Subgroups — C₂×C₇₁×#1556 #31838601

Order 18176.

1182 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#432×C₇₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#432×C₇₁	C₂	1	1	yes	maximal, characteristic
4	C₇₁×#1556	C₂	1	8	yes	maximal, direct product factor
5	C₂×#332×C₇₁	C₂	1	4	yes	maximal, complemented
6	C₂³×Q₈×C₇₁	—	2	1	no	—
7	C₂×C₄⋊Q₈×C₇₁	—	2	2	no	—
8	C₂×C₄⋊Q₈×C₇₁	—	2	2	no	—
9	C₂×C₄⋊Q₈×C₇₁	—	2	1	no	—
10	C₂×C₄⋊Q₈×C₇₁	—	2	1	no	—
11	C₂×C₄⋊Q₈×C₇₁	C₄	1	4	yes	—
12	C₂×C₄⋊Q₈×C₇₁	C₄	1	2	yes	—
13	C₂×C₄⋊Q₈×C₇₁	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₇₁	C₂²	1	4	yes	—
15	C₂²×C₄⋊C₄×C₇₁	—	2	1	no	—
16	C₂²×C₄⋊C₄×C₇₁	C₄	1	2	yes	—
17	C₂²×C₄²×C₇₁	C₂²	1	1	yes	characteristic
18	#432×C₇₁	—	2	2	no	—
19	#432×C₇₁	—	2	2	no	—
20	#432×C₇₁	C₂²	1	4	yes	—
21	#432×C₇₁	C₂²	1	4	yes	—
22	C₂×C₄⋊C₈×C₇₁	C₂²	1	2	yes	—
23	C₂×C₄⋊C₈×C₇₁	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₈×C₇₁	—	2	1	no	—
25	C₂×C₂²⋊C₈×C₇₁	—	2	1	no	—
26	C₂×#97×C₇₁	—	2	1	no	—
27	C₂×#97×C₇₁	—	2	1	no	—
28	#332×C₇₁	C₂²	1	16	yes	complemented
29	C₂²×Q₈×C₇₁	—	2	4	no	—
30	C₂²×Q₈×C₇₁	—	2	2	no	—
31	C₂²×Q₈×C₇₁	—	2	4	no	—
32	C₂²×Q₈×C₇₁	—	2	2	no	—
33	C₂²×Q₈×C₇₁	—	4	8	no	—
34	C₂³×C₄×C₇₁	—	2	2	no	—
35	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₇₁	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₇₁	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₇₁	—	2	2	no	—
39	C₂²×C₈×C₇₁	—	2	2	no	—
40	C₄⋊Q₈×C₇₁	—	2	4	no	—
41	C₄⋊Q₈×C₇₁	—	2	4	no	—
42	C₄⋊Q₈×C₇₁	—	2	4	no	—
43	C₄⋊Q₈×C₇₁	—	2	4	no	—
44	C₄⋊Q₈×C₇₁	—	2	4	no	—
45	C₄⋊Q₈×C₇₁	—	2	2	no	—
46	C₄⋊Q₈×C₇₁	—	2	2	no	—
47	C₄⋊Q₈×C₇₁	C₂×C₄	1	4	yes	—
48	C₄⋊Q₈×C₇₁	C₂×C₄	1	8	yes	—
49	C₄⋊Q₈×C₇₁	C₂³	1	4	yes	—
50	C₂×C₄⋊C₄×C₇₁	—	2	4	no	—
51	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₇₁	—	2	4	no	—
53	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₇₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	8	yes	—
57	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	4	yes	—
58	C₂×C₄²×C₇₁	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₇₁	D₄	1	2	yes	—
61	C₂×C₄²×C₇₁	D₄	1	2	yes	—
62	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
66	C₄⋊C₈×C₇₁	—	2	2	no	—
67	C₄⋊C₈×C₇₁	—	2	2	no	—
68	C₄⋊C₈×C₇₁	C₂³	1	4	yes	—
69	C₄⋊C₈×C₇₁	C₂³	1	4	yes	—
70	C₂²⋊C₈×C₇₁	—	2	4	no	—
71	C₂²⋊C₈×C₇₁	—	2	4	no	—
72	#97×C₇₁	—	2	4	no	—
73	#97×C₇₁	—	2	4	no	—
74	C₂⁴×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂×Q₈×C₇₁	—	2	8	no	—
76	C₂×Q₈×C₇₁	—	2	4	no	—
77	C₂×Q₈×C₇₁	—	2	4	no	—
78	C₂×Q₈×C₇₁	—	4	8	no	—
79	C₂×Q₈×C₇₁	—	4	16	no	—
80	C₂×Q₈×C₇₁	—	4	16	no	—
81	C₂×Q₈×C₇₁	—	4	8	no	—
82	C₂²×C₄×C₇₁	—	2	4	no	—
83	C₂²×C₄×C₇₁	—	2	4	no	—
84	C₂²×C₄×C₇₁	—	2	4	no	—
85	C₂²×C₄×C₇₁	—	2	8	no	—
86	C₂²×C₄×C₇₁	—	2	4	no	—
87	C₂²×C₄×C₇₁	—	4	8	no	—
88	C₂²×C₄×C₇₁	C₂²⋊C₄	1	2	yes	—
