Group #35320968 — subgroups

Subgroups — #35320968

Order 21248.

414 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 135 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×#19127739	C₂	1	1	yes	maximal, characteristic
2	C₂×#19127524	C₂	1	2	yes	maximal, complemented
3	#24907501	C₂	1	1	yes	maximal, characteristic
4	#24905562	C₂	1	2	yes	maximal, complemented
5	C₈₃×#2112	C₂	1	1	yes	maximal, characteristic
6	C₂×#14581751	—	2	1	no	—
7	C₂×#14581728	C₂²	1	1	yes	characteristic
8	C₂×#14581728	C₂²	1	1	yes	characteristic
9	#19127739	—	2	4	no	—
10	C₂×#14581726	—	2	1	no	—
11	C₂×#14581724	C₂²	1	2	yes	—
12	#19127665	—	2	1	no	—
13	#19127524	—	2	4	no	—
14	#19127466	—	2	1	no	—
15	C₂³×C₈×C₈₃	C₂²	1	1	yes	characteristic
16	C₂×M₃₂×C₈₃	C₂²	1	2	yes	—
17	C₂²⋊C₁₆×C₈₃	C₄	1	4	yes	complemented
18	C₂×#13050574	—	2	1	no	—
19	C₂×#13050574	—	2	1	no	—
20	#14581751	—	2	4	no	—
21	#14581751	—	4	2	no	—
22	C₂×C₄⋊Dic₈₃	—	2	2	no	—
23	C₂×C₂²⋊Dic₈₃	—	4	1	no	—
24	C₂×C₄×Dic₈₃	—	4	1	no	—
25	#14581728	—	2	2	no	—
26	#14581728	—	2	2	no	—
27	#14581726	—	2	4	no	—
28	#14581724	—	2	2	no	—
29	#14581724	D₄	1	4	yes	—
30	C₂²⋊(C₈₃⋊C₈)	—	4	2	no	—
31	C₂³×C₄×C₈₃	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₈₃	—	2	2	no	—
33	C₂²×C₈×C₈₃	—	2	2	no	—
34	C₂²×C₈×C₈₃	C₂×C₄	1	2	yes	—
35	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₈₃	Q₈	1	2	yes	—
37	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
38	M₃₂×C₈₃	—	2	2	no	—
39	M₃₂×C₈₃	—	2	2	no	—
40	C₂×C₁₆×C₈₃	C₂×C₄	1	4	yes	—
41	C₂²×Dic₈₃	—	4	2	no	—
42	#13050574	—	4	1	no	—
43	#13050574	—	4	1	no	—
44	#13050574	—	4	1	no	—
45	#13050574	—	4	1	no	—
46	C₂×C₈₃⋊C₈	—	4	1	no	—
47	C₂×C₈₃⋊C₈	—	4	1	no	—
48	C₄⋊Dic₈₃	—	2	4	no	—
49	C₄⋊Dic₈₃	—	4	2	no	—
50	C₂²⋊Dic₈₃	—	4	4	no	—
51	C₄×Dic₈₃	—	4	4	no	—
52	C₂⁴×C₈₃	SD₁₆	1	1	yes	characteristic
53	C₂²×C₄×C₈₃	—	2	1	no	—
54	C₂²×C₄×C₈₃	—	2	1	no	—
55	C₂²×C₄×C₈₃	—	2	1	no	—
56	C₂²×C₄×C₈₃	—	2	1	no	—
57	C₂²×C₄×C₈₃	C₄⋊C₄	1	2	yes	—
58	C₂²×C₄×C₈₃	SD₁₆	1	1	yes	characteristic
59	C₂²×C₄×C₈₃	SD₁₆	1	2	yes	—
60	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
61	C₂×C₈×C₈₃	—	2	1	no	—
62	C₂×C₈×C₈₃	—	2	1	no	—
63	C₂×C₈×C₈₃	—	2	4	no	—
64	C₂×C₈×C₈₃	—	2	4	no	—
65	C₂×C₈×C₈₃	C₄⋊C₄	1	2	yes	—
66	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₈×C₈₃	C₂×D₄	1	2	yes	—
68	C₂×C₈×C₈₃	C₂×Q₈	1	1	yes	characteristic
69	C₂×C₈×C₈₃	#41	1	2	yes	—
