Group #14574294 — subgroups

Subgroups — #14574294

Order 2432.

338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 125 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	#11927156	C₂	1	2	yes	maximal
2	#11926946	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926924	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926913	C₂	1	2	yes	maximal, complemented
5	#11926802	C₂	1	2	yes	maximal
6	#11926785	C₂	1	2	yes	maximal
7	#11926652	C₂	1	2	yes	maximal, complemented
8	C₄×Dic₇₆	C₂	1	2	yes	maximal, complemented
9	C₁₉×#405	C₂	1	1	yes	maximal, characteristic
10	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#117	C₂²	1	1	yes	characteristic
13	#10597370	C₂²	1	4	yes	—
14	C₂×Dic₇₆	C₂²	1	2	yes	—
15	C₂×Dic₇₆	C₂²	1	2	yes	—
16	#10597335	—	2	4	no	—
17	#10597325	—	2	4	no	—
18	#10597316	C₂²	1	2	yes	—
19	#10597315	C₂²	1	2	yes	—
20	C₄×Dic₃₈	C₂²	1	4	yes	—
21	C₁₉×#97	C₂²	1	1	yes	characteristic
22	C₁₉×#97	C₂²	1	1	yes	characteristic
23	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
25	#10597275	C₂²	1	2	yes	—
26	#10597274	C₂²	1	2	yes	—
27	#10597273	C₂²	1	4	yes	—
28	#10597273	C₂²	1	4	yes	—
29	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×Dic₃₈	C₂³	1	4	yes	—
31	M₁₆×C₁₉	—	2	2	no	—
32	C₂×C₈×C₁₉	—	2	2	no	—
33	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
34	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
37	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
38	C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
39	C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	C₄²×C₁₉	C₂³	1	1	yes	characteristic
41	C₂²⋊Dic₁₉	—	2	4	no	—
42	C₄⋊Dic₁₉	—	2	4	no	—
43	C₄⋊Dic₁₉	C₂³	1	4	yes	—
44	Dic₁₉⋊C₄	—	2	4	no	—
45	Dic₁₉⋊C₄	—	2	4	no	—
46	Dic₁₉⋊C₄	—	2	4	no	—
47	C₄×Dic₁₉	—	2	4	no	—
48	Dic₇₆	—	2	4	no	—
49	Dic₇₆	—	2	4	no	—
50	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
56	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
57	C₂×Dic₁₉	—	2	4	no	—
58	C₂×Dic₁₉	—	2	4	no	—
59	Dic₃₈	—	2	4	no	—
60	Dic₃₈	—	2	4	no	—
61	C₈×C₁₉	—	2	1	no	—
62	C₈×C₁₉	—	2	1	no	—
63	C₈×C₁₉	#41	1	2	yes	—
64	C₈×C₁₉	#41	1	2	yes	—
65	#3177	—	19	1	no	maximal, Sylow
66	C₂²×C₁₉	—	2	1	no	—
67	C₂²×C₁₉	—	2	2	no	—
68	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
69	C₄×C₁₉	—	2	1	no	—
70	C₄×C₁₉	—	2	2	no	—
71	C₄×C₁₉	—	2	2	no	—
72	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
73	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
74	Dic₁₉	—	4	4	no	—
75	Dic₁₉	—	4	4	no	—
