Group #19134356 — subgroups

Subgroups — #19134356

Order 5504.

412 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 137 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×C₄²×D₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×(C₂×D₄₃)⋊C₈	C₂	1	2	yes	maximal
3	C₂×#13063235	C₂	1	2	yes	maximal, complemented
4	#14582654	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#336	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₄₃	C₄	1	2	yes	—
7	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
9	C₂×C₄×Dic₄₃	C₄	1	2	yes	—
10	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
11	C₄²×D₄₃	—	2	4	no	—
12	(C₂×D₄₃)⋊C₈	C₄	1	8	yes	complemented
13	#13063235	—	2	4	no	—
14	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
15	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	C₂³×D₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	C₂²×Dic₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×Dic₄₃	C₂×C₄	1	2	yes	—
21	C₂×C₄×D₄₃	—	2	4	no	—
22	C₂×C₄×D₄₃	—	2	2	no	—
23	C₂×C₄×D₄₃	—	2	1	no	—
24	C₂×C₄×D₄₃	—	2	1	no	—
25	C₂×C₄×D₄₃	—	2	4	no	—
26	C₂×C₄×D₄₃	—	2	4	no	—
27	C₂×C₄×D₄₃	C₂×C₄	1	4	yes	—
28	C₂×C₈×C₄₃	—	2	2	no	—
29	C₂×C₈×C₄₃	—	2	2	no	—
30	C₂×C₈×C₄₃	C₂×C₄	1	4	yes	complemented
31	C₄²×C₄₃	—	2	2	no	—
32	C₄×Dic₄₃	—	2	4	no	—
33	C₄×Dic₄₃	D₄	1	4	yes	—
34	C₂×C₄₃⋊C₈	—	2	2	no	—
35	C₂×C₄₃⋊C₈	—	2	2	no	—
36	C₂×C₄₃⋊C₈	C₂×C₄	1	4	yes	complemented
37	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
38	C₂²×D₄₃	—	2	1	no	—
39	C₂²×D₄₃	—	2	1	no	—
40	C₂²×D₄₃	—	2	2	no	—
41	C₂²×D₄₃	C₄²	1	2	yes	—
42	C₂²×D₄₃	M₁₆	1	4	yes	—
43	C₂×C₄×C₄₃	—	2	2	no	—
44	C₂×C₄×C₄₃	—	2	2	no	—
45	C₂×C₄×C₄₃	M₁₆	1	4	yes	—
46	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
47	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
53	C₂×Dic₄₃	—	2	2	no	—
54	C₂×Dic₄₃	C₄²	1	2	yes	—
55	C₂×Dic₄₃	C₂²⋊C₄	1	4	yes	—
56	C₄×D₄₃	—	2	16	no	—
57	C₄×D₄₃	—	2	4	no	—
58	C₄×D₄₃	—	2	4	no	—
59	C₈×C₄₃	—	2	4	no	—
60	C₄₃⋊C₈	—	2	4	no	—
61	C₂²×C₄₃	C₂×C₄²	1	1	yes	characteristic
62	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄₃	#117	1	1	yes	characteristic
64	C₂²×C₄₃	C₂×M₁₆	1	2	yes	—
65	C₂²×C₄₃	C₂×M₁₆	1	2	yes	—
66	C₂×D₄₃	—	2	2	no	—
67	C₂×D₄₃	—	2	2	no	—
68	C₂×D₄₃	—	2	4	no	—
69	C₂×D₄₃	—	2	4	no	—
70	C₂×D₄₃	#97	1	4	yes	complemented
71	C₄×C₄₃	—	2	4	no	—
72	C₄×C₄₃	C₄×D₄	1	2	yes	—
73	C₄×C₄₃	C₄×D₄	1	2	yes	—
74	Dic₄₃	—	2	2	no	—
75	Dic₄₃	—	2	4	no	—
76	#1749	—	43	1	no	maximal, Sylow
