Group #21425936 — subgroups

Subgroups — #21425936

Order 7552.

144 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 65 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	#16837818	C₂	1	1	yes	maximal, characteristic, complemented
2	#16837517	C₂	1	1	yes	maximal, characteristic
3	#16837222	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837187	C₂	1	1	yes	maximal, characteristic, complemented
5	#16837186	C₂	1	1	yes	maximal, characteristic, complemented
6	#16837177	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#504	C₂	1	1	yes	maximal, characteristic, complemented
8	#14273747	C₄	1	1	yes	characteristic
9	#14273733	C₂²	1	1	yes	characteristic
10	#14273667	C₂²	1	1	yes	characteristic
11	#14273666	—	2	1	no	—
12	C₂×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
13	C₁₆×D₅₉	—	2	1	no	—
14	#14273662	C₄	1	1	yes	characteristic
15	#14273654	C₄	1	1	yes	characteristic
16	#14273653	C₄	1	1	yes	characteristic
17	C₈×Dic₅₉	C₂²	1	1	yes	characteristic
18	#131×C₅₉	C₂²	1	1	yes	characteristic
19	M₃₂×C₅₉	—	2	1	no	—
20	M₃₂×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₆×C₅₉	—	2	1	no	—
22	C₂×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
23	#41×C₅₉	C₂×C₄	1	1	yes	characteristic
24	#11745685	C₂×C₄	1	1	yes	characteristic
25	M₁₆×C₅₉	—	2	1	no	—
26	M₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×C₅₉	—	2	1	no	—
28	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
29	#11745672	C₈	1	1	yes	characteristic
30	#11745671	C₈	1	1	yes	characteristic
31	#11745670	C₈	1	1	yes	characteristic
32	#11745669	C₈	1	1	yes	characteristic
33	C₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
34	#11745664	C₂×C₄	1	1	yes	characteristic
35	C₂×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
36	#11745659	—	2	1	no	—
37	C₈×D₅₉	—	2	1	no	—
38	C₁₆×C₅₉	—	2	1	no	—
39	C₁₆×C₅₉	D₄	1	1	yes	characteristic
40	C₁₆×C₅₉	D₄	1	1	yes	characteristic
41	C₅₉⋊C₁₆	—	2	1	no	—
42	C₅₉⋊C₁₆	—	2	1	no	—
43	Q₈×C₅₉	C₂×C₈	1	1	yes	characteristic
44	D₄×C₅₉	—	2	1	no	—
45	D₄×C₅₉	C₂×C₈	1	1	yes	characteristic
46	C₂×C₄×C₅₉	—	2	1	no	—
47	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
48	C₂²⋊D₅₉	—	2	1	no	—
49	C₂×Dic₅₉	—	2	1	no	—
50	D₂₃₆	C₂×C₈	1	1	yes	characteristic
51	C₄×D₅₉	—	2	1	no	—
52	Dic₁₁₈	C₂×C₈	1	1	yes	characteristic
53	C₈×C₅₉	—	2	1	no	—
54	C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
55	C₈×C₅₉	#41	1	1	yes	characteristic
56	C₅₉⋊C₈	—	2	1	no	—
57	C₅₉⋊C₈	C₂×C₈	1	1	yes	characteristic
