Subgroups — #46798488

Order 33777.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26014629	C₃	1	1	yes	maximal, characteristic
2	#26014609	C₃	1	2	yes	maximal, complemented
3	C₃×C₂₇×C₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented
4	#16836730	C₉	1	2	yes	—
5	#16836729	—	3	1	no	—
6	#16836728	—	3	1	no	—
7	C₃²⋊(C₁₃₉⋊C₃)	C₉	1	1	yes	characteristic
8	C₉×C₁₃₉⋊C₃	—	3	1	no	—
9	C₁₃₉⋊C₂₇	—	3	2	no	—
10	C₃×C₉×C₁₃₉	C₃²	1	1	yes	characteristic
11	C₂₇×C₁₃₉	—	3	1	no	—
12	C₃²×C₁₃₉	C₃×C₉	1	1	yes	characteristic
13	C₃×C₁₃₉⋊C₃	—	3	1	no	—
14	C₉×C₁₃₉	H(3,𝔽₃)	1	1	yes	characteristic
15	C₉×C₁₃₉	3₋¹⁺²	1	1	yes	characteristic
16	C₉×C₁₃₉	3₋¹⁺²	1	1	yes	characteristic
17	C₁₃₉⋊C₉	—	3	2	no	—
18	C₃×C₁₃₉	—	3	1	no	—
19	C₃×C₁₃₉	C₃²⋊C₉	1	1	yes	characteristic
20	C₁₃₉⋊C₃	—	9	1	no	—
21	#6872	—	139	1	no	maximal, Sylow
22	C₁₃₉	#6872	1	1	yes	characteristic, complemented, Sylow
23	#737	—	139	1	no	—
24	C₂₇⋊C₃	—	139	2	no	—
25	C₃×C₂₇	C₁₃₉⋊C₃	1	1	yes	characteristic, complemented
26	3₋¹⁺²	—	139	2	no	—
27	3₋¹⁺²	—	417	1	no	—
28	3₋¹⁺²	—	417	1	no	—
29	H(3,𝔽₃)	—	139	1	no	—
30	C₃×C₉	—	417	1	no	—
31	C₃×C₉	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
32	C₂₇	—	3	1	no	—
33	C₂₇	—	417	2	no	—
34	C₃²	—	417	1	no	—
35	C₃²	C₉×C₁₃₉⋊C₃	1	1	yes	characteristic
36	C₉	—	417	2	no	—
37	C₉	C₃²⋊(C₁₃₉⋊C₃)	1	1	yes	characteristic
38	C₉	#16836728	1	1	yes	characteristic
39	C₉	#16836729	1	1	yes	characteristic
40	C₃	—	3	1	no	—
41	C₃	—	1251	1	no	—
42	C₃	(C₃×C₁₃₉⋊C₃)⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₃²⋊(C₁₃₉⋊C₃)
commutator	C₃²×C₁₃₉	C₃×C₉
Frattini	C₃×C₉	C₃×C₁₃₉⋊C₃
Fitting	C₃×C₂₇×C₁₃₉	C₃
socle	C₃×C₁₃₉	C₃²⋊C₉
prime radical	C₃²⋊(C₁₃₉⋊C₃)	C₉
cosocle	C₃×C₉×C₁₃₉	C₃²
hypercenter	C₃×C₂₇	C₁₃₉⋊C₃
hypocenter	C₁₃₉	#6872
LCS	G ▷ C₃²×C₁₃₉ ▷ C₃×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₉ ◁ C₃×C₉ ◁ C₃×C₂₇

Complements

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

N	H ≅ G/N	type
2. #26014609	C₃	semidirect
3. C₃×C₂₇×C₁₃₉	C₃	semidirect
22. C₁₃₉	#6872	semidirect
25. C₃×C₂₇	C₁₃₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#26014629	3
#26014609	3
C₃×C₂₇×C₁₃₉	3
#6872	139