Subgroups — #46798635

Order 33777.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26014628	C₃	1	3	yes	maximal, complemented
2	C₃×C₉×C₁₃₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
3	#26014619	C₃	1	2	yes	maximal, complemented
4	#26014613	C₃	1	3	yes	maximal, complemented
5	#26014610	C₃	1	3	yes	maximal, complemented
6	#732×C₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃²×C₁₃₉⋊C₃	C₃²	1	1	yes	characteristic
8	#16836730	—	3	6	no	—
9	#16836730	C₃²	1	6	yes	—
10	C₃×C₁₃₉⋊C₉	—	3	3	no	—
11	C₃×C₁₃₉⋊C₉	C₃²	1	1	yes	characteristic
12	C₃×C₁₃₉⋊C₉	C₃²	1	1	yes	characteristic
13	C₉×C₁₃₉⋊C₃	—	3	1	no	—
14	C₉×C₁₃₉⋊C₃	—	3	2	no	—
15	H(3,𝔽₃)×C₁₃₉	C₃²	1	3	yes	—
16	C₃×C₉×C₁₃₉	C₃²	1	1	yes	characteristic
17	C₃²×C₁₃₉	—	3	3	no	—
18	C₃²×C₁₃₉	C₃³	1	1	yes	characteristic
19	C₃×C₁₃₉⋊C₃	—	3	1	no	—
20	C₃×C₁₃₉⋊C₃	—	3	3	no	—
21	C₉×C₁₃₉	—	3	1	no	—
22	C₁₃₉⋊C₉	—	3	1	no	—
23	C₁₃₉⋊C₉	—	3	6	no	—
24	C₁₃₉⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic
25	C₁₃₉⋊C₉	H(3,𝔽₃)	1	2	yes	—
26	C₃×C₁₃₉	—	3	1	no	—
27	C₃×C₁₃₉	—	9	3	no	—
28	C₃×C₁₃₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
29	C₁₃₉⋊C₃	—	3	3	no	—
30	#6908	—	139	1	no	maximal, Sylow
31	C₁₃₉	#6908	1	1	yes	characteristic, complemented, Sylow
32	#737	—	139	3	no	—
33	C₃²×C₉	—	139	1	no	—
34	#733	—	139	2	no	—
35	#732	C₁₃₉⋊C₃	1	1	yes	characteristic, complemented
36	#731	—	139	3	no	—
37	AΣL(1,𝔽₂₇)	—	139	3	no	—
38	C₃³	—	139	1	no	—
39	3₋¹⁺²	—	139	6	no	—
40	3₋¹⁺²	—	417	6	no	—
41	H(3,𝔽₃)	C₃×C₁₃₉⋊C₃	1	3	yes	—
42	C₃×C₉	—	139	1	no	—
43	C₃×C₉	—	139	1	no	—
44	C₃×C₉	—	417	1	no	—
45	C₃×C₉	—	417	2	no	—
46	C₃×C₉	—	417	3	no	—
47	C₃×C₉	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
48	C₃²	—	3	3	no	—
49	C₃²	—	417	3	no	—
50	C₃²	—	417	1	no	—
51	C₃²	C₃²×C₁₃₉⋊C₃	1	1	yes	characteristic
52	C₉	—	3	1	no	—
53	C₉	—	139	1	no	—
54	C₉	—	139	2	no	—
55	C₉	—	417	1	no	—
56	C₉	—	417	6	no	—
57	C₃	—	3	1	no	—
58	C₃	—	9	3	no	—
59	C₃	—	417	3	no	—
60	C₃	H(3,𝔽₃)×C₁₃₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃	H(3,𝔽₃)×C₁₃₉⋊C₃
commutator, cosocle	C₃²×C₁₃₉	C₃³
Frattini	C₃²	C₃²×C₁₃₉⋊C₃
Fitting	#732×C₁₃₉	C₃
socle	C₃×C₁₃₉	C₃×H(3,𝔽₃)
hypercenter	#732	C₁₃₉⋊C₃
hypocenter	C₁₃₉	#6908
LCS	G ▷ C₃²×C₁₃₉ ▷ C₃×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₃ ◁ C₃² ◁ #732

Complements

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

N	H ≅ G/N	type
1. #26014628	C₃	semidirect
2. C₃×C₉×C₁₃₉⋊C₃	C₃	semidirect
3. #26014619	C₃	semidirect
4. #26014613	C₃	semidirect
5. #26014610	C₃	semidirect
6. #732×C₁₃₉	C₃	semidirect
31. C₁₃₉	#6908	semidirect
35. #732	C₁₃₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#26014628	3
C₃×C₉×C₁₃₉⋊C₃	3
#26014619	3
#26014613	3
#26014610	3
#732×C₁₃₉	3
#6908	139