Group #35322917 — subgroups

Subgroups — #35322917

Order 21248.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 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×#19128081	C₂	1	1	yes	maximal, characteristic
2	C₂×#19127518	C₂	1	2	yes	maximal
3	#24909184	C₂	1	2	yes	maximal
4	#24907342	C₂	1	1	yes	maximal, characteristic
5	C₂×#364×C₈₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₃₂	—	2	1	no	—
7	C₂²×Dic₃₃₂	C₂²	1	2	yes	—
8	C₂×#14581792	—	2	1	no	—
9	#19128081	—	2	2	no	—
10	#19128081	C₄	1	4	yes	complemented
11	C₂×#14581728	C₂²	1	1	yes	characteristic
12	#19127739	C₂²	1	1	yes	characteristic
13	#19127656	—	2	1	no	—
14	#19127518	—	2	4	no	—
15	#19127506	—	2	4	no	—
16	#19127461	—	2	1	no	—
17	C₂×M₃₂×C₈₃	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
19	#364×C₈₃	—	2	2	no	—
20	C₂²×Dic₁₆₆	—	2	2	no	—
21	C₂×Dic₃₃₂	—	2	4	no	—
22	C₂×Dic₃₃₂	—	2	2	no	—
23	C₂×Dic₃₃₂	—	2	2	no	—
24	C₂×Dic₃₃₂	—	2	2	no	—
25	C₂×Dic₃₃₂	—	2	2	no	—
26	C₂×Dic₃₃₂	—	2	2	no	—
27	C₂×Dic₃₃₂	—	4	1	no	—
28	C₂×Dic₃₃₂	—	4	1	no	—
29	C₂×Dic₃₃₂	—	4	2	no	—
30	C₂×Dic₃₃₂	C₂×C₄	1	4	yes	—
31	C₂×#13050574	—	2	1	no	—
32	#14581792	—	2	4	no	—
33	#14581792	—	4	2	no	—
34	#14581751	—	2	1	no	—
35	C₂×C₄⋊Dic₈₃	—	4	2	no	—
36	#14581728	—	2	1	no	—
37	#14581728	D₄	1	2	yes	—
38	#14581726	D₄	1	2	yes	—
39	#14581724	—	2	1	no	—
40	#14581702	—	4	1	no	—
41	C₈×Dic₈₃	—	4	1	no	—
42	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
44	C₂×C₄²×C₈₃	D₄	1	1	yes	characteristic
45	M₃₂×C₈₃	—	2	2	no	—
46	M₃₂×C₈₃	—	2	2	no	—
47	C₂×C₁₆×C₈₃	—	2	2	no	—
48	C₄×C₈×C₈₃	C₂×C₄	1	2	yes	—
49	C₄×C₈×C₈₃	D₄	1	2	yes	—
50	C₂×Dic₁₆₆	—	2	4	no	—
51	C₂×Dic₁₆₆	—	4	2	no	—
52	C₂×Dic₁₆₆	—	4	2	no	—
53	C₂×Dic₁₆₆	—	4	2	no	—
54	C₂×Dic₁₆₆	—	4	2	no	—
55	C₂×Dic₁₆₆	—	4	2	no	—
56	C₂²×Dic₈₃	—	4	2	no	—
57	Dic₃₃₂	—	2	4	no	—
58	Dic₃₃₂	—	2	4	no	—
59	Dic₃₃₂	—	4	4	no	—
60	Dic₃₃₂	—	4	4	no	—
61	Dic₃₃₂	—	4	2	no	—
62	Dic₃₃₂	—	4	2	no	—
63	#13050574	—	2	2	no	—
64	#13050574	—	4	1	no	—
65	C₂×C₈₃⋊C₈	—	4	1	no	—
66	C₄⋊Dic₈₃	—	2	2	no	—
67	C₄⋊Dic₈₃	—	4	8	no	—
68	C₂²⋊Dic₈₃	—	4	1	no	—
69	C₄×Dic₈₃	—	4	1	no	—
70	C₂²×C₄×C₈₃	—	2	1	no	—
71	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
73	C₂×C₈×C₈₃	D₈	1	1	yes	characteristic
74	C₂×C₈×C₈₃	D₈	1	1	yes	characteristic
75	C₂×C₈×C₈₃	SD₁₆	1	2	yes	—
76	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
78	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
79	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
80	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
81	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
