Subgroups — #21419312

Order 7533.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11719689	C₃	1	3	yes	maximal, complemented
2	C₃²⋊(C₃₁⋊C₉)	C₃	1	9	yes	maximal, complemented
3	C₃⁴×C₃₁	C₃	1	1	yes	maximal, characteristic
4	C₃³×C₃₁	—	3	3	no	—
5	C₃³×C₃₁	—	3	9	no	—
6	C₃³×C₃₁	C₃²	1	1	yes	characteristic
7	C₃³×C₃₁	C₃²	1	3	yes	—
8	#11719689	—	3	9	no	—
9	C₃×C₃₁⋊C₉	C₃²	1	9	yes	complemented
10	C₃²×C₃₁	—	3	27	no	—
11	C₃²×C₃₁	—	3	3	no	—
12	C₃²×C₃₁	—	3	3	no	—
13	C₃²×C₃₁	—	3	6	no	—
14	C₃²×C₃₁	H(3,𝔽₃)	1	3	yes	—
15	C₃²×C₃₁	3₋¹⁺²	1	9	yes	complemented
16	C₃²×C₃₁	C₃³	1	1	yes	characteristic
17	C₃₁⋊C₉	—	3	9	no	—
18	#6891	—	31	1	no	maximal, Sylow
19	C₃×C₃₁	—	3	3	no	—
20	C₃×C₃₁	—	3	9	no	—
21	C₃×C₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
22	C₃×C₃₁	C₃×3₋¹⁺²	1	3	yes	—
23	C₃⁴	C₃₁⋊C₃	1	1	yes	characteristic
24	C₃×3₋¹⁺²	—	31	3	no	—
25	C₃²⋊C₉	—	31	9	no	—
26	C₃₁	#6891	1	1	yes	characteristic, complemented, Sylow
27	C₃³	—	3	9	no	—
28	C₃³	—	3	3	no	—
29	C₃³	C₃×C₃₁⋊C₃	1	3	yes	—
30	C₃³	C₃×C₃₁⋊C₃	1	1	yes	characteristic
31	3₋¹⁺²	—	93	9	no	—
32	C₃×C₉	—	31	9	no	—
33	C₃²	—	3	27	no	—
34	C₃²	—	3	3	no	—
35	C₃²	—	3	6	no	—
36	C₃²	—	3	3	no	—
37	C₃²	#11719689	1	9	yes	complemented
38	C₃²	C₃²⋊(C₃₁⋊C₃)	1	3	yes	—
39	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
40	C₉	—	93	9	no	—
41	C₃	—	3	9	no	—
42	C₃	—	3	3	no	—
43	C₃	C₃×C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
44	C₃	C₃×#11719689	1	3	yes	—

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