Subgroups — #36379788

Order 22599.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14578886	C₃	1	1	yes	maximal, characteristic
2	#21419230	C₃	1	2	yes	maximal
3	C₃×C₃₁×#733	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₃₁⋊C₉	—	3	1	no	—
5	#14578886	—	3	3	no	—
6	C₃²⋊(C₃₁⋊C₉)	—	3	2	no	—
7	C₃×3₋¹⁺²×C₃₁	—	3	1	no	—
8	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
9	C₃₁×#733	—	3	2	no	—
10	C₃₁×#733	C₉	1	3	yes	complemented
11	C₃³×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
12	3₋¹⁺²×C₃₁	—	3	3	no	—
13	3₋¹⁺²×C₃₁	—	9	1	no	—
14	3₋¹⁺²×C₃₁	—	9	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	C₃×C₉×C₃₁	C₃×C₉	1	1	yes	characteristic
20	C₃×C₉×C₃₁	3₋¹⁺²	1	2	yes	—
21	C₃×C₃₁⋊C₉	—	3	3	no	—
22	C₃×C₃₁⋊C₉	—	9	1	no	—
23	C₃×C₃₁⋊C₉	—	9	2	no	—
24	C₃×C₃₁⋊C₉	—	9	2	no	—
25	#10624529	—	31	1	no	maximal, Sylow
26	C₃²×C₃₁	—	3	1	no	—
27	C₃²×C₃₁	—	3	2	no	—
28	C₃²×C₃₁	C₃²⋊C₉	1	1	yes	characteristic
29	C₃²×C₃₁	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
30	C₃²×C₃₁	#731	1	1	yes	characteristic
31	C₃²×C₃₁	#732	1	1	yes	characteristic
32	C₉×C₃₁	—	3	1	no	—
33	C₉×C₃₁	—	3	2	no	—
34	C₉×C₃₁	—	9	3	no	—
35	C₃₁⋊C₉	—	9	3	no	—
36	C₃₁⋊C₉	—	27	2	no	—
37	C₃×#733	C₃₁⋊C₃	1	1	yes	characteristic
38	C₃×C₉⋊C₉	—	31	1	no	—
39	#6868	—	31	2	no	—
40	C₃×C₃₁	—	3	1	no	—
41	C₃×C₃₁	—	3	1	no	—
42	C₃×C₃₁	—	3	1	no	—
43	C₃×C₃₁	H(3,𝔽₃)⋊C₉	1	1	yes	characteristic
44	C₃×C₃₁	#6882	1	1	yes	characteristic
45	C₃×C₃₁	#6883	1	2	yes	—
46	C₃×3₋¹⁺²	—	3	1	no	—
47	C₃²×C₉	—	93	1	no	—
48	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
49	#733	—	3	2	no	—
50	#733	C₃₁⋊C₉	1	3	yes	complemented
51	C₉⋊C₉	—	93	3	no	—
52	C₃²⋊C₉	—	93	2	no	—
53	C₃₁	#10624529	1	1	yes	characteristic, complemented, Sylow
54	C₃³	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
55	3₋¹⁺²	—	3	3	no	—
56	3₋¹⁺²	—	9	1	no	—
57	3₋¹⁺²	—	9	1	no	—
58	C₃×C₉	—	3	1	no	—
59	C₃×C₉	—	3	1	no	—
60	C₃×C₉	—	3	1	no	—
61	C₃×C₉	—	9	1	no	—
62	C₃×C₉	—	279	1	no	—
63	C₃×C₉	—	279	2	no	—
64	C₃×C₉	—	279	2	no	—
65	C₃×C₉	—	93	3	no	—
66	C₃×C₉	C₃×C₃₁⋊C₉	1	1	yes	characteristic
67	C₃×C₉	#11719689	1	2	yes	—
68	C₃²	—	3	1	no	—
69	C₃²	—	3	2	no	—
70	C₃²	C₃²⋊(C₃₁⋊C₉)	1	1	yes	characteristic
71	C₃²	#14578893	1	1	yes	characteristic
72	C₃²	#14578896	1	1	yes	characteristic
73	C₃²	#14578899	1	1	yes	characteristic
74	C₉	—	3	1	no	—
75	C₉	—	3	2	no	—
76	C₉	—	9	3	no	—
77	C₉	—	279	3	no	—
78	C₉	—	837	2	no	—
79	C₃	—	3	1	no	—
80	C₃	—	3	1	no	—
81	C₃	—	3	1	no	—
82	C₃	H(3,𝔽₃)⋊(C₃₁⋊C₉)	1	1	yes	characteristic
83	C₃	#21419278	1	1	yes	characteristic
84	C₃	#21419280	1	2	yes	—

	subgroup	G/H
center	C₃²	#14578899
commutator	C₃×C₉×C₃₁	C₃×C₉
Frattini	C₃²×C₉	C₃×C₃₁⋊C₃
Fitting	C₃×C₃₁×#733	C₃
socle	C₃²×C₃₁	#732
prime radical	C₃³×C₃₁	H(3,𝔽₃)
cosocle	C₃²×C₉×C₃₁	C₃²
hypercenter	C₃×#733	C₃₁⋊C₃
hypocenter	C₃₁	#10624529
LCS	G ▷ C₃×C₉×C₃₁ ▷ C₃²×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²×C₉ ◁ C₃×#733

Complements

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

N	H ≅ G/N	type
10. C₃₁×#733	C₉	semidirect
50. #733	C₃₁⋊C₉	semidirect
53. C₃₁	#10624529	semidirect

Maximal subgroups

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

subgroup	index
C₃×#14578886	3
#21419230	3
C₃×C₃₁×#733	3
#10624529	31