Group #19135751 — subgroups

Subgroups — #19135751

Order 5504.

282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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	#14583530	C₂	1	1	yes	maximal, characteristic, complemented
2	#14582904	C₂	1	2	yes	maximal
3	#14582668	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582659	C₂	1	2	yes	maximal, complemented
5	C₄₃×#390	C₂	1	1	yes	maximal, characteristic
6	C₂×#10621877	C₂²	1	2	yes	—
7	#13063324	—	2	2	no	—
8	#13063316	—	2	2	no	—
9	#13063304	—	2	2	no	—
10	#13063284	C₂²	1	2	yes	—
11	#13063246	—	2	2	no	—
12	#13063246	—	2	2	no	—
13	C₂²×D₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
16	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄₃	—	2	1	no	—
18	C₂×D₄×C₄₃	—	2	1	no	—
19	C₂×D₄×C₄₃	—	2	2	no	—
20	C₂×D₄×C₄₃	—	2	2	no	—
21	C₂×D₄×C₄₃	Q₈	1	2	yes	complemented
22	C₂²×C₄×C₄₃	—	2	1	no	—
23	C₂²×C₄×C₄₃	D₄	1	2	yes	—
24	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
25	C₂×Dic₈₆	—	2	2	no	—
26	C₄⋊C₄×C₄₃	—	2	2	no	—
27	C₂²⋊C₄×C₄₃	—	4	4	no	—
28	C₄²×C₄₃	—	2	2	no	—
29	C₂²⋊Dic₄₃	—	2	2	no	—
30	C₄⋊Dic₄₃	—	2	2	no	—
31	C₄⋊Dic₄₃	D₄	1	2	yes	—
32	C₄⋊Dic₄₃	D₄	1	2	yes	—
33	Dic₄₃⋊C₄	—	2	4	no	—
34	C₄×Dic₄₃	—	2	2	no	—
35	#10621877	—	2	2	no	—
36	#10621877	—	2	2	no	—
37	C₂×C₄₃⋊C₈	—	2	2	no	—
38	C₂³×C₄₃	—	2	2	no	—
39	C₂³×C₄₃	—	4	2	no	—
40	C₂³×C₄₃	—	4	2	no	—
41	C₂³×C₄₃	—	4	1	no	—
42	C₂³×C₄₃	—	4	1	no	—
43	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
44	D₄×C₄₃	—	2	4	no	—
45	D₄×C₄₃	—	4	2	no	—
46	C₂×C₄×C₄₃	—	2	2	no	—
47	C₂×C₄×C₄₃	—	2	2	no	—
48	C₂×C₄×C₄₃	—	4	1	no	—
49	C₂×C₄×C₄₃	—	4	1	no	—
50	C₂×C₄×C₄₃	—	4	2	no	—
51	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
52	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
53	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
54	C₂×C₄×C₄₃	#41	1	2	yes	—
55	C₂×Dic₄₃	—	2	2	no	—
56	C₂×Dic₄₃	—	2	2	no	—
57	Dic₈₆	—	8	2	no	—
58	C₄₃⋊C₈	—	4	2	no	—
59	C₂²×C₄₃	—	2	1	no	—
60	C₂²×C₄₃	—	2	1	no	—
61	C₂²×C₄₃	—	4	4	no	—
62	C₂²×C₄₃	—	4	2	no	—
63	C₂²×C₄₃	—	8	2	no	—
64	C₂²×C₄₃	—	8	1	no	—
65	C₂²×C₄₃	—	8	1	no	—
66	C₂²×C₄₃	#120	1	1	yes	characteristic
67	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
68	C₂²×C₄₃	#124	1	1	yes	characteristic
69	C₄×C₄₃	—	4	2	no	—
70	C₄×C₄₃	—	4	2	no	—
71	C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
72	C₄×C₄₃	#124	1	2	yes	—
73	Dic₄₃	—	4	2	no	—
74	Dic₄₃	—	4	2	no	—
75	#2027	—	43	1	no	maximal, Sylow
76	C₂×C₄₃	—	2	1	no	—
77	C₂×C₄₃	—	2	1	no	—
78	C₂×C₄₃	—	8	2	no	—
79	C₂×C₄₃	#393	1	1	yes	characteristic
80	C₂×C₄₃	#453	1	1	yes	characteristic
81	C₂×C₄₃	#454	1	1	yes	characteristic
82	#544	—	43	1	no	—
83	#418	—	43	2	no	—
84	#390	D₄₃	1	1	yes	characteristic
85	#343	—	43	1	no	—
86	#339	—	43	2	no	—
87	C₄₃	#2027	1	1	yes	characteristic, complemented, Sylow
88	C₂²×D₄	C₂×D₄₃	1	1	yes	characteristic
89	C₂×M₁₆	—	43	2	no	—
90	C₄⋊Q₈	—	86	2	no	—
91	#125	—	86	2	no	—
92	C₂²⋊Q₈	—	86	2	no	—
93	#117	—	43	2	no	—
94	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
95	C₂×C₂²⋊C₄	—	2	2	no	—
96	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
97	#102	—	86	2	no	—
98	#102	—	86	2	no	—
99	C₂⁴	—	2	1	no	—
100	C₂×Q₈	—	86	2	no	—
101	C₂×D₄	—	2	1	no	—
102	C₂×D₄	—	2	2	no	—
103	C₂×D₄	—	2	2	no	—
104	C₂×D₄	Dic₈₆	1	2	yes	complemented
105	C₂²×C₄	—	2	1	no	—
106	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
107	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
108	M₁₆	—	86	2	no	—
109	M₁₆	—	86	2	no	—
110	C₂×C₈	—	86	2	no	—
111	C₄⋊C₄	—	2	2	no	—
112	C₄⋊C₄	—	43	2	no	—
113	C₄⋊C₄	—	43	2	no	—
114	C₄⋊C₄	—	86	2	no	—
115	C₄⋊C₄	—	86	4	no	—
116	C₂²⋊C₄	—	4	4	no	—
117	C₂²⋊C₄	—	86	2	no	—
118	C₄²	—	2	2	no	—
119	C₄²	—	86	2	no	—
120	C₂³	—	2	2	no	—
121	C₂³	—	4	2	no	—
122	C₂³	—	4	2	no	—
123	C₂³	—	4	1	no	—
124	C₂³	—	4	1	no	—
125	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
126	Q₈	—	344	2	no	—
127	D₄	—	2	4	no	—
128	D₄	—	4	2	no	—
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	2	2	no	—
131	C₂×C₄	—	4	1	no	—
132	C₂×C₄	—	4	1	no	—
133	C₂×C₄	—	4	2	no	—
134	C₂×C₄	—	86	2	no	—
135	C₂×C₄	—	86	2	no	—
136	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
137	C₂×C₄	#10621898	1	1	yes	characteristic
138	C₂×C₄	D₄×D₄₃	1	2	yes	—
139	C₂×C₄	#10621900	1	2	yes	—
140	C₈	—	172	2	no	—
141	C₂²	—	2	1	no	—
142	C₂²	—	2	1	no	—
143	C₂²	—	4	4	no	—
144	C₂²	—	4	2	no	—
145	C₂²	—	8	2	no	—
146	C₂²	—	8	1	no	—
147	C₂²	—	8	1	no	—
148	C₂²	#13063293	1	1	yes	characteristic
149	C₂²	#13063304	1	1	yes	characteristic
150	C₂²	#13063312	1	1	yes	characteristic
151	C₄	—	4	2	no	—
152	C₄	—	4	2	no	—
153	C₄	—	172	2	no	—
154	C₄	—	172	2	no	—
155	C₄	#13063302	1	2	yes	—
156	C₄	#13063311	1	2	yes	—
157	C₂	—	2	1	no	—
158	C₂	—	2	1	no	—
159	C₂	—	8	2	no	—
160	C₂	#14582811	1	1	yes	characteristic
161	C₂	#14583066	1	1	yes	characteristic
162	C₂	#14583071	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583530

