Group #21425838 — subgroups

Subgroups — #362×D₅₉ #21425838

Order 7552.

216 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 67 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×Q₁₆×D₅₉	C₂	1	1	yes	maximal, characteristic
2	M₃₂×D₅₉	C₂	1	1	yes	maximal, characteristic
3	#108×D₅₉	C₂	1	1	yes	maximal, characteristic
4	#16837219	C₂	1	1	yes	maximal, characteristic, complemented
5	#16837218	C₂	1	1	yes	maximal, characteristic, complemented
6	#16837217	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#362	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×D₅₉	—	2	1	no	—
9	C₂×Dic₂₃₆	C₂²	1	1	yes	characteristic
10	C₂×#11745672	—	2	1	no	—
11	Q₁₆×D₅₉	—	2	1	no	—
12	Q₁₆×D₅₉	—	2	1	no	—
13	Q₁₆×D₅₉	C₄	1	2	yes	—
14	Q₁₆×D₅₉	C₄	1	2	yes	—
15	M₁₆×D₅₉	—	2	1	no	—
16	C₂×C₈×D₅₉	C₂²	1	1	yes	characteristic
17	#14273667	C₂²	1	1	yes	characteristic
18	#14273666	—	2	1	no	—
19	C₁₆×D₅₉	—	2	1	no	—
20	#14273663	C₂²	1	1	yes	characteristic
21	#14273662	—	2	1	no	—
22	C₂×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
23	M₃₂×C₅₉	C₂²	1	1	yes	characteristic
24	#108×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×Q₈×C₅₉	—	2	1	no	—
26	Q₈×D₅₉	—	2	2	no	—
27	Q₈×D₅₉	—	2	2	no	—
28	Q₈×D₅₉	—	4	1	no	—
29	Q₈×D₅₉	—	4	1	no	—
30	C₂×C₄×D₅₉	—	4	1	no	—
31	C₂×C₄×D₅₉	D₄	1	1	yes	characteristic
32	C₂×Dic₁₁₈	—	2	1	no	—
33	C₂×Dic₁₁₈	—	4	1	no	—
34	Q₁₆×C₅₉	—	2	1	no	—
35	Q₁₆×C₅₉	C₂×C₄	1	2	yes	—
36	M₁₆×C₅₉	—	2	1	no	—
37	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
38	#11745672	—	2	2	no	—
39	#11745672	—	2	2	no	—
40	#11745664	—	2	1	no	—
41	C₂×C₅₉⋊C₈	D₄	1	1	yes	characteristic
42	Dic₂₃₆	—	2	1	no	—
43	Dic₂₃₆	C₂×C₄	1	2	yes	—
44	#11745659	—	4	1	no	—
45	C₈×D₅₉	—	4	1	no	—
46	C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
47	C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
48	C₈×D₅₉	D₄	1	1	yes	characteristic
49	C₈×D₅₉	D₄	1	1	yes	characteristic
50	C₁₆×C₅₉	—	2	1	no	—
51	C₅₉⋊C₁₆	—	2	1	no	—
52	C₂²×D₅₉	SD₁₆	1	1	yes	characteristic
53	Q₈×C₅₉	—	2	2	no	—
54	Q₈×C₅₉	—	4	1	no	—
55	C₂×C₄×C₅₉	—	4	1	no	—
56	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
57	C₂×Dic₅₉	—	4	1	no	—
58	C₂×Dic₅₉	SD₁₆	1	1	yes	characteristic
59	C₄×D₅₉	—	4	2	no	—
60	C₄×D₅₉	—	4	2	no	—
61	C₄×D₅₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₄×D₅₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₄×D₅₉	D₈	1	1	yes	characteristic
64	C₄×D₅₉	D₈	1	1	yes	characteristic
65	Dic₁₁₈	—	2	2	no	—
66	Dic₁₁₈	—	4	1	no	—
67	Dic₁₁₈	—	4	2	no	—
68	Dic₁₁₈	—	4	2	no	—
69	C₈×C₅₉	—	4	1	no	—
70	C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
71	C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
72	C₅₉⋊C₈	—	4	1	no	—
73	C₅₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
74	C₅₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
