Group #19136019 — subgroups

Subgroups — #19136019

Order 5504.

256 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 81 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×(C₂×D₄₃)⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#14582756	C₂	1	2	yes	maximal
3	#14582662	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582661	C₂	1	2	yes	maximal, complemented
5	C₂×#107×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
7	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
9	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
10	(C₂×D₄₃)⋊C₈	—	2	2	no	—
11	C₄₃⋊#95	—	2	2	no	—
12	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
14	#107×C₄₃	—	2	2	no	—
15	C₂³×D₄₃	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₄₃	—	2	2	no	—
17	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
18	C₂²×Dic₄₃	—	2	2	no	—
19	C₂²×Dic₄₃	D₄	1	1	yes	characteristic
20	C₂×C₄×D₄₃	—	2	1	no	—
21	C₂×C₄×D₄₃	—	2	1	no	—
22	C₂×C₄×D₄₃	—	2	2	no	—
23	C₂×C₄×D₄₃	—	2	2	no	—
24	C₂×C₈×C₄₃	—	2	2	no	—
25	C₂×C₈×C₄₃	D₄	1	2	yes	—
26	C₄⋊C₄×C₄₃	—	2	2	no	—
27	C₄⋊C₄×C₄₃	—	2	2	no	—
28	(C₂×D₄₃)⋊C₄	—	4	4	no	—
29	C₄⋊Dic₄₃	—	2	2	no	—
30	C₄⋊Dic₄₃	—	2	2	no	—
31	C₂×C₄₃⋊C₈	—	2	1	no	—
32	C₂×C₄₃⋊C₈	—	2	2	no	—
33	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
34	C₂²×D₄₃	—	2	1	no	—
35	C₂²×D₄₃	—	2	2	no	—
36	C₂²×D₄₃	—	2	1	no	—
37	C₂²×D₄₃	—	2	2	no	—
38	C₂²×D₄₃	D₈	1	2	yes	—
39	C₂×C₄×C₄₃	—	4	2	no	—
40	C₂×C₄×C₄₃	—	4	2	no	—
41	C₂×C₄×C₄₃	—	4	2	no	—
42	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₄₃	#41	1	2	yes	—
44	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
45	C₂×C₄×C₄₃	#41	1	2	yes	—
46	C₂×Dic₄₃	—	2	1	no	—
47	C₂×Dic₄₃	—	2	2	no	—
48	C₂×Dic₄₃	—	4	2	no	—
49	C₂×Dic₄₃	—	4	2	no	—
50	C₂×Dic₄₃	—	4	2	no	—
51	C₄×D₄₃	—	4	1	no	—
52	C₄×D₄₃	—	4	1	no	—
53	C₄×D₄₃	—	4	2	no	—
54	C₈×C₄₃	—	2	2	no	—
55	C₄₃⋊C₈	—	4	1	no	—
56	C₂²×C₄₃	#121	1	1	yes	characteristic
57	C₂²×C₄₃	#123	1	2	yes	—
58	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
59	C₂²×C₄₃	#135	1	1	yes	characteristic
60	C₂²×C₄₃	#137	1	2	yes	—
61	C₂×D₄₃	—	2	2	no	—
62	C₂×D₄₃	—	2	4	no	—
63	C₂×D₄₃	—	4	1	no	—
64	C₂×D₄₃	—	4	1	no	—
65	C₂×D₄₃	—	4	2	no	—
66	C₄×C₄₃	—	8	2	no	—
67	C₄×C₄₃	#123	1	1	yes	characteristic
68	C₄×C₄₃	#124	1	1	yes	characteristic
69	C₄×C₄₃	#126	1	2	yes	—
70	Dic₄₃	—	4	1	no	—
71	Dic₄₃	—	8	2	no	—
72	#2075	—	43	1	no	maximal, Sylow
73	C₂×C₄₃	#397	1	1	yes	characteristic
74	C₂×C₄₃	#466	1	1	yes	characteristic
75	C₂×C₄₃	#470	1	1	yes	characteristic
76	C₂×C₄₃	#480	1	2	yes	—
77	C₂×C₄₃	#485	1	2	yes	—
78	D₄₃	—	4	2	no	—
79	C₂×#107	D₄₃	1	1	yes	characteristic, complemented
80	C₂×C₂²⋊C₈	—	43	1	no	—
81	#380	—	43	2	no	—
82	#340	—	43	1	no	—
83	#340	—	43	2	no	—
84	C₄₃	#2075	1	1	yes	characteristic, complemented, Sylow
85	C₂³×C₄	—	43	1	no	—
86	C₂²×C₈	—	43	1	no	—
87	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
88	C₂×C₄⋊C₄	—	43	2	no	—
89	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
90	C₂×C₂²⋊C₄	—	86	2	no	—
91	#107	—	2	2	no	—
92	C₂²⋊C₈	—	86	2	no	—
93	#95	—	86	2	no	—
94	C₂⁴	—	43	1	no	—
95	C₂²×C₄	—	2	2	no	—
96	C₂²×C₄	—	43	1	no	—
97	C₂²×C₄	—	86	2	no	—
98	C₂²×C₄	—	86	1	no	—
99	C₂²×C₄	—	86	2	no	—
100	C₂²×C₄	—	86	1	no	—
101	C₂²×C₄	—	86	2	no	—
102	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
103	C₂×C₈	—	2	2	no	—
104	C₂×C₈	—	86	2	no	—
105	C₂×C₈	—	86	1	no	—
106	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
107	C₄⋊C₄	—	2	2	no	—
108	C₄⋊C₄	—	2	2	no	—
109	C₄⋊C₄	—	86	2	no	—
110	C₄⋊C₄	—	86	2	no	—
111	C₂²⋊C₄	—	172	4	no	—
112	C₂³	—	43	2	no	—
113	C₂³	—	86	1	no	—
114	C₂³	—	86	2	no	—
115	C₂³	—	86	1	no	—
116	C₂³	—	86	2	no	—
117	C₂³	D₄×D₄₃	1	1	yes	characteristic
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	—	4	2	no	—
120	C₂×C₄	—	4	2	no	—
121	C₂×C₄	—	86	1	no	—
122	C₂×C₄	—	86	2	no	—
123	C₂×C₄	—	172	2	no	—
124	C₂×C₄	—	172	2	no	—
125	C₂×C₄	—	172	2	no	—
126	C₂×C₄	—	172	1	no	—
127	C₂×C₄	—	172	1	no	—
128	C₂×C₄	—	172	2	no	—
129	C₂×C₄	#10621898	1	2	yes	—
130	C₂×C₄	#10621900	1	1	yes	characteristic
131	C₂×C₄	#10621902	1	2	yes	—
132	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
133	C₈	—	2	2	no	—
134	C₈	—	172	1	no	—
135	C₂²	—	86	2	no	—
136	C₂²	—	86	4	no	—
137	C₂²	—	172	1	no	—
138	C₂²	—	172	1	no	—
139	C₂²	—	172	2	no	—
140	C₂²	#13063296	1	1	yes	characteristic
141	C₂²	#13063310	1	2	yes	—
142	C₂²	D₈×D₄₃	1	1	yes	characteristic
143	C₂²	#13063344	1	1	yes	characteristic
144	C₂²	#13063357	1	2	yes	—
145	C₄	—	8	2	no	—
146	C₄	—	344	2	no	—
147	C₄	—	172	1	no	—
148	C₄	#13063308	1	1	yes	characteristic
149	C₄	#13063314	1	1	yes	characteristic
150	C₄	#13063320	1	2	yes	—
151	C₂	—	172	2	no	—
152	C₂	#14582825	1	1	yes	characteristic
153	C₂	#14583132	1	1	yes	characteristic
154	C₂	#14583154	1	1	yes	characteristic
155	C₂	#14583214	1	2	yes	—
156	C₂	#14583242	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×(C₂×D₄₃)⋊C₈

