Group #14575428 — subgroups

Subgroups — #14575428

Order 2432.

460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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	#11927350	C₂	1	4	yes	maximal, complemented
2	#11926804	C₂	1	4	yes	maximal, complemented
3	#11926726	C₂	1	2	yes	maximal, complemented
4	#11926711	C₂	1	2	yes	maximal, complemented
5	#11926662	C₂	1	2	yes	maximal, complemented
6	C₁₉×#492	C₂	1	1	yes	maximal, characteristic, complemented
7	#10597433	C₂²	1	2	yes	—
8	#10597430	C₂²	1	2	yes	complemented
9	C₂×SD₁₆×C₁₉	C₂²	1	4	yes	complemented
10	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
11	C₁₉×#127	C₂²	1	1	yes	characteristic
12	#10597388	C₂²	1	4	yes	complemented
13	#10597378	C₂²	1	4	yes	—
14	#10597362	—	2	4	no	—
15	#10597361	—	2	4	no	—
16	#10597360	—	2	4	no	—
17	SD₁₆×D₁₉	—	2	4	no	—
18	#10597350	C₂²	1	2	yes	—
19	#10597347	C₂²	1	4	yes	complemented
20	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
21	#10597293	C₂²	1	2	yes	complemented
22	#10597290	C₂²	1	2	yes	complemented
23	#10597276	C₂²	1	2	yes	complemented
24	#10597262	C₂²	1	4	yes	complemented
25	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
26	C₂×D₄×C₁₉	—	4	1	no	—
27	C₂×D₄×C₁₉	C₂³	1	2	yes	—
28	C₂×C₂²⋊D₁₉	—	4	2	no	—
29	#64545	—	2	4	no	—
30	Q₈×D₁₉	—	2	4	no	—
31	#64543	—	2	4	no	—
32	D₄×D₁₉	—	2	4	no	—
33	#64541	—	4	2	no	—
34	#64541	C₂³	1	4	yes	—
35	SD₁₆×C₁₉	—	2	4	no	—
36	SD₁₆×C₁₉	—	2	4	no	—
37	C₂×C₈×C₁₉	C₂³	1	2	yes	—
38	C₄⋊C₄×C₁₉	—	4	1	no	—
39	C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	#64528	—	2	4	no	—
41	#64527	—	2	4	no	—
42	#64526	—	2	4	no	—
43	#64525	—	2	4	no	—
44	#64520	C₂³	1	4	yes	—
45	Dic₇₆	D₄	1	2	yes	complemented
46	D₁₅₂	D₄	1	2	yes	complemented
47	#64516	D₄	1	4	yes	complemented
48	#64515	—	2	4	no	—
49	C₈×D₁₉	—	2	4	no	—
50	C₂³×C₁₉	—	2	2	no	—
51	C₂²×D₁₉	—	4	2	no	—
52	Q₈×C₁₉	—	2	4	no	—
53	D₄×C₁₉	—	2	4	no	—
54	D₄×C₁₉	—	8	2	no	—
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
58	C₂²⋊D₁₉	—	2	4	no	—
59	C₂²⋊D₁₉	—	4	4	no	—
60	C₂×Dic₁₉	—	4	2	no	—
61	D₇₆	—	4	2	no	—
62	D₇₆	C₂×D₄	1	4	yes	—
63	C₄×D₁₉	—	2	4	no	—
64	C₄×D₁₉	—	4	4	no	—
65	Dic₃₈	—	4	2	no	—
66	Dic₃₈	C₂×D₄	1	4	yes	—
67	C₈×C₁₉	C₂×D₄	1	2	yes	—
68	C₈×C₁₉	C₂×D₄	1	2	yes	—
69	C₁₉⋊C₈	—	2	4	no	—
70	#3291	—	19	1	no	maximal, Sylow
71	C₂²×C₁₉	—	4	2	no	—
72	C₂²×C₁₉	—	8	2	no	—
73	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
74	C₂×D₁₉	—	2	4	no	—
75	C₂×D₁₉	—	16	2	no	—
76	C₄×C₁₉	—	2	2	no	—
77	C₄×C₁₉	—	4	2	no	—
78	C₄×C₁₉	C₂²×D₄	1	2	yes	—
79	Dic₁₉	—	2	4	no	—
80	#577	—	19	4	no	—
81	#492	D₁₉	1	1	yes	characteristic, complemented
82	#471	—	19	4	no	—
83	#456	—	19	2	no	—
84	#453	—	19	2	no	—
85	#443	—	19	2	no	—
86	C₂×C₁₉	—	2	1	no	—
87	C₂×C₁₉	—	8	2	no	—
88	C₂×C₁₉	D₄²	1	1	yes	characteristic
89	D₁₉	—	4	4	no	—
90	2₋¹⁺⁴	—	19	2	no	—
91	H(5,𝔽₂)	—	19	2	no	—
92	#137	—	19	4	no	—
93	#137	—	38	4	no	—
94	AGL(1,ℤ/8)	—	19	4	no	—
95	AGL(1,ℤ/8)	—	38	4	no	—
96	#135	—	19	2	no	—
97	#135	—	38	4	no	—
98	C₂×SD₁₆	—	38	4	no	—
99	C₂×SD₁₆	C₂×D₁₉	1	4	yes	complemented
100	#131	—	19	4	no	—
101	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
102	#127	C₂×D₁₉	1	1	yes	characteristic
103	#108	—	19	2	no	—
104	#104	—	19	4	no	—
105	#101	—	19	2	no	—
106	#100	—	19	2	no	—
107	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic, complemented
108	C₁₉	#3291	1	1	yes	characteristic, complemented, Sylow
109	#41	—	19	4	no	—
110	#41	—	38	4	no	—
111	#41	—	38	4	no	—
112	#41	—	76	2	no	—
113	C₂×Q₈	—	38	4	no	—
114	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
115	C₂×D₄	—	4	1	no	—
116	C₂×D₄	—	38	4	no	—
117	C₂×D₄	—	76	2	no	—
118	C₂×D₄	C₂²×D₁₉	1	2	yes	—
119	Q₁₆	—	19	2	no	—
120	Q₁₆	—	38	4	no	—
121	SD₁₆	—	2	4	no	—
122	SD₁₆	—	2	4	no	—
123	SD₁₆	—	19	4	no	—
124	SD₁₆	—	38	4	no	—
125	SD₁₆	—	38	4	no	—
126	D₈	—	19	2	no	—
127	D₈	—	38	4	no	—
128	M₁₆	—	19	4	no	—
129	M₁₆	—	38	4	no	—
130	C₂×C₈	—	38	4	no	—
131	C₂×C₈	C₂²×D₁₉	1	2	yes	—
132	C₄⋊C₄	—	4	1	no	—
133	C₄²	C₂²×D₁₉	1	1	yes	characteristic
134	C₂³	—	2	2	no	—
135	C₂³	—	76	2	no	—
136	Q₈	—	2	4	no	—
137	Q₈	—	19	4	no	—
138	Q₈	—	76	2	no	—
139	D₄	—	2	4	no	—
140	D₄	—	8	2	no	—
141	D₄	—	19	4	no	—
142	D₄	—	38	4	no	—
143	D₄	—	76	2	no	—
144	D₄	—	76	4	no	—
145	C₂×C₄	—	2	1	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	38	4	no	—
148	C₂×C₄	—	76	4	no	—
149	C₂×C₄	—	76	2	no	—
150	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
151	C₈	—	38	4	no	—
152	C₈	D₄×D₁₉	1	2	yes	—
153	C₈	D₄×D₁₉	1	2	yes	—
154	C₂²	—	4	2	no	—
155	C₂²	—	8	2	no	—
156	C₂²	—	38	4	no	—
157	C₂²	—	304	2	no	—
158	C₂²	#10597430	1	1	yes	characteristic
159	C₄	—	2	2	no	—
160	C₄	—	4	2	no	—
161	C₄	—	38	4	no	—
162	C₄	C₂×D₄×D₁₉	1	2	yes	—
163	C₂	—	2	1	no	—
164	C₂	—	8	2	no	—
165	C₂	—	76	4	no	—
166	C₂	#11927179	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927350

