Group #14564965 — subgroups

Subgroups — #14564965

Order 2432.

282 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 99 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	C₂×#10597265	C₂	1	2	yes	maximal
2	#11926442	C₂	1	1	yes	maximal, characteristic
3	#11926306	C₂	1	2	yes	maximal
4	#11926299	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₉	—	2	1	no	—
7	C₁₉×C₄⋊Q₈	—	2	4	no	—
8	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₉⋊C₄	—	2	1	no	—
14	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
15	C₁₉⋊#95	—	2	1	no	—
16	#10597265	—	2	4	no	—
17	C₂×Q₈×C₁₉	—	2	4	no	—
18	C₂×Q₈×C₁₉	—	4	2	no	—
19	C₂×Q₈×C₁₉	—	4	2	no	—
20	C₂²×C₄×C₁₉	—	2	2	no	—
21	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂²×Dic₁₉	—	2	1	no	—
25	C₂²×Dic₁₉	—	2	1	no	—
26	C₄⋊C₄×C₁₉	—	2	4	no	—
27	C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₄⋊C₄×C₁₉	D₄	1	4	yes	—
29	C₄²×C₁₉	—	2	2	no	—
30	C₄⋊Dic₁₉	—	2	1	no	—
31	C₄⋊Dic₁₉	—	2	2	no	—
32	C₄⋊Dic₁₉	Q₈	1	2	yes	complemented
33	Dic₁₉⋊C₄	—	4	2	no	—
34	C₂×C₁₉⋊C₈	—	2	2	no	—
35	C₂×C₁₉⋊C₈	—	2	2	no	—
36	C₂×C₁₉⋊C₈	Q₈	1	4	yes	complemented
37	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
38	Q₈×C₁₉	—	4	8	no	—
39	C₂×C₄×C₁₉	—	2	1	no	—
40	C₂×C₄×C₁₉	—	2	1	no	—
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	—	2	4	no	—
44	C₂×C₄×C₁₉	—	4	2	no	—
45	C₂×C₄×C₁₉	—	4	2	no	—
46	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
47	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
48	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
49	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
50	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
52	C₂×Dic₁₉	—	2	2	no	—
53	C₂×Dic₁₉	—	4	1	no	—
54	C₂×Dic₁₉	—	4	1	no	—
55	C₂×Dic₁₉	—	4	1	no	—
56	C₂×Dic₁₉	—	4	1	no	—
57	C₂×Dic₁₉	—	4	1	no	—
58	C₁₉⋊C₈	—	2	4	no	—
59	#2058	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	#120	1	1	yes	characteristic
61	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
62	C₂²×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
63	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
64	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
65	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
66	C₂²×C₁₉	#137	1	1	yes	characteristic
67	C₄×C₁₉	—	2	2	no	—
68	C₄×C₁₉	—	2	2	no	—
69	C₄×C₁₉	—	4	4	no	—
70	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
71	C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
72	Dic₁₉	—	4	2	no	—
73	Dic₁₉	—	8	1	no	—
74	C₂×C₄⋊Q₈	D₁₉	1	1	yes	characteristic
75	C₂×#106	—	19	2	no	—
76	#389	—	19	1	no	—
77	#340	—	19	2	no	—
78	#336	—	19	1	no	—
79	C₂×C₁₉	#395	1	1	yes	characteristic
80	C₂×C₁₉	#448	1	1	yes	characteristic
81	C₂×C₁₉	#450	1	1	yes	characteristic
82	C₂×C₁₉	#475	1	1	yes	characteristic
83	C₂×C₁₉	#476	1	1	yes	characteristic
84	C₂×C₁₉	#498	1	1	yes	characteristic
85	C₂×C₁₉	#501	1	1	yes	characteristic
86	C₂²×Q₈	—	2	1	no	—
87	C₂²×C₈	—	19	2	no	—
88	C₄⋊Q₈	—	2	4	no	—
89	C₂×C₄⋊C₄	—	2	1	no	—
90	C₂×C₄⋊C₄	—	19	1	no	—
91	C₂×C₄⋊C₄	—	19	1	no	—
92	C₂×C₄⋊C₄	—	38	1	no	—
93	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
94	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
95	#106	—	38	4	no	—
96	#95	—	38	1	no	—
97	C₁₉	#2058	1	1	yes	characteristic, complemented, Sylow
98	C₂×Q₈	—	2	4	no	—
99	C₂×Q₈	—	4	2	no	—
100	C₂×Q₈	—	4	2	no	—
101	C₂²×C₄	—	2	2	no	—
102	C₂²×C₄	—	38	1	no	—
103	C₂²×C₄	—	38	1	no	—
104	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
105	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
106	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
107	C₂×C₈	—	19	4	no	—
108	C₂×C₈	—	38	2	no	—
109	C₂×C₈	—	38	2	no	—
110	C₄⋊C₄	—	2	4	no	—
111	C₄⋊C₄	—	2	2	no	—
112	C₄⋊C₄	—	19	2	no	—
113	C₄⋊C₄	—	38	1	no	—
114	C₄⋊C₄	—	38	2	no	—
115	C₄⋊C₄	—	76	2	no	—
116	C₄⋊C₄	C₂²⋊D₁₉	1	4	yes	—
117	C₄²	—	2	2	no	—
118	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
119	Q₈	—	4	8	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	2	4	no	—
125	C₂×C₄	—	4	2	no	—
126	C₂×C₄	—	4	2	no	—
127	C₂×C₄	—	38	2	no	—
128	C₂×C₄	—	76	1	no	—
129	C₂×C₄	—	76	1	no	—
130	C₂×C₄	—	76	1	no	—
131	C₂×C₄	—	76	1	no	—
132	C₂×C₄	—	76	1	no	—
133	C₂×C₄	#64526	1	2	yes	—
134	C₂×C₄	#64527	1	2	yes	—
135	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
136	C₂×C₄	Q₈×D₁₉	1	2	yes	—
137	C₂×C₄	#64545	1	1	yes	characteristic
138	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
139	C₈	—	38	4	no	—
140	C₂²	#10597378	1	1	yes	characteristic
141	C₂²	C₂×#64526	1	1	yes	characteristic
142	C₂²	C₂×#64527	1	1	yes	characteristic
143	C₂²	#10597388	1	1	yes	characteristic
144	C₂²	#10597390	1	1	yes	characteristic
145	C₂²	#10597392	1	1	yes	characteristic
146	C₂²	#10597399	1	1	yes	characteristic
147	C₄	—	2	2	no	—
148	C₄	—	2	2	no	—
149	C₄	—	4	4	no	—
150	C₄	—	76	2	no	—
151	C₄	—	152	1	no	—
152	C₄	#10597390	1	2	yes	—
153	C₄	#10597392	1	2	yes	—
154	C₂	#11926463	1	1	yes	characteristic
155	C₂	#11926683	1	1	yes	characteristic
156	C₂	#11926695	1	1	yes	characteristic
157	C₂	#11926826	1	1	yes	characteristic
158	C₂	#11926831	1	1	yes	characteristic
159	C₂	#11926940	1	1	yes	characteristic
160	C₂	#11926950	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597265

