Group #19103257 — subgroups

Subgroups — #19103257

Order 5103.

758 conjugacy classes of subgroups; only the 301 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 301 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×#10588061	C₃	1	1	yes	maximal, characteristic
2	#13133596	C₃	1	3	yes	maximal, complemented
3	#13133592	C₃	1	6	yes	maximal, complemented
4	#13133576	C₃	1	9	yes	maximal, complemented
5	#13133565	C₃	1	6	yes	maximal, complemented
6	#13133552	C₃	1	3	yes	maximal
7	C₉×#4428	C₃	1	9	yes	maximal, complemented
8	#13133530	C₃	1	1	yes	maximal, characteristic, complemented
9	C₃×C₉×C₇⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
10	C₇×#6887	C₃	1	1	yes	maximal, characteristic, complemented
11	#10624879	—	7	1	no	maximal, Sylow
12	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
13	C₃×C₇⋊H(3,𝔽₃)	C₃²	1	1	yes	characteristic
14	C₃×#4430	C₃²	1	2	yes	—
15	C₃²×C₇⋊C₉	C₃²	1	3	yes	—
16	#10588061	—	3	9	no	—
17	C₃×#4428	C₃²	1	9	yes	—
18	C₃×#4428	C₃²	1	3	yes	—
19	C₃×#4427	C₃²	1	3	yes	—
20	C₃×C₉×ΓL(1,𝔽₈)	C₃²	1	3	yes	—
21	C₇×C₉⋊C₉	C₃²	1	3	yes	—
22	C₇×C₉⋊C₉	C₃²	1	3	yes	—
23	C₇×C₃²⋊C₉	C₃²	1	3	yes	—
24	C₇×C₉²	C₃²	1	3	yes	—
25	C₃²⋊(C₇⋊C₉)	C₃²	1	3	yes	—
26	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	18	yes	—
27	#10588036	C₃²	1	3	yes	—
28	#10588036	C₃²	1	18	yes	—
29	#10588035	C₃²	1	3	yes	—
30	(C₇⋊C₉)⋊C₉	C₃²	1	18	yes	—
31	(C₇⋊C₉)⋊C₉	C₃²	1	18	yes	—
32	C₉×C₇⋊C₉	C₃²	1	3	yes	—
33	C₉×C₇⋊C₉	C₃²	1	2	yes	—
34	C₉×C₇⋊C₉	C₃²	1	1	yes	characteristic
35	C₉×C₇⋊C₉	C₃²	1	3	yes	—
36	C₉×C₇⋊C₉	C₃²	1	3	yes	—
37	C₃×#737	—	7	1	no	—
38	#6900	—	7	3	no	—
39	#6899	—	7	6	no	—
40	#6896	—	7	9	no	—
41	#6894	—	7	6	no	—
42	C₉⋊H(3,𝔽₃)	—	7	3	no	—
43	C₉×3₋¹⁺²	—	7	9	no	—
44	#6887	—	7	1	no	—
45	#6887	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
46	C₃×C₉²	—	7	1	no	—
47	C₃³×C₇	C₃³	1	1	yes	characteristic
48	C₃²×ΓL(1,𝔽₈)	C₃³	1	3	yes	—
49	C₃×C₇×C₉	3₋¹⁺²	1	9	yes	complemented
50	C₃×C₇×C₉	C₃³	1	9	yes	—
51	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
52	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
53	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
54	C₇⋊H(3,𝔽₃)	—	3	3	no	—
55	#4430	—	3	6	no	—
56	C₃×C₇⋊C₉	—	3	9	no	—
57	C₃×C₇⋊C₉	C₃³	1	6	yes	—
58	C₃×C₇⋊C₉	C₃³	1	9	yes	—
59	C₃×C₇⋊C₉	C₃³	1	6	yes	—
60	C₃×C₇⋊C₉	C₃³	1	3	yes	—