76	#541	—	19	2	no	—
77	#499	—	19	1	no	—
78	#494	—	19	1	no	—
79	#491	—	19	2	no	—
80	#470	—	19	2	no	—
81	#467	—	19	2	no	—
82	#441	—	19	2	no	—
83	C₄×Q₁₆	—	19	2	no	—
84	#405	D₁₉	1	1	yes	characteristic
85	C₂×C₁₉	—	4	1	no	—
86	C₂×C₁₉	#532	1	1	yes	characteristic
87	C₂×C₁₉	#578	1	2	yes	—
88	C₂×Q₁₆	—	19	2	no	—
89	C₂×Q₁₆	—	19	2	no	—
90	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
91	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
92	C₄⋊Q₈	—	19	2	no	—
93	#126	—	38	4	no	—
94	#125	—	19	2	no	—
95	#125	—	38	4	no	—
96	C₂²⋊Q₈	—	19	4	no	—
97	C₄×Q₈	—	19	4	no	—
98	#117	C₂×D₁₉	1	1	yes	characteristic
99	#107	—	19	2	no	—
100	#106	—	19	2	no	—
101	#103	—	19	4	no	—
102	#103	—	19	4	no	—
103	#97	C₂×D₁₉	1	1	yes	characteristic
104	#97	C₂×D₁₉	1	1	yes	characteristic
105	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
106	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
107	C₁₉	#3177	1	1	yes	characteristic, complemented, Sylow
108	C₂×Q₈	—	19	4	no	—
109	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
110	Q₁₆	—	38	4	no	—
111	Q₁₆	—	38	4	no	—
112	M₁₆	—	2	2	no	—
113	C₂×C₈	—	2	2	no	—
114	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
115	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
116	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
117	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
118	C₄⋊C₄	—	19	4	no	—
119	C₄⋊C₄	—	38	4	no	—
120	C₄⋊C₄	—	38	4	no	—
121	C₄⋊C₄	—	38	4	no	—
122	C₄⋊C₄	—	38	4	no	—
123	C₄⋊C₄	D₇₆	1	2	yes	—
124	C₂²⋊C₄	—	38	4	no	—
125	C₂²⋊C₄	D₇₆	1	2	yes	—
126	C₄²	—	38	4	no	—
127	C₄²	C₂²×D₁₉	1	1	yes	characteristic
128	C₄²	C₂²×D₁₉	1	1	yes	characteristic
129	C₂³	C₂×D₇₆	1	1	yes	characteristic
130	Q₈	—	38	4	no	—
131	Q₈	—	38	4	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	38	4	no	—
135	C₂×C₄	—	38	4	no	—
136	C₂×C₄	C₂×D₇₆	1	2	yes	—
137	C₂×C₄	C₂×D₇₆	1	2	yes	—
138	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
139	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
140	C₈	—	2	1	no	—
141	C₈	—	2	1	no	—
142	C₈	#64541	1	2	yes	—
143	C₈	#64541	1	2	yes	—
144	C₂²	—	2	1	no	—
145	C₂²	—	2	2	no	—
146	C₂²	C₂²×D₇₆	1	1	yes	characteristic
147	C₄	—	2	1	no	—
148	C₄	—	2	2	no	—
149	C₄	—	2	2	no	—
150	C₄	—	76	4	no	—
151	C₄	—	76	4	no	—
152	C₄	C₂×#64541	1	1	yes	characteristic
153	C₄	C₂×#64541	1	1	yes	characteristic
154	C₂	—	4	1	no	—
155	C₂	#11927094	1	1	yes	characteristic
156	C₂	#11927361	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927156