70	C₁₆×C₈₃	—	2	4	no	—
71	C₂³×C₈₃	—	2	1	no	—
72	C₂³×C₈₃	—	2	1	no	—
73	C₂³×C₈₃	—	4	2	no	—
74	C₂³×C₈₃	#106	1	2	yes	—
75	C₂³×C₈₃	C₂×SD₁₆	1	1	yes	characteristic
76	C₂×C₄×C₈₃	—	2	1	no	—
77	C₂×C₄×C₈₃	—	2	1	no	—
78	C₂×C₄×C₈₃	—	2	2	no	—
79	C₂×C₄×C₈₃	—	2	2	no	—
80	C₂×C₄×C₈₃	—	2	2	no	—
81	C₂×C₄×C₈₃	—	2	2	no	—
82	C₂×C₄×C₈₃	#106	1	2	yes	—
83	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₈₃	#120	1	1	yes	characteristic
85	C₂×C₄×C₈₃	#123	1	1	yes	characteristic
86	C₂×C₄×C₈₃	C₂×SD₁₆	1	1	yes	characteristic
87	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	1	yes	characteristic
88	C₂×C₄×C₈₃	#137	1	1	yes	characteristic
89	C₂×Dic₈₃	—	4	4	no	—
90	C₂×Dic₈₃	—	8	4	no	—
91	C₈×C₈₃	—	2	2	no	—
92	C₈×C₈₃	C₄×D₄	1	2	yes	—
93	C₈×C₈₃	C₂²⋊Q₈	1	2	yes	—
94	C₈₃⋊C₈	—	8	1	no	—
95	C₈₃⋊C₈	—	8	1	no	—
96	C₂²×C₈₃	—	2	2	no	—
97	C₂²×C₈₃	—	2	2	no	—
98	C₂²×C₈₃	—	2	4	no	—
99	C₂²×C₈₃	—	4	2	no	—
100	C₂²×C₈₃	—	4	2	no	—
101	C₂²×C₈₃	C₂×#106	1	1	yes	characteristic
102	C₂²×C₈₃	#450	1	1	yes	characteristic
103	C₂²×C₈₃	#483	1	1	yes	characteristic
104	C₄×C₈₃	—	2	2	no	—
105	C₄×C₈₃	#385	1	1	yes	characteristic
106	C₄×C₈₃	#428	1	1	yes	characteristic
107	C₄×C₈₃	#448	1	1	yes	characteristic
108	C₄×C₈₃	#481	1	1	yes	characteristic
109	Dic₈₃	—	8	4	no	—
110	#12930	—	83	1	no	maximal, Sylow
111	C₂×C₈₃	—	2	1	no	—
112	C₂×C₈₃	—	2	1	no	—
113	C₂×C₈₃	—	4	2	no	—
114	C₂×C₈₃	#1853	1	1	yes	characteristic
115	C₂×C₈₃	#2155	1	2	yes	—
116	C₂×#427	—	83	1	no	—
117	C₂×#365	—	83	2	no	—
118	#2112	D₈₃	1	1	yes	characteristic
119	#1810	—	83	1	no	—
120	#1383	—	83	2	no	—
121	C₈₃	#12930	1	1	yes	characteristic, complemented, Sylow
122	C₂³×C₈	C₂×D₈₃	1	1	yes	characteristic
123	C₂×#117	—	166	1	no	—
124	C₂×M₃₂	C₂×D₈₃	1	2	yes	—
125	C₂×#108	—	83	1	no	—
126	C₂×#108	—	83	1	no	—
127	#427	—	166	4	no	—
128	C₂×#107	—	166	1	no	—
129	C₂×#106	—	83	2	no	—
130	#407	—	166	1	no	—
131	#365	—	166	4	no	—
132	C₂²⋊C₁₆	Dic₈₃	1	4	yes	complemented
133	#341	—	166	1	no	—
134	C₂³×C₄	D₃₃₂	1	1	yes	characteristic
135	C₂×M₁₆	—	166	1	no	—
136	C₂×M₁₆	—	166	1	no	—
137	C₂²×C₈	—	2	2	no	—
138	C₂²×C₈	—	2	2	no	—
139	C₂²×C₈	Dic₁₆₆	1	2	yes	—
140	C₂²×C₈	D₃₃₂	1	1	yes	characteristic
141	C₂²×C₈	C₂×Dic₈₃	1	2	yes	—
142	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
143	#117	—	332	2	no	—
144	#117	—	166	4	no	—
145	C₂×C₄⋊C₄	—	166	2	no	—
