Group #14562229 — subgroups

Subgroups — #14562229

Order 2432.

226 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 77 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	C₄×#64520	C₂	1	1	yes	maximal, characteristic
3	#11926285	C₂	1	4	yes	maximal, complemented
4	C₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂×M₁₆×C₁₉	—	2	1	no	—
6	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
7	#10597372	C₄	1	2	yes	—
8	#10597370	—	2	1	no	—
9	#10597370	—	2	1	no	—
10	C₂×#64520	—	2	1	no	—
11	#10597316	C₂²	1	2	yes	—
12	#10597315	C₄	1	1	yes	characteristic
13	#10597315	C₄	1	1	yes	characteristic
14	C₄×Dic₃₈	—	2	1	no	—
15	C₄×Dic₃₈	—	2	1	no	—
16	C₁₉×#97	C₂²	1	2	yes	—
17	C₄×C₈×C₁₉	—	2	1	no	—
18	#10597260	C₂²	1	2	yes	—
19	C₄×C₁₉⋊C₈	—	2	1	no	—
20	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂×Dic₃₈	—	2	1	no	—
24	C₂×Dic₃₈	—	2	1	no	—
25	M₁₆×C₁₉	—	2	4	no	—
26	C₂×C₈×C₁₉	—	2	2	no	—
27	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₄²×C₁₉	D₄	1	1	yes	characteristic
29	C₄²×C₁₉	D₄	1	1	yes	characteristic
30	C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²⋊Dic₁₉	—	2	2	no	—
32	C₄⋊Dic₁₉	—	2	1	no	—
33	C₄⋊Dic₁₉	—	2	1	no	—
34	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
35	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
36	Dic₁₉⋊C₄	—	2	2	no	—
37	Dic₁₉⋊C₄	—	2	2	no	—
38	C₄×Dic₁₉	—	2	2	no	—
39	#64520	—	2	4	no	—
40	C₂×C₁₉⋊C₈	—	2	2	no	—
41	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×Dic₁₉	—	2	2	no	—
52	C₂×Dic₁₉	—	2	2	no	—
53	Dic₃₈	—	4	2	no	—
54	Dic₃₈	—	4	2	no	—
55	C₈×C₁₉	—	2	4	no	—
56	C₁₉⋊C₈	—	2	4	no	—
57	#1526	—	19	1	no	maximal, Sylow
58	C₂²×C₁₉	—	2	1	no	—
59	C₂²×C₁₉	—	2	1	no	—
60	C₂²×C₁₉	—	2	1	no	—
61	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
62	C₄×C₁₉	—	2	1	no	—
63	C₄×C₁₉	—	2	1	no	—
64	C₄×C₁₉	—	2	1	no	—
65	C₄×C₁₉	#101	1	2	yes	—
66	C₄×C₁₉	#104	1	2	yes	—
67	C₄×C₁₉	#104	1	2	yes	—
68	Dic₁₉	—	4	2	no	—
69	Dic₁₉	—	4	2	no	—
70	#533	—	19	1	no	—
71	C₄×M₁₆	—	19	1	no	—
72	C₄×M₁₆	D₁₉	1	1	yes	characteristic
73	#330	—	19	4	no	—
74	C₂×C₁₉	—	4	1	no	—
75	C₂×C₁₉	C₂×#101	1	1	yes	characteristic
76	C₂×C₁₉	C₂×#104	1	1	yes	characteristic
77	C₂×C₁₉	C₂×#104	1	1	yes	characteristic
78	C₂×M₁₆	—	2	1	no	—
79	C₂×M₁₆	—	38	1	no	—
80	C₄⋊Q₈	—	19	1	no	—
81	C₄⋊Q₈	—	19	1	no	—
82	#125	—	19	2	no	—
83	C₂²⋊Q₈	—	38	1	no	—
84	C₂²⋊Q₈	—	38	1	no	—
85	C₄×Q₈	—	38	1	no	—
86	C₄×Q₈	—	38	1	no	—
87	#117	—	19	2	no	—
88	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
89	#97	—	19	2	no	—
90	#97	C₂×D₁₉	1	2	yes	—
91	C₄×C₈	—	2	1	no	—
92	C₄×C₈	—	38	1	no	—
93	C₁₉	#1526	1	1	yes	characteristic, complemented, Sylow
94	C₂×Q₈	—	38	1	no	—
95	C₂×Q₈	—	38	1	no	—
96	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
97	C₂²×C₄	D₇₆	1	1	yes	characteristic
98	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
99	M₁₆	—	2	4	no	—
100	M₁₆	—	38	4	no	—
101	C₂×C₈	—	2	2	no	—
102	C₂×C₈	—	38	2	no	—
103	C₄⋊C₄	—	19	2	no	—
104	C₄⋊C₄	—	19	2	no	—
105	C₄⋊C₄	—	38	1	no	—
106	C₄⋊C₄	—	38	1	no	—
107	C₄⋊C₄	—	38	2	no	—
108	C₄⋊C₄	—	38	2	no	—
109	C₂²⋊C₄	—	38	2	no	—
110	C₄²	—	38	2	no	—
111	C₄²	C₄×D₁₉	1	1	yes	characteristic
112	C₄²	D₇₆	1	1	yes	characteristic
113	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
114	C₄²	C₂²×D₁₉	1	1	yes	characteristic
115	C₂³	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
116	Q₈	—	76	2	no	—
117	Q₈	—	76	2	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	38	2	no	—
122	C₂×C₄	—	38	2	no	—
123	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
124	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
125	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
126	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
127	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
128	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
129	C₈	—	2	4	no	—
130	C₈	—	38	4	no	—
131	C₂²	—	2	1	no	—
132	C₂²	—	2	1	no	—
133	C₂²	—	2	1	no	—
134	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
135	C₄	—	2	1	no	—
136	C₄	—	2	1	no	—
137	C₄	—	2	1	no	—
138	C₄	—	76	2	no	—
139	C₄	—	76	2	no	—
140	C₄	#10597262	1	2	yes	—
141	C₄	#10597281	1	2	yes	—
142	C₄	#10597282	1	2	yes	—
143	C₂	—	4	1	no	—
144	C₂	C₂×#10597281	1	1	yes	characteristic
145	C₂	C₂×#10597282	1	1	yes	characteristic
146	C₂	C₂×#10597262	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927101

