Group #14574219 — subgroups

Subgroups — #14574219

Order 2432.

368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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	#11927099	C₂	1	2	yes	maximal
2	#11926949	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926894	C₂	1	2	yes	maximal, complemented
4	#11926782	C₂	1	4	yes	maximal
5	Q₁₆×Dic₁₉	C₂	1	4	yes	maximal, complemented
6	C₄×C₈×D₁₉	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#494	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₁₆×C₁₉	C₂²	1	4	yes	—
9	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
10	#10597392	C₂²	1	4	yes	—
11	Q₈×Dic₁₉	C₂²	1	4	yes	—
12	C₂×C₈×D₁₉	C₂²	1	2	yes	—
13	#10597343	—	2	2	no	—
14	#10597338	—	2	2	no	—
15	#10597336	—	2	2	no	—
16	#10597333	—	2	2	no	—
17	C₄²×D₁₉	C₂²	1	1	yes	characteristic
18	#10597315	C₂²	1	2	yes	—
19	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	#10597292	C₂²	1	8	yes	—
21	#10597275	C₂²	1	4	yes	—
22	C₈×Dic₁₉	C₂²	1	2	yes	—
23	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×Q₈×C₁₉	C₂³	1	4	yes	—
25	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
28	C₂×Dic₃₈	—	2	2	no	—
29	Q₁₆×C₁₉	—	2	8	no	—
30	C₂×C₈×C₁₉	C₂³	1	2	yes	—
31	C₄⋊C₄×C₁₉	—	2	2	no	—
32	C₄⋊C₄×C₁₉	—	2	2	no	—
33	C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	(C₂×D₁₉)⋊C₄	—	2	4	no	—
35	C₄⋊Dic₁₉	—	2	2	no	—
36	C₄⋊Dic₁₉	—	2	4	no	—
37	C₄⋊Dic₁₉	C₂³	1	4	yes	—
38	Dic₁₉⋊C₄	—	2	4	no	—
39	C₄×Dic₁₉	—	2	4	no	—
40	C₄×Dic₁₉	D₄	1	1	yes	characteristic
41	C₄×Dic₁₉	D₄	1	1	yes	characteristic
42	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
43	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
44	C₈×D₁₉	—	2	4	no	—
45	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
46	Q₈×C₁₉	—	2	8	no	—
47	C₂×C₄×C₁₉	—	2	4	no	—
48	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
51	C₂×Dic₁₉	—	2	4	no	—
52	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
55	C₄×D₁₉	—	2	2	no	—
56	C₄×D₁₉	—	2	2	no	—
57	C₄×D₁₉	Q₁₆	1	4	yes	complemented
58	Dic₃₈	—	4	4	no	—
59	C₈×C₁₉	#41	1	4	yes	—
60	C₁₉⋊C₈	—	2	2	no	—
61	#3170	—	19	1	no	maximal, Sylow
62	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
63	C₂×D₁₉	—	2	1	no	—
64	C₂×D₁₉	—	2	1	no	—
65	C₂×D₁₉	C₂×Q₁₆	1	2	yes	—
66	C₄×C₁₉	—	4	4	no	—
67	C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
68	C₄×C₁₉	#135	1	2	yes	—
