Group #13252869 — subgroups

Subgroups — #13252869

Order 1792.

478 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 159 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	C₇×#2862	C₂	1	1	yes	maximal, characteristic
2	C₂×#89342	C₂	1	2	yes	maximal
3	C₂×#89342	C₂	1	2	yes	maximal
4	#11727146	C₂	1	1	yes	maximal, characteristic
5	C₄×C₄⋊(C₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
6	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₇×#391	—	2	1	no	—
9	C₇×#391	—	2	1	no	—
10	C₇×#391	—	2	2	no	—
11	C₇×#382	C₄	1	4	yes	—
12	C₄³×C₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	2	yes	—
15	C₂×C₄×C₇⋊C₈	—	2	1	no	—
16	#89342	—	2	4	no	—
17	#89342	—	2	4	no	—
18	#89319	—	2	1	no	—
19	#89319	—	2	2	no	—
20	#9700	—	7	1	no	maximal, Sylow
21	C₂²×C₇×Q₈	—	2	1	no	—
22	C₂²×C₇×Q₈	—	2	1	no	—
23	C₇×C₄⋊Q₈	—	2	2	no	—
24	C₇×C₄⋊Q₈	—	2	2	no	—
25	C₇×C₄⋊Q₈	—	2	2	no	—
26	C₇×C₄⋊Q₈	—	2	2	no	—
27	C₂×C₇×C₄⋊C₄	—	2	1	no	—
28	C₂×C₇×C₄⋊C₄	—	2	1	no	—
29	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
30	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
32	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₇	D₄	1	2	yes	—
35	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
36	C₂²×C₇⋊C₈	—	2	2	no	—
37	C₂²×C₇⋊C₈	—	2	2	no	—
38	C₇×#95	—	2	4	no	—
39	C₇×#95	—	2	4	no	—
40	C₄⋊(C₇⋊C₈)	—	2	2	no	—
41	C₄⋊(C₇⋊C₈)	—	2	2	no	—
42	C₄⋊(C₇⋊C₈)	—	2	2	no	—
43	C₄⋊(C₇⋊C₈)	D₄	1	4	yes	—
44	C₄×C₇⋊C₈	—	4	2	no	—
45	#2862	D₇	1	1	yes	characteristic
46	#1831	—	7	1	no	—
47	C₄×C₄⋊C₈	—	7	1	no	—
48	C₂×#332	—	7	2	no	—
49	C₂×#332	—	7	2	no	—
50	C₂×C₇×Q₈	—	4	2	no	—
51	C₂×C₇×Q₈	—	4	1	no	—
52	C₂×C₇×Q₈	—	4	1	no	—
53	C₂×C₇×Q₈	—	4	2	no	—
54	C₂×C₇×Q₈	—	4	4	no	—
55	C₂×C₇×Q₈	—	4	1	no	—
56	C₂×C₇×Q₈	—	4	1	no	—
57	C₂²×C₄×C₇	—	2	2	no	—
58	C₂²×C₄×C₇	—	2	2	no	—
59	C₂²×C₄×C₇	C₂²⋊C₄	1	2	yes	—
60	C₂²×C₄×C₇	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
64	C₇×C₄⋊C₄	—	2	4	no	—
65	C₇×C₄⋊C₄	—	2	4	no	—
66	C₇×C₄⋊C₄	—	4	2	no	—
67	C₇×C₄⋊C₄	—	4	1	no	—
68	C₇×C₄⋊C₄	—	4	1	no	—
69	C₄²×C₇	—	2	4	no	—
70	C₄²×C₇	—	2	4	no	—
71	C₄²×C₇	—	2	2	no	—
72	C₄²×C₇	—	2	1	no	—
73	C₄²×C₇	—	2	1	no	—
74	C₄²×C₇	C₂×D₄	1	2	yes	—
75	C₄²×C₇	#41	1	2	yes	—
76	C₂×C₇⋊C₈	—	2	4	no	—
77	C₂×C₇⋊C₈	—	4	2	no	—
