Group #14565347 — subgroups

Subgroups — #14565347

Order 2432.

232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 93 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×#10597269	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597275	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926348	C₂	1	2	yes	maximal, complemented
4	#11926345	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#135	C₂	1	1	yes	maximal, characteristic
6	C₂×#41×C₁₉	—	2	1	no	—
7	C₁₉×#135	—	2	2	no	—
8	C₁₉×#135	C₄	1	4	yes	complemented
9	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×SD₁₆×C₁₉	—	2	1	no	—
11	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	—	2	1	no	—
14	#10597275	—	2	1	no	—
15	#10597275	C₂²	1	2	yes	—
16	#10597269	—	2	2	no	—
17	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
18	#41×C₁₉	—	2	4	no	—
19	#41×C₁₉	—	4	2	no	—
20	C₂×Q₈×C₁₉	—	2	1	no	—
21	C₂×D₄×C₁₉	—	2	1	no	—
22	C₂×D₄×C₁₉	—	4	1	no	—
23	C₂²×C₄×C₁₉	—	4	1	no	—
24	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×Dic₁₉	—	4	1	no	—
26	Q₁₆×C₁₉	—	2	1	no	—
27	Q₁₆×C₁₉	C₂×C₄	1	2	yes	complemented
28	SD₁₆×C₁₉	—	2	4	no	—
29	D₈×C₁₉	—	2	1	no	—
30	D₈×C₁₉	C₂×C₄	1	2	yes	complemented
31	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
32	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
33	C₂×C₈×C₁₉	D₄	1	2	yes	—
34	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
35	C₄⋊Dic₁₉	—	2	2	no	—
36	C₄⋊Dic₁₉	—	4	1	no	—
37	C₁₉⋊C₁₆	—	2	2	no	—
38	C₂³×C₁₉	—	4	1	no	—
39	C₂³×C₁₉	D₈	1	1	yes	characteristic
40	Q₈×C₁₉	—	2	2	no	—
41	Q₈×C₁₉	—	4	1	no	—
42	D₄×C₁₉	—	2	2	no	—
43	D₄×C₁₉	—	4	4	no	—
44	D₄×C₁₉	—	4	1	no	—
45	C₂×C₄×C₁₉	—	4	1	no	—
46	C₂×C₄×C₁₉	—	4	4	no	—
47	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
48	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
49	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
50	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×Dic₁₉	—	4	2	no	—
52	C₂×Dic₁₉	—	8	2	no	—
53	C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
54	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
55	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
56	#2139	—	19	1	no	maximal, Sylow
57	C₂²×C₁₉	—	2	1	no	—
58	C₂²×C₁₉	—	2	1	no	—
59	C₂²×C₁₉	—	4	2	no	—
60	C₂²×C₁₉	—	8	1	no	—
61	C₂²×C₁₉	—	8	1	no	—
62	C₂²×C₁₉	#102	1	2	yes	—
63	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
64	C₄×C₁₉	—	4	2	no	—
65	C₄×C₁₉	#102	1	2	yes	—
66	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
68	Dic₁₉	—	8	2	no	—
69	C₂×#135	D₁₉	1	1	yes	characteristic
70	C₂×M₃₂	—	19	1	no	—
71	C₂×#107	—	19	1	no	—
72	#358	—	19	2	no	—
73	#357	—	19	2	no	—
74	C₂×C₁₉	—	2	2	no	—
75	C₂×C₁₉	—	8	2	no	—
76	C₂×C₁₉	C₂×#102	1	1	yes	characteristic
77	C₂×C₁₉	#509	1	1	yes	characteristic
78	C₂×C₁₉	#510	1	1	yes	characteristic
79	C₂×#41	—	2	1	no	—
80	#135	—	2	2	no	—
81	#135	Dic₁₉	1	4	yes	complemented
82	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic
83	C₂×SD₁₆	—	2	1	no	—
84	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
85	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
86	C₂×C₄⋊C₄	—	38	1	no	—
87	M₃₂	—	38	2	no	—
88	C₂×C₁₆	—	19	2	no	—
89	#107	—	19	2	no	—
90	#107	—	38	1	no	—
91	C₁₉	#2139	1	1	yes	characteristic, complemented, Sylow
92	#41	—	2	4	no	—
93	#41	—	4	2	no	—
94	C₂×Q₈	—	2	1	no	—
95	C₂×D₄	—	2	1	no	—
96	C₂×D₄	—	4	1	no	—
97	C₂²×C₄	—	4	1	no	—
98	C₂²×C₄	—	76	1	no	—
99	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
100	Q₁₆	—	2	1	no	—
101	Q₁₆	C₂×Dic₁₉	1	2	yes	complemented
102	SD₁₆	—	2	4	no	—
103	D₈	—	2	1	no	—
104	D₈	C₂×Dic₁₉	1	2	yes	complemented
105	C₂×C₈	C₂×Dic₁₉	1	2	yes	—
106	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
107	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
108	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
109	C₄⋊C₄	—	38	2	no	—
110	C₄⋊C₄	—	76	1	no	—
111	C₁₆	—	38	2	no	—
112	C₂³	—	4	1	no	—
113	C₂³	#64525	1	1	yes	characteristic
114	Q₈	—	2	2	no	—
115	Q₈	—	4	1	no	—
116	D₄	—	2	2	no	—
117	D₄	—	4	4	no	—
118	D₄	—	4	1	no	—
119	C₂×C₄	—	4	1	no	—
120	C₂×C₄	—	4	4	no	—
121	C₂×C₄	—	76	2	no	—
122	C₂×C₄	—	152	2	no	—
123	C₂×C₄	#64525	1	1	yes	characteristic
124	C₂×C₄	#64526	1	2	yes	—
125	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
126	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
127	C₈	C₂²⋊Dic₁₉	1	2	yes	—
128	C₈	C₂²×Dic₁₉	1	1	yes	characteristic
129	C₈	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
130	C₂²	—	2	1	no	—
131	C₂²	—	2	1	no	—
132	C₂²	—	4	2	no	—
133	C₂²	—	8	1	no	—
134	C₂²	—	8	1	no	—
135	C₂²	#10597289	1	2	yes	—
136	C₂²	C₂×#64525	1	1	yes	characteristic
137	C₄	—	4	2	no	—
138	C₄	—	152	2	no	—
139	C₄	#10597289	1	2	yes	—
140	C₄	C₂×#64526	1	1	yes	characteristic
141	C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
142	C₂	—	2	2	no	—
143	C₂	—	8	2	no	—
144	C₂	C₂×#10597289	1	1	yes	characteristic
145	C₂	#11926979	1	1	yes	characteristic
146	C₂	#11926984	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597269

