Group #14554410 — subgroups

Subgroups — C₃×#10624791 #14554410

Order 2187.

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

normal subgroups only

This group has 842 conjugacy classes of subgroups — too many to draw. Only its 296 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	C₃²×#733	C₃	1	1	yes	maximal, characteristic
2	C₃×#6894	C₃	1	3	yes	maximal
3	C₃²×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
4	#10624791	C₃	1	27	yes	maximal, direct product factor
5	C₃×3₋¹⁺²⋊C₉	C₃	1	6	yes	maximal
6	C₃×#6868	C₃	1	2	yes	maximal
7	C₃²×3₋¹⁺²	C₃²	1	3	yes	—
8	C₃³×C₉	C₃²	1	1	yes	characteristic
9	C₃³×C₉	C₃²	1	2	yes	—
10	C₃³×C₉	C₃²	1	1	yes	characteristic
11	C₃×#733	—	3	9	no	—
12	C₃×#733	C₃²	1	9	yes	—
13	#6894	—	3	18	no	—
14	#6894	C₃²	1	27	yes	—
15	C₃×C₉⋊C₉	—	3	6	no	—
16	C₃×C₉⋊C₉	—	3	3	no	—
17	C₃×C₉⋊C₉	—	3	9	no	—
18	C₃×C₉⋊C₉	C₃²	1	9	yes	—
19	C₃×C₃²⋊C₉	C₃²	1	6	yes	—
20	3₋¹⁺²⋊C₉	C₃²	1	54	yes	—
21	#6868	C₃²	1	18	yes	—
22	C₃⁴	C₃³	1	1	yes	characteristic
23	C₃×3₋¹⁺²	—	3	6	no	—
24	C₃×3₋¹⁺²	—	3	9	no	—
25	C₃×3₋¹⁺²	—	3	18	no	—
26	C₃×3₋¹⁺²	C₃³	1	9	yes	—
27	C₃²×C₉	—	3	2	no	—
28	C₃²×C₉	—	3	1	no	—
29	C₃²×C₉	—	3	6	no	—
30	C₃²×C₉	—	3	4	no	—
31	C₃²×C₉	—	3	2	no	—
32	C₃²×C₉	—	3	3	no	—
33	C₃²×C₉	—	3	6	no	—
34	C₃²×C₉	—	9	3	no	—
35	C₃²×C₉	—	9	6	no	—
36	C₃²×C₉	H(3,𝔽₃)	1	3	yes	—
37	C₃²×C₉	H(3,𝔽₃)	1	6	yes	—
38	C₃²×C₉	3₋¹⁺²	1	9	yes	—
39	C₃²×C₉	C₃³	1	3	yes	—
40	C₃²×C₉	C₃³	1	6	yes	—
41	C₃²×C₉	C₃³	1	3	yes	—
42	#733	—	3	27	no	—
43	C₉⋊C₉	—	3	27	no	—
44	C₉⋊C₉	—	3	81	no	—
45	C₃²⋊C₉	—	3	12	no	—
46	C₃²⋊C₉	C₃³	1	18	yes	—
47	C₃³	—	3	3	no	—
48	C₃³	—	3	6	no	—
49	C₃³	C₃×H(3,𝔽₃)	1	2	yes	—
50	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
51	C₃³	C₃×3₋¹⁺²	1	3	yes	—
52	C₃³	#737	1	6	yes	—
53	C₃³	C₃⁴	1	1	yes	characteristic
54	3₋¹⁺²	—	3	9	no	—
55	3₋¹⁺²	—	3	18	no	—
56	3₋¹⁺²	—	9	18	no	—
57	C₃×C₉	—	3	9	no	—
58	C₃×C₉	—	3	3	no	—
59	C₃×C₉	—	3	6	no	—
60	C₃×C₉	—	3	18	no	—
61	C₃×C₉	—	3	9	no	—
62	C₃×C₉	—	3	18	no	—
63	C₃×C₉	—	3	6	no	—
64	C₃×C₉	—	3	9	no	—
65	C₃×C₉	—	9	6	no	—
66	C₃×C₉	—	9	3	no	—
67	C₃×C₉	—	9	12	no	—
68	C₃×C₉	—	9	18	no	—
69	C₃×C₉	—	9	6	no	—
70	C₃×C₉	—	9	9	no	—
71	C₃×C₉	—	9	6	no	—
72	C₃×C₉	C₃×H(3,𝔽₃)	1	9	yes	—
73	C₃×C₉	C₃×3₋¹⁺²	1	9	yes	—
74	C₃²	—	3	9	no	—
75	C₃²	—	3	18	no	—
76	C₃²	—	3	2	no	—
77	C₃²	—	3	1	no	—
78	C₃²	—	3	4	no	—
79	C₃²	—	3	2	no	—
80	C₃²	C₉⋊H(3,𝔽₃)	1	6	yes	—
81	C₃²	C₉⋊H(3,𝔽₃)	1	3	yes	—
82	C₃²	#6912	1	3	yes	—
83	C₃²	#6913	1	6	yes	—
84	C₃²	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
85	C₃²	C₃²×3₋¹⁺²	1	1	yes	characteristic
86	C₃²	C₃×#737	1	2	yes	—
87	C₉	—	3	9	no	—
88	C₉	—	3	9	no	—
89	C₉	—	9	9	no	—
90	C₉	—	9	18	no	—
91	C₉	—	9	6	no	—
92	C₃	—	3	1	no	—
93	C₃	—	3	2	no	—
94	C₃	—	3	6	no	—
95	C₃	#10624791	1	9	yes	direct product factor
96	C₃	C₃×C₉⋊H(3,𝔽₃)	1	1	yes	characteristic
97	C₃	C₃×#6912	1	1	yes	characteristic
98	C₃	C₃×#6913	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×#733

