Group #14572113 — subgroups

Subgroups — #14572113

Order 2432.

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

normal subgroups only

This group has 756 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×#10597435	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×#10597280	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	#10597435	—	2	4	no	—
8	#10597435	—	2	4	no	—
9	C₂×#64545	C₄	1	2	yes	—
10	C₂×D₄×D₁₉	C₄	1	6	yes	—
11	C₂×#64541	C₂²	1	3	yes	—
12	C₂²×D₇₆	C₂²	1	3	yes	—
13	C₁₉×#131	—	2	4	no	—
14	C₂×M₁₆×C₁₉	C₂²	1	6	yes	complemented
15	#10597394	—	2	4	no	—
16	C₂×#64520	C₂²	1	6	yes	complemented
17	#10597281	C₂²	1	4	yes	complemented
18	#10597280	C₂²	1	12	yes	complemented
19	C₂³×D₁₉	C₂×C₄	1	6	yes	—
20	#41×C₁₉	D₄	1	4	yes	—
21	#41×C₁₉	D₄	1	4	yes	—
22	C₂×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×D₄×C₁₉	C₂×C₄	1	3	yes	—
24	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
25	C₂×C₂²⋊D₁₉	C₂×C₄	1	6	yes	—
26	#64545	—	2	8	no	—
27	D₄×D₁₉	—	2	24	no	—
28	#64541	—	2	6	no	—
29	#64541	—	2	6	no	—
30	C₂×D₇₆	—	2	6	no	—
31	C₂×D₇₆	—	2	6	no	—
32	C₂×D₇₆	C₂×C₄	1	6	yes	—
33	C₂×D₇₆	C₂³	1	3	yes	—
34	C₂×C₄×D₁₉	C₂×C₄	1	6	yes	—
35	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
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	—	2	12	no	—
44	C₂²×D₁₉	—	8	6	no	—
45	C₂²×D₁₉	C₂²×C₄	1	6	yes	—
46	Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
47	D₄×C₁₉	C₂²⋊C₄	1	12	yes	—
48	C₂×C₄×C₁₉	C₂²×C₄	1	3	yes	—
49	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
50	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
51	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
52	C₂²⋊D₁₉	—	2	12	no	—
53	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
54	D₇₆	—	2	12	no	—
55	D₇₆	—	2	3	no	—
56	D₇₆	—	2	3	no	—
57	C₄×D₁₉	—	2	12	no	—
58	Dic₃₈	—	2	1	no	—
59	Dic₃₈	—	2	1	no	—
60	C₈×C₁₉	—	2	4	no	—
61	C₁₉⋊C₈	—	2	4	no	—
62	#2888	—	19	1	no	maximal, Sylow
63	C₂²×C₁₉	—	4	3	no	—
64	C₂²×C₁₉	C₂×C₂²⋊C₄	1	6	yes	—
65	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
66	C₂×D₁₉	—	2	6	no	—
67	C₂×D₁₉	—	4	6	no	—
68	C₂×D₁₉	—	8	12	no	—
69	C₄×C₁₉	C₂×C₂²⋊C₄	1	6	yes	—
70	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
71	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
72	Dic₁₉	—	2	2	no	—
73	C₂×H(5,𝔽₂)	—	19	1	no	—
74	#568	—	19	1	no	—
75	#568	D₁₉	1	1	yes	characteristic, complemented
76	#413	—	19	6	no	—
77	C₂×#100	—	19	6	no	—
78	C₂×C₁₉	—	2	1	no	—
79	C₂×C₁₉	—	2	6	no	—
80	C₂×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
81	D₁₉	—	4	6	no	—
82	H(5,𝔽₂)	—	38	4	no	—
83	H(5,𝔽₂)	—	38	4	no	—
84	C₂×#41	—	19	2	no	—
85	C₂×#41	—	19	3	no	—
86	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
87	C₂²×D₄	—	19	6	no	—
88	C₂²×D₄	—	19	3	no	—
89	#131	—	2	4	no	—
90	#131	—	38	4	no	—
91	C₂×M₁₆	—	19	6	no	—
92	C₂×M₁₆	C₂×D₁₉	1	6	yes	complemented
93	#101	—	19	4	no	—
94	#100	—	19	12	no	—
95	C₁₉	#2888	1	1	yes	characteristic, complemented, Sylow
96	C₂⁴	—	19	6	no	—
97	#41	—	38	8	no	—
98	#41	—	38	6	no	—
99	#41	—	38	6	no	—
100	#41	D₇₆	1	4	yes	—
101	#41	C₂²⋊D₁₉	1	4	yes	—
102	C₂×Q₈	—	19	1	no	—
103	C₂×Q₈	C₄×D₁₉	1	1	yes	characteristic
104	C₂×D₄	—	19	6	no	—
105	C₂×D₄	—	19	6	no	—
106	C₂×D₄	—	19	3	no	—
107	C₂×D₄	—	38	24	no	—
108	C₂×D₄	—	38	6	no	—
109	C₂×D₄	—	38	6	no	—
110	C₂×D₄	C₄×D₁₉	1	3	yes	—
111	C₂²×C₄	—	19	6	no	—
112	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
113	M₁₆	—	2	6	no	—
114	M₁₆	—	19	4	no	—
115	M₁₆	—	38	6	no	—
116	M₁₆	C₂²×D₁₉	1	4	yes	—
117	C₂×C₈	—	2	6	no	—
118	C₂×C₈	—	38	6	no	—
119	C₂³	—	19	6	no	—
120	C₂³	—	38	12	no	—
121	C₂³	—	152	6	no	—
122	C₂³	C₂×C₄×D₁₉	1	3	yes	—
123	Q₈	—	38	1	no	—
124	Q₈	—	38	1	no	—
125	Q₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
126	D₄	—	38	12	no	—
127	D₄	—	38	3	no	—
128	D₄	—	38	3	no	—
129	D₄	—	38	12	no	—
130	D₄	(C₂×D₁₉)⋊C₄	1	12	yes	—
131	C₂×C₄	—	19	2	no	—
132	C₂×C₄	—	38	12	no	—
133	C₂×C₄	C₂×C₄×D₁₉	1	3	yes	—
134	C₂×C₄	C₂×D₇₆	1	6	yes	—
135	C₂×C₄	C₂×C₂²⋊D₁₉	1	6	yes	—
136	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
137	C₈	—	2	4	no	—
138	C₈	—	38	4	no	—
139	C₂²	—	4	3	no	—
140	C₂²	—	38	6	no	—
141	C₂²	—	76	6	no	—
142	C₂²	—	152	12	no	—
143	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	6	yes	—
144	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
145	C₄	—	38	2	no	—
146	C₄	C₂×(C₂×D₁₉)⋊C₄	1	6	yes	—
147	C₄	C₂²×D₇₆	1	1	yes	characteristic
148	C₄	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
149	C₂	—	2	1	no	—
150	C₂	—	2	6	no	—
151	C₂	—	76	6	no	—
152	C₂	C₂²×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597435