78	C₂×C₇⋊C₈	—	4	2	no	—
79	C₂×C₇⋊C₈	—	4	2	no	—
80	C₂×C₇⋊C₈	—	4	4	no	—
81	C₂×C₄⋊Q₈	C₂×D₇	1	1	yes	characteristic
82	C₂×C₄⋊Q₈	C₂×D₇	1	1	yes	characteristic
83	C₂×C₄⋊C₈	—	7	2	no	—
84	C₂×C₄⋊C₈	—	7	2	no	—
85	C₂×C₄×C₈	—	14	1	no	—
86	#391	—	2	1	no	—
87	#391	—	2	2	no	—
88	#391	—	2	1	no	—
89	#382	Dic₇	1	4	yes	—
90	C₄³	C₂×D₇	1	1	yes	characteristic
91	#336	—	14	2	no	—
92	#336	—	14	1	no	—
93	#332	—	14	4	no	—
94	#332	—	14	4	no	—
95	C₂³×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
96	C₇×Q₈	—	8	2	no	—
97	C₇×Q₈	—	8	2	no	—
98	C₇×Q₈	—	8	2	no	—
99	C₇×Q₈	—	8	2	no	—
100	C₂×C₄×C₇	—	2	2	no	—
101	C₂×C₄×C₇	—	2	2	no	—
102	C₂×C₄×C₇	—	2	2	no	—
103	C₂×C₄×C₇	—	2	2	no	—
104	C₂×C₄×C₇	—	2	2	no	—
105	C₂×C₄×C₇	—	2	2	no	—
106	C₂×C₄×C₇	—	4	2	no	—
107	C₂×C₄×C₇	—	4	2	no	—
108	C₂×C₄×C₇	—	4	4	no	—
109	C₂×C₄×C₇	—	4	2	no	—
110	C₂×C₄×C₇	—	4	2	no	—
111	C₂×C₄×C₇	#101	1	4	yes	—
112	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
113	C₂×C₄×C₇	#121	1	2	yes	—
114	C₂×C₄×C₇	#124	1	1	yes	characteristic
115	C₂×C₄×C₇	#127	1	1	yes	characteristic
116	C₂×C₄×C₇	#135	1	2	yes	—
117	C₂×C₄×C₇	#135	1	4	yes	—
118	C₂×C₄×C₇	AGL(1,ℤ/8)	1	1	yes	characteristic
119	C₂×C₄×C₇	#137	1	1	yes	characteristic
120	C₇⋊C₈	—	4	4	no	—
121	C₇⋊C₈	—	8	2	no	—
122	C₂²×Q₈	—	2	1	no	—
123	C₂²×Q₈	—	2	1	no	—
124	C₂²×C₈	—	14	2	no	—
125	C₂²×C₈	—	14	2	no	—
126	C₄⋊Q₈	—	2	2	no	—
127	C₄⋊Q₈	—	2	2	no	—
128	C₄⋊Q₈	—	2	2	no	—
129	C₄⋊Q₈	—	2	2	no	—
130	C₂×C₄⋊C₄	—	2	1	no	—
131	C₂×C₄⋊C₄	—	2	1	no	—
132	C₂×C₄⋊C₄	C₂×Dic₇	1	2	yes	—
133	C₂×C₄⋊C₄	C₂×Dic₇	1	2	yes	—
134	C₂×C₄²	C₂×Dic₇	1	2	yes	—
135	C₂×C₄²	C₂²⋊D₇	1	1	yes	characteristic
136	C₂×C₄²	C₂²⋊D₇	1	2	yes	—
137	C₂×C₄²	C₂²⋊D₇	1	1	yes	characteristic
138	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
139	C₄⋊C₈	—	7	4	no	—
140	C₄⋊C₈	—	14	2	no	—
141	C₄⋊C₈	—	14	2	no	—
142	C₄⋊C₈	—	14	2	no	—
143	C₄×C₈	—	28	2	no	—
144	#95	—	2	4	no	—
145	#95	—	2	4	no	—
146	C₂²×C₇	#390	1	1	yes	characteristic
147	C₂²×C₇	C₂×#101	1	2	yes	—
148	C₂²×C₇	#416	1	1	yes	characteristic
149	C₂²×C₇	#416	1	2	yes	—
150	C₂²×C₇	#417	1	1	yes	characteristic
151	C₄×C₇	—	2	4	no	—
152	C₄×C₇	—	2	2	no	—
153	C₄×C₇	—	4	2	no	—
154	C₄×C₇	—	8	2	no	—
155	C₄×C₇	—	8	2	no	—
156	C₄×C₇	#463	1	2	yes	—
157	C₄×C₇	#464	1	2	yes	—
