Group #41005267 — subgroups

Subgroups — #41005267

Order 26973.

296 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688504	C₃	1	3	yes	maximal
2	#22582441	C₃	1	6	yes	maximal
3	#22582441	C₃	1	1	yes	maximal, characteristic
4	#22582441	C₃	1	1	yes	maximal, characteristic
5	#22582441	C₃	1	1	yes	maximal, characteristic
6	C₃×C₃₇×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
7	C₃²×#66524	C₃²	1	3	yes	—
8	C₃²×#66524	C₃²	1	3	yes	—
9	C₃²×#66524	C₃²	1	3	yes	—
10	#15688504	—	3	9	no	—
11	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
12	C₃²×C₉×C₃₇	C₃²	1	2	yes	—
13	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
14	C₃₇×C₉⋊C₉	—	3	3	no	—
15	C₃³×C₃₇	C₃³	1	1	yes	characteristic
16	C₃×C₉×C₃₇	—	3	1	no	—
17	C₃×C₉×C₃₇	—	3	1	no	—
18	C₃×C₉×C₃₇	—	3	1	no	—
19	C₃×C₉×C₃₇	—	3	2	no	—
20	C₃×C₉×C₃₇	—	3	1	no	—
21	C₃×C₉×C₃₇	—	3	3	no	—
22	C₃×C₉×C₃₇	—	3	6	no	—
23	C₃×C₉×C₃₇	3₋¹⁺²	1	3	yes	—
24	C₃×#66524	—	3	3	no	—
25	C₃×#66524	—	3	6	no	—
26	C₃×#66524	—	3	3	no	—
27	C₃×#66524	—	3	3	no	—
28	C₃×#66524	—	3	3	no	—
29	C₃×#66524	—	3	3	no	—
30	C₃×#66524	—	3	6	no	—
31	C₃×#66524	—	3	6	no	—
32	C₃×#66524	3₋¹⁺²	1	9	yes	—
33	#10624577	—	37	1	no	maximal, Sylow
34	C₃²×C₃₇	C₃×3₋¹⁺²	1	3	yes	—
35	C₃²×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
36	C₃²×C₃₇	#737	1	1	yes	characteristic
37	C₃²×C₃₇	#737	1	1	yes	characteristic
38	C₃²×C₃₇	#737	1	1	yes	characteristic
39	C₃²×C₃₇	#737	1	6	yes	—
40	C₉×C₃₇	—	3	3	no	—
41	C₉×C₃₇	—	9	2	no	—
42	C₉×C₃₇	—	9	1	no	—
43	#66524	—	3	9	no	—
44	#66524	—	9	3	no	—
45	#66524	—	9	3	no	—
46	C₃×C₉⋊C₉	—	37	3	no	—
47	C₃×C₉⋊C₉	C₃₇⋊C₃	1	1	yes	characteristic
48	#6855	—	37	1	no	—
49	#6855	—	37	6	no	—
50	#6855	—	37	1	no	—
51	#6855	—	37	1	no	—
52	C₃×C₃₇	#6895	1	3	yes	—
53	C₃×C₃₇	#6895	1	1	yes	characteristic
54	C₃×C₃₇	#6899	1	2	yes	—
55	C₃×C₃₇	#6899	1	3	yes	—
56	C₃×C₃₇	#6899	1	3	yes	—
57	C₃×C₃₇	#6900	1	1	yes	characteristic
58	C₃²×C₉	—	37	3	no	—
59	C₃²×C₉	—	37	3	no	—
60	C₃²×C₉	—	37	3	no	—
61	C₃²×C₉	C₃×C₃₇⋊C₃	1	2	yes	—
62	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
63	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
64	C₉⋊C₉	—	3	3	no	—
65	C₉⋊C₉	—	111	9	no	—
66	C₃₇	#10624577	1	1	yes	characteristic, complemented, Sylow
67	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
68	C₃×C₉	—	3	1	no	—
69	C₃×C₉	—	3	1	no	—
70	C₃×C₉	—	3	1	no	—
71	C₃×C₉	—	3	3	no	—
72	C₃×C₉	—	3	2	no	—
73	C₃×C₉	—	3	1	no	—
74	C₃×C₉	—	3	6	no	—
75	C₃×C₉	—	37	9	no	—
76	C₃×C₉	—	111	3	no	—
77	C₃×C₉	—	111	3	no	—
78	C₃×C₉	—	111	3	no	—
79	C₃×C₉	—	111	3	no	—
80	C₃×C₉	—	111	6	no	—
81	C₃×C₉	—	111	6	no	—
82	C₃×C₉	—	111	3	no	—
83	C₃×C₉	—	111	6	no	—
84	C₃×C₉	#11758608	1	3	yes	—
85	C₃²	3₋¹⁺²×C₃₇⋊C₃	1	3	yes	—
86	C₃²	C₃×#11758608	1	1	yes	characteristic
87	C₃²	#15688531	1	1	yes	characteristic
88	C₃²	#15688531	1	1	yes	characteristic
89	C₃²	#15688531	1	1	yes	characteristic
90	C₃²	#15688532	1	6	yes	—
91	C₉	—	3	3	no	—
92	C₉	—	9	2	no	—
93	C₉	—	9	1	no	—
94	C₉	—	333	3	no	—
95	C₉	—	333	3	no	—
96	C₉	—	111	9	no	—
97	C₃	#22582577	1	3	yes	—
98	C₃	#22582578	1	1	yes	characteristic
99	C₃	#22582594	1	2	yes	—
100	C₃	#22582597	1	3	yes	—
101	C₃	#22582598	1	3	yes	—
102	C₃	#22582601	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×#15688504

