Group #19103248 — subgroups

Subgroups — #19103248

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	#13133593	C₃	1	3	yes	maximal, complemented
2	#13133586	C₃	1	6	yes	maximal, complemented
3	#13133572	C₃	1	9	yes	maximal, complemented
4	#13133560	C₃	1	6	yes	maximal, complemented
5	#13133548	C₃	1	3	yes	maximal
6	C₉×#4430	C₃	1	9	yes	maximal, complemented
7	#13133530	C₃	1	1	yes	maximal, characteristic, complemented
8	#13133530	C₃	1	1	yes	maximal, characteristic, complemented
9	C₃×C₉×C₇⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
10	C₃×C₇×#737	C₃	1	1	yes	maximal, characteristic
11	#10624879	—	7	1	no	maximal, Sylow
12	C₇×#737	—	3	9	no	—
13	C₃×C₇×3₋¹⁺²	C₃²	1	3	yes	—
14	C₃×C₇×3₋¹⁺²	C₃²	1	3	yes	—
15	C₃×C₇×3₋¹⁺²	C₃²	1	2	yes	—
16	C₃×C₇×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
17	C₃²×C₇×C₉	C₃²	1	3	yes	—
18	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
19	C₃×#4430	C₃²	1	9	yes	—
20	C₃²×C₇⋊C₉	C₃²	1	3	yes	—
21	C₃²⋊(C₇⋊C₉)	C₃²	1	18	yes	—
22	C₃²⋊(C₇⋊C₉)	C₃²	1	3	yes	—
23	C₃²⋊(C₇⋊C₉)	C₃²	1	3	yes	—
24	#10588036	C₃²	1	3	yes	—
25	#10588036	C₃²	1	3	yes	—
26	#10588035	C₃²	1	3	yes	—
27	#10588035	C₃²	1	3	yes	—
28	(C₇⋊C₉)⋊C₉	C₃²	1	36	yes	—
29	(C₇⋊C₉)⋊C₉	C₃²	1	18	yes	—
30	C₉×C₇⋊C₉	C₃²	1	3	yes	—
31	C₉×C₇⋊C₉	C₃²	1	2	yes	—
32	C₉×C₇⋊C₉	C₃²	1	1	yes	characteristic
33	C₉×C₇⋊C₉	C₃²	1	3	yes	—
34	C₉×C₇⋊C₉	C₃²	1	3	yes	—
35	C₉×C₇⋊C₉	C₃²	1	3	yes	—
36	C₃×#737	ΓL(1,𝔽₈)	1	1	yes	characteristic
37	#6900	—	7	3	no	—
38	#6899	—	7	6	no	—
39	#6896	—	7	9	no	—
40	#6894	—	7	6	no	—
41	C₉⋊H(3,𝔽₃)	—	7	3	no	—
42	C₉×3₋¹⁺²	—	7	9	no	—
43	#6887	—	7	1	no	—
44	#6887	—	7	1	no	—
45	C₃×C₉²	—	7	1	no	—
46	C₃³×C₇	C₃³	1	3	yes	—
47	C₃³×C₇	C₃³	1	1	yes	characteristic
48	C₇×3₋¹⁺²	—	3	6	no	—
49	C₇×3₋¹⁺²	—	3	9	no	—
50	C₇×3₋¹⁺²	—	3	9	no	—
51	C₇×H(3,𝔽₃)	—	3	3	no	—
52	C₃×C₇×C₉	—	3	9	no	—
53	C₃×C₇×C₉	3₋¹⁺²	1	9	yes	complemented
54	C₃×C₇×C₉	C₃³	1	6	yes	—
55	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
56	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
57	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
58	#4430	—	3	27	no	—
59	C₃×C₇⋊C₉	—	3	9	no	—
60	C₃×C₇⋊C₉	C₃³	1	6	yes	—
61	C₃×C₇⋊C₉	C₃³	1	9	yes	—
62	C₃×C₇⋊C₉	C₃³	1	9	yes	—
63	C₃×C₇⋊C₉	C₃³	1	3	yes	—
64	#737	—	3	9	no	—
65	C₃×3₋¹⁺²	—	7	9	no	—
66	C₃×3₋¹⁺²	C₃×ΓL(1,𝔽₈)	1	2	yes	—
67	C₃×3₋¹⁺²	C₃×ΓL(1,𝔽₈)	1	3	yes	—
68	C₃×3₋¹⁺²	C₃×ΓL(1,𝔽₈)	1	3	yes	—
69	C₃×H(3,𝔽₃)	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
70	C₃²×C₉	—	7	3	no	—
71	C₃²×C₉	C₃×ΓL(1,𝔽₈)	1	3	yes	—
72	C₃²×C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
73	C₉⋊C₉	—	7	36	no	—
74	C₉⋊C₉	—	7	18	no	—
75	C₉⋊C₉	—	7	3	no	—
76	C₉⋊C₉	—	7	3	no	—
77	C₉⋊C₉	—	7	3	no	—
78	C₉⋊C₉	—	7	3	no	—
79	C₃²⋊C₉	—	7	3	no	—
80	C₃²⋊C₉	—	7	3	no	—
81	C₃²⋊C₉	—	7	18	no	—
82	C₉²	—	7	3	no	—
83	C₉²	—	7	2	no	—
84	C₉²	—	7	1	no	—
85	C₉²	—	7	3	no	—
86	C₉²	—	7	3	no	—
87	C₉²	—	7	3	no	—
88	C₃²×C₇	—	3	3	no	—
89	C₃²×C₇	—	3	3	no	—
90	C₃²×C₇	—	3	9	no	—
91	C₃²×C₇	C₃×3₋¹⁺²	1	3	yes	—
92	C₃²×C₇	C₃⁴	1	1	yes	characteristic
93	C₇×C₉	—	3	6	no	—
94	C₇×C₉	C₃×3₋¹⁺²	1	3	yes	—
95	C₇×C₉	C₃×3₋¹⁺²	1	3	yes	—
96	C₇×C₉	C₃×3₋¹⁺²	1	3	yes	—
97	C₇⋊C₉	—	3	6	no	—
98	C₇⋊C₉	—	3	9	no	—
99	C₇⋊C₉	—	3	9	no	—
100	C₇⋊C₉	#737	1	9	yes	complemented
101	C₃³	C₃²×ΓL(1,𝔽₈)	1	3	yes	—
102	C₃³	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
103	3₋¹⁺²	—	3	6	no	—
104	3₋¹⁺²	—	3	9	no	—
105	3₋¹⁺²	—	3	9	no	—
106	3₋¹⁺²	—	21	27	no	—
107	H(3,𝔽₃)	—	3	3	no	—
108	C₃×C₉	—	3	9	no	—
109	C₃×C₉	—	7	3	no	—
110	C₃×C₉	—	7	6	no	—
111	C₃×C₉	—	7	9	no	—
112	C₃×C₉	—	7	9	no	—
113	C₃×C₉	—	21	9	no	—
114	C₃×C₉	#4430	1	9	yes	complemented
115	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	6	yes	—
116	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
117	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
118	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
119	C₃×C₇	—	3	3	no	—
120	C₃×C₇	—	9	3	no	—
121	C₃×C₇	C₃²×3₋¹⁺²	1	1	yes	characteristic
122	C₃×C₇	C₃×#737	1	3	yes	—
123	C₃²	—	3	3	no	—
124	C₃²	—	3	3	no	—
125	C₃²	—	3	9	no	—
126	C₃²	C₃×#4430	1	3	yes	—
127	C₃²	C₃³×ΓL(1,𝔽₈)	1	1	yes	characteristic
128	C₉	—	3	6	no	—
129	C₉	—	7	9	no	—
130	C₉	—	21	6	no	—
131	C₉	—	21	9	no	—
132	C₉	—	21	9	no	—
133	C₉	C₃×#4430	1	3	yes	—
134	C₉	C₃×#4430	1	3	yes	—
135	C₉	C₃×#4430	1	3	yes	—
136	C₇	#10624879	1	1	yes	characteristic, complemented, Sylow
137	C₃	—	3	3	no	—
138	C₃	—	9	3	no	—
139	C₃	C₃²×#4430	1	1	yes	characteristic
140	C₃	ΓL(1,𝔽₈)×#737	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13133593