C₂

yes

maximal, characteristic

#11927311

C₂

yes

maximal, characteristic, complemented

#11926526

C₂

yes

maximal, complemented

C₂×#10597280

C₂

yes

maximal, complemented

C₁₉×#568

C₂

yes

maximal, characteristic, complemented

C₂×#41×C₁₉

C₂²

yes

—

—

C₄

yes

—

C₂×D₄×D₁₉

C₄

yes

—

C₂×#64541

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

—

C₁₉×#131

—

C₂×M₁₆×C₁₉

C₂²

yes

complemented

#10597394

—

C₂×#64520

C₂²

yes

complemented

#10597281

C₂²

yes

complemented

#10597280

C₂²

yes

complemented

C₂³×D₁₉

C₂×C₄

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

—

#64545

—

D₄×D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂×C₄

yes

—

C₂×D₇₆

C₂³

yes

—

C₂×C₄×D₁₉

C₂×C₄

yes

—

C₂×Dic₃₈

C₂³

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

C₂³

yes

—

C₂×C₈×C₁₉

—

#64520

—

#64520

C₂³

yes

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²×C₄

yes

—

C₂²×D₁₉

—

C₂²×D₁₉

—

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

C₂²×C₄

yes

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2888

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

—

C₂²×C₁₉

C₂³×C₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

—

C₄×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

C₂²×D₄

yes

characteristic

Dic₁₉

—

C₂×H(5,𝔽₂)

