Group #14576774 — subgroups

Subgroups — #14576774

Order 2432.

370 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 129 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	#11927349	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926980	C₂	1	3	yes	maximal, complemented
3	#11926979	C₂	1	3	yes	maximal, complemented
4	#11926974	C₂	1	3	yes	maximal, complemented
5	C₂×#10597283	C₂	1	3	yes	maximal, complemented
6	#11926961	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#576	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×H(5,𝔽₂)	—	2	1	no	—
9	#10597435	—	2	1	no	—
10	C₁₉×AGL(1,ℤ/8)	—	2	3	no	—
11	C₁₉×#135	C₂²	1	3	yes	complemented
12	C₂×D₈×C₁₉	C₂²	1	3	yes	complemented
13	C₁₉×#131	C₂²	1	1	yes	characteristic
14	#10597354	—	2	3	no	—
15	#10597350	C₂²	1	3	yes	complemented
16	C₂×D₁₅₂	C₂²	1	3	yes	complemented
17	#10597286	C₂²	1	1	yes	characteristic, complemented
18	#10597285	C₂²	1	3	yes	complemented
19	#10597284	C₂²	1	3	yes	complemented
20	#10597283	C₂²	1	3	yes	complemented
21	#10597283	C₂²	1	6	yes	complemented
22	#10597269	C₂²	1	3	yes	complemented
23	C₂×C₁₉⋊C₁₆	C₂²	1	3	yes	complemented
24	#41×C₁₉	—	2	3	no	—
25	#41×C₁₉	—	4	1	no	—
26	#41×C₁₉	D₄	1	1	yes	characteristic
27	C₂×D₄×C₁₉	—	2	3	no	—
28	C₂×D₄×C₁₉	—	4	3	no	—
29	#64545	—	4	1	no	—
30	D₄×D₁₉	—	4	3	no	—
31	#64541	—	2	3	no	—
32	C₂×D₇₆	—	2	3	no	—
33	Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
34	SD₁₆×C₁₉	—	2	3	no	—
35	D₈×C₁₉	—	2	3	no	—
36	D₈×C₁₉	C₂³	1	3	yes	—
37	M₁₆×C₁₉	D₄	1	3	yes	—
38	C₂×C₈×C₁₉	C₂³	1	3	yes	—
39	Dic₇₆	C₂³	1	1	yes	characteristic
40	D₁₅₂	—	2	3	no	—
41	D₁₅₂	C₂³	1	3	yes	—
42	#64516	—	2	3	no	—
43	C₁₉⋊C₁₆	C₂³	1	1	yes	characteristic
44	C₁₉⋊C₁₆	C₂³	1	3	yes	—
45	C₂³×C₁₉	—	4	3	no	—
46	C₂²×D₁₉	—	4	3	no	—
47	Q₈×C₁₉	—	2	1	no	—
48	Q₈×C₁₉	D₈	1	1	yes	characteristic
49	D₄×C₁₉	—	2	3	no	—
50	D₄×C₁₉	—	4	3	no	—
51	D₄×C₁₉	—	4	3	no	—
52	D₄×C₁₉	D₈	1	3	yes	—
53	C₂×C₄×C₁₉	—	4	3	no	—
54	C₂×C₄×C₁₉	C₂×D₄	1	3	yes	—
55	C₂²⋊D₁₉	—	4	3	no	—
56	D₇₆	—	2	3	no	—
57	D₇₆	—	4	3	no	—
58	C₄×D₁₉	—	4	3	no	—
59	Dic₃₈	—	2	1	no	—
60	C₈×C₁₉	C₂×D₄	1	3	yes	—
61	C₈×C₁₉	C₂⁴	1	1	yes	characteristic
62	#3415	—	19	1	no	maximal, Sylow
63	C₂²×C₁₉	—	4	3	no	—
64	C₂²×C₁₉	—	16	3	no	—
