Subgroups — #30685270

Order 17091.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152733	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃²⋊(C₂₁₁⋊C₃)	C₃	1	1	yes	maximal, characteristic
3	C₃×C₂₁₁⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	3₋¹⁺²×C₂₁₁	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃²×C₂₁₁	C₃²	1	1	yes	characteristic
6	C₃×C₂₁₁⋊C₃	—	3	1	no	—
7	C₉×C₂₁₁	—	3	1	no	—
8	C₂₁₁⋊C₉	—	3	1	no	—
9	C₂₁₁⋊C₉	—	3	1	no	—
10	C₃×C₂₁₁	—	3	1	no	—
11	C₃×C₂₁₁	H(3,𝔽₃)	1	1	yes	characteristic
12	C₂₁₁⋊C₃	—	9	1	no	—
13	C₂₁₁	#731	1	1	yes	characteristic, complemented, Sylow
14	#731	—	211	1	no	maximal, Sylow
15	3₋¹⁺²	—	211	1	no	—
16	3₋¹⁺²	C₂₁₁⋊C₃	1	1	yes	characteristic, complemented
17	H(3,𝔽₃)	—	211	1	no	—
18	C₃×C₉	—	211	1	no	—
19	C₃²	—	633	1	no	—
20	C₃²	C₃×C₂₁₁⋊C₃	1	1	yes	characteristic
21	C₉	—	3	1	no	—
22	C₉	—	633	1	no	—
23	C₉	—	633	1	no	—
24	C₃	—	3	1	no	—
25	C₃	—	1899	1	no	—
26	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.