Group #22590464 — subgroups

Subgroups — #22590464

Order 9088.

140 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 43 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×#14556074	C₂	1	1	yes	maximal, characteristic, complemented
2	#17986417	C₂	1	1	yes	maximal, characteristic
3	#17986275	C₂	1	1	yes	maximal, characteristic
4	#17986271	C₂	1	1	yes	maximal, characteristic
5	#17985828	C₂	1	1	yes	maximal, characteristic, complemented
6	#17985816	C₂	1	1	yes	maximal, characteristic, complemented
7	#362×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#14556161	—	2	1	no	—
9	#14556159	—	2	1	no	—
10	C₂×Dic₂₈₄	C₂²	1	1	yes	characteristic
11	#14556134	C₂²	1	1	yes	characteristic
12	#14556074	—	2	1	no	—
13	#14556074	—	2	1	no	—
14	#14556067	—	2	1	no	—
15	C₂×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
16	C₁₆×D₇₁	—	2	1	no	—
17	#14556064	C₂²	1	1	yes	characteristic
18	#14556047	—	2	1	no	—
19	#14556046	—	2	1	no	—
20	C₂×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
21	M₃₂×C₇₁	C₂²	1	1	yes	characteristic
22	#108×C₇₁	C₂²	1	1	yes	characteristic
23	#11765865	D₄	1	1	yes	characteristic
24	C₂×Dic₁₄₂	—	2	1	no	—
25	Dic₂₈₄	—	2	1	no	—
26	Dic₂₈₄	—	2	1	no	—
27	Dic₂₈₄	—	4	1	no	—
28	#11765855	—	4	1	no	—
29	#11765854	—	4	1	no	—
30	#11765852	—	4	1	no	—
31	#11765849	—	2	1	no	—
32	#11765849	D₄	1	1	yes	characteristic
33	#11765848	—	2	1	no	—
34	C₈×D₇₁	—	2	1	no	—
35	C₇₁⋊C₁₆	D₄	1	1	yes	characteristic
36	C₇₁⋊C₁₆	D₄	1	1	yes	characteristic
37	C₂×Q₈×C₇₁	—	2	1	no	—
38	Q₁₆×C₇₁	—	2	1	no	—
39	Q₁₆×C₇₁	—	2	1	no	—
40	M₁₆×C₇₁	—	2	1	no	—
41	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
42	C₁₆×C₇₁	—	2	1	no	—
43	Q₈×C₇₁	—	4	1	no	—
44	Q₈×C₇₁	—	4	1	no	—
45	C₂×C₄×C₇₁	—	4	1	no	—
46	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
47	C₂²⋊D₇₁	—	2	1	no	—
48	C₂×Dic₇₁	—	4	1	no	—
49	D₂₈₄	D₈	1	1	yes	characteristic
50	C₄×D₇₁	—	2	1	no	—
51	Dic₁₄₂	—	4	1	no	—
52	Dic₁₄₂	—	4	1	no	—
53	Dic₁₄₂	D₈	1	1	yes	characteristic
54	C₈×C₇₁	—	4	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	C₇₁⋊C₈	—	4	1	no	—
59	C₂²×C₇₁	#135	1	1	yes	characteristic
