characteristic, complemented, Sylow
22	C₃×3₋¹⁺²	C₁₂₇⋊C₃	1	1	yes	characteristic
23	C₃²⋊C₉	—	127	1	no	—
24	C₃²⋊C₉	—	127	2	no	—
25	C₃³	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
26	3₋¹⁺²	—	3	3	no	—
27	C₃×C₉	—	3	1	no	—
28	C₃×C₉	—	381	1	no	—
29	C₃×C₉	—	381	2	no	—
30	C₃²	—	3	1	no	—
31	C₃²	—	3	2	no	—
32	C₃²	—	3	1	no	—
33	C₃²	C₃²⋊(C₁₂₇⋊C₃)	1	1	yes	characteristic
34	C₉	—	3	3	no	—
35	C₉	—	1143	1	no	—
36	C₉	—	1143	2	no	—
37	C₃	—	9	1	no	—
38	C₃	#23779842	1	1	yes	characteristic
39	C₃	#23779846	1	2	yes	—
40	C₃	#23779849	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊(C₁₂₇⋊C₃)
commutator, prime radical, cosocle	C₃³×C₁₂₇	C₃²
Frattini	C₃³	C₃×C₁₂₇⋊C₃
Fitting	C₃×3₋¹⁺²×C₁₂₇	C₃
socle	C₃²×C₁₂₇	H(3,𝔽₃)
hypercenter	C₃×3₋¹⁺²	C₁₂₇⋊C₃
hypocenter	C₁₂₇	#6858
LCS	G ▷ C₃³×C₁₂₇ ▷ C₃²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×3₋¹⁺²

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

N	H ≅ G/N	type
21. C₁₂₇	#6858	semidirect

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