Subgroups — #46798474

Order 33777.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²⋊(C₁₃₉⋊C₉)	C₃	1	3	yes	maximal
2	C₃²×C₉×C₁₃₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₃₉⋊C₉	—	3	3	no	—
4	C₃³×C₁₃₉	C₃²	1	1	yes	characteristic
5	C₃×C₉×C₁₃₉	—	3	1	no	—
6	C₃×C₉×C₁₃₉	—	3	2	no	—
7	C₃×C₉×C₁₃₉	C₉	1	3	yes	complemented
8	C₃²×C₁₃₉	—	3	3	no	—
9	C₃²×C₁₃₉	C₃×C₉	1	1	yes	characteristic
10	C₃²×C₁₃₉	H(3,𝔽₃)	1	1	yes	characteristic
11	C₃²×C₁₃₉	3₋¹⁺²	1	2	yes	—
12	C₉×C₁₃₉	—	3	3	no	—
13	C₁₃₉⋊C₉	—	9	3	no	—
14	C₃×C₁₃₉	—	3	1	no	—
15	C₃×C₁₃₉	—	3	2	no	—
16	C₃×C₁₃₉	C₃²⋊C₉	1	1	yes	characteristic
17	C₃×C₁₃₉	#731	1	3	yes	—
18	#6867	—	139	1	no	maximal, Sylow
19	C₁₃₉	#6867	1	1	yes	characteristic, complemented, Sylow
20	C₃²×C₉	C₁₃₉⋊C₃	1	1	yes	characteristic
21	C₃²⋊C₉	—	139	3	no	—
22	C₃³	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
23	C₃×C₉	—	3	1	no	—
24	C₃×C₉	—	3	2	no	—
25	C₃×C₉	—	417	3	no	—
26	C₃×C₉	C₁₃₉⋊C₉	1	3	yes	complemented
27	C₃²	—	3	3	no	—
28	C₃²	C₃×C₁₃₉⋊C₉	1	1	yes	characteristic
29	C₃²	C₃²⋊(C₁₃₉⋊C₃)	1	1	yes	characteristic
30	C₃²	#16836730	1	2	yes	—
31	C₉	—	3	3	no	—
32	C₉	—	1251	3	no	—
33	C₃	—	3	1	no	—
34	C₃	—	3	2	no	—
35	C₃	C₃²⋊(C₁₃₉⋊C₉)	1	1	yes	characteristic
36	C₃	#26014614	1	3	yes	—

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

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