Group #13256402 — subgroups

Subgroups — #13256402

Order 1792.

574 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 139 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×C₇×#494	C₂	1	1	yes	maximal, characteristic
2	C₂×#89866	C₂	1	2	yes	maximal
3	C₂×#89342	C₂	1	2	yes	maximal
4	#11727542	C₂	1	1	yes	maximal, characteristic
5	#11725460	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₇×Q₁₆	—	2	2	no	—
7	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₂×C₄×Dic₁₄	C₂²	1	1	yes	characteristic
9	C₇×#494	—	2	4	no	—
10	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
11	#89866	—	2	4	no	—
12	#89866	—	2	4	no	—
13	C₂×#6384	—	2	2	no	—
14	C₂×#6382	—	2	2	no	—
15	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	2	yes	—
17	#89345	—	2	2	no	—
18	#89342	—	2	4	no	—
19	#10276	—	7	1	no	maximal, Sylow
20	C₂²×C₇×Q₈	—	2	2	no	—
21	C₂²×Dic₁₄	D₄	1	1	yes	characteristic
22	C₂×C₇×Q₁₆	—	2	8	no	—
23	C₂×C₇×Q₁₆	—	4	4	no	—
24	C₂×C₇×Q₁₆	—	4	4	no	—
25	C₂²×C₇×C₈	D₄	1	2	yes	—
26	C₇×C₄⋊Q₈	—	2	2	no	—
27	C₇×C₄⋊Q₈	—	2	2	no	—
28	C₇×C₄⋊Q₈	—	2	2	no	—
29	C₇×C₄⋊Q₈	D₄	1	4	yes	—
30	C₂×C₇×C₄⋊C₄	—	2	2	no	—
31	C₂×C₇×C₄⋊C₄	—	2	2	no	—
32	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
33	C₂×C₄⋊Dic₇	D₄	1	1	yes	characteristic
34	C₂×Dic₇⋊C₄	—	2	1	no	—
35	C₂×C₄×Dic₇	—	2	1	no	—
36	C₂²×C₇⋊C₈	—	2	2	no	—
37	C₂²×C₇⋊C₈	—	2	1	no	—
38	C₄×Dic₁₄	—	2	2	no	—
39	C₄×Dic₁₄	—	2	2	no	—
40	C₄×C₇×C₈	—	2	2	no	—
41	#6384	—	2	8	no	—
42	#6382	—	2	8	no	—
43	C₄⋊(C₇⋊C₈)	—	2	2	no	—
44	C₄⋊(C₇⋊C₈)	—	2	2	no	—
45	C₄⋊(C₇⋊C₈)	D₄	1	4	yes	—
46	C₂×#494	D₇	1	1	yes	characteristic
47	C₂×#475	—	7	2	no	—
48	#1984	—	7	1	no	—
49	C₂×#332	—	7	2	no	—
50	#1277	—	7	1	no	—
51	C₂×C₇×Q₈	—	2	4	no	—
52	C₂×C₇×Q₈	—	4	2	no	—
53	C₂×C₇×Q₈	—	4	4	no	—
54	C₂×C₇×Q₈	—	4	4	no	—
55	C₂²×C₄×C₇	—	4	2	no	—
56	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₇	#41	1	1	yes	characteristic
59	C₂²×Dic₇	—	2	1	no	—
60	C₂²×Dic₇	—	2	1	no	—
61	C₂×Dic₁₄	—	2	2	no	—
62	C₂×Dic₁₄	—	2	2	no	—
63	C₂×Dic₁₄	—	2	1	no	—
64	C₂×Dic₁₄	Q₁₆	1	2	yes	complemented
65	C₇×Q₁₆	—	4	16	no	—
66	C₂×C₇×C₈	—	2	2	no	—
67	C₂×C₇×C₈	—	2	2	no	—
68	C₂×C₇×C₈	SD₁₆	1	4	yes	—
69	C₇×C₄⋊C₄	—	2	4	no	—
70	C₇×C₄⋊C₄	—	2	4	no	—
71	C₇×C₄⋊C₄	—	4	2	no	—
72	C₇×C₄⋊C₄	—	4	2	no	—
73	C₄²×C₇	C₂×D₄	1	2	yes	—
74	C₄²×C₇	C₂×D₄	1	2	yes	—
75	C₄⋊Dic₇	—	2	2	no	—
76	Dic₇⋊C₄	—	4	2	no	—
77	C₄×Dic₇	—	4	1	no	—