146	C₂×C₂²⋊C₄	—	332	1	no	—
147	C₂×C₄²	—	332	1	no	—
148	M₃₂	—	2	2	no	—
149	M₃₂	—	2	2	no	—
150	C₂×C₁₆	C₂×Dic₈₃	1	4	yes	—
151	#108	—	166	2	no	—
152	#108	—	166	2	no	—
153	#107	—	166	4	no	—
154	#106	—	83	4	no	—
155	#106	—	166	2	no	—
156	C₂²⋊C₈	—	332	2	no	—
157	C₂⁴	#13050579	1	1	yes	characteristic
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	2	1	no	—
160	C₂²×C₄	—	2	1	no	—
161	C₂²×C₄	—	2	1	no	—
162	C₂²×C₄	—	332	2	no	—
163	C₂²×C₄	C₄⋊Dic₈₃	1	2	yes	—
164	C₂²×C₄	#13050579	1	2	yes	—
165	C₂²×C₄	#13050579	1	1	yes	characteristic
166	C₂²×C₄	C₂×D₃₃₂	1	1	yes	characteristic
167	M₁₆	—	332	1	no	—
168	M₁₆	—	332	1	no	—
169	M₁₆	—	332	1	no	—
170	M₁₆	—	332	1	no	—
171	C₂×C₈	—	2	1	no	—
172	C₂×C₈	—	2	1	no	—
173	C₂×C₈	—	2	4	no	—
174	C₂×C₈	—	2	4	no	—
175	C₂×C₈	—	332	1	no	—
176	C₂×C₈	—	332	1	no	—
177	C₂×C₈	C₄⋊Dic₈₃	1	2	yes	—
178	C₂×C₈	C₂²×Dic₈₃	1	1	yes	characteristic
179	C₂×C₈	D₄×D₈₃	1	2	yes	—
180	C₂×C₈	C₂×Dic₁₆₆	1	1	yes	characteristic
181	C₂×C₈	#13050589	1	2	yes	—
182	C₄⋊C₄	—	332	2	no	—
183	C₄⋊C₄	—	166	4	no	—
184	C₂²⋊C₄	—	332	4	no	—
185	C₄²	—	332	4	no	—
186	C₁₆	—	2	4	no	—
187	C₂³	—	2	1	no	—
188	C₂³	—	2	1	no	—
189	C₂³	—	4	2	no	—
190	C₂³	#14581724	1	2	yes	—
191	C₂³	C₂×#13050579	1	1	yes	characteristic
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	332	4	no	—
199	C₂×C₄	—	664	4	no	—
200	C₂×C₄	#14581724	1	2	yes	—
201	C₂×C₄	C₂×C₄⋊Dic₈₃	1	1	yes	characteristic
202	C₂×C₄	#14581762	1	1	yes	characteristic
203	C₂×C₄	#14581776	1	1	yes	characteristic
204	C₂×C₄	C₂×#13050579	1	1	yes	characteristic
205	C₂×C₄	#14581820	1	1	yes	characteristic
206	C₂×C₄	#14581825	1	1	yes	characteristic
207	C₈	—	2	2	no	—
208	C₈	—	664	1	no	—
209	C₈	—	664	1	no	—
210	C₈	D₄×Dic₈₃	1	2	yes	—
211	C₈	#14581769	1	2	yes	—
212	C₂²	—	2	2	no	—
213	C₂²	—	2	2	no	—
214	C₂²	—	2	4	no	—
215	C₂²	—	4	2	no	—
216	C₂²	—	4	2	no	—
217	C₂²	C₂×#14581724	1	1	yes	characteristic
218	C₂²	#19127854	1	1	yes	characteristic
219	C₂²	#19128032	1	1	yes	characteristic
220	C₄	—	2	2	no	—
221	C₄	—	664	4	no	—
222	C₄	#19127576	1	1	yes	characteristic
223	C₄	#19127743	1	1	yes	characteristic
224	C₄	#19127842	1	1	yes	characteristic
225	C₄	#19128020	1	1	yes	characteristic
226	C₂	—	2	1	no	—
227	C₂	—	2	1	no	—
228	C₂	—	4	2	no	—
229	C₂	#24907658	1	1	yes	characteristic
230	C₂	#24909236	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19127739

