Group #19100261 — subgroups

Subgroups — C₇×#10624852 #19100261

Order 5103.

188 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 68 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	C₇×#6913	C₃	1	2	yes	maximal, complemented
2	C₇×#6912	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇×#6900	C₃	1	1	yes	maximal, characteristic, complemented
4	C₇×#6883	C₃	1	2	yes	maximal, complemented
5	C₇×#6882	C₃	1	2	yes	maximal, complemented
6	C₇×#6882	C₃	1	1	yes	maximal, characteristic, complemented
7	C₇×#6881	C₃	1	1	yes	maximal, characteristic, complemented
8	C₇×#6880	C₃	1	1	yes	maximal, characteristic, complemented
9	C₇×#6878	C₃	1	2	yes	maximal, complemented
10	#10624852	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₇×#737	—	3	2	no	—
12	C₃×C₇×3₋¹⁺²	—	3	1	no	—
13	C₃×C₇×3₋¹⁺²	—	3	1	no	—
14	C₃×C₇×3₋¹⁺²	C₃²	1	1	yes	characteristic
15	C₇×#733	—	3	2	no	—
16	C₇×#733	C₃²	1	2	yes	—
17	C₇×#733	C₃²	1	2	yes	—
18	C₇×#733	C₃²	1	1	yes	characteristic
19	C₇×#733	C₃²	1	2	yes	—
20	C₇×#732	C₃²	1	2	yes	—
21	C₇×#731	—	3	2	no	—
22	C₇×AΣL(1,𝔽₂₇)	—	3	2	no	—
23	C₇×C₉⋊C₉	—	3	2	no	—
24	C₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
25	C₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
26	C₇×C₉²	C₃²	1	1	yes	characteristic
27	#6913	C₃×C₇	1	2	yes	complemented
28	#6912	C₃×C₇	1	1	yes	characteristic, complemented
29	#6900	C₃×C₇	1	1	yes	characteristic, complemented
30	#6883	C₃×C₇	1	2	yes	complemented
31	#6882	C₃×C₇	1	2	yes	complemented
32	#6882	C₃×C₇	1	1	yes	characteristic, complemented
33	#6881	C₃×C₇	1	1	yes	characteristic, complemented
34	#6880	C₃×C₇	1	1	yes	characteristic, complemented
35	#6878	C₃×C₇	1	2	yes	complemented
36	C₃³×C₇	H(3,𝔽₃)	1	1	yes	characteristic
37	C₇×3₋¹⁺²	—	3	2	no	—
38	C₇×3₋¹⁺²	—	3	2	no	—
39	C₇×3₋¹⁺²	—	3	2	no	—
40	C₇×3₋¹⁺²	—	3	1	no	—
41	C₇×3₋¹⁺²	—	9	1	no	—
42	C₇×3₋¹⁺²	—	9	3	no	—
43	C₇×3₋¹⁺²	—	9	4	no	—
44	C₇×3₋¹⁺²	—	9	2	no	—
45	C₇×H(3,𝔽₃)	—	3	2	no	—
46	C₃×C₇×C₉	—	3	1	no	—
47	C₃×C₇×C₉	—	3	1	no	—
48	C₃×C₇×C₉	—	3	1	no	—
49	C₃×C₇×C₉	—	9	2	no	—
50	C₃×C₇×C₉	—	9	1	no	—
51	C₃×C₇×C₉	H(3,𝔽₃)	1	2	yes	—
52	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
53	#737	—	3	2	no	—
54	C₃×3₋¹⁺²	—	3	1	no	—
55	C₃×3₋¹⁺²	—	3	1	no	—
56	C₃×3₋¹⁺²	C₃²×C₇	1	1	yes	characteristic
57	#733	—	3	2	no	—
58	#733	C₃²×C₇	1	2	yes	—
59	#733	C₃²×C₇	1	1	yes	characteristic
60	#733	C₃²×C₇	1	2	yes	—
61	#733	C₃²×C₇	1	2	yes	—
62	#732	C₃²×C₇	1	2	yes	—
63	#731	—	3	2	no	—
64	AΣL(1,𝔽₂₇)	—	3	2	no	—
65	C₉⋊C₉	—	3	2	no	—
66	C₉⋊C₉	C₃²×C₇	1	1	yes	characteristic
67	C₉⋊C₉	C₃²×C₇	1	1	yes	characteristic
68	C₉²	C₃²×C₇	1	1	yes	characteristic
69	C₃²×C₇	—	3	1	no	—
70	C₃²×C₇	—	9	1	no	—
71	C₃²×C₇	—	9	2	no	—
72	C₃²×C₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
73	C₇×C₉	—	3	3	no	—
74	C₇×C₉	—	3	2	no	—
75	C₇×C₉	—	3	1	no	—
76	C₇×C₉	—	9	1	no	—
77	C₇×C₉	—	9	1	no	—
78	C₇×C₉	—	9	2	no	—
79	C₇×C₉	—	9	2	no	—
80	C₇×C₉	—	9	2	no	—
81	C₇×C₉	—	9	1	no	—
82	C₃³	C₇×H(3,𝔽₃)	1	1	yes	characteristic
83	3₋¹⁺²	—	3	2	no	—
84	3₋¹⁺²	—	3	2	no	—
85	3₋¹⁺²	—	3	2	no	—
86	3₋¹⁺²	—	3	1	no	—
87	3₋¹⁺²	—	9	1	no	—
88	3₋¹⁺²	—	9	3	no	—
89	3₋¹⁺²	—	9	4	no	—
90	3₋¹⁺²	—	9	2	no	—
91	H(3,𝔽₃)	—	3	2	no	—
92	C₃×C₉	—	3	1	no	—
93	C₃×C₉	—	3	1	no	—
94	C₃×C₉	—	3	1	no	—
95	C₃×C₉	—	9	2	no	—
96	C₃×C₉	—	9	1	no	—
97	C₃×C₉	C₇×H(3,𝔽₃)	1	2	yes	—
98	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
99	C₃×C₇	—	3	1	no	—
100	C₃×C₇	—	9	1	no	—
101	C₃×C₇	—	27	2	no	—
102	C₃×C₇	#6911	1	1	yes	characteristic
103	C₃²	—	3	1	no	—
104	C₃²	—	9	1	no	—
105	C₃²	—	9	2	no	—
106	C₃²	C₃×C₇×H(3,𝔽₃)	1	1	yes	characteristic
107	C₉	—	3	3	no	—
108	C₉	—	3	2	no	—
109	C₉	—	3	1	no	—
110	C₉	—	9	1	no	—
111	C₉	—	9	1	no	—
112	C₉	—	9	2	no	—
113	C₉	—	9	2	no	—
114	C₉	—	9	2	no	—
115	C₉	—	9	1	no	—
116	C₇	#10624852	1	1	yes	characteristic, direct product factor, Sylow
117	C₃	—	3	1	no	—
118	C₃	—	9	1	no	—
119	C₃	—	27	2	no	—
120	C₃	C₇×#6911	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₇×#6913

