Group #14550877 — subgroups

Subgroups — #14550877

Order 2187.

164 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 44 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	C₉×#733	C₃	1	1	yes	maximal, characteristic
2	C₉×#733	C₃	1	2	yes	maximal
3	#10624551	C₃	1	1	yes	maximal, characteristic
4	#10624494	C₃	1	1	yes	maximal, characteristic
5	#10624493	C₃	1	2	yes	maximal
6	#10624491	C₃	1	1	yes	maximal, characteristic
7	#10624490	C₃	1	2	yes	maximal
8	#10624483	C₃	1	2	yes	maximal
9	#10624482	C₃	1	1	yes	maximal, characteristic
10	C₃×#733	C₃²	1	2	yes	—
11	C₃×#733	C₃²	1	1	yes	characteristic
12	C₉×3₋¹⁺²	—	3	1	no	—
13	C₉×3₋¹⁺²	—	3	2	no	—
14	C₃×C₉²	C₃²	1	1	yes	characteristic
15	3₋¹⁺²⋊C₉	—	3	1	no	—
16	3₋¹⁺²⋊C₉	—	3	1	no	—
17	3₋¹⁺²⋊C₉	—	3	2	no	—
18	3₋¹⁺²⋊C₉	—	3	2	no	—
19	#6868	C₃²	1	1	yes	characteristic
20	#6868	C₃²	1	2	yes	—
21	#6868	C₃²	1	1	yes	characteristic
22	#6868	C₃²	1	2	yes	—
23	#6855	—	3	1	no	—
24	#6855	—	3	1	no	—
25	#6855	—	3	1	no	—
26	#6855	C₃²	1	1	yes	characteristic
27	#6855	C₃²	1	2	yes	—
28	C₃×3₋¹⁺²	—	3	2	no	—
29	C₃×3₋¹⁺²	—	3	1	no	—
30	C₃²×C₉	—	3	1	no	—
31	C₃²×C₉	—	3	2	no	—
32	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
33	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
34	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
35	C₃²×C₉	C₃³	1	1	yes	characteristic
36	#733	—	3	6	no	—
37	#733	—	3	3	no	—
38	C₉⋊C₉	—	9	2	no	—
39	C₉⋊C₉	—	9	2	no	—
40	C₉⋊C₉	—	9	2	no	—
41	C₃²⋊C₉	—	3	1	no	—
42	C₃²⋊C₉	—	3	2	no	—
43	C₃²⋊C₉	—	3	1	no	—
44	C₃²⋊C₉	—	3	2	no	—
45	C₉²	—	3	2	no	—
46	C₉²	—	3	1	no	—
47	C₉²	—	9	2	no	—
48	C₉²	—	9	1	no	—
49	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
50	3₋¹⁺²	—	3	6	no	—
51	3₋¹⁺²	—	3	3	no	—
52	3₋¹⁺²	—	9	2	no	—
53	3₋¹⁺²	—	9	2	no	—
54	3₋¹⁺²	—	9	2	no	—
55	C₃×C₉	—	3	1	no	—
56	C₃×C₉	—	3	1	no	—
57	C₃×C₉	—	3	1	no	—
58	C₃×C₉	—	3	2	no	—
59	C₃×C₉	—	3	1	no	—
60	C₃×C₉	—	9	1	no	—
61	C₃×C₉	—	9	2	no	—
62	C₃×C₉	—	9	1	no	—
63	C₃×C₉	—	9	1	no	—
64	C₃×C₉	—	9	1	no	—
65	C₃×C₉	—	9	1	no	—
66	C₃×C₉	—	9	2	no	—
67	C₃×C₉	—	9	1	no	—
68	C₃×C₉	—	9	2	no	—
69	C₃×C₉	—	9	1	no	—
70	C₃×C₉	—	9	2	no	—
71	C₃×C₉	—	9	2	no	—
72	C₃×C₉	—	9	1	no	—
73	C₃×C₉	—	9	1	no	—
74	C₃×C₉	—	9	2	no	—
75	C₃×C₉	—	9	1	no	—
76	C₃×C₉	—	9	2	no	—
77	C₃×C₉	#732	1	2	yes	—
78	C₃×C₉	#732	1	1	yes	characteristic
79	C₃²	—	3	1	no	—
80	C₃²	—	3	1	no	—
81	C₃²	—	3	1	no	—
82	C₃²	C₃×#732	1	1	yes	characteristic
83	C₃²	#6908	1	2	yes	—
84	C₃²	#6908	1	1	yes	characteristic
85	C₉	—	3	2	no	—
86	C₉	—	3	1	no	—
87	C₉	—	9	1	no	—
88	C₉	—	9	6	no	—
89	C₉	—	9	3	no	—
90	C₉	—	9	1	no	—
91	C₉	—	9	1	no	—
92	C₉	—	27	1	no	—
93	C₉	—	27	2	no	—
94	C₉	—	27	2	no	—
95	C₉	—	27	1	no	—
96	C₉	—	27	1	no	—
97	C₉	—	27	2	no	—
98	C₃	—	3	1	no	—
99	C₃	—	3	2	no	—
100	C₃	#10624585	1	1	yes	characteristic
101	C₃	#10624841	1	1	yes	characteristic
102	C₃	#10624847	1	1	yes	characteristic
103	C₃	#10624849	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#733

