Group #15765527 — subgroups

Subgroups — #15765527

Order 3328.

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×#11718360	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718681	C₂	1	2	yes	maximal
3	C₂×#11718074	C₂	1	2	yes	maximal
4	#13112671	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×Dic₅₂	—	2	2	no	—
8	C₂×#88123	C₂²	1	2	yes	—
9	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×#88075	—	2	2	no	—
12	#11718681	—	2	4	no	—
13	#11718681	—	2	4	no	—
14	C₂×#88048	—	2	2	no	—
15	C₂×C₄⋊#1055	C₂²	1	2	yes	—
16	#11718360	—	2	4	no	—
17	C₁₃×#336	—	2	2	no	—
18	#11718074	—	2	4	no	—
19	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
20	C₂²×Dic₂₆	—	2	2	no	—
21	C₂²×C₈×C₁₃	—	2	1	no	—
22	C₂²×C₈×C₁₃	D₄	1	2	yes	—
23	C₄×Q₈×C₁₃	—	2	2	no	—
24	C₄×Q₈×C₁₃	—	2	2	no	—
25	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
26	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₃	—	2	1	no	—
28	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
29	C₂×C₄⋊Dic₁₃	—	2	2	no	—
30	C₂×C₄⋊Dic₁₃	—	2	2	no	—
31	C₂²×#1055	—	2	2	no	—
32	C₂×Dic₅₂	—	2	8	no	—
33	C₂×Dic₅₂	—	4	4	no	—
34	C₂×Dic₅₂	—	4	4	no	—
35	#88123	—	2	2	no	—
36	#88123	—	2	2	no	—
37	#88123	—	2	2	no	—
38	#88123	D₄	1	4	yes	—
39	C₁₃×C₄⋊C₈	—	2	2	no	—
40	C₄×C₈×C₁₃	—	2	2	no	—
41	#88075	—	2	8	no	—
42	#88048	—	2	8	no	—
43	C₄⋊#1055	—	2	2	no	—
44	C₄⋊#1055	D₄	1	4	yes	—
45	#10276	—	13	1	no	maximal, Sylow
46	C₂×Q₈×C₁₃	—	2	1	no	—
47	C₂×Q₈×C₁₃	—	2	2	no	—
48	C₂×Q₈×C₁₃	—	2	2	no	—
49	C₂×Q₈×C₁₃	Q₁₆	1	2	yes	complemented
50	C₂²×C₄×C₁₃	—	2	1	no	—
51	C₂²×C₄×C₁₃	—	2	1	no	—
52	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
55	C₂²×Dic₁₃	—	4	2	no	—
56	C₂×Dic₂₆	—	2	4	no	—
57	C₂×Dic₂₆	—	4	4	no	—
58	C₂×Dic₂₆	—	4	4	no	—
59	C₂×Dic₂₆	—	4	2	no	—
60	C₂×C₈×C₁₃	—	2	2	no	—
61	C₂×C₈×C₁₃	—	2	2	no	—
62	C₂×C₈×C₁₃	—	4	1	no	—
63	C₂×C₈×C₁₃	—	4	2	no	—
64	C₂×C₈×C₁₃	SD₁₆	1	4	yes	—
65	C₁₃×C₄⋊C₄	—	2	2	no	—
66	C₁₃×C₄⋊C₄	—	4	2	no	—
67	C₄²×C₁₃	—	4	1	no	—
68	C₄²×C₁₃	—	4	1	no	—
69	C₄²×C₁₃	C₂×D₄	1	2	yes	—
70	C₄²×C₁₃	C₂×D₄	1	2	yes	—
71	C₄⋊Dic₁₃	—	2	4	no	—
72	C₄⋊Dic₁₃	—	2	4	no	—
73	C₄⋊Dic₁₃	—	4	2	no	—
74	C₄⋊Dic₁₃	—	4	2	no	—
75	C₂×#1055	—	2	4	no	—
76	C₂×#1055	—	4	2	no	—
77	C₂×#1055	—	4	2	no	—
78	Dic₅₂	—	4	16	no	—
79	C₂×#494	—	13	1	no	—
80	C₂×#475	—	13	2	no	—
81	#1984	D₁₃	1	1	yes	characteristic
82	C₂×#332	—	13	2	no	—
83	#1277	—	13	1	no	—
84	C₂³×C₁₃	#121	1	1	yes	characteristic
