Subgroups — #36379589

Order 22599.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14578902	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×#14578900	C₃	1	1	yes	maximal, characteristic
3	#21419228	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#6867	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃×#11719689	—	3	1	no	—
6	C₃×C₃²⋊(C₃₁⋊C₃)	—	3	1	no	—
7	#14578902	—	3	3	no	—
8	#14578900	—	3	3	no	—
9	C₃²⋊(C₃₁⋊C₉)	—	3	1	no	—
10	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
11	C₃₁×C₃²⋊C₉	—	3	1	no	—
12	C₃³×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃²×C₃₁⋊C₃	—	9	1	no	—
14	C₃×C₉×C₃₁	—	3	1	no	—
15	C₃×C₉×C₃₁	—	3	1	no	—
16	C₃×C₉×C₃₁	—	3	1	no	—
17	C₃×C₉×C₃₁	—	3	1	no	—
18	C₃×C₉×C₃₁	—	9	1	no	—
19	C₃²⋊(C₃₁⋊C₃)	—	3	3	no	—
20	C₃²⋊(C₃₁⋊C₃)	—	9	1	no	—
21	C₃²⋊(C₃₁⋊C₃)	—	9	1	no	—
22	#11719689	—	3	3	no	—
23	#11719689	—	9	1	no	—
24	#11719689	—	9	1	no	—
25	C₃×C₃₁⋊C₉	—	9	1	no	—
26	C₃×C₃₁⋊C₉	—	9	1	no	—
27	#10624478	—	31	1	no	maximal, Sylow
28	C₃²×C₃₁	—	9	1	no	—
29	C₃²×C₃₁	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
30	C₃²×C₃₁	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
31	C₃²×C₃₁	#732	1	1	yes	characteristic
32	C₃²×C₃₁	#732	1	1	yes	characteristic
33	C₃×C₃₁⋊C₃	—	9	3	no	—
34	C₃×C₃₁⋊C₃	—	27	3	no	—
35	C₉×C₃₁	—	9	1	no	—
36	C₉×C₃₁	—	27	1	no	—
37	C₃₁⋊C₉	—	9	3	no	—
38	C₃₁⋊C₉	—	27	1	no	—
39	C₃×#733	—	31	1	no	—
40	C₃×#732	—	31	1	no	—
41	#6867	—	31	1	no	—
42	#6867	C₃₁⋊C₃	1	1	yes	characteristic, complemented
43	C₃×C₃₁	—	3	1	no	—
44	C₃×C₃₁	—	3	1	no	—
45	C₃×C₃₁	—	3	1	no	—
46	C₃×C₃₁	—	3	1	no	—
47	C₃×C₃₁	#6856	1	1	yes	characteristic
48	C₃₁⋊C₃	—	27	3	no	—
49	C₃×3₋¹⁺²	—	93	1	no	—
50	C₃×H(3,𝔽₃)	—	93	1	no	—
51	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
52	#733	—	93	3	no	—
53	#732	—	93	3	no	—
54	C₃²⋊C₉	—	3	1	no	—
55	C₃²⋊C₉	—	93	1	no	—
56	C₃₁	#10624478	1	1	yes	characteristic, complemented, Sylow
57	C₃³	—	279	1	no	—
58	C₃³	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
59	3₋¹⁺²	—	279	1	no	—
60	3₋¹⁺²	—	279	1	no	—
61	3₋¹⁺²	—	93	3	no	—
62	H(3,𝔽₃)	—	279	1	no	—
63	H(3,𝔽₃)	—	279	1	no	—
64	H(3,𝔽₃)	—	93	3	no	—
65	C₃×C₉	—	3	1	no	—
66	C₃×C₉	—	3	1	no	—
67	C₃×C₉	—	3	1	no	—
68	C₃×C₉	—	3	1	no	—
69	C₃×C₉	—	9	1	no	—
70	C₃×C₉	—	279	1	no	—
71	C₃×C₉	—	279	1	no	—
72	C₃²	—	9	1	no	—
73	C₃²	—	279	3	no	—
74	C₃²	—	837	3	no	—
75	C₃²	#14578895	1	1	yes	characteristic
76	C₃²	#14578895	1	1	yes	characteristic
77	C₃²	#14578899	1	1	yes	characteristic
78	C₃²	#14578900	1	1	yes	characteristic
79	C₉	—	9	1	no	—
80	C₉	—	279	3	no	—
81	C₉	—	27	1	no	—
82	C₉	—	837	1	no	—
83	C₃	—	3	1	no	—
84	C₃	—	3	1	no	—
85	C₃	—	3	1	no	—
86	C₃	—	3	1	no	—
87	C₃	—	837	3	no	—
88	C₃	#21419201	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#21419201
commutator, cosocle	C₃²×C₉×C₃₁	C₃²
Frattini	C₃²×C₉	C₃×C₃₁⋊C₃
Fitting	C₃₁×#6867	C₃
socle	C₃×C₃₁	#6856
prime radical	C₃×#14578900	C₃
hypercenter	#6867	C₃₁⋊C₃
hypocenter	C₃₁	#10624478
LCS	G ▷ C₃²×C₉×C₃₁ ▷ C₃³×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ #6867

Complements

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

N	H ≅ G/N	type
1. C₃×#14578902	C₃	semidirect
3. #21419228	C₃	semidirect
4. C₃₁×#6867	C₃	semidirect
42. #6867	C₃₁⋊C₃	semidirect
56. C₃₁	#10624478	semidirect

Maximal subgroups

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

subgroup	index
C₃×#14578902	3
C₃×#14578900	3
#21419228	3
C₃₁×#6867	3
#10624478	31