Group #31915965 — subgroups

Subgroups — #31915965

Order 18176.

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×#17986379	C₂	1	1	yes	maximal, characteristic
2	C₂×#17985816	C₂	1	2	yes	maximal
3	#22590061	C₂	1	2	yes	maximal
4	#22588219	C₂	1	1	yes	maximal, characteristic
5	C₂×#364×C₇₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₂₈₄	—	2	1	no	—
7	C₂²×Dic₂₈₄	C₂²	1	2	yes	—
8	C₂×#14556128	—	2	1	no	—
9	#17986379	—	2	2	no	—
10	#17986379	C₄	1	4	yes	complemented
11	C₂×#14556064	C₂²	1	1	yes	characteristic
12	#17986037	C₂²	1	1	yes	characteristic
13	#17985954	—	2	1	no	—
14	#17985816	—	2	4	no	—
15	#17985804	—	2	4	no	—
16	#17985759	—	2	1	no	—
17	C₂×M₃₂×C₇₁	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
19	#364×C₇₁	—	2	2	no	—
20	C₂²×Dic₁₄₂	—	2	2	no	—
21	C₂×Dic₂₈₄	—	2	4	no	—
22	C₂×Dic₂₈₄	—	2	2	no	—
23	C₂×Dic₂₈₄	—	2	2	no	—
24	C₂×Dic₂₈₄	—	2	2	no	—
25	C₂×Dic₂₈₄	—	2	2	no	—
26	C₂×Dic₂₈₄	—	2	2	no	—
27	C₂×Dic₂₈₄	—	4	1	no	—
28	C₂×Dic₂₈₄	—	4	1	no	—
29	C₂×Dic₂₈₄	—	4	2	no	—
30	C₂×Dic₂₈₄	C₂×C₄	1	4	yes	—
31	C₂×#11765849	—	2	1	no	—
32	#14556128	—	2	4	no	—
33	#14556128	—	4	2	no	—
34	#14556087	—	2	1	no	—
35	C₂×C₄⋊Dic₇₁	—	4	2	no	—
36	#14556064	—	2	1	no	—
37	#14556064	D₄	1	2	yes	—
38	#14556062	D₄	1	2	yes	—
39	#14556060	—	2	1	no	—
40	#14556038	—	4	1	no	—
41	C₈×Dic₇₁	—	4	1	no	—
42	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
44	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
45	M₃₂×C₇₁	—	2	2	no	—
46	M₃₂×C₇₁	—	2	2	no	—
47	C₂×C₁₆×C₇₁	—	2	2	no	—
48	C₄×C₈×C₇₁	C₂×C₄	1	2	yes	—
49	C₄×C₈×C₇₁	D₄	1	2	yes	—
50	C₂×Dic₁₄₂	—	2	4	no	—
51	C₂×Dic₁₄₂	—	4	2	no	—
52	C₂×Dic₁₄₂	—	4	2	no	—
53	C₂×Dic₁₄₂	—	4	2	no	—
54	C₂×Dic₁₄₂	—	4	2	no	—
55	C₂×Dic₁₄₂	—	4	2	no	—
56	C₂²×Dic₇₁	—	4	2	no	—
57	Dic₂₈₄	—	2	4	no	—
58	Dic₂₈₄	—	2	4	no	—
59	Dic₂₈₄	—	4	4	no	—
60	Dic₂₈₄	—	4	4	no	—
61	Dic₂₈₄	—	4	2	no	—
62	Dic₂₈₄	—	4	2	no	—
63	#11765849	—	2	2	no	—
64	#11765849	—	4	1	no	—
65	C₂×C₇₁⋊C₈	—	4	1	no	—
66	C₄⋊Dic₇₁	—	2	2	no	—
67	C₄⋊Dic₇₁	—	4	8	no	—
68	C₂²⋊Dic₇₁	—	4	1	no	—
69	C₄×Dic₇₁	—	4	1	no	—
70	C₂²×C₄×C₇₁	—	2	1	no	—
71	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₇₁	C₂²⋊C₄	1	2	yes	—
73	C₂×C₈×C₇₁	D₈	1	1	yes	characteristic
74	C₂×C₈×C₇₁	D₈	1	1	yes	characteristic
75	C₂×C₈×C₇₁	SD₁₆	1	2	yes	—
76	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
78	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
79	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
80	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
81	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
82	C₄²×C₇₁	—	2	1	no	—
83	C₄²×C₇₁	C₂²⋊C₄	1	2	yes	—
