Subgroups — #36379522

Order 22599.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14578892	C₃	1	1	yes	maximal, characteristic
2	C₉×#11719689	C₃	1	1	yes	maximal, characteristic
3	C₃²⋊(C₃₁⋊C₂₇)	C₃	1	1	yes	maximal, characteristic
4	C₃₁×C₃²⋊C₂₇	C₃	1	1	yes	maximal, characteristic
5	C₃×#11719689	C₉	1	1	yes	characteristic
6	#14578892	—	3	3	no	—
7	C₃×C₃₁⋊C₂₇	—	3	1	no	—
8	C₃×C₃₁⋊C₂₇	—	3	1	no	—
9	(C₃₁⋊C₉)⋊C₉	—	3	1	no	—
10	(C₃₁⋊C₉)⋊C₉	—	3	1	no	—
11	C₃²⋊(C₃₁⋊C₉)	C₉	1	1	yes	characteristic
12	C₃²⋊(C₃₁⋊C₉)	C₉	1	1	yes	characteristic
13	C₉×C₃₁⋊C₉	—	3	1	no	—
14	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
15	C₃×C₂₇×C₃₁	—	3	1	no	—
16	C₃³×C₃₁	C₃×C₉	1	1	yes	characteristic
17	C₃×C₉×C₃₁	—	3	1	no	—
18	C₃×C₉×C₃₁	—	3	1	no	—
19	C₃×C₉×C₃₁	—	3	1	no	—
20	C₃×C₉×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃×C₉×C₃₁	3₋¹⁺²	1	1	yes	characteristic
22	C₃×C₉×C₃₁	3₋¹⁺²	1	1	yes	characteristic
23	#11719689	—	3	3	no	—
24	C₃×C₃₁⋊C₉	—	3	1	no	—
25	C₃×C₃₁⋊C₉	—	3	1	no	—
26	C₃×C₃₁⋊C₉	—	3	1	no	—
27	C₂₇×C₃₁	—	9	1	no	—
28	C₃₁⋊C₂₇	—	3	3	no	—
29	C₃₁⋊C₂₇	—	9	1	no	—
30	#10624455	—	31	1	no	maximal, Sylow
31	C₃²×C₃₁	—	3	1	no	—
32	C₃²×C₃₁	—	3	1	no	—
33	C₃²×C₃₁	—	3	1	no	—
34	C₃²×C₃₁	—	3	1	no	—
35	C₃²×C₃₁	C₃²⋊C₉	1	1	yes	characteristic
36	C₉×C₃₁	—	3	1	no	—
37	C₉×C₃₁	—	3	1	no	—
38	C₉×C₃₁	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
39	C₉×C₃₁	#731	1	1	yes	characteristic
40	C₉×C₃₁	#733	1	1	yes	characteristic
41	C₃₁⋊C₉	—	3	3	no	—
42	C₃₁⋊C₉	—	9	1	no	—
43	C₃₁⋊C₉	—	9	1	no	—
44	C₃×C₂₇⋊C₃	—	31	1	no	—
45	C₉×3₋¹⁺²	—	31	1	no	—
46	C₃²⋊C₂₇	—	31	1	no	—
47	C₃²⋊C₂₇	C₃₁⋊C₃	1	1	yes	characteristic
48	C₃×C₃₁	—	9	1	no	—
49	C₃×C₃₁	#6869	1	1	yes	characteristic
50	C₃×C₃₁	3₋¹⁺²⋊C₉	1	1	yes	characteristic
51	C₃×C₃₁	#6872	1	1	yes	characteristic
52	C₃×C₃₁	#6873	1	1	yes	characteristic
53	C₃×3₋¹⁺²	—	31	1	no	—
54	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
55	C₂₇⋊C₃	—	93	3	no	—
56	C₃×C₂₇	—	3	1	no	—
57	C₃×C₂₇	—	93	1	no	—
58	C₃×C₂₇	—	93	1	no	—
59	C₉⋊C₉	—	93	1	no	—
60	C₉⋊C₉	—	93	1	no	—
61	C₃²⋊C₉	—	31	1	no	—
62	C₃²⋊C₉	—	31	1	no	—
63	C₉²	—	93	1	no	—
64	C₃₁	#10624455	1	1	yes	characteristic, complemented, Sylow
65	C₃³	C₉×C₃₁⋊C₃	1	1	yes	characteristic
66	3₋¹⁺²	—	93	3	no	—
67	C₃×C₉	—	3	1	no	—
68	C₃×C₉	—	3	1	no	—
69	C₃×C₉	—	3	1	no	—
70	C₃×C₉	—	93	1	no	—
71	C₃×C₉	—	93	1	no	—
72	C₃×C₉	—	93	1	no	—
73	C₃×C₉	#11719686	1	1	yes	characteristic
74	C₃×C₉	#11719687	1	1	yes	characteristic
75	C₃×C₉	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
76	C₂₇	—	9	1	no	—
77	C₂₇	—	279	1	no	—
78	C₂₇	—	93	3	no	—
79	C₃²	—	3	1	no	—
80	C₃²	—	3	1	no	—
81	C₃²	—	3	1	no	—
82	C₃²	—	3	1	no	—
83	C₃²	(C₃×C₃₁⋊C₃)⋊C₉	1	1	yes	characteristic
84	C₉	—	3	1	no	—
85	C₉	—	3	1	no	—
86	C₉	—	279	1	no	—
87	C₉	—	279	1	no	—
88	C₉	—	93	3	no	—
89	C₉	#14578893	1	1	yes	characteristic
90	C₉	#14578898	1	1	yes	characteristic
91	C₉	#14578901	1	1	yes	characteristic
92	C₃	—	9	1	no	—
93	C₃	#21419231	1	1	yes	characteristic
94	C₃	#21419236	1	1	yes	characteristic
95	C₃	#21419242	1	1	yes	characteristic
96	C₃	#21419243	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₃₁⋊C₃)
commutator, prime radical	C₃³×C₃₁	C₃×C₉
Frattini	C₃²×C₉	C₃×C₃₁⋊C₃
Fitting	C₃₁×C₃²⋊C₂₇	C₃
socle	C₃²×C₃₁	C₃²⋊C₉
cosocle	C₃²×C₉×C₃₁	C₃²
hypercenter	C₃²⋊C₂₇	C₃₁⋊C₃
hypocenter	C₃₁	#10624455
LCS	G ▷ C₃³×C₃₁ ▷ C₃²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ C₃²⋊C₂₇

Complements

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

N	H ≅ G/N	type
64. C₃₁	#10624455	semidirect

Maximal subgroups

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

subgroup	index
C₃×#14578892	3
C₉×#11719689	3
C₃²⋊(C₃₁⋊C₂₇)	3
C₃₁×C₃²⋊C₂₇	3
#10624455	31