Group #14565674 — subgroups

Subgroups — #14565674

Order 2432.

174 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 49 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×#10597257	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597284	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926919	C₂	1	1	yes	maximal, characteristic
4	#11926638	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926344	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
9	#10597386	—	2	1	no	—
10	C₂×#64525	—	2	1	no	—
11	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
12	C₂×D₁₅₂	C₂²	1	1	yes	characteristic
13	#10597333	—	2	1	no	—
14	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#107	C₂²	1	1	yes	characteristic
16	#10597284	—	2	2	no	—
17	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
19	#10597267	—	2	1	no	—
20	#10597257	—	2	2	no	—
21	C₂×D₄×C₁₉	—	2	1	no	—
22	C₂×C₂²⋊D₁₉	—	4	1	no	—
23	C₂×C₂²⋊D₁₉	—	4	1	no	—
24	C₂×D₇₆	—	2	1	no	—
25	C₂×Dic₃₈	—	2	1	no	—
26	D₈×C₁₉	—	2	1	no	—
27	D₈×C₁₉	—	2	1	no	—
28	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
29	C₄⋊C₄×C₁₉	—	2	1	no	—
30	#64525	—	4	2	no	—
31	Dic₁₉⋊C₄	—	4	1	no	—
32	C₄×Dic₁₉	—	4	1	no	—
33	C₄×Dic₁₉	D₄	1	1	yes	characteristic
34	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
35	Dic₇₆	—	2	1	no	—
36	Dic₇₆	D₄	1	2	yes	complemented
37	D₁₅₂	—	2	1	no	—
38	D₁₅₂	—	2	1	no	—
39	C₁₆×C₁₉	—	2	1	no	—
40	C₁₉⋊C₁₆	—	2	1	no	—
41	C₂³×C₁₉	—	4	1	no	—
42	C₂²×D₁₉	—	4	1	no	—
43	D₄×C₁₉	—	4	1	no	—
44	D₄×C₁₉	—	4	1	no	—
45	C₂×C₄×C₁₉	—	4	1	no	—
46	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₂²⋊D₁₉	—	8	2	no	—
48	C₂²⋊D₁₉	—	8	2	no	—
49	C₂×Dic₁₉	—	4	1	no	—
50	C₂×Dic₁₉	D₈	1	1	yes	characteristic
51	C₂×Dic₁₉	D₈	1	1	yes	characteristic
52	D₇₆	—	4	1	no	—
53	D₇₆	—	4	1	no	—
54	Dic₃₈	—	2	2	no	—
55	Dic₃₈	—	4	1	no	—
56	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₈×C₁₉	#41	1	1	yes	characteristic
58	C₁₉⋊C₈	—	2	1	no	—
59	#2207	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	—	8	1	no	—
61	C₂²×C₁₉	—	8	1	no	—
62	C₂²×C₁₉	—	8	1	no	—
63	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
64	C₂×D₁₉	—	8	1	no	—
65	C₂×D₁₉	—	8	1	no	—
66	C₂×D₁₉	—	8	1	no	—
67	C₄×C₁₉	—	8	1	no	—
68	C₄×C₁₉	#121	1	1	yes	characteristic
69	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