89	C₂²×C₄×C₇₁	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₇₁	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₇₁	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
100	C₂×C₈×C₇₁	—	2	4	no	—
101	C₂×C₈×C₇₁	—	2	4	no	—
102	C₂×C₈×C₇₁	—	4	4	no	—
103	C₂×C₈×C₇₁	—	4	4	no	—
104	C₄⋊C₄×C₇₁	—	2	8	no	—
105	C₄⋊C₄×C₇₁	—	2	4	no	—
106	C₄⋊C₄×C₇₁	—	2	8	no	—
107	C₄⋊C₄×C₇₁	—	2	4	no	—
108	C₄⋊C₄×C₇₁	—	2	4	no	—
109	C₄⋊C₄×C₇₁	C₂²×C₄	1	8	yes	—
110	C₄²×C₇₁	C₂²⋊C₄	1	2	yes	—
111	C₄²×C₇₁	C₂²⋊C₄	1	2	yes	—
112	C₄²×C₇₁	C₂²⋊C₄	1	2	yes	—
113	C₄²×C₇₁	C₂²×C₄	1	2	yes	—
114	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₇₁	C₂×D₄	1	2	yes	—
116	C₄²×C₇₁	C₂×D₄	1	2	yes	—
117	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
120	C₂³×C₇₁	—	2	2	no	—
121	C₂³×C₇₁	—	2	2	no	—
122	C₂³×C₇₁	#101	1	4	yes	—
123	C₂³×C₇₁	C₂×C₂²⋊C₄	1	2	yes	—
124	C₂³×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	Q₈×C₇₁	—	4	16	no	—
126	Q₈×C₇₁	—	4	8	no	—
127	Q₈×C₇₁	—	4	8	no	—
128	C₂×C₄×C₇₁	—	2	4	no	—
129	C₂×C₄×C₇₁	—	2	2	no	—
130	C₂×C₄×C₇₁	—	2	4	no	—
131	C₂×C₄×C₇₁	—	2	2	no	—
132	C₂×C₄×C₇₁	—	2	2	no	—
133	C₂×C₄×C₇₁	—	2	2	no	—
134	C₂×C₄×C₇₁	—	2	4	no	—
135	C₂×C₄×C₇₁	—	2	4	no	—
136	C₂×C₄×C₇₁	—	2	4	no	—
137	C₂×C₄×C₇₁	—	2	4	no	—
138	C₂×C₄×C₇₁	—	2	8	no	—
139	C₂×C₄×C₇₁	—	4	16	no	—
140	C₂×C₄×C₇₁	—	4	8	no	—
141	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	2	yes	—
142	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	4	yes	—
148	C₂×C₄×C₇₁	#137	1	4	yes	—
149	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
152	C₈×C₇₁	—	4	4	no	—
153	C₈×C₇₁	—	4	4	no	—
154	C₂²×C₇₁	—	2	8	no	—
155	C₂²×C₇₁	—	2	2	no	—
156	C₂²×C₇₁	—	2	2	no	—
157	C₂²×C₇₁	C₂×#101	1	4	yes	—
158	C₂²×C₇₁	C₂×#101	1	2	yes	—
159	C₂²×C₇₁	#418	1	2	yes	—
160	C₂²×C₇₁	#419	1	2	yes	—
161	C₂²×C₇₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
162	C₄×C₇₁	—	2	1	no	—
163	C₄×C₇₁	—	2	2	no	—
164	C₄×C₇₁	—	2	1	no	—
165	C₄×C₇₁	—	2	2	no	—
166	C₄×C₇₁	—	2	2	no	—
167	C₄×C₇₁	—	4	8	no	—
168	C₄×C₇₁	#418	1	2	yes	—
169	C₄×C₇₁	#419	1	2	yes	—
170	C₄×C₇₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
171	C₄×C₇₁	C₂×#137	1	2	yes	—
172	C₂×#1556	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂×C₇₁	—	2	4	no	—
174	C₂×C₇₁	#1556	1	4	yes	direct product factor
175	C₂×C₇₁	C₂²×#101	1	1	yes	characteristic
176	C₂×C₇₁	C₂×#418	1	1	yes	characteristic
177	C₂×C₇₁	C₂×#419	1	1	yes	characteristic
178	C₂²×C₄⋊Q₈	C₂×C₇₁	1	1	yes	characteristic
179	C₂×#432	C₂×C₇₁	1	1	yes	characteristic
180	C₂×#432	C₂×C₇₁	1	1	yes	characteristic
181	#1556	C₂×C₇₁	1	8	yes	direct product factor
182	C₂×#332	C₂×C₇₁	1	4	yes	complemented
183	C₇₁	C₂×#1556	1	1	yes	characteristic, direct product factor, Sylow
184	C₂³×Q₈	—	2	1	no	—
185	C₂×C₄⋊Q₈	—	2	1	no	—
186	C₂×C₄⋊Q₈	—	2	1	no	—
187	C₂×C₄⋊Q₈	—	2	2	no	—
188	C₂×C₄⋊Q₈	—	2	2	no	—
189	C₂×C₄⋊Q₈	C₄×C₇₁	1	2	yes	—
190	C₂×C₄⋊Q₈	C₄×C₇₁	1	4	yes	—