76	C₂×D₅₉	—	2	2	no	—
77	C₂×D₅₉	#102	1	1	yes	characteristic
78	C₂×D₅₉	#102	1	1	yes	characteristic
79	C₄×C₅₉	—	4	2	no	—
80	C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
82	Dic₅₉	—	4	2	no	—
83	Dic₅₉	#102	1	1	yes	characteristic
84	Dic₅₉	#102	1	1	yes	characteristic
85	C₂×#362	—	59	1	no	maximal, Sylow
86	C₂×C₅₉	—	2	1	no	—
87	C₂×C₅₉	C₂×#102	1	1	yes	characteristic
88	D₅₉	—	2	1	no	—
89	D₅₉	#362	1	2	yes	direct product factor
90	C₂²×Q₁₆	—	59	1	no	—
91	C₂×M₃₂	—	59	1	no	—
92	C₂×#108	—	59	1	no	—
93	#362	—	59	1	no	—
94	#362	—	59	1	no	—
95	#362	—	59	1	no	—
96	#362	D₅₉	1	1	yes	characteristic, direct product factor
97	C₅₉	C₂×#362	1	1	yes	characteristic, complemented, Sylow
98	C₂²×Q₈	—	118	1	no	—
99	C₂×Q₁₆	—	59	2	no	—
100	C₂×Q₁₆	—	59	2	no	—
101	C₂×Q₁₆	—	59	1	no	—
102	C₂×Q₁₆	—	118	1	no	—
103	C₂×Q₁₆	—	118	1	no	—
104	C₂×Q₁₆	—	118	1	no	—
105	C₂×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
106	C₂×M₁₆	—	118	1	no	—
107	C₂²×C₈	—	59	1	no	—
108	M₃₂	—	59	1	no	—
109	M₃₂	—	118	1	no	—
110	M₃₂	C₂×D₅₉	1	1	yes	characteristic
111	C₂×C₁₆	—	118	1	no	—
112	#108	—	59	1	no	—
113	#108	—	118	1	no	—
114	#108	C₂×D₅₉	1	1	yes	characteristic
115	C₂×Q₈	—	2	1	no	—
116	C₂×Q₈	—	118	2	no	—
117	C₂×Q₈	—	118	2	no	—
118	C₂×Q₈	—	118	1	no	—
119	C₂×Q₈	—	236	1	no	—
120	C₂×Q₈	—	236	1	no	—
121	C₂×Q₈	—	236	1	no	—
122	C₂²×C₄	—	59	1	no	—
123	C₂²×C₄	—	236	1	no	—
124	Q₁₆	—	2	1	no	—
125	Q₁₆	—	59	2	no	—
126	Q₁₆	—	118	2	no	—
127	Q₁₆	—	118	2	no	—
128	Q₁₆	—	118	1	no	—
129	Q₁₆	C₄×D₅₉	1	2	yes	—
130	M₁₆	—	2	1	no	—
131	M₁₆	—	118	1	no	—
132	M₁₆	—	236	1	no	—
133	C₂×C₈	—	59	1	no	—
134	C₂×C₈	—	59	1	no	—
135	C₂×C₈	—	59	1	no	—
136	C₂×C₈	—	59	1	no	—
137	C₂×C₈	—	59	1	no	—
138	C₂×C₈	—	236	1	no	—
139	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
140	C₁₆	—	2	1	no	—
141	C₁₆	—	118	1	no	—
142	C₂³	—	59	1	no	—
143	Q₈	—	2	2	no	—
144	Q₈	—	4	1	no	—
145	Q₈	—	118	2	no	—
146	Q₈	—	236	2	no	—
147	Q₈	—	236	2	no	—
148	Q₈	—	236	1	no	—
149	C₂×C₄	—	4	1	no	—
150	C₂×C₄	—	59	1	no	—
151	C₂×C₄	—	59	1	no	—
152	C₂×C₄	—	59	1	no	—
153	C₂×C₄	—	59	1	no	—
154	C₂×C₄	—	59	1	no	—
155	C₂×C₄	—	236	2	no	—
156	C₂×C₄	—	236	2	no	—
157	C₂×C₄	—	236	1	no	—
158	C₂×C₄	D₄×D₅₉	1	1	yes	characteristic
159	C₈	—	4	1	no	—
160	C₈	—	59	1	no	—
161	C₈	—	59	1	no	—
162	C₈	—	236	1	no	—
163	C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
164	C₈	D₄×D₅₉	1	1	yes	characteristic
165	C₂²	—	59	1	no	—
166	C₂²	—	59	1	no	—
167	C₂²	—	118	2	no	—
168	C₂²	SD₁₆×D₅₉	1	1	yes	characteristic
169	C₄	—	4	2	no	—
170	C₄	—	59	1	no	—
171	C₄	—	59	1	no	—
172	C₄	—	236	2	no	—
173	C₄	C₂²⋊C₄×D₅₉	1	1	yes	characteristic
174	C₄	D₈×D₅₉	1	1	yes	characteristic
175	C₂	—	2	1	no	—
176	C₂	—	59	2	no	—
177	C₂	—	118	1	no	—
178	C₂	#102×D₅₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₁₆×D₅₉