77	C₂×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₄₃	C₂×#97	1	1	yes	characteristic
79	C₂×C₄₃	C₄×M₁₆	1	1	yes	characteristic
80	C₂×C₄₃	#407	1	2	yes	—
81	C₂×C₄₃	#432	1	2	yes	—
82	D₄₃	—	2	4	no	—
83	C₂²×C₄²	—	43	1	no	—
84	C₂×C₂²⋊C₈	—	43	2	no	—
85	C₂×#97	—	43	2	no	—
86	#336	—	43	1	no	—
87	#336	D₄₃	1	1	yes	characteristic, complemented
88	C₄₃	#1749	1	1	yes	characteristic, complemented, Sylow
89	C₂³×C₄	—	43	1	no	—
90	C₂³×C₄	—	43	2	no	—
91	C₂²×C₈	—	43	2	no	—
92	C₂²×C₈	C₂×D₄₃	1	2	yes	—
93	C₂×C₄²	—	43	1	no	—
94	C₂×C₄²	—	43	2	no	—
95	C₂×C₄²	—	86	4	no	—
96	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
97	C₂²⋊C₈	—	43	8	no	—
98	#97	—	86	4	no	—
99	C₂⁴	—	43	1	no	—
100	C₂²×C₄	—	43	1	no	—
101	C₂²×C₄	—	43	2	no	—
102	C₂²×C₄	—	43	4	no	—
103	C₂²×C₄	—	86	4	no	—
104	C₂²×C₄	—	86	4	no	—
105	C₂²×C₄	—	86	4	no	—
106	C₂²×C₄	—	86	2	no	—
107	C₂²×C₄	—	86	1	no	—
108	C₂²×C₄	—	86	1	no	—
109	C₂²×C₄	C₄×D₄₃	1	2	yes	—
110	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
111	C₂×C₈	—	2	2	no	—
112	C₂×C₈	—	2	2	no	—
113	C₂×C₈	—	43	4	no	—
114	C₂×C₈	—	86	2	no	—
115	C₂×C₈	—	86	2	no	—
116	C₂×C₈	C₄×D₄₃	1	4	yes	complemented
117	C₄²	—	2	2	no	—
118	C₄²	—	43	4	no	—
119	C₄²	—	86	4	no	—
120	C₂³	—	43	2	no	—
121	C₂³	—	43	4	no	—
122	C₂³	—	86	1	no	—
123	C₂³	—	86	1	no	—
124	C₂³	—	86	2	no	—
125	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	43	2	no	—
129	C₂×C₄	—	43	4	no	—
130	C₂×C₄	—	86	16	no	—
131	C₂×C₄	—	86	1	no	—
132	C₂×C₄	—	86	1	no	—
133	C₂×C₄	—	86	2	no	—
134	C₂×C₄	—	86	2	no	—
135	C₂×C₄	—	86	4	no	—
136	C₂×C₄	—	86	4	no	—
137	C₂×C₄	#10621872	1	4	yes	—
138	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
139	C₂×C₄	D₄×D₄₃	1	2	yes	—
140	C₂×C₄	#10621900	1	1	yes	characteristic
141	C₂×C₄	#10621902	1	1	yes	characteristic
142	C₈	—	2	4	no	—
143	C₈	—	86	4	no	—
144	C₂²	—	43	4	no	—
145	C₂²	—	86	2	no	—
146	C₂²	—	86	4	no	—
147	C₂²	—	86	4	no	—
148	C₂²	—	86	2	no	—
149	C₂²	C₄²×D₄₃	1	1	yes	characteristic
150	C₂²	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
151	C₂²	#13063283	1	1	yes	characteristic
152	C₂²	M₁₆×D₄₃	1	2	yes	—
153	C₂²	C₂×#10621872	1	2	yes	—
154	C₄	—	2	4	no	—
155	C₄	—	86	4	no	—
156	C₄	—	86	2	no	—
157	C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
158	C₄	#13063287	1	2	yes	—
159	C₂	—	86	4	no	—
160	C₂	#14582746	1	1	yes	characteristic
161	C₂	#97×D₄₃	1	1	yes	characteristic
162	C₂	C₄×#10621872	1	1	yes	characteristic
163	C₂	#14582861	1	2	yes	—
164	C₂	#14582955	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄²×D₄₃