84	C₁₆×C₇₁	—	4	2	no	—
85	C₂³×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
86	C₂×C₄×C₇₁	—	2	4	no	—
87	C₂×C₄×C₇₁	—	2	2	no	—
88	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
90	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
91	C₂×C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
92	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
93	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
94	C₂×Dic₇₁	—	4	4	no	—
95	C₂×Dic₇₁	—	4	2	no	—
96	C₂×Dic₇₁	—	8	2	no	—
97	C₂×Dic₇₁	—	8	2	no	—
98	Dic₁₄₂	—	4	4	no	—
99	Dic₁₄₂	—	4	4	no	—
100	Dic₁₄₂	—	8	2	no	—
101	Dic₁₄₂	—	8	2	no	—
102	C₈×C₇₁	#102	1	2	yes	—
103	C₈×C₇₁	#102	1	2	yes	—
104	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
105	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
106	C₈×C₇₁	#124	1	1	yes	characteristic
107	C₈×C₇₁	#127	1	1	yes	characteristic
108	C₇₁⋊C₈	—	4	2	no	—
109	C₂²×C₇₁	—	2	2	no	—
110	C₂²×C₇₁	#418	1	1	yes	characteristic
111	C₂²×C₇₁	#459	1	1	yes	characteristic
112	C₂²×C₇₁	#460	1	1	yes	characteristic
113	C₄×C₇₁	—	2	4	no	—
114	C₄×C₇₁	#390	1	1	yes	characteristic
115	C₄×C₇₁	C₂×#102	1	1	yes	characteristic
116	C₄×C₇₁	#459	1	1	yes	characteristic
117	C₄×C₇₁	#460	1	1	yes	characteristic
118	Dic₇₁	—	8	2	no	—
119	Dic₇₁	—	8	4	no	—
120	#13262	—	71	1	no	maximal, Sylow
121	C₂×C₇₁	—	2	1	no	—
122	C₂×C₇₁	—	2	1	no	—
123	C₂×C₇₁	#1982	1	1	yes	characteristic
124	C₂×C₇₁	#2214	1	2	yes	—
125	C₂×#494	—	71	1	no	—
126	C₂×#364	D₇₁	1	1	yes	characteristic
127	C₂×#362	—	71	2	no	—
128	#2141	—	71	2	no	—
129	#1772	—	71	1	no	—
130	C₇₁	#13262	1	1	yes	characteristic, complemented, Sylow
131	C₂²×Q₁₆	—	71	2	no	—
132	C₂²×Q₁₆	—	142	1	no	—
133	C₂×C₄⋊Q₈	—	142	1	no	—
134	C₂×M₃₂	C₂×D₇₁	1	2	yes	—
135	#494	—	71	4	no	—
136	#494	—	142	2	no	—
137	C₂×#108	—	71	1	no	—
138	#427	—	71	1	no	—
139	#405	—	142	1	no	—
140	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
141	#364	—	2	2	no	—
142	#362	—	142	4	no	—
143	#358	—	142	4	no	—
144	#339	—	142	1	no	—
145	C₂²×Q₈	—	142	2	no	—
146	C₂×Q₁₆	—	284	1	no	—
147	C₂×Q₁₆	—	284	1	no	—
148	C₂×Q₁₆	—	284	2	no	—
149	C₂×Q₁₆	—	71	4	no	—
150	C₂×Q₁₆	—	142	4	no	—
151	C₂×Q₁₆	—	142	2	no	—
152	C₂×Q₁₆	—	142	2	no	—
153	C₂×Q₁₆	—	142	2	no	—
154	C₂×Q₁₆	—	142	2	no	—
155	C₂×Q₁₆	—	142	2	no	—
156	C₂×M₁₆	—	142	1	no	—
157	C₂²×C₈	D₂₈₄	1	1	yes	characteristic
158	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
159	C₄⋊Q₈	—	284	2	no	—
160	C₄⋊Q₈	—	142	4	no	—
161	#117	—	142	1	no	—
162	C₂×C₄⋊C₄	—	284	2	no	—
163	C₂×C₄²	D₂₈₄	1	1	yes	characteristic
164	M₃₂	—	2	2	no	—
165	M₃₂	—	2	2	no	—
166	C₂×C₁₆	—	2	2	no	—
