Group #14572740 — subgroups

Subgroups — #14572740

Order 2432.

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

normal subgroups only

This group has 314 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	#11927101	C₂	1	1	yes	maximal, characteristic
2	#11926673	C₂	1	4	yes	maximal, complemented
3	#11926672	C₂	1	4	yes	maximal, complemented
4	#11926602	C₂	1	4	yes	maximal
5	#11926601	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#432	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
8	#10597372	C₂²	1	2	yes	—
9	#10597370	C₄	1	2	yes	—
10	#10597370	C₄	1	2	yes	—
11	#10597316	C₄	1	2	yes	—
12	#10597315	C₄	1	1	yes	characteristic
13	#10597315	C₄	1	1	yes	characteristic
14	C₄×Dic₃₈	C₂²	1	2	yes	—
15	C₄×Dic₃₈	C₂²	1	2	yes	—
16	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
17	C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₁₉×#97	C₂²	1	2	yes	—
19	C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
20	#10597272	C₂²	1	4	yes	—
21	Dic₁₉⋊C₈	C₂²	1	8	yes	—
22	C₈×Dic₁₉	C₂²	1	4	yes	—
23	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
24	#10597260	C₂²	1	2	yes	—
25	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
29	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
30	C₂×C₈×C₁₉	C₂³	1	4	yes	—
31	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	C₂²⋊Dic₁₉	C₂×C₄	1	4	yes	—
36	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
37	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
38	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
39	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
40	Dic₁₉⋊C₄	C₂×C₄	1	4	yes	—
41	Dic₁₉⋊C₄	C₂×C₄	1	4	yes	—
42	C₄×Dic₁₉	C₂³	1	4	yes	—
43	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
44	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	—	2	2	no	—
46	C₂×C₄×C₁₉	—	4	1	no	—
47	C₂×C₄×C₁₉	—	4	1	no	—
48	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
54	C₂×Dic₁₉	C₂²×C₄	1	4	yes	—
55	C₂×Dic₁₉	C₂²×C₄	1	4	yes	—
56	Dic₃₈	—	4	2	no	—
57	Dic₃₈	—	4	2	no	—
58	C₈×C₁₉	—	2	4	no	—
59	C₁₉⋊C₈	—	2	4	no	—
60	#2987	—	19	1	no	maximal, Sylow
61	C₂²×C₁₉	—	2	1	no	—
62	C₂²×C₁₉	—	2	1	no	—
63	C₂²×C₁₉	—	2	1	no	—
64	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
65	C₄×C₁₉	—	2	1	no	—
66	C₄×C₁₉	—	2	1	no	—
67	C₄×C₁₉	—	2	1	no	—
68	C₄×C₁₉	—	2	1	no	—
69	C₄×C₁₉	—	2	1	no	—
70	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
71	Dic₁₉	—	2	4	no	—
72	Dic₁₉	—	2	4	no	—
73	#533	—	19	1	no	—
74	#446	—	19	4	no	—
75	#446	—	19	4	no	—
76	#433	—	19	4	no	—
77	#432	—	19	1	no	—
78	#432	D₁₉	1	1	yes	characteristic
79	C₂×C₁₉	—	4	1	no	—
80	C₂×C₁₉	#519	1	1	yes	characteristic
81	C₂×C₁₉	#568	1	1	yes	characteristic
82	C₂×C₁₉	#568	1	1	yes	characteristic
83	C₄⋊Q₈	—	19	1	no	—
84	C₄⋊Q₈	—	19	1	no	—
85	#125	—	19	2	no	—
86	C₂²⋊Q₈	—	19	2	no	—
87	C₂²⋊Q₈	—	19	2	no	—
88	C₄×Q₈	—	19	2	no	—
89	C₄×Q₈	—	19	2	no	—
90	#117	—	19	2	no	—
91	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
92	C₄⋊C₈	—	19	8	no	—
93	C₄⋊C₈	—	19	2	no	—
94	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
95	C₂²⋊C₈	—	19	2	no	—
96	C₂²⋊C₈	C₂×D₁₉	1	2	yes	—
97	#97	—	19	4	no	—
98	#97	—	19	2	no	—
99	#97	C₂×D₁₉	1	2	yes	—
100	C₄×C₈	—	19	4	no	—
101	C₁₉	#2987	1	1	yes	characteristic, complemented, Sylow
102	C₂×Q₈	—	19	2	no	—
103	C₂×Q₈	—	19	2	no	—
104	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
105	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
106	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
107	C₂×C₈	—	19	4	no	—
108	C₂×C₈	C₂²×D₁₉	1	4	yes	—
109	C₄⋊C₄	—	19	4	no	—
110	C₄⋊C₄	—	19	4	no	—
111	C₄⋊C₄	—	19	2	no	—
112	C₄⋊C₄	—	19	2	no	—
113	C₄⋊C₄	—	19	2	no	—
114	C₄⋊C₄	—	19	2	no	—
115	C₂²⋊C₄	—	19	4	no	—
116	C₄²	—	19	4	no	—
117	C₄²	C₄×D₁₉	1	1	yes	characteristic
118	C₄²	C₄×D₁₉	1	1	yes	characteristic
119	C₄²	C₂²×D₁₉	1	1	yes	characteristic
120	C₄²	C₂²×D₁₉	1	1	yes	characteristic
121	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
122	Q₈	—	76	2	no	—
123	Q₈	—	76	2	no	—
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	4	1	no	—
126	C₂×C₄	—	4	1	no	—
127	C₂×C₄	—	19	4	no	—
128	C₂×C₄	—	19	4	no	—
129	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
130	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
131	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
132	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
133	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
134	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
135	C₈	—	2	4	no	—
136	C₈	—	38	4	no	—
137	C₂²	—	2	1	no	—
138	C₂²	—	2	1	no	—
139	C₂²	—	2	1	no	—
140	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
141	C₄	—	2	1	no	—
142	C₄	—	2	1	no	—
143	C₄	—	2	1	no	—
144	C₄	—	2	1	no	—
145	C₄	—	2	1	no	—
146	C₄	—	38	4	no	—
147	C₄	—	38	4	no	—
148	C₄	#10597436	1	2	yes	—
149	C₂	—	4	1	no	—
150	C₂	#11927021	1	1	yes	characteristic
151	C₂	#11927310	1	1	yes	characteristic
152	C₂	#11927310	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927101

