Group #14565324 — subgroups

Subgroups — #14565324

Order 2432.

230 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 73 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×#10597293	C₂	1	2	yes	maximal, complemented
2	#11926343	C₂	1	2	yes	maximal, complemented
3	#11926341	C₂	1	2	yes	maximal, complemented
4	C₁₉×#536	C₂	1	1	yes	maximal, characteristic
5	C₂×#41×C₁₉	C₄	1	1	yes	characteristic
6	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
8	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₁₉×#124	C₄	1	1	yes	characteristic
10	C₁₉×#124	C₂²	1	1	yes	characteristic
11	C₁₉×#123	—	2	2	no	—
12	C₁₉×C₂²⋊Q₈	—	2	2	no	—
13	C₁₉×#117	C₄	1	1	yes	characteristic
14	C₂×#64520	—	2	2	no	—
15	#10597293	—	2	2	no	—
16	#10597293	C₂²	1	4	yes	—
17	#41×C₁₉	—	4	2	no	—
18	C₂×Q₈×C₁₉	—	4	2	no	—
19	C₂×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×Q₈×C₁₉	D₄	1	2	yes	—
22	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
23	C₂×D₄×C₁₉	—	2	1	no	—
24	C₂×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	—	2	1	no	—
26	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	D₄	1	2	yes	—
28	C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂²⋊C₄×C₁₉	—	2	1	no	—
32	C₂²⋊C₄×C₁₉	—	2	2	no	—
33	C₂²⋊C₄×C₁₉	—	2	2	no	—
34	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
36	#64520	—	2	4	no	—
37	#64520	—	4	2	no	—
38	C₂×C₁₉⋊C₈	—	4	2	no	—
39	C₂³×C₁₉	—	2	1	no	—
40	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
41	Q₈×C₁₉	—	4	1	no	—
42	Q₈×C₁₉	—	4	2	no	—
43	Q₈×C₁₉	—	4	1	no	—
44	Q₈×C₁₉	—	4	1	no	—
45	D₄×C₁₉	—	4	1	no	—
46	D₄×C₁₉	—	4	2	no	—
47	C₂×C₄×C₁₉	—	2	2	no	—
48	C₂×C₄×C₁₉	—	2	2	no	—
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	4	2	no	—
54	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
55	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
58	C₁₉⋊C₈	—	4	4	no	—
59	#2133	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	—	4	1	no	—
61	C₂²×C₁₉	—	4	2	no	—
62	C₂²×C₁₉	—	4	1	no	—
63	C₂²×C₁₉	#99	1	2	yes	—
64	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₄×C₁₉	—	2	2	no	—
66	C₄×C₁₉	—	2	1	no	—
67	C₄×C₁₉	—	2	2	no	—
68	C₄×C₁₉	—	2	1	no	—
69	C₄×C₁₉	—	4	1	no	—
70	C₄×C₁₉	—	4	1	no	—
71	C₄×C₁₉	—	4	1	no	—
72	#536	D₁₉	1	1	yes	characteristic
73	C₂×#101	—	19	2	no	—
74	#356	—	19	2	no	—
75	#355	—	19	2	no	—
76	C₂×C₁₉	—	2	1	no	—
77	C₂×C₁₉	—	2	2	no	—
78	C₂×C₁₉	—	8	1	no	—
79	C₂×C₁₉	C₂×#99	1	1	yes	characteristic
80	C₂×#41	Dic₁₉	1	1	yes	characteristic
81	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
82	C₂×M₁₆	—	38	2	no	—
83	C₄⋊Q₈	Dic₁₉	1	1	yes	characteristic
84	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
85	#124	Dic₁₉	1	1	yes	characteristic
86	#124	C₂×D₁₉	1	1	yes	characteristic
87	#123	—	2	2	no	—
88	C₂²⋊Q₈	—	2	2	no	—
89	#117	Dic₁₉	1	1	yes	characteristic
90	#101	—	19	4	no	—
91	#101	—	38	2	no	—
92	C₁₉	#2133	1	1	yes	characteristic, complemented, Sylow
93	#41	—	4	2	no	—
94	C₂×Q₈	—	4	2	no	—
95	C₂×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
96	C₂×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
97	C₂×Q₈	C₂²⋊D₁₉	1	2	yes	—
98	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
99	C₂×D₄	—	2	1	no	—
100	C₂×D₄	C₂×Dic₁₉	1	1	yes	characteristic
101	C₂²×C₄	—	2	1	no	—
102	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
103	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
104	M₁₆	—	38	4	no	—
105	M₁₆	—	76	2	no	—
106	C₂×C₈	—	76	2	no	—
107	C₄⋊C₄	—	2	1	no	—
108	C₄⋊C₄	—	2	2	no	—
109	C₄⋊C₄	—	2	2	no	—
110	C₂²⋊C₄	—	2	1	no	—
111	C₂²⋊C₄	—	2	2	no	—
112	C₂²⋊C₄	—	2	2	no	—
113	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
114	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
115	C₂³	—	2	1	no	—
116	C₂³	C₂²⋊Dic₁₉	1	1	yes	characteristic
117	Q₈	—	4	1	no	—
118	Q₈	—	4	2	no	—
119	Q₈	—	4	1	no	—
120	Q₈	—	4	1	no	—
121	D₄	—	4	1	no	—
122	D₄	—	4	2	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	4	2	no	—
130	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
131	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
132	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
133	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
134	C₈	—	76	4	no	—
135	C₂²	—	4	1	no	—
136	C₂²	—	4	2	no	—
137	C₂²	—	4	1	no	—
138	C₂²	#10597291	1	2	yes	—
139	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
140	C₄	—	2	2	no	—
141	C₄	—	2	1	no	—
142	C₄	—	2	2	no	—
143	C₄	—	2	1	no	—
144	C₄	—	4	1	no	—
145	C₄	—	4	1	no	—
146	C₄	—	4	1	no	—
147	C₂	—	2	1	no	—
148	C₂	—	2	2	no	—
149	C₂	—	8	1	no	—
150	C₂	C₂×#10597291	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597293