C₃

yes

maximal

#22582441

C₃

yes

maximal

#22582441

C₃

yes

maximal, characteristic

#22582441

C₃

yes

maximal, characteristic

#22582441

C₃

yes

maximal, characteristic

C₃×C₃₇×C₉⋊C₉

C₃

yes

maximal, characteristic

C₃²×#66524

C₃²

yes

—

C₃²×#66524

C₃²

yes

—

C₃²×#66524

C₃²

yes

—

#15688504

—

C₃²×C₉×C₃₇

C₃²

yes

characteristic

C₃²×C₉×C₃₇

C₃²

yes

—

C₃²×C₉×C₃₇

C₃²

yes

characteristic

C₃₇×C₉⋊C₉

—

C₃³×C₃₇

C₃³

yes

characteristic

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

3₋¹⁺²

yes

—

—

—

—

—

—

—

—

—

3₋¹⁺²

yes

—

#10624577

—

maximal, Sylow

C₃²×C₃₇

C₃×3₋¹⁺²

yes

—

C₃²×C₃₇

C₃×3₋¹⁺²

yes

C₃²×C₃₇

yes

C₃²×C₃₇

yes

C₃²×C₃₇

yes

C₃²×C₃₇

yes

—

C₉×C₃₇

—

C₉×C₃₇

—

C₉×C₃₇

—

#66524

—

#66524

—

#66524

—

C₃×C₉⋊C₉

—

C₃×C₉⋊C₉

C₃₇⋊C₃

yes

—

—

—

—

C₃×C₃₇

#6895

yes

—

C₃×C₃₇

#6895

yes

characteristic

C₃×C₃₇

#6899

yes

—

C₃×C₃₇

#6899

yes

—

C₃×C₃₇

#6899

yes

—

C₃×C₃₇

#6900

yes

characteristic

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

C₃×C₃₇⋊C₃

yes

—

C₃²×C₉

C₃×C₃₇⋊C₃

yes

characteristic

C₃²×C₉

C₃×C₃₇⋊C₃

yes

characteristic

C₉⋊C₉

—

C₉⋊C₉

—

111

—

C₃₇

#10624577

yes

characteristic, complemented, Sylow

C₃³

C₃²×C₃₇⋊C₃

yes

characteristic

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

#11758608

yes

—

C₃²

3₋¹⁺²×C₃₇⋊C₃

yes

—

C₃²

yes

C₃²

yes

C₃²

yes

C₃²

yes

C₃²

yes

—

C₉

—

C₉

—

C₉

—

C₉

—

333

—

C₉

—

333

—

C₉

—

111

—

C₃

#22582577

yes

—

C₃

#22582578

yes

characteristic

C₃

#22582594

yes

—

100

C₃

#22582597

yes

—

101

C₃

#22582598

yes

—

102

C₃

#22582601

yes

characteristic

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₃₇⋊C₃
commutator, socle, prime radical, cosocle	C₃³×C₃₇	C₃³
Fitting	C₃×C₃₇×C₉⋊C₉	C₃
hypercenter	C₃×C₉⋊C₉	C₃₇⋊C₃
hypocenter	C₃₇	#10624577
LCS	G ▷ C₃³×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃³ ◁ C₃×C₉⋊C₉

subgroup

G/H

center, Frattini

C₃³

C₃²×C₃₇⋊C₃

commutator, socle, prime radical, cosocle

C₃³×C₃₇

C₃³

Fitting

C₃×C₃₇×C₉⋊C₉

C₃

hypercenter

C₃×C₉⋊C₉

C₃₇⋊C₃

C₃₇

G ▷ C₃³×C₃₇ ▷ C₃₇

C₁ ◁ C₃³ ◁ C₃×C₉⋊C₉

N	H ≅ G/N	type
66. C₃₇	#10624577	semidirect

H ≅ G/N

type

66. C₃₇

#10624577

semidirect

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

subgroup	index
C₃×#15688504	3
#22582441	3
C₃×C₃₇×C₉⋊C₉	3
#10624577	37

subgroup

index

C₃×#15688504

#22582441

C₃×C₃₇×C₉⋊C₉

#10624577

Subgroups — #41005267

Conjugacy classes of subgroups

Complements

Maximal subgroups