C₂

yes

maximal, characteristic

C₂×#19127524

C₂

yes

maximal, complemented

#24907501

C₂

yes

maximal, characteristic

#24905562

C₂

yes

maximal, complemented

C₈₃×#2112

C₂

yes

maximal, characteristic

C₂×#14581751

—

C₂×#14581728

C₂²

yes

characteristic

C₂×#14581728

C₂²

yes

—

—

C₂²

yes

—

#19127665

—

#19127524

—

#19127466

—

C₂³×C₈×C₈₃

C₂²

yes

characteristic

C₂×M₃₂×C₈₃

C₂²

yes

—

C₂²⋊C₁₆×C₈₃

C₄

yes

—

—

—

—

C₂×C₄⋊Dic₈₃

—

C₂×C₂²⋊Dic₈₃

—

C₂×C₄×Dic₈₃

—

—

—

—

—

D₄

yes

—

C₂²⋊(C₈₃⋊C₈)

—

C₂³×C₄×C₈₃

D₄

yes

characteristic

C₂²×C₈×C₈₃

—

C₂²×C₈×C₈₃

—

C₂²×C₈×C₈₃

C₂×C₄

yes

—

C₂²×C₈×C₈₃

D₄

yes

characteristic

C₂²×C₈×C₈₃

Q₈

yes

—

C₂²×C₈×C₈₃

C₂³

yes

characteristic

M₃₂×C₈₃

—

M₃₂×C₈₃

—

C₂×C₁₆×C₈₃

C₂×C₄

yes

—

C₂²×Dic₈₃

—

—

—

—

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₂²⋊Dic₈₃

—

C₄×Dic₈₃

—

C₂⁴×C₈₃

SD₁₆

yes

characteristic

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

C₄⋊C₄

yes

—

C₂²×C₄×C₈₃

SD₁₆

yes

characteristic

C₂²×C₄×C₈₃

SD₁₆

yes

—

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

C₄⋊C₄

yes

—

C₂×C₈×C₈₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₃

C₂×D₄

yes

—

C₂×C₈×C₈₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₈₃

#41

yes

—

C₁₆×C₈₃

—

C₂³×C₈₃

—

C₂³×C₈₃

—

C₂³×C₈₃

—

C₂³×C₈₃

#106

yes

—

C₂³×C₈₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

#106

yes

—

C₂×C₄×C₈₃

C₂×C₄⋊C₄

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

C₂×SD₁₆

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₈×C₈₃

—

C₈×C₈₃

C₄×D₄

yes

—

C₈×C₈₃

C₂²⋊Q₈

yes

—

C₈₃⋊C₈

—

C₈₃⋊C₈

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

—

100

C₂²×C₈₃

—

101

C₂²×C₈₃

C₂×#106

yes

characteristic

102

C₂²×C₈₃

#450

yes

characteristic

103

C₂²×C₈₃

#483

yes

characteristic

104

C₄×C₈₃

—

105

C₄×C₈₃

#385

yes

characteristic

106

C₄×C₈₃

#428

yes

characteristic

107

C₄×C₈₃

#448

yes

characteristic

108

C₄×C₈₃

#481

yes

characteristic

109

Dic₈₃

—

110

#12930

—

maximal, Sylow

111

C₂×C₈₃

—

112

C₂×C₈₃

—

113

C₂×C₈₃

—

114

C₂×C₈₃

#1853

yes

characteristic

115

C₂×C₈₃

#2155

yes

—

116

C₂×#427

—

117

C₂×#365

—

118

#2112

D₈₃

yes

characteristic

119

#1810

—

120

#1383

—

121

C₈₃

#12930

yes

characteristic, complemented, Sylow

122

C₂³×C₈

C₂×D₈₃

yes

characteristic

123

C₂×#117

—

166

—

124

C₂×M₃₂

C₂×D₈₃

yes

—

125

C₂×#108

—

126

C₂×#108

—

127

#427

—

166

—

128

C₂×#107

—

166

—

129

C₂×#106

—

130

#407

—

166

—

131

#365

—

166

—

132

C₂²⋊C₁₆

Dic₈₃

yes

complemented

133

#341

—

166

—

134

C₂³×C₄

D₃₃₂

yes

characteristic

135

C₂×M₁₆

—

166

—

136

C₂×M₁₆

—

166

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₂²×C₈

Dic₁₆₆

yes

—

140

C₂²×C₈

D₃₃₂

yes

characteristic

141

C₂²×C₈

C₂×Dic₈₃

yes

—

142

C₂²×C₈

C₂²×D₈₃

yes

characteristic

143

#117

—

332

—

144

#117

—

166

—

145

C₂×C₄⋊C₄

—

166

—

146

C₂×C₂²⋊C₄

—

332

—

147

C₂×C₄²

—

332

—

148

M₃₂

—

149

M₃₂

—

150

