Subgroups — #36382140

Order 22599.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14578902	C₃	1	2	yes	maximal
2	#21419296	C₃	1	1	yes	maximal, characteristic
3	#21419274	C₃	1	9	yes	maximal, complemented
4	C₃×C₃₁×#733	C₃	1	1	yes	maximal, characteristic
5	C₃×#11719689	—	3	2	no	—
6	#14578902	—	3	2	no	—
7	#14578902	—	3	2	no	—
8	#14578902	C₃²	1	6	yes	—
9	#14578887	C₃²	1	3	yes	—
10	#14578886	—	3	1	no	—
11	C₃²⋊(C₃₁⋊C₉)	—	3	1	no	—
12	C₉×C₃₁⋊C₉	—	3	1	no	—
13	C₃×3₋¹⁺²×C₃₁	—	3	1	no	—
14	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
15	C₃₁×#733	—	3	1	no	—
16	C₃₁×#733	—	3	1	no	—
17	C₃₁×#733	C₃²	1	3	yes	—
18	C₃³×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
19	3₋¹⁺²×C₃₁	—	3	3	no	—
20	3₋¹⁺²×C₃₁	—	9	2	no	—
21	C₃×C₉×C₃₁	—	3	2	no	—
22	C₃×C₉×C₃₁	—	3	1	no	—
23	C₃×C₉×C₃₁	—	9	1	no	—
24	C₃×C₉×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
25	C₃×C₉×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
26	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
27	#11719689	—	3	6	no	—
28	#11719689	—	9	2	no	—
29	#11719689	—	9	2	no	—
30	C₃×C₃₁⋊C₉	—	3	3	no	—
31	C₃×C₃₁⋊C₉	—	9	2	no	—
32	#10624847	—	31	1	no	maximal, Sylow
33	C₃²×C₃₁	—	9	1	no	—
34	C₃²×C₃₁	#732	1	2	yes	—
35	C₃²×C₃₁	#732	1	1	yes	characteristic
36	C₃²×C₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
37	C₉×C₃₁	—	3	1	no	—
38	C₉×C₃₁	—	3	1	no	—
39	C₉×C₃₁	—	3	1	no	—
40	C₉×C₃₁	—	9	3	no	—
41	C₃₁⋊C₉	—	9	3	no	—
42	C₃₁⋊C₉	—	9	6	no	—
43	C₃×#733	—	31	2	no	—
44	C₃×#733	C₃₁⋊C₃	1	1	yes	characteristic
45	#6887	—	31	1	no	—
46	#6882	—	31	9	no	—
47	C₃×C₃₁	—	3	1	no	—
48	C₃×C₃₁	—	3	2	no	—
49	C₃×C₃₁	—	3	1	no	—
50	C₃×C₃₁	C₃×#732	1	1	yes	characteristic
51	C₃×3₋¹⁺²	—	3	1	no	—
52	C₃×3₋¹⁺²	—	93	2	no	—
53	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
54	#733	—	3	1	no	—
55	#733	—	3	1	no	—
56	#733	—	31	6	no	—
57	#733	—	93	2	no	—
58	#733	—	93	2	no	—
59	#733	C₃×C₃₁⋊C₃	1	3	yes	—
60	C₉⋊C₉	—	31	3	no	—
61	C₉⋊C₉	—	93	1	no	—
62	C₃²⋊C₉	—	93	1	no	—
63	C₉²	—	93	1	no	—
64	C₃₁	#10624847	1	1	yes	characteristic, complemented, Sylow
65	C₃³	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
66	3₋¹⁺²	—	3	3	no	—
67	3₋¹⁺²	—	9	2	no	—
68	3₋¹⁺²	—	279	2	no	—
69	3₋¹⁺²	—	279	2	no	—
70	3₋¹⁺²	—	93	6	no	—
71	C₃×C₉	—	3	1	no	—
72	C₃×C₉	—	3	2	no	—
73	C₃×C₉	—	9	1	no	—
74	C₃×C₉	—	279	2	no	—
75	C₃×C₉	—	93	3	no	—
76	C₃×C₉	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
77	C₃×C₉	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
78	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
79	C₃²	—	9	1	no	—
80	C₃²	#14578899	1	1	yes	characteristic
81	C₃²	#14578899	1	2	yes	—
82	C₃²	C₃×C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
83	C₉	—	3	1	no	—
84	C₉	—	3	1	no	—
85	C₉	—	3	1	no	—
86	C₉	—	9	3	no	—
87	C₉	—	279	3	no	—
88	C₉	—	279	6	no	—
89	C₃	—	3	1	no	—
90	C₃	—	3	1	no	—
91	C₃	—	3	2	no	—
92	C₃	C₃×#14578899	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×#14578899
commutator, cosocle	C₃×C₉×C₃₁	C₃³
Frattini	C₃×C₉	C₃²×C₃₁⋊C₃
Fitting	C₃×C₃₁×#733	C₃
socle	C₃×C₃₁	C₃×#732
prime radical	C₃³×C₃₁	H(3,𝔽₃)
hypercenter	C₃×#733	C₃₁⋊C₃
hypocenter	C₃₁	#10624847
LCS	G ▷ C₃×C₉×C₃₁ ▷ C₃²×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ C₃×#733

Complements

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

N	H ≅ G/N	type
3. #21419274	C₃	semidirect
64. C₃₁	#10624847	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
#21419296	3
#21419274	3
C₃×C₃₁×#733	3
#10624847	31