70	Dic₁₉	—	2	1	no	—
71	Dic₁₉	—	4	2	no	—
72	Dic₁₉	SD₃₂	1	2	yes	complemented
73	C₂×SD₃₂	—	19	1	no	—
74	C₂×SD₃₂	—	19	1	no	—
75	#493	—	19	1	no	—
76	C₄×Q₁₆	—	19	1	no	—
77	C₄⋊C₁₆	—	19	1	no	—
78	#357	—	19	1	no	—
79	#357	D₁₉	1	1	yes	characteristic, complemented
80	C₂×C₁₉	—	16	1	no	—
81	C₂×C₁₉	#459	1	1	yes	characteristic
82	C₂×C₁₉	C₂×SD₃₂	1	1	yes	characteristic
83	C₂×C₁₉	#509	1	1	yes	characteristic
84	D₁₉	—	16	1	no	—
85	C₂×Q₁₆	—	19	1	no	—
86	C₂×D₈	—	19	1	no	—
87	C₂×D₈	—	38	1	no	—
88	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
89	#127	—	38	1	no	—
90	C₄×Q₈	—	38	1	no	—
91	SD₃₂	—	38	2	no	—
92	SD₃₂	—	38	2	no	—
93	C₂×C₁₆	—	19	1	no	—
94	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
95	#107	C₂×D₁₉	1	1	yes	characteristic
96	#103	—	38	1	no	—
97	C₄×C₈	—	19	1	no	—
98	C₁₉	#2207	1	1	yes	characteristic, complemented, Sylow
99	C₂×Q₈	—	38	1	no	—
100	C₂×D₄	—	2	1	no	—
101	C₂×D₄	—	38	1	no	—
102	C₂×D₄	—	76	1	no	—
103	C₂×D₄	—	76	1	no	—
104	Q₁₆	—	19	2	no	—
105	Q₁₆	—	38	1	no	—
106	D₈	—	2	1	no	—
107	D₈	—	2	1	no	—
108	D₈	—	38	1	no	—
109	D₈	—	38	1	no	—
110	D₈	—	76	2	no	—
111	C₂×C₈	—	19	1	no	—
112	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
113	C₄⋊C₄	—	2	1	no	—
114	C₄⋊C₄	—	76	1	no	—
115	C₄²	—	19	1	no	—
116	C₄²	—	76	1	no	—
117	C₁₆	—	2	1	no	—
118	C₁₆	—	38	1	no	—
119	C₂³	—	4	1	no	—
120	C₂³	—	76	1	no	—
121	Q₈	—	38	2	no	—
122	Q₈	—	76	1	no	—
123	D₄	—	4	1	no	—
124	D₄	—	4	1	no	—
125	D₄	—	76	1	no	—
126	D₄	—	76	1	no	—
127	D₄	—	152	2	no	—
128	D₄	—	152	2	no	—
129	C₂×C₄	—	4	1	no	—
130	C₂×C₄	—	19	1	no	—
131	C₂×C₄	—	19	1	no	—
132	C₂×C₄	—	76	1	no	—
133	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
134	C₈	—	38	1	no	—
135	C₈	#64541	1	1	yes	characteristic
136	C₈	D₄×D₁₉	1	1	yes	characteristic
137	C₂²	—	8	1	no	—
138	C₂²	—	8	1	no	—
139	C₂²	—	8	1	no	—
140	C₂²	—	152	1	no	—
141	C₂²	—	152	1	no	—
142	C₂²	—	152	1	no	—
143	C₂²	D₈×D₁₉	1	1	yes	characteristic
144	C₄	—	8	1	no	—
145	C₄	—	19	2	no	—
146	C₄	—	38	1	no	—
147	C₄	—	76	2	no	—
148	C₄	#10597330	1	1	yes	characteristic
149	C₄	#10597360	1	1	yes	characteristic
150	C₂	—	16	1	no	—
151	C₂	—	304	1	no	—
152	C₂	#11926738	1	1	yes	characteristic
153	C₂	SD₃₂×D₁₉	1	1	yes	characteristic
154	C₂	#11926978	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597257