C₃

yes

maximal, characteristic

C₉×#733

C₃

yes

maximal

#10624551

C₃

yes

maximal, characteristic

#10624494

C₃

yes

maximal, characteristic

#10624493

C₃

yes

maximal

#10624491

C₃

yes

maximal, characteristic

#10624490

C₃

yes

maximal

#10624483

C₃

yes

maximal

#10624482

C₃

yes

maximal, characteristic

C₃×#733

C₃²

yes

—

C₃×#733

C₃²

yes

characteristic

C₉×3₋¹⁺²

—

C₉×3₋¹⁺²

—

C₃×C₉²

C₃²

yes

characteristic

3₋¹⁺²⋊C₉

—

3₋¹⁺²⋊C₉

—

3₋¹⁺²⋊C₉

—

3₋¹⁺²⋊C₉

—

#6868

C₃²

yes

characteristic

#6868

C₃²

yes

—

#6868

C₃²

yes

characteristic

#6868

C₃²

yes

—

—

—

—

C₃²

yes

characteristic

#6855

C₃²

yes

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

yes

C₃²×C₉

yes

C₃²×C₉

yes

C₃²×C₉

C₃³

yes

characteristic

#733

—

#733

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₉²

—

C₉²

—

C₉²

—

C₉²

—

C₃³

C₃×H(3,𝔽₃)

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

#732

yes

—

C₃×C₉

#732

yes

characteristic

C₃²

—

C₃²

—

C₃²

—

C₃²

C₃×#732

yes

characteristic

C₃²

#6908

yes

—

C₃²

#6908

yes

characteristic

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

C₃

—

C₃

—

100

C₃

#10624585

yes

characteristic

101

C₃

#10624841

yes

characteristic

102

C₃

#10624847

yes

characteristic

103

C₃

#10624849

yes

characteristic

	subgroup	G/H
center, socle	C₃²	C₃×#732
commutator, Frattini, cosocle	C₃²×C₉	C₃³
prime radical	C₃³	C₃×H(3,𝔽₃)
LCS	G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃² ◁ C₃²×C₉ ◁ C₃×C₉² ◁ G
LECS	G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁

subgroup

G/H

center, socle

C₃²

C₃×#732

commutator, Frattini, cosocle

C₃²×C₉

C₃³

prime radical

C₃³

C₃×H(3,𝔽₃)

LCS

G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁

UCS

C₁ ◁ C₃² ◁ C₃²×C₉ ◁ C₃×C₉² ◁ G

LECS

G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁

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

subgroup	index
C₉×#733	3
#10624551	3
#10624494	3
#10624493	3
#10624491	3
#10624490	3
#10624483	3
#10624482	3

subgroup

index

Subgroups — #14550877

Conjugacy classes of subgroups

Maximal subgroups