C₂

yes

maximal, characteristic

C₄×#64520

C₂

yes

maximal, characteristic

#11926285

C₂

yes

maximal, complemented

C₄×M₁₆×C₁₉

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597372

C₄

yes

—

—

—

—

C₂²

yes

—

#10597315

C₄

yes

characteristic

#10597315

C₄

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×#97

C₂²

yes

—

C₄×C₈×C₁₉

—

#10597260

C₂²

yes

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

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

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1526

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#101

yes

—

C₄×C₁₉

#104

yes

—

C₄×C₁₉

#104

yes

—

Dic₁₉

—

Dic₁₉

—

#533

—

C₄×M₁₆

—

C₄×M₁₆

D₁₉

yes

characteristic

#330

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₂×M₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#97

—

#97

C₂×D₁₉

yes

—

C₄×C₈

—

C₄×C₈

—

C₁₉

#1526

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

C₄×D₁₉

yes

characteristic

C₂²×C₄

D₇₆

yes

characteristic

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

M₁₆

—

100

M₁₆

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₂²⋊C₄

—

110

C₄²

—

111

C₄²

C₄×D₁₉

yes

characteristic

112

C₄²

D₇₆

yes

characteristic

113

C₄²

C₂²⋊D₁₉

yes

characteristic

114

C₄²

C₂²×D₁₉

yes

characteristic

115

C₂³

(C₂×D₁₉)⋊C₄

yes

characteristic

116

Q₈

—

117

Q₈

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

124

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

125

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

126

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

127

C₂×C₄

C₂×D₇₆

yes

characteristic

128

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

129

C₈

—

130

C₈

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

#10597262

yes

—

141

C₄

#10597281

yes

—

142

C₄

#10597282

yes

—

143

C₂

—

144

C₂

C₂×#10597281

yes

characteristic

145

C₂

C₂×#10597282

yes

characteristic

146

C₂

C₂×#10597262

yes

characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₁₉)⋊C₄
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₄²	C₂²×D₁₉
Fitting	C₄×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×C₁₉	C₂²⋊C₄
cosocle	C₄²×C₁₉	C₂³
hypercenter	C₄×M₁₆	D₁₉
hypocenter	C₁₉	#1526
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×M₁₆

subgroup

G/H

center

C₂×C₄

(C₂×D₁₉)⋊C₄

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₄²

C₂²×D₁₉

Fitting

C₄×M₁₆×C₁₉

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂³×C₁₉

C₂²⋊C₄

cosocle

C₄²×C₁₉

C₂³

hypercenter

C₄×M₁₆

D₁₉

hypocenter

C₁₉

#1526

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×M₁₆

N	H ≅ G/N	type
3. #11926285	C₂	semidirect
93. C₁₉	#1526	semidirect

H ≅ G/N

type

3. #11926285

C₂

semidirect

93. C₁₉

#1526

semidirect

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

subgroup	index
#11927101	2
C₄×#64520	2
#11926285	2
C₄×M₁₆×C₁₉	2
#1526	19

subgroup

index

C₄×M₁₆×C₁₉

Subgroups — #14562229

Conjugacy classes of subgroups

Complements

Maximal subgroups