Group #22590599 — subgroups

Subgroups — #22590599

Order 9088.

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

normal subgroups only

This group has 184 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	C₂×#14556074	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14556072	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14556071	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14556069	C₂	1	1	yes	maximal, characteristic
5	#17986383	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×C₇₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	#495×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₂₈₄	C₂²	1	1	yes	characteristic
9	C₂×#11765854	—	2	1	no	—
10	C₂×D₅₆₈	C₂²	1	1	yes	characteristic
11	#14556116	—	2	1	no	—
12	#14556074	—	2	2	no	—
13	#14556072	—	2	2	no	—
14	#14556071	—	2	2	no	—
15	#14556069	—	2	2	no	—
16	C₂×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
18	C₂×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
19	C₂×SD₁₆×C₇₁	—	2	1	no	—
20	C₂×D₈×C₇₁	C₂²	1	1	yes	characteristic
21	#124×C₇₁	—	2	1	no	—
22	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
23	C₂×Dic₁₄₂	—	2	1	no	—
24	C₂×D₂₈₄	—	2	1	no	—
25	Dic₂₈₄	—	2	1	no	—
26	Dic₂₈₄	—	2	1	no	—
27	#11765854	—	4	2	no	—
28	D₅₆₈	—	2	1	no	—
29	D₅₆₈	—	2	1	no	—
30	(C₂×D₇₁)⋊C₄	—	4	2	no	—
31	C₇₁⋊C₁₆	D₄	1	2	yes	—
32	C₇₁⋊C₁₆	D₄	1	2	yes	—
33	C₂×Q₈×C₇₁	—	2	1	no	—
34	C₂×D₄×C₇₁	—	2	1	no	—
35	Q₁₆×C₇₁	—	2	1	no	—
36	Q₁₆×C₇₁	—	2	1	no	—
37	SD₁₆×C₇₁	—	4	2	no	—
38	D₈×C₇₁	—	2	1	no	—
39	D₈×C₇₁	—	2	1	no	—
40	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
41	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
42	C₂²⋊C₄×C₇₁	—	4	2	no	—
43	C₄²×C₇₁	D₄	1	1	yes	characteristic
44	C₂³×C₇₁	—	4	1	no	—
45	C₂²×D₇₁	—	4	1	no	—
46	Q₈×C₇₁	—	4	1	no	—
47	Q₈×C₇₁	—	4	1	no	—
48	D₄×C₇₁	—	4	1	no	—
49	D₄×C₇₁	—	4	1	no	—
50	C₂×C₄×C₇₁	—	4	1	no	—
51	C₂×C₄×C₇₁	D₈	1	2	yes	—
52	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
53	C₂×Dic₇₁	—	4	1	no	—
54	D₂₈₄	—	4	1	no	—
55	D₂₈₄	—	4	1	no	—
56	Dic₁₄₂	—	4	1	no	—
57	Dic₁₄₂	—	4	1	no	—
58	C₈×C₇₁	D₈	1	2	yes	—
59	C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
60	C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₇₁	—	8	1	no	—
62	C₂²×C₇₁	—	8	2	no	—
63	C₂²×C₇₁	C₂×D₈	1	1	yes	characteristic
64	C₂×D₇₁	—	8	1	no	—
65	C₂×D₇₁	—	8	2	no	—
66	C₄×C₇₁	—	2	2	no	—
