Group #14562082 — subgroups

Subgroups — #14562082

Order 2432.

252 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 93 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	#11926601	C₂	1	1	yes	maximal, characteristic
2	C₄×#64520	C₂	1	1	yes	maximal, characteristic
3	Q₈⋊(C₁₉⋊C₈)	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₈×C₁₉	C₄	1	1	yes	characteristic
6	C₄×Q₈×C₁₉	—	2	1	no	—
7	C₄×Q₈×C₁₉	—	2	1	no	—
8	C₄×Q₈×C₁₉	C₄	1	2	yes	—
9	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
10	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
11	C₂×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
12	C₂×C₄²×C₁₉	—	2	1	no	—
13	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×#64520	—	2	1	no	—
15	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
16	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
17	#10597260	—	2	1	no	—
18	#10597260	—	2	1	no	—
19	C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
20	C₂×Q₈×C₁₉	—	2	4	no	—
21	C₂×Q₈×C₁₉	—	2	1	no	—
22	C₂×Q₈×C₁₉	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₁₉	—	2	1	no	—
24	C₂²×C₄×C₁₉	—	2	1	no	—
25	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₄²×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	#64520	—	2	4	no	—
39	C₂×C₁₉⋊C₈	—	2	2	no	—
40	C₂×C₁₉⋊C₈	—	2	2	no	—
41	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
42	Q₈×C₁₉	—	2	4	no	—
43	Q₈×C₁₉	—	2	2	no	—
44	Q₈×C₁₉	M₁₆	1	4	yes	complemented
45	C₂×C₄×C₁₉	—	2	4	no	—
46	C₂×C₄×C₁₉	—	2	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	2	no	—
51	C₂×C₄×C₁₉	—	4	2	no	—
52	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
53	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
54	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₁₉⋊C₈	—	2	4	no	—
59	C₁₉⋊C₈	—	4	2	no	—
60	#1491	—	19	1	no	maximal, Sylow
61	C₂²×C₁₉	—	2	1	no	—
62	C₂²×C₁₉	—	2	1	no	—
63	C₂²×C₁₉	#104	1	2	yes	—
64	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₄×C₁₉	—	2	4	no	—
66	C₄×C₁₉	—	2	1	no	—
67	C₄×C₁₉	—	2	1	no	—
68	C₄×C₁₉	—	2	1	no	—
69	C₄×C₁₉	—	2	1	no	—
70	C₄×C₁₉	—	4	2	no	—
71	C₄×C₁₉	C₂×M₁₆	1	2	yes	—
72	C₄×C₁₉	#137	1	2	yes	—
73	C₂×C₄×Q₈	D₁₉	1	1	yes	characteristic
74	#432	—	19	1	no	—
75	C₄×M₁₆	—	19	1	no	—
76	Q₈⋊C₈	—	19	4	no	—
77	C₂×C₁₉	—	2	2	no	—
78	C₂×C₁₉	#407	1	1	yes	characteristic
79	C₂×C₁₉	#419	1	1	yes	characteristic
80	C₂×C₁₉	C₂×#104	1	1	yes	characteristic
81	C₂²×Q₈	Dic₁₉	1	1	yes	characteristic
82	C₂×M₁₆	—	38	1	no	—
83	C₄×Q₈	—	2	1	no	—
84	C₄×Q₈	—	2	1	no	—
85	C₄×Q₈	Dic₁₉	1	2	yes	—
86	C₄×Q₈	C₂×D₁₉	1	2	yes	—
87	C₂×C₄⋊C₄	—	2	1	no	—
88	C₂×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
89	C₂×C₄²	—	2	1	no	—
90	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
91	C₄⋊C₈	—	19	2	no	—
92	C₂²⋊C₈	—	38	1	no	—
93	#97	—	38	1	no	—
94	#97	—	38	1	no	—
95	C₄×C₈	—	19	2	no	—
96	C₁₉	#1491	1	1	yes	characteristic, complemented, Sylow
97	C₂×Q₈	—	2	4	no	—
98	C₂×Q₈	—	2	1	no	—
99	C₂×Q₈	C₂×Dic₁₉	1	2	yes	—
100	C₂²×C₄	—	2	1	no	—
101	C₂²×C₄	—	2	1	no	—
102	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
103	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
104	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
105	M₁₆	—	38	4	no	—
106	C₂×C₈	—	38	2	no	—
107	C₂×C₈	—	38	2	no	—
108	C₄⋊C₄	—	2	2	no	—
109	C₄⋊C₄	—	2	1	no	—
110	C₄⋊C₄	—	2	2	no	—
111	C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
112	C₄²	—	2	2	no	—
113	C₄²	—	2	2	no	—
114	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
115	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
116	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
117	C₄²	C₂²×D₁₉	1	1	yes	characteristic
118	C₂³	C₂²⋊Dic₁₉	1	1	yes	characteristic
119	Q₈	—	2	4	no	—
120	Q₈	—	2	2	no	—
121	Q₈	#64520	1	4	yes	complemented
122	C₂×C₄	—	2	4	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	4	2	no	—
129	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
130	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
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	1	yes	characteristic
134	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
135	C₈	—	38	4	no	—
136	C₈	—	76	2	no	—
137	C₂²	—	2	1	no	—
138	C₂²	—	2	1	no	—
139	C₂²	#10597294	1	2	yes	—
140	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
141	C₄	—	2	1	no	—
142	C₄	—	2	1	no	—
143	C₄	—	2	1	no	—
144	C₄	—	2	4	no	—
145	C₄	—	2	1	no	—
146	C₄	—	4	2	no	—
147	C₄	C₂×#64520	1	2	yes	—
148	C₄	#10597388	1	2	yes	—
149	C₂	—	2	2	no	—
150	C₂	#11926508	1	1	yes	characteristic
151	C₂	#11926553	1	1	yes	characteristic
152	C₂	C₂×#10597294	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926601

