Group #19137064 — subgroups

Subgroups — C₂×#14582805 #19137064

Order 5504.

928 conjugacy classes of subgroups; only the 381 normal subgroups are shown.

normal subgroups only

This group has 928 conjugacy classes of subgroups — too many to draw. Only its 381 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	C₂³×Dic₈₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	#14582805	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄₃⋊#95	C₂	1	4	yes	maximal
5	C₂²×C₄²×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₆	—	2	4	no	—
7	C₂²×Dic₈₆	—	2	4	no	—
8	C₂²×Dic₈₆	C₄	1	8	yes	complemented
9	C₂²×Dic₈₆	C₂²	1	4	yes	—
10	C₂³×Dic₄₃	C₂²	1	2	yes	—
11	C₂³×Dic₄₃	C₂²	1	2	yes	—
12	C₂×C₄⋊Dic₄₃	—	2	4	no	—
13	C₂×C₄⋊Dic₄₃	C₂²	1	4	yes	—
14	C₄₃⋊#95	C₂²	1	16	yes	—
15	C₂³×C₄×C₄₃	C₂²	1	2	yes	—
16	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₄²×C₄₃	—	2	4	no	—
18	C₂×C₄²×C₄₃	C₂²	1	4	yes	—
19	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
20	C₂²×C₄×C₄₃	—	2	4	no	—
21	C₂²×C₄×C₄₃	—	2	4	no	—
22	C₂²×C₄×C₄₃	C₂×C₄	1	4	yes	—
23	C₂²×C₄×C₄₃	D₄	1	4	yes	—
24	C₂²×C₄×C₄₃	D₄	1	4	yes	—
25	C₂²×C₄×C₄₃	Q₈	1	8	yes	complemented
26	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
27	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
28	C₂²×Dic₄₃	—	2	4	no	—
29	C₂²×Dic₄₃	—	2	4	no	—
30	C₂²×Dic₄₃	—	2	4	no	—
31	C₂²×Dic₄₃	—	2	8	no	—
32	C₂²×Dic₄₃	C₂×C₄	1	8	yes	—
33	C₂²×Dic₄₃	C₂³	1	4	yes	—
34	C₂²×Dic₄₃	C₂³	1	4	yes	—
35	C₂×Dic₈₆	—	2	32	no	—
36	C₂×Dic₈₆	—	2	8	no	—
37	C₂×Dic₈₆	—	2	8	no	—
38	C₂×Dic₈₆	C₂×C₄	1	16	yes	complemented
39	C₄²×C₄₃	—	2	8	no	—
40	C₄⋊Dic₄₃	—	2	8	no	—
41	C₂³×C₄₃	C₂²×C₄	1	2	yes	—
42	C₂³×C₄₃	C₂×D₄	1	2	yes	—
43	C₂³×C₄₃	C₂×D₄	1	2	yes	—
44	C₂³×C₄₃	C₂×Q₈	1	4	yes	—
45	C₂³×C₄₃	#41	1	4	yes	—
46	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
47	C₂×C₄×C₄₃	—	2	16	no	—
48	C₂×C₄×C₄₃	—	2	4	no	—
49	C₂×C₄×C₄₃	—	2	4	no	—
50	C₂×C₄×C₄₃	C₂²⋊C₄	1	16	yes	—
51	C₂×C₄×C₄₃	C₂²×C₄	1	4	yes	—
52	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
53	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
54	C₂×C₄×C₄₃	C₂×Q₈	1	8	yes	complemented
55	C₂×Dic₄₃	—	2	16	no	—
56	C₂×Dic₄₃	—	2	4	no	—
57	C₂×Dic₄₃	—	2	4	no	—
58	C₂×Dic₄₃	—	2	4	no	—
59	C₂×Dic₄₃	—	2	8	no	—
60	C₂×Dic₄₃	—	4	8	no	—
61	C₂×Dic₄₃	C₂²×C₄	1	8	yes	—
62	Dic₈₆	—	2	32	no	—
63	C₂²×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
64	C₂²×C₄₃	C₄×Q₈	1	8	yes	—
65	C₂²×C₄₃	C₂²⋊Q₈	1	8	yes	—
66	C₂²×C₄₃	#124	1	4	yes	—
67	C₂²×C₄₃	C₄⋊Q₈	1	4	yes	—
68	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
69	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
70	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
71	C₂²×C₄₃	C₂²×Q₈	1	2	yes	—
72	C₂²×C₄₃	C₂×#41	1	2	yes	—
73	C₄×C₄₃	—	2	8	no	—
74	C₄×C₄₃	C₂×C₂²⋊C₄	1	8	yes	—
75	Dic₄₃	—	2	8	no	—
76	Dic₄₃	—	4	4	no	—
77	C₂×#391	—	43	1	no	maximal, Sylow
