Group #14564545 — subgroups

Subgroups — #14564545

Order 2432.

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

normal subgroups only

This group has 316 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	C₂²×D₁₅₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597276	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926548	C₂	1	2	yes	maximal, complemented
4	C₂×#10597280	C₂	1	2	yes	maximal, complemented
5	C₁₉×#405	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₇₆	C₂²	1	2	yes	—
7	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#117	C₂²	1	1	yes	characteristic
10	C₂×#64520	C₂²	1	2	yes	—
11	C₂×D₁₅₂	—	2	2	no	—
12	C₂×D₁₅₂	—	2	1	no	—
13	C₂×D₁₅₂	—	2	1	no	—
14	C₂×D₁₅₂	C₄	1	4	yes	complemented
15	C₁₉×#97	—	2	1	no	—
16	C₄×C₈×C₁₉	—	2	1	no	—
17	#10597280	—	2	4	no	—
18	#10597276	—	2	2	no	—
19	#10597266	—	2	4	no	—
20	C₂³×D₁₉	—	2	2	no	—
21	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×D₇₆	—	2	2	no	—
23	C₂×D₇₆	—	2	2	no	—
24	C₂×D₇₆	—	2	2	no	—
25	C₂×D₇₆	—	2	2	no	—
26	C₂×D₇₆	—	2	2	no	—
27	C₂×D₇₆	C₂×C₄	1	4	yes	—
28	M₁₆×C₁₉	—	2	1	no	—
29	M₁₆×C₁₉	D₄	1	2	yes	—
30	C₂×C₈×C₁₉	—	2	1	no	—
31	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
32	C₂×C₈×C₁₉	D₄	1	2	yes	—
33	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
34	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
35	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
36	C₂²⋊C₄×C₁₉	—	2	1	no	—
37	C₄²×C₁₉	—	2	1	no	—
38	#64520	—	2	2	no	—
39	#64520	—	2	2	no	—
40	C₂×C₁₉⋊C₈	—	2	2	no	—
41	D₁₅₂	—	2	4	no	—
42	D₁₅₂	—	2	4	no	—
43	C₂³×C₁₉	#41	1	1	yes	characteristic
44	C₂²×D₁₉	—	2	4	no	—
45	C₂²×D₁₉	—	4	2	no	—
46	C₂²×D₁₉	—	4	2	no	—
47	C₂²×D₁₉	—	8	4	no	—
48	C₂×C₄×C₁₉	—	2	2	no	—
49	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
55	D₇₆	—	2	4	no	—
56	D₇₆	—	2	4	no	—
57	D₇₆	—	4	2	no	—
58	D₇₆	—	4	2	no	—
59	C₈×C₁₉	—	2	2	no	—
60	C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
61	C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
62	C₁₉⋊C₈	—	4	2	no	—
63	#1978	—	19	1	no	maximal, Sylow
64	C₂²×C₁₉	—	2	2	no	—
65	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
66	C₂²×C₁₉	#121	1	1	yes	characteristic
67	C₂²×C₁₉	#124	1	1	yes	characteristic
68	C₂×D₁₉	—	4	4	no	—
69	C₂×D₁₉	—	8	4	no	—
70	C₂×D₁₉	—	8	4	no	—
71	C₂×D₁₉	—	8	4	no	—
72	C₄×C₁₉	—	4	2	no	—
73	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
74	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
75	C₄×C₁₉	#121	1	1	yes	characteristic
76	C₄×C₁₉	#127	1	1	yes	characteristic
77	C₂²×D₈	—	19	1	no	—
78	C₂×#108	—	19	1	no	—
79	#418	—	19	2	no	—
