Group #14562292 — subgroups

Subgroups — #14562292

Order 2432.

212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 97 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	#11926597	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#11926293	C₂	1	2	yes	maximal, complemented
4	#11926290	C₂	1	2	yes	maximal, complemented
5	C₁₉×#533	C₂	1	1	yes	maximal, characteristic
6	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₁₉×#125	—	2	1	no	—
9	C₁₉×C₂²⋊Q₈	—	2	1	no	—
10	C₁₉×C₂²⋊Q₈	C₄	1	2	yes	—
11	C₄×Q₈×C₁₉	—	2	1	no	—
12	C₄×Q₈×C₁₉	C₄	1	2	yes	—
13	C₁₉×#117	—	2	1	no	—
14	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₁₉⋊C₈	—	2	1	no	—
16	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
17	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
18	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
19	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
20	C₄×C₁₉⋊C₈	—	2	1	no	—
21	C₂×Q₈×C₁₉	—	2	1	no	—
22	C₂×Q₈×C₁₉	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
26	C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂²⋊C₄×C₁₉	—	2	2	no	—
33	C₄²×C₁₉	—	2	2	no	—
34	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₄²×C₁₉	D₄	1	1	yes	characteristic
36	C₄²×C₁₉	D₄	1	1	yes	characteristic
37	C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₂×C₁₉⋊C₈	—	2	2	no	—
39	C₂×C₁₉⋊C₈	—	2	2	no	—
40	C₂×C₁₉⋊C₈	—	4	2	no	—
41	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
42	Q₈×C₁₉	—	4	2	no	—
43	Q₈×C₁₉	—	4	2	no	—
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	—	2	2	no	—
46	C₂×C₄×C₁₉	—	2	2	no	—
47	C₂×C₄×C₁₉	—	4	1	no	—
48	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
52	C₂×C₄×C₁₉	Q₁₆	1	2	yes	—
53	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
54	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₁₉⋊C₈	—	4	2	no	—
57	C₁₉⋊C₈	—	4	2	no	—
58	#1542	—	19	1	no	maximal, Sylow
59	C₂²×C₁₉	—	2	1	no	—
60	C₂²×C₁₉	—	2	1	no	—
61	C₂²×C₁₉	#103	1	2	yes	—
62	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₄×C₁₉	—	2	1	no	—
64	C₄×C₁₉	—	2	1	no	—
65	C₄×C₁₉	—	2	1	no	—
66	C₄×C₁₉	—	4	2	no	—
67	C₄×C₁₉	—	4	2	no	—
68	C₄×C₁₉	#103	1	2	yes	—
69	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
70	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
71	C₄×C₁₉	#135	1	2	yes	—
72	#533	D₁₉	1	1	yes	characteristic
73	#431	—	19	1	no	—
74	C₂×C₄⋊C₈	—	19	1	no	—
75	#333	—	19	2	no	—
76	#332	—	19	2	no	—
77	C₂×C₁₉	—	2	2	no	—
78	C₂×C₁₉	#413	1	1	yes	characteristic
79	C₂×C₁₉	C₂×#103	1	1	yes	characteristic
80	C₂×C₁₉	#416	1	1	yes	characteristic
81	C₂²×C₈	—	38	1	no	—
82	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
83	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
84	#125	—	2	1	no	—
85	C₂²⋊Q₈	—	2	1	no	—
86	C₂²⋊Q₈	Dic₁₉	1	2	yes	—
87	C₄×Q₈	—	2	1	no	—
88	C₄×Q₈	Dic₁₉	1	2	yes	—
89	#117	—	2	1	no	—
90	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
91	C₄⋊C₈	—	19	2	no	—
92	C₄⋊C₈	—	19	2	no	—
93	C₄⋊C₈	—	38	1	no	—
94	C₂²⋊C₈	—	38	1	no	—
95	C₄×C₈	—	38	1	no	—
96	C₁₉	#1542	1	1	yes	characteristic, complemented, Sylow
97	C₂×Q₈	—	2	1	no	—
98	C₂×Q₈	C₂×Dic₁₉	1	2	yes	—
99	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
100	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
101	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
102	C₂×C₈	—	38	2	no	—
103	C₂×C₈	—	38	2	no	—
104	C₂×C₈	—	76	2	no	—
105	C₄⋊C₄	—	2	2	no	—
106	C₄⋊C₄	—	2	2	no	—
107	C₄⋊C₄	—	2	1	no	—
108	C₄⋊C₄	—	2	1	no	—
109	C₄⋊C₄	—	2	1	no	—
110	C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
111	C₂²⋊C₄	—	2	2	no	—
112	C₄²	—	2	2	no	—
113	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
114	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
115	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
116	C₄²	C₂²×D₁₉	1	1	yes	characteristic
117	C₂³	C₂²⋊Dic₁₉	1	1	yes	characteristic
118	Q₈	—	4	2	no	—
119	Q₈	—	4	2	no	—
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	4	1	no	—
124	C₂×C₄	#64527	1	2	yes	—
125	C₂×C₄	#64528	1	2	yes	—
126	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
127	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
128	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
129	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
130	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
131	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
132	C₈	—	76	2	no	—
133	C₈	—	76	2	no	—
134	C₂²	—	2	1	no	—
135	C₂²	—	2	1	no	—
136	C₂²	#10597292	1	2	yes	—
137	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
138	C₄	—	2	1	no	—
139	C₄	—	2	1	no	—
140	C₄	—	2	1	no	—
141	C₄	—	4	2	no	—
142	C₄	—	4	2	no	—
143	C₄	#10597292	1	2	yes	—
144	C₄	C₂×#64527	1	1	yes	characteristic
145	C₄	C₂×#64528	1	1	yes	characteristic
146	C₄	#10597396	1	2	yes	—
147	C₂	—	2	2	no	—
148	C₂	#11926528	1	1	yes	characteristic
149	C₂	C₂×#10597292	1	1	yes	characteristic
150	C₂	#11926540	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926597