61	#4428	—	3	9	no	—
62	#4428	—	3	27	no	—
63	#4427	—	3	9	no	—
64	C₉×ΓL(1,𝔽₈)	—	3	9	no	—
65	#737	—	21	9	no	—
66	C₃×3₋¹⁺²	—	7	2	no	—
67	C₃×3₋¹⁺²	—	7	3	no	—
68	C₃×3₋¹⁺²	—	7	3	no	—
69	C₃×3₋¹⁺²	—	7	9	no	—
70	C₃×H(3,𝔽₃)	—	7	1	no	—
71	C₃²×C₉	—	7	3	no	—
72	C₃²×C₉	—	7	3	no	—
73	C₃²×C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
74	C₉⋊C₉	—	7	18	no	—
75	C₉⋊C₉	—	7	18	no	—
76	C₉⋊C₉	—	7	3	no	—
77	C₉⋊C₉	—	7	3	no	—
78	C₉⋊C₉	—	7	18	no	—
79	C₉⋊C₉	C₃×ΓL(1,𝔽₈)	1	3	yes	—
80	C₉⋊C₉	C₃×ΓL(1,𝔽₈)	1	3	yes	—
81	C₃²⋊C₉	—	7	3	no	—
82	C₃²⋊C₉	—	7	18	no	—
83	C₃²⋊C₉	C₃×ΓL(1,𝔽₈)	1	3	yes	—
84	C₉²	—	7	3	no	—
85	C₉²	—	7	2	no	—
86	C₉²	—	7	1	no	—
87	C₉²	—	7	3	no	—
88	C₉²	—	7	3	no	—
89	C₉²	C₃×ΓL(1,𝔽₈)	1	3	yes	—
90	C₃²×C₇	—	3	3	no	—
91	C₃²×C₇	C₃×3₋¹⁺²	1	3	yes	—
92	C₃²×C₇	C₃⁴	1	1	yes	characteristic
93	C₃×ΓL(1,𝔽₈)	—	3	3	no	—
94	C₃×ΓL(1,𝔽₈)	—	3	9	no	—
95	C₇×C₉	—	3	9	no	—
96	C₇×C₉	C₃×3₋¹⁺²	1	3	yes	—
97	C₇×C₉	C₃×3₋¹⁺²	1	3	yes	—
98	C₇×C₉	C₃×3₋¹⁺²	1	3	yes	—
99	C₇⋊C₉	—	3	6	no	—
100	C₇⋊C₉	—	3	9	no	—
101	C₇⋊C₉	—	3	6	no	—
102	C₇⋊C₉	#737	1	9	yes	complemented
103	C₃³	—	7	3	no	—
104	C₃³	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
105	3₋¹⁺²	—	21	27	no	—
106	3₋¹⁺²	—	21	6	no	—
107	3₋¹⁺²	—	21	9	no	—
108	3₋¹⁺²	—	21	9	no	—
109	H(3,𝔽₃)	—	21	3	no	—
110	C₃×C₉	—	7	3	no	—
111	C₃×C₉	—	7	6	no	—
112	C₃×C₉	—	7	9	no	—
113	C₃×C₉	—	7	6	no	—
114	C₃×C₉	—	21	9	no	—
115	C₃×C₉	—	21	9	no	—
116	C₃×C₉	#4428	1	9	yes	complemented
117	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	9	yes	—
118	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
119	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
120	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
121	C₃×C₇	—	3	3	no	—
122	C₃×C₇	C₃²×3₋¹⁺²	1	1	yes	characteristic
123	C₃×C₇	C₃×#737	1	3	yes	—
124	ΓL(1,𝔽₈)	—	9	3	no	—
125	C₃²	—	3	3	no	—
126	C₃²	—	21	3	no	—
127	C₃²	—	21	9	no	—
128	C₃²	C₃×#4428	1	3	yes	—
129	C₃²	C₃³×ΓL(1,𝔽₈)	1	1	yes	characteristic
130	C₉	—	3	9	no	—
131	C₉	—	7	9	no	—
132	C₉	—	21	6	no	—
133	C₉	—	21	6	no	—
134	C₉	—	21	9	no	—
135	C₉	C₃×#4428	1	3	yes	—
136	C₉	C₃×#4428	1	3	yes	—
137	C₉	C₃×#4428	1	3	yes	—
138	C₇	#10624879	1	1	yes	characteristic, complemented, Sylow
139	C₃	—	3	3	no	—
140	C₃	—	63	3	no	—
141	C₃	C₃²×#4428	1	1	yes	characteristic
142	C₃	ΓL(1,𝔽₈)×#737	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×#10588061

