Group #14563303 — subgroups

Subgroups — #14563303

Order 2432.

242 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 61 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	#11926921	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926920	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926920	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926918	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926892	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926266	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₁₉×#127	C₂²	1	1	yes	characteristic
10	C₂×#64527	—	2	2	no	—
11	C₂×#64525	—	2	2	no	—
12	C₂×#64525	—	2	2	no	—
13	C₂×D₁₅₂	—	2	2	no	—
14	#10597320	C₂²	1	1	yes	characteristic
15	#10597320	C₂²	1	1	yes	characteristic
16	C₁₉×#102	—	2	2	no	—
17	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	#10597266	—	2	2	no	—
19	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Q₈×C₁₉	—	2	1	no	—
22	C₂×D₄×C₁₉	—	2	1	no	—
23	C₂×D₄×C₁₉	—	2	1	no	—
24	C₂×D₄×C₁₉	—	2	1	no	—
25	C₂×D₇₆	—	2	1	no	—
26	C₂×D₇₆	—	2	1	no	—
27	C₂×D₇₆	—	2	1	no	—
28	C₂×D₇₆	—	2	1	no	—
29	C₂×D₇₆	—	2	1	no	—
30	C₂×D₇₆	—	2	1	no	—
31	C₂×C₈×C₁₉	D₄	1	2	yes	—
32	C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	#64527	—	4	4	no	—
36	#64525	—	4	4	no	—
37	#64525	—	4	4	no	—
38	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
39	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
40	D₁₅₂	—	4	4	no	—
41	C₂³×C₁₉	—	4	1	no	—
42	C₂²×D₁₉	—	4	1	no	—
43	C₂²×D₁₉	—	4	1	no	—
44	Q₈×C₁₉	—	4	2	no	—
45	D₄×C₁₉	—	4	2	no	—
46	D₄×C₁₉	—	4	2	no	—
47	D₄×C₁₉	—	4	2	no	—
48	C₂×C₄×C₁₉	—	4	1	no	—
49	C₂×C₄×C₁₉	C₂×D₄	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	D₇₆	—	4	2	no	—
53	D₇₆	—	4	2	no	—
54	D₇₆	—	4	2	no	—
55	D₇₆	—	4	2	no	—
56	D₇₆	—	4	2	no	—
57	D₇₆	—	4	2	no	—
58	C₈×C₁₉	—	2	2	no	—
59	C₁₉⋊C₈	—	2	2	no	—
60	C₁₉⋊C₈	D₈	1	4	yes	complemented
61	#1721	—	19	1	no	maximal, Sylow
62	C₂²×C₁₉	—	8	1	no	—
63	C₂²×C₁₉	—	8	1	no	—
64	C₂²×C₁₉	—	8	1	no	—
65	C₂²×C₁₉	#127	1	1	yes	characteristic
66	C₂×D₁₉	—	8	1	no	—
67	C₂×D₁₉	—	8	1	no	—
68	C₂×D₁₉	—	8	1	no	—
69	C₂×D₁₉	—	8	1	no	—
70	C₂×D₁₉	—	8	1	no	—
71	C₂×D₁₉	—	8	1	no	—
72	C₄×C₁₉	—	8	1	no	—
73	C₄×C₁₉	C₂×D₈	1	2	yes	—
74	C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
75	C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
76	#493	—	19	1	no	—
77	#493	—	19	1	no	—
78	#493	—	19	1	no	—
79	#492	—	19	1	no	—
80	#486	—	19	1	no	—
81	#486	D₁₉	1	1	yes	characteristic, complemented
82	#322	—	19	1	no	—
83	C₂×C₁₉	—	16	1	no	—
84	C₂×C₁₉	#493	1	1	yes	characteristic
85	C₂×C₁₉	#496	1	1	yes	characteristic
86	C₂×C₁₉	#496	1	1	yes	characteristic
87	D₁₉	—	16	1	no	—
88	D₁₉	—	16	1	no	—
89	C₂×SD₁₆	—	38	2	no	—
90	C₂×D₈	—	38	2	no	—
91	C₂×D₈	—	38	2	no	—
92	C₂×D₈	—	38	2	no	—
93	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
94	#127	—	19	1	no	—
95	#127	—	19	1	no	—
96	#127	C₂×D₁₉	1	1	yes	characteristic
97	#102	—	2	2	no	—
98	#102	—	38	2	no	—
99	C₄×C₈	—	19	1	no	—
100	C₄×C₈	—	19	1	no	—
101	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
102	C₁₉	#1721	1	1	yes	characteristic, complemented, Sylow
103	C₂×Q₈	—	2	1	no	—
104	C₂×D₄	—	2	1	no	—
105	C₂×D₄	—	2	1	no	—
106	C₂×D₄	—	2	1	no	—
107	C₂×D₄	—	38	1	no	—
108	C₂×D₄	—	38	1	no	—
109	C₂×D₄	—	38	1	no	—
110	C₂×D₄	—	38	1	no	—
111	C₂×D₄	—	38	1	no	—
112	C₂×D₄	—	38	1	no	—
113	SD₁₆	—	76	4	no	—
114	D₈	—	76	4	no	—
115	D₈	—	76	4	no	—
116	D₈	—	76	4	no	—
117	C₂×C₈	—	19	2	no	—
118	C₂×C₈	—	19	2	no	—
119	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
120	C₄⋊C₄	—	2	1	no	—
121	C₄⋊C₄	—	2	1	no	—
122	C₄²	C₂²×D₁₉	1	1	yes	characteristic
123	C₂³	—	4	1	no	—
124	C₂³	—	76	1	no	—
125	C₂³	—	76	1	no	—
126	Q₈	—	4	2	no	—
127	D₄	—	4	2	no	—
128	D₄	—	4	2	no	—
129	D₄	—	4	2	no	—
130	D₄	—	76	2	no	—
131	D₄	—	76	2	no	—
132	D₄	—	76	2	no	—
133	D₄	—	76	2	no	—
134	D₄	—	76	2	no	—
135	D₄	—	76	2	no	—
136	C₂×C₄	—	4	1	no	—
137	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
138	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
139	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
140	C₈	—	2	2	no	—
141	C₈	—	19	4	no	—
142	C₈	—	38	2	no	—
143	C₂²	—	8	1	no	—
144	C₂²	—	8	1	no	—
145	C₂²	—	8	1	no	—
146	C₂²	—	152	1	no	—
147	C₂²	—	152	1	no	—
148	C₂²	—	152	1	no	—
149	C₂²	—	152	1	no	—
150	C₂²	—	152	1	no	—
151	C₂²	—	152	1	no	—
152	C₂²	#10597386	1	1	yes	characteristic
153	C₄	—	8	1	no	—
154	C₄	D₈×D₁₉	1	2	yes	—
155	C₄	#10597360	1	2	yes	—
156	C₄	#10597395	1	2	yes	—
157	C₂	—	16	1	no	—
158	C₂	—	304	1	no	—
159	C₂	—	304	1	no	—
160	C₂	#11926919	1	1	yes	characteristic
161	C₂	#11926930	1	1	yes	characteristic
162	C₂	#11926934	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926921