C₂

yes

maximal, characteristic

#14582756

C₂

yes

maximal

#14582662

C₂

yes

maximal, characteristic, complemented

#14582661

C₂

yes

maximal, complemented

C₂×#107×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₃

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₈

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

#107×C₄₃

—

C₂³×D₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

D₄

yes

characteristic

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

D₈

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

#121

yes

characteristic

C₂²×C₄₃

#123

yes

—

C₂²×C₄₃

C₂×D₈

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#485

yes

—

D₄₃

—

C₂×#107

D₄₃

yes

characteristic, complemented

C₂×C₂²⋊C₈

—

#380

—

#340

—

#340

—

C₄₃

#2075

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₂²⋊C₄

—

#107

—

C₂²⋊C₈

—

#95

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

C₂²×D₄₃

yes

characteristic

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

C₂²⋊D₄₃

yes

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₂²⋊C₄

—

172

—

112

C₂³

—

113

C₂³

—

114

C₂³

—

115

C₂³

—

116

C₂³

—

117

C₂³

D₄×D₄₃

yes

characteristic

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

172

—

124

C₂×C₄

—

172

—

125

C₂×C₄

—

172

—

126

C₂×C₄

—

172

—

127

C₂×C₄

—

172

—

128

C₂×C₄

—

172

—

129

C₂×C₄

#10621898

yes

—

130

C₂×C₄

#10621900

yes

characteristic

131

C₂×C₄

#10621902

yes

—

132

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

133

C₈

—

134

C₈

—

172

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

172

—

138

C₂²

—

172

—

139

C₂²

—

172

—

140

C₂²

#13063296

yes

characteristic

141

C₂²

#13063310

yes

—

142

C₂²

D₈×D₄₃

yes

characteristic

143

C₂²

#13063344

yes

characteristic

144

C₂²

#13063357

yes

—

145

C₄

—

146

C₄

—

344

—

147

C₄

—

172

—

148

C₄

#13063308

yes

characteristic

149

C₄

#13063314

yes

characteristic

150

C₄

#13063320

yes

—

151

C₂

—

172

—

152

C₂

#14582825

yes

characteristic

153

C₂

#14583132

yes

characteristic

154

C₂

#14583154

yes

characteristic

155

C₂

#14583214

yes

—

156

C₂

#14583242

yes

—

	subgroup	G/H
center	C₂³	D₄×D₄₃
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×#107×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×#107	D₄₃
hypocenter	C₄₃	#2075
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

subgroup

G/H

center

C₂³

D₄×D₄₃

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×#107×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

N	H ≅ G/N	type
3. #14582662	C₂	semidirect
4. #14582661	C₂	semidirect
5. C₂×#107×C₄₃	C₂	semidirect
79. C₂×#107	D₄₃	semidirect
84. C₄₃	#2075	semidirect

H ≅ G/N

type

3. #14582662

C₂

semidirect

4. #14582661

C₂

semidirect

5. C₂×#107×C₄₃

C₂

semidirect

79. C₂×#107

D₄₃

semidirect

84. C₄₃

#2075

semidirect

Subgroups — #19136019

Conjugacy classes of subgroups

Complements