C₃

yes

maximal, complemented

C₇×#6912

C₃

yes

maximal, characteristic, complemented

C₇×#6900

C₃

yes

maximal, characteristic, complemented

C₇×#6883

C₃

yes

maximal, complemented

C₇×#6882

C₃

yes

maximal, complemented

C₇×#6882

C₃

yes

maximal, characteristic, complemented

C₇×#6881

C₃

yes

maximal, characteristic, complemented

C₇×#6880

C₃

yes

maximal, characteristic, complemented

C₇×#6878

C₃

yes

maximal, complemented

#10624852

C₇

yes

maximal, characteristic, direct product factor, Sylow

C₇×#737

—

C₃×C₇×3₋¹⁺²

—

C₃×C₇×3₋¹⁺²

—

C₃×C₇×3₋¹⁺²

C₃²

yes

characteristic

C₇×#733

—

C₇×#733

C₃²

yes

—

C₇×#733

C₃²

yes

—

C₇×#733

C₃²

yes

characteristic

C₇×#733

C₃²

yes

—

C₇×#732

C₃²

yes

—

C₇×#731

—

C₇×AΣL(1,𝔽₂₇)

—

C₇×C₉⋊C₉

—

C₇×C₉⋊C₉

C₃²

yes

characteristic

C₇×C₉⋊C₉

C₃²

yes

characteristic

C₇×C₉²

C₃²

yes

characteristic

#6913

C₃×C₇

yes

complemented

#6912

C₃×C₇

yes

characteristic, complemented

#6900

C₃×C₇

yes

characteristic, complemented

#6883

C₃×C₇

yes

complemented

#6882

C₃×C₇

yes

complemented

#6882

C₃×C₇

yes

characteristic, complemented

#6881

C₃×C₇

yes

characteristic, complemented

#6880

C₃×C₇

yes

characteristic, complemented

#6878

C₃×C₇

yes

complemented

C₃³×C₇

H(3,𝔽₃)

yes

characteristic

C₇×3₋¹⁺²

—

C₇×3₋¹⁺²

—

C₇×3₋¹⁺²

—

C₇×3₋¹⁺²

—

C₇×3₋¹⁺²

—

C₇×3₋¹⁺²

—

C₇×3₋¹⁺²

—

C₇×3₋¹⁺²

—

C₇×H(3,𝔽₃)

