Group #14571628 — subgroups

Subgroups — #14571628

Order 2432.

432 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 157 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	#11926465	C₂	1	4	yes	maximal
2	#11926464	C₂	1	2	yes	maximal
3	#11926451	C₂	1	2	yes	maximal
4	#11926450	C₂	1	2	yes	maximal
5	#11926448	C₂	1	4	yes	maximal
6	C₁₉×#391	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×Dic₃₈	C₂²	1	2	yes	—
9	C₂²×Dic₃₈	C₂²	1	2	yes	—
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
13	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
14	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
15	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
16	C₁₉×#95	C₂²	1	4	yes	—
17	C₁₉⋊#95	C₂²	1	2	yes	—
18	C₁₉⋊#95	C₂²	1	4	yes	—
19	C₁₉⋊#95	C₂²	1	4	yes	—
20	C₁₉⋊#95	C₂²	1	4	yes	—
21	C₂×Q₈×C₁₉	—	4	1	no	—
22	C₂×Q₈×C₁₉	—	4	1	no	—
23	C₂×Q₈×C₁₉	Q₈	1	4	yes	complemented
24	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
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	—	4	2	no	—
31	C₂×Dic₃₈	—	4	2	no	—
32	C₂×Dic₃₈	—	4	4	no	—
33	C₂×Dic₃₈	—	4	2	no	—
34	C₂×Dic₃₈	Q₈	1	8	yes	complemented
35	C₄⋊C₄×C₁₉	—	4	1	no	—
36	C₄²×C₁₉	—	4	1	no	—
37	C₄⋊Dic₁₉	—	4	2	no	—
38	C₄⋊Dic₁₉	—	4	2	no	—
39	Dic₁₉⋊C₄	—	4	4	no	—
40	C₄×Dic₁₉	—	4	2	no	—
41	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
42	Q₈×C₁₉	—	4	4	no	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	—	2	2	no	—
46	C₂×C₄×C₁₉	—	2	2	no	—
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	2	1	no	—
49	C₂×C₄×C₁₉	—	2	4	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
52	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
53	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
54	C₂×Dic₁₉	—	2	4	no	—
55	C₂×Dic₁₉	—	2	4	no	—
56	C₂×Dic₁₉	—	2	4	no	—
57	C₂×Dic₁₉	—	2	4	no	—
58	C₂×Dic₁₉	—	2	4	no	—
59	C₂×Dic₁₉	C₂×Q₈	1	8	yes	—
60	Dic₃₈	—	4	8	no	—
61	Dic₃₈	—	4	8	no	—
62	#2811	—	19	1	no	maximal, Sylow
63	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
64	C₂²×C₁₉	C₂²×Q₈	1	2	yes	—
65	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
66	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
67	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
68	C₄×C₁₉	—	2	4	no	—
69	C₄×C₁₉	—	2	4	no	—
70	C₄×C₁₉	—	2	2	no	—
71	C₄×C₁₉	—	4	2	no	—
72	Dic₁₉	—	2	8	no	—
73	Dic₁₉	—	4	4	no	—
74	#395	—	19	2	no	—
75	#395	—	19	4	no	—
76	#391	—	19	2	no	—
77	#391	—	19	2	no	—
78	#391	—	19	4	no	—
79	#391	D₁₉	1	1	yes	characteristic
80	C₂×C₁₉	#543	1	2	yes	—
81	C₂×C₁₉	#543	1	1	yes	characteristic
82	C₂×C₁₉	Q₈²	1	1	yes	characteristic
83	C₂×C₁₉	Q₈²	1	2	yes	—
84	C₂×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
85	C₂²×Q₈	—	19	2	no	—
86	C₂²×Q₈	—	19	2	no	—
87	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
88	C₂×C₄⋊C₄	—	19	4	no	—
89	C₂×C₄⋊C₄	—	19	2	no	—
90	C₂×C₄⋊C₄	—	19	2	no	—
91	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
92	C₂×C₄²	—	19	2	no	—
93	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
94	#95	—	19	2	no	—
95	#95	—	19	4	no	—
96	#95	—	19	4	no	—
97	#95	—	19	4	no	—
98	#95	C₂×D₁₉	1	4	yes	—
99	C₁₉	#2811	1	1	yes	characteristic, complemented, Sylow
100	C₂×Q₈	—	4	1	no	—
101	C₂×Q₈	—	4	1	no	—
102	C₂×Q₈	—	19	8	no	—
103	C₂×Q₈	—	76	2	no	—
104	C₂×Q₈	—	76	2	no	—
105	C₂×Q₈	—	76	2	no	—
106	C₂×Q₈	—	76	4	no	—
107	C₂×Q₈	Dic₃₈	1	4	yes	complemented
108	C₂²×C₄	—	19	4	no	—
109	C₂²×C₄	—	19	4	no	—
110	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
111	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
112	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
113	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
114	C₄⋊C₄	—	4	1	no	—
115	C₄⋊C₄	—	76	4	no	—
116	C₄⋊C₄	—	76	2	no	—
117	C₄⋊C₄	—	76	2	no	—
118	C₄²	—	4	1	no	—
119	C₄²	—	76	2	no	—
120	C₂³	C₂³×D₁₉	1	1	yes	characteristic
121	Q₈	—	4	4	no	—
122	Q₈	—	76	8	no	—
123	Q₈	—	76	8	no	—
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	2	2	no	—
131	C₂×C₄	—	2	4	no	—
132	C₂×C₄	—	19	8	no	—
133	C₂×C₄	—	38	4	no	—
134	C₂×C₄	—	38	4	no	—
135	C₂×C₄	—	38	4	no	—
136	C₂×C₄	—	38	4	no	—
137	C₂×C₄	—	38	4	no	—
138	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
139	C₂×C₄	C₂×Dic₃₈	1	4	yes	—
140	C₂×C₄	Q₈×D₁₉	1	4	yes	—
141	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
142	C₂²	#10597430	1	1	yes	characteristic
143	C₂²	#10597430	1	1	yes	characteristic
144	C₂²	C₂×Q₈×D₁₉	1	2	yes	—
145	C₂²	#10597435	1	2	yes	—
146	C₄	—	2	4	no	—
147	C₄	—	2	2	no	—
148	C₄	—	2	4	no	—
149	C₄	—	4	2	no	—
150	C₄	—	38	8	no	—
151	C₄	—	76	4	no	—
152	C₂	#11927169	1	2	yes	—
153	C₂	#11927170	1	1	yes	characteristic
154	C₂	#11927274	1	1	yes	characteristic
155	C₂	Q₈×Dic₃₈	1	2	yes	—
156	C₂	#11927286	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926465

