Group #22590442 — subgroups

Subgroups — #22590442

Order 9088.

170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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×#14556069	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14556067	C₂	1	1	yes	maximal, characteristic, complemented
3	#17986236	C₂	1	1	yes	maximal, characteristic, complemented
4	#17986232	C₂	1	1	yes	maximal, characteristic, complemented
5	#17985826	C₂	1	1	yes	maximal, characteristic, complemented
6	#17985801	C₂	1	1	yes	maximal, characteristic, complemented
7	#357×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₅₆₈	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₇₁	C₂²	1	1	yes	characteristic
10	#14556103	—	2	1	no	—
11	#14556099	—	2	1	no	—
12	#14556069	—	2	2	no	—
13	#14556067	—	2	2	no	—
14	C₂×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
15	#14556062	C₂²	1	1	yes	characteristic
16	#14556049	—	2	1	no	—
17	#14556048	—	2	1	no	—
18	C₂×D₈×C₇₁	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
20	#107×C₇₁	C₂²	1	1	yes	characteristic
21	C₂×D₂₈₄	—	2	1	no	—
22	C₂×D₂₈₄	—	4	1	no	—
23	C₂×C₂²⋊D₇₁	—	4	1	no	—
24	C₂×C₄×D₇₁	D₄	1	1	yes	characteristic
25	D₅₆₈	—	2	1	no	—
26	D₅₆₈	—	2	1	no	—
27	C₂×C₇₁⋊C₈	D₄	1	1	yes	characteristic
28	C₈×D₇₁	—	2	1	no	—
29	C₈×D₇₁	—	2	1	no	—
30	C₄⋊Dic₇₁	—	2	1	no	—
31	C₂²⋊Dic₇₁	—	4	1	no	—
32	(C₂×D₇₁)⋊C₄	—	4	1	no	—
33	C₇₁⋊C₁₆	D₄	1	2	yes	complemented
34	C₂×D₄×C₇₁	—	2	1	no	—
35	D₈×C₇₁	—	2	1	no	—
36	D₈×C₇₁	—	2	1	no	—
37	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
38	C₄⋊C₄×C₇₁	—	2	1	no	—
39	C₁₆×C₇₁	—	2	1	no	—
40	C₂³×C₇₁	—	4	1	no	—
41	C₂²×D₇₁	—	4	1	no	—
42	C₂²×D₇₁	D₈	1	1	yes	characteristic
43	D₄×C₇₁	—	4	1	no	—
44	D₄×C₇₁	—	4	1	no	—
45	C₂×C₄×C₇₁	—	4	1	no	—
46	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
47	C₂²⋊D₇₁	—	8	2	no	—
48	C₂×Dic₇₁	—	4	1	no	—
49	C₂×Dic₇₁	D₈	1	1	yes	characteristic
50	D₂₈₄	—	4	1	no	—
51	D₂₈₄	—	4	1	no	—
52	D₂₈₄	—	8	2	no	—
53	C₄×D₇₁	—	2	1	no	—
54	C₄×D₇₁	—	2	1	no	—
55	C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
56	C₈×C₇₁	#41	1	1	yes	characteristic
57	C₇₁⋊C₈	—	2	1	no	—
58	C₂²×C₇₁	—	8	1	no	—
59	C₂²×C₇₁	—	8	1	no	—
60	C₂²×C₇₁	—	8	1	no	—
61	C₂²×C₇₁	C₂×D₈	1	1	yes	characteristic
62	C₂×D₇₁	—	2	1	no	—
63	C₂×D₇₁	—	2	1	no	—
64	C₂×D₇₁	—	2	1	no	—
65	C₂×D₇₁	—	8	1	no	—
66	C₂×D₇₁	—	8	1	no	—
67	C₂×D₇₁	—	8	1	no	—
68	C₄×C₇₁	—	8	1	no	—
69	C₄×C₇₁	#121	1	1	yes	characteristic
70	C₄×C₇₁	#135	1	1	yes	characteristic
71	Dic₇₁	—	2	1	no	—
72	Dic₇₁	—	8	1	no	—
73	C₂×C₇₁	—	16	1	no	—
74	C₂×C₇₁	#466	1	1	yes	characteristic
75	C₂×C₇₁	#509	1	1	yes	characteristic
76	C₂×C₇₁	#509	1	1	yes	characteristic
77	D₇₁	—	4	1	no	—
78	D₇₁	—	16	1	no	—
79	#2218	—	71	1	no	maximal, Sylow
80	C₇₁	#2218	1	1	yes	characteristic, complemented, Sylow
81	C₂×D₁₆	—	71	1	no	—
82	C₂×M₃₂	—	71	1	no	—
83	#466	—	71	1	no	—
84	#466	—	71	1	no	—
85	#367	—	71	1	no	—
86	#357	—	71	1	no	—
87	#357	D₇₁	1	1	yes	characteristic, complemented
88	C₂×D₈	—	71	1	no	—
89	C₂×D₈	C₂×D₇₁	1	1	yes	characteristic
90	C₂²×C₈	—	71	1	no	—
91	#121	—	142	1	no	—
92	#121	—	142	1	no	—
93	D₁₆	—	142	2	no	—
94	M₃₂	—	142	2	no	—
95	C₂×C₁₆	—	71	1	no	—
96	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
97	#107	—	71	1	no	—
98	#107	C₂×D₇₁	1	1	yes	characteristic
99	#102	—	142	1	no	—
100	#102	—	142	1	no	—
101	C₂×D₄	—	2	1	no	—
102	C₂×D₄	—	284	1	no	—
103	C₂×D₄	—	284	1	no	—
104	C₂×D₄	—	142	1	no	—
105	C₂²×C₄	—	71	1	no	—
106	D₈	—	2	1	no	—
107	D₈	—	2	1	no	—
108	D₈	—	142	1	no	—
109	D₈	—	142	1	no	—
110	C₂×C₈	—	71	1	no	—
111	C₂×C₈	—	142	1	no	—
112	C₂×C₈	—	142	1	no	—
113	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
114	C₄⋊C₄	—	2	1	no	—
115	C₄⋊C₄	—	142	1	no	—
116	C₂²⋊C₄	—	284	1	no	—
117	C₂²⋊C₄	—	284	1	no	—
118	C₁₆	—	2	1	no	—
119	C₁₆	—	71	2	no	—
120	C₂³	—	4	1	no	—
121	C₂³	—	284	1	no	—
122	C₂³	—	71	1	no	—
123	D₄	—	4	1	no	—
124	D₄	—	4	1	no	—
125	D₄	—	284	1	no	—
126	D₄	—	284	1	no	—
127	D₄	—	568	2	no	—
128	D₄	—	568	2	no	—
129	C₂×C₄	—	4	1	no	—
130	C₂×C₄	—	284	1	no	—
131	C₂×C₄	—	71	1	no	—
132	C₂×C₄	—	142	1	no	—
133	C₂×C₄	—	142	1	no	—
134	C₂×C₄	D₄×D₇₁	1	1	yes	characteristic
135	C₈	—	142	1	no	—
136	C₈	D₄×D₇₁	1	1	yes	characteristic
137	C₈	#11765865	1	1	yes	characteristic
138	C₂²	—	8	1	no	—
139	C₂²	—	8	1	no	—
140	C₂²	—	8	1	no	—
141	C₂²	—	568	1	no	—
142	C₂²	—	568	1	no	—
143	C₂²	—	568	1	no	—
144	C₂²	—	142	1	no	—
145	C₂²	—	142	1	no	—
146	C₂²	—	142	1	no	—
147	C₂²	D₈×D₇₁	1	1	yes	characteristic
148	C₄	—	8	1	no	—
149	C₄	—	568	1	no	—
150	C₄	—	142	1	no	—
151	C₄	#14556101	1	1	yes	characteristic
152	C₄	#14556149	1	1	yes	characteristic
153	C₂	—	16	1	no	—
154	C₂	—	284	1	no	—
155	C₂	—	1136	1	no	—
156	C₂	#17986234	1	1	yes	characteristic
157	C₂	#17986433	1	1	yes	characteristic
158	C₂	#17986436	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556069