C₃

yes

maximal, complemented

#13133586

C₃

yes

maximal, complemented

#13133572

C₃

yes

maximal, complemented

#13133560

C₃

yes

maximal, complemented

#13133548

C₃

yes

maximal

C₉×#4430

C₃

yes

maximal, complemented

#13133530

C₃

yes

maximal, characteristic, complemented

#13133530

C₃

yes

maximal, characteristic, complemented

C₃×C₉×C₇⋊C₉

C₃

yes

maximal, characteristic, complemented

C₃×C₇×#737

C₃

yes

maximal, characteristic

#10624879

—

maximal, Sylow

C₇×#737

—

C₃×C₇×3₋¹⁺²

C₃²

yes

—

C₃×C₇×3₋¹⁺²

C₃²

yes

—

C₃×C₇×3₋¹⁺²

C₃²

yes

—

C₃×C₇×H(3,𝔽₃)

C₃²

yes

characteristic

C₃²×C₇×C₉

C₃²

yes

—

C₃²×C₇×C₉

C₃²

yes

characteristic

C₃×#4430

C₃²

yes

—

C₃²×C₇⋊C₉

C₃²

yes

—

C₃²⋊(C₇⋊C₉)

C₃²

yes

—

C₃²⋊(C₇⋊C₉)

C₃²

yes

—

C₃²⋊(C₇⋊C₉)

C₃²

yes

—

#10588036

C₃²

yes

—

#10588036

C₃²

yes

—

#10588035

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×C₇⋊C₉

C₃²

yes

—

yes

—

—

—

—

C₉⋊H(3,𝔽₃)

—

C₉×3₋¹⁺²

—

#6887

—

#6887

—

C₃×C₉²

—

C₃³×C₇

C₃³

yes

—

C₃³×C₇

C₃³

yes

characteristic

C₇×3₋¹⁺²

—

C₇×3₋¹⁺²

—

C₇×3₋¹⁺²

—

C₇×H(3,𝔽₃)