82	C₄²×C₈₃	—	2	1	no	—
83	C₄²×C₈₃	C₂²⋊C₄	1	2	yes	—
84	C₁₆×C₈₃	—	4	2	no	—
85	C₂³×C₈₃	AGL(1,ℤ/8)	1	1	yes	characteristic
86	C₂×C₄×C₈₃	—	2	4	no	—
87	C₂×C₄×C₈₃	—	2	2	no	—
88	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
90	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
91	C₂×C₄×C₈₃	C₂×D₈	1	1	yes	characteristic
92	C₂×C₄×C₈₃	C₂×SD₁₆	1	1	yes	characteristic
93	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	1	yes	characteristic
94	C₂×Dic₈₃	—	4	4	no	—
95	C₂×Dic₈₃	—	4	2	no	—
96	C₂×Dic₈₃	—	8	2	no	—
97	C₂×Dic₈₃	—	8	2	no	—
98	Dic₁₆₆	—	4	4	no	—
99	Dic₁₆₆	—	4	4	no	—
100	Dic₁₆₆	—	8	2	no	—
101	Dic₁₆₆	—	8	2	no	—
102	C₈×C₈₃	#102	1	2	yes	—
103	C₈×C₈₃	#102	1	2	yes	—
104	C₈×C₈₃	C₄×D₄	1	1	yes	characteristic
105	C₈×C₈₃	C₄×D₄	1	1	yes	characteristic
106	C₈×C₈₃	#124	1	1	yes	characteristic
107	C₈×C₈₃	#127	1	1	yes	characteristic
108	C₈₃⋊C₈	—	4	2	no	—
109	C₂²×C₈₃	—	2	2	no	—
110	C₂²×C₈₃	#418	1	1	yes	characteristic
111	C₂²×C₈₃	#459	1	1	yes	characteristic
112	C₂²×C₈₃	#460	1	1	yes	characteristic
113	C₄×C₈₃	—	2	4	no	—
114	C₄×C₈₃	#390	1	1	yes	characteristic
115	C₄×C₈₃	C₂×#102	1	1	yes	characteristic
116	C₄×C₈₃	#459	1	1	yes	characteristic
117	C₄×C₈₃	#460	1	1	yes	characteristic
118	Dic₈₃	—	8	2	no	—
119	Dic₈₃	—	8	4	no	—
120	#13262	—	83	1	no	maximal, Sylow
121	C₂×C₈₃	—	2	1	no	—
122	C₂×C₈₃	—	2	1	no	—
123	C₂×C₈₃	#1982	1	1	yes	characteristic
124	C₂×C₈₃	#2214	1	2	yes	—
125	C₂×#494	—	83	1	no	—
126	C₂×#364	D₈₃	1	1	yes	characteristic
127	C₂×#362	—	83	2	no	—
128	#2141	—	83	2	no	—
129	#1772	—	83	1	no	—
130	C₈₃	#13262	1	1	yes	characteristic, complemented, Sylow
131	C₂²×Q₁₆	—	83	2	no	—
132	C₂²×Q₁₆	—	166	1	no	—
133	C₂×C₄⋊Q₈	—	166	1	no	—
134	C₂×M₃₂	C₂×D₈₃	1	2	yes	—
135	#494	—	83	4	no	—
136	#494	—	166	2	no	—
137	C₂×#108	—	83	1	no	—
138	#427	—	83	1	no	—
139	#405	—	166	1	no	—
140	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
141	#364	—	2	2	no	—
142	#362	—	166	4	no	—
143	#358	—	166	4	no	—
144	#339	—	166	1	no	—
145	C₂²×Q₈	—	166	2	no	—
146	C₂×Q₁₆	—	332	1	no	—
147	C₂×Q₁₆	—	332	1	no	—
148	C₂×Q₁₆	—	332	2	no	—
149	C₂×Q₁₆	—	83	4	no	—
150	C₂×Q₁₆	—	166	4	no	—
151	C₂×Q₁₆	—	166	2	no	—
152	C₂×Q₁₆	—	166	2	no	—
153	C₂×Q₁₆	—	166	2	no	—
154	C₂×Q₁₆	—	166	2	no	—
155	C₂×Q₁₆	—	166	2	no	—
156	C₂×M₁₆	—	166	1	no	—
157	C₂²×C₈	D₃₃₂	1	1	yes	characteristic
158	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
159	C₄⋊Q₈	—	332	2	no	—
160	C₄⋊Q₈	—	166	4	no	—
161	#117	—	166	1	no	—
162	C₂×C₄⋊C₄	—	332	2	no	—
163	C₂×C₄²	D₃₃₂	1	1	yes	characteristic
164	M₃₂	—	2	2	no	—
165	M₃₂	—	2	2	no	—
166	C₂×C₁₆	—	2	2	no	—
