Group #14573401 — subgroups

Subgroups — C₂×#11926830 #14573401

Order 2432.

416 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 173 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×#10597315	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic
3	#11926830	C₂	1	8	yes	maximal, direct product factor
4	C₂×#10597274	C₂	1	2	yes	maximal
5	C₂×#10597273	C₂	1	2	yes	maximal
6	C₂×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₃₈	—	2	1	no	—
8	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₉	—	2	1	no	—
12	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
13	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	C₂×Dic₁₉⋊C₄	—	2	1	no	—
15	C₂×C₄×Dic₁₉	—	2	1	no	—
16	#10597315	—	2	2	no	—
17	#10597315	C₂²	1	4	yes	—
18	C₄×Dic₃₈	—	2	2	no	—
19	C₄×Dic₃₈	C₂²	1	4	yes	—
20	C₁₉×C₄⋊C₈	C₂²	1	4	yes	—
21	#10597274	C₂²	1	8	yes	—
22	#10597273	C₂²	1	8	yes	—
23	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₉	—	2	1	no	—
27	C₂²×Dic₁₉	—	2	2	no	—
28	C₂²×Dic₁₉	—	2	1	no	—
29	C₂×Dic₃₈	—	2	1	no	—
30	C₂×Dic₃₈	—	2	2	no	—
31	C₂×Dic₃₈	—	2	4	no	—
32	C₂×Dic₃₈	—	4	4	no	—
33	C₂×Dic₃₈	Q₈	1	4	yes	complemented
34	C₂×Dic₃₈	C₂³	1	2	yes	—
35	C₂×C₈×C₁₉	—	2	4	no	—
36	C₂×C₈×C₁₉	C₂³	1	4	yes	—
37	C₄²×C₁₉	D₄	1	2	yes	—
38	C₄²×C₁₉	C₂³	1	2	yes	—
39	C₄⋊Dic₁₉	—	2	1	no	—
40	C₄⋊Dic₁₉	—	2	2	no	—
41	C₄⋊Dic₁₉	—	2	4	no	—
42	C₄⋊Dic₁₉	C₂³	1	4	yes	—
43	C₄⋊Dic₁₉	C₂³	1	2	yes	—
44	Dic₁₉⋊C₄	—	2	4	no	—
45	C₄×Dic₁₉	—	2	4	no	—
46	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	—	2	2	no	—
48	C₂×C₄×C₁₉	SD₁₆	1	4	yes	—
49	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
50	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
52	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
53	C₂×C₄×C₁₉	#41	1	2	yes	—
54	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
55	C₂×Dic₁₉	—	2	4	no	—
56	C₂×Dic₁₉	—	2	2	no	—
57	C₂×Dic₁₉	—	2	2	no	—
58	C₂×Dic₁₉	—	2	4	no	—
59	C₂×Dic₁₉	—	4	4	no	—
60	C₂×Dic₁₉	—	4	2	no	—
61	Dic₃₈	—	2	4	no	—
62	Dic₃₈	—	2	2	no	—
63	Dic₃₈	—	4	8	no	—
64	Dic₃₈	C₂×Q₈	1	4	yes	complemented
65	C₈×C₁₉	—	2	4	no	—
66	C₂×#475	—	19	1	no	maximal, Sylow
67	C₂²×C₁₉	C₂²⋊Q₈	1	2	yes	—
68	C₂²×C₁₉	C₂×SD₁₆	1	2	yes	—
69	C₂²×C₁₉	#137	1	2	yes	—
70	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
71	C₄×C₁₉	—	2	2	no	—
72	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
73	C₄×C₁₉	C₂×SD₁₆	1	4	yes	—
74	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
75	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
76	Dic₁₉	—	2	4	no	—
77	Dic₁₉	—	4	4	no	—
78	Dic₁₉	—	4	2	no	—