C₂

yes

maximal, complemented

#11926804

C₂

yes

maximal, complemented

#11926726

C₂

yes

maximal, complemented

#11926711

C₂

yes

maximal, complemented

#11926662

C₂

yes

maximal, complemented

C₁₉×#492

C₂

yes

maximal, characteristic, complemented

#10597433

C₂²

yes

—

#10597430

C₂²

yes

complemented

C₂×SD₁₆×C₁₉

C₂²

yes

complemented

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic, complemented

C₁₉×#127

C₂²

yes

characteristic

#10597388

C₂²

yes

complemented

#10597378

C₂²

yes

—

#10597362

—

#10597361

—

#10597360

—

SD₁₆×D₁₉

—

#10597350

C₂²

yes

—

#10597347

C₂²

yes

complemented

C₄×C₈×C₁₉

C₂²

yes

characteristic, complemented

#10597293

C₂²

yes

complemented

#10597290

C₂²

yes

complemented

#10597276

C₂²

yes

complemented

#10597262

C₂²

yes

complemented

C₂×Q₈×C₁₉

C₂³

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂³

yes

—

C₂×C₂²⋊D₁₉

—

#64545

—

Q₈×D₁₉

—

#64543

—

D₄×D₁₉

—

#64541

—

#64541

C₂³

yes

—

SD₁₆×C₁₉

—

SD₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

—

—

—

—

C₂³

yes

—

Dic₇₆

D₄

yes

complemented

D₁₅₂

D₄

yes

complemented

#64516

D₄

yes

complemented

#64515

—

C₈×D₁₉

—

C₂³×C₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

C₂×D₄

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

C₂×D₄

yes

—

C₈×C₁₉

C₂×D₄

yes

—

C₈×C₁₉

C₂×D₄

yes

—

C₁₉⋊C₈

—

#3291

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

H(5,𝔽₂)