C₃

yes

maximal, characteristic

#13133596

C₃

yes

maximal, complemented

#13133592

C₃

yes

maximal, complemented

#13133576

C₃

yes

maximal, complemented

#13133565

C₃

yes

maximal, complemented

#13133552

C₃

yes

maximal

C₉×#4428

C₃

yes

maximal, complemented

#13133530

C₃

yes

maximal, characteristic, complemented

C₃×C₉×C₇⋊C₉

C₃

yes

maximal, characteristic, complemented

C₇×#6887

C₃

yes

maximal, characteristic, complemented

#10624879

—

maximal, Sylow

C₃²×C₇×C₉

C₃²

yes

characteristic

C₃×C₇⋊H(3,𝔽₃)

C₃²

yes

characteristic

C₃×#4430

C₃²

yes

—

C₃²×C₇⋊C₉

C₃²

yes

—

#10588061

—

C₃×#4428

C₃²

yes

—

C₃×#4428

C₃²

yes

—

C₃×#4427

C₃²

yes

—

C₃×C₉×ΓL(1,𝔽₈)

C₃²

yes

—

C₇×C₉⋊C₉

C₃²

yes

—

C₇×C₉⋊C₉

C₃²

yes

—

C₇×C₃²⋊C₉

C₃²

yes

—

C₇×C₉²

C₃²

yes

—

C₃²⋊(C₇⋊C₉)

C₃²

yes

—

(C₃×ΓL(1,𝔽₈))⋊C₉

C₃²

yes

—

#10588036

C₃²

yes

—

#10588036

C₃²

yes

—

#10588035

C₃²

yes

—

(C₇⋊C₉)⋊C₉

C₃²

yes

—

(C₇⋊C₉)⋊C₉

C₃²

yes

—

C₉×C₇⋊C₉

C₃²

yes

—

C₉×C₇⋊C₉

C₃²

yes

—

C₉×C₇⋊C₉

C₃²

yes

characteristic

C₉×C₇⋊C₉

C₃²

yes

—

C₉×C₇⋊C₉

C₃²

yes

—

—

—

—

—

—

C₉⋊H(3,𝔽₃)

—

C₉×3₋¹⁺²

—

#6887

—

#6887

ΓL(1,𝔽₈)

yes

characteristic, complemented

C₃×C₉²

—

C₃³×C₇

C₃³

yes

characteristic

C₃²×ΓL(1,𝔽₈)

C₃³

yes

—

C₃×C₇×C₉

3₋¹⁺²

yes

complemented

C₃×C₇×C₉

C₃³

yes

—

C₃×C₇×C₉

C₃³

yes

characteristic

C₃×C₇×C₉

C₃³

yes

characteristic

C₃×C₇×C₉

C₃³

yes

characteristic

C₇⋊H(3,𝔽₃)

—

#4430

—

C₃×C₇⋊C₉

—

C₃×C₇⋊C₉

C₃³

yes

—

C₃×C₇⋊C₉

C₃³

yes

—

C₃×C₇⋊C₉

C₃³

yes

—

C₃×C₇⋊C₉

C₃³

yes

—

—

—

—

—

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×H(3,𝔽₃)

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

C₃×ΓL(1,𝔽₈)

yes

characteristic

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

C₃×ΓL(1,𝔽₈)

yes

—

C₉⋊C₉

C₃×ΓL(1,𝔽₈)

yes

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

C₃×ΓL(1,𝔽₈)

yes

—

C₉²

—

C₉²

—

C₉²

—

C₉²

—

C₉²

—

C₉²

C₃×ΓL(1,𝔽₈)

yes

—

C₃²×C₇

—

C₃²×C₇

C₃×3₋¹⁺²

yes

—

C₃²×C₇

C₃⁴

yes

characteristic

C₃×ΓL(1,𝔽₈)

—

C₃×ΓL(1,𝔽₈)

