Group #14572117 — subgroups

Subgroups — #14572117

Order 2432.

704 conjugacy classes of subgroups; only the 249 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 249 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	C₂×#10597436	C₂	1	1	yes	maximal, characteristic
2	#11927311	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926526	C₂	1	6	yes	maximal, complemented
4	C₂×#10597281	C₂	1	6	yes	maximal, complemented
5	C₁₉×#568	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
7	#10597436	—	2	4	no	—
8	#10597436	—	2	4	no	—
9	C₂×Q₈×D₁₉	C₄	1	2	yes	—
10	C₂×#64543	C₄	1	6	yes	—
11	C₂×#64541	C₂²	1	3	yes	—
12	C₂²×Dic₃₈	C₂²	1	3	yes	—
13	C₁₉×#131	—	2	4	no	—
14	C₂×M₁₆×C₁₉	C₂²	1	6	yes	—
15	#10597394	—	2	4	no	—
16	C₂×#64520	C₂²	1	6	yes	—
17	#10597281	C₂²	1	12	yes	—
18	#10597280	C₂²	1	4	yes	—
19	#41×C₁₉	D₄	1	4	yes	—
20	#41×C₁₉	D₄	1	4	yes	—
21	C₂×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂×D₄×C₁₉	C₂×C₄	1	3	yes	—
23	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
24	C₂×C₂²⋊D₁₉	C₂×C₄	1	6	yes	—
25	C₂²×Dic₁₉	C₂×C₄	1	6	yes	—
26	Q₈×D₁₉	—	2	8	no	—
27	#64543	—	2	24	no	—
28	#64541	—	2	6	no	—
29	#64541	—	2	6	no	—
30	C₂×D₇₆	C₂³	1	1	yes	characteristic
31	C₂×C₄×D₁₉	C₂×C₄	1	6	yes	—
32	C₂×Dic₃₈	—	2	6	no	—
33	C₂×Dic₃₈	—	2	6	no	—
34	C₂×Dic₃₈	C₂×C₄	1	6	yes	—
35	C₂×Dic₃₈	C₂³	1	3	yes	—
36	M₁₆×C₁₉	—	2	6	no	—
37	M₁₆×C₁₉	C₂³	1	4	yes	—
38	C₂×C₈×C₁₉	—	2	6	no	—
39	#64520	—	2	6	no	—
40	#64520	C₂³	1	4	yes	—
41	C₂×C₁₉⋊C₈	—	2	6	no	—
42	C₂³×C₁₉	C₂²×C₄	1	3	yes	—
43	C₂²×D₁₉	C₂²×C₄	1	2	yes	—
44	Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
45	D₄×C₁₉	C₂²⋊C₄	1	12	yes	—
46	C₂×C₄×C₁₉	C₂²×C₄	1	3	yes	—
47	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
48	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
49	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
50	C₂²⋊D₁₉	—	2	12	no	—
51	C₂×Dic₁₉	—	2	12	no	—
52	C₂×Dic₁₉	C₂²×C₄	1	6	yes	—
53	D₇₆	—	2	1	no	—
54	D₇₆	—	2	1	no	—
55	C₄×D₁₉	—	2	12	no	—
56	Dic₃₈	—	2	12	no	—
57	Dic₃₈	—	2	3	no	—
58	Dic₃₈	—	2	3	no	—
59	C₈×C₁₉	—	2	4	no	—
60	C₁₉⋊C₈	—	2	4	no	—
61	#2889	—	19	1	no	maximal, Sylow
62	C₂²×C₁₉	—	4	3	no	—
63	C₂²×C₁₉	C₂×C₂²⋊C₄	1	6	yes	—
64	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
65	C₂×D₁₉	—	2	2	no	—
66	C₂×D₁₉	—	4	2	no	—
67	C₄×C₁₉	C₂×C₂²⋊C₄	1	6	yes	—