158	C₄×C₇	#488	1	2	yes	—
159	C₄×C₇	#495	1	2	yes	—
160	C₂×Q₈	—	4	1	no	—
161	C₂×Q₈	—	4	2	no	—
162	C₂×Q₈	—	4	1	no	—
163	C₂×Q₈	—	4	1	no	—
164	C₂×Q₈	—	4	2	no	—
165	C₂×Q₈	—	4	4	no	—
166	C₂×Q₈	—	4	1	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	C₂²⋊Dic₇	1	2	yes	—
170	C₂²×C₄	C₂²⋊Dic₇	1	2	yes	—
171	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
172	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
173	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
174	C₂×C₈	—	14	4	no	—
175	C₂×C₈	—	28	2	no	—
176	C₂×C₈	—	28	2	no	—
177	C₂×C₈	—	28	2	no	—
178	C₂×C₈	—	28	4	no	—
179	C₄⋊C₄	—	2	4	no	—
180	C₄⋊C₄	—	2	4	no	—
181	C₄⋊C₄	—	4	1	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₄⋊C₄	—	4	1	no	—
184	C₄²	—	2	4	no	—
185	C₄²	—	2	1	no	—
186	C₄²	—	2	4	no	—
187	C₄²	—	2	2	no	—
188	C₄²	—	2	1	no	—
189	C₄²	D₄×D₇	1	2	yes	—
190	C₄²	#1159	1	2	yes	—
191	C₂×C₇	#1544	1	2	yes	—
192	C₂×C₇	#1552	1	2	yes	—
193	C₂×C₇	#1958	1	1	yes	characteristic
194	C₂×C₇	#1966	1	1	yes	characteristic
195	C₂×C₇	#1983	1	1	yes	characteristic
196	C₂³	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
197	Q₈	—	8	2	no	—
198	Q₈	—	8	2	no	—
199	Q₈	—	8	2	no	—
200	Q₈	—	8	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	#6410	1	4	yes	—
213	C₂×C₄	D₄×Dic₇	1	2	yes	—
214	C₂×C₄	#6499	1	1	yes	characteristic
215	C₂×C₄	#6501	1	2	yes	—
216	C₂×C₄	#6503	1	1	yes	characteristic
217	C₂×C₄	#6512	1	1	yes	characteristic
218	C₂×C₄	#6513	1	2	yes	—
219	C₂×C₄	#6513	1	4	yes	—
220	C₂×C₄	#6514	1	1	yes	characteristic
221	C₈	—	28	4	no	—
222	C₈	—	56	2	no	—
223	C₇	#9700	1	1	yes	characteristic, complemented, Sylow
224	C₂²	#89993	1	1	yes	characteristic
225	C₂²	C₂×#6410	1	2	yes	—
226	C₂²	#90004	1	1	yes	characteristic
227	C₂²	#90005	1	1	yes	characteristic
228	C₂²	#90005	1	2	yes	—
229	C₄	—	2	2	no	—
230	C₄	—	2	4	no	—
231	C₄	—	4	2	no	—
232	C₄	—	8	2	no	—
233	C₄	—	8	2	no	—
234	C₄	#89826	1	2	yes	—
235	C₄	#89828	1	2	yes	—
236	C₄	#89829	1	2	yes	—
237	C₄	#89831	1	2	yes	—
238	C₂	#11729475	1	1	yes	characteristic
239	C₂	#11729479	1	1	yes	characteristic
240	C₂	#11729543	1	1	yes	characteristic
241	C₂	#11729583	1	2	yes	—
242	C₂	#11729585	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₇×#2862

