Subgroups — #30685269

Order 17091.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152733	C₃	1	2	yes	maximal, complemented
2	C₃²⋊(C₂₁₁⋊C₃)	C₃	1	1	yes	maximal, characteristic
3	C₃×C₉×C₂₁₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₂₁₁	C₃²	1	1	yes	characteristic
5	C₃×C₂₁₁⋊C₃	—	3	1	no	—
6	C₉×C₂₁₁	—	3	1	no	—
7	C₂₁₁⋊C₉	—	3	2	no	—
8	C₃×C₂₁₁	—	3	1	no	—
9	C₃×C₂₁₁	H(3,𝔽₃)	1	1	yes	characteristic
10	C₂₁₁⋊C₃	—	9	1	no	—
11	C₂₁₁	#731	1	1	yes	characteristic, complemented, Sylow
12	#731	—	211	1	no	maximal, Sylow
13	3₋¹⁺²	—	211	2	no	—
14	H(3,𝔽₃)	—	211	1	no	—
15	C₃×C₉	C₂₁₁⋊C₃	1	1	yes	characteristic, complemented
16	C₃²	—	633	1	no	—
17	C₃²	C₃×C₂₁₁⋊C₃	1	1	yes	characteristic
18	C₉	—	3	1	no	—
19	C₉	—	633	2	no	—
20	C₃	—	3	1	no	—
21	C₃	—	1899	1	no	—
22	C₃	C₃²⋊(C₂₁₁⋊C₃)	1	1	yes	characteristic

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.