Group #21426150 — subgroups

Subgroups — #21426150

Order 7552.

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×#14273672	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14273668	C₂	1	1	yes	maximal, characteristic
3	#16837785	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837484	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₅₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#16837205	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₂₃₆	C₂²	1	1	yes	characteristic
9	C₂×#11745670	—	2	1	no	—
10	C₂×D₄₇₂	C₂²	1	1	yes	characteristic
11	#14273714	—	2	1	no	—
12	#14273689	—	2	1	no	—
13	#14273672	—	2	2	no	—
14	#14273668	—	2	2	no	—
15	C₂×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
16	#14273647	—	2	1	no	—
17	C₈×Dic₅₉	C₂²	1	1	yes	characteristic
18	C₂×D₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
20	#107×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×D₄×C₅₉	—	2	1	no	—
22	C₂×D₂₃₆	—	2	1	no	—
23	C₂×C₄×D₅₉	—	4	1	no	—
24	C₂×Dic₁₁₈	—	2	1	no	—
25	D₈×C₅₉	—	2	1	no	—
26	D₈×C₅₉	—	2	1	no	—
27	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
28	C₄⋊C₄×C₅₉	—	2	1	no	—
29	C₂²⋊Dic₅₉	—	4	1	no	—
30	C₂²⋊Dic₅₉	—	4	1	no	—
31	#11745670	—	4	2	no	—
32	(C₂×D₅₉)⋊C₄	—	4	1	no	—
33	C₄×Dic₅₉	D₄	1	1	yes	characteristic
34	C₂×C₅₉⋊C₈	D₄	1	1	yes	characteristic
35	Dic₂₃₆	—	2	1	no	—
36	Dic₂₃₆	—	2	1	no	—
37	D₄₇₂	—	2	1	no	—
38	D₄₇₂	D₄	1	2	yes	—
39	C₁₆×C₅₉	—	2	1	no	—
40	C₅₉⋊C₁₆	—	2	1	no	—
41	C₂³×C₅₉	—	4	1	no	—
42	C₂²×D₅₉	—	4	1	no	—
43	D₄×C₅₉	—	4	1	no	—
44	D₄×C₅₉	—	4	1	no	—
45	C₂×C₄×C₅₉	—	4	1	no	—
46	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
47	C₂×Dic₅₉	—	4	1	no	—
48	C₂×Dic₅₉	D₈	1	1	yes	characteristic
49	C₂×Dic₅₉	D₈	1	1	yes	characteristic
50	D₂₃₆	—	2	2	no	—
51	D₂₃₆	—	4	1	no	—
52	C₄×D₅₉	—	8	2	no	—
53	Dic₁₁₈	—	4	1	no	—
54	Dic₁₁₈	—	4	1	no	—
55	C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
56	C₈×C₅₉	#41	1	1	yes	characteristic
57	C₅₉⋊C₈	—	2	1	no	—
58	C₂²×C₅₉	—	8	1	no	—
59	C₂²×C₅₉	—	8	1	no	—
60	C₂²×C₅₉	—	8	1	no	—
61	C₂²×C₅₉	C₂×D₈	1	1	yes	characteristic
62	C₂×D₅₉	—	4	2	no	—
63	C₂×D₅₉	—	8	1	no	—
64	C₂×D₅₉	—	8	1	no	—
65	C₄×C₅₉	—	8	1	no	—
66	C₄×C₅₉	#121	1	1	yes	characteristic
67	C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