79	C₂×C₄⋊Q₈	—	19	1	no	—
80	C₂×C₄×Q₈	—	19	1	no	—
81	#475	—	19	8	no	—
82	C₂×#106	—	19	2	no	—
83	C₂×C₄⋊C₈	D₁₉	1	1	yes	characteristic
84	C₂×#103	—	19	2	no	—
85	C₂×C₁₉	#475	1	4	yes	complemented
86	C₂×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
88	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
89	C₂²×Q₈	—	19	1	no	—
90	C₂²×Q₈	—	38	1	no	—
91	C₂²×C₈	C₂×D₁₉	1	2	yes	—
92	C₄⋊Q₈	—	19	4	no	—
93	C₄⋊Q₈	—	38	2	no	—
94	C₄×Q₈	—	19	4	no	—
95	C₄×Q₈	—	38	2	no	—
96	C₂×C₄⋊C₄	—	19	1	no	—
97	C₂×C₄⋊C₄	—	19	2	no	—
98	C₂×C₄⋊C₄	—	38	1	no	—
99	C₂×C₄⋊C₄	—	38	1	no	—
100	C₂×C₄²	—	38	1	no	—
101	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
102	#106	—	19	8	no	—
103	C₄⋊C₈	C₂×D₁₉	1	4	yes	—
104	#103	—	19	8	no	—
105	C₁₉	C₂×#475	1	1	yes	characteristic, complemented, Sylow
106	C₂×Q₈	—	19	4	no	—
107	C₂×Q₈	—	19	2	no	—
108	C₂×Q₈	—	38	1	no	—
109	C₂×Q₈	—	38	4	no	—
110	C₂×Q₈	—	38	2	no	—
111	C₂×Q₈	—	76	4	no	—
112	C₂²×C₄	—	38	1	no	—
113	C₂²×C₄	—	38	1	no	—
114	C₂²×C₄	—	38	2	no	—
115	C₂²×C₄	D₇₆	1	1	yes	characteristic
116	C₂²×C₄	D₇₆	1	1	yes	characteristic
117	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
118	C₂×C₈	—	2	4	no	—
119	C₂×C₈	C₂²×D₁₉	1	4	yes	—
120	C₄⋊C₄	—	19	4	no	—
121	C₄⋊C₄	—	19	2	no	—
122	C₄⋊C₄	—	38	4	no	—
123	C₄⋊C₄	—	38	1	no	—
124	C₄⋊C₄	—	38	2	no	—
125	C₄⋊C₄	—	38	4	no	—
126	C₄²	—	38	4	no	—
127	C₄²	D₇₆	1	2	yes	—
128	C₄²	C₂²×D₁₉	1	2	yes	—
129	C₂³	C₂×D₇₆	1	1	yes	characteristic
130	Q₈	—	19	4	no	—
131	Q₈	—	38	2	no	—
132	Q₈	—	38	4	no	—
133	Q₈	—	76	8	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	38	2	no	—
136	C₂×C₄	—	38	4	no	—
137	C₂×C₄	—	38	2	no	—
138	C₂×C₄	—	38	4	no	—
139	C₂×C₄	—	76	4	no	—
140	C₂×C₄	—	76	2	no	—
141	C₂×C₄	#64516	1	4	yes	—
142	C₂×C₄	C₂×D₇₆	1	2	yes	—
143	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
144	C₂×C₄	C₂×D₇₆	1	2	yes	—
145	C₂×C₄	#64543	1	2	yes	—
146	C₂×C₄	Q₈×D₁₉	1	2	yes	—
147	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
148	C₈	—	2	4	no	—
149	C₂²	#10597343	1	2	yes	—
150	C₂²	C₂×#64516	1	2	yes	—
151	C₂²	#10597355	1	2	yes	—
152	C₂²	C₂²×D₇₆	1	1	yes	characteristic
153	C₄	—	2	2	no	—
154	C₄	—	38	4	no	—
155	C₄	—	76	4	no	—
156	C₄	—	76	2	no	—
157	C₄	#10597343	1	2	yes	—
158	C₄	C₂×#64516	1	4	yes	—
159	C₄	C₂×#64543	1	1	yes	characteristic
160	C₄	C₂×Q₈×D₁₉	1	1	yes	characteristic
161	C₂	#11926830	1	4	yes	direct product factor
162	C₂	C₂×#10597343	1	1	yes	characteristic
163	C₂	C₂²×#64516	1	1	yes	characteristic
164	C₂	C₂×#10597355	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597315