60	C₂×D₇₁	—	2	1	no	—
61	C₄×C₇₁	—	8	1	no	—
62	C₄×C₇₁	#121	1	1	yes	characteristic
63	C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
64	Dic₇₁	—	2	1	no	—
65	Dic₇₁	—	8	1	no	—
66	C₂×C₇₁	—	2	1	no	—
67	C₂×C₇₁	#466	1	1	yes	characteristic
68	D₇₁	—	4	1	no	—
69	#2222	—	71	1	no	maximal, Sylow
70	C₇₁	#2222	1	1	yes	characteristic, complemented, Sylow
71	C₂×Q₃₂	—	71	1	no	—
72	#504	—	71	1	no	—
73	#473	—	71	1	no	—
74	#473	—	71	1	no	—
75	#368	—	71	1	no	—
76	#362	—	71	1	no	—
77	#362	D₇₁	1	1	yes	characteristic, complemented
78	#137	—	142	1	no	—
79	#137	—	142	1	no	—
80	C₂×Q₁₆	—	71	1	no	—
81	C₂×Q₁₆	C₂×D₇₁	1	1	yes	characteristic
82	#131	—	71	1	no	—
83	Q₃₂	—	142	1	no	—
84	Q₃₂	—	142	1	no	—
85	M₃₂	—	142	1	no	—
86	M₃₂	C₂×D₇₁	1	1	yes	characteristic
87	C₂×C₁₆	—	71	1	no	—
88	C₂×C₁₆	—	142	1	no	—
89	#108	—	71	1	no	—
90	#108	C₂×D₇₁	1	1	yes	characteristic
91	#101	—	142	1	no	—
92	#101	—	142	1	no	—
93	#41	—	71	1	no	—
94	C₂×Q₈	—	2	1	no	—
95	C₂×Q₈	—	142	1	no	—
96	Q₁₆	—	2	1	no	—
97	Q₁₆	—	2	1	no	—
98	Q₁₆	—	284	1	no	—
99	Q₁₆	—	284	1	no	—
100	Q₁₆	—	142	1	no	—
101	Q₁₆	—	142	1	no	—
102	SD₁₆	—	284	1	no	—
103	SD₁₆	—	284	1	no	—
104	M₁₆	—	2	1	no	—
105	M₁₆	—	71	1	no	—
106	M₁₆	—	142	1	no	—
107	M₁₆	—	142	1	no	—
108	C₂×C₈	—	142	1	no	—
109	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
110	C₁₆	—	2	1	no	—
111	C₁₆	—	71	1	no	—
112	C₁₆	—	71	1	no	—
113	Q₈	—	4	1	no	—
114	Q₈	—	4	1	no	—
115	Q₈	—	284	1	no	—
116	Q₈	—	284	1	no	—
117	Q₈	—	71	1	no	—
118	D₄	—	71	1	no	—
119	D₄	—	142	1	no	—
120	C₂×C₄	—	4	1	no	—
121	C₂×C₄	—	284	1	no	—
122	C₂×C₄	—	142	1	no	—
123	C₂×C₄	D₄×D₇₁	1	1	yes	characteristic
124	C₈	—	4	1	no	—
125	C₈	—	284	1	no	—
126	C₈	—	142	1	no	—
127	C₈	D₄×D₇₁	1	1	yes	characteristic
128	C₈	#11765865	1	1	yes	characteristic
129	C₂²	—	142	1	no	—
130	C₂²	#14556149	1	1	yes	characteristic
131	C₄	—	8	1	no	—
132	C₄	—	568	1	no	—
133	C₄	—	142	1	no	—
134	C₄	#14556101	1	1	yes	characteristic
135	C₄	D₈×D₇₁	1	1	yes	characteristic
136	C₂	—	2	1	no	—
137	C₂	—	284	1	no	—
138	C₂	#17986234	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556074