167	#108	—	83	2	no	—
168	#108	—	166	1	no	—
169	#107	—	83	2	no	—
170	#106	—	166	1	no	—
171	#97	—	332	1	no	—
172	C₄×C₈	—	332	1	no	—
173	C₄×C₈	C₄×D₈₃	1	2	yes	—
174	C₄×C₈	C₂²⋊D₈₃	1	2	yes	—
175	C₂×Q₈	—	332	2	no	—
176	C₂×Q₈	—	332	2	no	—
177	C₂×Q₈	—	332	2	no	—
178	C₂×Q₈	—	332	2	no	—
179	C₂×Q₈	—	332	2	no	—
180	C₂×Q₈	—	166	4	no	—
181	C₂²×C₄	—	2	1	no	—
182	C₂²×C₄	—	332	2	no	—
183	C₂²×C₄	C₂×D₃₃₂	1	1	yes	characteristic
184	Q₁₆	—	332	2	no	—
185	Q₁₆	—	332	2	no	—
186	Q₁₆	—	332	4	no	—
187	Q₁₆	—	332	4	no	—
188	Q₁₆	—	166	4	no	—
189	Q₁₆	—	166	4	no	—
190	M₁₆	—	332	1	no	—
191	M₁₆	—	166	2	no	—
192	C₂×C₈	—	332	1	no	—
193	C₂×C₈	(C₂×D₈₃)⋊C₄	1	2	yes	—
194	C₂×C₈	D₆₆₄	1	1	yes	characteristic
195	C₂×C₈	D₆₆₄	1	1	yes	characteristic
196	C₂×C₈	#13050579	1	2	yes	—
197	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
198	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
199	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
200	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
201	C₂×C₈	#13050591	1	1	yes	characteristic
202	C₂×C₈	#13050591	1	1	yes	characteristic
203	C₄⋊C₄	—	332	8	no	—
204	C₄⋊C₄	—	166	2	no	—
205	C₂²⋊C₄	—	332	1	no	—
206	C₄²	—	2	1	no	—
207	C₄²	—	332	1	no	—
208	C₄²	(C₂×D₈₃)⋊C₄	1	2	yes	—
209	C₁₆	—	4	2	no	—
210	C₂³	#14581820	1	1	yes	characteristic
211	Q₈	—	332	4	no	—
212	Q₈	—	332	4	no	—
213	Q₈	—	664	2	no	—
214	Q₈	—	664	2	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	332	2	no	—
218	C₂×C₄	—	332	4	no	—
219	C₂×C₄	—	664	2	no	—
220	C₂×C₄	—	664	2	no	—
221	C₂×C₄	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
222	C₂×C₄	#14581767	1	1	yes	characteristic
223	C₂×C₄	#14581767	1	1	yes	characteristic
224	C₂×C₄	C₂×D₆₆₄	1	1	yes	characteristic
225	C₂×C₄	C₂×#13050579	1	1	yes	characteristic
226	C₂×C₄	#14581820	1	1	yes	characteristic
227	C₈	—	332	2	no	—
228	C₈	#14581714	1	2	yes	—
229	C₈	#14581714	1	2	yes	—
230	C₈	#14581754	1	1	yes	characteristic
231	C₈	#14581754	1	1	yes	characteristic
232	C₈	#14581781	1	1	yes	characteristic
233	C₈	#14581788	1	1	yes	characteristic
234	C₂²	—	2	2	no	—
235	C₂²	#19127707	1	1	yes	characteristic
236	C₂²	#19127897	1	1	yes	characteristic
237	C₂²	#19127902	1	1	yes	characteristic
238	C₄	—	2	4	no	—
239	C₄	—	664	4	no	—
240	C₄	—	664	2	no	—
241	C₄	#19127602	1	1	yes	characteristic
242	C₄	C₂×#14581714	1	1	yes	characteristic
243	C₄	#19127897	1	1	yes	characteristic
244	C₄	#19127902	1	1	yes	characteristic
245	C₂	—	2	1	no	—
246	C₂	—	2	1	no	—
247	C₂	#24908389	1	1	yes	characteristic
248	C₂	#24909545	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19128081