C₂

yes

maximal, characteristic, complemented

#11926920

C₂

yes

maximal, characteristic, complemented

#11926920

C₂

yes

maximal, characteristic, complemented

#11926918

C₂

yes

maximal, characteristic, complemented

#11926892

C₂

yes

maximal, characteristic, complemented

#11926266

C₂

yes

maximal, characteristic, complemented

C₁₉×#486

C₂

yes

maximal, characteristic, complemented

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#127

C₂²

yes

—

—

—

C₂×D₁₅₂

—

#10597320

C₂²

yes

characteristic

#10597320

C₂²

yes

characteristic

C₁₉×#102

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597266

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

—

—

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

—

D₁₅₂

—

C₂³×C₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

D₈

yes

complemented

#1721

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#127

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×D₈

yes

—

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

—

—

—

—

—

D₁₉

yes

characteristic, complemented

#322

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

D₁₉

—

C₂×SD₁₆

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

C₂×D₁₉

yes

—

—

C₂×D₁₉

yes

characteristic

#102

—

#102

—

C₄×C₈

—

100

C₄×C₈

—

101

C₄×C₈

C₂×D₁₉

yes

characteristic

102

C₁₉

#1721

yes

characteristic, complemented, Sylow

103

C₂×Q₈

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂×D₄

—

112

C₂×D₄

—

113

SD₁₆

—

114

D₈

—

115

D₈

—

116

D₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

C₂²⋊D₁₉

yes

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄²

C₂²×D₁₉

yes

characteristic

123

C₂³

—

124

C₂³

—

125

C₂³

—

126

Q₈

—

127

D₄

—

128

D₄

—

129

D₄

—

130

D₄

—

131

D₄

—

132

D₄

—

133

D₄

—

134

D₄

—

135

D₄

—

136

C₂×C₄

—

137

C₂×C₄

D₄×D₁₉

yes

characteristic

138

C₂×C₄

D₄×D₁₉

yes

characteristic

139

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

140

C₈

—

141

C₈

—

142

C₈

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

152

—

147

C₂²

—

152

—

148

C₂²

—

152

—

149

C₂²

—

152

—

150

C₂²

—

152

—

151

C₂²

—

152

—

152

C₂²

#10597386

yes

characteristic

153

C₄

—

154

C₄

D₈×D₁₉

yes

—

155

C₄

#10597360

yes

—

156

C₄

#10597395

yes

—

157

C₂

—

158

C₂

—

304

—

159

C₂

—

304

—

160

C₂

#11926919

yes

characteristic

161

C₂

#11926930

yes

characteristic

162

C₂

#11926934

yes

characteristic

	subgroup	G/H
center	C₂²	#10597386
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#486	C₂
socle	C₂²×C₁₉	#127
hypercenter	#486	D₁₉
hypocenter	C₁₉	#1721
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #486

subgroup

G/H

center

C₂²

#10597386

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#486

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #486

N	H ≅ G/N	type
1. #11926921	C₂	semidirect
2. #11926920	C₂	semidirect
3. #11926920	C₂	semidirect
4. #11926918	C₂	semidirect
5. #11926892	C₂	semidirect
6. #11926266	C₂	semidirect
7. C₁₉×#486	C₂	semidirect
60. C₁₉⋊C₈	D₈	semidirect
81. #486	D₁₉	semidirect
102. C₁₉	#1721	semidirect

H ≅ G/N

type

1. #11926921

C₂

semidirect

2. #11926920

C₂

semidirect

3. #11926920

C₂

semidirect

4. #11926918

C₂

semidirect

5. #11926892

C₂

semidirect

6. #11926266

C₂

semidirect

7. C₁₉×#486

C₂

semidirect

60. C₁₉⋊C₈

D₈

semidirect

81. #486

D₁₉

semidirect

102. C₁₉

#1721

semidirect

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

subgroup	index
#11926921	2
#11926920	2
#11926918	2
#11926892	2
#11926266	2
C₁₉×#486	2
#1721	19

subgroup

index

C₁₉×#486

Subgroups — #14563303

Conjugacy classes of subgroups

Complements

Maximal subgroups