C₂

yes

maximal, characteristic

M₃₂×D₅₉

C₂

yes

maximal, characteristic

#108×D₅₉

C₂

yes

maximal, characteristic

#16837219

C₂

yes

maximal, characteristic, complemented

#16837218

C₂

yes

maximal, characteristic, complemented

#16837217

C₂

yes

maximal, characteristic, complemented

C₅₉×#362

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₅₉

—

C₂×Dic₂₃₆

C₂²

yes

characteristic

C₂×#11745672

—

Q₁₆×D₅₉

—

Q₁₆×D₅₉

—

Q₁₆×D₅₉

C₄

yes

—

Q₁₆×D₅₉

C₄

yes

—

M₁₆×D₅₉

—

C₂×C₈×D₅₉

C₂²

yes

characteristic

#14273667

C₂²

yes

characteristic

#14273666

—

C₁₆×D₅₉

—

#14273663

C₂²

yes

characteristic

#14273662

—

C₂×Q₁₆×C₅₉

C₂²

yes

characteristic

M₃₂×C₅₉

C₂²

yes

characteristic

#108×C₅₉

C₂²

yes

characteristic

C₂×Q₈×C₅₉

—

Q₈×D₅₉

—

Q₈×D₅₉

—

Q₈×D₅₉

—

Q₈×D₅₉

—

C₂×C₄×D₅₉

—

C₂×C₄×D₅₉

D₄

yes

characteristic

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

Q₁₆×C₅₉

—

Q₁₆×C₅₉

C₂×C₄

yes

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

C₂³

yes

—

—

—

C₂×C₅₉⋊C₈

D₄

yes

characteristic

Dic₂₃₆

—

Dic₂₃₆

C₂×C₄

yes

—

#11745659

—

C₈×D₅₉

—

C₈×D₅₉

C₂×C₄

yes

characteristic

C₈×D₅₉

C₂×C₄

yes

characteristic

C₈×D₅₉

D₄

yes

characteristic

C₈×D₅₉

D₄

yes

characteristic

C₁₆×C₅₉

—

C₅₉⋊C₁₆

—

C₂²×D₅₉

SD₁₆

yes

characteristic

Q₈×C₅₉

—

Q₈×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

SD₁₆

yes

characteristic

C₄×D₅₉

—

C₄×D₅₉

—

C₄×D₅₉

C₂²⋊C₄

yes

characteristic

C₄×D₅₉

C₂²⋊C₄

yes

characteristic

C₄×D₅₉

D₈

yes

characteristic

C₄×D₅₉

D₈

yes

characteristic

Dic₁₁₈

—

Dic₁₁₈

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

—

C₈×C₅₉

C₂²×C₄

yes

characteristic

C₈×C₅₉

C₂×D₄

yes

characteristic

C₅₉⋊C₈

—

C₅₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₅₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂²×C₅₉

