Subgroups — #36379817

Order 22599.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21419268	C₃	1	1	yes	maximal, characteristic, complemented
2	#21419265	C₃	1	1	yes	maximal, characteristic
3	C₉×C₃₁⋊C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#6880	C₃	1	1	yes	maximal, characteristic, complemented
5	#14578902	—	3	1	no	—
6	#14578900	—	3	1	no	—
7	C₃×C₃₁⋊C₂₇	—	3	1	no	—
8	C₃₁×#733	—	3	1	no	—
9	C₉²×C₃₁	C₃²	1	1	yes	characteristic
10	3₋¹⁺²×C₃₁	—	9	1	no	—
11	C₃×C₉×C₃₁	—	3	1	no	—
12	C₃×C₉×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃²⋊(C₃₁⋊C₃)	—	9	1	no	—
14	#11719689	—	9	1	no	—
15	C₃₁⋊C₂₇	—	3	3	no	—
16	#10624537	—	31	1	no	maximal, Sylow
17	C₃²×C₃₁	#732	1	1	yes	characteristic
18	C₃×C₃₁⋊C₃	—	27	1	no	—
19	C₉×C₃₁	—	3	3	no	—
20	C₉×C₃₁	—	3	1	no	—
21	C₉×C₃₁	—	27	1	no	—
22	C₃₁⋊C₉	—	27	1	no	—
23	#6880	—	31	1	no	—
24	#6880	C₃₁⋊C₃	1	1	yes	characteristic, complemented
25	#6879	—	31	1	no	—
26	C₉×C₂₇	—	31	1	no	—
27	C₃×C₃₁	—	3	1	no	—
28	C₃×C₃₁	#6879	1	1	yes	characteristic
29	C₃₁⋊C₃	—	81	1	no	—
30	#733	—	3	1	no	—
31	#733	—	93	1	no	—
32	#732	—	93	1	no	—
33	C₃×C₂₇	—	93	1	no	—
34	C₉²	C₃×C₃₁⋊C₃	1	1	yes	characteristic
35	C₃₁	#10624537	1	1	yes	characteristic, complemented, Sylow
36	3₋¹⁺²	—	9	1	no	—
37	3₋¹⁺²	—	279	1	no	—
38	H(3,𝔽₃)	—	279	1	no	—
39	C₃×C₉	—	3	1	no	—
40	C₃×C₉	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
41	C₂₇	—	93	3	no	—
42	C₃²	—	837	1	no	—
43	C₃²	#14578899	1	1	yes	characteristic
44	C₉	—	3	3	no	—
45	C₉	—	3	1	no	—
46	C₉	—	27	1	no	—
47	C₉	—	837	1	no	—
48	C₃	—	3	1	no	—
49	C₃	—	2511	1	no	—
50	C₃	#21419264	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#21419264
commutator, cosocle	C₉²×C₃₁	C₃²
Frattini	C₉²	C₃×C₃₁⋊C₃
Fitting	C₃₁×#6880	C₃
socle	C₃×C₃₁	#6879
prime radical	#21419265	C₃
hypercenter	#6880	C₃₁⋊C₃
hypocenter	C₃₁	#10624537
LCS	G ▷ C₉²×C₃₁ ▷ C₃×C₉×C₃₁ ▷ C₃²×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃×C₉ ◁ C₉² ◁ #6880

Complements

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

N	H ≅ G/N	type
1. #21419268	C₃	semidirect
3. C₉×C₃₁⋊C₂₇	C₃	semidirect
4. C₃₁×#6880	C₃	semidirect
24. #6880	C₃₁⋊C₃	semidirect
35. C₃₁	#10624537	semidirect

Maximal subgroups

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

subgroup	index
#21419268	3
#21419265	3
C₉×C₃₁⋊C₂₇	3
C₃₁×#6880	3
#10624537	31