Group #22587791 — subgroups

Subgroups — #22587791

Order 9088.

160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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	#17986350	C₂	1	1	yes	maximal, characteristic, complemented
2	#17986289	C₂	1	1	yes	maximal, characteristic
3	#17986279	C₂	1	1	yes	maximal, characteristic
4	#17985752	C₂	1	1	yes	maximal, characteristic, complemented
5	#17985747	C₂	1	1	yes	maximal, characteristic, complemented
6	#17985746	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×D₄×C₇₁	C₂	1	1	yes	maximal, characteristic
8	#14556128	C₂²	1	1	yes	characteristic
9	#14556128	C₂²	1	1	yes	characteristic
10	#14556061	—	2	1	no	—
11	#14556059	—	2	1	no	—
12	C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
13	C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
14	#14556053	—	2	1	no	—
15	#14556053	—	2	1	no	—
16	#14556049	—	2	1	no	—
17	#14556049	—	2	1	no	—
18	C₂²×C₈×C₇₁	—	2	1	no	—
19	C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
20	C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
21	C₂²⋊C₈×C₇₁	—	2	1	no	—
22	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
23	C₂×Dic₁₄₂	—	2	1	no	—
24	C₂×Dic₁₄₂	—	2	1	no	—
25	C₂×C₇₁⋊C₈	—	2	1	no	—
26	C₂×C₇₁⋊C₈	—	2	1	no	—
27	C₄⋊Dic₇₁	—	2	1	no	—
28	C₄⋊Dic₇₁	—	2	1	no	—
29	C₄⋊Dic₇₁	—	2	1	no	—
30	C₄⋊Dic₇₁	—	2	1	no	—
31	C₂×D₄×C₇₁	D₄	1	1	yes	characteristic
32	C₂²×C₄×C₇₁	—	2	1	no	—
33	C₂×C₈×C₇₁	—	2	1	no	—
34	C₂×C₈×C₇₁	—	4	2	no	—
35	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
36	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
37	C₄⋊C₄×C₇₁	D₄	1	1	yes	characteristic
38	C₂²⋊C₄×C₇₁	—	2	1	no	—
39	C₄²×C₇₁	C₂³	1	1	yes	characteristic
40	C₂³×C₇₁	—	2	1	no	—
41	D₄×C₇₁	—	2	1	no	—
42	D₄×C₇₁	Q₁₆	1	2	yes	—
43	C₂×C₄×C₇₁	—	2	1	no	—
44	C₂×C₄×C₇₁	—	4	1	no	—
45	C₂×C₄×C₇₁	—	4	1	no	—
46	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₇₁	#41	1	1	yes	characteristic
49	C₂×Dic₇₁	—	4	1	no	—
50	C₂×Dic₇₁	—	4	1	no	—
51	Dic₁₄₂	—	4	1	no	—
52	Dic₁₄₂	—	4	1	no	—
53	Dic₁₄₂	—	8	1	no	—
54	C₈×C₇₁	—	2	1	no	—
55	C₈×C₇₁	—	2	1	no	—
56	C₈×C₇₁	—	4	1	no	—
57	C₇₁⋊C₈	—	4	1	no	—
58	C₇₁⋊C₈	—	4	1	no	—
59	C₂²×C₇₁	—	2	2	no	—
60	C₂²×C₇₁	—	4	1	no	—
61	C₂²×C₇₁	—	4	1	no	—
62	C₂²×C₇₁	#121	1	1	yes	characteristic
63	C₄×C₇₁	—	2	1	no	—
64	C₄×C₇₁	—	4	1	no	—
65	C₄×C₇₁	C₂×Q₁₆	1	1	yes	characteristic
66	C₄×C₇₁	#135	1	1	yes	characteristic
67	C₄×C₇₁	#135	1	1	yes	characteristic
