Subgroups — #46798606

Order 33777.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16836729	C₃	1	4	yes	maximal
2	#26014603	C₃	1	8	yes	maximal, complemented
3	C₉²×C₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₁₃₉⋊C₃	C₃²	1	1	yes	characteristic
5	#16836729	—	3	12	no	—
6	C₃×C₁₃₉⋊C₉	C₃²	1	8	yes	—
7	C₃×C₉×C₁₃₉	C₃²	1	4	yes	—
8	C₃²×C₁₃₉	C₃³	1	1	yes	characteristic
9	C₃×C₁₃₉⋊C₃	—	3	4	no	—
10	C₉×C₁₃₉	3₋¹⁺²	1	12	yes	complemented
11	C₁₃₉⋊C₉	—	3	8	no	—
12	C₃×C₁₃₉	C₃×3₋¹⁺²	1	4	yes	—
13	C₁₃₉⋊C₃	—	9	1	no	—
14	#6900	—	139	1	no	maximal, Sylow
15	C₁₃₉	#6900	1	1	yes	characteristic, complemented, Sylow
16	C₃×3₋¹⁺²	—	139	4	no	—
17	C₉⋊C₉	—	139	8	no	—
18	C₉²	C₁₃₉⋊C₃	1	1	yes	characteristic, complemented
19	C₃³	—	139	1	no	—
20	3₋¹⁺²	—	417	12	no	—
21	C₃×C₉	—	139	8	no	—
22	C₃×C₉	C₃×C₁₃₉⋊C₃	1	4	yes	—
23	C₃²	—	417	4	no	—
24	C₃²	C₃²×C₁₃₉⋊C₃	1	1	yes	characteristic
25	C₉	—	417	8	no	—
26	C₉	#16836729	1	12	yes	complemented
27	C₃	—	1251	1	no	—
28	C₃	C₃×#16836729	1	4	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.