167	#108	—	71	2	no	—
168	#108	—	142	1	no	—
169	#107	—	71	2	no	—
170	#106	—	142	1	no	—
171	#97	—	284	1	no	—
172	C₄×C₈	—	284	1	no	—
173	C₄×C₈	C₄×D₇₁	1	2	yes	—
174	C₄×C₈	C₂²⋊D₇₁	1	2	yes	—
175	C₂×Q₈	—	284	2	no	—
176	C₂×Q₈	—	284	2	no	—
177	C₂×Q₈	—	284	2	no	—
178	C₂×Q₈	—	284	2	no	—
179	C₂×Q₈	—	284	2	no	—
180	C₂×Q₈	—	142	4	no	—
181	C₂²×C₄	—	2	1	no	—
182	C₂²×C₄	—	284	2	no	—
183	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
184	Q₁₆	—	284	4	no	—
185	Q₁₆	—	284	4	no	—
186	Q₁₆	—	284	2	no	—
187	Q₁₆	—	284	2	no	—
188	Q₁₆	—	142	4	no	—
189	Q₁₆	—	142	4	no	—
190	M₁₆	—	284	1	no	—
191	M₁₆	—	142	2	no	—
192	C₂×C₈	—	284	1	no	—
193	C₂×C₈	(C₂×D₇₁)⋊C₄	1	2	yes	—
194	C₂×C₈	D₅₆₈	1	1	yes	characteristic
195	C₂×C₈	D₅₆₈	1	1	yes	characteristic
196	C₂×C₈	#11765854	1	2	yes	—
197	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
198	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
199	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
200	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
201	C₂×C₈	#11765866	1	1	yes	characteristic
202	C₂×C₈	#11765866	1	1	yes	characteristic
203	C₄⋊C₄	—	284	8	no	—
204	C₄⋊C₄	—	142	2	no	—
205	C₂²⋊C₄	—	284	1	no	—
206	C₄²	—	2	1	no	—
207	C₄²	—	284	1	no	—
208	C₄²	(C₂×D₇₁)⋊C₄	1	2	yes	—
209	C₁₆	—	4	2	no	—
210	C₂³	#14556156	1	1	yes	characteristic
211	Q₈	—	284	4	no	—
212	Q₈	—	284	4	no	—
213	Q₈	—	568	2	no	—
214	Q₈	—	568	2	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	284	2	no	—
218	C₂×C₄	—	284	4	no	—
219	C₂×C₄	—	568	2	no	—
220	C₂×C₄	—	568	2	no	—
221	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
222	C₂×C₄	#14556103	1	1	yes	characteristic
223	C₂×C₄	#14556103	1	1	yes	characteristic
224	C₂×C₄	C₂×D₅₆₈	1	1	yes	characteristic
225	C₂×C₄	C₂×#11765854	1	1	yes	characteristic
226	C₂×C₄	#14556156	1	1	yes	characteristic
227	C₈	—	284	2	no	—
228	C₈	#14556050	1	2	yes	—
229	C₈	#14556050	1	2	yes	—
230	C₈	#14556090	1	1	yes	characteristic
231	C₈	#14556090	1	1	yes	characteristic
232	C₈	#14556117	1	1	yes	characteristic
233	C₈	#14556124	1	1	yes	characteristic
234	C₂²	—	2	2	no	—
235	C₂²	#17986005	1	1	yes	characteristic
236	C₂²	#17986195	1	1	yes	characteristic
237	C₂²	#17986200	1	1	yes	characteristic
238	C₄	—	2	4	no	—
239	C₄	—	568	4	no	—
240	C₄	—	568	2	no	—
241	C₄	#17985900	1	1	yes	characteristic
242	C₄	C₂×#14556050	1	1	yes	characteristic
243	C₄	#17986195	1	1	yes	characteristic
244	C₄	#17986200	1	1	yes	characteristic
245	C₂	—	2	1	no	—
246	C₂	—	2	1	no	—
247	C₂	#22589266	1	1	yes	characteristic
248	C₂	#22590422	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17986379