65	C₂²×C₁₉	C₂×D₈	1	3	yes	—
66	C₂×D₁₉	—	4	3	no	—
67	C₂×D₁₉	—	16	3	no	—
68	C₄×C₁₉	—	4	1	no	—
69	C₄×C₁₉	C₂×D₈	1	3	yes	—
70	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
71	Dic₁₉	—	4	1	no	—
72	#576	—	19	1	no	—
73	#576	D₁₉	1	1	yes	characteristic, complemented
74	#509	—	19	3	no	—
75	#509	—	19	3	no	—
76	#508	—	19	3	no	—
77	C₂×D₁₆	—	19	3	no	—
78	#504	—	19	1	no	—
79	C₂×C₁₉	—	2	3	no	—
80	C₂×C₁₉	—	8	3	no	—
81	C₂×C₁₉	C₂²×D₈	1	1	yes	characteristic
82	D₁₉	—	8	3	no	—
83	H(5,𝔽₂)	—	2	1	no	—
84	H(5,𝔽₂)	—	38	1	no	—
85	AGL(1,ℤ/8)	—	2	3	no	—
86	AGL(1,ℤ/8)	—	38	3	no	—
87	#135	—	19	3	no	—
88	#135	C₂×D₁₉	1	3	yes	complemented
89	C₂×D₈	—	19	3	no	—
90	C₂×D₈	C₂×D₁₉	1	3	yes	complemented
91	#131	C₂×D₁₉	1	1	yes	characteristic
92	Q₃₂	—	19	1	no	—
93	SD₃₂	—	19	3	no	—
94	SD₃₂	—	19	3	no	—
95	D₁₆	—	19	3	no	—
96	D₁₆	—	19	6	no	—
97	M₃₂	—	19	3	no	—
98	C₂×C₁₆	—	19	3	no	—
99	C₁₉	#3415	1	1	yes	characteristic, complemented, Sylow
100	#41	—	2	3	no	—
101	#41	—	4	1	no	—
102	#41	—	38	3	no	—
103	#41	—	76	1	no	—
104	#41	C₂²⋊D₁₉	1	1	yes	characteristic
105	C₂×D₄	—	2	3	no	—
106	C₂×D₄	—	4	3	no	—
107	C₂×D₄	—	38	3	no	—
108	C₂×D₄	—	76	3	no	—
109	Q₁₆	—	19	1	no	—
110	Q₁₆	C₂²×D₁₉	1	1	yes	characteristic
111	SD₁₆	—	2	3	no	—
112	SD₁₆	—	38	3	no	—
113	D₈	—	2	3	no	—
114	D₈	—	19	3	no	—
115	D₈	—	38	3	no	—
116	D₈	C₂²×D₁₉	1	3	yes	—
117	M₁₆	C₂²⋊D₁₉	1	3	yes	—
118	C₂×C₈	C₂²×D₁₉	1	3	yes	—
119	C₁₆	—	19	1	no	—
120	C₁₆	—	19	3	no	—
121	C₂³	—	4	3	no	—
122	C₂³	—	76	3	no	—
123	Q₈	—	2	1	no	—
124	Q₈	—	38	1	no	—
125	Q₈	#64525	1	1	yes	characteristic
126	D₄	—	2	3	no	—
127	D₄	—	4	3	no	—
128	D₄	—	4	3	no	—
129	D₄	—	38	3	no	—
130	D₄	—	76	3	no	—
131	D₄	—	76	3	no	—
132	D₄	#64525	1	3	yes	—
133	C₂×C₄	—	4	3	no	—
134	C₂×C₄	—	76	3	no	—
135	C₂×C₄	C₂×C₂²⋊D₁₉	1	3	yes	—
136	C₈	C₂×C₂²⋊D₁₉	1	3	yes	—
137	C₈	C₂³×D₁₉	1	1	yes	characteristic
138	C₂²	—	4	3	no	—
139	C₂²	—	16	3	no	—
140	C₂²	—	304	3	no	—
141	C₂²	—	76	3	no	—
142	C₂²	C₂×#64525	1	3	yes	—
143	C₄	—	4	1	no	—
144	C₄	—	76	1	no	—
145	C₄	C₂×#64525	1	3	yes	—
146	C₄	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
147	C₂	—	2	3	no	—
148	C₂	—	8	3	no	—
149	C₂	—	152	3	no	—
150	C₂	C₂²×#64525	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927349

