Group #14550835 — subgroups

Subgroups — C₃×#10624484 #14550835

Order 2187.

476 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 62 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×#732	C₃	1	1	yes	maximal, characteristic
2	C₃×#6895	C₃	1	2	yes	maximal, complemented
3	C₃×#6867	C₃	1	1	yes	maximal, characteristic, complemented
4	#10624484	C₃	1	9	yes	maximal, direct product factor
5	C₃²×H(3,𝔽₃)	—	3	1	no	—
6	C₃³×C₉	C₃²	1	1	yes	characteristic
7	C₃×#732	—	3	6	no	—
8	C₃×#732	—	3	3	no	—
9	C₃×#732	—	3	2	no	—
10	C₃×#732	C₃²	1	3	yes	—
11	#6895	—	3	4	no	—
12	#6895	—	3	12	no	—
13	#6895	C₃²	1	6	yes	complemented
14	C₃×C₉⋊C₉	—	3	6	no	—
15	C₃×C₃²⋊C₉	—	3	2	no	—
16	C₃×C₃²⋊C₉	—	3	1	no	—
17	#6867	—	3	2	no	—
18	#6867	C₃²	1	3	yes	complemented
19	C₃⁴	—	9	1	no	—
20	C₃⁴	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃×H(3,𝔽₃)	—	3	6	no	—
22	C₃×H(3,𝔽₃)	—	3	3	no	—
23	C₃×H(3,𝔽₃)	—	3	3	no	—
24	C₃×H(3,𝔽₃)	—	9	4	no	—
25	C₃×H(3,𝔽₃)	—	9	2	no	—
26	C₃×H(3,𝔽₃)	—	9	2	no	—
27	C₃²×C₉	—	3	2	no	—
28	C₃²×C₉	—	3	4	no	—
29	C₃²×C₉	—	3	2	no	—
30	C₃²×C₉	—	3	1	no	—
31	C₃²×C₉	—	3	6	no	—
32	C₃²×C₉	—	3	2	no	—
33	C₃²×C₉	—	3	1	no	—
34	C₃²×C₉	—	9	1	no	—
35	C₃²×C₉	H(3,𝔽₃)	1	2	yes	—
36	C₃²×C₉	C₃³	1	1	yes	characteristic
37	#732	—	3	9	no	—
38	#732	—	3	18	no	—
39	C₉⋊C₉	—	3	18	no	—
40	C₉⋊C₉	—	3	36	no	—
41	C₃²⋊C₉	—	3	12	no	—
42	C₃²⋊C₉	—	3	6	no	—
43	C₃²⋊C₉	—	3	3	no	—
44	C₃²⋊C₉	—	9	2	no	—
45	C₃³	—	9	3	no	—
46	C₃³	—	9	6	no	—
47	C₃³	—	9	3	no	—
48	C₃³	—	9	3	no	—
49	C₃³	—	27	9	no	—
50	C₃³	AΣL(1,𝔽₂₇)	1	2	yes	—
51	C₃³	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
52	C₃³	AΣL(1,𝔽₂₇)	1	4	yes	—
53	C₃³	AΣL(1,𝔽₂₇)	1	2	yes	—
54	C₃³	#731	1	1	yes	characteristic
55	C₃³	#731	1	2	yes	—
56	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
57	H(3,𝔽₃)	—	3	9	no	—
58	H(3,𝔽₃)	—	9	12	no	—
59	H(3,𝔽₃)	—	9	6	no	—
60	H(3,𝔽₃)	—	9	6	no	—
61	C₃×C₉	—	3	18	no	—
62	C₃×C₉	—	3	4	no	—
63	C₃×C₉	—	3	2	no	—
64	C₃×C₉	—	3	2	no	—
65	C₃×C₉	—	3	1	no	—
66	C₃×C₉	—	3	2	no	—
67	C₃×C₉	—	3	1	no	—
68	C₃×C₉	—	9	18	no	—
69	C₃×C₉	—	9	4	no	—
70	C₃×C₉	—	9	2	no	—
71	C₃×C₉	—	9	2	no	—
72	C₃×C₉	—	9	1	no	—
73	C₃×C₉	—	9	3	no	—
74	C₃×C₉	—	27	3	no	—
75	C₃²	—	3	6	no	—
76	C₃²	—	3	3	no	—
77	C₃²	—	3	3	no	—
78	C₃²	—	9	4	no	—
79	C₃²	—	9	2	no	—
80	C₃²	—	9	2	no	—
81	C₃²	—	9	1	no	—
82	C₃²	—	9	9	no	—
83	C₃²	—	27	18	no	—
84	C₃²	—	27	9	no	—
85	C₃²	—	27	9	no	—
86	C₃²	#6857	1	4	yes	—
87	C₃²	#6857	1	2	yes	—
88	C₃²	#6857	1	2	yes	—
89	C₃²	#6857	1	1	yes	characteristic
90	C₃²	C₃×AΣL(1,𝔽₂₇)	1	2	yes	—
91	C₃²	C₃×AΣL(1,𝔽₂₇)	1	1	yes	characteristic
92	C₃²	C₃×#731	1	1	yes	characteristic
93	C₉	—	9	18	no	—
94	C₉	—	9	2	no	—
95	C₉	—	9	1	no	—
96	C₉	—	27	3	no	—
97	C₃	—	3	2	no	—
98	C₃	—	3	1	no	—
99	C₃	—	3	2	no	—
100	C₃	—	3	1	no	—
101	C₃	—	3	4	no	—
102	C₃	—	3	2	no	—
103	C₃	—	27	9	no	—
104	C₃	#10624484	1	3	yes	direct product factor
105	C₃	C₃×#6857	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×#732