—

C₇×C₉

—

C₇×C₉

C₃×3₋¹⁺²

yes

—

C₇×C₉

C₃×3₋¹⁺²

yes

—

C₇×C₉

C₃×3₋¹⁺²

yes

—

C₇⋊C₉

—

100

C₇⋊C₉

—

101

C₇⋊C₉

—

102

C₇⋊C₉

#737

yes

complemented

103

C₃³

—

104

C₃³

C₃²×ΓL(1,𝔽₈)

yes

characteristic

105

3₋¹⁺²

—

106

3₋¹⁺²

—

107

3₋¹⁺²

—

108

3₋¹⁺²

—

109

H(3,𝔽₃)

—

110

C₃×C₉

—

111

C₃×C₉

—

112

C₃×C₉

—

113

C₃×C₉

—

114

C₃×C₉

—

115

C₃×C₉

—

116

C₃×C₉

#4428

yes

complemented

117

C₃×C₉

C₃²×ΓL(1,𝔽₈)

yes

—

118

C₃×C₉

C₃²×ΓL(1,𝔽₈)

yes

characteristic

119

C₃×C₉

C₃²×ΓL(1,𝔽₈)

yes

characteristic

120

C₃×C₉

C₃²×ΓL(1,𝔽₈)

yes

characteristic

121

C₃×C₇

—

122

C₃×C₇

C₃²×3₋¹⁺²

yes

characteristic

123

C₃×C₇

C₃×#737

yes

—

124

ΓL(1,𝔽₈)

—

125

C₃²

—

126

C₃²

—

127

C₃²

—

128

C₃²

C₃×#4428

yes

—

129

C₃²

C₃³×ΓL(1,𝔽₈)

yes

characteristic

130

C₉

—

131

C₉

—

132

C₉

—

133

C₉

—

134

C₉

—

135

C₉

C₃×#4428

yes

—

136

C₉

C₃×#4428

yes

—

137

C₉

C₃×#4428

yes

—

138

C₇

#10624879

yes

characteristic, complemented, Sylow

139

C₃

—

140

C₃

—

141

C₃

C₃²×#4428

yes

characteristic

142

C₃

ΓL(1,𝔽₈)×#737

yes

—

	subgroup	G/H
center	C₃×C₉	C₃²×ΓL(1,𝔽₈)
commutator, socle	C₃²×C₇	C₃⁴
Frattini	C₃²	C₃³×ΓL(1,𝔽₈)
Fitting	C₇×#6887	C₃
hypercenter	#6887	ΓL(1,𝔽₈)
hypocenter	C₇	#10624879
LCS	G ▷ C₃²×C₇ ▷ C₇
UCS	C₁ ◁ C₃×C₉ ◁ #6887

subgroup

G/H

center

C₃×C₉

C₃²×ΓL(1,𝔽₈)

commutator, socle

C₃²×C₇

C₃⁴

Frattini

C₃²

C₃³×ΓL(1,𝔽₈)

C₃

C₇

G ▷ C₃²×C₇ ▷ C₇

C₁ ◁ C₃×C₉ ◁ #6887

N	H ≅ G/N	type
2. #13133596	C₃	semidirect
3. #13133592	C₃	semidirect
4. #13133576	C₃	semidirect
5. #13133565	C₃	semidirect
7. C₉×#4428	C₃	semidirect
8. #13133530	C₃	semidirect
9. C₃×C₉×C₇⋊C₉	C₃	semidirect
10. C₇×#6887	C₃	semidirect
45. #6887	ΓL(1,𝔽₈)	semidirect
49. C₃×C₇×C₉	3₋¹⁺²	semidirect
102. C₇⋊C₉	#737	semidirect
116. C₃×C₉	#4428	semidirect
138. C₇	#10624879	semidirect

H ≅ G/N

type

2. #13133596

C₃

semidirect

3. #13133592

C₃

semidirect

4. #13133576

C₃

semidirect

5. #13133565

C₃

semidirect

7. C₉×#4428

C₃

semidirect

8. #13133530

C₃

semidirect

9. C₃×C₉×C₇⋊C₉

C₃

semidirect

10. C₇×#6887

C₃

semidirect

45. #6887

ΓL(1,𝔽₈)

semidirect

49. C₃×C₇×C₉

3₋¹⁺²

semidirect

102. C₇⋊C₉

#737

semidirect

116. C₃×C₉

#4428

semidirect

138. C₇

#10624879

semidirect

Subgroups — #19103257

Conjugacy classes of subgroups

Complements