68	C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
69	Dic₇₁	—	8	1	no	—
70	Dic₇₁	—	8	1	no	—
71	C₂×C₇₁	—	4	2	no	—
72	C₂×C₇₁	#463	1	1	yes	characteristic
73	C₂×C₇₁	#467	1	1	yes	characteristic
74	C₂×C₇₁	#471	1	1	yes	characteristic
75	#1683	—	71	1	no	maximal, Sylow
76	C₇₁	#1683	1	1	yes	characteristic, complemented, Sylow
77	#487	—	71	1	no	—
78	#476	—	71	1	no	—
79	#474	—	71	1	no	—
80	C₈×D₄	D₇₁	1	1	yes	characteristic
81	#335	—	71	1	no	—
82	#333	—	71	1	no	—
83	#332	—	71	1	no	—
84	C₂²×C₈	—	2	1	no	—
85	C₄⋊Q₈	—	71	1	no	—
86	C₄⋊Q₈	—	71	1	no	—
87	C₄×D₄	C₂×D₇₁	1	1	yes	characteristic
88	#107	—	142	1	no	—
89	#106	—	142	1	no	—
90	C₄⋊C₈	—	71	1	no	—
91	C₄⋊C₈	—	71	1	no	—
92	C₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
93	#103	—	142	1	no	—
94	#103	—	142	1	no	—
95	#102	—	142	1	no	—
96	#102	—	142	1	no	—
97	C₂²⋊C₈	—	2	1	no	—
98	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
99	C₂×Q₈	—	142	1	no	—
100	C₂×Q₈	—	142	1	no	—
101	C₂×D₄	D₂₈₄	1	1	yes	characteristic
102	C₂²×C₄	—	2	1	no	—
103	C₂×C₈	—	2	1	no	—
104	C₂×C₈	—	4	2	no	—
105	C₂×C₈	—	142	1	no	—
106	C₂×C₈	—	142	1	no	—
107	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
108	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
109	C₄⋊C₄	—	142	1	no	—
110	C₄⋊C₄	—	142	1	no	—
111	C₄⋊C₄	—	142	1	no	—
112	C₄⋊C₄	—	142	1	no	—
113	C₄⋊C₄	D₂₈₄	1	1	yes	characteristic
114	C₂²⋊C₄	—	2	1	no	—
115	C₄²	C₂²×D₇₁	1	1	yes	characteristic
116	C₂³	—	2	1	no	—
117	Q₈	—	284	1	no	—
118	Q₈	—	284	1	no	—
119	Q₈	—	568	1	no	—
120	D₄	—	2	1	no	—
121	D₄	Dic₂₈₄	1	2	yes	—
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	4	1	no	—
124	C₂×C₄	—	4	1	no	—
125	C₂×C₄	—	284	1	no	—
126	C₂×C₄	—	284	1	no	—
127	C₂×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
128	C₂×C₄	C₂×D₂₈₄	1	1	yes	characteristic
129	C₂×C₄	#11765865	1	1	yes	characteristic
130	C₈	—	2	1	no	—
131	C₈	—	2	1	no	—
132	C₈	—	4	1	no	—
133	C₈	—	284	1	no	—
134	C₈	—	284	1	no	—
135	C₂²	—	2	2	no	—
136	C₂²	—	4	1	no	—
137	C₂²	—	4	1	no	—
138	C₂²	#14556102	1	1	yes	characteristic
139	C₄	—	2	1	no	—
140	C₄	—	4	1	no	—
141	C₄	—	568	1	no	—
142	C₄	—	568	1	no	—
143	C₄	C₂×Dic₂₈₄	1	1	yes	characteristic
144	C₄	#14556148	1	1	yes	characteristic
145	C₄	#14556150	1	1	yes	characteristic
146	C₄	#14556154	1	1	yes	characteristic
147	C₂	—	4	2	no	—
148	C₂	#17986214	1	1	yes	characteristic
149	C₂	#17986240	1	1	yes	characteristic
150	C₂	#17986262	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17986350