85	Q₈×C₁₃	—	2	4	no	—
86	Q₈×C₁₃	—	4	2	no	—
87	C₂×C₄×C₁₃	—	2	2	no	—
88	C₂×C₄×C₁₃	—	2	2	no	—
89	C₂×C₄×C₁₃	—	4	1	no	—
90	C₂×C₄×C₁₃	—	4	1	no	—
91	C₂×C₄×C₁₃	—	4	1	no	—
92	C₂×C₄×C₁₃	—	4	2	no	—
93	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
94	C₂×C₄×C₁₃	#120	1	2	yes	—
95	C₂×C₄×C₁₃	#121	1	2	yes	—
96	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
97	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
98	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
99	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
100	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
101	C₂×C₄×C₁₃	#137	1	2	yes	—
102	C₂×Dic₁₃	—	4	4	no	—
103	C₂×Dic₁₃	—	8	4	no	—
104	Dic₂₆	—	4	8	no	—
105	Dic₂₆	—	8	2	no	—
106	Dic₂₆	—	8	2	no	—
107	C₈×C₁₃	—	2	4	no	—
108	C₈×C₁₃	—	8	1	no	—
109	#1055	—	4	4	no	—
110	C₂²×Q₁₆	—	26	2	no	—
111	C₂×C₄⋊Q₈	—	13	2	no	—
112	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
113	#494	—	26	4	no	—
114	#475	—	26	4	no	—
115	#475	—	26	4	no	—
116	C₂×#106	—	26	2	no	—
117	C₂×C₄⋊C₈	—	13	2	no	—
118	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
119	C₂×#103	—	26	2	no	—
120	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
121	#336	—	2	2	no	—
122	#332	—	26	4	no	—
123	C₂²×C₁₃	#392	1	1	yes	characteristic
124	C₂²×C₁₃	#460	1	2	yes	—
125	C₂²×C₁₃	#467	1	1	yes	characteristic
126	C₂²×C₁₃	#470	1	1	yes	characteristic
127	C₂²×C₁₃	#473	1	2	yes	—
128	C₄×C₁₃	—	2	2	no	—
129	C₄×C₁₃	—	4	2	no	—
130	C₄×C₁₃	—	8	1	no	—
131	C₄×C₁₃	#450	1	2	yes	—
132	C₄×C₁₃	#451	1	2	yes	—
133	C₄×C₁₃	#452	1	2	yes	—
134	C₄×C₁₃	#492	1	1	yes	characteristic
135	C₄×C₁₃	#496	1	1	yes	characteristic
136	Dic₁₃	—	8	4	no	—
137	C₂²×Q₈	—	26	2	no	—
138	C₂²×Q₈	D₅₂	1	1	yes	characteristic
139	C₂×Q₁₆	—	26	8	no	—
140	C₂×Q₁₆	—	52	4	no	—
141	C₂×Q₁₆	—	52	4	no	—
142	C₂²×C₈	—	2	1	no	—
143	C₂²×C₈	—	26	2	no	—
144	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
145	C₄⋊Q₈	—	13	4	no	—
146	C₄⋊Q₈	—	26	2	no	—
147	C₄⋊Q₈	—	26	2	no	—
148	C₄⋊Q₈	—	26	2	no	—
149	C₄×Q₈	—	2	2	no	—
150	C₄×Q₈	—	2	2	no	—
151	C₂×C₄⋊C₄	—	2	1	no	—
152	C₂×C₄⋊C₄	—	26	2	no	—
153	C₂×C₄⋊C₄	—	26	2	no	—
154	C₂×C₄⋊C₄	D₅₂	1	1	yes	characteristic
155	C₂×C₄²	—	2	1	no	—
156	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
157	#106	—	26	8	no	—
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	13	4	no	—
160	C₄⋊C₈	—	26	2	no	—
161	#103	—	26	8	no	—
162	C₄×C₈	—	2	2	no	—