C₂

yes

maximal, characteristic, complemented

C₂×#14556067

C₂

yes

maximal, characteristic, complemented

#17986236

C₂

yes

maximal, characteristic, complemented

#17986232

C₂

yes

maximal, characteristic, complemented

#17985826

C₂

yes

maximal, characteristic, complemented

#17985801

C₂

yes

maximal, characteristic, complemented

#357×C₇₁

C₂

yes

maximal, characteristic, complemented

C₂×D₅₆₈

C₂²

yes

characteristic

C₂×C₈×D₇₁

C₂²

yes

—

—

—

—

C₂×C₇₁⋊C₁₆

C₂²

yes

characteristic

#14556062

C₂²

yes

characteristic

#14556049

—

#14556048

—

C₂×D₈×C₇₁

C₂²

yes

characteristic

C₂×C₁₆×C₇₁

C₂²

yes

characteristic

#107×C₇₁

C₂²

yes

characteristic

C₂×D₂₈₄

—

C₂×D₂₈₄

—

C₂×C₂²⋊D₇₁

—

C₂×C₄×D₇₁

D₄

yes

characteristic

D₅₆₈

—

D₅₆₈

—

C₂×C₇₁⋊C₈

D₄

yes

characteristic

C₈×D₇₁

—

C₈×D₇₁

—

C₄⋊Dic₇₁

—

C₂²⋊Dic₇₁

—

(C₂×D₇₁)⋊C₄

—

C₇₁⋊C₁₆

D₄

yes

complemented

C₂×D₄×C₇₁

—

D₈×C₇₁

—

D₈×C₇₁

—

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₄⋊C₄×C₇₁

—

C₁₆×C₇₁

—

C₂³×C₇₁

—

C₂²×D₇₁

—

C₂²×D₇₁

D₈

yes

characteristic

D₄×C₇₁

—

D₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂²⋊D₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