68	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
69	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
70	Dic₁₉	—	2	6	no	—
71	C₂×2₋¹⁺⁴	—	19	1	no	—
72	#568	—	19	1	no	—
73	#568	D₁₉	1	1	yes	characteristic, complemented
74	#413	—	19	6	no	—
75	C₂×#101	—	19	6	no	—
76	C₂×C₁₉	—	2	1	no	—
77	C₂×C₁₉	—	2	6	no	—
78	C₂×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
79	D₁₉	—	4	2	no	—
80	2₋¹⁺⁴	—	38	4	no	—
81	2₋¹⁺⁴	—	38	4	no	—
82	C₂×#41	—	19	6	no	—
83	C₂×#41	—	19	3	no	—
84	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
85	C₂²×Q₈	—	19	2	no	—
86	C₂²×Q₈	—	19	3	no	—
87	#131	—	2	4	no	—
88	#131	—	38	4	no	—
89	C₂×M₁₆	—	19	6	no	—
90	C₂×M₁₆	C₂×D₁₉	1	6	yes	—
91	#101	—	19	12	no	—
92	#100	—	19	4	no	—
93	C₁₉	#2889	1	1	yes	characteristic, complemented, Sylow
94	#41	—	38	24	no	—
95	#41	—	38	6	no	—
96	#41	—	38	6	no	—
97	#41	D₇₆	1	4	yes	—
98	#41	C₂²⋊D₁₉	1	4	yes	—
99	C₂×Q₈	—	19	6	no	—
100	C₂×Q₈	—	19	3	no	—
101	C₂×Q₈	—	38	8	no	—
102	C₂×Q₈	—	38	6	no	—
103	C₂×Q₈	—	38	6	no	—
104	C₂×Q₈	C₄×D₁₉	1	1	yes	characteristic
105	C₂×D₄	—	19	6	no	—
106	C₂×D₄	—	19	1	no	—
107	C₂×D₄	C₄×D₁₉	1	3	yes	—
108	C₂²×C₄	—	19	6	no	—
109	C₂²×C₄	—	19	6	no	—
110	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
111	M₁₆	—	2	6	no	—
112	M₁₆	—	19	4	no	—
113	M₁₆	—	38	6	no	—
114	M₁₆	C₂²×D₁₉	1	4	yes	—
115	C₂×C₈	—	2	6	no	—
116	C₂×C₈	—	38	6	no	—
117	C₂³	—	19	2	no	—
118	C₂³	C₂×C₄×D₁₉	1	3	yes	—
119	Q₈	—	38	3	no	—
120	Q₈	—	38	3	no	—
121	Q₈	—	38	12	no	—
122	Q₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
123	D₄	—	38	12	no	—
124	D₄	—	38	1	no	—
125	D₄	—	38	1	no	—
126	D₄	(C₂×D₁₉)⋊C₄	1	12	yes	—
127	C₂×C₄	—	19	6	no	—
128	C₂×C₄	—	38	12	no	—
129	C₂×C₄	—	38	12	no	—
130	C₂×C₄	C₂×C₄×D₁₉	1	3	yes	—
131	C₂×C₄	C₂×D₇₆	1	6	yes	—
132	C₂×C₄	C₂×C₂²⋊D₁₉	1	6	yes	—
133	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
134	C₈	—	2	4	no	—
135	C₈	—	38	4	no	—
136	C₂²	—	4	3	no	—
137	C₂²	—	38	2	no	—
138	C₂²	—	76	2	no	—
139	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	6	yes	—
140	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
141	C₄	—	38	6	no	—
142	C₄	C₂×(C₂×D₁₉)⋊C₄	1	6	yes	—
143	C₄	C₂²×D₇₆	1	1	yes	characteristic
144	C₄	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
145	C₂	—	2	1	no	—
146	C₂	—	2	6	no	—
147	C₂	—	76	2	no	—
148	C₂	C₂²×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597436

