Group #19103254 — subgroups

Subgroups — #19103254

Order 5103.

758 conjugacy classes of subgroups; only the 310 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 310 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	#13133595	C₃	1	3	yes	maximal, complemented
3	#13133587	C₃	1	6	yes	maximal, complemented
4	#13133573	C₃	1	9	yes	maximal, complemented
5	#13133564	C₃	1	6	yes	maximal, complemented
6	#13133551	C₃	1	3	yes	maximal
7	C₉×#4428	C₃	1	9	yes	maximal, complemented
8	#13133530	C₃	1	2	yes	maximal, complemented
9	C₃×C₇×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
10	#10624879	—	7	1	no	maximal, Sylow
11	C₃²×C₇×C₉	C₃²	1	3	yes	—
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	#10588061	—	3	9	no	—
16	C₃×#4428	C₃²	1	9	yes	—
17	C₃×#4428	C₃²	1	3	yes	—
18	C₃×#4427	C₃²	1	3	yes	—
19	C₃×C₉×ΓL(1,𝔽₈)	C₃²	1	3	yes	—
20	C₇×C₉²	C₃²	1	3	yes	—
21	C₇×C₉²	C₃²	1	2	yes	—
22	C₇×C₉²	C₃²	1	1	yes	characteristic
23	C₇×C₉²	C₃²	1	3	yes	—
24	C₃²⋊(C₇⋊C₉)	C₃²	1	6	yes	—
25	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	18	yes	—
26	#10588036	C₃²	1	18	yes	—
27	#10588036	C₃²	1	6	yes	—
28	#10588035	C₃²	1	6	yes	—
29	(C₇⋊C₉)⋊C₉	C₃²	1	36	yes	—
30	C₉×C₇⋊C₉	C₃²	1	6	yes	—
31	C₃×#737	—	7	1	no	—
32	#6900	—	7	3	no	—
33	#6899	—	7	6	no	—
34	#6896	—	7	9	no	—
35	#6894	—	7	6	no	—
36	C₉⋊H(3,𝔽₃)	—	7	3	no	—
37	C₉×3₋¹⁺²	—	7	9	no	—
38	#6887	—	7	2	no	—
39	C₃×C₉²	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
40	C₃³×C₇	C₃³	1	1	yes	characteristic
41	C₃²×ΓL(1,𝔽₈)	C₃³	1	3	yes	—
42	C₃×C₇×C₉	—	3	9	no	—
43	C₃×C₇×C₉	3₋¹⁺²	1	9	yes	complemented
44	C₃×C₇×C₉	C₃³	1	6	yes	—
45	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
46	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
47	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
48	C₃×C₇×C₉	C₃³	1	3	yes	—
49	C₇⋊H(3,𝔽₃)	—	3	3	no	—
50	#4430	—	3	6	no	—
51	C₃×C₇⋊C₉	C₃³	1	18	yes	—
52	C₃×C₇⋊C₉	C₃³	1	6	yes	—
53	#4428	—	3	9	no	—
54	#4428	—	3	27	no	—
55	#4427	—	3	9	no	—
56	C₉×ΓL(1,𝔽₈)	—	3	9	no	—
57	#737	—	21	9	no	—
58	C₃×3₋¹⁺²	—	7	2	no	—
59	C₃×3₋¹⁺²	—	7	3	no	—
60	C₃×3₋¹⁺²	—	7	3	no	—
61	C₃×3₋¹⁺²	—	7	9	no	—
62	C₃×H(3,𝔽₃)	—	7	1	no	—
63	C₃²×C₉	—	7	3	no	—
64	C₃²×C₉	C₃×ΓL(1,𝔽₈)	1	3	yes	—
65	C₃²×C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
66	C₉⋊C₉	—	7	36	no	—
67	C₉⋊C₉	—	7	6	no	—
68	C₉⋊C₉	—	7	6	no	—
69	C₉⋊C₉	—	7	18	no	—
70	C₃²⋊C₉	—	7	6	no	—
71	C₃²⋊C₉	—	7	18	no	—
72	C₉²	—	7	6	no	—
73	C₉²	C₃×ΓL(1,𝔽₈)	1	3	yes	—
74	C₉²	C₃×ΓL(1,𝔽₈)	1	2	yes	—
75	C₉²	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
76	C₉²	C₃×ΓL(1,𝔽₈)	1	3	yes	—
77	C₃²×C₇	—	3	3	no	—
78	C₃²×C₇	C₃×3₋¹⁺²	1	3	yes	—
79	C₃²×C₇	C₃⁴	1	1	yes	characteristic
80	C₃×ΓL(1,𝔽₈)	—	3	3	no	—
81	C₃×ΓL(1,𝔽₈)	—	3	9	no	—
82	C₇×C₉	—	3	6	no	—
83	C₇×C₉	C₃×3₋¹⁺²	1	3	yes	—
84	C₇×C₉	C₃×3₋¹⁺²	1	3	yes	—
85	C₇×C₉	C₃×3₋¹⁺²	1	3	yes	—
86	C₇×C₉	#737	1	9	yes	complemented
87	C₇⋊C₉	—	3	6	no	—
88	C₇⋊C₉	—	3	18	no	—
89	C₃³	—	7	3	no	—
90	C₃³	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
91	3₋¹⁺²	—	21	6	no	—
92	3₋¹⁺²	—	21	9	no	—
93	3₋¹⁺²	—	21	9	no	—
94	3₋¹⁺²	—	21	27	no	—
95	H(3,𝔽₃)	—	21	3	no	—
96	C₃×C₉	—	3	9	no	—
97	C₃×C₉	—	7	18	no	—
98	C₃×C₉	—	7	6	no	—
99	C₃×C₉	—	21	9	no	—
100	C₃×C₉	#4428	1	9	yes	complemented
101	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	6	yes	—
102	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
103	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
104	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	3	yes	—
105	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
106	C₃×C₇	—	3	3	no	—
107	C₃×C₇	C₃²×3₋¹⁺²	1	1	yes	characteristic
108	C₃×C₇	C₃×#737	1	3	yes	—
109	ΓL(1,𝔽₈)	—	9	3	no	—
110	C₃²	—	3	3	no	—
111	C₃²	—	21	3	no	—
112	C₃²	—	21	9	no	—
113	C₃²	C₃×#4428	1	3	yes	—
114	C₃²	C₃³×ΓL(1,𝔽₈)	1	1	yes	characteristic
115	C₉	—	3	6	no	—
116	C₉	—	21	6	no	—
117	C₉	—	21	18	no	—
118	C₉	C₃×#4428	1	3	yes	—
119	C₉	C₃×#4428	1	3	yes	—
120	C₉	C₃×#4428	1	3	yes	—
121	C₉	#10588061	1	9	yes	complemented
122	C₇	#10624879	1	1	yes	characteristic, complemented, Sylow
123	C₃	—	3	3	no	—
124	C₃	—	63	3	no	—
125	C₃	C₃²×#4428	1	1	yes	characteristic
126	C₃	C₃×#10588061	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×#10588061

