Group #14573980 — subgroups

Subgroups — #14573980

Order 2432.

392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 133 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	#11927101	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926912	C₂	1	2	yes	maximal, complemented
3	#11926908	C₂	1	2	yes	maximal, complemented
4	#11926903	C₂	1	4	yes	maximal, complemented
5	#11926540	C₂	1	4	yes	maximal, complemented
6	C₂×#10597260	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#532	C₂	1	1	yes	maximal, characteristic
8	C₂×#41×C₁₉	C₂²	1	2	yes	—
9	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₁₉×#127	C₂²	1	1	yes	characteristic
11	C₁₉×#124	C₂²	1	2	yes	—
12	C₁₉×#121	—	2	2	no	—
13	C₄×D₄×C₁₉	—	2	2	no	—
14	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	#10597372	C₂²	1	2	yes	—
16	#10597370	—	2	2	no	—
17	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
18	#10597316	C₂²	1	2	yes	—
19	#10597315	C₂²	1	2	yes	—
20	C₄×Dic₃₈	—	2	2	no	—
21	#10597292	C₂²	1	8	yes	—
22	#10597289	C₂²	1	8	yes	—
23	#10597260	C₂²	1	2	yes	—
24	#10597260	C₂²	1	2	yes	—
25	#41×C₁₉	—	2	8	no	—
26	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
27	C₂×D₄×C₁₉	—	2	2	no	—
28	C₂×D₄×C₁₉	—	2	2	no	—
29	C₂×D₄×C₁₉	C₂³	1	2	yes	—
30	C₂²×C₄×C₁₉	—	2	2	no	—
31	C₂²×C₄×C₁₉	D₄	1	2	yes	—
32	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂×Dic₃₈	—	2	2	no	—
34	C₄⋊C₄×C₁₉	—	2	2	no	—
35	C₂²⋊C₄×C₁₉	—	2	4	no	—
36	C₄²×C₁₉	D₄	1	2	yes	—
37	C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	C₂²⋊Dic₁₉	—	2	2	no	—
40	C₄⋊Dic₁₉	—	2	2	no	—
41	C₄⋊Dic₁₉	C₂³	1	4	yes	—
42	Dic₁₉⋊C₄	—	2	4	no	—
43	C₄×Dic₁₉	—	2	2	no	—
44	C₂×C₁₉⋊C₈	—	2	4	no	—
45	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
46	C₂³×C₁₉	—	2	2	no	—
47	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
48	Q₈×C₁₉	—	2	4	no	—
49	D₄×C₁₉	—	2	4	no	—
50	D₄×C₁₉	—	4	4	no	—
51	D₄×C₁₉	—	4	4	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	4	2	no	—
54	C₂×C₄×C₁₉	—	4	4	no	—
55	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
56	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
57	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#41	1	4	yes	—
59	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
60	C₂×Dic₁₉	—	2	4	no	—
61	Dic₃₈	—	4	4	no	—
62	C₁₉⋊C₈	—	2	4	no	—
63	#3135	—	19	1	no	maximal, Sylow
64	C₂²×C₁₉	—	2	2	no	—
65	C₂²×C₁₉	—	4	2	no	—
66	C₂²×C₁₉	—	4	4	no	—
67	C₂²×C₁₉	#124	1	2	yes	—
68	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
69	C₄×C₁₉	—	2	2	no	—
70	C₄×C₁₉	—	2	2	no	—
71	C₄×C₁₉	—	4	2	no	—
72	C₄×C₁₉	#124	1	2	yes	—
73	C₄×C₁₉	C₂×#41	1	2	yes	—
74	Dic₁₉	—	4	4	no	—
75	#533	—	19	1	no	—
76	#532	D₁₉	1	1	yes	characteristic
77	#491	—	19	2	no	—
78	#490	—	19	2	no	—
79	#489	—	19	4	no	—
80	#416	—	19	4	no	—
81	C₂×#97	—	19	1	no	—
82	C₂×C₁₉	—	2	2	no	—
83	C₂×C₁₉	—	8	2	no	—
84	C₂×C₁₉	C₂×#124	1	1	yes	characteristic
85	C₂×C₁₉	#575	1	2	yes	—
86	C₂×#41	C₂×D₁₉	1	2	yes	—
87	C₂²×C₈	—	19	2	no	—
88	C₄⋊Q₈	—	19	2	no	—
89	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
90	#127	C₂×D₁₉	1	1	yes	characteristic
91	#125	—	19	2	no	—
92	#124	C₂×D₁₉	1	2	yes	—
93	C₂²⋊Q₈	—	38	2	no	—
94	#121	—	2	2	no	—
95	C₄×Q₈	—	38	2	no	—
96	C₄×D₄	—	2	2	no	—
97	#117	—	19	2	no	—
98	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
99	#103	—	19	8	no	—
100	#102	—	19	8	no	—
101	#97	—	19	2	no	—
102	#97	—	19	2	no	—
103	C₁₉	#3135	1	1	yes	characteristic, complemented, Sylow
104	#41	—	2	8	no	—
105	C₂×Q₈	—	38	2	no	—
106	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
107	C₂×D₄	—	2	2	no	—
108	C₂×D₄	—	2	2	no	—
109	C₂×D₄	C₂²×D₁₉	1	2	yes	—
110	C₂²×C₄	—	2	2	no	—
111	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
112	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
113	C₂×C₈	—	19	4	no	—
114	C₂×C₈	—	38	4	no	—
115	C₄⋊C₄	—	2	2	no	—
116	C₄⋊C₄	—	19	4	no	—
117	C₄⋊C₄	—	38	4	no	—
118	C₄⋊C₄	—	38	2	no	—
119	C₂²⋊C₄	—	2	4	no	—
120	C₂²⋊C₄	—	38	2	no	—
121	C₄²	—	38	2	no	—
122	C₄²	C₂²⋊D₁₉	1	2	yes	—
123	C₄²	C₂²×D₁₉	1	1	yes	characteristic
124	C₄²	C₂²×D₁₉	1	1	yes	characteristic
125	C₂³	—	2	2	no	—
126	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
127	Q₈	—	2	4	no	—
128	Q₈	—	76	4	no	—
129	D₄	—	2	4	no	—
130	D₄	—	4	4	no	—
131	D₄	—	4	4	no	—
132	C₂×C₄	—	2	2	no	—
133	C₂×C₄	—	4	2	no	—
134	C₂×C₄	—	4	4	no	—
135	C₂×C₄	—	38	4	no	—
136	C₂×C₄	#64543	1	4	yes	—
137	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
138	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
139	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
140	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
141	C₈	—	38	4	no	—
142	C₂²	—	2	2	no	—
143	C₂²	—	4	2	no	—
144	C₂²	—	4	4	no	—
145	C₂²	#10597382	1	2	yes	—
146	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
147	C₄	—	2	2	no	—
148	C₄	—	2	2	no	—
149	C₄	—	4	2	no	—
150	C₄	—	76	4	no	—
151	C₄	#10597382	1	2	yes	—
152	C₄	C₂×#64543	1	2	yes	—
153	C₂	—	2	2	no	—
154	C₂	—	8	2	no	—
155	C₂	C₂×#10597382	1	1	yes	characteristic
156	C₂	#11927342	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927101