C₂

yes

maximal, characteristic

C₂×#89342

C₂

yes

maximal

C₂×#89342

C₂

yes

maximal

#11727146

C₂

yes

maximal, characteristic

C₄×C₄⋊(C₇⋊C₈)

C₂

yes

maximal, characteristic

C₂×C₇×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₇×C₄⋊Q₈

C₂²

yes

—

—

—

C₄

yes

—

C₄³×C₇

C₂²

yes

characteristic

C₂×C₄⋊(C₇⋊C₈)

C₂²

yes

—

C₂×C₄⋊(C₇⋊C₈)

C₂²

yes

—

C₂×C₄×C₇⋊C₈

—

—

—

—

—

—

C₂²×C₇×Q₈

—

C₂²×C₇×Q₈

—

C₇×C₄⋊Q₈

—

C₇×C₄⋊Q₈

—

C₇×C₄⋊Q₈

—

C₇×C₄⋊Q₈

—

C₂×C₇×C₄⋊C₄

—

C₂×C₇×C₄⋊C₄

—

C₂×C₇×C₄⋊C₄

C₂×C₄

yes

—

C₂×C₇×C₄⋊C₄

C₂×C₄

yes

—

C₂×C₄²×C₇

C₂×C₄

yes

—

C₂×C₄²×C₇

D₄

yes

characteristic

C₂×C₄²×C₇

D₄

yes

characteristic

C₂×C₄²×C₇

D₄

yes

—

C₂×C₄²×C₇

C₂³

yes

characteristic

C₂²×C₇⋊C₈

—

C₂²×C₇⋊C₈

—

C₇×#95

—

C₇×#95

—

C₄⋊(C₇⋊C₈)

—

C₄⋊(C₇⋊C₈)

—

C₄⋊(C₇⋊C₈)

—

C₄⋊(C₇⋊C₈)

D₄

yes

—

C₄×C₇⋊C₈

—

#2862

D₇

yes

characteristic

#1831

—

C₄×C₄⋊C₈

—

C₂×#332

—

C₂×#332

—

C₂×C₇×Q₈

—

C₂×C₇×Q₈

—

C₂×C₇×Q₈

—

C₂×C₇×Q₈

—

C₂×C₇×Q₈

—

C₂×C₇×Q₈

—

C₂×C₇×Q₈

—

C₂²×C₄×C₇

—

C₂²×C₄×C₇

—

C₂²×C₄×C₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₇

C₂×D₄

yes

characteristic

C₇×C₄⋊C₄

—

C₇×C₄⋊C₄

—

C₇×C₄⋊C₄

—

C₇×C₄⋊C₄

—

C₇×C₄⋊C₄

—

C₄²×C₇

—

C₄²×C₇

—

C₄²×C₇

—

C₄²×C₇

—

C₄²×C₇

—

C₄²×C₇

C₂×D₄

yes

—

C₄²×C₇

#41

yes

—

C₂×C₇⋊C₈

—

C₂×C₇⋊C₈

—

C₂×C₇⋊C₈

—

C₂×C₇⋊C₈

—

C₂×C₇⋊C₈

—

C₂×C₄⋊Q₈

C₂×D₇

yes

characteristic

C₂×C₄⋊Q₈

C₂×D₇

yes

characteristic

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

—

—

—

—

Dic₇

yes

—

C₄³

C₂×D₇

yes

—

—

—

—

C₂³×C₇

C₂×C₂²⋊C₄

yes

characteristic

C₇×Q₈

—

C₇×Q₈

—

C₇×Q₈

—

C₇×Q₈

—

100

C₂×C₄×C₇

—

101

C₂×C₄×C₇

—

102

C₂×C₄×C₇

—

103

C₂×C₄×C₇

—

104

C₂×C₄×C₇

—

105

C₂×C₄×C₇

—

106

C₂×C₄×C₇

—

107

C₂×C₄×C₇

—

108

C₂×C₄×C₇

—

109

C₂×C₄×C₇

—

110

C₂×C₄×C₇

—

111

C₂×C₄×C₇

#101

yes

—

112

C₂×C₄×C₇

C₄×D₄

yes

—

113

C₂×C₄×C₇

#121

yes

—

114

C₂×C₄×C₇

#124

yes

characteristic

115

C₂×C₄×C₇

#127

yes

characteristic

116

C₂×C₄×C₇

#135

yes

—

117

C₂×C₄×C₇

#135

yes

—

118

C₂×C₄×C₇

AGL(1,ℤ/8)