C₃

yes

maximal, characteristic

#13133595

C₃

yes

maximal, complemented

#13133587

C₃

yes

maximal, complemented

#13133573

C₃

yes

maximal, complemented

#13133564

C₃

yes

maximal, complemented

#13133551

C₃

yes

maximal

C₉×#4428

C₃

yes

maximal, complemented

#13133530

C₃

yes

maximal, complemented

C₃×C₇×C₉²

C₃

yes

maximal, characteristic, complemented

#10624879

—

maximal, Sylow

C₃²×C₇×C₉

C₃²

yes

—

C₃²×C₇×C₉

C₃²

yes

characteristic

C₃×C₇⋊H(3,𝔽₃)

C₃²

yes

characteristic

C₃×#4430

C₃²

yes

—

#10588061

—

C₃×#4428

C₃²

yes

—

C₃×#4428

C₃²

yes

—

C₃×#4427

C₃²

yes

—

C₃×C₉×ΓL(1,𝔽₈)

C₃²

yes

—

C₇×C₉²

C₃²

yes

—

C₇×C₉²

C₃²

yes

—

C₇×C₉²

C₃²

yes

characteristic

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

—

C₉×C₇⋊C₉

C₃²

yes

—

—

—

—

—

—

C₉⋊H(3,𝔽₃)

—

C₉×3₋¹⁺²

—

#6887

—

C₃×C₉²

ΓL(1,𝔽₈)

yes

characteristic, complemented

C₃³×C₇

C₃³

yes

characteristic

C₃²×ΓL(1,𝔽₈)