78	C₄×Dic₇	—	4	1	no	—
79	C₂×C₇⋊C₈	—	2	4	no	—
80	C₂×C₇⋊C₈	—	4	2	no	—
81	C₂×C₇⋊C₈	—	4	2	no	—
82	C₂×C₇⋊C₈	—	4	1	no	—
83	C₂×C₇⋊C₈	—	4	2	no	—
84	C₂²×Q₁₆	—	2	2	no	—
85	C₂×C₄⋊Q₈	C₂×D₇	1	2	yes	—
86	C₂×C₄×Q₈	—	7	1	no	—
87	#494	—	2	4	no	—
88	#475	—	14	4	no	—
89	#475	—	14	4	no	—
90	C₂×#106	—	14	2	no	—
91	C₂×C₄⋊C₈	—	7	2	no	—
92	C₂×C₄⋊C₈	—	7	1	no	—
93	C₂×#103	—	14	2	no	—
94	C₂×C₄×C₈	C₂×D₇	1	1	yes	characteristic
95	#336	—	14	2	no	—
96	#332	—	14	4	no	—
97	C₂³×C₇	#121	1	1	yes	characteristic
98	C₇×Q₈	—	4	8	no	—
99	C₇×Q₈	—	8	2	no	—
100	C₇×Q₈	—	8	2	no	—
101	C₂×C₄×C₇	—	2	2	no	—
102	C₂×C₄×C₇	—	4	4	no	—
103	C₂×C₄×C₇	—	8	4	no	—
104	C₂×C₄×C₇	#120	1	2	yes	—
105	C₂×C₄×C₇	#120	1	1	yes	characteristic
106	C₂×C₄×C₇	#121	1	2	yes	—
107	C₂×C₄×C₇	#127	1	1	yes	characteristic
108	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
109	C₂×C₄×C₇	C₂×Q₁₆	1	1	yes	characteristic
110	C₂×C₄×C₇	#135	1	1	yes	characteristic
111	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
112	C₂×C₄×C₇	#137	1	2	yes	—
113	C₂×Dic₇	—	2	2	no	—
114	C₂×Dic₇	—	4	1	no	—
115	C₂×Dic₇	—	4	1	no	—
116	C₂×Dic₇	—	4	1	no	—
117	C₂×Dic₇	—	4	2	no	—
118	Dic₁₄	—	2	4	no	—
119	Dic₁₄	—	4	2	no	—
120	C₇×C₈	—	2	4	no	—
121	C₇⋊C₈	—	4	4	no	—
122	C₇⋊C₈	—	8	1	no	—
123	C₂²×Q₈	—	2	2	no	—
124	C₂²×Q₈	—	7	1	no	—
125	C₂×Q₁₆	—	2	8	no	—
126	C₂×Q₁₆	—	4	4	no	—
127	C₂×Q₁₆	—	4	4	no	—
128	C₂²×C₈	—	14	2	no	—
129	C₂²×C₈	—	14	1	no	—
130	C₂²×C₈	C₂²⋊D₇	1	2	yes	—
131	C₄⋊Q₈	—	2	2	no	—
132	C₄⋊Q₈	—	2	2	no	—
133	C₄⋊Q₈	—	2	2	no	—
134	C₄⋊Q₈	C₂²⋊D₇	1	4	yes	—
135	C₄×Q₈	—	14	2	no	—
136	C₄×Q₈	—	14	2	no	—
137	C₂×C₄⋊C₄	—	2	2	no	—
138	C₂×C₄⋊C₄	—	2	2	no	—
139	C₂×C₄⋊C₄	—	7	1	no	—
140	C₂×C₄⋊C₄	—	14	1	no	—
141	C₂×C₄²	—	14	1	no	—
142	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
143	#106	—	14	8	no	—
144	C₄⋊C₈	—	7	4	no	—
145	C₄⋊C₈	—	14	2	no	—
146	C₄⋊C₈	—	14	2	no	—
147	#103	—	14	8	no	—
148	C₄×C₈	—	2	2	no	—
149	C₂²×C₇	#392	1	1	yes	characteristic
150	C₂²×C₇	#460	1	2	yes	—
151	C₂²×C₇	#467	1	1	yes	characteristic
152	C₂²×C₇	#470	1	1	yes	characteristic
153	C₂²×C₇	#473	1	2	yes	—
154	C₄×C₇	—	2	2	no	—
155	C₄×C₇	—	8	4	no	—
156	C₄×C₇	#450	1	2	yes	—
157	C₄×C₇	#451	1	2	yes	—
158	C₄×C₇	#452	1	2	yes	—
159	C₄×C₇	#492	1	1	yes	characteristic
160	C₄×C₇	#496	1	1	yes	characteristic
161	Dic₇	—	4	2	no	—
162	Dic₇	—	8	1	no	—
163	C₂×Q₈	—	2	4	no	—
164	C₂×Q₈	—	4	2	no	—