C₂

yes

maximal, characteristic, complemented

#17986289

C₂

yes

maximal, characteristic

#17986279

C₂

yes

maximal, characteristic

#17985752

C₂

yes

maximal, characteristic, complemented

#17985747

C₂

yes

maximal, characteristic, complemented

#17985746

C₂

yes

maximal, characteristic, complemented

C₈×D₄×C₇₁

C₂

yes

maximal, characteristic

#14556128

C₂²

yes

characteristic

#14556128

C₂²

yes

characteristic

#14556061

—

#14556059

—

C₄⋊(C₇₁⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₇₁⋊C₈)

C₂²

yes

—

—

—

—

C₂²×C₈×C₇₁

—

C₄×D₄×C₇₁

C₂²

yes

characteristic

C₄⋊C₈×C₇₁

C₂²

yes

characteristic

C₂²⋊C₈×C₇₁

—

C₄×C₈×C₇₁

C₂²

yes

characteristic

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₂×D₄×C₇₁

D₄

yes

characteristic

C₂²×C₄×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

D₄

yes

characteristic

C₄⋊C₄×C₇₁

D₄

yes

characteristic

C₂²⋊C₄×C₇₁

—

C₄²×C₇₁

C₂³

yes

characteristic

C₂³×C₇₁

—

D₄×C₇₁

—

D₄×C₇₁

Q₁₆

yes

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×C₄×C₇₁

#41

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

—

Dic₁₄₂

—

Dic₁₄₂

—

Dic₁₄₂

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

C₇₁⋊C₈

—

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

#121

yes

characteristic

C₄×C₇₁

—

C₄×C₇₁

—

C₄×C₇₁

C₂×Q₁₆

yes

C₄×C₇₁

yes

C₄×C₇₁

yes

C₄×C₇₁

yes

Dic₇₁

—

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

yes

C₂×C₇₁

yes

C₂×C₇₁

yes

—

C₇₁

yes

characteristic, complemented, Sylow

#487

—

#476

—

#474

—

C₈×D₄

D₇₁

yes

—

—

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄×D₄

C₂×D₇₁

yes

characteristic

#107

—

142

—

#106

—

142

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₇₁

yes

characteristic

#103

—

142

—

#103

—

142

—

#102

—

142

—

#102

—

142

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₇₁

yes

characteristic

C₂×Q₈

—

142

—

100

C₂×Q₈

—

142

—

101

C₂×D₄

D₂₈₄

yes

characteristic

102

C₂²×C₄

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

142

—

106

C₂×C₈

—

142

—

107

C₂×C₈

C₂²⋊D₇₁

yes

characteristic

108

C₂×C₈

C₂²⋊D₇₁

yes

characteristic

109

C₄⋊C₄

—

142

—

110

C₄⋊C₄

—

142

—

111

C₄⋊C₄

—

142

—

112

C₄⋊C₄

—

142

—

113

C₄⋊C₄

D₂₈₄

yes

characteristic

114

C₂²⋊C₄

—

115

C₄²

C₂²×D₇₁

yes

characteristic

116

C₂³

—

117

Q₈

—

284

—

118

Q₈

—

284

—

119

Q₈

—

568

—

120

D₄

—

121

D₄

Dic₂₈₄

yes

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

284

—

126

C₂×C₄

—

284

—

127

C₂×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

128

C₂×C₄

C₂×D₂₈₄

yes

characteristic

129

C₂×C₄

#11765865

yes

characteristic

130

C₈

—

131

C₈

—

132

C₈

—

133

C₈

—

284

—

134

C₈

—

284

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

#14556102

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

568

—

142

C₄

—

568

—

143

C₄

C₂×Dic₂₈₄

yes

characteristic

144

C₄

#14556148

yes

characteristic

145

C₄

#14556150

yes

characteristic

146

C₄

#14556154

yes

characteristic

147

C₂

—

148

C₂

#17986214

yes

characteristic

149

C₂

#17986240

yes

characteristic

150

C₂

#17986262

yes

characteristic

	subgroup	G/H
center	C₂²	#14556102
commutator	C₄²×C₇₁	C₂³
Frattini	C₄²	C₂²×D₇₁
Fitting	C₈×D₄×C₇₁	C₂
socle	C₂²×C₇₁	#121
hypercenter	C₈×D₄	D₇₁
hypocenter	C₇₁	#1683
LCS	G ▷ C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈×D₄

subgroup

G/H

center

C₂²

#14556102

commutator

C₄²×C₇₁

C₂³

Frattini

C₄²

C₂²×D₇₁

Fitting

C₈×D₄×C₇₁

C₂

socle

C₂²×C₇₁

#121

hypercenter

C₈×D₄

D₇₁

hypocenter

C₇₁

#1683

LCS

G ▷ C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈×D₄

N	H ≅ G/N	type
1. #17986350	C₂	semidirect
4. #17985752	C₂	semidirect
5. #17985747	C₂	semidirect
6. #17985746	C₂	semidirect
76. C₇₁	#1683	semidirect

H ≅ G/N

type

1. #17986350

C₂

semidirect

4. #17985752

C₂

semidirect

5. #17985747

C₂

semidirect

6. #17985746

C₂

semidirect

76. C₇₁

#1683

semidirect

Subgroups — #22587791

Conjugacy classes of subgroups

Complements