—

C₃×C₇×C₉

—

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

#4430

—

C₃×C₇⋊C₉

—

C₃×C₇⋊C₉

C₃³

yes

—

C₃×C₇⋊C₉

C₃³

yes

—

C₃×C₇⋊C₉

C₃³

yes

—

C₃×C₇⋊C₉

C₃³

yes

—

#737

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

C₃×ΓL(1,𝔽₈)

yes

—

C₃×3₋¹⁺²

C₃×ΓL(1,𝔽₈)

yes

—

C₃×3₋¹⁺²

C₃×ΓL(1,𝔽₈)

yes

—

C₃×H(3,𝔽₃)

C₃×ΓL(1,𝔽₈)

yes

characteristic

C₃²×C₉

—

C₃²×C₉

C₃×ΓL(1,𝔽₈)

yes

—

C₃²×C₉

C₃×ΓL(1,𝔽₈)

yes

characteristic

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₉²

—

C₉²

—

C₉²

—

C₉²

—

C₉²

—

C₉²

—

C₃²×C₇

—

C₃²×C₇

—

C₃²×C₇

—

C₃²×C₇

C₃×3₋¹⁺²

yes

—

C₃²×C₇

C₃⁴

yes

characteristic

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

—

C₇⋊C₉

—

C₇⋊C₉

—

100

C₇⋊C₉

#737

yes

complemented

101

C₃³

C₃²×ΓL(1,𝔽₈)

yes

—

102

C₃³

C₃²×ΓL(1,𝔽₈)

yes

characteristic

103

3₋¹⁺²

—

104

3₋¹⁺²

—

105

3₋¹⁺²

—

106

3₋¹⁺²

—

107

H(3,𝔽₃)

—

108

C₃×C₉

—

109

C₃×C₉

—

110

C₃×C₉

—

111

C₃×C₉

—

112

C₃×C₉

—

113

C₃×C₉

—

114

C₃×C₉

#4430

yes

complemented

115

C₃×C₉

C₃²×ΓL(1,𝔽₈)

yes

—

116

C₃×C₉

C₃²×ΓL(1,𝔽₈)

yes

characteristic

117

C₃×C₉

C₃²×ΓL(1,𝔽₈)

yes

characteristic

118

C₃×C₉

C₃²×ΓL(1,𝔽₈)

yes

characteristic

119

C₃×C₇

—

120

C₃×C₇

—

121

C₃×C₇

C₃²×3₋¹⁺²

yes

characteristic

122

C₃×C₇

C₃×#737

yes

—

123

C₃²

—

124

C₃²

—

125

C₃²

—

126

C₃²

C₃×#4430

yes

—

127

C₃²

C₃³×ΓL(1,𝔽₈)

yes

characteristic

128

C₉

—

129

C₉

—

130

C₉

—

131

C₉

—

132

C₉

—

133

C₉

C₃×#4430

yes

—

134

C₉

C₃×#4430

yes

—

135

C₉

C₃×#4430

yes

—

136

C₇

#10624879

yes

characteristic, complemented, Sylow

137

C₃

—

138

C₃

—

139

C₃

C₃²×#4430

yes

characteristic

140

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	C₃×C₇×#737	C₃
hypercenter	C₃×#737	ΓL(1,𝔽₈)
hypocenter	C₇	#10624879
LCS	G ▷ C₃²×C₇ ▷ C₇
UCS	C₁ ◁ C₃×C₉ ◁ C₃×#737

subgroup

G/H

center

C₃×C₉

C₃²×ΓL(1,𝔽₈)

commutator, socle

C₃²×C₇

C₃⁴

Frattini

C₃²

C₃³×ΓL(1,𝔽₈)

Fitting

C₃×C₇×#737

C₃

C₇

G ▷ C₃²×C₇ ▷ C₇

C₁ ◁ C₃×C₉ ◁ C₃×#737

N	H ≅ G/N	type
1. #13133593	C₃	semidirect
2. #13133586	C₃	semidirect
3. #13133572	C₃	semidirect
4. #13133560	C₃	semidirect
6. C₉×#4430	C₃	semidirect
7. #13133530	C₃	semidirect
8. #13133530	C₃	semidirect
9. C₃×C₉×C₇⋊C₉	C₃	semidirect
53. C₃×C₇×C₉	3₋¹⁺²	semidirect
100. C₇⋊C₉	#737	semidirect
114. C₃×C₉	#4430	semidirect
136. C₇	#10624879	semidirect

H ≅ G/N

type

1. #13133593

C₃

semidirect

2. #13133586

C₃

semidirect

3. #13133572

C₃

semidirect

4. #13133560

C₃

semidirect

6. C₉×#4430

C₃

semidirect

7. #13133530

C₃

semidirect

8. #13133530

C₃

semidirect

9. C₃×C₉×C₇⋊C₉

C₃

semidirect

53. C₃×C₇×C₉

3₋¹⁺²

semidirect

100. C₇⋊C₉

#737

semidirect

114. C₃×C₉

#4430

semidirect

136. C₇

#10624879

semidirect

Subgroups — #19103248

Conjugacy classes of subgroups

Complements