C₃

yes

maximal, characteristic

C₃×#6894

C₃

yes

maximal

C₃²×C₉⋊C₉

C₃

yes

maximal, characteristic

#10624791

C₃

yes

maximal, direct product factor

C₃×3₋¹⁺²⋊C₉

C₃

yes

maximal

C₃×#6868

C₃

yes

maximal

C₃²×3₋¹⁺²

C₃²

yes

—

C₃³×C₉

C₃²

yes

characteristic

C₃³×C₉

C₃²

yes

—

C₃³×C₉

C₃²

yes

characteristic

C₃×#733

—

C₃×#733

C₃²

yes

—

#6894

—

#6894

C₃²

yes

—

C₃×C₉⋊C₉

—

C₃×C₉⋊C₉

—

C₃×C₉⋊C₉

—

C₃×C₉⋊C₉

C₃²

yes

—

C₃×C₃²⋊C₉

C₃²

yes

—

3₋¹⁺²⋊C₉

C₃²

yes

—

#6868

C₃²

yes

—

C₃⁴

C₃³

yes

characteristic

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

C₃³

yes

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

H(3,𝔽₃)

yes

—

C₃²×C₉

H(3,𝔽₃)

yes

—

C₃²×C₉

3₋¹⁺²

yes

—

C₃²×C₉

C₃³

yes

—

C₃²×C₉

C₃³

yes

—

C₃²×C₉

C₃³

yes

—

#733

—

C₉⋊C₉

—

C₉⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

C₃³

yes

—

C₃³

—

C₃³

—

C₃³

C₃×H(3,𝔽₃)

yes

—

C₃³

C₃×H(3,𝔽₃)

yes

characteristic

C₃³

C₃×3₋¹⁺²

yes

—

C₃³

#737

yes

—

C₃³

C₃⁴

yes

characteristic

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×H(3,𝔽₃)

yes

—

C₃×C₉

C₃×3₋¹⁺²

yes

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

C₉⋊H(3,𝔽₃)

yes

—

C₃²

C₉⋊H(3,𝔽₃)

yes

—

C₃²

#6912

yes

—

C₃²

#6913

yes

—

C₃²

C₃²×H(3,𝔽₃)

yes

characteristic

C₃²

C₃²×3₋¹⁺²

yes

characteristic

C₃²

C₃×#737

yes

—

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

C₃

—

C₃

—

C₃

—

C₃

#10624791

yes

direct product factor

C₃

C₃×C₉⋊H(3,𝔽₃)

yes

C₃

yes

C₃

yes

—

	subgroup	G/H
center, socle	C₃³	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃⁴
prime radical	C₃⁴	C₃³
LCS	G ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃³ ◁ C₃³×C₉ ◁ G
LECS	G ▷ C₃³ ▷ C₃ ▷ C₁

subgroup

G/H

center, socle

C₃³

C₃×H(3,𝔽₃)

commutator, Frattini, cosocle

C₃³

C₃⁴

prime radical

C₃⁴

C₃³

LCS

G ▷ C₃³ ▷ C₃ ▷ C₁

UCS

C₁ ◁ C₃³ ◁ C₃³×C₉ ◁ G

LECS

G ▷ C₃³ ▷ C₃ ▷ C₁

N	H ≅ G/N	type
4. #10624791	C₃	direct (N × H)
95. C₃	#10624791	direct (N × H)

H ≅ G/N

type

4. #10624791

C₃

direct (N × H)

95. C₃

#10624791

direct (N × H)

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

subgroup	index
C₃²×#733	3
C₃×#6894	3
C₃²×C₉⋊C₉	3
#10624791	3
C₃×3₋¹⁺²⋊C₉	3
C₃×#6868	3

subgroup

index

C₃²×#733

C₃×#6894

C₃²×C₉⋊C₉

#10624791

C₃×3₋¹⁺²⋊C₉

C₃×#6868

Subgroups — C₃×#10624791 #14554410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×#10624791 #14554410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10624791 #14554410