Group #14569743 — subgroups

Subgroups — #14569743

Order 2432.

844 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 165 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×#10597320	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597386	C₂	1	2	yes	maximal, complemented
3	C₂×#10597393	C₂	1	2	yes	maximal, complemented
4	#11926453	C₂	1	8	yes	maximal, complemented
5	#11926390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₂²⋊D₁₉	C₂²	1	8	yes	—
10	C₂²×D₇₆	C₂²	1	2	yes	—
11	C₂²×D₇₆	C₂²	1	4	yes	—
12	C₁₉×#124	—	2	4	no	—
13	C₂×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
14	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	#10597393	—	2	8	no	—
16	#10597386	—	2	8	no	—
17	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	8	yes	—
18	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
19	#10597320	—	2	4	no	—
20	C₁₉⋊#95	C₂²	1	4	yes	—
21	C₂⁴×C₁₉	C₂³	1	2	yes	—
22	C₂³×D₁₉	C₂³	1	4	yes	—
23	C₂×Q₈×C₁₉	—	2	4	no	—
24	C₂×Q₈×C₁₉	—	2	2	no	—
25	C₂×D₄×C₁₉	—	2	4	no	—
26	C₂×D₄×C₁₉	—	2	2	no	—
27	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
28	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
29	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×C₂²⋊D₁₉	—	2	16	no	—
31	C₂×C₂²⋊D₁₉	—	4	16	no	—
32	C₂²×Dic₁₉	C₂³	1	4	yes	—
33	C₂×D₇₆	—	2	4	no	—
34	C₂×D₇₆	—	2	4	no	—
35	C₂×D₇₆	—	2	8	no	—
36	C₂×D₇₆	—	2	4	no	—
37	C₂×D₇₆	—	4	8	no	—
38	C₂²⋊C₄×C₁₉	—	2	8	no	—
39	C₄²×C₁₉	D₄	1	4	yes	complemented
40	(C₂×D₁₉)⋊C₄	—	2	16	no	—
41	C₄×Dic₁₉	D₄	1	8	yes	complemented
42	C₂³×C₁₉	—	2	2	no	—
43	C₂³×C₁₉	—	2	4	no	—
44	C₂³×C₁₉	—	2	8	no	—
45	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
46	C₂²×D₁₉	—	2	4	no	—
47	C₂²×D₁₉	—	2	4	no	—
48	C₂²×D₁₉	—	2	4	no	—
49	C₂²×D₁₉	—	2	16	no	—
50	Q₈×C₁₉	—	4	4	no	—
51	D₄×C₁₉	—	4	4	no	—
52	C₂×C₄×C₁₉	—	2	4	no	—
53	C₂×C₄×C₁₉	—	2	4	no	—
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
56	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
57	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
58	C₂²⋊D₁₉	—	4	32	no	—
59	C₂×Dic₁₉	—	2	8	no	—
60	C₂×Dic₁₉	C₂×D₄	1	8	yes	—
61	D₇₆	—	4	16	no	—
62	D₇₆	—	4	8	no	—
63	#2657	—	19	1	no	maximal, Sylow
64	C₂²×C₁₉	—	4	2	no	—
65	C₂²×C₁₉	—	4	8	no	—
66	C₂²×C₁₉	—	4	4	no	—
67	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
68	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
69	C₂²×C₁₉	H(5,𝔽₂)	1	4	yes	—
70	C₂×D₁₉	—	4	4	no	—
71	C₂×D₁₉	—	4	8	no	—
72	C₂×D₁₉	—	4	8	no	—
73	C₂×D₁₉	—	4	8	no	—
74	C₄×C₁₉	—	2	4	no	—
75	C₄×C₁₉	—	4	2	no	—
