Group #16789954 — subgroups

Subgroups — #16789954

Order 3328.

478 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 148 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×C₄⋊#6092	C₂	1	2	yes	maximal, complemented
2	C₂×#11718259	C₂	1	2	yes	maximal
3	#13129875	C₂	1	2	yes	maximal, complemented
4	C₂×#11718369	C₂	1	1	yes	maximal, characteristic
5	C₂²×#6094	C₄	1	1	yes	characteristic
6	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
7	C₂×#88126	C₄	1	1	yes	characteristic
8	C₂²×#6092	C₂²	1	4	yes	—
9	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
10	C₂×#88055	C₄	1	1	yes	characteristic
11	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
13	#11718369	—	2	4	no	—
14	#11718259	—	2	4	no	—
15	C₄⋊#6092	—	2	4	no	—
16	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×#6103	C₈	1	2	yes	—
21	C₂×#6101	C₈	1	2	yes	—
22	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
24	C₂²×#1055	C₂³	1	1	yes	characteristic
25	C₂×#6094	—	2	2	no	—
26	C₂×#6094	—	2	2	no	—
27	C₂×#6094	—	2	2	no	—
28	C₂×C₈×D₁₃	—	2	2	no	—
29	C₂×C₈×D₁₃	—	2	2	no	—
30	C₂×C₈×D₁₃	D₄	1	2	yes	—
31	C₂×C₈×D₁₃	Q₈	1	2	yes	—
32	#88126	—	2	2	no	—
33	#88126	—	2	2	no	—
34	C₂×#6092	—	2	4	no	—
35	C₂×#6092	—	2	4	no	—
36	C₂×#6092	—	2	4	no	—
37	C₁₃×#97	—	2	2	no	—
38	#88055	—	2	2	no	—
39	C₈×Dic₁₃	—	2	2	no	—
40	C₄×#1055	D₄	1	4	yes	—
41	#12784	—	13	1	no	maximal, Sylow
42	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
44	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
46	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
47	C₂×C₄×D₁₃	—	2	1	no	—
48	C₂×C₄×D₁₃	—	2	1	no	—
49	C₂×C₄×D₁₃	—	2	1	no	—
50	C₂×C₄×D₁₃	—	2	1	no	—
51	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
52	C₂×C₄×D₁₃	M₁₆	1	2	yes	—
53	C₂×C₈×C₁₃	—	2	1	no	—
54	C₂×C₈×C₁₃	—	2	1	no	—
55	C₂×C₈×C₁₃	—	2	1	no	—
56	C₂×C₈×C₁₃	—	2	1	no	—
57	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
58	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
59	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
60	C₄²×C₁₃	M₁₆	1	2	yes	—
61	#6103	—	2	4	no	—
62	#6101	—	2	4	no	—
63	C₄×Dic₁₃	—	2	1	no	—
64	C₄×Dic₁₃	—	2	1	no	—
65	C₂×#1055	—	2	1	no	—
66	C₂×#1055	—	2	1	no	—
67	C₂×#1055	C₂²⋊C₄	1	2	yes	—
68	C₂×#1055	C₂×D₄	1	1	yes	characteristic
69	C₂×#1055	C₂×D₄	1	2	yes	—
70	C₂×#1055	C₂×Q₈	1	1	yes	characteristic
71	C₂×#1055	#41	1	2	yes	—
72	#6094	—	2	8	no	—
73	C₈×D₁₃	—	2	4	no	—