C₃³

yes

—

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

C₃×C₇×C₉

C₃³

yes

—

C₇⋊H(3,𝔽₃)

—

#4430

—

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

C₃×ΓL(1,𝔽₈)

yes

—

C₃²×C₉

C₃×ΓL(1,𝔽₈)

yes

characteristic

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₉²

—

C₉²

C₃×ΓL(1,𝔽₈)

yes

—

C₉²

C₃×ΓL(1,𝔽₈)

yes

—

C₉²

C₃×ΓL(1,𝔽₈)

yes

characteristic

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

#737

yes

complemented

C₇⋊C₉

—

C₇⋊C₉

—

C₃³

—

C₃³

C₃²×ΓL(1,𝔽₈)

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

H(3,𝔽₃)

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

100

C₃×C₉

#4428

yes

complemented

101

C₃×C₉

C₃²×ΓL(1,𝔽₈)

yes

—

102

C₃×C₉

C₃²×ΓL(1,𝔽₈)

yes

characteristic

103

C₃×C₉

C₃²×ΓL(1,𝔽₈)

yes

characteristic

104

C₃×C₉

C₃²×ΓL(1,𝔽₈)

yes

—

105

C₃×C₉

C₃²×ΓL(1,𝔽₈)

yes

characteristic

106

C₃×C₇

—

107

C₃×C₇

C₃²×3₋¹⁺²

yes

characteristic

108

C₃×C₇

C₃×#737

yes

—

109

ΓL(1,𝔽₈)

—

110

C₃²

—

111

C₃²

—

112

C₃²

—

113

C₃²

C₃×#4428

yes

—

114

C₃²

C₃³×ΓL(1,𝔽₈)

yes

characteristic

115

C₉

—

116

C₉

—

117

C₉

—

118

C₉

C₃×#4428

yes

—

119

C₉

C₃×#4428

yes

—

120

C₉

C₃×#4428

yes

—

121

C₉

#10588061

yes

complemented

122

C₇

#10624879

yes

characteristic, complemented, Sylow

123

C₃

—

124

C₃

—

125

C₃

C₃²×#4428

yes

characteristic

126

C₃

C₃×#10588061

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×C₉²	C₃
hypercenter	C₃×C₉²	ΓL(1,𝔽₈)
hypocenter	C₇	#10624879
LCS	G ▷ C₃²×C₇ ▷ C₇
UCS	C₁ ◁ C₃×C₉ ◁ C₃×C₉²

subgroup

G/H

center

C₃×C₉

C₃²×ΓL(1,𝔽₈)

commutator, socle

C₃²×C₇

C₃⁴

Frattini

C₃²

C₃³×ΓL(1,𝔽₈)

Fitting

C₃×C₇×C₉²

C₃

C₃×C₉²

C₇

G ▷ C₃²×C₇ ▷ C₇

C₁ ◁ C₃×C₉ ◁ C₃×C₉²

N	H ≅ G/N	type
2. #13133595	C₃	semidirect
3. #13133587	C₃	semidirect
4. #13133573	C₃	semidirect
5. #13133564	C₃	semidirect
7. C₉×#4428	C₃	semidirect
8. #13133530	C₃	semidirect
9. C₃×C₇×C₉²	C₃	semidirect
39. C₃×C₉²	ΓL(1,𝔽₈)	semidirect
43. C₃×C₇×C₉	3₋¹⁺²	semidirect
86. C₇×C₉	#737	semidirect
100. C₃×C₉	#4428	semidirect
121. C₉	#10588061	semidirect
122. C₇	#10624879	semidirect

H ≅ G/N

type

2. #13133595

C₃

semidirect

3. #13133587

C₃

semidirect

4. #13133573

C₃

semidirect

5. #13133564

C₃

semidirect

7. C₉×#4428

C₃

semidirect

8. #13133530

C₃

semidirect

9. C₃×C₇×C₉²

C₃

semidirect

39. C₃×C₉²

ΓL(1,𝔽₈)

semidirect

43. C₃×C₇×C₉

3₋¹⁺²

semidirect

86. C₇×C₉

#737

semidirect

100. C₃×C₉

#4428

semidirect

121. C₉

#10588061

semidirect

122. C₇

#10624879

semidirect

Subgroups — #19103254

Conjugacy classes of subgroups

Complements