C₂

yes

maximal, characteristic

#11927311

C₂

yes

maximal, characteristic, complemented

#11926526

C₂

yes

maximal, complemented

C₂×#10597281

C₂

yes

maximal, complemented

C₁₉×#568

C₂

yes

maximal, characteristic, complemented

C₂×#41×C₁₉

C₂²

yes

characteristic

#10597436

—

#10597436

—

C₂×Q₈×D₁₉

C₄

yes

—

C₂×#64543

C₄

yes

—

C₂×#64541

C₂²

yes

—

C₂²×Dic₃₈

C₂²

yes

—

C₁₉×#131

—

C₂×M₁₆×C₁₉

C₂²

yes

—

#10597394

—

C₂×#64520

C₂²

yes

—

#10597281

C₂²

yes

—

#10597280

C₂²

yes

—

#41×C₁₉

D₄

yes

—

#41×C₁₉

D₄

yes

—

C₂×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂×D₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂×C₂²⋊D₁₉

C₂×C₄

yes

—

C₂²×Dic₁₉

C₂×C₄

yes

—

Q₈×D₁₉

—

#64543

—

#64541

—

#64541

—

C₂×D₇₆

C₂³

yes

characteristic

C₂×C₄×D₁₉

C₂×C₄

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂×C₄

yes

—

C₂×Dic₃₈

C₂³

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

C₂³

yes

—

C₂×C₈×C₁₉

—

#64520

—

#64520

C₂³

yes

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²×C₄

yes

—

C₂²×D₁₉

C₂²×C₄

yes

—

Q₈×C₁₉

C₂²⋊C₄

yes

—

D₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂²×C₄

yes

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2889

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

—

C₂²×C₁₉

C₂³×C₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

—

C₄×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

C₂²×D₄

yes

characteristic

Dic₁₉

—

C₂×2₋¹⁺⁴

—

#568

—

#568

D₁₉

yes

characteristic, complemented

#413

—

C₂×#101

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂²×C₂²⋊C₄

yes

characteristic

D₁₉

—

2₋¹⁺⁴

—

2₋¹⁺⁴

—

C₂×#41

—

C₂×#41

—

C₂×#41

C₂×D₁₉

yes

characteristic

C₂²×Q₈

—

C₂²×Q₈

—

#131

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

#101

—

#100

—

C₁₉

#2889

yes

characteristic, complemented, Sylow

—

—

—

D₇₆

yes

—

#41

C₂²⋊D₁₉

yes

—

C₂×Q₈

—

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

C₄×D₁₉

yes

characteristic

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

C₄×D₁₉

yes

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

C₂²×D₁₉

yes

—

111

M₁₆

—

112

M₁₆

—

113

M₁₆

—

114

M₁₆

C₂²×D₁₉

yes

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂³

—

118

C₂³

C₂×C₄×D₁₉

yes

—

119

Q₈

—

120

Q₈

—

121

Q₈

—

122

Q₈

(C₂×D₁₉)⋊C₄

yes

—

123

D₄

—

124

D₄

—

125

D₄

—

126

D₄

(C₂×D₁₉)⋊C₄

yes

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

C₂×C₄×D₁₉

yes

—

131

C₂×C₄

C₂×D₇₆

yes

—

132

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

133

C₂×C₄

C₂³×D₁₉

yes

characteristic

134

C₈

—

135

C₈

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

—

140

C₂²

C₂²×C₄×D₁₉

yes

characteristic

141

C₄

—

142

C₄

C₂×(C₂×D₁₉)⋊C₄

yes

—

143

C₄

C₂²×D₇₆

yes

characteristic

144

C₄

C₂²×C₂²⋊D₁₉

yes

characteristic

145

C₂

—

146

C₂

—

147

C₂

—

148

C₂

C₂²×(C₂×D₁₉)⋊C₄

yes

characteristic

	subgroup	G/H
center	C₂	C₂²×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₁₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#568	C₂
socle	C₂×C₁₉	C₂²×C₂²⋊C₄
prime radical	C₂×#10597436	C₂
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#568	D₁₉
hypocenter	C₁₉	#2889
LCS	G ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×#41 ◁ #568

subgroup

G/H

center

C₂

C₂²×(C₂×D₁₉)⋊C₄

commutator

C₂²×C₁₉

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#568

C₂

socle

C₂×C₁₉

C₂²×C₂²⋊C₄

prime radical

C₂×#10597436

C₂

cosocle

C₂×C₄×C₁₉

C₂⁴

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×#41 ◁ #568

N	H ≅ G/N	type
2. #11927311	C₂	semidirect
3. #11926526	C₂	semidirect
4. C₂×#10597281	C₂	semidirect
5. C₁₉×#568	C₂	semidirect
73. #568	D₁₉	semidirect
93. C₁₉	#2889	semidirect

H ≅ G/N

type

2. #11927311

C₂

semidirect

3. #11926526

C₂

semidirect

4. C₂×#10597281

C₂

semidirect

5. C₁₉×#568

C₂

semidirect

73. #568

D₁₉

semidirect

93. C₁₉

#2889

semidirect

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

subgroup	index
C₂×#10597436	2
#11927311	2
#11926526	2
C₂×#10597281	2
C₁₉×#568	2
#2889	19

subgroup

index

C₁₉×#568

Subgroups — #14572117

Conjugacy classes of subgroups

Complements

Maximal subgroups