Group #19135923 — subgroups

Subgroups — #19135923

Order 5504.

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

normal subgroups only

This group has 282 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	C₂×#13063325	C₂	1	1	yes	maximal, characteristic
2	C₂×#13063258	C₂	1	2	yes	maximal
3	#14582661	C₂	1	2	yes	maximal
4	#14582654	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#389	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₆	—	2	1	no	—
7	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
8	#13063325	—	2	4	no	—
9	C₂×C₄⋊Dic₄₃	—	2	1	no	—
10	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
11	#13063258	—	2	4	no	—
12	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
13	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	#95×C₄₃	—	2	1	no	—
17	C₂²×C₄×C₄₃	—	2	1	no	—
18	C₂²×C₄×C₄₃	—	2	1	no	—
19	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
22	C₂²×Dic₄₃	—	2	2	no	—
23	C₂×Dic₈₆	—	2	4	no	—
24	C₂×Dic₈₆	—	4	2	no	—
25	C₂×Dic₈₆	—	4	2	no	—
26	C₄⋊C₄×C₄₃	—	2	1	no	—
27	C₄⋊C₄×C₄₃	—	2	2	no	—
28	C₄⋊C₄×C₄₃	—	4	2	no	—
29	C₄⋊C₄×C₄₃	Q₈	1	2	yes	complemented
30	C₄²×C₄₃	—	2	2	no	—
31	C₄⋊Dic₄₃	—	2	4	no	—
32	C₄⋊Dic₄₃	—	2	2	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	Q₈	1	4	yes	complemented
37	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₄₃	—	2	1	no	—
39	C₂×C₄×C₄₃	—	2	1	no	—
40	C₂×C₄×C₄₃	—	2	1	no	—
41	C₂×C₄×C₄₃	—	2	1	no	—
42	C₂×C₄×C₄₃	—	2	2	no	—
43	C₂×C₄×C₄₃	—	4	1	no	—
44	C₂×C₄×C₄₃	—	4	1	no	—
45	C₂×C₄×C₄₃	—	4	1	no	—
46	C₂×C₄×C₄₃	—	4	1	no	—
47	C₂×C₄×C₄₃	—	4	1	no	—
48	C₂×C₄×C₄₃	D₈	1	2	yes	—
49	C₂×C₄×C₄₃	Q₁₆	1	2	yes	—
50	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
51	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
52	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
53	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
54	C₂×Dic₄₃	—	2	4	no	—
55	C₂×Dic₄₃	—	4	2	no	—
56	C₂×Dic₄₃	—	4	2	no	—
57	Dic₈₆	—	4	8	no	—
58	C₄₃⋊C₈	—	2	4	no	—
59	C₂²×C₄₃	#120	1	1	yes	characteristic
60	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
61	C₂²×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
62	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
63	C₂²×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
64	C₂²×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
65	C₂²×C₄₃	#137	1	1	yes	characteristic
66	C₄×C₄₃	—	2	2	no	—
67	C₄×C₄₃	—	2	2	no	—
68	C₄×C₄₃	—	4	2	no	—
69	C₄×C₄₃	—	8	1	no	—
70	C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
71	C₄×C₄₃	C₄⋊Q₈	1	2	yes	—
72	Dic₄₃	—	4	4	no	—
73	#2057	—	43	1	no	maximal, Sylow
74	C₂×C₄₃	#395	1	1	yes	characteristic
75	C₂×C₄₃	#447	1	1	yes	characteristic
76	C₂×C₄₃	#451	1	1	yes	characteristic
77	C₂×C₄₃	#474	1	1	yes	characteristic
78	C₂×C₄₃	#477	1	1	yes	characteristic
79	C₂×C₄₃	#500	1	1	yes	characteristic
80	C₂×C₄₃	#501	1	1	yes	characteristic
81	C₂×C₄⋊Q₈	—	43	1	no	—
82	C₂×#107	—	43	2	no	—
83	#389	D₄₃	1	1	yes	characteristic
84	#340	—	43	2	no	—
85	#336	—	43	1	no	—
86	C₄₃	#2057	1	1	yes	characteristic, complemented, Sylow
87	C₂²×Q₈	—	86	1	no	—
88	C₂²×C₈	—	43	2	no	—
89	C₄⋊Q₈	—	86	4	no	—
90	C₂×C₄⋊C₄	—	2	1	no	—
91	C₂×C₄⋊C₄	—	43	2	no	—
92	C₂×C₄⋊C₄	—	86	1	no	—
93	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
94	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
95	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
96	#107	—	86	4	no	—
97	#95	—	2	1	no	—
98	C₂×Q₈	—	86	4	no	—
99	C₂×Q₈	—	172	2	no	—
100	C₂×Q₈	—	172	2	no	—
101	C₂²×C₄	—	2	1	no	—
102	C₂²×C₄	—	2	1	no	—
103	C₂²×C₄	—	86	2	no	—
104	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
105	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
106	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
107	C₂×C₈	—	43	4	no	—
108	C₂×C₈	—	86	2	no	—
109	C₂×C₈	—	86	2	no	—
110	C₄⋊C₄	—	2	1	no	—
111	C₄⋊C₄	—	2	2	no	—
112	C₄⋊C₄	—	4	2	no	—
113	C₄⋊C₄	—	43	4	no	—
114	C₄⋊C₄	—	86	4	no	—
115	C₄⋊C₄	—	86	2	no	—
116	C₄⋊C₄	Dic₈₆	1	2	yes	complemented
117	C₄²	—	2	2	no	—
118	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
119	Q₈	—	172	8	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	4	1	no	—
126	C₂×C₄	—	4	1	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	—	4	1	no	—
129	C₂×C₄	—	4	1	no	—
130	C₂×C₄	—	86	4	no	—
131	C₂×C₄	—	172	2	no	—
132	C₂×C₄	—	172	2	no	—
133	C₂×C₄	#10621882	1	2	yes	—
134	C₂×C₄	#10621885	1	2	yes	—
135	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
136	C₂×C₄	#10621898	1	1	yes	characteristic
137	C₂×C₄	D₄×D₄₃	1	2	yes	—
138	C₂×C₄	Q₈×D₄₃	1	2	yes	—
139	C₈	—	86	4	no	—
140	C₂²	#13063293	1	1	yes	characteristic
141	C₂²	#13063304	1	1	yes	characteristic
142	C₂²	#13063323	1	1	yes	characteristic
143	C₂²	C₂×#10621882	1	1	yes	characteristic
144	C₂²	C₂×#10621885	1	1	yes	characteristic
145	C₂²	#13063350	1	1	yes	characteristic
146	C₂²	#13063355	1	1	yes	characteristic
147	C₄	—	2	2	no	—
148	C₄	—	2	2	no	—
149	C₄	—	4	2	no	—
150	C₄	—	8	1	no	—
151	C₄	—	172	4	no	—
152	C₄	#13063303	1	2	yes	—
153	C₄	#13063324	1	2	yes	—
154	C₂	#14582819	1	1	yes	characteristic
155	C₂	#14583032	1	1	yes	characteristic
156	C₂	#14583054	1	1	yes	characteristic
157	C₂	#14583179	1	1	yes	characteristic
158	C₂	#14583194	1	1	yes	characteristic
159	C₂	#14583302	1	1	yes	characteristic
160	C₂	#14583309	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063325

