Group #14574076 — subgroups

Subgroups — C₂×#11926939 #14574076

Order 2432.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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	C₂²×#64528	C₂	1	2	yes	maximal, complemented
2	C₂²×#64526	C₂	1	2	yes	maximal
3	C₂×#10597315	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926939	C₂	1	8	yes	maximal, direct product factor
5	C₂×#10597260	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#124	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₈	C₂²	1	2	yes	—
10	C₁₉×#124	—	2	2	no	—
11	C₁₉×#124	C₂²	1	4	yes	—
12	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
13	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×#64528	—	2	8	no	—
15	C₂×#64528	C₂²	1	8	yes	complemented
16	C₂×#64526	—	2	8	no	—
17	C₂×#64526	C₂²	1	8	yes	—
18	C₂×C₄⋊Dic₁₉	—	2	2	no	—
19	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
20	#10597315	—	2	2	no	—
21	#10597315	C₂²	1	4	yes	complemented
22	#10597260	C₂²	1	4	yes	complemented
23	C₂⁴×C₁₉	—	2	1	no	—
24	C₂×Q₈×C₁₉	—	2	1	no	—
25	C₂×Q₈×C₁₉	—	2	4	no	—
26	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
27	C₂×D₄×C₁₉	—	2	4	no	—
28	C₂×D₄×C₁₉	—	2	1	no	—
29	C₂×D₄×C₁₉	C₂³	1	2	yes	—
30	C₂²×C₄×C₁₉	—	2	1	no	—
31	C₂²×C₄×C₁₉	D₄	1	2	yes	—
32	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂²×Dic₁₉	—	2	2	no	—
34	C₂×Dic₃₈	—	2	4	no	—
35	C₂×Dic₃₈	—	2	4	no	—
36	C₂×Dic₃₈	—	2	2	no	—
37	C₂×Dic₃₈	C₂³	1	4	yes	—
38	C₂²⋊C₄×C₁₉	—	2	8	no	—
39	C₄²×C₁₉	D₄	1	2	yes	—
40	C₄²×C₁₉	C₂³	1	2	yes	—
41	#64528	—	2	16	no	—
42	#64526	—	2	16	no	—
43	C₄⋊Dic₁₉	—	2	8	no	—
44	C₂×C₁₉⋊C₈	D₄	1	8	yes	—
45	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
46	C₂³×C₁₉	—	2	2	no	—
47	C₂³×C₁₉	—	4	2	no	—
48	C₂³×C₁₉	—	4	4	no	—
49	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
50	Q₈×C₁₉	—	2	4	no	—
51	Q₈×C₁₉	—	4	2	no	—
52	D₄×C₁₉	—	2	4	no	—
53	D₄×C₁₉	—	4	2	no	—
54	C₂×C₄×C₁₉	—	2	4	no	—
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	—	4	2	no	—
57	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
58	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
59	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
61	C₂×Dic₁₉	—	2	4	no	—
62	C₂×Dic₁₉	—	4	4	no	—
63	Dic₃₈	—	2	4	no	—
64	Dic₃₈	—	2	4	no	—
65	Dic₃₈	—	4	4	no	—
66	C₁₉⋊C₈	C₂×D₄	1	8	yes	—
67	C₂×#497	—	19	1	no	maximal, Sylow
68	C₂²×C₁₉	—	4	2	no	—
69	C₂²×C₁₉	—	4	4	no	—
70	C₂²×C₁₉	—	8	4	no	—
71	C₂²×C₁₉	#127	1	2	yes	—
72	C₂²×C₁₉	#137	1	4	yes	—
73	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
74	C₄×C₁₉	—	2	4	no	—
75	C₄×C₁₉	—	4	2	no	—
76	C₄×C₁₉	#127	1	2	yes	—