C₂×SD₁₆

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

yes

C₂×D₅₉

yes

C₄×C₅₉

—

C₄×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₅₉

C₂×D₈

yes

characteristic

Dic₅₉

—

Dic₅₉

yes

Dic₅₉

yes

—

C₂×C₅₉

—

C₂×C₅₉

C₂×#102

yes

characteristic

D₅₉

—

D₅₉

#362

yes

direct product factor

C₂²×Q₁₆

—

C₂×M₃₂

—

—

—

—

—

D₅₉

yes

characteristic, direct product factor

C₅₉

C₂×#362

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

118

—

C₂×Q₁₆

—

100

C₂×Q₁₆

—

101

C₂×Q₁₆

—

102

C₂×Q₁₆

—

118

—

103

C₂×Q₁₆

—

118

—

104

C₂×Q₁₆

—

118

—

105

C₂×Q₁₆

C₂×D₅₉

yes

characteristic

106

C₂×M₁₆

—

118

—

107

C₂²×C₈

—

108

M₃₂

—

109

M₃₂

—

118

—

110

M₃₂

C₂×D₅₉

yes

characteristic

111

C₂×C₁₆

—

118

—

112

#108

—

113

#108

—

118

—

114

#108

C₂×D₅₉

yes

characteristic

115

C₂×Q₈

—

116

C₂×Q₈

—

118

—

117

C₂×Q₈

—

118

—

118

C₂×Q₈

—

118

—

119

C₂×Q₈

—

236

—

120

C₂×Q₈

—

236

—

121

C₂×Q₈

—

236

—

122

C₂²×C₄

—

123

C₂²×C₄

—

236

—

124

Q₁₆

—

125

Q₁₆

—

126

Q₁₆

—

118

—

127

Q₁₆

—

118

—

128

Q₁₆

—

118

—

129

Q₁₆

C₄×D₅₉

yes

—

130

M₁₆

—

131

M₁₆

—

118

—

132

M₁₆

—

236

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

236

—

139

C₂×C₈

C₂²×D₅₉

yes

characteristic

140

C₁₆

—

141

C₁₆

—

118

—

142

C₂³

—

143

Q₈

—

144

Q₈

—

145

Q₈

—

118

—

146

Q₈

—

236

—

147

Q₈

—

236

—

148

Q₈

—

236

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

236

—

156

C₂×C₄

—

236

—

157

C₂×C₄

—

236

—

158

C₂×C₄

D₄×D₅₉

yes

characteristic

159

C₈

—

160

C₈

—

161

C₈

—

162

C₈

—

236

—

163

C₈

C₂×C₄×D₅₉

yes

characteristic

164

C₈

D₄×D₅₉

yes

characteristic

165

C₂²

—

166

C₂²

—

167

C₂²

—

118

—

168

C₂²

SD₁₆×D₅₉

yes

characteristic

169

C₄

—

170

C₄

—

171

C₄

—

172

C₄

—

236

—

173

C₄

C₂²⋊C₄×D₅₉

yes

characteristic

174

C₄

D₈×D₅₉

yes

characteristic

175

C₂

—

176

C₂

—

177

C₂

—

118

—

178

C₂

#102×D₅₉

yes

characteristic

	subgroup	G/H
center	C₂	#102×D₅₉
commutator	C₈×C₅₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#362	C₂
socle	C₂×C₅₉	C₂×#102
hypercenter	#362	D₅₉
hypocenter	C₅₉	C₂×#362
LCS	G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #362

subgroup

G/H

center

C₂

#102×D₅₉

commutator

C₈×C₅₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₅₉

Fitting

C₅₉×#362

C₂

C₂×C₅₉

D₅₉

C₅₉

G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #362

N	H ≅ G/N	type
4. #16837219	C₂	semidirect
5. #16837218	C₂	semidirect
6. #16837217	C₂	semidirect
7. C₅₉×#362	C₂	semidirect
89. D₅₉	#362	direct (N × H)
96. #362	D₅₉	direct (N × H)
97. C₅₉	C₂×#362	semidirect

H ≅ G/N

type

4. #16837219

C₂

semidirect

5. #16837218

C₂

semidirect

6. #16837217

C₂

semidirect

7. C₅₉×#362

C₂

semidirect

89. D₅₉

#362

direct (N × H)

96. #362

D₅₉

direct (N × H)

97. C₅₉

C₂×#362

semidirect

Subgroups — #362×D₅₉ #21425838

Conjugacy classes of subgroups

Complements

Subgroups — #362×D59 #21425838

Conjugacy classes of subgroups

Complements

Subgroups — #362×D₅₉ #21425838