Group #14564802 — subgroups

Subgroups — #14564802

Order 2432.

290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 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	#11927170	C₂	1	1	yes	maximal, characteristic
2	#11926407	C₂	1	2	yes	maximal
3	#11926311	C₂	1	1	yes	maximal, characteristic
4	#11926310	C₂	1	2	yes	maximal
5	C₁₉×#381	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
10	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
11	#10597370	—	2	2	no	—
12	#10597324	—	2	4	no	—
13	C₁₉×#95	—	2	2	no	—
14	C₁₉⋊#95	—	2	4	no	—
15	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
16	C₂²×C₄×C₁₉	—	2	2	no	—
17	C₂²×C₄×C₁₉	—	2	1	no	—
18	C₂²×C₄×C₁₉	—	2	1	no	—
19	C₂²×C₄×C₁₉	—	2	2	no	—
20	C₂²×C₄×C₁₉	—	2	1	no	—
21	C₂²×C₄×C₁₉	D₄	1	2	yes	—
22	C₂²×C₄×C₁₉	Q₈	1	2	yes	complemented
23	C₂²×Dic₁₉	—	2	2	no	—
24	C₂²×Dic₁₉	D₄	1	4	yes	—
25	C₂×Dic₃₈	—	2	2	no	—
26	C₂²⋊C₄×C₁₉	—	2	2	no	—
27	C₂²⋊C₄×C₁₉	—	2	2	no	—
28	C₂²⋊Dic₁₉	—	2	2	no	—
29	C₂²⋊Dic₁₉	—	2	2	no	—
30	C₂²⋊Dic₁₉	—	2	2	no	—
31	C₂²⋊Dic₁₉	—	2	2	no	—
32	C₄⋊Dic₁₉	—	2	2	no	—
33	Dic₁₉⋊C₄	—	2	4	no	—
34	C₂³×C₁₉	—	4	2	no	—
35	C₂³×C₁₉	C₂×D₄	1	2	yes	—
36	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₂³×C₁₉	C₂×Q₈	1	1	yes	characteristic
38	C₂³×C₁₉	#41	1	1	yes	characteristic
39	C₂³×C₁₉	#41	1	2	yes	—
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	2	4	no	—
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	4	1	no	—
44	C₂×C₄×C₁₉	—	4	1	no	—
45	C₂×C₄×C₁₉	—	4	2	no	—
46	C₂×C₄×C₁₉	—	4	2	no	—
47	C₂×C₄×C₁₉	—	4	2	no	—
48	C₂×C₄×C₁₉	—	4	1	no	—
49	C₂×Dic₁₉	—	2	4	no	—
50	C₂×Dic₁₉	—	4	4	no	—
51	C₂×Dic₁₉	—	4	4	no	—
52	C₂×Dic₁₉	—	4	2	no	—
53	Dic₃₈	—	8	2	no	—
54	#2030	—	19	1	no	maximal, Sylow
55	C₂²×C₁₉	—	2	4	no	—
56	C₂²×C₁₉	—	2	2	no	—
57	C₂²×C₁₉	—	4	1	no	—
58	C₂²×C₁₉	—	4	1	no	—
59	C₂²×C₁₉	—	4	2	no	—
60	C₂²×C₁₉	#120	1	1	yes	characteristic
61	C₂²×C₁₉	C₂²⋊Q₈	1	2	yes	—
62	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
63	C₂²×C₁₉	#124	1	1	yes	characteristic
64	C₂²×C₁₉	#124	1	2	yes	—
65	C₄×C₁₉	—	4	2	no	—
66	C₄×C₁₉	—	4	2	no	—
67	C₄×C₁₉	—	8	1	no	—
68	Dic₁₉	—	4	4	no	—
69	Dic₁₉	—	8	2	no	—
70	#543	—	19	1	no	—
71	#381	—	19	2	no	—
72	#381	D₁₉	1	1	yes	characteristic
73	#342	—	19	2	no	—
74	#342	—	19	1	no	—
75	C₂×C₁₉	—	2	2	no	—
76	C₂×C₁₉	—	2	1	no	—
77	C₂×C₁₉	—	2	2	no	—
78	C₂×C₁₉	—	2	1	no	—
79	C₂×C₁₉	#393	1	1	yes	characteristic
80	C₂×C₁₉	#458	1	2	yes	—
81	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
82	C₂²⋊Q₈	—	38	4	no	—
83	C₂²⋊Q₈	—	38	2	no	—
84	C₂×C₂²⋊C₄	—	19	2	no	—
85	C₂×C₂²⋊C₄	—	19	2	no	—
86	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
87	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
88	#95	—	2	2	no	—
89	#95	—	38	4	no	—
90	C₁₉	#2030	1	1	yes	characteristic, complemented, Sylow
91	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
92	C₂×Q₈	—	38	2	no	—
93	C₂²×C₄	—	2	1	no	—
94	C₂²×C₄	—	2	2	no	—
95	C₂²×C₄	—	2	2	no	—
96	C₂²×C₄	—	2	1	no	—
97	C₂²×C₄	—	2	1	no	—
98	C₂²×C₄	—	19	4	no	—
99	C₂²×C₄	—	38	2	no	—
100	C₂²×C₄	Dic₃₈	1	2	yes	complemented
101	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
102	C₄⋊C₄	—	38	4	no	—
103	C₄⋊C₄	—	38	2	no	—
104	C₂²⋊C₄	—	2	2	no	—
105	C₂²⋊C₄	—	2	2	no	—
106	C₂²⋊C₄	—	38	2	no	—
107	C₂²⋊C₄	—	38	2	no	—
108	C₂²⋊C₄	—	38	2	no	—
109	C₂²⋊C₄	—	38	2	no	—
110	C₂³	—	4	2	no	—
111	C₂³	C₂×Dic₃₈	1	1	yes	characteristic
112	C₂³	#64541	1	1	yes	characteristic
113	C₂³	D₄×D₁₉	1	2	yes	—
114	C₂³	#64543	1	2	yes	—
115	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
116	Q₈	—	152	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	2	4	no	—
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	4	1	no	—
121	C₂×C₄	—	4	1	no	—
122	C₂×C₄	—	4	2	no	—
123	C₂×C₄	—	4	2	no	—
124	C₂×C₄	—	4	2	no	—
125	C₂×C₄	—	4	1	no	—
126	C₂×C₄	—	38	4	no	—
127	C₂×C₄	—	76	4	no	—
128	C₂×C₄	—	76	4	no	—
129	C₂×C₄	—	76	2	no	—
130	C₂²	—	2	2	no	—
131	C₂²	—	2	4	no	—
132	C₂²	—	4	1	no	—
133	C₂²	—	4	1	no	—
134	C₂²	—	4	2	no	—
135	C₂²	#10597324	1	2	yes	—
136	C₂²	#10597331	1	2	yes	—
137	C₂²	#10597370	1	1	yes	characteristic
138	C₂²	#10597382	1	1	yes	characteristic
139	C₂²	#10597383	1	1	yes	characteristic
140	C₄	—	4	2	no	—
141	C₄	—	4	2	no	—
142	C₄	—	8	1	no	—
143	C₄	—	76	4	no	—
144	C₄	—	152	2	no	—
145	C₂	—	2	1	no	—
146	C₂	—	2	2	no	—
147	C₂	—	2	2	no	—
148	C₂	—	2	1	no	—
149	C₂	#11926456	1	1	yes	characteristic
150	C₂	#11926733	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927170