74	C₈×D₁₃	—	2	4	no	—
75	#6092	—	4	4	no	—
76	C₂×#405	—	13	1	no	—
77	C₂×C₄⋊C₁₆	—	13	2	no	—
78	C₂×C₂²⋊C₁₆	—	13	2	no	—
79	#1374	—	13	2	no	—
80	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
81	C₂²×D₁₃	—	2	1	no	—
82	C₂²×D₁₃	—	2	1	no	—
83	C₂²×D₁₃	—	2	4	no	—
84	C₂²×D₁₃	C₄⋊C₈	1	2	yes	—
85	C₂×C₄×C₁₃	—	2	4	no	—
86	C₂×C₄×C₁₃	C₂²⋊C₈	1	4	yes	—
87	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
91	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
92	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
93	C₂×Dic₁₃	—	2	1	no	—
94	C₂×Dic₁₃	—	2	1	no	—
95	C₂×Dic₁₃	—	2	2	no	—
96	C₂×Dic₁₃	—	2	4	no	—
97	C₂×Dic₁₃	C₄⋊C₈	1	2	yes	—
98	C₄×D₁₃	—	2	2	no	—
99	C₄×D₁₃	—	2	2	no	—
100	C₄×D₁₃	—	2	2	no	—
101	C₄×D₁₃	—	2	2	no	—
102	C₈×C₁₃	—	2	2	no	—
103	C₈×C₁₃	—	2	2	no	—
104	#1055	—	2	2	no	—
105	#1055	#121	1	2	yes	—
106	#1055	C₂²⋊Q₈	1	2	yes	—
107	C₂²×M₁₆	—	13	1	no	—
108	C₂³×C₈	—	13	1	no	—
109	C₂×#117	—	13	1	no	—
110	C₂²×C₁₆	—	13	4	no	—
111	#405	—	26	4	no	—
112	C₂×#97	—	13	1	no	—
113	C₂×#97	#261	1	1	yes	characteristic
114	C₂×C₄×C₈	—	13	1	no	—
115	C₂×C₄×C₈	—	13	1	no	—
116	C₄⋊C₁₆	—	26	4	no	—
117	C₂²⋊C₁₆	—	26	4	no	—
118	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
119	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
120	C₂²×C₁₃	#431	1	1	yes	characteristic
121	C₂²×C₁₃	#504	1	4	yes	—
122	C₂×D₁₃	—	2	2	no	—
123	C₂×D₁₃	—	2	4	no	—
124	C₂×D₁₃	—	4	2	no	—
125	C₂×D₁₃	—	4	2	no	—
126	C₄×C₁₃	—	2	4	no	—
127	C₄×C₁₃	#380	1	1	yes	characteristic
128	C₄×C₁₃	#407	1	1	yes	characteristic
129	C₄×C₁₃	#423	1	1	yes	characteristic
130	C₄×C₁₃	#432	1	1	yes	characteristic
131	Dic₁₃	—	2	2	no	—
132	Dic₁₃	—	4	2	no	—
133	C₂³×C₄	—	13	1	no	—
134	C₂×M₁₆	—	26	2	no	—
135	C₂×M₁₆	—	26	2	no	—
136	C₂×M₁₆	—	26	2	no	—
137	C₂²×C₈	—	13	1	no	—
138	C₂²×C₈	—	13	1	no	—
139	C₂²×C₈	—	13	2	no	—
140	C₂²×C₈	—	13	2	no	—
141	C₂²×C₈	—	26	2	no	—
142	C₂²×C₈	—	26	2	no	—
143	C₂²×C₈	C₂×#261	1	1	yes	characteristic
144	C₂²×C₈	C₂×#261	1	1	yes	characteristic
145	#117	—	26	2	no	—
146	#117	—	26	2	no	—
147	C₂×C₄⋊C₄	—	13	2	no	—
148	C₂×C₂²⋊C₄	—	13	2	no	—
149	C₂×C₄²	—	13	1	no	—
150	C₂×C₄²	C₂×#261	1	1	yes	characteristic
151	C₂×C₁₆	—	26	4	no	—
152	C₂×C₁₆	—	26	4	no	—
153	C₂×C₁₆	—	26	4	no	—
154	#97	—	2	2	no	—
155	#97	—	26	2	no	—
156	C₄×C₈	—	13	4	no	—
157	C₄×C₈	—	26	2	no	—
158	C₂×C₁₃	#1797	1	1	yes	characteristic
159	C₂×C₁₃	#2113	1	2	yes	—
160	C₂×C₁₃	#2151	1	2	yes	—