C₂

yes

maximal, characteristic

C₄×#64520

C₂

yes

maximal, characteristic

Q₈⋊(C₁₉⋊C₈)

C₂

yes

maximal, complemented

C₂×C₄×Q₈×C₁₉

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₄

yes

characteristic

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

C₄

yes

—

C₄×Q₈×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₄

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×#64520

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

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

C₂×C₄

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

M₁₆

yes

complemented

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

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

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

—

#1491

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#104

yes

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×M₁₆

yes

—

C₄×C₁₉

#137

yes

—

C₂×C₄×Q₈

D₁₉

yes

characteristic

#432

—

C₄×M₁₆

—

Q₈⋊C₈

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

Dic₁₉

yes

characteristic

C₂×M₁₆

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

Dic₁₉

yes

—

C₄×Q₈

C₂×D₁₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

Dic₁₉

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

—

C₁₉

#1491

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂×Dic₁₉

yes

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

103

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

104

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

105

M₁₆

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

C₂×Dic₁₉

yes

—

112

C₄²

—

113

C₄²

—

114

C₄²

C₂×Dic₁₉

yes

characteristic

115

C₄²

C₂²⋊D₁₉

yes

characteristic

116

C₄²

C₂²⋊D₁₉

yes

characteristic

117

C₄²

C₂²×D₁₉

yes

characteristic

118

C₂³

C₂²⋊Dic₁₉

yes

characteristic

119

Q₈

—

120

Q₈

—

121

Q₈

#64520

yes

complemented

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

130

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

131

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

132

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

133

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

134

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

135

C₈

—

136

C₈

—

137

C₂²

—

138

C₂²

—

139

C₂²

#10597294

yes

—

140

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

C₂×#64520

yes

—

148

C₄

#10597388

yes

—

149

C₂

—

150

C₂

#11926508

yes

characteristic

151

C₂

#11926553

yes

characteristic

152

C₂

C₂×#10597294

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₄²	C₂²×D₁₉
Fitting	C₂×C₄×Q₈×C₁₉	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×C₁₉	C₂²⋊C₄
cosocle	C₄²×C₁₉	C₂³
hypercenter	C₂×C₄×Q₈	D₁₉
hypocenter	C₁₉	#1491
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×Q₈

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₄²

C₂²×D₁₉

Fitting

C₂×C₄×Q₈×C₁₉

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂³×C₁₉

C₂²⋊C₄

cosocle

C₄²×C₁₉

C₂³

hypercenter

C₂×C₄×Q₈

D₁₉

hypocenter

C₁₉

#1491

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×Q₈

N	H ≅ G/N	type
3. Q₈⋊(C₁₉⋊C₈)	C₂	semidirect
44. Q₈×C₁₉	M₁₆	semidirect
96. C₁₉	#1491	semidirect
121. Q₈	#64520	semidirect

H ≅ G/N

type

3. Q₈⋊(C₁₉⋊C₈)

C₂

semidirect

44. Q₈×C₁₉

M₁₆

semidirect

96. C₁₉

#1491

semidirect

121. Q₈

#64520

semidirect

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

subgroup	index
#11926601	2
C₄×#64520	2
Q₈⋊(C₁₉⋊C₈)	2
C₂×C₄×Q₈×C₁₉	2
#1491	19

subgroup

index

#11926601

C₄×#64520

Q₈⋊(C₁₉⋊C₈)

C₂×C₄×Q₈×C₁₉

#1491

Subgroups — #14562082

Conjugacy classes of subgroups

Complements

Maximal subgroups