68	Dic₅₉	—	2	1	no	—
69	Dic₅₉	—	2	1	no	—
70	Dic₅₉	—	8	1	no	—
71	#2210	—	59	1	no	maximal, Sylow
72	C₂×C₅₉	—	16	1	no	—
73	C₂×C₅₉	#459	1	1	yes	characteristic
74	C₂×C₅₉	#508	1	1	yes	characteristic
75	C₂×C₅₉	#509	1	1	yes	characteristic
76	D₅₉	—	8	2	no	—
77	C₂×SD₃₂	—	59	1	no	—
78	C₂×D₁₆	—	59	1	no	—
79	#495	—	59	1	no	—
80	C₄×D₈	—	59	1	no	—
81	C₄⋊C₁₆	—	59	1	no	—
82	#358	—	59	1	no	—
83	#357	D₅₉	1	1	yes	characteristic, complemented
84	C₅₉	#2210	1	1	yes	characteristic, complemented, Sylow
85	C₂×Q₁₆	—	59	1	no	—
86	C₂×SD₁₆	—	118	1	no	—
87	C₂×D₈	—	59	1	no	—
88	C₂×D₈	C₂×D₅₉	1	1	yes	characteristic
89	#124	—	118	1	no	—
90	C₄×D₄	—	118	1	no	—
91	SD₃₂	—	118	2	no	—
92	D₁₆	—	118	2	no	—
93	C₂×C₁₆	—	59	1	no	—
94	C₂×C₁₆	C₂×D₅₉	1	1	yes	characteristic
95	#107	C₂×D₅₉	1	1	yes	characteristic
96	#102	—	118	1	no	—
97	C₄×C₈	—	59	1	no	—
98	C₂×Q₈	—	118	1	no	—
99	C₂×D₄	—	2	1	no	—
100	C₂×D₄	—	118	1	no	—
101	C₂²×C₄	—	236	1	no	—
102	Q₁₆	—	118	1	no	—
103	Q₁₆	—	118	1	no	—
104	SD₁₆	—	236	2	no	—
105	D₈	—	2	1	no	—
106	D₈	—	2	1	no	—
107	D₈	—	59	2	no	—
108	D₈	—	118	1	no	—
109	C₂×C₈	—	59	1	no	—
110	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
111	C₄⋊C₄	—	2	1	no	—
112	C₂²⋊C₄	—	236	1	no	—
113	C₂²⋊C₄	—	236	1	no	—
114	C₂²⋊C₄	—	236	1	no	—
115	C₄²	—	59	1	no	—
116	C₁₆	—	2	1	no	—
117	C₁₆	—	118	1	no	—
118	C₂³	—	4	1	no	—
119	C₂³	—	236	1	no	—
120	Q₈	—	236	1	no	—
121	Q₈	—	236	1	no	—
122	D₄	—	4	1	no	—
123	D₄	—	4	1	no	—
124	D₄	—	118	2	no	—
125	D₄	—	236	1	no	—
126	C₂×C₄	—	4	1	no	—
127	C₂×C₄	—	59	1	no	—
128	C₂×C₄	—	59	1	no	—
129	C₂×C₄	—	472	2	no	—
130	C₂×C₄	—	236	1	no	—
131	C₂×C₄	D₄×D₅₉	1	1	yes	characteristic
132	C₈	—	118	1	no	—
133	C₈	#11745685	1	1	yes	characteristic
134	C₈	D₄×D₅₉	1	1	yes	characteristic
135	C₂²	—	8	1	no	—
136	C₂²	—	8	1	no	—
137	C₂²	—	8	1	no	—
138	C₂²	—	472	1	no	—
139	C₂²	—	472	1	no	—
140	C₂²	—	236	2	no	—
141	C₂²	D₈×D₅₉	1	1	yes	characteristic
142	C₄	—	8	1	no	—
143	C₄	—	118	1	no	—
144	C₄	—	118	1	no	—
145	C₄	—	472	1	no	—
146	C₄	#14273700	1	1	yes	characteristic
147	C₄	#14273754	1	1	yes	characteristic
148	C₂	—	16	1	no	—
149	C₂	—	472	2	no	—
150	C₂	#16837596	1	1	yes	characteristic
151	C₂	#16837833	1	1	yes	characteristic
152	C₂	#16837836	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273672