161	C₂×C₁₃	#2164	1	2	yes	—
162	D₁₃	—	4	2	no	—
163	C₂⁴	—	13	1	no	—
164	C₂²×C₄	—	13	1	no	—
165	C₂²×C₄	—	13	2	no	—
166	C₂²×C₄	—	13	2	no	—
167	C₂²×C₄	—	13	2	no	—
168	C₂²×C₄	—	26	1	no	—
169	C₂²×C₄	—	26	1	no	—
170	C₂²×C₄	—	26	1	no	—
171	C₂²×C₄	—	26	1	no	—
172	C₂²×C₄	D₁₃⋊C₈	1	2	yes	—
173	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
174	M₁₆	—	26	8	no	—
175	C₂×C₈	—	2	1	no	—
176	C₂×C₈	—	2	1	no	—
177	C₂×C₈	—	2	1	no	—
178	C₂×C₈	—	2	1	no	—
179	C₂×C₈	—	13	1	no	—
180	C₂×C₈	—	13	1	no	—
181	C₂×C₈	—	13	2	no	—
182	C₂×C₈	—	13	2	no	—
183	C₂×C₈	—	13	2	no	—
184	C₂×C₈	—	26	4	no	—
185	C₂×C₈	—	26	4	no	—
186	C₂×C₈	—	26	1	no	—
187	C₂×C₈	—	26	1	no	—
188	C₂×C₈	#6118	1	2	yes	—
189	C₂×C₈	C₄⋊#261	1	2	yes	—
190	C₄⋊C₄	—	26	4	no	—
191	C₂²⋊C₄	—	26	4	no	—
192	C₄²	—	26	1	no	—
193	C₄²	—	26	1	no	—
194	C₄²	#6118	1	2	yes	—
195	C₄²	C₂²⋊#261	1	2	yes	—
196	C₁₆	—	52	4	no	—
197	C₁₃	#12784	1	1	yes	characteristic, complemented, Sylow
198	C₂³	—	13	2	no	—
199	C₂³	—	26	1	no	—
200	C₂³	—	26	4	no	—
201	C₂³	—	26	1	no	—
202	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
203	C₂×C₄	—	2	4	no	—
204	C₂×C₄	—	13	2	no	—
205	C₂×C₄	—	26	1	no	—
206	C₂×C₄	—	26	1	no	—
207	C₂×C₄	—	26	2	no	—
208	C₂×C₄	—	26	2	no	—
209	C₂×C₄	—	26	2	no	—
210	C₂×C₄	—	26	2	no	—
211	C₂×C₄	—	26	4	no	—
212	C₂×C₄	—	26	2	no	—
213	C₂×C₄	#88111	1	4	yes	—
214	C₂×C₄	C₂×#6118	1	1	yes	characteristic
215	C₂×C₄	C₂×#6118	1	1	yes	characteristic
216	C₂×C₄	D₁₃⋊M₁₆	1	1	yes	characteristic
217	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
218	C₂×C₄	#88237	1	1	yes	characteristic
219	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
220	C₈	—	2	2	no	—
221	C₈	—	2	2	no	—
222	C₈	—	13	2	no	—
223	C₈	—	13	2	no	—
224	C₈	—	26	2	no	—
225	C₂²	—	26	4	no	—
226	C₂²	—	26	2	no	—
227	C₂²	—	52	2	no	—
228	C₂²	—	52	2	no	—
229	C₂²	D₁₃⋊(C₄⋊C₈)	1	1	yes	characteristic
230	C₂²	#11719051	1	1	yes	characteristic
231	C₂²	#11719096	1	4	yes	—
232	C₂²	C₂×#88111	1	1	yes	characteristic
233	C₄	—	2	4	no	—
234	C₄	—	26	2	no	—
235	C₄	—	52	2	no	—
236	C₄	#11719052	1	1	yes	characteristic
237	C₄	#11719054	1	1	yes	characteristic
238	C₄	#11719127	1	1	yes	characteristic
239	C₄	#11719136	1	1	yes	characteristic
240	C₂	—	52	2	no	—
241	C₂	#13130691	1	1	yes	characteristic
242	C₂	#13131068	1	2	yes	—
243	C₂	#13131172	1	2	yes	—
244	C₂	#13131204	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#6092