C₂

yes

maximal, characteristic

C₂×#13063258

C₂

yes

maximal

#14582661

C₂

yes

maximal

#14582654

C₂

yes

maximal, characteristic

C₄₃×#389

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

—

C₂²×C₄₃⋊C₈

C₂²

yes

—

#13063325

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

#13063258

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#95×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

Q₈

yes

complemented

C₄²×C₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

Q₈

yes

complemented

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

D₈

yes

—

C₂×C₄×C₄₃

Q₁₆

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

C₄₃⋊C₈

—

C₂²×C₄₃

#120

yes

characteristic

C₂²×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₄₃

C₄⋊Q₈

yes

characteristic

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂²×C₄₃

C₂×Q₁₆

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊Q₈

yes

—

C₄×C₄₃

C₄⋊Q₈

yes

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄⋊Q₈

—

C₂×#107

—

#389

D₄₃

yes

characteristic

#340

—

#336

—

C₄₃

#2057

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×C₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

C₂×C₄²

C₂×D₄₃

yes

characteristic

#107

—

#95

—

C₂×Q₈

—

C₂×Q₈

—

172

—

100

C₂×Q₈

—

172

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

105

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

106

C₂²×C₄

C₂²×D₄₃

yes

characteristic

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

Dic₈₆

yes

complemented

117

C₄²

—

118

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

119

Q₈

—

172

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

172

—

132

C₂×C₄

—

172

—

133

C₂×C₄

#10621882

yes

—

134

C₂×C₄

#10621885

yes

—

135

C₂×C₄

C₂×Dic₈₆

yes

characteristic

136

C₂×C₄

#10621898

yes

characteristic

137

C₂×C₄

D₄×D₄₃

yes

—

138

C₂×C₄

Q₈×D₄₃

yes

—

139

C₈

—

140

C₂²

#13063293

yes

characteristic

141

C₂²

#13063304

yes

characteristic

142

C₂²

#13063323

yes

characteristic

143

C₂²

C₂×#10621882

yes

characteristic

144

C₂²

C₂×#10621885

yes

characteristic

145

C₂²

#13063350

yes

characteristic

146

C₂²

#13063355

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

172

—

152

C₄

#13063303

yes

—

153

C₄

#13063324

yes

—

154

C₂

#14582819

yes

characteristic

155

C₂

#14583032

yes

characteristic

156

C₂

#14583054

yes

characteristic

157

C₂

#14583179

yes

characteristic

158

C₂

#14583194

yes

characteristic

159

C₂

#14583302

yes

characteristic

160

C₂

#14583309

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₃
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#389	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	#389	D₄₃
hypocenter	C₄₃	#2057
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #389

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₃

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#389

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #389

N	H ≅ G/N	type
29. C₄⋊C₄×C₄₃	Q₈	semidirect
36. C₂×C₄₃⋊C₈	Q₈	semidirect
86. C₄₃	#2057	semidirect
116. C₄⋊C₄	Dic₈₆	semidirect

H ≅ G/N

type

29. C₄⋊C₄×C₄₃

Q₈

semidirect

36. C₂×C₄₃⋊C₈

Q₈

semidirect

86. C₄₃

#2057

semidirect

116. C₄⋊C₄

Dic₈₆

semidirect

Subgroups — #19135923

Conjugacy classes of subgroups

Complements