67	C₄×C₇₁	—	8	1	no	—
68	C₄×C₇₁	#127	1	1	yes	characteristic
69	C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
70	Dic₇₁	—	8	1	no	—
71	C₂×C₇₁	—	16	1	no	—
72	C₂×C₇₁	#493	1	1	yes	characteristic
73	C₂×C₇₁	#508	1	2	yes	—
74	D₇₁	—	16	1	no	—
75	#2249	—	71	1	no	maximal, Sylow
76	C₇₁	#2249	1	1	yes	characteristic, complemented, Sylow
77	C₂×Q₃₂	—	71	1	no	—
78	C₂×SD₃₂	—	71	1	no	—
79	C₂×SD₃₂	—	71	1	no	—
80	C₂×D₁₆	—	71	1	no	—
81	#495	—	71	1	no	—
82	#495	D₇₁	1	1	yes	characteristic, complemented
83	C₄×C₁₆	—	71	1	no	—
84	C₂×Q₁₆	—	71	1	no	—
85	C₂×Q₁₆	C₂×D₇₁	1	1	yes	characteristic
86	C₂×SD₁₆	—	2	1	no	—
87	C₂×SD₁₆	—	142	1	no	—
88	C₂×D₈	—	71	1	no	—
89	C₂×D₈	C₂×D₇₁	1	1	yes	characteristic
90	#124	—	2	1	no	—
91	#124	—	142	1	no	—
92	Q₃₂	—	142	2	no	—
93	SD₃₂	—	142	2	no	—
94	SD₃₂	—	142	2	no	—
95	D₁₆	—	142	2	no	—
96	C₂×C₁₆	—	71	1	no	—
97	C₂×C₁₆	—	71	1	no	—
98	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
99	C₂×Q₈	—	2	1	no	—
100	C₂×Q₈	—	142	1	no	—
101	C₂×D₄	—	2	1	no	—
102	C₂×D₄	—	142	1	no	—
103	Q₁₆	—	2	1	no	—
104	Q₁₆	—	2	1	no	—
105	Q₁₆	—	142	1	no	—
106	Q₁₆	—	142	1	no	—
107	SD₁₆	—	4	2	no	—
108	SD₁₆	—	284	2	no	—
109	D₈	—	2	1	no	—
110	D₈	—	2	1	no	—
111	D₈	—	142	1	no	—
112	D₈	—	142	1	no	—
113	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
114	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
115	C₂²⋊C₄	—	4	2	no	—
116	C₂²⋊C₄	—	284	2	no	—
117	C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
118	C₁₆	—	71	2	no	—
119	C₁₆	—	71	2	no	—
120	C₂³	—	4	1	no	—
121	C₂³	—	284	1	no	—
122	Q₈	—	4	1	no	—
123	Q₈	—	4	1	no	—
124	Q₈	—	284	1	no	—
125	Q₈	—	284	1	no	—
126	D₄	—	4	1	no	—
127	D₄	—	4	1	no	—
128	D₄	—	284	1	no	—
129	D₄	—	284	1	no	—
130	C₂×C₄	—	4	1	no	—
131	C₂×C₄	—	284	1	no	—
132	C₂×C₄	#11765850	1	2	yes	—
133	C₂×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
134	C₈	#11765850	1	2	yes	—
135	C₈	D₄×D₇₁	1	1	yes	characteristic
136	C₈	D₄×D₇₁	1	1	yes	characteristic
137	C₂²	—	8	1	no	—
138	C₂²	—	8	2	no	—
139	C₂²	—	568	1	no	—
140	C₂²	—	568	2	no	—
141	C₂²	C₂×#11765850	1	1	yes	characteristic
142	C₄	—	2	2	no	—
143	C₄	—	8	1	no	—
144	C₄	—	568	1	no	—
145	C₄	#14556124	1	1	yes	characteristic
146	C₄	C₂×#11765850	1	1	yes	characteristic
147	C₂	—	16	1	no	—
148	C₂	—	1136	1	no	—
149	C₂	#17986375	1	1	yes	characteristic
150	C₂	#17986429	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556074