C₂

yes

maximal, characteristic

C₂×#19127518

C₂

yes

maximal

#24909184

C₂

yes

maximal

#24907342

C₂

yes

maximal, characteristic

C₂×#364×C₈₃

C₂

yes

maximal, characteristic

C₂²×Dic₃₃₂

—

C₂²×Dic₃₃₂

C₂²

yes

—

C₂×#14581792

—

#19128081

—

#19128081

C₄

yes

complemented

C₂×#14581728

C₂²

yes

characteristic

#19127739

C₂²

yes

—

—

—

—

C₂×M₃₂×C₈₃

C₂²

yes

—

C₂×C₄×C₈×C₈₃

C₂²

yes

characteristic

#364×C₈₃

—

C₂²×Dic₁₆₆

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

C₂×C₄

yes

—

—

—

—

—

C₂×C₄⋊Dic₈₃

—

#14581728

—

#14581728

D₄

yes

—

#14581726

D₄

yes

—

#14581724

—

#14581702

—

C₈×Dic₈₃

—

C₂²×C₈×C₈₃

D₄

yes

characteristic

C₂²×C₈×C₈₃

C₂³

yes

characteristic

C₂×C₄²×C₈₃

D₄

yes

characteristic

M₃₂×C₈₃

—

M₃₂×C₈₃

—

C₂×C₁₆×C₈₃

—

C₄×C₈×C₈₃

C₂×C₄

yes

—

C₄×C₈×C₈₃

D₄

yes

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂²×Dic₈₃

—

Dic₃₃₂

—

Dic₃₃₂

—

Dic₃₃₂

—

Dic₃₃₂

—

Dic₃₃₂

—

Dic₃₃₂

—

#13050574

—

#13050574

—

C₂×C₈₃⋊C₈

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₂²⋊Dic₈₃

—

C₄×Dic₈₃

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂×C₈×C₈₃

C₂²⋊C₄

yes

—

C₂×C₈×C₈₃

D₈

yes

characteristic

C₂×C₈×C₈₃

D₈

yes

characteristic

C₂×C₈×C₈₃

SD₁₆

yes

—

C₂×C₈×C₈₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₃

C₂×D₄

yes

characteristic

C₂×C₈×C₈₃

C₂×D₄

yes

characteristic

C₂×C₈×C₈₃

C₂×D₄

yes

C₂×C₈×C₈₃

yes

C₂×C₈×C₈₃

yes

C₄²×C₈₃

—

C₄²×C₈₃

C₂²⋊C₄

yes

—

C₁₆×C₈₃

—

C₂³×C₈₃

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₂×C₂²⋊C₄

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

C₂×D₈

yes

characteristic

C₂×C₄×C₈₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₈₃

AGL(1,ℤ/8)

