Group #19134630 — subgroups

Subgroups — #19134630

Order 5504.

292 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 97 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	C₂²×C₈×D₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#13063261	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582862	C₂	1	2	yes	maximal
4	#14582663	C₂	1	2	yes	maximal, complemented
5	C₂×#108×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
7	C₂×#10621877	C₂²	1	2	yes	—
8	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₄₃	—	2	2	no	—
10	C₂×C₈×D₄₃	—	2	2	no	—
11	C₂×C₈×D₄₃	C₄	1	4	yes	—
12	#13063261	—	2	2	no	—
13	(C₂×D₄₃)⋊C₈	—	2	4	no	—
14	C₂×M₁₆×C₄₃	C₂²	1	2	yes	—
15	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	#108×C₄₃	—	2	2	no	—
17	C₂³×D₄₃	Q₈	1	1	yes	characteristic
18	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	C₂²×Dic₄₃	Q₈	1	1	yes	characteristic
20	C₂×C₄×D₄₃	—	2	1	no	—
21	C₂×C₄×D₄₃	—	2	1	no	—
22	C₂×C₄×D₄₃	—	2	1	no	—
23	C₂×C₄×D₄₃	—	2	1	no	—
24	C₂×C₄×D₄₃	C₂×C₄	1	2	yes	—
25	C₂×C₄×D₄₃	D₄	1	2	yes	—
26	M₁₆×C₄₃	—	2	2	no	—
27	M₁₆×C₄₃	—	2	2	no	—
28	C₂×C₈×C₄₃	—	2	2	no	—
29	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
30	C₂×C₈×C₄₃	D₄	1	2	yes	—
31	C₂×C₈×C₄₃	D₄	1	2	yes	—
32	#10621877	—	2	2	no	—
33	#10621877	—	2	2	no	—
34	C₂×C₄₃⋊C₈	—	2	1	no	—
35	C₂×C₄₃⋊C₈	—	2	1	no	—
36	C₂×C₄₃⋊C₈	—	2	2	no	—
37	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
38	C₈×D₄₃	—	2	8	no	—
39	C₂³×C₄₃	C₂×Q₈	1	1	yes	characteristic
40	C₂²×D₄₃	—	2	1	no	—
41	C₂²×D₄₃	—	2	1	no	—
42	C₂²×D₄₃	—	2	4	no	—
43	C₂²×D₄₃	C₄⋊C₄	1	2	yes	—
44	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
49	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
50	C₂×Dic₄₃	—	2	1	no	—
51	C₂×Dic₄₃	—	2	1	no	—
52	C₂×Dic₄₃	C₄⋊C₄	1	2	yes	—
53	C₄×D₄₃	—	2	2	no	—
54	C₄×D₄₃	—	2	2	no	—
55	C₄×D₄₃	—	2	2	no	—
56	C₄×D₄₃	—	2	2	no	—
57	C₈×C₄₃	—	4	2	no	—
58	C₈×C₄₃	C₂²⋊C₄	1	4	yes	—
59	C₄₃⋊C₈	—	2	2	no	—
60	C₄₃⋊C₈	—	4	2	no	—
61	C₂²×C₄₃	—	2	2	no	—
62	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
64	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
65	C₂×D₄₃	—	2	4	no	—
66	C₂×D₄₃	—	2	4	no	—
67	C₂×D₄₃	—	2	2	no	—
68	C₂×D₄₃	—	2	2	no	—
69	C₂×D₄₃	#108	1	4	yes	complemented
70	C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₄×C₄₃	#117	1	1	yes	characteristic
72	C₄×C₄₃	#121	1	1	yes	characteristic
73	C₄×C₄₃	#121	1	1	yes	characteristic
74	Dic₄₃	—	2	2	no	—
75	#1810	—	43	1	no	maximal, Sylow
76	C₂×C₄₃	—	2	1	no	—
77	C₂×C₄₃	—	2	1	no	—
