Group #14269411 — subgroups

Subgroups — #14269411

Order 1824.

136 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 40 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	D₃×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#11744926	C₂	1	1	yes	maximal, characteristic, complemented
3	#11744891	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64525	C₂	1	1	yes	maximal, characteristic, complemented
5	#11744825	C₂	1	1	yes	maximal, characteristic, complemented
6	#11744818	C₂	1	1	yes	maximal, characteristic, complemented
7	#11744816	C₂	1	1	yes	maximal, characteristic, complemented
8	#10597378	—	3	1	no	maximal, Hall
9	C₂²×D₃×C₁₉	—	2	1	no	—
10	C₃×D₄×C₁₉	C₂²	1	1	yes	characteristic
11	Dic₁₁₄	C₂²	1	1	yes	characteristic, complemented
12	C₁₉×#67	—	2	1	no	—
13	C₁₉×D₁₂	C₂²	1	1	yes	characteristic
14	C₄×D₃×C₁₉	C₂²	1	1	yes	characteristic
15	C₃×D₇₆	C₂²	1	1	yes	characteristic, complemented
16	#90695	—	2	1	no	—
17	Dic₃×D₁₉	—	2	1	no	—
18	C₃⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
20	C₂×D₄×C₁₉	—	3	1	no	—
21	#64541	—	3	1	no	—
22	#64526	—	3	1	no	—
23	#64526	—	3	1	no	—
24	#64525	—	3	1	no	—
25	#64525	D₃	1	1	yes	characteristic, complemented
26	#64520	—	3	1	no	—
27	C₂²×C₃×C₁₉	—	2	1	no	—
28	C₂×D₃×C₁₉	—	2	1	no	—
29	C₂×D₃×C₁₉	—	4	2	no	—
30	C₂×D₃×C₁₉	D₄	1	1	yes	characteristic
31	C₂×C₃×D₁₉	—	2	1	no	—
32	C₃×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	Dic₅₇	—	2	1	no	—
34	Dic₃×C₁₉	D₄	1	1	yes	characteristic
35	C₂³×C₁₉	—	6	1	no	—
36	D₄×C₁₉	—	3	1	no	—
37	D₄×C₁₉	—	6	1	no	—
38	D₄×C₁₉	C₂×D₃	1	1	yes	characteristic
39	C₂×C₄×C₁₉	—	3	1	no	—
40	C₂²⋊D₁₉	—	6	1	no	—
41	D₇₆	C₂×D₃	1	1	yes	characteristic, complemented
42	C₄×D₁₉	—	6	1	no	—
43	Dic₃₈	—	3	1	no	—
44	C₁₉⋊C₈	—	3	1	no	—
45	C₁₉⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
46	C₂×C₃×C₁₉	—	4	1	no	—
47	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₃×D₁₉	—	4	1	no	—
49	D₃×C₁₉	—	2	1	no	—
50	D₃×C₁₉	—	4	1	no	—
51	#911	—	19	1	no	maximal, Hall
52	C₂²×C₁₉	—	2	1	no	—
53	C₂²×C₁₉	—	3	1	no	—
54	C₂²×C₁₉	—	6	1	no	—
55	C₂²×C₁₉	—	12	2	no	—
56	C₂×D₁₉	—	2	1	no	—
57	C₄×C₁₉	—	3	1	no	—
58	C₄×C₁₉	C₂²×D₃	1	1	yes	characteristic
59	Dic₁₉	—	6	1	no	—
60	C₃×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Hall
61	#237	—	19	1	no	—
62	D₃×D₄	D₁₉	1	1	yes	characteristic, complemented
63	C₃×D₈	—	19	1	no	—
64	#214	—	19	1	no	—
65	#213	—	19	1	no	—
66	#204	—	19	1	no	—
67	ΓL(1,𝔽₂₅)	—	19	1	no	—
68	C₂×C₁₉	—	4	1	no	—
69	C₂×C₁₉	—	6	1	no	—
70	C₂×C₁₉	—	12	1	no	—
71	C₂×C₁₉	D₃×D₄	1	1	yes	characteristic
72	D₁₉	—	4	1	no	—
73	AGL(1,ℤ/8)	—	57	1	no	Sylow
74	C₂²×D₃	—	2	1	no	—
75	C₃×D₄	—	19	1	no	—
76	C₃×D₄	C₂×D₁₉	1	1	yes	characteristic
77	#67	—	2	1	no	—
78	#67	—	38	1	no	—
79	C₂×Dic₃	—	38	1	no	—
80	D₁₂	C₂×D₁₉	1	1	yes	characteristic
81	C₄×D₃	C₂×D₁₉	1	1	yes	characteristic
82	Dic₆	—	19	1	no	—
83	C₃×C₈	—	19	1	no	—
84	C₃⋊C₈	—	19	1	no	—
85	C₁₉	#911	1	1	yes	characteristic, complemented, Sylow
86	#41	—	57	1	no	—
87	C₂×D₄	—	3	1	no	—
88	SD₁₆	—	57	1	no	—
89	SD₁₆	—	57	1	no	—
90	D₈	—	19	1	no	—
91	D₈	—	57	1	no	—
92	M₁₆	—	57	1	no	—
93	C₂²×C₃	—	2	1	no	—
94	C₂²×C₃	—	38	1	no	—
95	C₂×D₃	—	2	1	no	—
96	C₂×D₃	—	4	2	no	—
97	C₂×D₃	C₂²⋊D₁₉	1	1	yes	characteristic
98	C₃×C₄	C₂²×D₁₉	1	1	yes	characteristic
99	Dic₃	—	38	1	no	—
100	Dic₃	C₂²⋊D₁₉	1	1	yes	characteristic
101	C₂³	—	6	1	no	—
102	Q₈	—	57	1	no	—
103	D₄	—	3	1	no	—
104	D₄	—	6	1	no	—
105	D₄	—	19	1	no	—
106	D₄	—	114	1	no	—
107	D₄	D₃×D₁₉	1	1	yes	characteristic
108	C₂×C₄	—	3	1	no	—
109	C₂×C₄	—	114	1	no	—
110	C₈	—	19	1	no	—
111	C₈	—	57	1	no	—
112	C₂×C₃	—	4	1	no	—
113	C₂×C₃	—	76	1	no	—
114	C₂×C₃	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
115	D₃	—	2	1	no	—
116	D₃	—	4	1	no	—
117	C₂²	—	2	1	no	—
118	C₂²	—	3	1	no	—
119	C₂²	—	6	1	no	—
120	C₂²	—	12	2	no	—
121	C₂²	—	38	1	no	—
122	C₄	—	3	1	no	—
123	C₄	—	114	1	no	—
124	C₄	C₂×D₃×D₁₉	1	1	yes	characteristic
125	C₃	#10597378	1	1	yes	characteristic, complemented, Sylow
126	C₂	—	4	1	no	—
127	C₂	—	6	1	no	—
128	C₂	—	12	1	no	—
129	C₂	—	76	1	no	—
130	C₂	D₃×C₂²⋊D₁₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₃×D₄×C₁₉