80	C₂×#100	—	19	2	no	—
81	#405	D₁₉	1	1	yes	characteristic, complemented
82	C₂×C₁₉	—	2	1	no	—
83	C₂×C₁₉	—	2	1	no	—
84	C₂×C₁₉	#390	1	1	yes	characteristic
85	C₂×C₁₉	#472	1	2	yes	—
86	D₁₉	—	8	4	no	—
87	C₂²×D₄	—	19	2	no	—
88	C₂×D₈	—	19	4	no	—
89	C₂×D₈	—	38	2	no	—
90	C₂×D₈	—	38	1	no	—
91	C₂×D₈	—	38	1	no	—
92	C₂×M₁₆	—	19	2	no	—
93	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
94	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
95	#117	C₂×D₁₉	1	1	yes	characteristic
96	#108	—	38	2	no	—
97	#102	—	38	4	no	—
98	#100	—	38	4	no	—
99	#97	—	2	1	no	—
100	C₄×C₈	—	2	1	no	—
101	C₁₉	#1978	1	1	yes	characteristic, complemented, Sylow
102	C₂⁴	—	38	2	no	—
103	C₂×D₄	—	19	4	no	—
104	C₂×D₄	—	38	2	no	—
105	C₂×D₄	—	38	2	no	—
106	C₂×D₄	—	38	2	no	—
107	C₂×D₄	—	38	2	no	—
108	C₂×D₄	—	38	2	no	—
109	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
110	D₈	—	38	4	no	—
111	D₈	—	38	4	no	—
112	M₁₆	—	2	1	no	—
113	M₁₆	—	38	2	no	—
114	M₁₆	—	38	2	no	—
115	M₁₆	D₇₆	1	2	yes	—
116	C₂×C₈	—	2	1	no	—
117	C₂×C₈	—	38	2	no	—
118	C₂×C₈	C₄×D₁₉	1	2	yes	—
119	C₂×C₈	D₇₆	1	2	yes	—
120	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
121	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
122	C₄⋊C₄	D₇₆	1	2	yes	—
123	C₂²⋊C₄	—	2	1	no	—
124	C₄²	—	2	1	no	—
125	C₂³	—	38	4	no	—
126	C₂³	—	76	2	no	—
127	C₂³	—	76	2	no	—
128	C₂³	—	152	4	no	—
129	C₂³	#64541	1	1	yes	characteristic
130	D₄	—	38	4	no	—
131	D₄	—	38	4	no	—
132	D₄	—	76	2	no	—
133	D₄	—	76	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
136	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
137	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
138	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
139	C₂×C₄	#64541	1	1	yes	characteristic
140	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
141	C₈	—	2	2	no	—
142	C₈	—	76	2	no	—
143	C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
144	C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
145	C₂²	—	2	2	no	—
146	C₂²	—	76	4	no	—
147	C₂²	—	152	4	no	—
148	C₂²	—	152	4	no	—
149	C₂²	—	152	4	no	—
150	C₂²	C₄×D₇₆	1	1	yes	characteristic
151	C₂²	#10597321	1	1	yes	characteristic
152	C₂²	#10597376	1	1	yes	characteristic
153	C₄	—	4	2	no	—
154	C₄	C₄×D₇₆	1	1	yes	characteristic
155	C₄	#10597320	1	1	yes	characteristic
156	C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
157	C₄	#10597376	1	1	yes	characteristic
158	C₂	—	2	1	no	—
159	C₂	—	2	1	no	—
160	C₂	—	152	4	no	—
161	C₂	#11926446	1	1	yes	characteristic
162	C₂	#11926814	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₁₅₂