163	C₂×C₁₃	#1670	1	2	yes	—
164	C₂×C₁₃	#1690	1	2	yes	—
165	C₂×C₁₃	#2001	1	1	yes	characteristic
166	C₂×C₁₃	#2014	1	1	yes	characteristic
167	C₂×C₁₃	#2020	1	1	yes	characteristic
168	C₂×Q₈	—	2	1	no	—
169	C₂×Q₈	—	2	2	no	—
170	C₂×Q₈	—	2	2	no	—
171	C₂×Q₈	—	26	4	no	—
172	C₂×Q₈	—	52	2	no	—
173	C₂×Q₈	—	52	4	no	—
174	C₂×Q₈	—	52	4	no	—
175	C₂×Q₈	Dic₅₂	1	2	yes	complemented
176	C₂²×C₄	—	2	1	no	—
177	C₂²×C₄	—	2	1	no	—
178	C₂²×C₄	—	52	2	no	—
179	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
180	C₂²×C₄	#6127	1	1	yes	characteristic
181	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
182	Q₁₆	—	52	16	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	4	1	no	—
186	C₂×C₈	—	4	2	no	—
187	C₂×C₈	—	26	4	no	—
188	C₂×C₈	—	52	2	no	—
189	C₂×C₈	—	52	2	no	—
190	C₂×C₈	#6106	1	4	yes	—
191	C₄⋊C₄	—	2	2	no	—
192	C₄⋊C₄	—	4	2	no	—
193	C₄⋊C₄	—	26	4	no	—
194	C₄⋊C₄	—	26	4	no	—
195	C₄⋊C₄	—	52	2	no	—
196	C₄⋊C₄	—	52	2	no	—
197	C₄²	—	4	1	no	—
198	C₄²	—	4	1	no	—
199	C₄²	D₄×D₁₃	1	2	yes	—
200	C₄²	D₄×D₁₃	1	2	yes	—
201	C₁₃	#10276	1	1	yes	characteristic, complemented, Sylow
202	C₂³	#88184	1	1	yes	characteristic
203	Q₈	—	2	4	no	—
204	Q₈	—	4	2	no	—
205	Q₈	—	52	8	no	—
206	Q₈	—	104	2	no	—
207	Q₈	—	104	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	4	1	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	52	4	no	—
215	C₂×C₄	—	104	4	no	—
216	C₂×C₄	#88136	1	2	yes	—
217	C₂×C₄	#88138	1	2	yes	—
218	C₂×C₄	#88158	1	1	yes	characteristic
219	C₂×C₄	C₂×Dic₅₂	1	1	yes	characteristic
220	C₂×C₄	#88163	1	2	yes	—
221	C₂×C₄	#88191	1	1	yes	characteristic
222	C₂×C₄	#88194	1	1	yes	characteristic
223	C₂×C₄	C₂×#6106	1	2	yes	—
224	C₂×C₄	#88203	1	2	yes	—
225	C₈	—	2	4	no	—
226	C₈	—	8	1	no	—
227	C₈	—	52	4	no	—
228	C₂²	#11718621	1	1	yes	characteristic
229	C₂²	#11718688	1	2	yes	—
230	C₂²	#11718777	1	1	yes	characteristic
231	C₂²	#11718798	1	1	yes	characteristic
232	C₂²	#11718804	1	2	yes	—
233	C₄	—	2	2	no	—
234	C₄	—	4	2	no	—
235	C₄	—	8	1	no	—
236	C₄	—	104	4	no	—
237	C₄	#11718394	1	2	yes	—
238	C₄	#11718400	1	2	yes	—
239	C₄	#11718707	1	2	yes	—
240	C₄	#11718719	1	1	yes	characteristic
241	C₄	#11718746	1	1	yes	characteristic
242	C₂	#13114206	1	2	yes	—
243	C₂	#13114330	1	2	yes	—
244	C₂	#13115846	1	1	yes	characteristic
245	C₂	#13115923	1	1	yes	characteristic
246	C₂	#13115957	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718360

