Subgroups — #36379813

Order 22599.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21419268	C₃	1	2	yes	maximal
2	C₉×C₃₁⋊C₂₇	C₃	1	1	yes	maximal, characteristic
3	C₃₁×#6880	C₃	1	1	yes	maximal, characteristic
4	#14578902	—	3	2	no	—
5	C₃×C₃₁⋊C₂₇	—	3	1	no	—
6	C₃₁×#733	—	3	1	no	—
7	C₉²×C₃₁	C₃²	1	1	yes	characteristic
8	3₋¹⁺²×C₃₁	—	9	1	no	—
9	C₃×C₉×C₃₁	—	3	1	no	—
10	C₃×C₉×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
11	#11719689	—	9	2	no	—
12	C₃₁⋊C₂₇	—	3	3	no	—
13	#10624536	—	31	1	no	maximal, Sylow
14	C₃²×C₃₁	#732	1	1	yes	characteristic
15	C₉×C₃₁	—	3	3	no	—
16	C₉×C₃₁	—	3	1	no	—
17	C₉×C₃₁	—	27	1	no	—
18	C₃₁⋊C₉	—	27	2	no	—
19	#6880	—	31	2	no	—
20	#6880	C₃₁⋊C₃	1	1	yes	characteristic
21	C₉×C₂₇	—	31	1	no	—
22	C₃×C₃₁	—	3	1	no	—
23	C₃×C₃₁	#6879	1	1	yes	characteristic
24	#733	—	3	1	no	—
25	#733	—	93	2	no	—
26	C₃×C₂₇	—	93	1	no	—
27	C₉²	C₃×C₃₁⋊C₃	1	1	yes	characteristic
28	C₃₁	#10624536	1	1	yes	characteristic, complemented, Sylow
29	3₋¹⁺²	—	9	1	no	—
30	3₋¹⁺²	—	279	2	no	—
31	C₃×C₉	—	3	1	no	—
32	C₃×C₉	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
33	C₂₇	—	93	3	no	—
34	C₃²	#14578899	1	1	yes	characteristic
35	C₉	—	3	3	no	—
36	C₉	—	3	1	no	—
37	C₉	—	27	1	no	—
38	C₉	—	837	2	no	—
39	C₃	—	3	1	no	—
40	C₃	#21419264	1	1	yes	characteristic

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

N	H ≅ G/N	type
28. C₃₁	#10624536	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.