Group #14562290 — subgroups

Subgroups — #14562290

Order 2432.

212 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 89 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	C₂×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#11926292	C₂	1	2	yes	maximal, complemented
4	#11926291	C₂	1	2	yes	maximal, complemented
5	C₁₉×#431	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
7	#10597372	—	2	1	no	—
8	#10597370	—	2	1	no	—
9	#10597370	C₄	1	2	yes	—
10	C₂²×C₁₉⋊C₈	—	2	1	no	—
11	#10597316	—	2	1	no	—
12	#10597315	C₂²	1	1	yes	characteristic
13	#10597315	C₂²	1	1	yes	characteristic
14	C₄×Dic₃₈	—	2	1	no	—
15	C₄×Dic₃₈	C₄	1	2	yes	—
16	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
17	C₁₉×C₂²⋊C₈	—	2	1	no	—
18	C₄×C₈×C₁₉	—	2	1	no	—
19	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
20	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
21	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂×Dic₃₈	—	2	1	no	—
25	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
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	—	2	1	no	—
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	C₂×C₁₉⋊C₈	—	2	2	no	—
40	C₂×C₁₉⋊C₈	—	4	2	no	—
41	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	4	1	no	—
44	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
48	C₂×C₄×C₁₉	Q₁₆	1	2	yes	—
49	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂×Dic₁₉	—	2	2	no	—
53	C₂×Dic₁₉	—	2	2	no	—
54	Dic₃₈	—	4	2	no	—
55	Dic₃₈	—	4	2	no	—
56	C₈×C₁₉	—	4	2	no	—
57	C₁₉⋊C₈	—	4	2	no	—
58	#1542	—	19	1	no	maximal, Sylow
59	C₂²×C₁₉	—	2	1	no	—
60	C₂²×C₁₉	—	2	1	no	—
61	C₂²×C₁₉	#103	1	2	yes	—
62	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₄×C₁₉	—	2	1	no	—
64	C₄×C₁₉	—	2	1	no	—
65	C₄×C₁₉	—	2	1	no	—
66	C₄×C₁₉	#103	1	2	yes	—
67	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
68	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
69	C₄×C₁₉	#135	1	2	yes	—
70	Dic₁₉	—	4	2	no	—
71	Dic₁₉	—	4	2	no	—
72	#533	—	19	1	no	—
73	#431	D₁₉	1	1	yes	characteristic
74	C₂×C₄⋊C₈	—	19	1	no	—
75	#333	—	19	2	no	—
76	#332	—	19	2	no	—
77	C₂×C₁₉	—	2	2	no	—
78	C₂×C₁₉	#413	1	1	yes	characteristic
79	C₂×C₁₉	C₂×#103	1	1	yes	characteristic
80	C₂×C₁₉	#416	1	1	yes	characteristic
81	C₂²×C₈	—	38	1	no	—
82	C₄⋊Q₈	—	19	1	no	—
83	C₄⋊Q₈	—	19	1	no	—
84	#125	—	38	1	no	—
85	C₂²⋊Q₈	—	19	2	no	—
86	C₂²⋊Q₈	—	38	1	no	—
87	C₄×Q₈	—	19	2	no	—
88	C₄×Q₈	—	38	1	no	—
89	#117	—	38	1	no	—
90	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
91	C₄⋊C₈	—	19	2	no	—
92	C₄⋊C₈	—	38	1	no	—
93	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
94	C₂²⋊C₈	—	2	1	no	—
95	C₄×C₈	—	2	1	no	—
96	C₁₉	#1542	1	1	yes	characteristic, complemented, Sylow
97	C₂×Q₈	—	19	2	no	—
98	C₂×Q₈	—	38	1	no	—
99	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
100	C₂²×C₄	D₇₆	1	1	yes	characteristic
101	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
102	C₂×C₈	—	2	2	no	—
103	C₂×C₈	—	38	2	no	—
104	C₂×C₈	—	76	2	no	—
105	C₄⋊C₄	—	19	2	no	—
106	C₄⋊C₄	—	38	2	no	—
107	C₄⋊C₄	—	38	2	no	—
108	C₄⋊C₄	—	38	1	no	—
109	C₄⋊C₄	—	38	1	no	—
110	C₄⋊C₄	—	38	1	no	—
111	C₂²⋊C₄	—	38	2	no	—
112	C₄²	—	38	2	no	—
113	C₄²	C₄×D₁₉	1	1	yes	characteristic
114	C₄²	D₇₆	1	1	yes	characteristic
115	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
116	C₄²	C₂²×D₁₉	1	1	yes	characteristic
117	C₂³	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
118	Q₈	—	76	2	no	—
119	Q₈	—	76	2	no	—
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	4	1	no	—
122	C₂×C₄	—	38	2	no	—
123	C₂×C₄	—	38	2	no	—
124	C₂×C₄	#64516	1	2	yes	—
125	C₂×C₄	Dic₇₆	1	2	yes	—
126	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
127	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
128	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
129	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
130	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
131	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
132	C₈	—	4	2	no	—
133	C₈	—	76	2	no	—
134	C₂²	—	2	1	no	—
135	C₂²	—	2	1	no	—
136	C₂²	#10597273	1	2	yes	—
137	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
138	C₄	—	2	1	no	—
139	C₄	—	2	1	no	—
140	C₄	—	2	1	no	—
141	C₄	—	76	2	no	—
142	C₄	—	76	2	no	—
143	C₄	#10597273	1	2	yes	—
144	C₄	C₂×#64516	1	1	yes	characteristic
145	C₄	C₂×Dic₇₆	1	1	yes	characteristic
146	C₄	#10597396	1	2	yes	—
147	C₂	—	2	2	no	—
148	C₂	#11926526	1	1	yes	characteristic
149	C₂	C₂×#10597273	1	1	yes	characteristic
150	C₂	#11926538	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927101