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²×D₄

yes

—

Dic₁₉

—

#577

—

#492

D₁₉

yes

characteristic, complemented

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

D₄²

yes

characteristic

D₁₉

—

2₋¹⁺⁴

—

—

—

—

—

—

—

—

C₂×SD₁₆

—

C₂×SD₁₆

C₂×D₁₉

yes

complemented

100

#131

—

101

C₄⋊Q₈

C₂×D₁₉

yes

characteristic, complemented

102

#127

C₂×D₁₉

yes

characteristic

103

#108

—

104

#104

—

105

#101

—

106

#100

—

107

C₄×C₈

C₂×D₁₉

yes

characteristic, complemented

108

C₁₉

#3291

yes

characteristic, complemented, Sylow

109

#41

—

110

#41

—

111

#41

—

112

#41

—

113

C₂×Q₈

—

114

C₂×Q₈

C₂²×D₁₉

yes

—

115

C₂×D₄

—

116

C₂×D₄

—

117

C₂×D₄

—

118

C₂×D₄

C₂²×D₁₉

yes

—

119

Q₁₆

—

120

Q₁₆

—

121

SD₁₆

—

122

SD₁₆

—

123

SD₁₆

—

124

SD₁₆

—

125

SD₁₆

—

126

D₈

—

127

D₈

—

128

M₁₆

—

129

M₁₆

—

130

C₂×C₈

—

131

C₂×C₈

C₂²×D₁₉

yes

—

132

C₄⋊C₄

—

133

C₄²

C₂²×D₁₉

yes

characteristic

134

C₂³

—

135

C₂³

—

136

Q₈

—

137

Q₈

—

138

Q₈

—

139

D₄

—

140

D₄

—

141

D₄

—

142

D₄

—

143

D₄

—

144

D₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

C₂³×D₁₉

yes

characteristic

151

C₈

—

152

C₈

D₄×D₁₉

yes

—

153

C₈

D₄×D₁₉

yes

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

—

304

—

158

C₂²

#10597430

yes

characteristic

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

C₂×D₄×D₁₉

yes

—

163

C₂

—

164

C₂

—

165

C₂

—

166

C₂

#11927179

yes

characteristic

	subgroup	G/H
center	C₂	#11927179
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#492	C₂
socle	C₂×C₁₉	D₄²
hypercenter	#492	D₁₉
hypocenter	C₁₉	#3291
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #492

subgroup

G/H

center

C₂

#11927179

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#492

C₂

socle

C₂×C₁₉

D₄²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #492

N	H ≅ G/N	type
1. #11927350	C₂	semidirect
2. #11926804	C₂	semidirect
3. #11926726	C₂	semidirect
4. #11926711	C₂	semidirect
5. #11926662	C₂	semidirect
6. C₁₉×#492	C₂	semidirect
8. #10597430	C₂²	semidirect
9. C₂×SD₁₆×C₁₉	C₂²	semidirect
10. C₁₉×C₄⋊Q₈	C₂²	semidirect
12. #10597388	C₂²	semidirect
19. #10597347	C₂²	semidirect
20. C₄×C₈×C₁₉	C₂²	semidirect
21. #10597293	C₂²	semidirect
22. #10597290	C₂²	semidirect
23. #10597276	C₂²	semidirect
24. #10597262	C₂²	semidirect
45. Dic₇₆	D₄	semidirect
46. D₁₅₂	D₄	semidirect
47. #64516	D₄	semidirect
81. #492	D₁₉	semidirect
99. C₂×SD₁₆	C₂×D₁₉	semidirect
101. C₄⋊Q₈	C₂×D₁₉	semidirect
107. C₄×C₈	C₂×D₁₉	semidirect
108. C₁₉	#3291	semidirect

H ≅ G/N

type

1. #11927350

C₂

semidirect

2. #11926804

C₂

semidirect

3. #11926726

C₂

semidirect

4. #11926711

C₂

semidirect

5. #11926662

C₂

semidirect

6. C₁₉×#492

C₂

semidirect

8. #10597430

C₂²

semidirect

9. C₂×SD₁₆×C₁₉

C₂²

semidirect

10. C₁₉×C₄⋊Q₈

C₂²

semidirect

12. #10597388

C₂²

semidirect

19. #10597347

C₂²

semidirect

20. C₄×C₈×C₁₉

C₂²

semidirect

21. #10597293

C₂²

semidirect

22. #10597290

C₂²

semidirect

23. #10597276

C₂²

semidirect

24. #10597262

C₂²

semidirect

45. Dic₇₆

D₄

semidirect

46. D₁₅₂

D₄

semidirect

47. #64516

D₄

semidirect

81. #492

D₁₉

semidirect

99. C₂×SD₁₆

C₂×D₁₉

semidirect

101. C₄⋊Q₈

C₂×D₁₉

semidirect

107. C₄×C₈

C₂×D₁₉

semidirect

108. C₁₉

#3291

semidirect

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

subgroup	index
#11927350	2
#11926804	2
#11926726	2
#11926711	2
#11926662	2
C₁₉×#492	2
#3291	19

subgroup

index

C₁₉×#492

Subgroups — #14575428

Conjugacy classes of subgroups

Complements

Maximal subgroups