C₂

yes

maximal, characteristic, complemented

#11744926

C₂

yes

maximal, characteristic, complemented

#11744891

C₂

yes

maximal, characteristic, complemented

C₃×#64525

C₂

yes

maximal, characteristic, complemented

#11744825

C₂

yes

maximal, characteristic, complemented

#11744818

C₂

yes

maximal, characteristic, complemented

#11744816

C₂

yes

maximal, characteristic, complemented

#10597378

—

maximal, Hall

C₂²×D₃×C₁₉

—

C₃×D₄×C₁₉

C₂²

yes

characteristic

Dic₁₁₄

C₂²

yes

characteristic, complemented

C₁₉×#67

—

C₁₉×D₁₂

C₂²

yes

characteristic

C₄×D₃×C₁₉

C₂²

yes

characteristic

C₃×D₇₆

C₂²

yes

characteristic, complemented

#90695

—

Dic₃×D₁₉

—

C₃⋊(C₁₉⋊C₈)

C₂²

yes

characteristic, complemented

C₃×C₁₉⋊C₈

C₂²

yes

characteristic, complemented

C₂×D₄×C₁₉

—

—

—

—

—

D₃

yes

characteristic, complemented

#64520

—

C₂²×C₃×C₁₉

—

C₂×D₃×C₁₉

—

C₂×D₃×C₁₉

—

C₂×D₃×C₁₉

D₄

yes

characteristic

C₂×C₃×D₁₉

—

C₃×C₄×C₁₉

C₂³

yes

characteristic

Dic₅₇

—

Dic₃×C₁₉

D₄

yes

characteristic

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

C₂×D₃

yes

characteristic

C₂×C₄×C₁₉

—

C₂²⋊D₁₉

—

D₇₆

C₂×D₃

yes

characteristic, complemented

C₄×D₁₉

—

Dic₃₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

C₂×D₃

yes

characteristic, complemented

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

C₂×D₄

yes

characteristic

C₃×D₁₉

—

D₃×C₁₉

—

D₃×C₁₉

—

#911

—

maximal, Hall

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²×D₃

yes

characteristic

Dic₁₉

—

C₃×C₁₉

AGL(1,ℤ/8)

yes

characteristic, complemented, Hall

#237

—

D₃×D₄

D₁₉

yes

characteristic, complemented

C₃×D₈

—

#214

—

#213

—

#204

—

ΓL(1,𝔽₂₅)

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

D₃×D₄

yes

characteristic

D₁₉

—

AGL(1,ℤ/8)