78	C₂×C₄₃	#380	1	1	yes	characteristic
79	C₂×C₄₃	C₂×#108	1	2	yes	—
80	D₄₃	—	2	4	no	—
81	C₂³×C₈	—	43	1	no	—
82	C₂×#108	—	43	1	no	—
83	C₂×#108	D₄₃	1	1	yes	characteristic, complemented
84	#407	—	43	2	no	—
85	#341	—	43	2	no	—
86	C₄₃	#1810	1	1	yes	characteristic, complemented, Sylow
87	C₂³×C₄	—	43	1	no	—
88	C₂×M₁₆	—	43	2	no	—
89	C₂×M₁₆	C₂×D₄₃	1	2	yes	—
90	C₂²×C₈	—	43	1	no	—
91	C₂²×C₈	—	43	4	no	—
92	C₂²×C₈	—	86	2	no	—
93	C₂²×C₈	—	86	2	no	—
94	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
95	#108	—	2	2	no	—
96	#108	—	86	2	no	—
97	C₂²⋊C₈	—	86	4	no	—
98	C₂⁴	—	43	1	no	—
99	C₂²×C₄	—	43	1	no	—
100	C₂²×C₄	—	43	2	no	—
101	C₂²×C₄	—	43	2	no	—
102	C₂²×C₄	—	86	1	no	—
103	C₂²×C₄	—	86	1	no	—
104	C₂²×C₄	—	86	1	no	—
105	C₂²×C₄	—	86	1	no	—
106	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
107	M₁₆	—	2	2	no	—
108	M₁₆	—	2	2	no	—
109	M₁₆	—	86	2	no	—
110	M₁₆	—	86	2	no	—
111	C₂×C₈	—	2	2	no	—
112	C₂×C₈	—	43	2	no	—
113	C₂×C₈	—	86	1	no	—
114	C₂×C₈	—	86	1	no	—
115	C₂×C₈	—	86	8	no	—
116	C₂×C₈	—	86	2	no	—
117	C₂×C₈	C₄×D₄₃	1	2	yes	—
118	C₂×C₈	D₁₇₂	1	2	yes	—
119	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
120	C₂³	—	43	2	no	—
121	C₂³	—	86	4	no	—
122	C₂³	—	86	1	no	—
123	C₂³	—	86	1	no	—
124	C₂³	Q₈×D₄₃	1	1	yes	characteristic
125	C₂×C₄	—	43	2	no	—
126	C₂×C₄	—	86	1	no	—
127	C₂×C₄	—	86	1	no	—
128	C₂×C₄	—	86	2	no	—
129	C₂×C₄	—	86	2	no	—
130	C₂×C₄	—	86	2	no	—
131	C₂×C₄	—	86	2	no	—
132	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
133	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
134	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
135	C₂×C₄	#10621900	1	1	yes	characteristic
136	C₂×C₄	#10621902	1	1	yes	characteristic
137	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
138	C₈	—	4	2	no	—
139	C₈	—	86	2	no	—
140	C₈	—	172	2	no	—
141	C₈	(C₂×D₄₃)⋊C₄	1	4	yes	—
142	C₂²	—	2	2	no	—
143	C₂²	—	43	4	no	—
144	C₂²	—	86	4	no	—
145	C₂²	—	86	4	no	—
146	C₂²	—	86	2	no	—
147	C₂²	—	86	2	no	—
148	C₂²	C₄⋊C₄×D₄₃	1	1	yes	characteristic
149	C₂²	#13063301	1	1	yes	characteristic
150	C₂²	#13063305	1	1	yes	characteristic
151	C₄	—	86	2	no	—
152	C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
153	C₄	#13063283	1	1	yes	characteristic
154	C₄	#13063296	1	1	yes	characteristic
155	C₄	#13063300	1	1	yes	characteristic
156	C₂	—	2	1	no	—
157	C₂	—	2	1	no	—
158	C₂	—	86	4	no	—
159	C₂	#14582756	1	1	yes	characteristic
160	C₂	#108×D₄₃	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₈×D₄₃