76	C₄×C₁₉	#127	1	4	yes	—
77	Dic₁₉	—	2	8	no	—
78	C₂×#127	—	19	2	no	—
79	C₂×#127	—	19	1	no	—
80	C₂×#124	—	19	2	no	—
81	C₂×#124	D₁₉	1	1	yes	characteristic, complemented
82	#392	—	19	8	no	—
83	#376	—	19	1	no	—
84	C₂×C₁₉	—	8	2	no	—
85	C₂×C₁₉	C₂×#127	1	1	yes	characteristic
86	C₂×C₁₉	#535	1	2	yes	—
87	C₂×C₁₉	#535	1	4	yes	—
88	D₁₉	—	8	4	no	—
89	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
90	C₂²×D₄	—	19	8	no	—
91	C₂²×D₄	—	19	2	no	—
92	C₂²×D₄	—	19	4	no	—
93	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
94	#127	—	38	8	no	—
95	#127	—	38	4	no	—
96	#124	—	2	4	no	—
97	#124	—	38	8	no	—
98	C₂×C₂²⋊C₄	—	19	8	no	—
99	C₂×C₂²⋊C₄	C₂×D₁₉	1	4	yes	—
100	C₂×C₄²	—	19	2	no	—
101	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
102	#95	—	19	4	no	—
103	C₁₉	#2657	1	1	yes	characteristic, complemented, Sylow
104	C₂⁴	—	19	4	no	—
105	C₂⁴	C₂²×D₁₉	1	2	yes	—
106	C₂×Q₈	—	2	4	no	—
107	C₂×Q₈	—	2	2	no	—
108	C₂×D₄	—	2	4	no	—
109	C₂×D₄	—	2	2	no	—
110	C₂×D₄	—	38	16	no	—
111	C₂×D₄	—	38	4	no	—
112	C₂×D₄	—	38	4	no	—
113	C₂×D₄	—	38	8	no	—
114	C₂×D₄	—	38	4	no	—
115	C₂×D₄	—	76	8	no	—
116	C₂×D₄	—	76	16	no	—
117	C₂²×C₄	—	19	4	no	—
118	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
119	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
120	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
121	C₂²⋊C₄	—	2	8	no	—
122	C₂²⋊C₄	—	38	16	no	—
123	C₄²	—	19	8	no	—
124	C₄²	C₂²⋊D₁₉	1	4	yes	complemented
125	C₂³	—	2	4	no	—
126	C₂³	—	2	8	no	—
127	C₂³	—	2	2	no	—
128	C₂³	—	38	4	no	—
129	C₂³	—	38	4	no	—
130	C₂³	—	38	16	no	—
131	C₂³	—	38	4	no	—
132	C₂³	C₂³×D₁₉	1	1	yes	characteristic
133	Q₈	—	4	4	no	—
134	D₄	—	4	4	no	—
135	D₄	—	76	16	no	—
136	D₄	—	76	32	no	—
137	D₄	—	76	8	no	—
138	C₂×C₄	—	2	4	no	—
139	C₂×C₄	—	2	4	no	—
140	C₂×C₄	—	2	2	no	—
141	C₂×C₄	—	19	8	no	—
142	C₂×C₄	—	38	8	no	—
143	C₂×C₄	D₄×D₁₉	1	4	yes	—
144	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
145	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
146	C₂²	—	4	2	no	—
147	C₂²	—	4	4	no	—
148	C₂²	—	4	8	no	—
149	C₂²	—	76	4	no	—
150	C₂²	—	76	8	no	—
151	C₂²	—	76	8	no	—
152	C₂²	—	76	8	no	—
153	C₂²	C₂×D₄×D₁₉	1	2	yes	—
154	C₂²	#10597435	1	4	yes	—
155	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
156	C₄	—	2	4	no	—
157	C₄	—	4	2	no	—
158	C₄	—	38	8	no	—
159	C₄	#10597386	1	4	yes	—
160	C₂	—	8	2	no	—
161	C₂	—	152	4	no	—
162	C₂	C₂×#10597386	1	1	yes	characteristic
163	C₂	#11927108	1	2	yes	—
164	C₂	#11927112	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597320