C₂

yes

maximal, complemented

C₂×#11718259

C₂

yes

maximal

#13129875

C₂

yes

maximal, complemented

C₂×#11718369

C₂

yes

maximal, characteristic

C₂²×#6094

C₄

yes

characteristic

C₂²×C₈×D₁₃

C₂²

yes

characteristic

C₂×#88126

C₄

yes

characteristic

C₂²×#6092

C₂²

yes

—

C₂×C₁₃×#97

C₄

yes

characteristic

C₂×#88055

C₄

yes

characteristic

C₂×C₈×Dic₁₃

C₂²

yes

characteristic

C₂×C₄×#1055

C₂²

yes

—

—

—

C₂²×C₄×D₁₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₃

C₂×C₄

yes

characteristic

C₂×#6103

C₈

yes

—

C₂×#6101

C₈

yes

—

C₂×C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₂²×#1055

C₂×C₄

yes

characteristic

C₂²×#1055

C₂³

yes

—

—

—

C₂×C₈×D₁₃

—

C₂×C₈×D₁₃

—

C₂×C₈×D₁₃

D₄

yes

—

C₂×C₈×D₁₃

Q₈

yes

—

—

—

—

—

—

C₁₃×#97

—

#88055

—

C₈×Dic₁₃

—

C₄×#1055

D₄

yes

—

#12784

—

maximal, Sylow

C₂³×D₁₃

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₃

C₂×C₈

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×Dic₁₃

C₂×C₈

yes

—

C₂²×Dic₁₃

C₂×C₈

yes

characteristic

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

C₄⋊C₄

yes

—

C₂×C₄×D₁₃

M₁₆

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

M₁₆

yes

—

C₄²×C₁₃

C₂²⋊C₄

yes

—

C₄²×C₁₃

M₁₆

yes

—

#6103

—

#6101

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₂×#1055

—

C₂×#1055

—

C₂×#1055

C₂²⋊C₄

yes

—

C₂×#1055

C₂×D₄

yes

characteristic

C₂×#1055

C₂×D₄

yes

—

C₂×#1055

C₂×Q₈

yes

characteristic

C₂×#1055

#41

yes

—

#6094

—

C₈×D₁₃

—

C₈×D₁₃

—

#6092

—

C₂×#405

—

C₂×C₄⋊C₁₆

—

C₂×C₂²⋊C₁₆

—

#1374

—

C₂³×C₁₃

C₂²×C₈

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

C₄⋊C₈

yes

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊C₈

yes

—

C₂×C₄×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

#117

yes

characteristic

C₂×C₄×C₁₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₃

C₂×M₁₆

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₄⋊C₈

yes

—

C₄×D₁₃

—

C₄×D₁₃

—

100

C₄×D₁₃

—

101

C₄×D₁₃

—

102

C₈×C₁₃

—

103

C₈×C₁₃

—

104

#1055

—

105

#1055

#121

yes

—

106

#1055

C₂²⋊Q₈

yes

—

107

C₂²×M₁₆

—

108

C₂³×C₈

—

109

C₂×#117

—

110

C₂²×C₁₆

—

111

#405

—

112

C₂×#97

—

113

C₂×#97

#261

yes

characteristic

114

C₂×C₄×C₈

—

115

C₂×C₄×C₈

—

116

C₄⋊C₁₆

—

117

C₂²⋊C₁₆

—

118

C₂²×C₁₃

C₂×C₂²⋊C₈

yes

characteristic

119

C₂²×C₁₃

C₂×C₄⋊C₈

yes

characteristic

120

C₂²×C₁₃

#431

yes

characteristic

121

C₂²×C₁₃

#504

yes

—

122

C₂×D₁₃

—

123

C₂×D₁₃

—

124

C₂×D₁₃

—

125

C₂×D₁₃

—

126

C₄×C₁₃

—

127

C₄×C₁₃

#380

yes

characteristic

128

C₄×C₁₃

#407

yes

characteristic

129

C₄×C₁₃

#423

yes

characteristic

130

C₄×C₁₃

#432

yes

characteristic

131

Dic₁₃

—

132

Dic₁₃

—

133

C₂³×C₄

—

134

C₂×M₁₆

—

135

C₂×M₁₆

—

136

C₂×M₁₆

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₂²×C₈