165	C₂×Q₈	—	4	4	no	—
166	C₂×Q₈	—	4	4	no	—
167	C₂×Q₈	—	7	2	no	—
168	C₂×Q₈	—	14	1	no	—
169	C₂×Q₈	—	14	2	no	—
170	C₂×Q₈	—	14	2	no	—
171	C₂²×C₄	—	4	2	no	—
172	C₂²×C₄	—	14	1	no	—
173	C₂²×C₄	—	14	1	no	—
174	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
175	C₂²×C₄	#1159	1	1	yes	characteristic
176	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
177	Q₁₆	—	4	16	no	—
178	C₂×C₈	—	2	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	14	4	no	—
181	C₂×C₈	—	28	2	no	—
182	C₂×C₈	—	28	2	no	—
183	C₂×C₈	—	28	2	no	—
184	C₂×C₈	—	28	1	no	—
185	C₂×C₈	#1142	1	4	yes	—
186	C₄⋊C₄	—	2	4	no	—
187	C₄⋊C₄	—	2	4	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	—	4	2	no	—
190	C₄⋊C₄	—	14	2	no	—
191	C₄⋊C₄	—	28	2	no	—
192	C₄²	—	28	1	no	—
193	C₄²	—	28	1	no	—
194	C₄²	D₄×D₇	1	2	yes	—
195	C₄²	C₂×C₂²⋊D₇	1	2	yes	—
196	C₂×C₇	#1670	1	2	yes	—
197	C₂×C₇	#1690	1	2	yes	—
198	C₂×C₇	#2001	1	1	yes	characteristic
199	C₂×C₇	#2014	1	1	yes	characteristic
200	C₂×C₇	#2020	1	1	yes	characteristic
201	C₂³	#6501	1	1	yes	characteristic
202	Q₈	—	4	8	no	—
203	Q₈	—	8	2	no	—
204	Q₈	—	8	2	no	—
205	Q₈	—	14	4	no	—
206	Q₈	—	28	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	4	4	no	—
209	C₂×C₄	—	8	4	no	—
210	C₂×C₄	—	14	2	no	—
211	C₂×C₄	—	28	1	no	—
212	C₂×C₄	—	28	1	no	—
213	C₂×C₄	—	28	2	no	—
214	C₂×C₄	—	28	1	no	—
215	C₂×C₄	D₇×Q₁₆	1	1	yes	characteristic
216	C₂×C₄	#6481	1	2	yes	—
217	C₂×C₄	#6482	1	1	yes	characteristic
218	C₂×C₄	#6495	1	2	yes	—
219	C₂×C₄	C₂×#1142	1	2	yes	—
220	C₂×C₄	#6500	1	2	yes	—
221	C₂×C₄	#6502	1	2	yes	—
222	C₂×C₄	#6503	1	1	yes	characteristic
223	C₂×C₄	#6516	1	1	yes	characteristic
224	C₈	—	2	4	no	—
225	C₈	—	28	4	no	—
226	C₈	—	56	1	no	—
227	C₇	#10276	1	1	yes	characteristic, complemented, Sylow
228	C₂²	#89847	1	2	yes	—
229	C₂²	#89960	1	1	yes	characteristic
230	C₂²	#89961	1	1	yes	characteristic
231	C₂²	#89964	1	2	yes	—
232	C₂²	#89995	1	1	yes	characteristic
233	C₄	—	2	2	no	—
234	C₄	—	8	4	no	—
235	C₄	—	28	2	no	—
236	C₄	—	56	1	no	—
237	C₄	#89846	1	1	yes	characteristic
238	C₄	#89848	1	1	yes	characteristic
239	C₄	#89958	1	2	yes	—
240	C₄	#89959	1	2	yes	—
241	C₄	#89990	1	2	yes	—
242	C₂	#11729062	1	2	yes	—
243	C₂	#11729063	1	2	yes	—
244	C₂	#11729522	1	1	yes	characteristic
245	C₂	#11729825	1	1	yes	characteristic
246	C₂	#11729828	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₇×#494

