Subgroups — #46798461

Order 33777.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²⋊(C₁₃₉⋊C₉)	C₃	1	1	yes	maximal, characteristic
2	C₃²⋊(C₁₃₉⋊C₉)	C₃	1	2	yes	maximal
3	C₃²⋊C₉×C₁₃₉	C₃	1	1	yes	maximal, characteristic
4	C₃×C₁₃₉⋊C₉	—	3	1	no	—
5	C₃×C₁₃₉⋊C₉	—	3	2	no	—
6	C₃³×C₁₃₉	C₃²	1	1	yes	characteristic
7	C₃×C₉×C₁₃₉	—	3	1	no	—
8	C₃²×C₁₃₉	—	3	1	no	—
9	C₃²×C₁₃₉	—	3	1	no	—
10	C₃²×C₁₃₉	—	3	2	no	—
11	C₃²×C₁₃₉	H(3,𝔽₃)	1	1	yes	characteristic
12	C₉×C₁₃₉	—	9	1	no	—
13	C₁₃₉⋊C₉	—	9	1	no	—
14	C₁₃₉⋊C₉	—	9	2	no	—
15	C₃×C₁₃₉	—	9	1	no	—
16	C₃×C₁₃₉	#731	1	1	yes	characteristic
17	C₃×C₁₃₉	#732	1	1	yes	characteristic
18	C₃×C₁₃₉	#733	1	2	yes	—
19	#6861	—	139	1	no	maximal, Sylow
20	C₁₃₉	#6861	1	1	yes	characteristic, complemented, Sylow
21	C₃²⋊C₉	—	139	1	no	—
22	C₃²⋊C₉	—	139	2	no	—
23	C₃²⋊C₉	C₁₃₉⋊C₃	1	1	yes	characteristic
24	C₃³	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
25	C₃×C₉	—	3	1	no	—
26	C₃×C₉	—	417	1	no	—
27	C₃×C₉	—	417	2	no	—
28	C₃²	—	3	1	no	—
29	C₃²	—	3	1	no	—
30	C₃²	—	3	2	no	—
31	C₃²	C₃²⋊(C₁₃₉⋊C₃)	1	1	yes	characteristic
32	C₉	—	9	1	no	—
33	C₉	—	1251	1	no	—
34	C₉	—	1251	2	no	—
35	C₃	—	9	1	no	—
36	C₃	#26014614	1	1	yes	characteristic
37	C₃	#26014616	1	1	yes	characteristic
38	C₃	#26014618	1	2	yes	—

	subgroup	G/H
center	C₃²	C₃²⋊(C₁₃₉⋊C₃)
commutator, prime radical, cosocle	C₃³×C₁₃₉	C₃²
Frattini	C₃³	C₃×C₁₃₉⋊C₃
Fitting	C₃²⋊C₉×C₁₃₉	C₃
socle	C₃²×C₁₃₉	H(3,𝔽₃)
hypercenter	C₃²⋊C₉	C₁₃₉⋊C₃
hypocenter	C₁₃₉	#6861
LCS	G ▷ C₃³×C₁₃₉ ▷ C₃²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²⋊C₉

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

N	H ≅ G/N	type
20. C₁₃₉	#6861	semidirect

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