C₂

yes

maximal, characteristic, complemented

C₂×#10597275

C₂

yes

maximal, characteristic, complemented

#11926348

C₂

yes

maximal, complemented

#11926345

C₂

yes

maximal, complemented

C₂×C₁₉×#135

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

—

C₁₉×#135

—

C₁₉×#135

C₄

yes

complemented

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

—

#10597275

—

#10597275

C₂²

yes

—

#10597269

—

C₂×C₁₉⋊C₁₆

C₂²

yes

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×Dic₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

C₂×C₄

yes

complemented

SD₁₆×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

C₂×C₄

yes

complemented

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

—

C₂³×C₁₉

D₈

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

C₂²⋊C₄

yes

—

C₈×C₁₉

C₂²×C₄

yes

characteristic

C₈×C₁₉

C₂×D₄

yes

characteristic

#2139

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#102

yes

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

#102

yes

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

Dic₁₉

—

C₂×#135

D₁₉

yes

characteristic

C₂×M₃₂

—

C₂×#107

—

#358

—

#357

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×#41

—

#135

—

#135

Dic₁₉

yes

complemented

C₂×Q₁₆

C₂×D₁₉

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

C₂×D₁₉

yes

characteristic

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

M₃₂

—

C₂×C₁₆

—

#107

—

#107

—

C₁₉

#2139

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

100

Q₁₆

—

101

Q₁₆

C₂×Dic₁₉

yes

complemented

102

SD₁₆

—

103

D₈

—

104

D₈

C₂×Dic₁₉

yes

complemented

105

C₂×C₈

C₂×Dic₁₉

yes

—

106

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

107

C₂×C₈

C₂²⋊D₁₉

yes

—

108

C₂×C₈

C₂²×D₁₉

yes

characteristic

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₁₆

—

112

C₂³

—

113

C₂³

#64525

yes

characteristic

114

Q₈

—

115

Q₈

—

116

D₄

—

117

D₄

—

118

D₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

152

—

123

C₂×C₄

#64525

yes

characteristic

124

C₂×C₄

#64526

yes

—

125

C₂×C₄

C₂²⋊Dic₁₉

yes

—

126

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

127

C₈

C₂²⋊Dic₁₉

yes

—

128

C₈

C₂²×Dic₁₉

yes

characteristic

129

C₈

C₂×C₂²⋊D₁₉

yes

characteristic

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

#10597289

yes

—

136

C₂²

C₂×#64525

yes

characteristic

137

C₄

—

138

C₄

—

152

—

139

C₄

#10597289

yes

—

140

C₄

C₂×#64526

yes

characteristic

141

C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

142

C₂

—

143

C₂

—

144

C₂

C₂×#10597289

yes

characteristic

145

C₂

#11926979

yes

characteristic

146

C₂

#11926984

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#64525
commutator	C₈×C₁₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₉
Fitting, prime radical	C₂×C₁₉×#135	C₂
socle	C₂²×C₁₉	C₂×D₈
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	C₂×#135	D₁₉
hypocenter	C₁₉	#2139
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#135

subgroup

G/H

center

C₂²

C₂×#64525

commutator

C₈×C₁₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₁₉

Fitting, prime radical

C₂×C₁₉×#135

C₂

socle

C₂²×C₁₉

C₂×D₈

cosocle

C₂×C₈×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#135

N	H ≅ G/N	type
1. C₂×#10597269	C₂	semidirect
2. C₂×#10597275	C₂	semidirect
3. #11926348	C₂	semidirect
4. #11926345	C₂	semidirect
8. C₁₉×#135	C₄	semidirect
27. Q₁₆×C₁₉	C₂×C₄	semidirect
30. D₈×C₁₉	C₂×C₄	semidirect
81. #135	Dic₁₉	semidirect
91. C₁₉	#2139	semidirect
101. Q₁₆	C₂×Dic₁₉	semidirect
104. D₈	C₂×Dic₁₉	semidirect

H ≅ G/N

type

1. C₂×#10597269

C₂

semidirect

2. C₂×#10597275

C₂

semidirect

3. #11926348

C₂

semidirect

4. #11926345

C₂

semidirect

8. C₁₉×#135

C₄

semidirect

27. Q₁₆×C₁₉

C₂×C₄

semidirect

30. D₈×C₁₉

C₂×C₄

semidirect

81. #135

Dic₁₉

semidirect

91. C₁₉

#2139

semidirect

101. Q₁₆

C₂×Dic₁₉

semidirect

104. D₈

C₂×Dic₁₉

semidirect

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

subgroup	index
C₂×#10597269	2
C₂×#10597275	2
#11926348	2
#11926345	2
C₂×C₁₉×#135	2
#2139	19

subgroup

index

C₂×C₁₉×#135

Subgroups — #14565347

Conjugacy classes of subgroups

Complements

Maximal subgroups