C₂

yes

maximal

#11926442

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal

#11926299

C₂

yes

maximal, characteristic

C₂×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₁₉⋊#95

—

#10597265

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

Q₈

yes

complemented

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

Q₈

yes

complemented

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

C₄⋊Q₈

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

C₄⋊Q₈

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

D₁₉

yes

—

—

—

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

—

C₂²×C₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#106

—

#95

—

C₁₉

#2058

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

100

C₂×Q₈

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

105

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

106

C₂²×C₄

C₂²×D₁₉

yes

characteristic

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

C₂²⋊D₁₉

yes

—

117

C₄²

—

118

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

119

Q₈

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

#64526

yes

—

134

C₂×C₄

#64527

yes

—

135

C₂×C₄

Q₈×D₁₉

yes

characteristic

136

C₂×C₄

Q₈×D₁₉

yes

—

137

C₂×C₄

#64545

yes

characteristic

138

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

139

C₈

—

140

C₂²

#10597378

yes

characteristic

141

C₂²

C₂×#64526

yes

characteristic

142

C₂²

C₂×#64527

yes

characteristic

143

C₂²

#10597388

yes

characteristic

144

C₂²

#10597390

yes

characteristic

145

C₂²

#10597392

yes

characteristic

146

C₂²

#10597399

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

152

—

152

C₄

#10597390

yes

—

153

C₄

#10597392

yes

—

154

C₂

#11926463

yes

characteristic

155

C₂

#11926683

yes

characteristic

156

C₂

#11926695

yes

characteristic

157

C₂

#11926826

yes

characteristic

158

C₂

#11926831

yes

characteristic

159

C₂

#11926940

yes

characteristic

160

C₂

#11926950

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×C₄⋊Q₈	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	C₂×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#2058
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×C₄⋊Q₈

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

hypercenter

C₂×C₄⋊Q₈

D₁₉

hypocenter

C₁₉

#2058

LCS

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
32. C₄⋊Dic₁₉	Q₈	semidirect
36. C₂×C₁₉⋊C₈	Q₈	semidirect
97. C₁₉	#2058	semidirect

H ≅ G/N

type

32. C₄⋊Dic₁₉

Q₈

semidirect

36. C₂×C₁₉⋊C₈

Q₈

semidirect

97. C₁₉

#2058

semidirect

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

subgroup	index
C₂×#10597265	2
#11926442	2
#11926306	2
#11926299	2
C₂×C₁₉×C₄⋊Q₈	2
#2058	19

subgroup

index

C₂×C₁₉×C₄⋊Q₈

Subgroups — #14564965

Conjugacy classes of subgroups

Complements

Maximal subgroups