yes

characteristic

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

Dic₁₆₆

—

Dic₁₆₆

—

100

Dic₁₆₆

—

101

Dic₁₆₆

—

102

C₈×C₈₃

#102

yes

—

103

C₈×C₈₃

#102

yes

—

104

C₈×C₈₃

C₄×D₄

yes

characteristic

105

C₈×C₈₃

C₄×D₄

yes

characteristic

106

C₈×C₈₃

#124

yes

characteristic

107

C₈×C₈₃

#127

yes

characteristic

108

C₈₃⋊C₈

—

109

C₂²×C₈₃

—

110

C₂²×C₈₃

#418

yes

characteristic

111

C₂²×C₈₃

#459

yes

characteristic

112

C₂²×C₈₃

#460

yes

characteristic

113

C₄×C₈₃

—

114

C₄×C₈₃

#390

yes

characteristic

115

C₄×C₈₃

C₂×#102

yes

characteristic

116

C₄×C₈₃

#459

yes

characteristic

117

C₄×C₈₃

#460

yes

characteristic

118

Dic₈₃

—

119

Dic₈₃

—

120

#13262

—

maximal, Sylow

121

C₂×C₈₃

—

122

C₂×C₈₃

—

123

C₂×C₈₃

#1982

yes

characteristic

124

C₂×C₈₃

#2214

yes

—

125

C₂×#494

—

126

C₂×#364

D₈₃

yes

characteristic

127

C₂×#362

—

128

#2141

—

129

#1772

—

130

C₈₃

#13262

yes

characteristic, complemented, Sylow

131

C₂²×Q₁₆

—

132

C₂²×Q₁₆

—

166

—

133

C₂×C₄⋊Q₈

—

166

—

134

C₂×M₃₂

C₂×D₈₃

yes

—

135

#494

—

136

#494

—

166

—

137

C₂×#108

—

138

#427

—

139

#405

—

166

—

140

C₂×C₄×C₈

C₂×D₈₃

yes

characteristic

141

#364

—

142

#362

—

166

—

143

#358

—

166

—

144

#339

—

166

—

145

C₂²×Q₈

—

166

—

146

C₂×Q₁₆

—

332

—

147

C₂×Q₁₆

—

332

—

148

C₂×Q₁₆

—

332

—

149

C₂×Q₁₆

—

150

C₂×Q₁₆

—

166

—

151

C₂×Q₁₆

—

166

—

152

C₂×Q₁₆

—

166

—

153

C₂×Q₁₆

—

166

—

154

C₂×Q₁₆

—

166

—

155

C₂×Q₁₆

—

166

—

156

C₂×M₁₆

—

166

—

157

C₂²×C₈

D₃₃₂

yes

characteristic

158

C₂²×C₈

C₂²×D₈₃

yes

characteristic

159

C₄⋊Q₈

—

332

—

160

C₄⋊Q₈

—

166

—

161

#117

—

166

—

162

C₂×C₄⋊C₄

—

332

—

163

C₂×C₄²

D₃₃₂

yes

characteristic

164

M₃₂

—

165

M₃₂

—

166

C₂×C₁₆

—

167

#108

—

168

#108

—

166

—

169

#107

—

170

#106

—

166

—

171

#97

—

332

—

172

C₄×C₈

—

332

—

173

C₄×C₈

C₄×D₈₃

yes

—

174

C₄×C₈

C₂²⋊D₈₃

yes

—

175

C₂×Q₈

—

332

—

176

C₂×Q₈

—

332

—

177

C₂×Q₈

—

332

—

178

C₂×Q₈

—

332

—

179

C₂×Q₈

—

332

—

180

C₂×Q₈

—

166

—

181

C₂²×C₄

—

182

C₂²×C₄

—

332

—

183

C₂²×C₄

C₂×D₃₃₂

yes

characteristic

184

Q₁₆

—

332

—

185

Q₁₆

—

332

—

186

Q₁₆

—

332

—

187

Q₁₆

—

332

—

188

Q₁₆

—

166

—

189

Q₁₆

—

166

—

190

M₁₆

—

332

—

191

M₁₆

—

166

—

192

C₂×C₈

—

332

—

193

C₂×C₈

(C₂×D₈₃)⋊C₄

yes

—

194

C₂×C₈

D₆₆₄

yes

characteristic

195

C₂×C₈

D₆₆₄

yes

characteristic

196

C₂×C₈

#13050579

yes

—

197

C₂×C₈