C₂

yes

maximal, characteristic, complemented

#14582904

C₂

yes

maximal

#14582668

C₂

yes

maximal, characteristic, complemented

#14582659

C₂

yes

maximal, complemented

C₄₃×#390

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

—

—

—

—

C₂²

yes

—

#13063246

—

#13063246

—

C₂²×D₄×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₃

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂⁴×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

Q₈

yes

complemented

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂×Dic₈₆

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

—

C₄⋊Dic₄₃

D₄

yes

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#120

yes

characteristic

C₂²×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₄₃

#124

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊Q₈

yes

—

C₄×C₄₃

#124

yes

—

Dic₄₃

—

Dic₄₃

—

#2027

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

D₄₃

yes

characteristic

#343

—

#339

—

C₄₃

#2027

yes

characteristic, complemented, Sylow

C₂²×D₄

C₂×D₄₃

yes

characteristic

C₂×M₁₆

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

#117

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#102

—

#102

—

C₂⁴

—

100

C₂×Q₈

—

101

C₂×D₄

—

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂×D₄

Dic₈₆

yes

complemented

105

C₂²×C₄

—

106

C₂²×C₄

C₂²⋊D₄₃

yes

—

107

C₂²×C₄

C₂²×D₄₃

yes

characteristic

108

M₁₆

—

109

M₁₆

—

110

C₂×C₈

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₂²⋊C₄

—

117

C₂²⋊C₄

—

118

C₄²

—

119

C₄²

—

120

C₂³

—

121

C₂³

—

122

C₂³

—

123

C₂³

—

124

C₂³

—

125

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

126

Q₈

—

344

—

127

D₄

—

128

D₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

C₂×Dic₈₆

yes

characteristic

137

C₂×C₄

#10621898

yes

characteristic

138

C₂×C₄

D₄×D₄₃

yes

—

139

C₂×C₄

#10621900

yes

—

140

C₈

—

172

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

#13063293

yes

characteristic

149

C₂²

#13063304

yes

characteristic

150

C₂²

#13063312

yes

characteristic

151

C₄

—

152

C₄

—

153

C₄

—

172

—

154

C₄

—

172

—

155

C₄

#13063302

yes

—

156

C₄

#13063311

yes

—

157

C₂

—

158

C₂

—

159

C₂

—

160

C₂

#14582811

yes

characteristic

161

C₂

#14583066

yes

characteristic

162

C₂

#14583071

yes

characteristic

	subgroup	G/H
center	C₂²	#13063293
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#390	C₂
socle	C₂²×C₄₃	#120
hypercenter	#390	D₄₃
hypocenter	C₄₃	#2027
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #390

subgroup

G/H

center

C₂²

#13063293

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#390

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #390

N	H ≅ G/N	type
1. #14583530	C₂	semidirect
3. #14582668	C₂	semidirect
4. #14582659	C₂	semidirect
21. C₂×D₄×C₄₃	Q₈	semidirect
87. C₄₃	#2027	semidirect
104. C₂×D₄	Dic₈₆	semidirect

H ≅ G/N

type

1. #14583530

C₂

semidirect

3. #14582668

C₂

semidirect

4. #14582659

C₂

semidirect

21. C₂×D₄×C₄₃

Q₈

semidirect

87. C₄₃

#2027

semidirect

104. C₂×D₄

Dic₈₆

semidirect

Subgroups — #19135751

Conjugacy classes of subgroups

Complements