yes

characteristic

119

C₂×C₄×C₇

#137

yes

characteristic

120

C₇⋊C₈

—

121

C₇⋊C₈

—

122

C₂²×Q₈

—

123

C₂²×Q₈

—

124

C₂²×C₈

—

125

C₂²×C₈

—

126

C₄⋊Q₈

—

127

C₄⋊Q₈

—

128

C₄⋊Q₈

—

129

C₄⋊Q₈

—

130

C₂×C₄⋊C₄

—

131

C₂×C₄⋊C₄

—

132

C₂×C₄⋊C₄

C₂×Dic₇

yes

—

133

C₂×C₄⋊C₄

C₂×Dic₇

yes

—

134

C₂×C₄²

C₂×Dic₇

yes

—

135

C₂×C₄²

C₂²⋊D₇

yes

characteristic

136

C₂×C₄²

C₂²⋊D₇

yes

—

137

C₂×C₄²

C₂²⋊D₇

yes

characteristic

138

C₂×C₄²

C₂²×D₇

yes

characteristic

139

C₄⋊C₈

—

140

C₄⋊C₈

—

141

C₄⋊C₈

—

142

C₄⋊C₈

—

143

C₄×C₈

—

144

#95

—

145

#95

—

146

C₂²×C₇

#390

yes

characteristic

147

C₂²×C₇

C₂×#101

yes

—

148

C₂²×C₇

#416

yes

characteristic

149

C₂²×C₇

#416

yes

—

150

C₂²×C₇

#417

yes

characteristic

151

C₄×C₇

—

152

C₄×C₇

—

153

C₄×C₇

—

154

C₄×C₇

—

155

C₄×C₇

—

156

C₄×C₇

#463

yes

—

157

C₄×C₇

#464

yes

—

158

C₄×C₇

#488

yes

—

159

C₄×C₇

#495

yes

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

C₂²⋊Dic₇

yes

—

170

C₂²×C₄

C₂²⋊Dic₇

yes

—

171

C₂²×C₄

C₂²×Dic₇

yes

characteristic

172

C₂²×C₄

C₂×C₂²⋊D₇

yes

characteristic

173

C₂²×C₄

C₂×C₂²⋊D₇

yes

characteristic

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

188

C₄²

—

189

C₄²

D₄×D₇

yes

—

190

C₄²

#1159

yes

—

191

C₂×C₇

#1544

yes

—

192

C₂×C₇

#1552

yes

—

193

C₂×C₇

#1958

yes

characteristic

194

C₂×C₇

#1966

yes

characteristic

195

C₂×C₇

#1983

yes

characteristic

196

C₂³

C₂×C₂²⋊Dic₇

yes

characteristic

197

Q₈

—

198

Q₈

—

199

Q₈

—

200

Q₈

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

#6410

yes

—

213

C₂×C₄

D₄×Dic₇

yes

—

214

C₂×C₄

#6499

yes

characteristic

215

C₂×C₄

#6501

yes

—

216

C₂×C₄

#6503

yes

characteristic

217

C₂×C₄

#6512

yes

characteristic

218

C₂×C₄

#6513

yes

—

219

C₂×C₄

#6513

yes

—

220

C₂×C₄

#6514

yes

characteristic

221

C₈

—

222

C₈

—

223

C₇

#9700

yes

characteristic, complemented, Sylow

224

C₂²

#89993

yes

characteristic

225

C₂²

C₂×#6410

yes

—

226

C₂²

#90004

yes

characteristic

227

C₂²

#90005

yes

characteristic

228

C₂²

#90005

yes

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

#89826

yes

—

235

C₄

#89828

yes

—

236

C₄

#89829

yes

—

237

C₄

#89831

yes

—

238

C₂

#11729475

yes

characteristic

239

C₂

#11729479

yes

characteristic

240

C₂

#11729543

yes

characteristic

241

C₂

#11729583

yes

—

242

C₂

#11729585

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₇
commutator	C₂²×C₄×C₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇
Fitting	C₇×#2862	C₂
socle, prime radical	C₂³×C₇	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₇	C₂³
hypercenter	#2862	D₇
hypocenter	C₇	#9700
LCS	G ▷ C₂²×C₄×C₇ ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2862

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₇

commutator

C₂²×C₄×C₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇

Fitting

C₇×#2862

C₂

socle, prime radical

C₂³×C₇

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₇

C₂³

D₇

C₇

G ▷ C₂²×C₄×C₇ ▷ C₂²×C₇ ▷ C₇

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #2862

N	H ≅ G/N	type
223. C₇	#9700	semidirect

H ≅ G/N

type

223. C₇

#9700

semidirect

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

subgroup	index
C₇×#2862	2
C₂×#89342	2
#11727146	2
C₄×C₄⋊(C₇⋊C₈)	2
#9700	7

subgroup

index

C₄×C₄⋊(C₇⋊C₈)

Subgroups — #13252869

Conjugacy classes of subgroups

Complements

Maximal subgroups