C₂

yes

maximal, characteristic

C₂×#13063261

C₂

yes

maximal, characteristic, complemented

#14582862

C₂

yes

maximal

#14582663

C₂

yes

maximal, complemented

C₂×#108×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₃

C₂²

yes

characteristic

C₂×#10621877

C₂²

yes

—

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

C₄

yes

—

#13063261

—

(C₂×D₄₃)⋊C₈

—

C₂×M₁₆×C₄₃

C₂²

yes

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

#108×C₄₃

—

C₂³×D₄₃

Q₈

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

Q₈

yes

characteristic

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

C₂×C₄

yes

—

C₂×C₄×D₄₃

D₄

yes

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

D₄

yes

—

C₂×C₈×C₄₃

D₄

yes

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₈×D₄₃

—

C₂³×C₄₃

C₂×Q₈

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₄⋊C₄

yes

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₈×C₄₃

C₂²⋊C₄

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

#108

yes

complemented

C₄×C₄₃

C₂×C₂²⋊C₄

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

#1810

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#380

yes

characteristic

C₂×C₄₃

C₂×#108

yes

—

D₄₃

—

C₂³×C₈

—

C₂×#108

—

C₂×#108

D₄₃

yes

characteristic, complemented

#407

—

#341

—

C₄₃

#1810

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

#108

—

#108

—

C₂²⋊C₈

—

C₂⁴

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

C₂²×D₄₃

yes

characteristic

107

M₁₆

—

108

M₁₆

—

109

M₁₆

—

110

M₁₆

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

C₄×D₄₃

yes

—

118

C₂×C₈

D₁₇₂

yes

—

119

C₂×C₈

C₂²⋊D₄₃

yes

—

120

C₂³

—

121

C₂³

—

122

C₂³

—

123

C₂³

—

124

C₂³

Q₈×D₄₃

yes

characteristic

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

133

C₂×C₄

C₂×D₁₇₂

yes

characteristic

134

C₂×C₄

D₄×D₄₃

yes

characteristic

135

C₂×C₄

#10621900

yes

characteristic

136

C₂×C₄

#10621902

yes

characteristic

137

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

138

C₈

—

139

C₈

—

140

C₈

—

172

—

141

C₈

(C₂×D₄₃)⋊C₄

yes

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

C₄⋊C₄×D₄₃

yes

characteristic

149

C₂²

#13063301

yes

characteristic

150

C₂²

#13063305

yes

characteristic

151

C₄

—

152

C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

153

C₄

#13063283

yes

characteristic

154

C₄

#13063296

yes

characteristic

155

C₄

#13063300

yes

characteristic

156

C₂

—

157

C₂

—

158

C₂

—

159

C₂

#14582756

yes

characteristic

160

C₂

#108×D₄₃

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×#108×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄⋊C₄
hypercenter	C₂×#108	D₄₃
hypocenter	C₄₃	#1810
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×#108×C₄₃

C₂

socle

C₂²×C₄₃

C₂×C₄⋊C₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
2. C₂×#13063261	C₂	semidirect
4. #14582663	C₂	semidirect
5. C₂×#108×C₄₃	C₂	semidirect
69. C₂×D₄₃	#108	semidirect
83. C₂×#108	D₄₃	semidirect
86. C₄₃	#1810	semidirect

H ≅ G/N

type

2. C₂×#13063261

C₂

semidirect

4. #14582663

C₂

semidirect

5. C₂×#108×C₄₃

C₂

semidirect

69. C₂×D₄₃

#108

semidirect

83. C₂×#108

D₄₃

semidirect

86. C₄₃

#1810

semidirect

Subgroups — #19134630

Conjugacy classes of subgroups

Complements