—

#568

—

#568

D₁₉

yes

characteristic, complemented

#413

—

C₂×#100

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂²×C₂²⋊C₄

yes

characteristic

D₁₉

—

H(5,𝔽₂)

—

H(5,𝔽₂)

—

C₂×#41

—

C₂×#41

—

C₂×#41

C₂×D₁₉

yes

characteristic

C₂²×D₄

—

C₂²×D₄

—

#131

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

complemented

#101

—

#100

—

C₁₉

#2888

yes

characteristic, complemented, Sylow

C₂⁴

—

#41

—

#41

—

#41

—

100

#41

D₇₆

yes

—

101

#41

C₂²⋊D₁₉

yes

—

102

C₂×Q₈

—

103

C₂×Q₈

C₄×D₁₉

yes

characteristic

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

C₄×D₁₉

yes

—

111

C₂²×C₄

—

112

C₂²×C₄

C₂²×D₁₉

yes

—

113

M₁₆

—

114

M₁₆

—

115

M₁₆

—

116

M₁₆

C₂²×D₁₉

yes

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂³

—

120

C₂³

—

121

C₂³

—

152

—

122

C₂³

C₂×C₄×D₁₉

yes

—

123

Q₈

—

124

Q₈

—

125

Q₈

(C₂×D₁₉)⋊C₄

yes

—

126

D₄

—

127

D₄

—

128

D₄

—

129

D₄

—

130

D₄

(C₂×D₁₉)⋊C₄

yes

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

C₂×C₄×D₁₉

yes

—

134

C₂×C₄

C₂×D₇₆

yes

—

135

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

136

C₂×C₄

C₂³×D₁₉

yes

characteristic

137

C₈

—

138

C₈

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

152

—

143

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

—

144

C₂²

C₂²×C₄×D₁₉

yes

characteristic

145

C₄

—

146

C₄

C₂×(C₂×D₁₉)⋊C₄

yes

—

147

C₄

C₂²×D₇₆

yes

characteristic

148

C₄

C₂²×C₂²⋊D₁₉

yes

characteristic

149

C₂

—

150

C₂

—

151

C₂

—

152

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×#10597435	C₂
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#568	D₁₉
hypocenter	C₁₉	#2888
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×#10597435

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×#10597280	C₂	semidirect
5. C₁₉×#568	C₂	semidirect
14. C₂×M₁₆×C₁₉	C₂²	semidirect
16. C₂×#64520	C₂²	semidirect
17. #10597281	C₂²	semidirect
18. #10597280	C₂²	semidirect
75. #568	D₁₉	semidirect
92. C₂×M₁₆	C₂×D₁₉	semidirect
95. C₁₉	#2888	semidirect

H ≅ G/N

type

2. #11927311

C₂

semidirect

3. #11926526

C₂

semidirect

4. C₂×#10597280

C₂

semidirect

5. C₁₉×#568

C₂

semidirect

14. C₂×M₁₆×C₁₉

C₂²

semidirect

16. C₂×#64520

C₂²

semidirect

17. #10597281

C₂²

semidirect

18. #10597280

C₂²

semidirect

75. #568

D₁₉

semidirect

92. C₂×M₁₆

C₂×D₁₉

semidirect

95. C₁₉

#2888

semidirect

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

subgroup	index
C₂×#10597435	2
#11927311	2
#11926526	2
C₂×#10597280	2
C₁₉×#568	2
#2888	19

subgroup

index

C₁₉×#568

Subgroups — #14572113

Conjugacy classes of subgroups

Complements

Maximal subgroups