C₂

yes

maximal, characteristic, complemented

#17986417

C₂

yes

maximal, characteristic

#17986275

C₂

yes

maximal, characteristic

#17986271

C₂

yes

maximal, characteristic

#17985828

C₂

yes

maximal, characteristic, complemented

#17985816

C₂

yes

maximal, characteristic, complemented

#362×C₇₁

C₂

yes

maximal, characteristic, complemented

#14556161

—

#14556159

—

C₂×Dic₂₈₄

C₂²

yes

characteristic

#14556134

C₂²

yes

—

—

—

C₂×C₇₁⋊C₁₆

C₂²

yes

characteristic

C₁₆×D₇₁

—

#14556064

C₂²

yes

characteristic

#14556047

—

#14556046

—

C₂×Q₁₆×C₇₁

C₂²

yes

characteristic

M₃₂×C₇₁

C₂²

yes

characteristic

#108×C₇₁

C₂²

yes

characteristic

#11765865

D₄

yes

characteristic

C₂×Dic₁₄₂

—

Dic₂₈₄

—

Dic₂₈₄

—

Dic₂₈₄

—

—

—

—

—

D₄

yes

characteristic

#11765848

—

C₈×D₇₁

—

C₇₁⋊C₁₆

D₄

yes

characteristic

C₇₁⋊C₁₆

D₄

yes

characteristic

C₂×Q₈×C₇₁

—

Q₁₆×C₇₁

—

Q₁₆×C₇₁

—

M₁₆×C₇₁

—

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₁₆×C₇₁

—

Q₈×C₇₁

—

Q₈×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂²⋊D₇₁

—

C₂×Dic₇₁

—

D₂₈₄

D₈

yes

characteristic

C₄×D₇₁

—

Dic₁₄₂

—

Dic₁₄₂

—

Dic₁₄₂

D₈

yes

characteristic

C₈×C₇₁

—

C₈×C₇₁

C₂×D₄

yes

characteristic

C₈×C₇₁

#41

yes

characteristic

C₇₁⋊C₈

—

C₇₁⋊C₈

—

C₂²×C₇₁

#135

yes

characteristic

C₂×D₇₁

—

C₄×C₇₁

—

C₄×C₇₁

#121

yes

characteristic

C₄×C₇₁

C₂×D₈

yes

characteristic

Dic₇₁

—

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

#466

yes

characteristic

D₇₁

—

#2222

—

maximal, Sylow

C₇₁

#2222

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

—

—

—

—

—

D₇₁

yes

characteristic, complemented

#137

—

142

—

#137

—

142

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₇₁

yes

characteristic

#131

—

Q₃₂

—

142

—

Q₃₂

—

142

—

M₃₂

—

142

—

M₃₂

C₂×D₇₁

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

142

—

#108

—

#108

C₂×D₇₁

yes

characteristic

#101

—

142

—

#101

—

142

—

#41

—

C₂×Q₈

—

C₂×Q₈

—

142

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

284

—

Q₁₆

—

284

—

100

Q₁₆

—

142

—

101

Q₁₆

—

142

—

102

SD₁₆

—

284

—

103

SD₁₆

—

284

—

104

M₁₆

—

105

M₁₆

—

106

M₁₆

—

142

—

107

M₁₆

—

142

—

108

C₂×C₈

—

142

—

109

C₂×C₈

C₂²×D₇₁

yes

characteristic

110

C₁₆

—

111

C₁₆

—

112

C₁₆

—

113

Q₈

—

114

Q₈

—

115

Q₈

—

284

—

116

Q₈

—

284

—

117

Q₈

—

118

D₄

—

119

D₄

—

142

—

120

C₂×C₄

—

121

C₂×C₄

—

284

—

122

C₂×C₄

—

142

—

123

C₂×C₄

D₄×D₇₁

yes

characteristic

124

C₈

—

125

C₈

—

284

—

126

C₈

—

142

—

127

C₈

D₄×D₇₁

yes

characteristic

128

C₈

#11765865

yes

characteristic

129

C₂²

—

142

—

130

C₂²

#14556149

yes

characteristic

131

C₄

—

132

C₄

—

568

—

133

C₄

—

142

—

134

C₄

#14556101

yes

characteristic

135

C₄

D₈×D₇₁

yes

characteristic

136

C₂

—

137

C₂

—

284

—

138

C₂

#17986234

yes

characteristic

	subgroup	G/H
center	C₂	#17986234
commutator	C₂×C₈×C₇₁	C₂³
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	#362×C₇₁	C₂
socle	C₂×C₇₁	#466
hypercenter	#362	D₇₁
hypocenter	C₇₁	#2222
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #362

subgroup

G/H

center

C₂

#17986234

commutator

C₂×C₈×C₇₁

C₂³

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

#362×C₇₁

C₂

C₂×C₇₁

D₇₁

C₇₁

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #362

N	H ≅ G/N	type
1. C₂×#14556074	C₂	semidirect
5. #17985828	C₂	semidirect
6. #17985816	C₂	semidirect
7. #362×C₇₁	C₂	semidirect
70. C₇₁	#2222	semidirect
77. #362	D₇₁	semidirect

H ≅ G/N

type

1. C₂×#14556074

C₂

semidirect

5. #17985828

C₂

semidirect

6. #17985816

C₂

semidirect

7. #362×C₇₁

C₂

semidirect

70. C₇₁

#2222

semidirect

77. #362

D₇₁

semidirect

Subgroups — #22590464

Conjugacy classes of subgroups

Complements