C₂×C₁₆

C₂×Dic₈₃

yes

—

151

#108

—

166

—

152

#108

—

166

—

153

#107

—

166

—

154

#106

—

155

#106

—

166

—

156

C₂²⋊C₈

—

332

—

157

C₂⁴

#13050579

yes

characteristic

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

332

—

163

C₂²×C₄

C₄⋊Dic₈₃

yes

—

164

C₂²×C₄

#13050579

yes

—

165

C₂²×C₄

#13050579

yes

characteristic

166

C₂²×C₄

C₂×D₃₃₂

yes

characteristic

167

M₁₆

—

332

—

168

M₁₆

—

332

—

169

M₁₆

—

332

—

170

M₁₆

—

332

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

332

—

176

C₂×C₈

—

332

—

177

C₂×C₈

C₄⋊Dic₈₃

yes

—

178

C₂×C₈

C₂²×Dic₈₃

yes

characteristic

179

C₂×C₈

D₄×D₈₃

yes

—

180

C₂×C₈

C₂×Dic₁₆₆

yes

characteristic

181

C₂×C₈

#13050589

yes

—

182

C₄⋊C₄

—

332

—

183

C₄⋊C₄

—

166

—

184

C₂²⋊C₄

—

332

—

185

C₄²

—

332

—

186

C₁₆

—

187

C₂³

—

188

C₂³

—

189

C₂³

—

190

C₂³

#14581724

yes

—

191

C₂³

C₂×#13050579

yes

characteristic

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

332

—

199

C₂×C₄

—

664

—

200

C₂×C₄

#14581724

yes

—

201

C₂×C₄

C₂×C₄⋊Dic₈₃

yes

characteristic

202

C₂×C₄

#14581762

yes

characteristic

203

C₂×C₄

#14581776

yes

characteristic

204

C₂×C₄

C₂×#13050579

yes

characteristic

205

C₂×C₄

#14581820

yes

characteristic

206

C₂×C₄

#14581825

yes

characteristic

207

C₈

—

208

C₈

—

664

—

209

C₈

—

664

—

210

C₈

D₄×Dic₈₃

yes

—

211

C₈

#14581769

yes

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

C₂×#14581724

yes

characteristic

218

C₂²

#19127854

yes

characteristic

219

C₂²

#19128032

yes

characteristic

220

C₄

—

221

C₄

—

664

—

222

C₄

#19127576

yes

characteristic

223

C₄

#19127743

yes

characteristic

224

C₄

#19127842

yes

characteristic

225

C₄

#19128020

yes

characteristic

226

C₂

—

227

C₂

—

228

C₂

—

229

C₂

#24907658

yes

characteristic

230

C₂

#24909236

yes

—

	subgroup	G/H
center	C₂²	C₂×#14581724
commutator	C₂×C₈×C₈₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₈₃
Fitting	C₈₃×#2112	C₂
socle	C₂²×C₈₃	C₂×#106
prime radical	C₂⁴×C₈₃	SD₁₆
cosocle	C₂²×C₈×C₈₃	C₂³
hypercenter	#2112	D₈₃
hypocenter	C₈₃	#12930
LCS	G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #2112

subgroup

G/H

center

C₂²

C₂×#14581724

commutator

C₂×C₈×C₈₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₈₃

Fitting

C₈₃×#2112

C₂

socle

C₂²×C₈₃

C₂×#106

prime radical

C₂⁴×C₈₃

SD₁₆

cosocle

C₂²×C₈×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #2112

N	H ≅ G/N	type
2. C₂×#19127524	C₂	semidirect
4. #24905562	C₂	semidirect
17. C₂²⋊C₁₆×C₈₃	C₄	semidirect
121. C₈₃	#12930	semidirect
132. C₂²⋊C₁₆	Dic₈₃	semidirect

H ≅ G/N

type

2. C₂×#19127524

C₂

semidirect

4. #24905562

C₂

semidirect

17. C₂²⋊C₁₆×C₈₃

C₄

semidirect

121. C₈₃

#12930

semidirect

132. C₂²⋊C₁₆

Dic₈₃

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#19127739	2
C₂×#19127524	2
#24907501	2
#24905562	2
C₈₃×#2112	2
#12930	83

subgroup

index

C₈₃×#2112

Subgroups — #35320968

Conjugacy classes of subgroups

Complements

Maximal subgroups