78	C₂×C₄₃	#391	1	8	yes	complemented
79	C₂×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄₃	C₂×C₄×Q₈	1	2	yes	—
81	C₂×C₄₃	C₂×C₂²⋊Q₈	1	2	yes	—
82	C₂×C₄₃	C₂×#124	1	1	yes	characteristic
83	C₂×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
84	C₂³×Q₈	—	43	1	no	—
85	C₂²×C₄⋊C₄	—	43	1	no	—
86	C₂²×C₄²	D₄₃	1	1	yes	characteristic
87	#391	—	43	8	no	—
88	C₂×#95	—	43	4	no	—
89	C₄₃	C₂×#391	1	1	yes	characteristic, complemented, Sylow
90	C₂²×Q₈	—	43	4	no	—
91	C₂²×Q₈	—	43	8	no	—
92	C₂²×Q₈	—	86	4	no	—
93	C₂²×Q₈	—	86	4	no	—
94	C₂³×C₄	—	43	2	no	—
95	C₂³×C₄	—	43	2	no	—
96	C₂³×C₄	C₂×D₄₃	1	2	yes	—
97	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
98	C₂×C₄⋊C₄	—	43	4	no	—
99	C₂×C₄⋊C₄	—	86	4	no	—
100	C₂×C₄²	—	2	4	no	—
101	C₂×C₄²	C₂×D₄₃	1	4	yes	—
102	#95	—	43	16	no	—
103	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
104	C₂×Q₈	—	43	16	no	—
105	C₂×Q₈	—	86	32	no	—
106	C₂×Q₈	—	86	8	no	—
107	C₂×Q₈	—	86	8	no	—
108	C₂²×C₄	—	2	4	no	—
109	C₂²×C₄	—	2	4	no	—
110	C₂²×C₄	—	43	8	no	—
111	C₂²×C₄	—	43	4	no	—
112	C₂²×C₄	—	43	4	no	—
113	C₂²×C₄	—	86	4	no	—
114	C₂²×C₄	—	86	4	no	—
115	C₂²×C₄	—	86	4	no	—
116	C₂²×C₄	—	86	8	no	—
117	C₂²×C₄	Dic₈₆	1	8	yes	complemented
118	C₂²×C₄	C₄×D₄₃	1	4	yes	—
119	C₂²×C₄	D₁₇₂	1	4	yes	—
120	C₂²×C₄	C₂²⋊D₄₃	1	4	yes	—
121	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
122	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
123	C₄⋊C₄	—	86	8	no	—
124	C₄²	—	2	8	no	—
125	C₂³	C₂×Dic₈₆	1	4	yes	—
126	C₂³	C₂×C₄×D₄₃	1	2	yes	—
127	C₂³	C₂×D₁₇₂	1	2	yes	—
128	C₂³	#10621898	1	4	yes	—
129	C₂³	C₂×C₂²⋊D₄₃	1	2	yes	—
130	C₂³	C₂³×D₄₃	1	1	yes	characteristic
131	Q₈	—	86	32	no	—
132	C₂×C₄	—	2	16	no	—
133	C₂×C₄	—	2	4	no	—
134	C₂×C₄	—	2	4	no	—
135	C₂×C₄	—	43	8	no	—
136	C₂×C₄	—	86	16	no	—
137	C₂×C₄	—	86	4	no	—
138	C₂×C₄	—	86	4	no	—
139	C₂×C₄	—	86	4	no	—
140	C₂×C₄	—	86	8	no	—
141	C₂×C₄	—	172	8	no	—
142	C₂×C₄	(C₂×D₄₃)⋊C₄	1	16	yes	—
143	C₂×C₄	C₂×Dic₈₆	1	8	yes	complemented
144	C₂×C₄	C₂×C₄×D₄₃	1	4	yes	—
145	C₂×C₄	C₂×D₁₇₂	1	4	yes	—
146	C₂×C₄	C₂×C₂²⋊D₄₃	1	4	yes	—
147	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	4	yes	—
148	C₂²	C₄×Dic₈₆	1	8	yes	—
149	C₂²	#13063304	1	8	yes	—
150	C₂²	#13063313	1	4	yes	—
151	C₂²	#13063325	1	4	yes	—
152	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
153	C₂²	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
154	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
155	C₂²	C₂²×Dic₈₆	1	2	yes	—
156	C₂²	C₂×#10621898	1	2	yes	—
157	C₄	—	2	8	no	—
158	C₄	—	86	8	no	—
159	C₄	—	172	4	no	—
160	C₄	C₂×(C₂×D₄₃)⋊C₄	1	8	yes	—
161	C₂	#14582805	1	8	yes	direct product factor
162	C₂	C₂²×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
163	C₂	C₂×C₄×Dic₈₆	1	2	yes	—
164	C₂	C₂×#13063304	1	2	yes	—
165	C₂	C₂×#13063313	1	1	yes	characteristic
166	C₂	C₂×#13063325	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×Dic₈₆