58	C₅₉⋊C₈	C₂×C₈	1	1	yes	characteristic
59	C₂²×C₅₉	—	2	1	no	—
60	C₂²×C₅₉	#131	1	1	yes	characteristic
61	C₂×D₅₉	—	2	1	no	—
62	C₄×C₅₉	—	2	1	no	—
63	C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
64	C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
65	Dic₅₉	—	2	1	no	—
66	Dic₅₉	—	4	1	no	—
67	#2171	—	59	1	no	maximal, Sylow
68	C₂×C₅₉	—	2	1	no	—
69	C₂×C₅₉	—	4	1	no	—
70	C₂×C₅₉	C₈×D₄	1	1	yes	characteristic
71	D₅₉	—	4	1	no	—
72	#504	—	59	1	no	—
73	#504	D₅₉	1	1	yes	characteristic, complemented
74	#443	—	59	1	no	—
75	#364	—	59	1	no	—
76	#350	—	59	1	no	—
77	#350	—	59	1	no	—
78	#346	—	59	1	no	—
79	C₅₉	#2171	1	1	yes	characteristic, complemented, Sylow
80	#135	—	59	1	no	—
81	#131	—	59	1	no	—
82	#131	C₂×D₅₉	1	1	yes	characteristic
83	M₃₂	—	2	1	no	—
84	M₃₂	—	59	1	no	—
85	M₃₂	—	118	1	no	—
86	M₃₂	C₂×D₅₉	1	1	yes	characteristic
87	C₂×C₁₆	—	2	1	no	—
88	C₂×C₁₆	—	59	1	no	—
89	C₂×C₁₆	—	118	1	no	—
90	C₂×C₁₆	C₂×D₅₉	1	1	yes	characteristic
91	#108	—	59	1	no	—
92	#104	—	59	1	no	—
93	#104	—	59	1	no	—
94	C₄×C₈	—	59	1	no	—
95	#41	—	59	1	no	—
96	#41	C₄×D₅₉	1	1	yes	characteristic
97	Q₁₆	—	59	1	no	—
98	SD₁₆	—	59	1	no	—
99	SD₁₆	—	59	1	no	—
100	D₈	—	59	1	no	—
101	M₁₆	—	2	1	no	—
102	M₁₆	—	59	1	no	—
103	M₁₆	—	118	1	no	—
104	M₁₆	C₄×D₅₉	1	1	yes	characteristic
105	C₂×C₈	—	2	1	no	—
106	C₂×C₈	—	59	1	no	—
107	C₂×C₈	—	118	1	no	—
108	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
109	C₄²	—	59	1	no	—
110	C₁₆	—	2	1	no	—
111	C₁₆	—	118	1	no	—
112	C₁₆	—	118	1	no	—
113	C₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
114	C₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
115	Q₈	—	59	1	no	—
116	Q₈	C₈×D₅₉	1	1	yes	characteristic
117	D₄	—	2	1	no	—
118	D₄	—	59	1	no	—
119	D₄	—	118	1	no	—
120	D₄	C₈×D₅₉	1	1	yes	characteristic
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	118	1	no	—
123	C₂×C₄	—	118	1	no	—
124	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
125	C₈	—	2	1	no	—
126	C₈	—	59	1	no	—
127	C₈	—	59	1	no	—
128	C₈	—	118	1	no	—
129	C₈	#11745685	1	1	yes	characteristic
130	C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
131	C₂²	—	2	1	no	—
132	C₂²	—	118	1	no	—
133	C₂²	#14273733	1	1	yes	characteristic
134	C₄	—	2	1	no	—
135	C₄	—	118	1	no	—
136	C₄	—	236	1	no	—
137	C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
138	C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
139	C₂	—	2	1	no	—
140	C₂	—	4	1	no	—
141	C₂	—	236	1	no	—
142	C₂	C₈×C₂²⋊D₅₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837818