77	C₄×C₁₉	C₂²×D₄	1	2	yes	—
78	Dic₁₉	—	4	4	no	—
79	C₂²×Q₁₆	—	19	2	no	—
80	C₂²×SD₁₆	—	19	2	no	—
81	C₂×C₄⋊Q₈	—	19	1	no	—
82	C₂×#124	D₁₉	1	1	yes	characteristic
83	#497	—	19	8	no	—
84	C₂×#97	—	19	1	no	—
85	C₂×C₁₉	—	8	2	no	—
86	C₂×C₁₉	#497	1	4	yes	complemented
87	C₂×C₁₉	C₂×#127	1	1	yes	characteristic
88	C₂×C₁₉	C₂×#137	1	2	yes	—
89	C₂²×Q₈	—	19	2	no	—
90	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
91	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
92	C₂×Q₁₆	—	19	8	no	—
93	C₂×Q₁₆	—	38	8	no	—
94	C₂×SD₁₆	—	19	8	no	—
95	C₂×SD₁₆	—	38	8	no	—
96	C₂²×C₈	—	19	2	no	—
97	C₄⋊Q₈	—	19	4	no	—
98	C₄⋊Q₈	—	38	2	no	—
99	#124	—	2	2	no	—
100	#124	C₂×D₁₉	1	4	yes	—
101	C₂×C₄⋊C₄	—	38	2	no	—
102	C₂×C₂²⋊C₄	—	2	2	no	—
103	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
104	#97	—	19	4	no	—
105	C₁₉	C₂×#497	1	1	yes	characteristic, complemented, Sylow
106	C₂⁴	—	2	1	no	—
107	C₂×Q₈	—	2	1	no	—
108	C₂×Q₈	—	2	4	no	—
109	C₂×Q₈	—	19	4	no	—
110	C₂×Q₈	—	38	2	no	—
111	C₂×Q₈	—	38	4	no	—
112	C₂×Q₈	—	38	4	no	—
113	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
114	C₂×D₄	—	2	4	no	—
115	C₂×D₄	—	2	1	no	—
116	C₂×D₄	C₂²×D₁₉	1	2	yes	—
117	C₂²×C₄	—	2	1	no	—
118	C₂²×C₄	—	38	2	no	—
119	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
120	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
121	Q₁₆	—	38	16	no	—
122	SD₁₆	—	38	16	no	—
123	C₂×C₈	—	19	8	no	—
124	C₂×C₈	—	19	4	no	—
125	C₄⋊C₄	—	38	8	no	—
126	C₂²⋊C₄	—	2	8	no	—
127	C₄²	C₂²⋊D₁₉	1	2	yes	—
128	C₄²	C₂²×D₁₉	1	2	yes	—
129	C₂³	—	2	2	no	—
130	C₂³	—	4	2	no	—
131	C₂³	—	4	4	no	—
132	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
133	Q₈	—	2	4	no	—
134	Q₈	—	4	2	no	—
135	Q₈	—	38	4	no	—
136	Q₈	—	38	4	no	—
137	Q₈	—	76	4	no	—
138	D₄	—	2	4	no	—
139	D₄	—	4	2	no	—
140	C₂×C₄	—	2	4	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	4	2	no	—
143	C₂×C₄	—	38	4	no	—
144	C₂×C₄	—	76	4	no	—
145	C₂×C₄	D₄×D₁₉	1	4	yes	—
146	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
147	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
148	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
149	C₈	—	19	8	no	—
150	C₂²	—	4	4	no	—
151	C₂²	—	4	2	no	—
152	C₂²	—	8	4	no	—
153	C₂²	#10597386	1	2	yes	—
154	C₂²	#10597397	1	4	yes	—
155	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
156	C₄	—	2	4	no	—
157	C₄	—	4	2	no	—
158	C₄	—	76	4	no	—
159	C₄	#10597386	1	2	yes	—
160	C₄	C₂×D₄×D₁₉	1	2	yes	—
161	C₂	—	8	2	no	—
162	C₂	#11926939	1	4	yes	direct product factor
163	C₂	C₂×#10597386	1	1	yes	characteristic
164	C₂	C₂×#10597397	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64528

