Group #14569300 — subgroups

Subgroups — #14569300

Order 2432.

444 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 141 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	#11926480	C₂	1	2	yes	maximal
2	#11926456	C₂	1	2	yes	maximal
3	#11926448	C₂	1	4	yes	maximal, complemented
4	#11926431	C₂	1	4	yes	maximal, complemented
5	C₄×C₂²⋊Dic₁₉	C₂	1	2	yes	maximal
6	C₁₉×#381	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×Dic₃₈	C₂²	1	2	yes	—
9	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
12	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
13	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
14	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
15	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
16	C₁₉×#95	C₂²	1	4	yes	—
17	C₁₉⋊#95	C₂²	1	4	yes	—
18	C₁₉⋊#95	C₂²	1	2	yes	—
19	C₁₉⋊#95	C₂²	1	4	yes	—
20	C₁₉⋊#95	C₂²	1	2	yes	—
21	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	—	4	1	no	—
23	C₂²×C₄×C₁₉	—	4	1	no	—
24	C₂²×C₄×C₁₉	Q₈	1	4	yes	complemented
25	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
27	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
28	C₂²×Dic₁₉	C₂³	1	4	yes	—
29	C₂²×Dic₁₉	C₂³	1	4	yes	—
30	C₂×Dic₃₈	—	2	8	no	—
31	C₂×Dic₃₈	—	4	2	no	—
32	C₂²⋊C₄×C₁₉	—	4	1	no	—
33	C₂²⋊C₄×C₁₉	—	4	1	no	—
34	C₂²⋊Dic₁₉	—	2	8	no	—
35	C₄⋊Dic₁₉	—	4	2	no	—
36	Dic₁₉⋊C₄	—	2	8	no	—
37	C₄×Dic₁₉	—	4	2	no	—
38	C₄×Dic₁₉	—	4	2	no	—
39	C₂³×C₁₉	—	2	4	no	—
40	C₂³×C₁₉	—	2	1	no	—
41	C₂³×C₁₉	—	2	1	no	—
42	C₂³×C₁₉	C₂×Q₈	1	2	yes	—
43	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	—	2	2	no	—
46	C₂×C₄×C₁₉	—	2	4	no	—
47	C₂×C₄×C₁₉	—	2	4	no	—
48	C₂×C₄×C₁₉	—	2	2	no	—
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	4	4	no	—
51	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
52	C₂×Dic₁₉	—	2	4	no	—
53	C₂×Dic₁₉	—	2	4	no	—
54	C₂×Dic₁₉	—	2	4	no	—
55	C₂×Dic₁₉	—	2	4	no	—
56	C₂×Dic₁₉	—	2	4	no	—
57	C₂×Dic₁₉	#41	1	8	yes	—
58	Dic₃₈	—	4	8	no	—
59	#2607	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	—	2	4	no	—
61	C₂²×C₁₉	—	2	2	no	—
62	C₂²×C₁₉	—	4	2	no	—
63	C₂²×C₁₉	—	4	2	no	—
64	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
65	C₂²×C₁₉	C₂×#41	1	4	yes	—
66	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
67	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
68	C₄×C₁₉	—	2	4	no	—
69	C₄×C₁₉	—	4	2	no	—
70	C₄×C₁₉	—	4	2	no	—
71	Dic₁₉	—	2	8	no	—
72	Dic₁₉	—	4	4	no	—
73	#399	—	19	2	no	—
74	#393	—	19	2	no	—
75	#391	—	19	4	no	—
76	#387	—	19	4	no	—
77	#381	D₁₉	1	1	yes	characteristic
78	C₄×C₂²⋊C₄	—	19	2	no	—
79	C₂×C₁₉	—	4	2	no	—
80	C₂×C₁₉	#533	1	2	yes	—
81	C₂×C₁₉	#543	1	1	yes	characteristic
82	C₂×C₁₉	#551	1	2	yes	—
83	C₂×C₁₉	#559	1	2	yes	—
84	C₂²×Q₈	—	19	2	no	—
85	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
86	C₂×C₄⋊C₄	—	19	4	no	—
87	C₂×C₄⋊C₄	—	19	2	no	—
88	C₂×C₂²⋊C₄	—	19	4	no	—
89	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
90	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
91	C₂×C₄²	—	19	2	no	—
92	C₂×C₄²	—	19	2	no	—
93	#95	—	19	4	no	—
94	#95	—	19	2	no	—
95	#95	—	19	4	no	—
96	#95	—	19	2	no	—
97	#95	C₂×D₁₉	1	4	yes	—
98	C₁₉	#2607	1	1	yes	characteristic, complemented, Sylow
99	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
100	C₂×Q₈	—	38	8	no	—
101	C₂×Q₈	—	76	2	no	—
102	C₂²×C₄	—	4	1	no	—
103	C₂²×C₄	—	4	1	no	—
104	C₂²×C₄	—	19	4	no	—
105	C₂²×C₄	—	19	4	no	—
106	C₂²×C₄	Dic₃₈	1	4	yes	complemented
107	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
108	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
109	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
110	C₄⋊C₄	—	38	8	no	—
111	C₄⋊C₄	—	76	2	no	—
112	C₂²⋊C₄	—	4	1	no	—
113	C₂²⋊C₄	—	4	1	no	—
114	C₂²⋊C₄	—	38	8	no	—
115	C₄²	—	76	2	no	—
116	C₄²	—	76	2	no	—
117	C₂³	—	2	1	no	—
118	C₂³	—	2	1	no	—
119	C₂³	—	2	4	no	—
120	C₂³	C₂×Dic₃₈	1	2	yes	—
121	C₂³	C₂³×D₁₉	1	1	yes	characteristic
122	Q₈	—	76	8	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	2	4	no	—
128	C₂×C₄	—	2	4	no	—
129	C₂×C₄	—	4	4	no	—
130	C₂×C₄	—	19	8	no	—
131	C₂×C₄	—	38	4	no	—
132	C₂×C₄	—	38	4	no	—
133	C₂×C₄	—	38	4	no	—
134	C₂×C₄	—	38	4	no	—
135	C₂×C₄	—	38	4	no	—
136	C₂×C₄	C₂×Dic₃₈	1	4	yes	—
137	C₂²	—	2	4	no	—
138	C₂²	—	2	2	no	—
139	C₂²	—	4	2	no	—
140	C₂²	—	4	2	no	—
141	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
142	C₂²	#10597430	1	1	yes	characteristic
143	C₂²	#10597430	1	1	yes	characteristic
144	C₂²	#41×D₁₉	1	4	yes	—
145	C₄	—	2	4	no	—
146	C₄	—	4	2	no	—
147	C₄	—	4	2	no	—
148	C₄	—	38	8	no	—
149	C₄	—	76	4	no	—
150	C₂	—	4	2	no	—
151	C₂	#11927097	1	2	yes	—
152	C₂	#11927170	1	1	yes	characteristic
153	C₂	#11927222	1	2	yes	—
154	C₂	#11927278	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926480