191	C₂×C₄⋊Q₈	C₂²×C₇₁	1	2	yes	—
192	C₂×C₄⋊Q₈	C₂²×C₇₁	1	4	yes	—
193	C₂²×C₄⋊C₄	—	2	1	no	—
194	C₂²×C₄⋊C₄	C₄×C₇₁	1	2	yes	—
195	C₂²×C₄²	C₂²×C₇₁	1	1	yes	characteristic
196	#432	—	2	2	no	—
197	#432	—	2	2	no	—
198	#432	C₂²×C₇₁	1	4	yes	—
199	#432	C₂²×C₇₁	1	4	yes	—
200	C₂×C₄⋊C₈	C₂²×C₇₁	1	2	yes	—
201	C₂×C₄⋊C₈	C₂²×C₇₁	1	2	yes	—
202	C₂×C₂²⋊C₈	—	2	1	no	—
203	C₂×C₂²⋊C₈	—	2	1	no	—
204	C₂×#97	—	2	1	no	—
205	C₂×#97	—	2	1	no	—
206	#332	C₂²×C₇₁	1	16	yes	complemented
207	C₂²×Q₈	—	2	4	no	—
208	C₂²×Q₈	—	2	2	no	—
209	C₂²×Q₈	—	2	4	no	—
210	C₂²×Q₈	—	2	2	no	—
211	C₂²×Q₈	—	4	8	no	—
212	C₂³×C₄	—	2	2	no	—
213	C₂³×C₄	C₂×C₄×C₇₁	1	1	yes	characteristic
214	C₂³×C₄	D₄×C₇₁	1	1	yes	characteristic
215	C₂³×C₄	D₄×C₇₁	1	1	yes	characteristic
216	C₂²×C₈	—	2	2	no	—
217	C₂²×C₈	—	2	2	no	—
218	C₄⋊Q₈	—	2	4	no	—
219	C₄⋊Q₈	—	2	4	no	—
220	C₄⋊Q₈	—	2	4	no	—
221	C₄⋊Q₈	—	2	4	no	—
222	C₄⋊Q₈	—	2	4	no	—
223	C₄⋊Q₈	—	2	2	no	—
224	C₄⋊Q₈	—	2	2	no	—
225	C₄⋊Q₈	C₂×C₄×C₇₁	1	4	yes	—
226	C₄⋊Q₈	C₂×C₄×C₇₁	1	8	yes	—
227	C₄⋊Q₈	C₂³×C₇₁	1	4	yes	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	4	no	—
230	C₂×C₄⋊C₄	—	2	4	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	2	4	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	C₂×C₄×C₇₁	1	4	yes	—
235	C₂×C₄⋊C₄	C₂×C₄×C₇₁	1	8	yes	—
236	C₂×C₄²	C₂×C₄×C₇₁	1	1	yes	characteristic
237	C₂×C₄²	C₂×C₄×C₇₁	1	2	yes	—
238	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
239	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
240	C₂×C₄²	D₄×C₇₁	1	2	yes	—
241	C₂×C₄²	D₄×C₇₁	1	2	yes	—
242	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
244	C₄⋊C₈	—	2	2	no	—
245	C₄⋊C₈	—	2	2	no	—
246	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
247	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
248	C₂²⋊C₈	—	2	4	no	—
249	C₂²⋊C₈	—	2	4	no	—
250	#97	—	2	4	no	—
251	#97	—	2	4	no	—
252	C₂⁴	C₂²⋊C₄×C₇₁	1	1	yes	characteristic
253	C₂×Q₈	—	2	8	no	—
254	C₂×Q₈	—	2	4	no	—
255	C₂×Q₈	—	2	4	no	—
256	C₂×Q₈	—	4	8	no	—
257	C₂×Q₈	—	4	16	no	—
258	C₂×Q₈	—	4	16	no	—
259	C₂×Q₈	—	4	8	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	8	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	4	8	no	—
266	C₂²×C₄	C₂²⋊C₄×C₇₁	1	1	yes	characteristic
267	C₂²×C₄	C₂²⋊C₄×C₇₁	1	2	yes	—
268	C₂²×C₄	C₂²⋊C₄×C₇₁	1	1	yes	characteristic
269	C₂²×C₄	C₂²⋊C₄×C₇₁	1	2	yes	—
270	C₂²×C₄	C₂²⋊C₄×C₇₁	1	2	yes	—
271	C₂²×C₄	C₂²⋊C₄×C₇₁	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₄×C₇₁	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₇₁	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
275	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	4	4	no	—
281	C₂×C₈	—	4	4	no	—
282	C₄⋊C₄	—	2	8	no	—
283	C₄⋊C₄	—	2	4	no	—
284	C₄⋊C₄	—	2	8	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	C₂²×C₄×C₇₁	1	8	yes	—
288	C₄²	C₂²⋊C₄×C₇₁	1	2	yes	—
289	C₄²	C₂²⋊C₄×C₇₁	1	2	yes	—