C₂

yes

maximal, characteristic

C₂×#11718681

C₂

yes

maximal

C₂×#11718074

C₂

yes

maximal

#13112671

C₂

yes

maximal, characteristic

C₁₃×#1984

C₂

yes

maximal, characteristic

C₂×C₄×Q₈×C₁₃

C₂²

yes

characteristic

C₂²×Dic₅₂

—

C₂×#88123

C₂²

yes

—

C₂×C₁₃×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₃

C₂²

yes

—

—

—

—

C₂×C₄⋊#1055

C₂²

yes

—

#11718360

—

C₁₃×#336

—

#11718074

—

C₂²×Q₈×C₁₃

D₄

yes

characteristic

C₂²×Dic₂₆

—

C₂²×C₈×C₁₃

—

C₂²×C₈×C₁₃

D₄

yes

—

C₄×Q₈×C₁₃

—

C₄×Q₈×C₁₃

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

characteristic

C₂×C₄²×C₁₃

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

—

C₂²×#1055

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

—

—

—

D₄

yes

—

C₁₃×C₄⋊C₈

—

C₄×C₈×C₁₃

—

—

—

—

D₄

yes

—

#10276

—

maximal, Sylow

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

Q₁₆

yes

complemented

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

#41

yes

characteristic

C₂²×Dic₁₃

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

SD₁₆

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₂×#1055

—

C₂×#1055

—

C₂×#1055

—

Dic₅₂

—

C₂×#494

—

C₂×#475

—

#1984

D₁₃

yes

characteristic

C₂×#332

—

#1277

—

C₂³×C₁₃

#121

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#120

yes

characteristic

C₂×C₄×C₁₃

#120

yes

—

C₂×C₄×C₁₃

#121

yes

—

C₂×C₄×C₁₃

#127

yes

characteristic

C₂×C₄×C₁₃

C₂×SD₁₆

yes

—

C₂×C₄×C₁₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₃

#135

yes

characteristic

100

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

101

C₂×C₄×C₁₃

#137

yes

—

102

C₂×Dic₁₃

—

103

C₂×Dic₁₃

—

104

Dic₂₆

—

105

Dic₂₆

—

106

Dic₂₆

—

107

C₈×C₁₃

—

108

C₈×C₁₃

—

109

#1055

—

110

C₂²×Q₁₆

—

111

C₂×C₄⋊Q₈

—

112

C₂×C₄×Q₈

C₂×D₁₃

yes

characteristic

113

#494

—

114

#475

—

115

#475

—

116

C₂×#106

—

117

C₂×C₄⋊C₈

—

118

C₂×C₄⋊C₈

C₂×D₁₃

yes

characteristic

119

C₂×#103

—

120

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

121

#336

—

122

#332

—

123

C₂²×C₁₃

#392

yes

characteristic

124

C₂²×C₁₃

#460

yes

—

125

C₂²×C₁₃

#467

yes

characteristic

126

C₂²×C₁₃

#470

yes

characteristic

127

C₂²×C₁₃

#473

yes

—

128

C₄×C₁₃

—

129

C₄×C₁₃

—

130

C₄×C₁₃

—

131

C₄×C₁₃

#450

yes

—

132

C₄×C₁₃

#451

yes

—

133

C₄×C₁₃

#452

yes

—

134

C₄×C₁₃

#492

yes

characteristic

135

C₄×C₁₃

#496

yes

characteristic

136

Dic₁₃

—

137

C₂²×Q₈

—

138

C₂²×Q₈

D₅₂

yes

characteristic

139

C₂×Q₁₆

—

140

C₂×Q₁₆

—

141

C₂×Q₁₆

—

142

C₂²×C₈

—

143

C₂²×C₈

—

144

C₂²×C₈

C₂²⋊D₁₃

yes

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

149

C₄×Q₈

—

150

C₄×Q₈

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

D₅₂

yes

characteristic

155

C₂×C₄²

—

156

C₂×C₄²

C₂²×D₁₃

yes

characteristic