C₂

yes

maximal

#11926946

C₂

yes

maximal, characteristic, complemented

#11926924

C₂

yes

maximal, characteristic, complemented

#11926913

C₂

yes

maximal, complemented

#11926802

C₂

yes

maximal

#11926785

C₂

yes

maximal

#11926652

C₂

yes

maximal, complemented

C₄×Dic₇₆

C₂

yes

maximal, complemented

C₁₉×#405

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

#10597370

C₂²

yes

—

C₂×Dic₇₆

C₂²

yes

—

C₂×Dic₇₆

C₂²

yes

—

#10597335

—

#10597325

—

#10597316

C₂²

yes

—

#10597315

C₂²

yes

—

C₄×Dic₃₈

C₂²

yes

—

C₁₉×#97

C₂²

yes

characteristic

C₁₉×#97

C₂²

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597275

C₂²

yes

—

#10597274

C₂²

yes

—

#10597273

C₂²

yes

—

#10597273

C₂²

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×Dic₃₈

C₂³

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

D₄

yes

—

C₂²⋊C₄×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

Dic₇₆

—

Dic₇₆

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#41

yes

—

C₈×C₁₉

#41

yes

—

#3177

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×#41

yes

characteristic

C₄×C₁₉

C₂×#41

yes

characteristic

Dic₁₉

—

Dic₁₉

—

—

—

—

—

—

—

—

C₄×Q₁₆

—

#405

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

#532

yes

characteristic

C₂×C₁₉

#578

yes

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

—

#126

—

#125

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

C₂×D₁₉

yes

characteristic

#107

—

100

#106

—

101

#103

—

102

#103

—

103

#97

C₂×D₁₉

yes

characteristic

104

#97

C₂×D₁₉

yes

characteristic

105

C₄×C₈

C₂×D₁₉

yes

characteristic

106

C₄×C₈

C₂×D₁₉

yes

characteristic

107

C₁₉

#3177

yes

characteristic, complemented, Sylow

108

C₂×Q₈

—

109

C₂²×C₄

C₂²×D₁₉

yes

characteristic

110

Q₁₆

—

111

Q₁₆

—

112

M₁₆

—

113

C₂×C₈

—

114

C₂×C₈

C₂²×D₁₉

yes

characteristic

115

C₂×C₈

C₂²×D₁₉

yes

characteristic

116

C₂×C₈

C₂²×D₁₉

yes

characteristic

117

C₂×C₈

C₂²×D₁₉

yes

characteristic

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

D₇₆

yes

—

124

C₂²⋊C₄

—

125

C₂²⋊C₄

D₇₆

yes

—

126

C₄²

—

127

C₄²

C₂²×D₁₉

yes

characteristic

128

C₄²

C₂²×D₁₉

yes

characteristic

129

C₂³

C₂×D₇₆

yes

characteristic

130

Q₈

—

131

Q₈

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

C₂×D₇₆

yes

—

137

C₂×C₄

C₂×D₇₆

yes

—

138

C₂×C₄

C₂×D₇₆

yes

characteristic

139

C₂×C₄

C₂³×D₁₉

yes

characteristic

140

C₈

—

141

C₈

—

142

C₈

#64541

yes

—

143

C₈

#64541

yes

—

144

C₂²

—

145

C₂²

—

146

C₂²

C₂²×D₇₆

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

C₂×#64541

yes

characteristic

153

C₄

C₂×#64541

yes

characteristic

154

C₂

—

155

C₂

#11927094

yes

characteristic

156

C₂

#11927361

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₇₆
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#405	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#405	D₁₉
hypocenter	C₁₉	#3177
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

subgroup

G/H

center

C₂²

C₂²×D₇₆

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#405

C₂

socle

C₂²×C₁₉

C₂²×D₄

prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ #117 ◁ #405

N	H ≅ G/N	type
2. #11926946	C₂	semidirect
3. #11926924	C₂	semidirect
4. #11926913	C₂	semidirect
7. #11926652	C₂	semidirect
8. C₄×Dic₇₆	C₂	semidirect
107. C₁₉	#3177	semidirect

H ≅ G/N

type

2. #11926946

C₂

semidirect

3. #11926924

C₂

semidirect

4. #11926913

C₂

semidirect

7. #11926652

C₂

semidirect

8. C₄×Dic₇₆

C₂

semidirect

107. C₁₉

#3177

semidirect

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

subgroup	index
#11927156	2
#11926946	2
#11926924	2
#11926913	2
#11926802	2
#11926785	2
#11926652	2
C₄×Dic₇₆	2
C₁₉×#405	2
#3177	19

subgroup

index

C₄×Dic₇₆

C₁₉×#405

#3177

Subgroups — #14574294

Conjugacy classes of subgroups

Complements

Maximal subgroups