C₂

yes

maximal

#11926464

C₂

yes

maximal

#11926451

C₂

yes

maximal

#11926450

C₂

yes

maximal

#11926448

C₂

yes

maximal

C₁₉×#391

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂²×Dic₃₈

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

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

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

Q₈

yes

complemented

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

Q₈

yes

complemented

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

Q₈×C₁₉

—

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×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×Q₈

yes

—

Dic₃₈

—

Dic₃₈

—

#2811

—

maximal, Sylow

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₂²×C₁₉

C₂²×Q₈

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

#543

yes

—

C₂×C₁₉

#543

yes

characteristic

C₂×C₁₉

Q₈²

yes

characteristic

C₂×C₁₉

Q₈²

yes

—

C₂×C₁₉

H(3,𝔽₄)

yes

characteristic

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

—

—

—

—

C₂×D₁₉

yes

—

C₁₉

#2811

yes

characteristic, complemented, Sylow

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

Dic₃₈

yes

complemented

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

C₂²×D₁₉

yes

—

111

C₂²×C₄

C₂²×D₁₉

yes

characteristic

112

C₂²×C₄

C₂²×D₁₉

yes

—

113

C₂²×C₄

C₂²×D₁₉

yes

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄²

—

119

C₄²

—

120

C₂³

C₂³×D₁₉

yes

characteristic

121

Q₈

—

122

Q₈

—

123

Q₈

—

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

—

137

C₂×C₄

—

138

C₂×C₄

C₂×Dic₃₈

yes

—

139

C₂×C₄

C₂×Dic₃₈

yes

—

140

C₂×C₄

Q₈×D₁₉

yes

—

141

C₂²

C₂²×Dic₃₈

yes

characteristic

142

C₂²

#10597430

yes

characteristic

143

C₂²

#10597430

yes

characteristic

144

C₂²

C₂×Q₈×D₁₉

yes

—

145

C₂²

#10597435

yes

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₂

#11927169

yes

—

153

C₂

#11927170

yes

characteristic

154

C₂

#11927274

yes

characteristic

155

C₂

Q₈×Dic₃₈

yes

—

156

C₂

#11927286

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#391	C₂
hypercenter	#391	D₁₉
hypocenter	C₁₉	#2811
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #391

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, prime radical, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#391

C₂

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #391

N	H ≅ G/N	type
23. C₂×Q₈×C₁₉	Q₈	semidirect
34. C₂×Dic₃₈	Q₈	semidirect
99. C₁₉	#2811	semidirect
107. C₂×Q₈	Dic₃₈	semidirect

H ≅ G/N

type

23. C₂×Q₈×C₁₉

Q₈

semidirect

34. C₂×Dic₃₈

Q₈

semidirect

99. C₁₉

#2811

semidirect

107. C₂×Q₈

Dic₃₈

semidirect

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

subgroup	index
#11926465	2
#11926464	2
#11926451	2
#11926450	2
#11926448	2
C₁₉×#391	2
#2811	19

subgroup

index

C₁₉×#391

Subgroups — #14571628

Conjugacy classes of subgroups

Complements

Maximal subgroups