C₂

yes

maximal, characteristic

C₂×(C₂×D₄₃)⋊C₈

C₂

yes

maximal

C₂×#13063235

C₂

yes

maximal, complemented

#14582654

C₂

yes

maximal, characteristic, complemented

C₄₃×#336

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₃

C₄

yes

—

C₂²×C₄×D₄₃

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

—

C₂×C₄×Dic₄₃

C₄

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

C₄²×D₄₃

—

(C₂×D₄₃)⋊C₈

C₄

yes

complemented

#13063235

—

C₂²×C₈×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂³×D₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

complemented

C₄²×C₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

D₄

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

complemented

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

C₄²

yes

—

C₂²×D₄₃

M₁₆

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

M₁₆

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₄²

yes

—

C₂×Dic₄₃

C₂²⋊C₄

yes

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

C₂×C₄²

yes

characteristic

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₃

#117

yes

characteristic

C₂²×C₄₃

C₂×M₁₆

yes

—

C₂²×C₄₃

C₂×M₁₆

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

#97

yes

complemented

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

—

C₄×C₄₃

C₄×D₄

yes

—

Dic₄₃

—

Dic₄₃

—

#1749

—

maximal, Sylow

C₂×C₄₃

C₄×C₂²⋊C₄

yes

characteristic

C₂×C₄₃

C₂×#97

yes

characteristic

C₂×C₄₃

C₄×M₁₆

yes

characteristic

C₂×C₄₃

#407

yes

—

C₂×C₄₃

#432

yes

—

D₄₃

—

C₂²×C₄²

—

C₂×C₂²⋊C₈

—

C₂×#97

—

#336

—

#336

D₄₃

yes

characteristic, complemented

C₄₃

#1749

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

C₂×D₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₂²⋊C₈

—

#97

—

C₂⁴

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

C₄×D₄₃

yes

—

110

C₂²×C₄

C₂²×D₄₃

yes

characteristic

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

C₄×D₄₃

yes

complemented

117

C₄²

—

118

C₄²

—

119

C₄²

—

120

C₂³

—

121

C₂³

—

122

C₂³

—

123

C₂³

—

124

C₂³

—

125

C₂³

C₂×C₄×D₄₃

yes

characteristic

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

#10621872

yes

—

138

C₂×C₄

C₂×C₄×D₄₃

yes

—

139

C₂×C₄

D₄×D₄₃

yes

—

140

C₂×C₄

#10621900

yes

characteristic

141

C₂×C₄

#10621902

yes

characteristic

142

C₈

—

143

C₈

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

—

149

C₂²

C₄²×D₄₃

yes

characteristic

150

C₂²

C₂²⋊C₄×D₄₃

yes

characteristic

151

C₂²

#13063283

yes

characteristic

152

C₂²

M₁₆×D₄₃

yes

—

153

C₂²

C₂×#10621872

yes

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

(C₂²⋊D₄₃)⋊C₄

yes

—

158

C₄

#13063287

yes

—

159

C₂

—

160

C₂

#14582746

yes

characteristic

161

C₂

#97×D₄₃

yes

characteristic

162

C₂

C₄×#10621872

yes

characteristic

163

C₂

#14582861

yes

—

164

C₂

#14582955

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂×C₄²
Fitting	C₄₃×#336	C₂
socle	C₂³×C₄₃	C₂²×C₄
hypercenter	#336	D₄₃
hypocenter	C₄₃	#1749
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₄₃

commutator

C₂²×C₄₃

C₂×C₄²

Fitting

C₄₃×#336

C₂

socle

C₂³×C₄₃

C₂²×C₄

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
3. C₂×#13063235	C₂	semidirect
4. #14582654	C₂	semidirect
5. C₄₃×#336	C₂	semidirect
12. (C₂×D₄₃)⋊C₈	C₄	semidirect
30. C₂×C₈×C₄₃	C₂×C₄	semidirect
36. C₂×C₄₃⋊C₈	C₂×C₄	semidirect
70. C₂×D₄₃	#97	semidirect
87. #336	D₄₃	semidirect
88. C₄₃	#1749	semidirect
116. C₂×C₈	C₄×D₄₃	semidirect

H ≅ G/N

type

3. C₂×#13063235

C₂

semidirect

4. #14582654

C₂

semidirect

5. C₄₃×#336

C₂

semidirect

12. (C₂×D₄₃)⋊C₈

C₄

semidirect

30. C₂×C₈×C₄₃

C₂×C₄

semidirect

36. C₂×C₄₃⋊C₈

C₂×C₄

semidirect

70. C₂×D₄₃

#97

semidirect

87. #336

D₄₃

semidirect

88. C₄₃

#1749

semidirect

116. C₂×C₈

C₄×D₄₃

semidirect

Subgroups — #19134356

Conjugacy classes of subgroups

Complements