C₂

yes

maximal, characteristic, complemented

#11926980

C₂

yes

maximal, complemented

#11926979

C₂

yes

maximal, complemented

#11926974

C₂

yes

maximal, complemented

C₂×#10597283

C₂

yes

maximal, complemented

#11926961

C₂

yes

maximal, characteristic, complemented

C₁₉×#576

C₂

yes

maximal, characteristic, complemented

C₁₉×H(5,𝔽₂)

—

#10597435

—

C₁₉×AGL(1,ℤ/8)

—

C₁₉×#135

C₂²

yes

complemented

C₂×D₈×C₁₉

C₂²

yes

complemented

C₁₉×#131

C₂²

yes

characteristic

#10597354

—

#10597350

C₂²

yes

complemented

C₂×D₁₅₂

C₂²

yes

complemented

#10597286

C₂²

yes

characteristic, complemented

#10597285

C₂²

yes

complemented

#10597284

C₂²

yes

complemented

#10597283

C₂²

yes

complemented

#10597283

C₂²

yes

complemented

#10597269

C₂²

yes

complemented

C₂×C₁₉⋊C₁₆

C₂²

yes

complemented

#41×C₁₉

—

#41×C₁₉

—

#41×C₁₉

D₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

#64545

—

D₄×D₁₉

—

#64541

—

C₂×D₇₆

—

Q₁₆×C₁₉

C₂³

yes

characteristic

SD₁₆×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

C₂³

yes

—

M₁₆×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

C₂³

yes

—

Dic₇₆

C₂³

yes

characteristic

D₁₅₂

—

D₁₅₂

C₂³

yes

—

#64516

—

C₁₉⋊C₁₆

C₂³

yes

characteristic

C₁₉⋊C₁₆

C₂³

yes

—

C₂³×C₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

D₈

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

D₈

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂²⋊D₁₉

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

C₂×D₄

yes

—

C₈×C₁₉

C₂⁴

yes

characteristic

#3415

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×D₈

yes

—

C₄×C₁₉

C₂²×D₄

yes

characteristic

Dic₁₉

—

#576

—

#576

D₁₉

yes

characteristic, complemented

#509

—

#509

—

#508

—

C₂×D₁₆

—

#504

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂²×D₈

yes

characteristic

D₁₉

—

—

—

—

—

—

C₂×D₁₉

yes

complemented

C₂×D₈

—

C₂×D₈

C₂×D₁₉

yes

complemented

#131

C₂×D₁₉

yes

characteristic

Q₃₂

—

SD₃₂

—

SD₃₂

—

D₁₆

—

D₁₆

—

M₃₂

—

C₂×C₁₆

—

C₁₉

#3415

yes

characteristic, complemented, Sylow

100

#41

—

101

#41

—

102

#41

—

103

#41

—

104

#41

C₂²⋊D₁₉

yes

characteristic

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

109

Q₁₆

—

110

Q₁₆

C₂²×D₁₉

yes

characteristic

111

SD₁₆

—

112

SD₁₆

—

113

D₈

—

114

D₈

—

115

D₈

—

116

D₈

C₂²×D₁₉

yes

—

117

M₁₆

C₂²⋊D₁₉

yes

—

118

C₂×C₈

C₂²×D₁₉

yes

—

119

C₁₆

—

120

C₁₆

—

121

C₂³

—

122

C₂³

—

123

Q₈

—

124

Q₈

—

125

Q₈

#64525

yes