—

C₃×C₇×C₉

—

C₃×C₇×C₉

—

C₃×C₇×C₉

—

C₃×C₇×C₉

—

C₃×C₇×C₉

—

C₃×C₇×C₉

H(3,𝔽₃)

yes

—

C₃×C₇×C₉

C₃³

yes

characteristic

#737

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

C₃²×C₇

yes

characteristic

#733

—

#733

C₃²×C₇

yes

—

#733

C₃²×C₇

yes

characteristic

#733

C₃²×C₇

yes

—

#733

C₃²×C₇

yes

—

#732

C₃²×C₇

yes

—

#731

—

AΣL(1,𝔽₂₇)

—

C₉⋊C₉

—

C₉⋊C₉

C₃²×C₇

yes

characteristic

C₉⋊C₉

C₃²×C₇

yes

characteristic

C₉²

C₃²×C₇

yes

characteristic

C₃²×C₇

—

C₃²×C₇

—

C₃²×C₇

—

C₃²×C₇

C₃×H(3,𝔽₃)

yes

characteristic

C₇×C₉

—

C₇×C₉

—

C₇×C₉

—

C₇×C₉

—

C₇×C₉

—

C₇×C₉

—

C₇×C₉

—

C₇×C₉

—

C₇×C₉

—

C₃³

C₇×H(3,𝔽₃)

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

H(3,𝔽₃)

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₇×H(3,𝔽₃)

yes

—

C₃×C₉

C₃³×C₇

yes

characteristic

C₃×C₇

—

100

C₃×C₇

—

101

C₃×C₇

—

102

C₃×C₇

#6911

yes

characteristic

103

C₃²

—

104

C₃²

—

105

C₃²

—

106

C₃²

C₃×C₇×H(3,𝔽₃)

yes

characteristic

107

C₉

—

108

C₉

—

109

C₉

—

110

C₉

—

111

C₉

—

112

C₉

—

113

C₉

—

114

C₉

—

115

C₉

—

116

C₇

#10624852

yes

characteristic, direct product factor, Sylow

117

C₃

—

118

C₃

—

119

C₃

—

120

C₃

C₇×#6911

yes

characteristic

	subgroup	G/H
center, socle	C₃×C₇	#6911
commutator, Frattini	C₃×C₉	C₃³×C₇
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₇ ◁ C₃²×C₇ ◁ C₃×C₇×3₋¹⁺² ◁ G

subgroup

G/H

center, socle

C₃×C₇

#6911

commutator, Frattini

C₃×C₉

C₃³×C₇

LCS

G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁

UCS

C₁ ◁ C₃×C₇ ◁ C₃²×C₇ ◁ C₃×C₇×3₋¹⁺² ◁ G

N	H ≅ G/N	type
1. C₇×#6913	C₃	semidirect
2. C₇×#6912	C₃	semidirect
3. C₇×#6900	C₃	semidirect
4. C₇×#6883	C₃	semidirect
5. C₇×#6882	C₃	semidirect
6. C₇×#6882	C₃	semidirect
7. C₇×#6881	C₃	semidirect
8. C₇×#6880	C₃	semidirect
9. C₇×#6878	C₃	semidirect
10. #10624852	C₇	direct (N × H)
27. #6913	C₃×C₇	semidirect
28. #6912	C₃×C₇	semidirect
29. #6900	C₃×C₇	semidirect
30. #6883	C₃×C₇	semidirect
31. #6882	C₃×C₇	semidirect
32. #6882	C₃×C₇	semidirect
33. #6881	C₃×C₇	semidirect
34. #6880	C₃×C₇	semidirect
35. #6878	C₃×C₇	semidirect
116. C₇	#10624852	direct (N × H)

H ≅ G/N

type

1. C₇×#6913

C₃

semidirect

2. C₇×#6912

C₃

semidirect

3. C₇×#6900

C₃

semidirect

4. C₇×#6883

C₃

semidirect

5. C₇×#6882

C₃

semidirect

6. C₇×#6882

C₃

semidirect

7. C₇×#6881

C₃

semidirect

8. C₇×#6880

C₃

semidirect

9. C₇×#6878

C₃

semidirect

10. #10624852

C₇

direct (N × H)

27. #6913

C₃×C₇

semidirect

28. #6912

C₃×C₇

semidirect

29. #6900

C₃×C₇

semidirect

30. #6883

C₃×C₇

semidirect

31. #6882

C₃×C₇

semidirect

32. #6882

C₃×C₇

semidirect

33. #6881

C₃×C₇

semidirect

34. #6880

C₃×C₇

semidirect

35. #6878

C₃×C₇

semidirect

116. C₇

#10624852

direct (N × H)

Subgroups — C₇×#10624852 #19100261

Conjugacy classes of subgroups

Complements

Subgroups — C7×#10624852 #19100261

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624852 #19100261