C₃

yes

maximal, characteristic

C₃×#6895

C₃

yes

maximal, complemented

C₃×#6867

C₃

yes

maximal, characteristic, complemented

#10624484

C₃

yes

maximal, direct product factor

C₃²×H(3,𝔽₃)

—

C₃³×C₉

C₃²

yes

—

—

—

C₃²

yes

—

#6895

—

#6895

—

#6895

C₃²

yes

complemented

C₃×C₉⋊C₉

—

C₃×C₃²⋊C₉

—

C₃×C₃²⋊C₉

—

#6867

—

#6867

C₃²

yes

complemented

C₃⁴

—

C₃⁴

H(3,𝔽₃)

yes

characteristic

C₃×H(3,𝔽₃)

—

C₃×H(3,𝔽₃)

—

C₃×H(3,𝔽₃)

—

C₃×H(3,𝔽₃)

—

C₃×H(3,𝔽₃)

—

C₃×H(3,𝔽₃)

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

H(3,𝔽₃)

yes

—

C₃²×C₉

C₃³

yes

characteristic

#732

—

#732

—

C₉⋊C₉

—

C₉⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃³

—

C₃³

—

C₃³

—

C₃³

—

C₃³

—

C₃³

AΣL(1,𝔽₂₇)

yes

—

C₃³

AΣL(1,𝔽₂₇)

yes

characteristic

C₃³

AΣL(1,𝔽₂₇)

yes

—

C₃³

AΣL(1,𝔽₂₇)

yes

—

C₃³

#731

yes

characteristic

C₃³

#731

yes

—

C₃³

C₃×H(3,𝔽₃)

yes

—

—

—

—

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

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

#6857

yes

—

C₃²

#6857

yes

—

C₃²

#6857

yes

—

C₃²

#6857

yes

characteristic

C₃²

C₃×AΣL(1,𝔽₂₇)

yes

—

C₃²

C₃×AΣL(1,𝔽₂₇)

yes

characteristic

C₃²

C₃×#731

yes

characteristic

C₉

—

C₉

—

C₉

—

C₉

—

C₃

—

C₃

—

C₃

—

100

C₃

—

101

C₃

—

102

C₃

—

103

C₃

—

104

C₃

#10624484

yes

direct product factor

105

C₃

C₃×#6857

yes

characteristic

	subgroup	G/H
center, socle	C₃²	#6857
commutator, Frattini, cosocle	C₃²×C₉	C₃³
prime radical	C₃²×#732	C₃
LCS	G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃² ◁ C₃⁴ ◁ C₃³×C₉ ◁ G
LECS	G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁

subgroup

G/H

center, socle

C₃²

#6857

commutator, Frattini, cosocle

C₃²×C₉

C₃³

prime radical

C₃²×#732

C₃

LCS

G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁

UCS

C₁ ◁ C₃² ◁ C₃⁴ ◁ C₃³×C₉ ◁ G

LECS

G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁

N	H ≅ G/N	type
2. C₃×#6895	C₃	semidirect
3. C₃×#6867	C₃	semidirect
4. #10624484	C₃	direct (N × H)
13. #6895	C₃²	semidirect
18. #6867	C₃²	semidirect
104. C₃	#10624484	direct (N × H)

H ≅ G/N

type

2. C₃×#6895

C₃

semidirect

3. C₃×#6867

C₃

semidirect

4. #10624484

C₃

direct (N × H)

13. #6895

C₃²

semidirect

18. #6867

C₃²

semidirect

104. C₃

#10624484

direct (N × H)

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

subgroup	index
C₃²×#732	3
C₃×#6895	3
C₃×#6867	3
#10624484	3

subgroup

index

C₃²×#732

C₃×#6895

C₃×#6867

#10624484

Subgroups — C₃×#10624484 #14550835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×#10624484 #14550835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10624484 #14550835