C₂

yes

maximal, characteristic

C₂×#89866

C₂

yes

maximal

C₂×#89342

C₂

yes

maximal

#11727542

C₂

yes

maximal, characteristic

#11725460

C₂

yes

maximal, characteristic

C₂²×C₇×Q₁₆

—

C₂×C₇×C₄⋊Q₈

C₂²

yes

—

C₂×C₄×Dic₁₄

C₂²

yes

characteristic

C₇×#494

—

C₂×C₄×C₇×C₈

C₂²

yes

—

—

—

—

C₂×C₄⋊(C₇⋊C₈)

C₂²

yes

characteristic

C₂×C₄⋊(C₇⋊C₈)

C₂²

yes

—

—

—

—

C₂²×C₇×Q₈

—

C₂²×Dic₁₄

D₄

yes

characteristic

C₂×C₇×Q₁₆

—

C₂×C₇×Q₁₆

—

C₂×C₇×Q₁₆

—

C₂²×C₇×C₈

D₄

yes

—

C₇×C₄⋊Q₈

—

C₇×C₄⋊Q₈

—

C₇×C₄⋊Q₈

—

C₇×C₄⋊Q₈

D₄

yes

—

C₂×C₇×C₄⋊C₄

—

C₂×C₇×C₄⋊C₄

—

C₂×C₄²×C₇

C₂³

yes

characteristic

C₂×C₄⋊Dic₇

D₄

yes

characteristic

C₂×Dic₇⋊C₄

—

C₂×C₄×Dic₇

—

C₂²×C₇⋊C₈

—

C₂²×C₇⋊C₈

—

C₄×Dic₁₄

—

C₄×Dic₁₄

—

C₄×C₇×C₈

—

#6384

—

#6382

—

C₄⋊(C₇⋊C₈)

—

C₄⋊(C₇⋊C₈)

—

C₄⋊(C₇⋊C₈)

D₄

yes

—

C₂×#494

D₇

yes

—

—

—

—

C₂×C₇×Q₈

—

C₂×C₇×Q₈

—

C₂×C₇×Q₈

—

C₂×C₇×Q₈

—

C₂²×C₄×C₇

—

C₂²×C₄×C₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₇

#41

yes

characteristic

C₂²×Dic₇

—

C₂²×Dic₇

—

C₂×Dic₁₄

—

C₂×Dic₁₄

—

C₂×Dic₁₄

—

C₂×Dic₁₄

Q₁₆

yes

complemented

C₇×Q₁₆

—

C₂×C₇×C₈

—

C₂×C₇×C₈

—

C₂×C₇×C₈

SD₁₆

yes

—

C₇×C₄⋊C₄

—

C₇×C₄⋊C₄

—

C₇×C₄⋊C₄

—

C₇×C₄⋊C₄

—

C₄²×C₇

C₂×D₄

yes

—

C₄²×C₇

C₂×D₄

yes

—

C₄⋊Dic₇

—

Dic₇⋊C₄

—

C₄×Dic₇

—

C₄×Dic₇

—

C₂×C₇⋊C₈

—

C₂×C₇⋊C₈

—

C₂×C₇⋊C₈

—

C₂×C₇⋊C₈

—

C₂×C₇⋊C₈

—

C₂²×Q₁₆

—

C₂×C₄⋊Q₈

C₂×D₇

yes

—

C₂×C₄×Q₈

—

—

—

—

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×#103

—

C₂×C₄×C₈

C₂×D₇

yes

characteristic

#336

—

#332

—

C₂³×C₇

#121

yes

characteristic

C₇×Q₈

—

C₇×Q₈

—

100

C₇×Q₈

—

101

C₂×C₄×C₇

—

102

C₂×C₄×C₇

—

103

C₂×C₄×C₇

—

104

C₂×C₄×C₇

#120

yes

—

105

C₂×C₄×C₇

#120

yes

characteristic

106

C₂×C₄×C₇

#121

yes

—

107

C₂×C₄×C₇

#127

yes

characteristic

108

C₂×C₄×C₇

C₂×SD₁₆

yes

—

109

C₂×C₄×C₇

C₂×Q₁₆

yes

characteristic

110

C₂×C₄×C₇

#135

yes

characteristic

111

C₂×C₄×C₇

AGL(1,ℤ/8)