C₂

yes

maximal, characteristic

#11926407

C₂

yes

maximal

#11926311

C₂

yes

maximal, characteristic

#11926310

C₂

yes

maximal

C₁₉×#381

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

#10597370

—

#10597324

—

C₁₉×#95

—

C₁₉⋊#95

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

Q₈

yes

complemented

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

—

C₂×Dic₃₈

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂³×C₁₉

C₂×Q₈

yes

C₂³×C₁₉

yes

C₂³×C₁₉

yes

—

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×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

#2030

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#120

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

—

C₂²×C₁₉

C₂²⋊Q₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

#543

—

#381

—

#381

D₁₉

yes

characteristic

#342

—

#342

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#393

yes

characteristic

C₂×C₁₉

#458

yes

—

C₂³×C₄

C₂×D₁₉

yes

characteristic

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₂²⋊C₄

C₂×D₁₉

yes

characteristic

#95

—

#95

—

C₁₉

#2030

yes

characteristic, complemented, Sylow

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

Dic₃₈

yes

complemented

101

C₂²×C₄

C₂²⋊D₁₉

yes

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₂²⋊C₄

—

105

C₂²⋊C₄

—

106

C₂²⋊C₄

—

107

C₂²⋊C₄

—

108

C₂²⋊C₄

—

109

C₂²⋊C₄

—

110

C₂³

—

111

C₂³

C₂×Dic₃₈

yes

characteristic

112

C₂³

#64541

yes

characteristic

113

C₂³

D₄×D₁₉

yes

—

114

C₂³

#64543

yes

—

115

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

116

Q₈

—

152

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

#10597324

yes

—

136

C₂²

#10597331

yes

—

137

C₂²

#10597370

yes

characteristic

138

C₂²

#10597382

yes

characteristic

139

C₂²

#10597383

yes

characteristic

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

152

—

145

C₂

—

146

C₂

—

147

C₂

—

148

C₂

—

149

C₂

#11926456

yes

characteristic

150

C₂

#11926733

yes

—

	subgroup	G/H
center	C₂²	#10597383
commutator, prime radical, cosocle	C₂⁴×C₁₉	C₂³
Frattini	C₂⁴	C₂²×D₁₉
Fitting	C₁₉×#381	C₂
socle	C₂²×C₁₉	#120
hypercenter	#381	D₁₉
hypocenter	C₁₉	#2030
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #381

subgroup

G/H

center

C₂²

#10597383

commutator, prime radical, cosocle

C₂⁴×C₁₉

C₂³

Frattini

C₂⁴

C₂²×D₁₉

Fitting

C₁₉×#381

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂⁴ ◁ #381

N	H ≅ G/N	type
22. C₂²×C₄×C₁₉	Q₈	semidirect
90. C₁₉	#2030	semidirect
100. C₂²×C₄	Dic₃₈	semidirect

H ≅ G/N

type

22. C₂²×C₄×C₁₉

Q₈

semidirect

90. C₁₉

#2030

semidirect

100. C₂²×C₄

Dic₃₈

semidirect

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

subgroup	index
#11927170	2
#11926407	2
#11926311	2
#11926310	2
C₁₉×#381	2
#2030	19

subgroup

index

C₁₉×#381

Subgroups — #14564802

Conjugacy classes of subgroups

Complements

Maximal subgroups