C₂

yes

maximal, characteristic

C₂×C₄×Dic₃₈

C₂

yes

maximal, characteristic

#11926830

C₂

yes

maximal, direct product factor

C₂×#10597274

C₂

yes

maximal

C₂×#10597273

C₂

yes

maximal

C₂×C₁₉×C₄⋊C₈

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

—

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

#10597315

—

#10597315

C₂²

yes

—

C₄×Dic₃₈

—

C₄×Dic₃₈

C₂²

yes

—

C₁₉×C₄⋊C₈

C₂²

yes

—

#10597274

C₂²

yes

—

#10597273

C₂²

yes

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

Q₈

yes

complemented

C₂×Dic₃₈

C₂³

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

C₂×Q₈

yes

complemented

C₈×C₁₉

—

C₂×#475

—

maximal, Sylow

C₂²×C₁₉

C₂²⋊Q₈

yes

—

C₂²×C₁₉

C₂×SD₁₆

yes

—

C₂²×C₁₉

#137

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

C₂×SD₁₆

yes

—

C₄×C₁₉

C₂²×Q₈

yes

characteristic

C₄×C₁₉

C₂×#41

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

—

C₂×C₄×Q₈

—

#475

—

C₂×#106

—

C₂×C₄⋊C₈

D₁₉

yes

characteristic

C₂×#103

—

C₂×C₁₉

#475

yes

complemented

C₂×C₁₉

C₂×C₂²⋊Q₈

yes

characteristic

C₂×C₁₉

C₂²×SD₁₆

yes

characteristic

C₂×C₁₉

C₂×#137

yes

characteristic

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×C₈

C₂×D₁₉

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

100

C₂×C₄²

—

101

C₂×C₄²

C₂×D₁₉

yes

characteristic

102

#106

—

103

C₄⋊C₈

C₂×D₁₉

yes

—

104

#103

—

105

C₁₉

C₂×#475

yes

characteristic, complemented, Sylow

106

C₂×Q₈

—

107

C₂×Q₈

—

108

C₂×Q₈

—

109

C₂×Q₈

—

110

C₂×Q₈

—

111

C₂×Q₈

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

D₇₆

yes

characteristic

116

C₂²×C₄

D₇₆

yes

characteristic

117

C₂²×C₄

C₂²×D₁₉

yes

characteristic

118

C₂×C₈

—

119

C₂×C₈

C₂²×D₁₉

yes

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₄²

—

127

C₄²

D₇₆

yes

—

128

C₄²

C₂²×D₁₉

yes

—

129

C₂³

C₂×D₇₆

yes

characteristic

130

Q₈

—

131

Q₈

—

132

Q₈

—

133

Q₈

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

#64516

yes

—

142

C₂×C₄

C₂×D₇₆

yes

—

143

C₂×C₄

C₂×D₇₆

yes

characteristic

144

C₂×C₄

C₂×D₇₆

yes

—

145

C₂×C₄

#64543

yes

—

146

C₂×C₄

Q₈×D₁₉

yes

—

147

C₂×C₄

C₂³×D₁₉

yes

characteristic

148

C₈

—

149

C₂²

#10597343

yes

—

150

C₂²

C₂×#64516

yes

—

151

C₂²

#10597355

yes

—

152

C₂²

C₂²×D₇₆

yes

characteristic

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

#10597343

yes

—

158

C₄

C₂×#64516

yes

—

159

C₄

C₂×#64543

yes

characteristic

160

C₄

C₂×Q₈×D₁₉

yes

characteristic

161

C₂

#11926830

yes

direct product factor

162

C₂

C₂×#10597343

yes

characteristic

163

C₂

C₂²×#64516

yes

characteristic

164

C₂

C₂×#10597355

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₇₆
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₁₉×C₄⋊C₈	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	C₂×C₄⋊C₈	D₁₉
hypocenter	C₁₉	C₂×#475
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

subgroup

G/H

center

C₂³

C₂×D₇₆

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₂×C₁₉×C₄⋊C₈

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

hypercenter

C₂×C₄⋊C₈

D₁₉

hypocenter

C₁₉

C₂×#475

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
3. #11926830	C₂	direct (N × H)
33. C₂×Dic₃₈	Q₈	semidirect
64. Dic₃₈	C₂×Q₈	semidirect
85. C₂×C₁₉	#475	semidirect
105. C₁₉	C₂×#475	semidirect
161. C₂	#11926830	direct (N × H)

H ≅ G/N

type

3. #11926830

C₂

direct (N × H)

33. C₂×Dic₃₈

Q₈

semidirect

64. Dic₃₈

C₂×Q₈

semidirect

85. C₂×C₁₉

#475

semidirect

105. C₁₉

C₂×#475

semidirect

161. C₂

#11926830

direct (N × H)

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

subgroup	index
C₂×#10597315	2
C₂×C₄×Dic₃₈	2
#11926830	2
C₂×#10597274	2
C₂×#10597273	2
C₂×C₁₉×C₄⋊C₈	2
C₂×#475	19

subgroup

index

C₂×C₄×Dic₃₈

C₂×C₁₉×C₄⋊C₈

Subgroups — C₂×#11926830 #14573401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#11926830 #14573401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926830 #14573401