C₂×C₄×D₈₃

yes

characteristic

198

C₂×C₈

D₄×D₈₃

yes

characteristic

199

C₂×C₈

D₄×D₈₃

yes

characteristic

200

C₂×C₈

C₂×C₂²⋊D₈₃

yes

characteristic

201

C₂×C₈

#13050591

yes

characteristic

202

C₂×C₈

#13050591

yes

characteristic

203

C₄⋊C₄

—

332

—

204

C₄⋊C₄

—

166

—

205

C₂²⋊C₄

—

332

—

206

C₄²

—

207

C₄²

—

332

—

208

C₄²

(C₂×D₈₃)⋊C₄

yes

—

209

C₁₆

—

210

C₂³

#14581820

yes

characteristic

211

Q₈

—

332

—

212

Q₈

—

332

—

213

Q₈

—

664

—

214

Q₈

—

664

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

332

—

218

C₂×C₄

—

332

—

219

C₂×C₄

—

664

—

220

C₂×C₄

—

664

—

221

C₂×C₄

C₂×(C₂×D₈₃)⋊C₄

yes

characteristic

222

C₂×C₄

#14581767

yes

characteristic

223

C₂×C₄

#14581767

yes

characteristic

224

C₂×C₄

C₂×D₆₆₄

yes

characteristic

225

C₂×C₄

C₂×#13050579

yes

characteristic

226

C₂×C₄

#14581820

yes

characteristic

227

C₈

—

332

—

228

C₈

#14581714

yes

—

229

C₈

#14581714

yes

—

230

C₈

#14581754

yes

characteristic

231

C₈

#14581754

yes

characteristic

232

C₈

#14581781

yes

characteristic

233

C₈

#14581788

yes

characteristic

234

C₂²

—

235

C₂²

#19127707

yes

characteristic

236

C₂²

#19127897

yes

characteristic

237

C₂²

#19127902

yes

characteristic

238

C₄

—

239

C₄

—

664

—

240

C₄

—

664

—

241

C₄

#19127602

yes

characteristic

242

C₄

C₂×#14581714

yes

characteristic

243

C₄

#19127897

yes

characteristic

244

C₄

#19127902

yes

characteristic

245

C₂

—

246

C₂

—

247

C₂

#24908389

yes

characteristic

248

C₂

#24909545

yes

—

	subgroup	G/H
center	C₂²	#19127897
commutator	C₂×C₈×C₈₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₈₃
Fitting	C₂×#364×C₈₃	C₂
socle	C₂²×C₈₃	#459
prime radical	C₂³×C₈₃	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₈₃	C₂³
hypercenter	C₂×#364	D₈₃
hypocenter	C₈₃	#13262
LCS	G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#364

subgroup

G/H

center

C₂²

#19127897

commutator

C₂×C₈×C₈₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₈₃

Fitting

C₂×#364×C₈₃

C₂

C₂²×C₈₃

C₂³×C₈₃

C₂²×C₈×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#364

N	H ≅ G/N	type
10. #19128081	C₄	semidirect
130. C₈₃	#13262	semidirect

H ≅ G/N

type

10. #19128081

C₄

semidirect

130. C₈₃

#13262

semidirect

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

subgroup	index
C₂×#19128081	2
C₂×#19127518	2
#24909184	2
#24907342	2
C₂×#364×C₈₃	2
#13262	83

subgroup

index

C₂×#364×C₈₃

Subgroups — #35322917

Conjugacy classes of subgroups

Complements

Maximal subgroups