C₂

yes

maximal

#11926456

C₂

yes

maximal

#11926448

C₂

yes

maximal, complemented

#11926431

C₂

yes

maximal, complemented

C₄×C₂²⋊Dic₁₉

C₂

yes

maximal

C₁₉×#381

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₁₉×#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

Q₈

yes

complemented

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×Q₈

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

#41

yes

—

Dic₃₈

—

#2607

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic

C₄×C₂²⋊C₄

—

C₂×C₁₉

—

C₂×C₁₉

#533

yes

—

C₂×C₁₉

#543

yes

characteristic

C₂×C₁₉

#551

yes

—

C₂×C₁₉

#559

yes

—

C₂²×Q₈

—

C₂³×C₄

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₂²⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₄²

—

C₂×C₄²

—

—

—

—

—

C₂×D₁₉

yes

—

C₁₉

#2607

yes

characteristic, complemented, Sylow

C₂⁴

C₂²×D₁₉

yes

characteristic

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

Dic₃₈

yes

complemented

107

C₂²×C₄

C₂²×D₁₉

yes

—

108

C₂²×C₄

C₂²×D₁₉

yes

—

109

C₂²×C₄

C₂²×D₁₉

yes

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₂²⋊C₄

—

113

C₂²⋊C₄

—

114

C₂²⋊C₄

—

115

C₄²

—

116

C₄²

—

117

C₂³

—

118

C₂³

—

119

C₂³

—

120

C₂³

C₂×Dic₃₈

yes

—

121

C₂³

C₂³×D₁₉

yes

characteristic

122

Q₈

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

C₂×Dic₃₈

yes

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

C₂²×Dic₃₈

yes

characteristic

142

C₂²

#10597430

yes

characteristic

143

C₂²

#10597430

yes

characteristic

144

C₂²

#41×D₁₉

yes

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₂

—

151

C₂

#11927097

yes

—

152

C₂

#11927170

yes

characteristic

153

C₂

#11927222

yes

—

154

C₂

#11927278

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#381	C₂
prime radical	C₂⁴×C₁₉	C₂³
hypercenter	#381	D₁₉
hypocenter	C₁₉	#2607
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #381

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#381

C₂

prime radical

C₂⁴×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #381

N	H ≅ G/N	type
3. #11926448	C₂	semidirect
4. #11926431	C₂	semidirect
24. C₂²×C₄×C₁₉	Q₈	semidirect
98. C₁₉	#2607	semidirect
106. C₂²×C₄	Dic₃₈	semidirect

H ≅ G/N

type

3. #11926448

C₂

semidirect

4. #11926431

C₂

semidirect

24. C₂²×C₄×C₁₉

Q₈

semidirect

98. C₁₉

#2607

semidirect

106. C₂²×C₄

Dic₃₈

semidirect

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

subgroup	index
#11926480	2
#11926456	2
#11926448	2
#11926431	2
C₄×C₂²⋊Dic₁₉	2
C₁₉×#381	2
#2607	19

subgroup

index

C₄×C₂²⋊Dic₁₉

C₁₉×#381

#2607

Subgroups — #14569300

Conjugacy classes of subgroups

Complements

Maximal subgroups