D₈

yes

characteristic

D₂₈₄

—

D₂₈₄

—

D₂₈₄

—

C₄×D₇₁

—

C₄×D₇₁

—

C₈×C₇₁

C₂×D₄

yes

characteristic

C₈×C₇₁

#41

yes

characteristic

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

C₂×D₈

yes

characteristic

C₂×D₇₁

—

C₂×D₇₁

—

C₂×D₇₁

—

C₂×D₇₁

—

C₂×D₇₁

—

C₂×D₇₁

—

C₄×C₇₁

—

C₄×C₇₁

yes

C₄×C₇₁

yes

Dic₇₁

—

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

yes

C₂×C₇₁

yes

C₂×C₇₁

yes

D₇₁

—

D₇₁

—

#2218

—

maximal, Sylow

C₇₁

#2218

yes

characteristic, complemented, Sylow

C₂×D₁₆

—

C₂×M₃₂

—

—

—

—

—

D₇₁

yes

characteristic, complemented

C₂×D₈

—

C₂×D₈

C₂×D₇₁

yes

characteristic

C₂²×C₈

—

#121

—

142

—

#121

—

142

—

D₁₆

—

142

—

M₃₂

—

142

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₁

yes

characteristic

#107

—

#107

C₂×D₇₁

yes

characteristic

#102

—

142

—

100

#102

—

142

—

101

C₂×D₄

—

102

C₂×D₄

—

284

—

103

C₂×D₄

—

284

—

104

C₂×D₄

—

142

—

105

C₂²×C₄

—

106

D₈

—

107

D₈

—

108

D₈

—

142

—

109

D₈

—

142

—

110

C₂×C₈

—

111

C₂×C₈

—

142

—

112

C₂×C₈

—

142

—

113

C₂×C₈

C₂²×D₇₁

yes

characteristic

114

C₄⋊C₄

—

115

C₄⋊C₄

—

142

—

116

C₂²⋊C₄

—

284

—

117

C₂²⋊C₄

—

284

—

118

C₁₆

—

119

C₁₆

—

120

C₂³

—

121

C₂³

—

284

—

122

C₂³

—

123

D₄

—

124

D₄

—

125

D₄

—

284

—

126

D₄

—

284

—

127

D₄

—

568

—

128

D₄

—

568

—

129

C₂×C₄

—

130

C₂×C₄

—

284

—

131

C₂×C₄

—

132

C₂×C₄

—

142

—

133

C₂×C₄

—

142

—

134

C₂×C₄

D₄×D₇₁

yes

characteristic

135

C₈

—

142

—

136

C₈

D₄×D₇₁

yes

characteristic

137

C₈

#11765865

yes

characteristic

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

568

—

142

C₂²

—

568

—

143

C₂²

—

568

—

144

C₂²

—

142

—

145

C₂²

—

142

—

146

C₂²

—

142

—

147

C₂²

D₈×D₇₁

yes

characteristic

148

C₄

—

149

C₄

—

568

—

150

C₄

—

142

—

151

C₄

#14556101

yes

characteristic

152

C₄

#14556149

yes

characteristic

153

C₂

—

154

C₂

—

284

—

155

C₂

—

1136

—

156

C₂

#17986234

yes

characteristic

157

C₂

#17986433

yes

characteristic

158

C₂

#17986436

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₇₁
commutator	C₂×C₈×C₇₁	C₂³
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	#357×C₇₁	C₂
socle	C₂²×C₇₁	C₂×D₈
hypercenter	#357	D₇₁
hypocenter	C₇₁	#2218
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₇₁

commutator

C₂×C₈×C₇₁

C₂³

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

#357×C₇₁

C₂

socle

C₂²×C₇₁

C₂×D₈

D₇₁

C₇₁

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
1. C₂×#14556069	C₂	semidirect
2. C₂×#14556067	C₂	semidirect
3. #17986236	C₂	semidirect
4. #17986232	C₂	semidirect
5. #17985826	C₂	semidirect
6. #17985801	C₂	semidirect
7. #357×C₇₁	C₂	semidirect
33. C₇₁⋊C₁₆	D₄	semidirect
80. C₇₁	#2218	semidirect
87. #357	D₇₁	semidirect

H ≅ G/N

type

1. C₂×#14556069

C₂

semidirect

2. C₂×#14556067

C₂

semidirect

3. #17986236

C₂

semidirect

4. #17986232

C₂

semidirect

5. #17985826

C₂

semidirect

6. #17985801

C₂

semidirect

7. #357×C₇₁

C₂

semidirect

33. C₇₁⋊C₁₆

D₄

semidirect

80. C₇₁

#2218

semidirect

87. #357

D₇₁

semidirect

Subgroups — #22590442

Conjugacy classes of subgroups

Complements