—

140

C₂²×C₈

—

141

C₂²×C₈

—

142

C₂²×C₈

—

143

C₂²×C₈

C₂×#261

yes

characteristic

144

C₂²×C₈

C₂×#261

yes

characteristic

145

#117

—

146

#117

—

147

C₂×C₄⋊C₄

—

148

C₂×C₂²⋊C₄

—

149

C₂×C₄²

—

150

C₂×C₄²

C₂×#261

yes

characteristic

151

C₂×C₁₆

—

152

C₂×C₁₆

—

153

C₂×C₁₆

—

154

#97

—

155

#97

—

156

C₄×C₈

—

157

C₄×C₈

—

158

C₂×C₁₃

#1797

yes

characteristic

159

C₂×C₁₃

#2113

yes

—

160

C₂×C₁₃

#2151

yes

—

161

C₂×C₁₃

#2164

yes

—

162

D₁₃

—

163

C₂⁴

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

D₁₃⋊C₈

yes

—

173

C₂²×C₄

C₂²×#261

yes

characteristic

174

M₁₆

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

#6118

yes

—

189

C₂×C₈

C₄⋊#261

yes

—

190

C₄⋊C₄

—

191

C₂²⋊C₄

—

192

C₄²

—

193

C₄²

—

194

C₄²

#6118

yes

—

195

C₄²

C₂²⋊#261

yes

—

196

C₁₆

—

197

C₁₃

#12784

yes

characteristic, complemented, Sylow

198

C₂³

—

199

C₂³

—

200

C₂³

—

201

C₂³

—

202

C₂³

C₂×D₁₃⋊C₈

yes

characteristic

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

—

213

C₂×C₄

#88111

yes

—

214

C₂×C₄

C₂×#6118

yes

characteristic

215

C₂×C₄

C₂×#6118

yes

characteristic

216

C₂×C₄

D₁₃⋊M₁₆

yes

characteristic

217

C₂×C₄

C₂×C₄⋊#261

yes

characteristic

218

C₂×C₄

#88237

yes

characteristic

219

C₂×C₄

C₂×C₂²⋊#261

yes

characteristic

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

225

C₂²

—

226

C₂²

—

227

C₂²

—

228

C₂²

—

229

C₂²

D₁₃⋊(C₄⋊C₈)

yes

characteristic

230

C₂²

#11719051

yes

characteristic

231

C₂²

#11719096

yes

—

232

C₂²

C₂×#88111

yes

characteristic

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

#11719052

yes

characteristic

237

C₄

#11719054

yes

characteristic

238

C₄

#11719127

yes

characteristic

239

C₄

#11719136

yes

characteristic

240

C₂

—

241

C₂

#13130691

yes

characteristic

242

C₂

#13131068

yes

—

243

C₂

#13131172

yes

—

244

C₂

#13131204

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#261
commutator, socle	C₂³×C₁₃	C₂²×C₈
Fitting	C₂×C₁₃×#97	C₄
prime radical	C₂³×D₁₃	C₂×C₈
cosocle	C₂²×#1055	C₂³
hypercenter	C₂×#97	#261
hypocenter	C₁₃	#12784
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×#261

commutator, socle

C₂³×C₁₃

C₂²×C₈

Fitting

C₂×C₁₃×#97

C₄

prime radical

C₂³×D₁₃

C₂×C₈

cosocle

C₂²×#1055

C₂³

C₂×#97

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂²×C₄ ◁ C₂×#97

N	H ≅ G/N	type
1. C₂×C₄⋊#6092	C₂	semidirect
3. #13129875	C₂	semidirect
197. C₁₃	#12784	semidirect

H ≅ G/N

type

1. C₂×C₄⋊#6092

C₂

semidirect

3. #13129875

C₂

semidirect

197. C₁₃

#12784

semidirect

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

subgroup	index
C₂×C₄⋊#6092	2
C₂×#11718259	2
#13129875	2
C₂×#11718369	2
#12784	13

subgroup

index

C₂×C₄⋊#6092

Subgroups — #16789954

Conjugacy classes of subgroups

Complements

Maximal subgroups