C₂

yes

maximal, characteristic

C₂²×C₄⋊Dic₄₃

C₂

yes

maximal, characteristic

#14582805

C₂

yes

maximal, direct product factor

C₂×C₄₃⋊#95

C₂

yes

maximal

C₂²×C₄²×C₄₃

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

—

C₂²×Dic₈₆

—

C₂²×Dic₈₆

C₄

yes

complemented

C₂²×Dic₈₆

C₂²

yes

—

C₂³×Dic₄₃

C₂²

yes

—

C₂³×Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂³×C₄×C₄₃

C₂²

yes

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

C₂²

yes

—

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

Q₈

yes

complemented

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

C₂×C₄

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

C₂×C₄

yes

complemented

C₄²×C₄₃

—

C₄⋊Dic₄₃

—

C₂³×C₄₃

C₂²×C₄

yes

—

C₂³×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

C₂×Q₈

yes

—

C₂³×C₄₃

#41

yes

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

complemented

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²×C₄

yes

—

Dic₈₆

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

—

C₂²×C₄₃

C₄×Q₈

yes

—

C₂²×C₄₃

C₂²⋊Q₈

yes

—

C₂²×C₄₃

#124

yes

—

C₂²×C₄₃

C₄⋊Q₈

yes

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂²×Q₈

yes

—

C₂²×C₄₃

C₂×#41

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₂²⋊C₄

yes

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

C₂²×C₂²⋊C₄

yes

characteristic

C₂×C₄₃

C₂×C₄×Q₈

yes

—

C₂×C₄₃

C₂×C₂²⋊Q₈

yes

—

C₂×C₄₃

C₂×#124

yes

characteristic

C₂×C₄₃

C₂×C₄⋊Q₈

yes

characteristic

C₂³×Q₈

—

C₂²×C₄⋊C₄

—

C₂²×C₄²

D₄₃

yes

characteristic

#391

—

C₂×#95

—

C₄₃

C₂×#391

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×Q₈

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂×D₄₃

yes

—

C₂³×C₄

C₂×D₄₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

100

C₂×C₄²

—

101

C₂×C₄²

C₂×D₄₃

yes

—

102

#95

—

103

C₂⁴

C₂²×D₄₃

yes

characteristic

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

Dic₈₆

yes

complemented

118

C₂²×C₄

C₄×D₄₃

yes

—

119

C₂²×C₄

D₁₇₂

yes

—

120

C₂²×C₄

C₂²⋊D₄₃

yes

—

121

C₂²×C₄

C₂²×D₄₃

yes

—

122

C₂²×C₄

C₂²×D₄₃

yes

—

123

C₄⋊C₄

—

124

C₄²

—

125

C₂³

C₂×Dic₈₆

yes

—

126

C₂³

C₂×C₄×D₄₃

yes

—

127

C₂³

C₂×D₁₇₂

yes

—

128

C₂³

#10621898

yes

—

129

C₂³

C₂×C₂²⋊D₄₃

yes

—

130

C₂³