290	C₄²	C₂²⋊C₄×C₇₁	1	2	yes	—
291	C₄²	C₂²×C₄×C₇₁	1	2	yes	—
292	C₄²	C₂²×C₄×C₇₁	1	1	yes	characteristic
293	C₄²	C₂×D₄×C₇₁	1	2	yes	—
294	C₄²	C₂×D₄×C₇₁	1	2	yes	—
295	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
296	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
297	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
298	C₂³	—	2	2	no	—
299	C₂³	—	2	2	no	—
300	C₂³	#101×C₇₁	1	4	yes	—
301	C₂³	C₂×C₂²⋊C₄×C₇₁	1	2	yes	—
302	C₂³	C₂×C₂²⋊C₄×C₇₁	1	1	yes	characteristic
303	Q₈	—	4	16	no	—
304	Q₈	—	4	8	no	—
305	Q₈	—	4	8	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	4	16	no	—
318	C₂×C₄	—	4	8	no	—
319	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	2	yes	—
320	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	2	yes	—
321	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	2	yes	—
322	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	1	yes	characteristic
323	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	1	yes	characteristic
324	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	1	yes	characteristic
325	C₂×C₄	AGL(1,ℤ/8)×C₇₁	1	4	yes	—
326	C₂×C₄	#137×C₇₁	1	4	yes	—
327	C₂×C₄	C₂³×C₄×C₇₁	1	1	yes	characteristic
328	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
329	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
330	C₈	—	4	4	no	—
331	C₈	—	4	4	no	—
332	C₂²	—	2	8	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	2	no	—
335	C₂²	C₂×#101×C₇₁	1	4	yes	—
336	C₂²	C₂×#101×C₇₁	1	2	yes	—
337	C₂²	#418×C₇₁	1	2	yes	—
338	C₂²	#419×C₇₁	1	2	yes	—
339	C₂²	C₂²×C₂²⋊C₄×C₇₁	1	1	yes	characteristic
340	C₄	—	2	1	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	2	no	—
344	C₄	—	2	2	no	—
345	C₄	—	4	8	no	—
346	C₄	#418×C₇₁	1	2	yes	—
347	C₄	#419×C₇₁	1	2	yes	—
348	C₄	C₂×AGL(1,ℤ/8)×C₇₁	1	2	yes	—
349	C₄	C₂×#137×C₇₁	1	2	yes	—
350	C₂	—	2	4	no	—
351	C₂	C₇₁×#1556	1	4	yes	direct product factor
352	C₂	C₂²×#101×C₇₁	1	1	yes	characteristic
353	C₂	C₂×#418×C₇₁	1	1	yes	characteristic
354	C₂	C₂×#419×C₇₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₁	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₇₁
Frattini, cosocle	C₄²	C₂⁴×C₇₁
prime radical	C₂⁴×C₇₁	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇₁ ◁ C₂²×C₄²×C₇₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₇₁×#1556	C₂	direct (N × H)
5. C₂×#332×C₇₁	C₂	semidirect
28. #332×C₇₁	C₂²	semidirect
172. C₂×#1556	C₇₁	direct (N × H)
174. C₂×C₇₁	#1556	direct (N × H)
181. #1556	C₂×C₇₁	direct (N × H)
182. C₂×#332	C₂×C₇₁	semidirect
183. C₇₁	C₂×#1556	direct (N × H)
206. #332	C₂²×C₇₁	semidirect
351. C₂	C₇₁×#1556	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Q₈×C₇₁	2
C₂×#432×C₇₁	2
C₇₁×#1556	2
C₂×#332×C₇₁	2
C₂×#1556	71

Subgroups — C2×C71×#1556 #31838601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₁×#1556 #31838601