Group #14550672 — subgroups

Subgroups — #14550672

Order 2187.

575 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 575 conjugacy classes of subgroups — too many to draw. Only its 107 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	C₃²×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
3	C₃×3₋¹⁺²⋊C₉	C₃	1	6	yes	maximal
4	C₃×#6868	C₃	1	2	yes	maximal
5	#10624558	C₃	1	3	yes	maximal
6	C₃²×3₋¹⁺²	C₃²	1	3	yes	—
7	C₃³×C₉	C₃²	1	1	yes	characteristic
8	C₃³×C₉	C₃²	1	2	yes	—
9	C₃³×C₉	C₃²	1	1	yes	characteristic
10	C₃×#733	—	3	9	no	—
11	C₃×#733	—	3	3	no	—
12	C₃×C₉⋊C₉	—	3	3	no	—
13	C₃×C₉⋊C₉	—	3	6	no	—
14	C₃×C₉⋊C₉	—	3	3	no	—
15	C₃×C₃²⋊C₉	C₃²	1	6	yes	—
16	3₋¹⁺²⋊C₉	—	3	18	no	—
17	#6868	—	3	6	no	—
18	#6855	—	3	9	no	—
19	C₃⁴	C₃³	1	1	yes	characteristic
20	C₃×3₋¹⁺²	—	3	6	no	—
21	C₃×3₋¹⁺²	—	3	6	no	—
22	C₃×3₋¹⁺²	—	3	3	no	—
23	C₃×3₋¹⁺²	—	3	6	no	—
24	C₃×3₋¹⁺²	—	3	12	no	—
25	C₃×3₋¹⁺²	3₋¹⁺²	1	9	yes	—
26	C₃²×C₉	—	3	1	no	—
27	C₃²×C₉	—	3	2	no	—
28	C₃²×C₉	—	3	9	no	—
29	C₃²×C₉	—	3	2	no	—
30	C₃²×C₉	—	3	2	no	—
31	C₃²×C₉	—	3	2	no	—
32	C₃²×C₉	—	3	2	no	—
33	C₃²×C₉	—	3	1	no	—
34	C₃²×C₉	—	3	3	no	—
35	C₃²×C₉	—	3	3	no	—
36	C₃²×C₉	—	3	6	no	—
37	C₃²×C₉	—	3	6	no	—
38	C₃²×C₉	—	9	6	no	—
39	C₃²×C₉	H(3,𝔽₃)	1	3	yes	—
40	C₃²×C₉	H(3,𝔽₃)	1	3	yes	—
41	C₃²×C₉	H(3,𝔽₃)	1	6	yes	—
42	#733	—	3	27	no	—
43	C₉⋊C₉	—	3	27	no	—
44	C₃²⋊C₉	—	3	6	no	—
45	C₃²⋊C₉	—	3	12	no	—
46	C₃³	—	3	6	no	—
47	C₃³	—	3	3	no	—
48	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
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	3₋¹⁺²	—	3	9	no	—
54	3₋¹⁺²	—	3	18	no	—
55	3₋¹⁺²	—	9	12	no	—
56	3₋¹⁺²	—	9	6	no	—
57	C₃×C₉	—	3	9	no	—
58	C₃×C₉	—	3	18	no	—
59	C₃×C₉	—	3	3	no	—
60	C₃×C₉	—	3	6	no	—
61	C₃×C₉	—	3	3	no	—
62	C₃×C₉	—	3	6	no	—
63	C₃×C₉	—	3	3	no	—
64	C₃×C₉	—	3	9	no	—
65	C₃×C₉	—	3	6	no	—
66	C₃×C₉	—	9	6	no	—
67	C₃×C₉	—	9	6	no	—
68	C₃×C₉	—	9	6	no	—
69	C₃×C₉	—	9	3	no	—
70	C₃×C₉	—	9	6	no	—
71	C₃×C₉	—	9	3	no	—
72	C₃×C₉	—	9	6	no	—
73	C₃×C₉	—	9	6	no	—
74	C₃×C₉	—	9	18	no	—
75	C₃×C₉	—	9	6	no	—
76	C₃×C₉	#733	1	9	yes	complemented
77	C₃²	—	3	9	no	—
78	C₃²	—	3	18	no	—
79	C₃²	—	3	1	no	—
80	C₃²	—	3	2	no	—
81	C₃²	—	3	2	no	—
82	C₃²	—	3	2	no	—
83	C₃²	—	3	2	no	—
84	C₃²	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
85	C₃²	#6891	1	1	yes	characteristic
86	C₃²	C₉⋊H(3,𝔽₃)	1	6	yes	—
87	C₃²	C₉⋊H(3,𝔽₃)	1	3	yes	—
88	C₃²	#6893	1	2	yes	—
89	C₃²	C₃×#733	1	3	yes	—
90	C₃²	#6913	1	6	yes	—
91	C₉	—	3	9	no	—
92	C₉	—	9	3	no	—
93	C₉	—	9	9	no	—
94	C₉	—	9	6	no	—
95	C₉	—	27	6	no	—
96	C₃	—	3	1	no	—
97	C₃	—	3	6	no	—
98	C₃	—	3	2	no	—
99	C₃	#10624563	1	1	yes	characteristic
100	C₃	#10624733	1	1	yes	characteristic
101	C₃	#10624739	1	2	yes	—
102	C₃	#10624799	1	9	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×#733