157

#106

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

#103

—

162

C₄×C₈

—

163

C₂×C₁₃

#1670

yes

—

164

C₂×C₁₃

#1690

yes

—

165

C₂×C₁₃

#2001

yes

characteristic

166

C₂×C₁₃

#2014

yes

characteristic

167

C₂×C₁₃

#2020

yes

characteristic

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

Dic₅₂

yes

complemented

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

C₂×D₅₂

yes

characteristic

180

C₂²×C₄

#6127

yes

characteristic

181

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

182

Q₁₆

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

#6106

yes

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄²

—

198

C₄²

—

199

C₄²

D₄×D₁₃

yes

—

200

C₄²

D₄×D₁₃

yes

—

201

C₁₃

#10276

yes

characteristic, complemented, Sylow

202

C₂³

#88184

yes

characteristic

203

Q₈

—

204

Q₈

—

205

Q₈

—

206

Q₈

—

104

—

207

Q₈

—

104

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

104

—

216

C₂×C₄

#88136

yes

—

217

C₂×C₄

#88138

yes

—

218

C₂×C₄

#88158

yes

characteristic

219

C₂×C₄

C₂×Dic₅₂

yes

characteristic

220

C₂×C₄

#88163

yes

—

221

C₂×C₄

#88191

yes

characteristic

222

C₂×C₄

#88194

yes

characteristic

223

C₂×C₄

C₂×#6106

yes

—

224

C₂×C₄

#88203

yes

—

225

C₈

—

226

C₈

—

227

C₈

—

228

C₂²

#11718621

yes

characteristic

229

C₂²

#11718688

yes

—

230

C₂²

#11718777

yes

characteristic

231

C₂²

#11718798

yes

characteristic

232

C₂²

#11718804

yes

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

104

—

237

C₄

#11718394

yes

—

238

C₄

#11718400

yes

—

239

C₄

#11718707

yes

—

240

C₄

#11718719

yes

characteristic

241

C₄

#11718746

yes

characteristic

242

C₂

#13114206

yes

—

243

C₂

#13114330

yes

—

244

C₂

#13115846

yes

characteristic

245

C₂

#13115923

yes

characteristic

246

C₂

#13115957

yes

characteristic

	subgroup	G/H
center	C₂³	#88184
commutator, cosocle	C₂×C₄²×C₁₃	C₂³
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1984	C₂
socle, prime radical	C₂³×C₁₃	#121
hypercenter	#1984	D₁₃
hypocenter	C₁₃	#10276
LCS	G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1984

subgroup

G/H

center

C₂³

#88184

commutator, cosocle

C₂×C₄²×C₁₃

C₂³

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1984

C₂

C₂³×C₁₃

D₁₃

C₁₃

G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1984

N	H ≅ G/N	type
49. C₂×Q₈×C₁₃	Q₁₆	semidirect
175. C₂×Q₈	Dic₅₂	semidirect
201. C₁₃	#10276	semidirect

H ≅ G/N

type

49. C₂×Q₈×C₁₃

Q₁₆

semidirect

175. C₂×Q₈

Dic₅₂

semidirect

201. C₁₃

#10276

semidirect

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

subgroup	index
C₂×#11718360	2
C₂×#11718681	2
C₂×#11718074	2
#13112671	2
C₁₃×#1984	2
#10276	13

subgroup

index

C₁₃×#1984

Subgroups — #15765527

Conjugacy classes of subgroups

Complements

Maximal subgroups