C₂

yes

maximal, characteristic, complemented

C₂×#14556072

C₂

yes

maximal, characteristic, complemented

C₂×#14556071

C₂

yes

maximal, characteristic, complemented

C₂×#14556069

C₂

yes

maximal, characteristic

#17986383

C₂

yes

maximal, characteristic, complemented

C₄×C₇₁⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#495×C₇₁

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₈₄

C₂²

yes

characteristic

C₂×#11765854

—

C₂×D₅₆₈

C₂²

yes

—

—

—

—

—

C₂×C₇₁⋊C₁₆

C₂²

yes

characteristic

C₂×C₇₁⋊C₁₆

C₂²

yes

characteristic

C₂×Q₁₆×C₇₁

C₂²

yes

characteristic

C₂×SD₁₆×C₇₁

—

C₂×D₈×C₇₁

C₂²

yes

characteristic

#124×C₇₁

—

C₄×C₈×C₇₁

C₂²

yes

characteristic

C₂×Dic₁₄₂

—

C₂×D₂₈₄

—

Dic₂₈₄

—

Dic₂₈₄

—

#11765854

—

D₅₆₈

—

D₅₆₈

—

(C₂×D₇₁)⋊C₄

—

C₇₁⋊C₁₆

D₄

yes

—

C₇₁⋊C₁₆

D₄

yes

—

C₂×Q₈×C₇₁

—

C₂×D₄×C₇₁

—

Q₁₆×C₇₁

—

Q₁₆×C₇₁

—

SD₁₆×C₇₁

—

D₈×C₇₁

—

D₈×C₇₁

—

C₂×C₈×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₂²⋊C₄×C₇₁

—

C₄²×C₇₁

D₄

yes

characteristic

C₂³×C₇₁

—

C₂²×D₇₁

—

Q₈×C₇₁

—

Q₈×C₇₁

—

D₄×C₇₁

—

D₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

D₈

yes

—

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×Dic₇₁

—

D₂₈₄

—

D₂₈₄

—

Dic₁₄₂

—

Dic₁₄₂

—

C₈×C₇₁

D₈

yes

—

C₈×C₇₁

C₂×D₄

yes

characteristic

C₈×C₇₁

C₂×D₄

yes

characteristic

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

C₂×D₈

yes

characteristic

C₂×D₇₁

—

C₂×D₇₁

—

C₄×C₇₁

—

C₄×C₇₁

—

C₄×C₇₁

#127

yes

characteristic

C₄×C₇₁

C₂×D₈

yes

characteristic

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

#493

yes

characteristic

C₂×C₇₁

#508

yes

—

D₇₁

—

#2249

—

maximal, Sylow

C₇₁

#2249

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₂×SD₃₂

—

C₂×SD₃₂

—

C₂×D₁₆

—

#495

—

#495

D₇₁

yes

characteristic, complemented

C₄×C₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₇₁

yes

characteristic

C₂×SD₁₆

—

C₂×SD₁₆

—

142

—

C₂×D₈

—

C₂×D₈

C₂×D₇₁

yes

characteristic

#124

—

#124

—

142

—

Q₃₂

—

142

—

SD₃₂

—

142

—

SD₃₂

—

142

—

D₁₆

—

142

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄×C₈

C₂×D₇₁

yes

characteristic

C₂×Q₈

—

100

C₂×Q₈

—

142

—

101

C₂×D₄

—

102

C₂×D₄

—

142

—

103

Q₁₆

—

104

Q₁₆

—

105

Q₁₆

—

142

—

106

Q₁₆

—

142

—

107

SD₁₆

—

108

SD₁₆

—

284

—

109

D₈

—

110

D₈

—

111

D₈

—

142

—

112

D₈

—

142

—

113

C₂×C₈

C₂²⋊D₇₁

yes

characteristic

114

C₂×C₈

C₂²×D₇₁

yes

characteristic

115

C₂²⋊C₄

—

116

C₂²⋊C₄

—

284

—

117

C₄²

C₂²⋊D₇₁

yes

characteristic

118

C₁₆

—

119

C₁₆

—

120

C₂³

—

121

C₂³

—

284

—

122

Q₈

—

123

Q₈

—

124

Q₈

—

284

—

125

Q₈

—

284

—

126

D₄

—

127

D₄

—

128

D₄

—

284

—

129

D₄

—

284

—

130

C₂×C₄

—

131

C₂×C₄

—

284

—

132

C₂×C₄

#11765850

yes

—

133

C₂×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

134

C₈

#11765850

yes

—

135

C₈

D₄×D₇₁

yes

characteristic

136

C₈

D₄×D₇₁

yes

characteristic

137

C₂²

—

138

C₂²

—

139

C₂²

—

568

—

140

C₂²

—

568

—

141

C₂²

C₂×#11765850

yes

characteristic

142

C₄

—

143

C₄

—

144

C₄

—

568

—

145

C₄

#14556124

yes

characteristic

146

C₄

C₂×#11765850

yes

characteristic

147

C₂

—

148

C₂

—

1136

—

149

C₂

#17986375

yes

characteristic

150

C₂

#17986429

yes

—

	subgroup	G/H
center	C₂²	C₂×#11765850
commutator	C₂×C₈×C₇₁	C₂³
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	#495×C₇₁	C₂
socle	C₂²×C₇₁	C₂×D₈
hypercenter	#495	D₇₁
hypocenter	C₇₁	#2249
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

subgroup

G/H

center

C₂²

C₂×#11765850

commutator

C₂×C₈×C₇₁

C₂³

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

#495×C₇₁

C₂

socle

C₂²×C₇₁

C₂×D₈

D₇₁

C₇₁

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

N	H ≅ G/N	type
1. C₂×#14556074	C₂	semidirect
2. C₂×#14556072	C₂	semidirect
3. C₂×#14556071	C₂	semidirect
5. #17986383	C₂	semidirect
6. C₄×C₇₁⋊C₁₆	C₂	semidirect
7. #495×C₇₁	C₂	semidirect
76. C₇₁	#2249	semidirect
82. #495	D₇₁	semidirect

H ≅ G/N

type

1. C₂×#14556074

C₂

semidirect

2. C₂×#14556072

C₂

semidirect

3. C₂×#14556071

C₂

semidirect

5. #17986383

C₂

semidirect

6. C₄×C₇₁⋊C₁₆

C₂

semidirect

7. #495×C₇₁

C₂

semidirect

76. C₇₁

#2249

semidirect

82. #495

D₇₁

semidirect

Subgroups — #22590599

Conjugacy classes of subgroups

Complements