69	C₄×C₁₉	C₂×#41	1	2	yes	—
70	Dic₁₉	—	2	1	no	—
71	Dic₁₉	—	2	1	no	—
72	Dic₁₉	—	4	4	no	—
73	Dic₁₉	C₂×Q₁₆	1	2	yes	—
74	#533	—	19	2	no	—
75	#500	—	19	1	no	—
76	#494	D₁₉	1	1	yes	characteristic, complemented
77	#487	—	19	2	no	—
78	#467	—	19	4	no	—
79	C₄×Q₁₆	—	19	4	no	—
80	C₂×C₄×C₈	—	19	1	no	—
81	C₂×C₁₉	#532	1	1	yes	characteristic
82	C₂×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
83	C₂×C₁₉	C₂×#135	1	1	yes	characteristic
84	D₁₉	—	2	2	no	—
85	C₂×Q₁₆	C₂×D₁₉	1	4	yes	—
86	C₂²×C₈	—	19	2	no	—
87	C₄⋊Q₈	—	19	2	no	—
88	C₄⋊Q₈	C₂×D₁₉	1	2	yes	—
89	#125	—	38	2	no	—
90	C₂²⋊Q₈	—	19	4	no	—
91	C₂²⋊Q₈	—	38	2	no	—
92	C₄×Q₈	—	19	4	no	—
93	C₄×Q₈	—	38	2	no	—
94	#117	—	38	2	no	—
95	C₂×C₄²	—	19	1	no	—
96	#107	—	19	4	no	—
97	#103	—	19	8	no	—
98	C₄×C₈	—	19	2	no	—
99	C₄×C₈	—	19	1	no	—
100	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
101	C₁₉	#3170	1	1	yes	characteristic, complemented, Sylow
102	C₂×Q₈	—	38	2	no	—
103	C₂×Q₈	C₂²×D₁₉	1	4	yes	—
104	C₂²×C₄	—	19	1	no	—
105	C₂²×C₄	—	19	1	no	—
106	C₂²×C₄	—	19	1	no	—
107	Q₁₆	—	2	8	no	—
108	C₂×C₈	—	19	2	no	—
109	C₂×C₈	—	38	4	no	—
110	C₂×C₈	C₂²×D₁₉	1	2	yes	—
111	C₄⋊C₄	—	2	2	no	—
112	C₄⋊C₄	—	2	2	no	—
113	C₄⋊C₄	—	19	4	no	—
114	C₄⋊C₄	—	38	4	no	—
115	C₄⋊C₄	—	38	4	no	—
116	C₄⋊C₄	—	38	2	no	—
117	C₂²⋊C₄	—	38	4	no	—
118	C₄²	—	19	1	no	—
119	C₄²	—	19	1	no	—
120	C₄²	—	19	1	no	—
121	C₄²	—	38	4	no	—
122	C₄²	C₂²×D₁₉	1	1	yes	characteristic
123	C₂³	—	19	1	no	—
124	Q₈	—	2	8	no	—
125	Q₈	—	76	4	no	—
126	C₂×C₄	—	2	4	no	—
127	C₂×C₄	—	19	1	no	—
128	C₂×C₄	—	19	4	no	—
129	C₂×C₄	—	19	1	no	—
130	C₂×C₄	—	19	1	no	—
131	C₂×C₄	—	38	2	no	—
132	C₂×C₄	—	38	2	no	—
133	C₂×C₄	—	38	4	no	—
134	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
135	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
136	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
137	C₈	—	38	2	no	—
138	C₈	#64543	1	4	yes	—
139	C₂²	—	19	2	no	—
140	C₂²	—	38	1	no	—
141	C₂²	—	38	1	no	—
142	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
143	C₄	—	4	4	no	—
144	C₄	—	19	2	no	—
145	C₄	—	38	1	no	—
146	C₄	—	38	1	no	—
147	C₄	—	76	4	no	—
148	C₄	Q₁₆×D₁₉	1	2	yes	—
149	C₄	#10597365	1	2	yes	—
150	C₄	C₂×#64543	1	2	yes	—
151	C₂	—	38	2	no	—
152	C₂	#11927092	1	1	yes	characteristic
153	C₂	C₂×Q₁₆×D₁₉	1	1	yes	characteristic
154	C₂	C₂×#10597365	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927099

