Subgroups — #36379814

Order 22599.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21419268	C₃	1	3	yes	maximal
2	C₉×C₂₇×C₃₁	C₃	1	1	yes	maximal, characteristic
3	#14578902	—	3	3	no	—
4	C₃×C₂₇×C₃₁	—	3	1	no	—
5	C₉²×C₃₁	C₃²	1	1	yes	characteristic
6	C₃×C₉×C₃₁	—	3	1	no	—
7	C₃×C₉×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
8	#11719689	—	9	3	no	—
9	C₂₇×C₃₁	—	3	3	no	—
10	#10624536	—	31	1	no	maximal, Sylow
11	C₃²×C₃₁	#732	1	1	yes	characteristic
12	C₉×C₃₁	—	3	3	no	—
13	C₉×C₃₁	—	3	1	no	—
14	C₃₁⋊C₉	—	27	3	no	—
15	#6880	—	31	3	no	—
16	C₉×C₂₇	C₃₁⋊C₃	1	1	yes	characteristic
17	C₃×C₃₁	—	3	1	no	—
18	C₃×C₃₁	#6879	1	1	yes	characteristic
19	#733	—	93	3	no	—
20	C₃×C₂₇	—	3	1	no	—
21	C₉²	C₃×C₃₁⋊C₃	1	1	yes	characteristic
22	C₃₁	#10624536	1	1	yes	characteristic, complemented, Sylow
23	3₋¹⁺²	—	279	3	no	—
24	C₃×C₉	—	3	1	no	—
25	C₃×C₉	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
26	C₂₇	—	3	3	no	—
27	C₃²	#14578900	1	1	yes	characteristic
28	C₉	—	3	3	no	—
29	C₉	—	3	1	no	—
30	C₉	—	837	3	no	—
31	C₃	—	3	1	no	—
32	C₃	#21419265	1	1	yes	characteristic

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

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

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