C₃

yes

maximal, characteristic

C₃²×C₉⋊C₉

C₃

yes

maximal, characteristic

C₃×3₋¹⁺²⋊C₉

C₃

yes

maximal

C₃×#6868

C₃

yes

maximal

#10624558

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

—

C₃×C₉⋊C₉

—

C₃×C₉⋊C₉

—

C₃×C₉⋊C₉

—

C₃×C₃²⋊C₉

C₃²

yes

—

3₋¹⁺²⋊C₉

—

#6868

—

#6855

—

C₃⁴

C₃³

yes

characteristic

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

3₋¹⁺²

yes

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

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

H(3,𝔽₃)

yes

—

#733

—

C₉⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃³

—

C₃³

—

C₃³

C₃×H(3,𝔽₃)

yes

characteristic

C₃³

C₃×H(3,𝔽₃)

yes

—

C₃³

C₃×H(3,𝔽₃)

yes

characteristic

C₃³

C₃×3₋¹⁺²

yes

—

C₃³

#737

yes

—

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

#733

yes

complemented

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

C₃²⋊H(3,𝔽₃)

yes

characteristic

C₃²

#6891

yes

characteristic

C₃²

C₉⋊H(3,𝔽₃)

yes

—

C₃²

C₉⋊H(3,𝔽₃)

yes

—

C₃²

#6893

yes

—

C₃²

C₃×#733

yes

—

C₃²

#6913

yes

—

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

C₃

—

C₃

—

C₃

—

C₃

#10624563

yes

characteristic

100

C₃

#10624733

yes

characteristic

101

C₃

#10624739

yes

—

102

C₃

#10624799

yes

—

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

subgroup

G/H

center, socle

C₃³

C₃×H(3,𝔽₃)

commutator, Frattini, prime radical, cosocle

C₃⁴

C₃³

LCS

G ▷ C₃⁴ ▷ C₃ ▷ C₁

UCS

C₁ ◁ C₃³ ◁ C₃³×C₉ ◁ G

LECS

G ▷ C₃⁴ ▷ C₃ ▷ C₁

N	H ≅ G/N	type
76. C₃×C₉	#733	semidirect

H ≅ G/N

type

76. C₃×C₉

#733

semidirect

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

subgroup	index
C₃²×#733	3
C₃²×C₉⋊C₉	3
C₃×3₋¹⁺²⋊C₉	3
C₃×#6868	3
#10624558	3

subgroup

index

C₃²×#733

C₃²×C₉⋊C₉

C₃×3₋¹⁺²⋊C₉

C₃×#6868

#10624558

Subgroups — #14550672

Conjugacy classes of subgroups

Complements

Maximal subgroups