—

Sylow

C₂²×D₃

—

C₃×D₄

—

C₃×D₄

C₂×D₁₉

yes

characteristic

#67

—

#67

—

C₂×Dic₃

—

D₁₂

C₂×D₁₉

yes

characteristic

C₄×D₃

C₂×D₁₉

yes

characteristic

Dic₆

—

C₃×C₈

—

C₃⋊C₈

—

C₁₉

#911

yes

characteristic, complemented, Sylow

#41

—

C₂×D₄

—

SD₁₆

—

SD₁₆

—

D₈

—

D₈

—

M₁₆

—

C₂²×C₃

—

C₂²×C₃

—

C₂×D₃

—

C₂×D₃

—

C₂×D₃

C₂²⋊D₁₉

yes

characteristic

C₃×C₄

C₂²×D₁₉

yes

characteristic

Dic₃

—

100

Dic₃

C₂²⋊D₁₉

yes

characteristic

101

C₂³

—

102

Q₈

—

103

D₄

—

104

D₄

—

105

D₄

—

106

D₄

—

114

—

107

D₄

D₃×D₁₉

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

114

—

110

C₈

—

111

C₈

—

112

C₂×C₃

—

113

C₂×C₃

—

114

C₂×C₃

C₂×C₂²⋊D₁₉

yes

characteristic

115

D₃

—

116

D₃

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₄

—

123

C₄

—

114

—

124

C₄

C₂×D₃×D₁₉

yes

characteristic

125

C₃

#10597378

yes

characteristic, complemented, Sylow

126

C₂

—

127

C₂

—

128

C₂

—

129

C₂

—

130

C₂

D₃×C₂²⋊D₁₉

yes

characteristic

	subgroup	G/H
center	C₂	D₃×C₂²⋊D₁₉
commutator, cosocle	C₃×C₄×C₁₉	C₂³
Frattini	C₄	C₂×D₃×D₁₉
Fitting	C₃×D₄×C₁₉	C₂²
socle	C₂×C₃×C₁₉	C₂×D₄
hypercenter	D₄	D₃×D₁₉
hypocenter	C₃×C₁₉	AGL(1,ℤ/8)
LCS	G ▷ C₃×C₄×C₁₉ ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₄

subgroup

G/H

center

C₂

D₃×C₂²⋊D₁₉

commutator, cosocle

C₃×C₄×C₁₉

C₂³

Frattini

C₄

C₂×D₃×D₁₉

Fitting

C₃×D₄×C₁₉

C₂²

socle

C₂×C₃×C₁₉

C₂×D₄

hypercenter

D₄

D₃×D₁₉

hypocenter

C₃×C₁₉

AGL(1,ℤ/8)

LCS

G ▷ C₃×C₄×C₁₉ ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉

UCS

C₁ ◁ C₂ ◁ C₄ ◁ D₄

N	H ≅ G/N	type
1. D₃×D₄×C₁₉	C₂	semidirect
2. #11744926	C₂	semidirect
3. #11744891	C₂	semidirect
4. C₃×#64525	C₂	semidirect
5. #11744825	C₂	semidirect
6. #11744818	C₂	semidirect
7. #11744816	C₂	semidirect
11. Dic₁₁₄	C₂²	semidirect
15. C₃×D₇₆	C₂²	semidirect
18. C₃⋊(C₁₉⋊C₈)	C₂²	semidirect
19. C₃×C₁₉⋊C₈	C₂²	semidirect
25. #64525	D₃	semidirect
41. D₇₆	C₂×D₃	semidirect
45. C₁₉⋊C₈	C₂×D₃	semidirect
60. C₃×C₁₉	AGL(1,ℤ/8)	semidirect
62. D₃×D₄	D₁₉	semidirect
85. C₁₉	#911	semidirect
125. C₃	#10597378	semidirect

H ≅ G/N

type

1. D₃×D₄×C₁₉

C₂

semidirect

2. #11744926

C₂

semidirect

3. #11744891

C₂

semidirect

4. C₃×#64525

C₂

semidirect

5. #11744825

C₂

semidirect

6. #11744818

C₂

semidirect

7. #11744816

C₂

semidirect

11. Dic₁₁₄

C₂²

semidirect

15. C₃×D₇₆

C₂²

semidirect

18. C₃⋊(C₁₉⋊C₈)

C₂²

semidirect

19. C₃×C₁₉⋊C₈

C₂²

semidirect

25. #64525

D₃

semidirect

41. D₇₆

C₂×D₃

semidirect

45. C₁₉⋊C₈

C₂×D₃

semidirect

60. C₃×C₁₉

AGL(1,ℤ/8)

semidirect

62. D₃×D₄

D₁₉

semidirect

85. C₁₉

#911

semidirect

125. C₃

#10597378

semidirect

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

subgroup	index
D₃×D₄×C₁₉	2
#11744926	2
#11744891	2
C₃×#64525	2
#11744825	2
#11744818	2
#11744816	2
#10597378	3
#911	19

subgroup

index

D₃×D₄×C₁₉

Subgroups — #14269411

Conjugacy classes of subgroups

Complements

Maximal subgroups