C₂³×D₄₃

yes

characteristic

131

Q₈

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

172

—

142

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

143

C₂×C₄

C₂×Dic₈₆

yes

complemented

144

C₂×C₄

C₂×C₄×D₄₃

yes

—

145

C₂×C₄

C₂×D₁₇₂

yes

—

146

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

147

C₂²

C₂×(C₂×D₄₃)⋊C₄

yes

—

148

C₂²

C₄×Dic₈₆

yes

—

149

C₂²

#13063304

yes

—

150

C₂²

#13063313

yes

—

151

C₂²

#13063325

yes

—

152

C₂²

C₂²×C₄×D₄₃

yes

characteristic

153

C₂²

C₂²×C₂²⋊D₄₃

yes

characteristic

154

C₂²

C₂²×D₁₇₂

yes

characteristic

155

C₂²

C₂²×Dic₈₆

yes

—

156

C₂²

C₂×#10621898

yes

—

157

C₄

—

158

C₄

—

159

C₄

—

172

—

160

C₄

C₂×(C₂×D₄₃)⋊C₄

yes

—

161

C₂

#14582805

yes

direct product factor

162

C₂

C₂²×(C₂×D₄₃)⋊C₄

yes

characteristic

163

C₂

C₂×C₄×Dic₈₆

yes

—

164

C₂

C₂×#13063304

yes

—

165

C₂

C₂×#13063313

yes

characteristic

166

C₂

C₂×#13063325

yes

characteristic

	subgroup	G/H
center	C₂⁴	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂³×C₄
Frattini	C₂³	C₂³×D₄₃
Fitting	C₂²×C₄²×C₄₃	C₂
socle	C₂⁴×C₄₃	C₂³
hypercenter	C₂²×C₄²	D₄₃
hypocenter	C₄₃	C₂×#391
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

subgroup

G/H

center

C₂⁴

C₂²×D₄₃

commutator

C₂²×C₄₃

C₂³×C₄

Frattini

C₂³

C₂³×D₄₃

Fitting

C₂²×C₄²×C₄₃

C₂

socle

C₂⁴×C₄₃

C₂³

hypercenter

C₂²×C₄²

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂⁴ ◁ C₂²×C₄²

N	H ≅ G/N	type
3. #14582805	C₂	direct (N × H)
8. C₂²×Dic₈₆	C₄	semidirect
25. C₂²×C₄×C₄₃	Q₈	semidirect
38. C₂×Dic₈₆	C₂×C₄	semidirect
54. C₂×C₄×C₄₃	C₂×Q₈	semidirect
78. C₂×C₄₃	#391	semidirect
89. C₄₃	C₂×#391	semidirect
117. C₂²×C₄	Dic₈₆	semidirect
143. C₂×C₄	C₂×Dic₈₆	semidirect
161. C₂	#14582805	direct (N × H)

H ≅ G/N

type

3. #14582805

C₂

direct (N × H)

8. C₂²×Dic₈₆

C₄

semidirect

25. C₂²×C₄×C₄₃

Q₈

semidirect

38. C₂×Dic₈₆

C₂×C₄

semidirect

54. C₂×C₄×C₄₃

C₂×Q₈

semidirect

78. C₂×C₄₃

#391

semidirect

89. C₄₃

C₂×#391

semidirect

117. C₂²×C₄

Dic₈₆

semidirect

143. C₂×C₄

C₂×Dic₈₆

semidirect

161. C₂

#14582805

direct (N × H)

Subgroups — C₂×#14582805 #19137064

Conjugacy classes of subgroups

Complements

Subgroups — C2×#14582805 #19137064

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14582805 #19137064