yes

—

112

C₂×C₄×C₇

#137

yes

—

113

C₂×Dic₇

—

114

C₂×Dic₇

—

115

C₂×Dic₇

—

116

C₂×Dic₇

—

117

C₂×Dic₇

—

118

Dic₁₄

—

119

Dic₁₄

—

120

C₇×C₈

—

121

C₇⋊C₈

—

122

C₇⋊C₈

—

123

C₂²×Q₈

—

124

C₂²×Q₈

—

125

C₂×Q₁₆

—

126

C₂×Q₁₆

—

127

C₂×Q₁₆

—

128

C₂²×C₈

—

129

C₂²×C₈

—

130

C₂²×C₈

C₂²⋊D₇

yes

—

131

C₄⋊Q₈

—

132

C₄⋊Q₈

—

133

C₄⋊Q₈

—

134

C₄⋊Q₈

C₂²⋊D₇

yes

—

135

C₄×Q₈

—

136

C₄×Q₈

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄⋊C₄

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄²

—

142

C₂×C₄²

C₂²×D₇

yes

characteristic

143

#106

—

144

C₄⋊C₈

—

145

C₄⋊C₈

—

146

C₄⋊C₈

—

147

#103

—

148

C₄×C₈

—

149

C₂²×C₇

#392

yes

characteristic

150

C₂²×C₇

#460

yes

—

151

C₂²×C₇

#467

yes

characteristic

152

C₂²×C₇

#470

yes

characteristic

153

C₂²×C₇

#473

yes

—

154

C₄×C₇

—

155

C₄×C₇

—

156

C₄×C₇

#450

yes

—

157

C₄×C₇

#451

yes

—

158

C₄×C₇

#452

yes

—

159

C₄×C₇

#492

yes

characteristic

160

C₄×C₇

#496

yes

characteristic

161

Dic₇

—

162

Dic₇

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

D₄×D₇

yes

characteristic

175

C₂²×C₄

#1159

yes

characteristic

176

C₂²×C₄

C₂×C₂²⋊D₇

yes

characteristic

177

Q₁₆

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

#1142

yes

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄²

—

193

C₄²

—

194

C₄²

D₄×D₇

yes

—

195

C₄²

C₂×C₂²⋊D₇

yes

—

196

C₂×C₇

#1670

yes

—

197

C₂×C₇

#1690

yes

—

198

C₂×C₇

#2001

yes

characteristic

199

C₂×C₇

#2014

yes

characteristic

200

C₂×C₇

#2020

yes

characteristic

201

C₂³

#6501

yes

characteristic

202

Q₈

—

203

Q₈

—

204

Q₈

—

205

Q₈

—

206

Q₈

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

D₇×Q₁₆

yes

characteristic

216

C₂×C₄

#6481

yes

—

217

C₂×C₄

#6482

yes

characteristic

218

C₂×C₄

#6495

yes

—

219

C₂×C₄

C₂×#1142

yes

—

220

C₂×C₄

#6500

yes

—

221

C₂×C₄

#6502

yes

—

222

C₂×C₄

#6503

yes

characteristic

223

C₂×C₄

#6516

yes

characteristic

224

C₈

—

225

C₈

—

226

C₈

—

227

C₇

#10276

yes

characteristic, complemented, Sylow

228

C₂²

#89847

yes

—

229

C₂²

#89960

yes

characteristic

230

C₂²

#89961

yes

characteristic

231

C₂²

#89964

yes

—

232

C₂²

#89995

yes

characteristic

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

#89846

yes

characteristic

238

C₄

#89848

yes

characteristic

239

C₄

#89958

yes

—

240

C₄

#89959

yes

—

241

C₄

#89990

yes

—

242

C₂

#11729062

yes

—

243

C₂

#11729063

yes

—

244

C₂

#11729522

yes

characteristic

245

C₂

#11729825

yes

characteristic

246

C₂

#11729828

yes

characteristic

	subgroup	G/H
center	C₂³	#6501
commutator, cosocle	C₂×C₄²×C₇	C₂³
Frattini	C₂×C₄²	C₂²×D₇
Fitting	C₂×C₇×#494	C₂
socle, prime radical	C₂³×C₇	#121
hypercenter	C₂×#494	D₇
hypocenter	C₇	#10276
LCS	G ▷ C₂×C₄²×C₇ ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

subgroup

G/H

center

C₂³

#6501

commutator, cosocle

C₂×C₄²×C₇

C₂³

Frattini

C₂×C₄²

C₂²×D₇

Fitting

C₂×C₇×#494

C₂

C₂³×C₇

D₇

C₇

G ▷ C₂×C₄²×C₇ ▷ C₂²×C₇ ▷ C₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

N	H ≅ G/N	type
64. C₂×Dic₁₄	Q₁₆	semidirect
227. C₇	#10276	semidirect

H ≅ G/N

type

64. C₂×Dic₁₄

Q₁₆

semidirect

227. C₇

#10276

semidirect

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

subgroup	index
C₂×C₇×#494	2
C₂×#89866	2
C₂×#89342	2
#11727542	2
#11725460	2
#10276	7

subgroup

index

C₂×C₇×#494

Subgroups — #13256402

Conjugacy classes of subgroups

Complements

Maximal subgroups