C₂

yes

maximal, characteristic, complemented

C₂×#10597284

C₂

yes

maximal, characteristic, complemented

#11926919

C₂

yes

maximal, characteristic

#11926638

C₂

yes

maximal, characteristic, complemented

Dic₁₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#11926344

C₂

yes

maximal, characteristic, complemented

C₁₉×#357

C₂

yes

maximal, characteristic, complemented

C₂×D₈×C₁₉

C₂²

yes

characteristic

#10597386

—

C₂×#64525

—

C₂×Dic₇₆

C₂²

yes

characteristic

C₂×D₁₅₂

C₂²

yes

characteristic

#10597333

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#107

C₂²

yes

characteristic

#10597284

—

C₈×Dic₁₉

C₂²

yes

characteristic

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic

#10597267

—

#10597257

—

C₂×D₄×C₁₉

—

C₂×C₂²⋊D₁₉

—

C₂×C₂²⋊D₁₉

—

C₂×D₇₆

—

C₂×Dic₃₈

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

#64525

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

Dic₇₆

—

Dic₇₆

D₄

yes

complemented

D₁₅₂

—

D₁₅₂

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

—

C₂²×D₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²⋊D₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

D₈

yes

characteristic

C₂×Dic₁₉

D₈

yes

characteristic

D₇₆

—

D₇₆

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

#41

yes

characteristic

C₁₉⋊C₈

—

#2207

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

Dic₁₉

SD₃₂

yes

complemented

C₂×SD₃₂

—

C₂×SD₃₂

—

#493

—

C₄×Q₁₆

—

C₄⋊C₁₆

—

#357

—

#357

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

#459

yes

characteristic

C₂×C₁₉

C₂×SD₃₂

yes

characteristic

C₂×C₁₉

#509

yes

characteristic

D₁₉

—

C₂×Q₁₆

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

C₂×D₁₉

yes

characteristic

#127

—

C₄×Q₈

—

SD₃₂

—

SD₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

characteristic

#107

C₂×D₁₉

yes

characteristic

#103

—

C₄×C₈

—

C₁₉

#2207

yes

characteristic, complemented, Sylow

C₂×Q₈

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂×D₄

—

103

C₂×D₄

—

104

Q₁₆

—

105

Q₁₆

—

106

D₈

—

107

D₈

—

108

D₈

—

109

D₈

—

110

D₈

—

111

C₂×C₈

—

112

C₂×C₈

C₂²×D₁₉

yes

characteristic

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄²

—

116

C₄²

—

117

C₁₆

—

118

C₁₆

—

119

C₂³

—

120

C₂³

—

121

Q₈

—

122

Q₈

—

123

D₄

—

124

D₄

—

125

D₄

—

126

D₄

—

127

D₄

—

152

—

128

D₄

—

152

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

D₄×D₁₉

yes

characteristic

134

C₈

—

135

C₈

#64541

yes

characteristic

136

C₈

D₄×D₁₉

yes

characteristic

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

152

—

141

C₂²

—

152

—

142

C₂²

—

152

—

143

C₂²

D₈×D₁₉

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

#10597330

yes

characteristic

149

C₄

#10597360

yes

characteristic

150

C₂

—

151

C₂

—

304

—

152

C₂

#11926738

yes

characteristic

153

C₂

SD₃₂×D₁₉

yes

characteristic

154

C₂

#11926978

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₁₉
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#357	C₂
socle	C₂²×C₁₉	C₂×D₈
prime radical	#11926919	C₂
hypercenter	#357	D₁₉
hypocenter	C₁₉	#2207
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₁₉

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#357

C₂

socle

C₂²×C₁₉

C₂×D₈

C₂

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
1. C₂×#10597257	C₂	semidirect
2. C₂×#10597284	C₂	semidirect
4. #11926638	C₂	semidirect
5. Dic₁₉⋊C₁₆	C₂	semidirect
6. #11926344	C₂	semidirect
7. C₁₉×#357	C₂	semidirect
36. Dic₇₆	D₄	semidirect
72. Dic₁₉	SD₃₂	semidirect
79. #357	D₁₉	semidirect
98. C₁₉	#2207	semidirect

H ≅ G/N

type

1. C₂×#10597257

C₂

semidirect

2. C₂×#10597284

C₂

semidirect

4. #11926638

C₂

semidirect

5. Dic₁₉⋊C₁₆

C₂

semidirect

6. #11926344

C₂

semidirect

7. C₁₉×#357

C₂

semidirect

36. Dic₇₆

D₄

semidirect

72. Dic₁₉

SD₃₂

semidirect

79. #357

D₁₉

semidirect

98. C₁₉

#2207

semidirect

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

subgroup	index
C₂×#10597257	2
C₂×#10597284	2
#11926919	2
#11926638	2
Dic₁₉⋊C₁₆	2
#11926344	2
C₁₉×#357	2
#2207	19

subgroup

index

Dic₁₉⋊C₁₆

C₁₉×#357

Subgroups — #14565674

Conjugacy classes of subgroups

Complements

Maximal subgroups