C₂

yes

maximal, characteristic, complemented

#11926912

C₂

yes

maximal, complemented

#11926908

C₂

yes

maximal, complemented

#11926903

C₂

yes

maximal, complemented

#11926540

C₂

yes

maximal, complemented

C₂×#10597260

C₂

yes

maximal, characteristic, complemented

C₁₉×#532

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₂²

yes

—

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#127

C₂²

yes

characteristic

C₁₉×#124

C₂²

yes

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597372

C₂²

yes

—

#10597370

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597316

C₂²

yes

—

#10597315

C₂²

yes

—

C₄×Dic₃₈

—

#10597292

C₂²

yes

—

#10597289

C₂²

yes

—

#10597260

C₂²

yes

—

#10597260

C₂²

yes

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₂³

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

Dic₃₈

—

C₁₉⋊C₈

—

#3135

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#124

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#124

yes

—

C₄×C₁₉

C₂×#41

yes

—

Dic₁₉

—

#533

—

#532

D₁₉

yes

—

—

—

—

C₂×#97

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#124

yes

characteristic

C₂×C₁₉

#575

yes

—

C₂×#41

C₂×D₁₉

yes

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

#127

C₂×D₁₉

yes

characteristic

#125

—

#124

C₂×D₁₉

yes

—

C₂²⋊Q₈

—

#121

—

C₄×Q₈

—

C₄×D₄

—

#117

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#103

—

100

#102

—

101

#97

—

102

#97

—

103

C₁₉

#3135

yes

characteristic, complemented, Sylow

104

#41

—

105

C₂×Q₈

—

106

C₂×Q₈

C₂²×D₁₉

yes

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂×D₄

C₂²×D₁₉

yes

—

110

C₂²×C₄

—

111

C₂²×C₄

C₂²⋊D₁₉

yes

—

112

C₂²×C₄

C₂²×D₁₉

yes

characteristic

113

C₂×C₈

—

114

C₂×C₈

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₂²⋊C₄

—

120

C₂²⋊C₄

—

121

C₄²

—

122

C₄²

C₂²⋊D₁₉

yes

—

123

C₄²

C₂²×D₁₉

yes

characteristic

124

C₄²

C₂²×D₁₉

yes

characteristic

125

C₂³

—

126

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

127

Q₈

—

128

Q₈

—

129

D₄

—

130

D₄

—

131

D₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

#64543

yes

—

137

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

138

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

139

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

140

C₂×C₄

C₂³×D₁₉

yes

characteristic

141

C₈

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

#10597382

yes

—

146

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

#10597382

yes

—

152

C₄

C₂×#64543

yes

—

153

C₂

—

154

C₂

—

155

C₂

C₂×#10597382

yes

characteristic

156

C₂

#11927342

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting, prime radical	C₁₉×#532	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	#532	D₁₉
hypocenter	C₁₉	#3135
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #532

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting, prime radical

C₁₉×#532

C₂

socle

C₂²×C₁₉

C₂²×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #532

N	H ≅ G/N	type
1. #11927101	C₂	semidirect
2. #11926912	C₂	semidirect
3. #11926908	C₂	semidirect
4. #11926903	C₂	semidirect
5. #11926540	C₂	semidirect
6. C₂×#10597260	C₂	semidirect
103. C₁₉	#3135	semidirect

H ≅ G/N

type

1. #11927101

C₂

semidirect

2. #11926912

C₂

semidirect

3. #11926908

C₂

semidirect

4. #11926903

C₂

semidirect

5. #11926540

C₂

semidirect

6. C₂×#10597260

C₂

semidirect

103. C₁₉

#3135

semidirect

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

subgroup	index
#11927101	2
#11926912	2
#11926908	2
#11926903	2
#11926540	2
C₂×#10597260	2
C₁₉×#532	2
#3135	19

subgroup

index

C₁₉×#532

Subgroups — #14573980

Conjugacy classes of subgroups

Complements

Maximal subgroups