C₂

yes

maximal, characteristic

C₂×#17985816

C₂

yes

maximal

#22590061

C₂

yes

maximal

#22588219

C₂

yes

maximal, characteristic

C₂×#364×C₇₁

C₂

yes

maximal, characteristic

C₂²×Dic₂₈₄

—

C₂²×Dic₂₈₄

C₂²

yes

—

C₂×#14556128

—

#17986379

—

#17986379

C₄

yes

complemented

C₂×#14556064

C₂²

yes

characteristic

#17986037

C₂²

yes

—

—

—

—

C₂×M₃₂×C₇₁

C₂²

yes

—

C₂×C₄×C₈×C₇₁

C₂²

yes

characteristic

#364×C₇₁

—

C₂²×Dic₁₄₂

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

C₂×C₄

yes

—

—

—

—

—

C₂×C₄⋊Dic₇₁

—

#14556064

—

#14556064

D₄

yes

—

#14556062

D₄

yes

—

#14556060

—

#14556038

—

C₈×Dic₇₁

—

C₂²×C₈×C₇₁

D₄

yes

characteristic

C₂²×C₈×C₇₁

C₂³

yes

characteristic

C₂×C₄²×C₇₁

D₄

yes

characteristic

M₃₂×C₇₁

—

M₃₂×C₇₁

—

C₂×C₁₆×C₇₁

—

C₄×C₈×C₇₁

C₂×C₄

yes

—

C₄×C₈×C₇₁

D₄

yes

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂²×Dic₇₁

—

Dic₂₈₄

—

Dic₂₈₄

—

Dic₂₈₄

—

Dic₂₈₄

—

Dic₂₈₄

—

Dic₂₈₄

—

#11765849

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₂²⋊Dic₇₁

—

C₄×Dic₇₁

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×C₈×C₇₁

C₂²⋊C₄

yes

—

C₂×C₈×C₇₁

D₈

yes

characteristic

C₂×C₈×C₇₁

D₈

yes

characteristic

C₂×C₈×C₇₁

SD₁₆

yes

—

C₂×C₈×C₇₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

C₂×C₈×C₇₁

yes

C₂×C₈×C₇₁

yes

C₄²×C₇₁

—

C₄²×C₇₁

C₂²⋊C₄

yes

—

C₁₆×C₇₁

—

C₂³×C₇₁

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂×C₂²⋊C₄

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

C₂×D₈

yes

characteristic

C₂×C₄×C₇₁

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₇₁

AGL(1,ℤ/8)