C₂

yes

maximal, characteristic, complemented

C₂×#14273668

C₂

yes

maximal, characteristic

#16837785

C₂

yes

maximal, characteristic, complemented

#16837484

C₂

yes

maximal, characteristic, complemented

Dic₅₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#16837205

C₂

yes

maximal, characteristic, complemented

C₅₉×#357

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₃₆

C₂²

yes

characteristic

C₂×#11745670

—

C₂×D₄₇₂

C₂²

yes

—

—

—

—

C₂×C₅₉⋊C₁₆

C₂²

yes

characteristic

#14273647

—

C₈×Dic₅₉

C₂²

yes

characteristic

C₂×D₈×C₅₉

C₂²

yes

characteristic

C₂×C₁₆×C₅₉

C₂²

yes

characteristic

#107×C₅₉

C₂²

yes

characteristic

C₂×D₄×C₅₉

—

C₂×D₂₃₆

—

C₂×C₄×D₅₉

—

C₂×Dic₁₁₈

—

D₈×C₅₉

—

D₈×C₅₉

—

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₄⋊C₄×C₅₉

—

C₂²⋊Dic₅₉

—

C₂²⋊Dic₅₉

—

#11745670

—

(C₂×D₅₉)⋊C₄

—

C₄×Dic₅₉

D₄

yes

characteristic

C₂×C₅₉⋊C₈

D₄

yes

characteristic

Dic₂₃₆

—

Dic₂₃₆

—

D₄₇₂

—

D₄₇₂

D₄

yes

—

C₁₆×C₅₉

—

C₅₉⋊C₁₆

—

C₂³×C₅₉

—

C₂²×D₅₉

—

D₄×C₅₉

—

D₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

D₈

yes

characteristic

C₂×Dic₅₉

D₈

yes

characteristic

D₂₃₆

—

D₂₃₆

—

C₄×D₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

C₂×D₄

yes

characteristic

C₈×C₅₉

#41

yes

characteristic

C₅₉⋊C₈

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂×D₈

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

—

C₂×D₅₉

—

C₄×C₅₉

—

C₄×C₅₉

yes

C₄×C₅₉

yes

Dic₅₉

—

Dic₅₉

—

Dic₅₉

—

#2210

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

yes

C₂×C₅₉

yes

C₂×C₅₉

yes

D₅₉

—

C₂×SD₃₂

—

C₂×D₁₆

—

#495

—

C₄×D₈

—

C₄⋊C₁₆

—

#358

—

#357

D₅₉

yes

characteristic, complemented

C₅₉

#2210

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×SD₁₆

—

118

—

C₂×D₈

—

C₂×D₈

C₂×D₅₉

yes

characteristic

#124

—

118

—

C₄×D₄

—

118

—

SD₃₂

—

118

—

D₁₆

—

118

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₅₉

yes

characteristic

#107

C₂×D₅₉

yes

characteristic

#102

—

118

—

C₄×C₈

—

C₂×Q₈

—

118

—

C₂×D₄

—

100

C₂×D₄

—

118

—

101

C₂²×C₄

—

236

—

102

Q₁₆

—

118

—

103

Q₁₆

—

118

—

104

SD₁₆

—

236

—

105

D₈

—

106

D₈

—

107

D₈

—

108

D₈

—

118

—

109

C₂×C₈

—

110

C₂×C₈

C₂²×D₅₉

yes

characteristic

111

C₄⋊C₄

—

112

C₂²⋊C₄

—

236

—

113

C₂²⋊C₄

—

236

—

114

C₂²⋊C₄

—

236

—

115

C₄²

—

116

C₁₆

—

117

C₁₆

—

118

—

118

C₂³

—

119

C₂³

—

236

—

120

Q₈

—

236

—

121

Q₈

—

236

—

122

D₄

—

123

D₄

—

124

D₄

—

118

—

125

D₄

—

236

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

472

—

130

C₂×C₄

—

236

—

131

C₂×C₄

D₄×D₅₉

yes

characteristic

132

C₈

—

118

—

133

C₈

#11745685

yes

characteristic

134

C₈

D₄×D₅₉

yes

characteristic

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

472

—

139

C₂²

—

472

—

140

C₂²

—

236

—

141

C₂²

D₈×D₅₉

yes

characteristic

142

C₄

—

143

C₄

—

118

—

144

C₄

—

118

—

145

C₄

—

472

—

146

C₄

#14273700

yes

characteristic

147

C₄

#14273754

yes

characteristic

148

C₂

—

149

C₂

—

472

—

150

C₂

#16837596

yes

characteristic

151

C₂

#16837833

yes

characteristic

152

C₂

#16837836

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₅₉
commutator	C₂×C₈×C₅₉	C₂³
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#357	C₂
socle	C₂²×C₅₉	C₂×D₈
hypercenter	#357	D₅₉
hypocenter	C₅₉	#2210
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₅₉

commutator

C₂×C₈×C₅₉

C₂³

Frattini

C₂×C₈

C₂²×D₅₉

Fitting

C₅₉×#357

C₂

socle

C₂²×C₅₉

C₂×D₈

D₅₉

C₅₉

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
1. C₂×#14273672	C₂	semidirect
3. #16837785	C₂	semidirect
4. #16837484	C₂	semidirect
5. Dic₅₉⋊C₁₆	C₂	semidirect
6. #16837205	C₂	semidirect
7. C₅₉×#357	C₂	semidirect
83. #357	D₅₉	semidirect
84. C₅₉	#2210	semidirect

H ≅ G/N

type

1. C₂×#14273672

C₂

semidirect

3. #16837785

C₂

semidirect

4. #16837484

C₂

semidirect

5. Dic₅₉⋊C₁₆

C₂

semidirect

6. #16837205

C₂

semidirect

7. C₅₉×#357

C₂

semidirect

83. #357

D₅₉

semidirect

84. C₅₉

#2210

semidirect

Subgroups — #21426150

Conjugacy classes of subgroups

Complements