C₂

yes

maximal, characteristic, complemented

C₂×#10597386

C₂

yes

maximal, complemented

C₂×#10597393

C₂

yes

maximal, complemented

#11926453

C₂

yes

maximal, complemented

#11926390

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#124

C₂

yes

maximal, characteristic, complemented

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂²×C₂²⋊D₁₉

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

—

C₁₉×#124

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597393

—

#10597386

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

#10597320

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

—

C₂³×D₁₉

C₂³

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

complemented

(C₂×D₁₉)⋊C₄

—

C₄×Dic₁₉

D₄

yes

complemented

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×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

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

D₇₆

—

D₇₆

—

#2657

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#127

yes

—

Dic₁₉

—

—

—

—

D₁₉

yes

characteristic, complemented

#392

—

#376

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#127

yes

characteristic

C₂×C₁₉

#535

yes

—

C₂×C₁₉

#535

yes

—

D₁₉

—

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₂²×D₄

—

C₂²×D₄

—

C₂²×D₄

—

C₂²×D₄

C₂×D₁₉

yes

—

—

—

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

100

C₂×C₄²

—

101

C₂×C₄²

C₂×D₁₉

yes

characteristic

102

#95

—

103

C₁₉

#2657

yes

characteristic, complemented, Sylow

104

C₂⁴

—

105

C₂⁴

C₂²×D₁₉

yes

—

106

C₂×Q₈

—

107

C₂×Q₈

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂×D₄

—

112

C₂×D₄

—

113

C₂×D₄

—

114

C₂×D₄

—

115

C₂×D₄

—

116

C₂×D₄

—

117

C₂²×C₄

—

118

C₂²×C₄

C₂²×D₁₉

yes

—

119

C₂²×C₄

C₂²×D₁₉

yes

—

120

C₂²×C₄

C₂²×D₁₉

yes

characteristic

121

C₂²⋊C₄

—

122

C₂²⋊C₄

—

123

C₄²

—

124

C₄²

C₂²⋊D₁₉

yes

complemented

125

C₂³

—

126

C₂³

—

127

C₂³

—

128

C₂³

—

129

C₂³

—

130

C₂³

—

131

C₂³

—

132

C₂³

C₂³×D₁₉

yes

characteristic

133

Q₈

—

134

D₄

—

135

D₄

—

136

D₄

—

137

D₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

D₄×D₁₉

yes

—

144

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

145

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

146

C₂²

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

C₂×D₄×D₁₉

yes

—

154

C₂²

#10597435

yes

—

155

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

156

C₄

—

157

C₄

—

158

C₄

—

159

C₄

#10597386

yes

—

160

C₂

—

161

C₂

—

152

—

162

C₂

C₂×#10597386

yes

characteristic

163

C₂

#11927108

yes

—

164

C₂

#11927112

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×#124	C₂
hypercenter	C₂×#124	D₁₉
hypocenter	C₁₉	#2657
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×#124

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₁₉×#124

C₂

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×#124

N	H ≅ G/N	type
1. C₂×#10597320	C₂	semidirect
2. C₂×#10597386	C₂	semidirect
3. C₂×#10597393	C₂	semidirect
4. #11926453	C₂	semidirect
5. #11926390	C₂	semidirect
6. C₂×C₁₉×#124	C₂	semidirect
39. C₄²×C₁₉	D₄	semidirect
41. C₄×Dic₁₉	D₄	semidirect
81. C₂×#124	D₁₉	semidirect
103. C₁₉	#2657	semidirect
124. C₄²	C₂²⋊D₁₉	semidirect

H ≅ G/N

type

1. C₂×#10597320

C₂

semidirect

2. C₂×#10597386

C₂

semidirect

3. C₂×#10597393

C₂

semidirect

4. #11926453

C₂

semidirect

5. #11926390

C₂

semidirect

6. C₂×C₁₉×#124

C₂

semidirect

39. C₄²×C₁₉

D₄

semidirect

41. C₄×Dic₁₉

D₄

semidirect

81. C₂×#124

D₁₉

semidirect

103. C₁₉

#2657

semidirect

124. C₄²

C₂²⋊D₁₉

semidirect

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

subgroup	index
C₂×#10597320	2
C₂×#10597386	2
C₂×#10597393	2
#11926453	2
#11926390	2
C₂×C₁₉×#124	2
#2657	19

subgroup

index

C₂×C₁₉×#124

Subgroups — #14569743

Conjugacy classes of subgroups

Complements

Maximal subgroups