characteristic

126

D₄

—

127

D₄

—

128

D₄

—

129

D₄

—

130

D₄

—

131

D₄

—

132

D₄

#64525

yes

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

136

C₈

C₂×C₂²⋊D₁₉

yes

—

137

C₈

C₂³×D₁₉

yes

characteristic

138

C₂²

—

139

C₂²

—

140

C₂²

—

304

—

141

C₂²

—

142

C₂²

C₂×#64525

yes

—

143

C₄

—

144

C₄

—

145

C₄

C₂×#64525

yes

—

146

C₄

C₂²×C₂²⋊D₁₉

yes

characteristic

147

C₂

—

148

C₂

—

149

C₂

—

152

—

150

C₂

C₂²×#64525

yes

characteristic

	subgroup	G/H
center	C₂	C₂²×#64525
commutator, cosocle	C₈×C₁₉	C₂⁴
Frattini	C₈	C₂³×D₁₉
Fitting	C₁₉×#576	C₂
socle	C₂×C₁₉	C₂²×D₈
hypercenter	#576	D₁₉
hypocenter	C₁₉	#3415
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ #41 ◁ #131 ◁ #576

subgroup

G/H

center

C₂

C₂²×#64525

commutator, cosocle

C₈×C₁₉

C₂⁴

Frattini

C₈

C₂³×D₁₉

Fitting

C₁₉×#576

C₂

socle

C₂×C₁₉

C₂²×D₈

D₁₉

C₁₉

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ #41 ◁ #131 ◁ #576

N	H ≅ G/N	type
1. #11927349	C₂	semidirect
2. #11926980	C₂	semidirect
3. #11926979	C₂	semidirect
4. #11926974	C₂	semidirect
5. C₂×#10597283	C₂	semidirect
6. #11926961	C₂	semidirect
7. C₁₉×#576	C₂	semidirect
11. C₁₉×#135	C₂²	semidirect
12. C₂×D₈×C₁₉	C₂²	semidirect
15. #10597350	C₂²	semidirect
16. C₂×D₁₅₂	C₂²	semidirect
17. #10597286	C₂²	semidirect
18. #10597285	C₂²	semidirect
19. #10597284	C₂²	semidirect
20. #10597283	C₂²	semidirect
21. #10597283	C₂²	semidirect
22. #10597269	C₂²	semidirect
23. C₂×C₁₉⋊C₁₆	C₂²	semidirect
73. #576	D₁₉	semidirect
88. #135	C₂×D₁₉	semidirect
90. C₂×D₈	C₂×D₁₉	semidirect
99. C₁₉	#3415	semidirect

H ≅ G/N

type

1. #11927349

C₂

semidirect

2. #11926980

C₂

semidirect

3. #11926979

C₂

semidirect

4. #11926974

C₂

semidirect

5. C₂×#10597283

C₂

semidirect

6. #11926961

C₂

semidirect

7. C₁₉×#576

C₂

semidirect

11. C₁₉×#135

C₂²

semidirect

12. C₂×D₈×C₁₉

C₂²

semidirect

15. #10597350

C₂²

semidirect

16. C₂×D₁₅₂

C₂²

semidirect

17. #10597286

C₂²

semidirect

18. #10597285

C₂²

semidirect

19. #10597284

C₂²

semidirect

20. #10597283

C₂²

semidirect

21. #10597283

C₂²

semidirect

22. #10597269

C₂²

semidirect

23. C₂×C₁₉⋊C₁₆

C₂²

semidirect

73. #576

D₁₉

semidirect

88. #135

C₂×D₁₉

semidirect

90. C₂×D₈

C₂×D₁₉

semidirect

99. C₁₉

#3415

semidirect

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

subgroup	index
#11927349	2
#11926980	2
#11926979	2
#11926974	2
C₂×#10597283	2
#11926961	2
C₁₉×#576	2
#3415	19

subgroup

index

C₁₉×#576

Subgroups — #14576774

Conjugacy classes of subgroups

Complements

Maximal subgroups