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂

yes

maximal, characteristic

#11926293

C₂

yes

maximal, complemented

#11926290

C₂

yes

maximal, complemented

C₁₉×#533

C₂

yes

maximal, characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

C₄

yes

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

C₄

yes

—

C₁₉×#117

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

Q₁₆

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1542

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#103

yes

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#103

yes

—

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₄×C₁₉

C₂×Q₁₆

yes

characteristic

C₄×C₁₉

#135

yes

—

#533

D₁₉

yes

characteristic

#431

—

C₂×C₄⋊C₈

—

#333

—

#332

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

Dic₁₉

yes

—

C₄×Q₈

—

C₄×Q₈

Dic₁₉

yes

—

#117

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₁₉

#1542

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

100

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

101

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

C₂×Dic₁₉

yes

—

111

C₂²⋊C₄

—

112

C₄²

—

113

C₄²

C₂×Dic₁₉

yes

characteristic

114

C₄²

C₂²⋊D₁₉

yes

characteristic

115

C₄²

C₂²⋊D₁₉

yes

characteristic

116

C₄²

C₂²×D₁₉

yes

characteristic

117

C₂³

C₂²⋊Dic₁₉

yes

characteristic

118

Q₈

—

119

Q₈

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

#64527

yes

—

125

C₂×C₄

#64528

yes

—

126

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

127

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

128

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

129

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

130

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

131

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

132

C₈

—

133

C₈

—

134

C₂²

—

135

C₂²

—

136

C₂²

#10597292

yes

—

137

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

#10597292

yes

—

144

C₄

C₂×#64527

yes

characteristic

145

C₄

C₂×#64528

yes

characteristic

146

C₄

#10597396

yes

—

147

C₂

—

148

C₂

#11926528

yes

characteristic

149

C₂

C₂×#10597292

yes

characteristic

150

C₂

#11926540

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#533	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×C₁₉	C₂²⋊C₄
cosocle	C₄²×C₁₉	C₂³
hypercenter	#533	D₁₉
hypocenter	C₁₉	#1542
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #533

subgroup

G/H

center

C₂×C₄

C₂²⋊Dic₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#533

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂³×C₁₉

C₂²⋊C₄

cosocle

C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #533

N	H ≅ G/N	type
3. #11926293	C₂	semidirect
4. #11926290	C₂	semidirect
96. C₁₉	#1542	semidirect

H ≅ G/N

type

3. #11926293

C₂

semidirect

4. #11926290

C₂

semidirect

96. C₁₉

#1542

semidirect

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

subgroup	index
#11926597	2
C₂×C₄⋊(C₁₉⋊C₈)	2
#11926293	2
#11926290	2
C₁₉×#533	2
#1542	19

subgroup

index

C₂×C₄⋊(C₁₉⋊C₈)

C₁₉×#533

Subgroups — #14562292

Conjugacy classes of subgroups

Complements

Maximal subgroups