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

Dic₁₄₂

—

Dic₁₄₂

—

100

Dic₁₄₂

—

101

Dic₁₄₂

—

102

C₈×C₇₁

#102

yes

—

103

C₈×C₇₁

#102

yes

—

104

C₈×C₇₁

C₄×D₄

yes

characteristic

105

C₈×C₇₁

C₄×D₄

yes

characteristic

106

C₈×C₇₁

#124

yes

characteristic

107

C₈×C₇₁

#127

yes

characteristic

108

C₇₁⋊C₈

—

109

C₂²×C₇₁

—

110

C₂²×C₇₁

#418

yes

characteristic

111

C₂²×C₇₁

#459

yes

characteristic

112

C₂²×C₇₁

#460

yes

characteristic

113

C₄×C₇₁

—

114

C₄×C₇₁

#390

yes

characteristic

115

C₄×C₇₁

C₂×#102

yes

characteristic

116

C₄×C₇₁

#459

yes

characteristic

117

C₄×C₇₁

#460

yes

characteristic

118

Dic₇₁

—

119

Dic₇₁

—

120

#13262

—

maximal, Sylow

121

C₂×C₇₁

—

122

C₂×C₇₁

—

123

C₂×C₇₁

#1982

yes

characteristic

124

C₂×C₇₁

#2214

yes

—

125

C₂×#494

—

126

C₂×#364

D₇₁

yes

characteristic

127

C₂×#362

—

128

#2141

—

129

#1772

—

130

C₇₁

#13262

yes

characteristic, complemented, Sylow

131

C₂²×Q₁₆

—

132

C₂²×Q₁₆

—

142

—

133

C₂×C₄⋊Q₈

—

142

—

134

C₂×M₃₂

C₂×D₇₁

yes

—

135

#494

—

136

#494

—

142

—

137

C₂×#108

—

138

#427

—

139

#405

—

142

—

140

C₂×C₄×C₈

C₂×D₇₁

yes

characteristic

141

#364

—

142

#362

—

142

—

143

#358

—

142

—

144

#339

—

142

—

145

C₂²×Q₈

—

142

—

146

C₂×Q₁₆

—

284

—

147

C₂×Q₁₆

—

284

—

148

C₂×Q₁₆

—

284

—

149

C₂×Q₁₆

—

150

C₂×Q₁₆

—

142

—

151

C₂×Q₁₆

—

142

—

152

C₂×Q₁₆

—

142

—

153

C₂×Q₁₆

—

142

—

154

C₂×Q₁₆

—

142

—

155

C₂×Q₁₆

—

142

—

156

C₂×M₁₆

—

142

—

157

C₂²×C₈

D₂₈₄

yes

characteristic

158

C₂²×C₈

C₂²×D₇₁

yes

characteristic

159

C₄⋊Q₈

—

284

—

160

C₄⋊Q₈

—

142

—

161

#117

—

142

—

162

C₂×C₄⋊C₄

—

284

—

163

C₂×C₄²

D₂₈₄

yes

characteristic

164

M₃₂

—

165

M₃₂

—

166

C₂×C₁₆

—

167

#108

—

168

#108

—

142

—

169

#107

—

170

#106

—

142

—

171

#97

—

284

—

172

C₄×C₈

—

284

—

173

C₄×C₈

C₄×D₇₁

yes

—

174

C₄×C₈

C₂²⋊D₇₁

yes

—

175

C₂×Q₈

—

284

—

176

C₂×Q₈

—

284

—

177

C₂×Q₈

—

284

—

178

C₂×Q₈

—

284

—

179

C₂×Q₈

—

284

—

180

C₂×Q₈

—

142

—

181

C₂²×C₄

—

182

C₂²×C₄

—

284

—

183

C₂²×C₄

C₂×D₂₈₄

yes

characteristic

184

Q₁₆

—

284

—

185

Q₁₆

—

284

—

186

Q₁₆

—

284

—

187

Q₁₆

—

284

—

188

Q₁₆

—

142

—

189

Q₁₆

—

142

—

190

M₁₆

—

284

—

191

M₁₆

—

142

—

192

C₂×C₈

—

284

—

193

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

—

194

C₂×C₈

D₅₆₈

yes

characteristic

195

C₂×C₈

D₅₆₈

yes

characteristic

196

C₂×C₈

#11765854

yes

—

197

C₂×C₈

C₂×C₄×D₇₁

yes

characteristic

198

C₂×C₈

D₄×D₇₁

yes

characteristic

199

C₂×C₈

D₄×D₇₁

yes

characteristic

200

C₂×C₈

C₂×C₂²⋊D₇₁

yes

characteristic

201

C₂×C₈

#11765866

yes

characteristic

202

C₂×C₈

#11765866

yes

characteristic

203

C₄⋊C₄

—

284

—

204

C₄⋊C₄

—

142

—

205

C₂²⋊C₄

—

284

—

206

C₄²

—

207

C₄²

—

284

—

208

C₄²

(C₂×D₇₁)⋊C₄

yes

—

209

C₁₆

—

210

C₂³

#14556156

yes

characteristic

211

Q₈

—

284

—

212

Q₈

—

284

—

213

Q₈

—

568

—

214

Q₈

—

568

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

284

—

218

C₂×C₄

—

284

—

219

C₂×C₄

—

568

—

220

C₂×C₄

—

568

—

221

C₂×C₄

C₂×(C₂×D₇₁)⋊C₄

yes

characteristic

222

C₂×C₄

#14556103

yes

characteristic

223

C₂×C₄

#14556103

yes

characteristic

224

C₂×C₄

C₂×D₅₆₈

yes

characteristic

225

C₂×C₄

C₂×#11765854

yes

characteristic

226

C₂×C₄

#14556156

yes

characteristic

227

C₈

—

284

—

228

C₈

#14556050

yes

—

229

C₈

#14556050

yes

—

230

C₈

#14556090

yes

characteristic

231

C₈

#14556090

yes

characteristic

232

C₈

#14556117

yes

characteristic

233

C₈

#14556124

yes

characteristic

234

C₂²

—

235

C₂²

#17986005

yes

characteristic

236

C₂²

#17986195

yes

characteristic

237

C₂²

#17986200

yes

characteristic

238

C₄

—

239

C₄

—

568

—

240

C₄

—

568

—

241

C₄

#17985900

yes

characteristic

242

C₄

C₂×#14556050

yes

characteristic

243

C₄

#17986195

yes

characteristic

244

C₄

#17986200

yes

characteristic

245

C₂

—

246

C₂

—

247

C₂

#22589266

yes

characteristic

248

C₂

#22590422

yes

—

	subgroup	G/H
center	C₂²	#17986195
commutator	C₂×C₈×C₇₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₁
Fitting	C₂×#364×C₇₁	C₂
socle	C₂²×C₇₁	#459
prime radical	C₂³×C₇₁	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₇₁	C₂³
hypercenter	C₂×#364	D₇₁
hypocenter	C₇₁	#13262
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#364

subgroup

G/H

center

C₂²

#17986195

commutator

C₂×C₈×C₇₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₁

Fitting

C₂×#364×C₇₁

C₂

C₂²×C₇₁

C₂³×C₇₁

C₂²×C₈×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

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

N	H ≅ G/N	type
10. #17986379	C₄	semidirect
130. C₇₁	#13262	semidirect

H ≅ G/N

type

10. #17986379

C₄

semidirect

130. C₇₁

#13262

semidirect

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

subgroup	index
C₂×#17986379	2
C₂×#17985816	2
#22590061	2
#22588219	2
C₂×#364×C₇₁	2
#13262	71

subgroup

index

C₂×#364×C₇₁

Subgroups — #31915965

Conjugacy classes of subgroups

Complements

Maximal subgroups