C₂

yes

maximal, complemented

C₂²×#64526

C₂

yes

maximal

C₂×#10597315

C₂

yes

maximal, characteristic, complemented

#11926939

C₂

yes

maximal, direct product factor

C₂×#10597260

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#124

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₁₉×#124

—

C₁₉×#124

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×#64528

—

C₂×#64528

C₂²

yes

complemented

C₂×#64526

—

C₂×#64526

C₂²

yes

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597315

—

#10597315

C₂²

yes

complemented

#10597260

C₂²

yes

complemented

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂³

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂³

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

—

#64528

—

#64526

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₁₉⋊C₈

C₂×D₄

yes

—

C₂×#497

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#127

yes

—

C₂²×C₁₉

#137

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#127

yes

—

C₄×C₁₉

C₂²×D₄

yes

—

Dic₁₉

—

C₂²×Q₁₆

—

C₂²×SD₁₆

—

C₂×C₄⋊Q₈

—

C₂×#124

D₁₉

yes

characteristic

#497

—

C₂×#97

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₂²×D₄

C₂×D₁₉

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×SD₁₆

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

#124

—

100

#124

C₂×D₁₉

yes

—

101

C₂×C₄⋊C₄

—

102

C₂×C₂²⋊C₄

—

103

C₂×C₄²

C₂×D₁₉

yes

characteristic

104

#97

—

105

C₁₉

C₂×#497

yes

characteristic, complemented, Sylow

106

C₂⁴

—

107

C₂×Q₈

—

108

C₂×Q₈

—

109

C₂×Q₈

—

110

C₂×Q₈

—

111

C₂×Q₈

—

112

C₂×Q₈

—

113

C₂×Q₈

C₂²×D₁₉

yes

—

114

C₂×D₄

—

115

C₂×D₄

—

116

C₂×D₄

C₂²×D₁₉

yes

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

C₂²⋊D₁₉

yes

—

120

C₂²×C₄

C₂²×D₁₉

yes

characteristic

121

Q₁₆

—

122

SD₁₆

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₄⋊C₄

—

126

C₂²⋊C₄

—

127

C₄²

C₂²⋊D₁₉

yes

—

128

C₄²

C₂²×D₁₉

yes

—

129

C₂³

—

130

C₂³

—

131

C₂³

—

132

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

133

Q₈

—

134

Q₈

—

135

Q₈

—

136

Q₈

—

137

Q₈

—

138

D₄

—

139

D₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

D₄×D₁₉

yes

—

146

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

147

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

148

C₂×C₄

C₂³×D₁₉

yes

characteristic

149

C₈

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

#10597386

yes

—

154

C₂²

#10597397

yes

—

155

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

156

C₄

—

157

C₄

—

158

C₄

—

159

C₄

#10597386

yes

—

160

C₄

C₂×D₄×D₁₉

yes

—

161

C₂

—

162

C₂

#11926939

yes

direct product factor

163

C₂

C₂×#10597386

yes

characteristic

164

C₂

C₂×#10597397

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₁₉×#124	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂²×D₄×C₁₉	C₂²
hypercenter	C₂×#124	D₁₉
hypocenter	C₁₉	C₂×#497
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#124

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₂×C₁₉×#124

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂²×D₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#124

N	H ≅ G/N	type
1. C₂²×#64528	C₂	semidirect
3. C₂×#10597315	C₂	semidirect
4. #11926939	C₂	direct (N × H)
5. C₂×#10597260	C₂	semidirect
15. C₂×#64528	C₂²	semidirect
21. #10597315	C₂²	semidirect
22. #10597260	C₂²	semidirect
86. C₂×C₁₉	#497	semidirect
105. C₁₉	C₂×#497	semidirect
162. C₂	#11926939	direct (N × H)

H ≅ G/N

type

1. C₂²×#64528

C₂

semidirect

3. C₂×#10597315

C₂

semidirect

4. #11926939

C₂

direct (N × H)

5. C₂×#10597260

C₂

semidirect

15. C₂×#64528

C₂²

semidirect

21. #10597315

C₂²

semidirect

22. #10597260

C₂²

semidirect

86. C₂×C₁₉

#497

semidirect

105. C₁₉

C₂×#497

semidirect

162. C₂

#11926939

direct (N × H)

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

subgroup	index
C₂²×#64528	2
C₂²×#64526	2
C₂×#10597315	2
#11926939	2
C₂×#10597260	2
C₂×C₁₉×#124	2
C₂×#497	19

subgroup

index

C₂²×#64528

C₂²×#64526

C₂×C₁₉×#124

Subgroups — C₂×#11926939 #14574076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#11926939 #14574076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926939 #14574076