Subgroups — #30685285

Order 17091.

66 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	#19152732	C₃	1	3	yes	maximal, complemented
3	#19152731	C₃	1	3	yes	maximal, complemented
4	C₃²⋊(C₂₁₁⋊C₃)	C₃	1	1	yes	maximal, characteristic
5	C₃×C₂₁₁⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
6	C₉×C₂₁₁⋊C₃	C₃	1	3	yes	maximal, complemented
7	3₋¹⁺²×C₂₁₁	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₂₁₁	C₃²	1	1	yes	characteristic
9	C₃×C₂₁₁⋊C₃	C₃²	1	3	yes	—
10	C₉×C₂₁₁	C₃²	1	3	yes	—
11	C₂₁₁⋊C₉	C₃²	1	1	yes	characteristic
12	C₂₁₁⋊C₉	C₃²	1	3	yes	—
13	C₂₁₁⋊C₉	C₃²	1	1	yes	characteristic
14	C₂₁₁⋊C₉	C₃²	1	1	yes	characteristic
15	C₃×C₂₁₁	—	3	1	no	—
16	C₃×C₂₁₁	C₃³	1	1	yes	characteristic
17	C₂₁₁⋊C₃	—	3	3	no	—
18	C₂₁₁	#737	1	1	yes	characteristic, complemented, Sylow
19	#737	—	211	1	no	maximal, Sylow
20	3₋¹⁺²	—	211	1	no	—
21	3₋¹⁺²	—	211	3	no	—
22	3₋¹⁺²	—	211	3	no	—
23	3₋¹⁺²	C₂₁₁⋊C₃	1	1	yes	characteristic, complemented
24	H(3,𝔽₃)	—	211	1	no	—
25	C₃×C₉	—	211	1	no	—
26	C₃×C₉	—	211	3	no	—
27	C₃²	—	211	3	no	—
28	C₃²	C₃×C₂₁₁⋊C₃	1	1	yes	characteristic
29	C₉	—	211	1	no	—
30	C₉	—	211	1	no	—
31	C₉	—	211	1	no	—
32	C₉	—	211	3	no	—
33	C₉	C₃×C₂₁₁⋊C₃	1	3	yes	—
34	C₃	—	3	1	no	—
35	C₃	—	633	3	no	—
36	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.