Subgroups — #36379812

Order 22599.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21419265	C₃	1	3	yes	maximal, complemented
2	C₉×C₂₇×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
3	#14578900	—	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	C₃²⋊(C₃₁⋊C₃)	—	9	3	no	—
9	C₂₇×C₃₁	—	3	3	no	—
10	#10624535	—	31	1	no	maximal, Sylow
11	C₃²×C₃₁	#732	1	1	yes	characteristic
12	C₃×C₃₁⋊C₃	—	27	3	no	—
13	C₉×C₃₁	—	3	3	no	—
14	C₉×C₃₁	—	3	1	no	—
15	#6879	—	31	3	no	—
16	C₉×C₂₇	C₃₁⋊C₃	1	1	yes	characteristic, complemented
17	C₃×C₃₁	—	3	1	no	—
18	C₃×C₃₁	#6879	1	1	yes	characteristic
19	C₃₁⋊C₃	—	81	3	no	—
20	#732	—	93	3	no	—
21	C₃×C₂₇	—	3	1	no	—
22	C₉²	C₃×C₃₁⋊C₃	1	1	yes	characteristic
23	C₃₁	#10624535	1	1	yes	characteristic, complemented, Sylow
24	H(3,𝔽₃)	—	279	3	no	—
25	C₃×C₉	—	3	1	no	—
26	C₃×C₉	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
27	C₂₇	—	3	3	no	—
28	C₃²	—	837	3	no	—
29	C₃²	#14578900	1	1	yes	characteristic
30	C₉	—	3	3	no	—
31	C₉	—	3	1	no	—
32	C₃	—	3	1	no	—
33	C₃	—	2511	3	no	—
34	C₃	#21419265	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.