C₂

yes

maximal, characteristic

#11926673

C₂

yes

maximal, complemented

#11926672

C₂

yes

maximal, complemented

#11926602

C₂

yes

maximal

#11926601

C₂

yes

maximal, characteristic

C₁₉×#432

C₂

yes

maximal, characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597372

C₂²

yes

—

#10597370

C₄

yes

—

#10597370

C₄

yes

—

#10597316

C₄

yes

—

#10597315

C₄

yes

characteristic

#10597315

C₄

yes

characteristic

C₄×Dic₃₈

C₂²

yes

—

C₄×Dic₃₈

C₂²

yes

—

C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×C₂²⋊C₈

C₂²

yes

—

C₁₉×#97

C₂²

yes

—

C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

#10597272

C₂²

yes

—

Dic₁₉⋊C₈

C₂²

yes

—

C₈×Dic₁₉

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#10597260

C₂²

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×Dic₃₈

C₂×C₄

yes

—

C₂×Dic₃₈

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

C₂×C₄

yes

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

Dic₁₉⋊C₄

C₂×C₄

yes

—

Dic₁₉⋊C₄

C₂×C₄

yes

—

C₄×Dic₁₉

C₂³

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

C₂²×C₄

yes

—

C₂×Dic₁₉

C₂²×C₄

yes

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2987

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂³×C₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

2₋¹⁺⁴

yes

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₉

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

C₂×D₁₉

yes

—

#97

—

#97

—

#97

C₂×D₁₉

yes

—

100

C₄×C₈

—

101

C₁₉

#2987

yes

characteristic, complemented, Sylow

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂²×C₄

C₄×D₁₉

yes

characteristic

105

C₂²×C₄

C₄×D₁₉

yes

characteristic

106

C₂²×C₄

C₂²×D₁₉

yes

characteristic

107

C₂×C₈

—

108

C₂×C₈

C₂²×D₁₉

yes

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₂²⋊C₄

—

116

C₄²

—

117

C₄²

C₄×D₁₉

yes

characteristic

118

C₄²

C₄×D₁₉

yes

characteristic

119

C₄²

C₂²×D₁₉

yes

characteristic

120

C₄²

C₂²×D₁₉

yes

characteristic

121

C₂³

C₂×C₄×D₁₉

yes

characteristic

122

Q₈

—

123

Q₈

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

130

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

131

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

132

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

133

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

134

C₂×C₄

C₂³×D₁₉

yes

characteristic

135

C₈

—

136

C₈

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

C₂²×C₄×D₁₉

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

#10597436

yes

—

149

C₂

—

150

C₂

#11927021

yes

characteristic

151

C₂

#11927310

yes

characteristic

152

C₂

#11927310

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉
commutator, socle	C₂²×C₁₉	C₂³×C₄
Fitting	C₁₉×#432	C₂
prime radical	C₂³×C₁₉	C₂²×C₄
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#432	D₁₉
hypocenter	C₁₉	#2987
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #432

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₁₉

commutator, socle

C₂²×C₁₉

C₂³×C₄

Fitting

C₁₉×#432

C₂

prime radical

C₂³×C₁₉

C₂²×C₄

cosocle

C₂×C₄×C₁₉

C₂⁴

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄ ◁ #432

N	H ≅ G/N	type
2. #11926673	C₂	semidirect
3. #11926672	C₂	semidirect
101. C₁₉	#2987	semidirect

H ≅ G/N

type

2. #11926673

C₂

semidirect

3. #11926672

C₂

semidirect

101. C₁₉

#2987

semidirect

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

subgroup	index
#11927101	2
#11926673	2
#11926672	2
#11926602	2
#11926601	2
C₁₉×#432	2
#2987	19

subgroup

index

C₁₉×#432

Subgroups — #14572740

Conjugacy classes of subgroups

Complements

Maximal subgroups