C₂

yes

maximal, complemented

#11926343

C₂

yes

maximal, complemented

#11926341

C₂

yes

maximal, complemented

C₁₉×#536

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₄

yes

characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

C₄

yes

characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#124

C₄

yes

characteristic

C₁₉×#124

C₂²

yes

characteristic

C₁₉×#123

—

C₁₉×C₂²⋊Q₈

—

C₁₉×#117

C₄

yes

—

—

C₂²

yes

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂×Q₈×C₁₉

D₄

yes

—

C₂×Q₈×C₁₉

C₂³

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×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

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₁₉⋊C₈

—

#2133

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#99

yes

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

#536

D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#99

yes

characteristic

C₂×#41

Dic₁₉

yes

characteristic

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₂×M₁₆

—

C₄⋊Q₈

Dic₁₉

yes

characteristic

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

#124

Dic₁₉

yes

characteristic

#124

C₂×D₁₉

yes

characteristic

#123

—

C₂²⋊Q₈

—

#117

Dic₁₉

yes

characteristic

#101

—

#101

—

C₁₉

#2133

yes

characteristic, complemented, Sylow

#41

—

C₂×Q₈

—

C₂×Q₈

C₂×Dic₁₉

yes

characteristic

C₂×Q₈

C₂×Dic₁₉

yes

characteristic

C₂×Q₈

C₂²⋊D₁₉

yes

—

C₂×Q₈

C₂²×D₁₉

yes

characteristic

C₂×D₄

—

100

C₂×D₄

C₂×Dic₁₉

yes

characteristic

101

C₂²×C₄

—

102

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

103

C₂²×C₄

C₂²⋊D₁₉

yes

—

104

M₁₆

—

105

M₁₆

—

106

C₂×C₈

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₂²⋊C₄

—

111

C₂²⋊C₄

—

112

C₂²⋊C₄

—

113

C₄²

C₂×Dic₁₉

yes

characteristic

114

C₄²

C₂×Dic₁₉

yes

characteristic

115

C₂³

—

116

C₂³

C₂²⋊Dic₁₉

yes

characteristic

117

Q₈

—

118

Q₈

—

119

Q₈

—

120

Q₈

—

121

D₄

—

122

D₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

C₂²⋊Dic₁₉

yes

—

131

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

132

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

133

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

134

C₈

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

#10597291

yes

—

139

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₂

—

148

C₂

—

149

C₂

—

150

C₂

C₂×#10597291

yes

characteristic

	subgroup	G/H
center	C₂	C₂×#10597291
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂×Q₈	C₂²×D₁₉
Fitting	C₁₉×#536	C₂
socle	C₂×C₁₉	C₂×#99
prime radical	C₂×#41×C₁₉	C₄
cosocle	C₂×Q₈×C₁₉	C₂³
hypercenter	#536	D₁₉
hypocenter	C₁₉	#2133
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂²×Q₈ ◁ #536

subgroup

G/H

center

C₂

C₂×#10597291

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂×Q₈

C₂²×D₁₉

Fitting

C₁₉×#536

C₂

socle

C₂×C₁₉

C₂×#99

prime radical

C₂×#41×C₁₉

C₄

cosocle

C₂×Q₈×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂³ ◁ C₂²×Q₈ ◁ #536

N	H ≅ G/N	type
1. C₂×#10597293	C₂	semidirect
2. #11926343	C₂	semidirect
3. #11926341	C₂	semidirect
92. C₁₉	#2133	semidirect

H ≅ G/N

type

1. C₂×#10597293

C₂

semidirect

2. #11926343

C₂

semidirect

3. #11926341

C₂

semidirect

92. C₁₉

#2133

semidirect

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

subgroup	index
C₂×#10597293	2
#11926343	2
#11926341	2
C₁₉×#536	2
#2133	19

subgroup

index

C₁₉×#536

Subgroups — #14565324

Conjugacy classes of subgroups

Complements

Maximal subgroups