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂

yes

maximal, characteristic

#11926292

C₂

yes

maximal, complemented

#11926291

C₂

yes

maximal, complemented

C₁₉×#431

C₂

yes

maximal, characteristic

C₂×C₄²×C₁₉

C₂²

yes

—

—

C₄

yes

—

C₂²×C₁₉⋊C₈

—

#10597316

—

#10597315

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

C₄

yes

—

C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂×C₄

yes

—

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

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²⋊C₄

yes

characteristic

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

SD₁₆

yes

—

C₂×C₄×C₁₉

Q₁₆

yes

—

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

—

#1542

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#103

yes

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#103

yes

—

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₄×C₁₉

C₂×Q₁₆

yes

characteristic

C₄×C₁₉

#135

yes

—

Dic₁₉

—

Dic₁₉

—

#533

—

#431

D₁₉

yes

characteristic

C₂×C₄⋊C₈

—

#333

—

#332

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

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

—

C₄×C₈

—

C₁₉

#1542

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

C₄×D₁₉

yes

characteristic

100

C₂²×C₄

D₇₆

yes

characteristic

101

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₂²⋊C₄

—

112

C₄²

—

113

C₄²

C₄×D₁₉

yes

characteristic

114

C₄²

D₇₆

yes

characteristic

115

C₄²

C₂²⋊D₁₉

yes

characteristic

116

C₄²

C₂²×D₁₉

yes

characteristic

117

C₂³

(C₂×D₁₉)⋊C₄

yes

characteristic

118

Q₈

—

119

Q₈

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

#64516

yes

—

125

C₂×C₄

Dic₇₆

yes

—

126

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

127

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

128

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

129

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

130

C₂×C₄

C₂×D₇₆

yes

characteristic

131

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

132

C₈

—

133

C₈

—

134

C₂²

—

135

C₂²

—

136

C₂²

#10597273

yes

—

137

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

#10597273

yes

—

144

C₄

C₂×#64516

yes

characteristic

145

C₄

C₂×Dic₇₆

yes

characteristic

146

C₄

#10597396

yes

—

147

C₂

—

148

C₂

#11926526

yes

characteristic

149

C₂

C₂×#10597273

yes

characteristic

150

C₂

#11926538

yes

characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₁₉)⋊C₄
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#431	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×C₁₉	C₂²⋊C₄
cosocle	C₄²×C₁₉	C₂³
hypercenter	#431	D₁₉
hypocenter	C₁₉	#1542
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

subgroup

G/H

center

C₂×C₄

(C₂×D₁₉)⋊C₄

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#431

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂³×C₁₉

C₂²⋊C₄

cosocle

C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

N	H ≅ G/N	type
3. #11926292	C₂	semidirect
4. #11926291	C₂	semidirect
96. C₁₉	#1542	semidirect

H ≅ G/N

type

3. #11926292

C₂

semidirect

4. #11926291

C₂

semidirect

96. C₁₉

#1542

semidirect

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

subgroup	index
#11927101	2
C₂×C₄⋊(C₁₉⋊C₈)	2
#11926292	2
#11926291	2
C₁₉×#431	2
#1542	19

subgroup

index

C₂×C₄⋊(C₁₉⋊C₈)

C₁₉×#431

Subgroups — #14562290

Conjugacy classes of subgroups

Complements

Maximal subgroups