C₂

yes

maximal, characteristic

C₂×#10597276

C₂

yes

maximal, characteristic, complemented

#11926548

C₂

yes

maximal, complemented

C₂×#10597280

C₂

yes

maximal, complemented

C₁₉×#405

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₂²

yes

—

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

C₂×D₁₅₂

—

C₂×D₁₅₂

—

C₂×D₁₅₂

—

C₂×D₁₅₂

C₄

yes

complemented

C₁₉×#97

—

C₄×C₈×C₁₉

—

#10597280

—

#10597276

—

#10597266

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂×C₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

D₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

D₁₅₂

—

D₁₅₂

—

C₂³×C₁₉

#41

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₈×C₁₉

C₂²⋊C₄

yes

—

C₈×C₁₉

C₂²⋊C₄

yes

—

C₁₉⋊C₈

—

#1978

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₄×D₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂²×D₈

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#390

yes

characteristic

C₂×C₁₉

#472

yes

—

D₁₉

—

C₂²×D₄

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂²×C₈

C₂×D₁₉

yes

characteristic

#117

C₂×D₁₉

yes

—

—

—

—

100

C₄×C₈

—

101

C₁₉

#1978

yes

characteristic, complemented, Sylow

102

C₂⁴

—

103

C₂×D₄

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂²×C₄

C₂²×D₁₉

yes

characteristic

110

D₈

—

111

D₈

—

112

M₁₆

—

113

M₁₆

—

114

M₁₆

—

115

M₁₆

D₇₆

yes

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

C₄×D₁₉

yes

—

119

C₂×C₈

D₇₆

yes

—

120

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

121

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

122

C₄⋊C₄

D₇₆

yes

—

123

C₂²⋊C₄

—

124

C₄²

—

125

C₂³

—

126

C₂³

—

127

C₂³

—

128

C₂³

—

152

—

129

C₂³

#64541

yes

characteristic

130

D₄

—

131

D₄

—

132

D₄

—

133

D₄

—

134

C₂×C₄

—

135

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

136

C₂×C₄

C₂×D₇₆

yes

characteristic

137

C₂×C₄

C₂×D₇₆

yes

characteristic

138

C₂×C₄

C₂×D₇₆

yes

characteristic

139

C₂×C₄

#64541

yes

characteristic

140

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

141

C₈

—

142

C₈

—

143

C₈

(C₂×D₁₉)⋊C₄

yes

—

144

C₈

(C₂×D₁₉)⋊C₄

yes

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

152

—

148

C₂²

—

152

—

149

C₂²

—

152

—

150

C₂²

C₄×D₇₆

yes

characteristic

151

C₂²

#10597321

yes

characteristic

152

C₂²

#10597376

yes

characteristic

153

C₄

—

154

C₄

C₄×D₇₆

yes

characteristic

155

C₄

#10597320

yes

characteristic

156

C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

157

C₄

#10597376

yes

characteristic

158

C₂

—

159

C₂

—

160

C₂

—

152

—

161

C₂

#11926446

yes

characteristic

162

C₂

#11926814

yes

—

	subgroup	G/H
center	C₂²	#10597376
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#405	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂²×D₁₅₂	C₂
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#405	D₁₉
hypocenter	C₁₉	#1978
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #405

subgroup

G/H

center

C₂²

#10597376

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#405

C₂

socle

C₂²×C₁₉

#121

prime radical

C₂²×D₁₅₂

C₂

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #405

N	H ≅ G/N	type
2. C₂×#10597276	C₂	semidirect
3. #11926548	C₂	semidirect
4. C₂×#10597280	C₂	semidirect
5. C₁₉×#405	C₂	semidirect
14. C₂×D₁₅₂	C₄	semidirect
81. #405	D₁₉	semidirect
101. C₁₉	#1978	semidirect

H ≅ G/N

type

2. C₂×#10597276

C₂

semidirect

3. #11926548

C₂

semidirect

4. C₂×#10597280

C₂

semidirect

5. C₁₉×#405

C₂

semidirect

14. C₂×D₁₅₂

C₄

semidirect

81. #405

D₁₉

semidirect

101. C₁₉

#1978

semidirect

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

subgroup	index
C₂²×D₁₅₂	2
C₂×#10597276	2
#11926548	2
C₂×#10597280	2
C₁₉×#405	2
#1978	19

subgroup

index

C₂²×D₁₅₂

C₁₉×#405

Subgroups — #14564545

Conjugacy classes of subgroups

Complements

Maximal subgroups