C₂

yes

maximal, characteristic, complemented

#16837517

C₂

yes

maximal, characteristic

#16837222

C₂

yes

maximal, characteristic, complemented

#16837187

C₂

yes

maximal, characteristic, complemented

#16837186

C₂

yes

maximal, characteristic, complemented

#16837177

C₂

yes

maximal, characteristic, complemented

C₅₉×#504

C₂

yes

maximal, characteristic, complemented

#14273747

C₄

yes

characteristic

#14273733

C₂²

yes

characteristic

#14273667

C₂²

yes

characteristic

#14273666

—

C₂×C₅₉⋊C₁₆

C₂²

yes

characteristic

C₁₆×D₅₉

—

#14273662

C₄

yes

characteristic

#14273654

C₄

yes

characteristic

#14273653

C₄

yes

characteristic

C₈×Dic₅₉

C₂²

yes

characteristic

#131×C₅₉

C₂²

yes

characteristic

M₃₂×C₅₉

—

M₃₂×C₅₉

C₂²

yes

characteristic

C₂×C₁₆×C₅₉

—

C₂×C₁₆×C₅₉

C₂²

yes

characteristic

#41×C₅₉

C₂×C₄

yes

characteristic

#11745685

C₂×C₄

yes

characteristic

M₁₆×C₅₉

—

M₁₆×C₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂³

yes

characteristic

#11745672

C₈

yes

characteristic

#11745671

C₈

yes

characteristic

#11745670

C₈

yes

characteristic

#11745669

C₈

yes

characteristic

C₄×Dic₅₉

C₂×C₄

yes

characteristic

#11745664

C₂×C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₂×C₄

yes

characteristic

#11745659

—

C₈×D₅₉

—

C₁₆×C₅₉

—

C₁₆×C₅₉

D₄

yes

characteristic

C₁₆×C₅₉

D₄

yes

characteristic

C₅₉⋊C₁₆

—

C₅₉⋊C₁₆

—

Q₈×C₅₉

C₂×C₈

yes

characteristic

D₄×C₅₉

—

D₄×C₅₉

C₂×C₈

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂²⋊D₅₉

—

C₂×Dic₅₉

—

D₂₃₆

C₂×C₈

yes

characteristic

C₄×D₅₉

—

Dic₁₁₈

C₂×C₈

yes

characteristic

C₈×C₅₉

—

C₈×C₅₉

C₂×D₄

yes

characteristic

C₈×C₅₉

#41

yes

characteristic

C₅₉⋊C₈

—

C₅₉⋊C₈

C₂×C₈

yes

characteristic

C₅₉⋊C₈

C₂×C₈

yes

characteristic

C₂²×C₅₉

—

C₂²×C₅₉

#131

yes

characteristic

C₂×D₅₉

—

C₄×C₅₉

—

C₄×C₅₉

C₄×D₄

yes

characteristic

C₄×C₅₉

C₂²×C₈

yes

characteristic

Dic₅₉

—

Dic₅₉

—

#2171

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

C₈×D₄

yes

characteristic

D₅₉

—

#504

—

#504

D₅₉

yes

characteristic, complemented

—

—

—

—

—

C₅₉

#2171

yes

characteristic, complemented, Sylow

#135

—

#131

—

#131

C₂×D₅₉

yes

characteristic

M₃₂

—

M₃₂

—

M₃₂

—

118

—

M₃₂

C₂×D₅₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

118

—

C₂×C₁₆

C₂×D₅₉

yes

—

—

—

C₄×C₈

—

#41

—

#41

C₄×D₅₉

yes

characteristic

Q₁₆

—

SD₁₆

—

SD₁₆

—

100

D₈

—

101

M₁₆

—

102

M₁₆

—

103

M₁₆

—

118

—

104

M₁₆

C₄×D₅₉

yes

characteristic

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

118

—

108

C₂×C₈

C₂²×D₅₉

yes

characteristic

109

C₄²

—

110

C₁₆

—

111

C₁₆

—

118

—

112

C₁₆

—

118

—

113

C₁₆

C₂²⋊D₅₉

yes

characteristic

114

C₁₆

C₂²⋊D₅₉

yes

characteristic

115

Q₈

—

116

Q₈

C₈×D₅₉

yes

characteristic

117

D₄

—

118

D₄

—

119

D₄

—

118

—

120

D₄

C₈×D₅₉

yes

characteristic

121

C₂×C₄

—

122

C₂×C₄

—

118

—

123

C₂×C₄

—

118

—

124

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

—

118

—

129

C₈

#11745685

yes

characteristic

130

C₈

C₂×C₂²⋊D₅₉

yes

characteristic

131

C₂²

—

132

C₂²

—

118

—

133

C₂²

#14273733

yes

characteristic

134

C₄

—

135

C₄

—

118

—

136

C₄

—

236

—

137

C₄

C₄×C₂²⋊D₅₉

yes

characteristic

138

C₄

C₂×C₈×D₅₉

yes

characteristic

139

C₂

—

140

C₂

—

141

C₂

—

236

—

142

C₂

C₈×C₂²⋊D₅₉

yes

characteristic

	subgroup	G/H
center	C₈	C₂×C₂²⋊D₅₉
commutator	C₄×C₅₉	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#504	C₂
socle	C₂×C₅₉	C₈×D₄
hypercenter	#504	D₅₉
hypocenter	C₅₉	#2171
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ #504

subgroup

G/H

center

C₈

C₂×C₂²⋊D₅₉

commutator

C₄×C₅₉

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₅₉

Fitting

C₅₉×#504

C₂

socle

C₂×C₅₉

C₈×D₄

D₅₉

C₅₉

G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ #504

N	H ≅ G/N	type
1. #16837818	C₂	semidirect
3. #16837222	C₂	semidirect
4. #16837187	C₂	semidirect
5. #16837186	C₂	semidirect
6. #16837177	C₂	semidirect
7. C₅₉×#504	C₂	semidirect
73. #504	D₅₉	semidirect
79. C₅₉	#2171	semidirect

H ≅ G/N

type

1. #16837818

C₂

semidirect

3. #16837222

C₂

semidirect

4. #16837187

C₂

semidirect

5. #16837186

C₂

semidirect

6. #16837177

C₂

semidirect

7. C₅₉×#504

C₂

semidirect

73. #504

D₅₉

semidirect

79. C₅₉

#2171

semidirect

Subgroups — #21425936

Conjugacy classes of subgroups

Complements