C₂

yes

maximal

#11926949

C₂

yes

maximal, characteristic, complemented

#11926894

C₂

yes

maximal, complemented

#11926782

C₂

yes

maximal

Q₁₆×Dic₁₉

C₂

yes

maximal, complemented

C₄×C₈×D₁₉

C₂

yes

maximal, characteristic

C₁₉×#494

C₂

yes

maximal, characteristic, complemented

C₂×Q₁₆×C₁₉

C₂²

yes

—

C₁₉×C₄⋊Q₈

C₂²

yes

—

#10597392

C₂²

yes

—

Q₈×Dic₁₉

C₂²

yes

—

C₂×C₈×D₁₉

C₂²

yes

—

—

—

—

—

C₄²×D₁₉

C₂²

yes

characteristic

#10597315

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597292

C₂²

yes

—

#10597275

C₂²

yes

—

C₈×Dic₁₉

C₂²

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

C₂³

yes

—

C₂×C₄×D₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

C₂³

yes

characteristic

C₂×Dic₃₈

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

—

C₈×D₁₉

—

C₂²×D₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

Q₁₆

yes

complemented

Dic₃₈

—

C₈×C₁₉

#41

yes

—

C₁₉⋊C₈

—

#3170

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

C₂×Q₁₆

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₂×Q₁₆

yes

—

C₄×C₁₉

#135

yes

—

C₄×C₁₉

C₂×#41

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

C₂×Q₁₆

yes

—

#533

—

#500

—

#494

D₁₉

yes

characteristic, complemented

#487

—

#467

—

C₄×Q₁₆

—

C₂×C₄×C₈

—

C₂×C₁₉

#532

yes

characteristic

C₂×C₁₉

C₂²×Q₁₆

yes

characteristic

C₂×C₁₉

C₂×#135

yes

characteristic

D₁₉

—

C₂×Q₁₆

C₂×D₁₉

yes

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₉

yes

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

#107

—

#103

—

C₄×C₈

—

C₄×C₈

—

100

C₄×C₈

C₂×D₁₉

yes

characteristic

101

C₁₉

#3170

yes

characteristic, complemented, Sylow

102

C₂×Q₈

—

103

C₂×Q₈

C₂²×D₁₉

yes

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

Q₁₆

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

C₂²×D₁₉

yes

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₂²⋊C₄

—

118

C₄²

—

119

C₄²

—

120

C₄²

—

121

C₄²

—

122

C₄²

C₂²×D₁₉

yes

characteristic

123

C₂³

—

124

Q₈

—

125

Q₈

—

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

D₄×D₁₉

yes

characteristic

135

C₂×C₄

D₄×D₁₉

yes

characteristic

136

C₂×C₄

C₂³×D₁₉

yes

characteristic

137

C₈

—

138

C₈

#64543

yes

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

C₂×D₄×D₁₉

yes

characteristic

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

Q₁₆×D₁₉

yes

—

149

C₄

#10597365

yes

—

150

C₄

C₂×#64543

yes

—

151

C₂

—

152

C₂

#11927092

yes

characteristic

153

C₂

C₂×Q₁₆×D₁₉

yes

characteristic

154

C₂

C₂×#10597365

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#494	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂²×D₁₉	C₂×D₄
hypercenter	#494	D₁₉
hypocenter	C₁₉	#3170
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

C₂×D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#494

C₂

socle

C₂²×C₁₉

C₂²×D₄

prime radical

C₂²×D₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
2. #11926949	C₂	semidirect
3. #11926894	C₂	semidirect
5. Q₁₆×Dic₁₉	C₂	semidirect
7. C₁₉×#494	C₂	semidirect
57. C₄×D₁₉	Q₁₆	semidirect
76. #494	D₁₉	semidirect
101. C₁₉	#3170	semidirect

H ≅ G/N

type

2. #11926949

C₂

semidirect

3. #11926894

C₂

semidirect

5. Q₁₆×Dic₁₉

C₂

semidirect

7. C₁₉×#494

C₂

semidirect

57. C₄×D₁₉

Q₁₆

semidirect

76. #494

D₁₉

semidirect

101. C₁₉

#3170

semidirect

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

subgroup	index
#11927099	2
#11926949	2
#11926894	2
#11926782	2
Q₁₆×Dic₁₉	2
C₄×C₈×D₁₉	2
C₁₉×#494	2
#3170	19

subgroup

index

Q₁₆×Dic₁₉

C₄×C₈×D₁₉

C₁₉×#494

#3170

Subgroups — #14574219

Conjugacy classes of subgroups

Complements

Maximal subgroups