Subgroups — #2171×D₇₁ #32150682

Order 18176.

654 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#504×D₇₁	C₂	1	2	yes	maximal, complemented
2	#443×D₇₁	C₂	1	1	yes	maximal, characteristic
3	#22590183	C₂	1	1	yes	maximal, characteristic, complemented
4	#22590182	C₂	1	1	yes	maximal, characteristic, complemented
5	#22590181	C₂	1	1	yes	maximal, characteristic, complemented
6	#22590180	C₂	1	2	yes	maximal, complemented
7	#22590179	C₂	1	2	yes	maximal, complemented
8	#364×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#350×D₇₁	C₂	1	2	yes	maximal, complemented
10	#346×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#2171	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₇₁	C₄	1	1	yes	characteristic
13	#131×D₇₁	C₂²	1	2	yes	—
14	#17986417	—	2	2	no	—
15	#17986417	C₂²	1	2	yes	complemented
16	#17986416	C₂²	1	2	yes	complemented
17	#17986415	—	2	2	no	—
18	#17986415	C₂²	1	2	yes	complemented
19	M₃₂×D₇₁	—	2	2	no	—
20	M₃₂×D₇₁	C₂²	1	2	yes	—
21	C₂×C₁₆×D₇₁	—	2	2	no	—
22	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic
24	#17986117	C₂²	1	1	yes	characteristic
25	#17986116	C₄	1	1	yes	characteristic
26	#17986115	C₄	1	1	yes	characteristic
27	#17986114	C₂²	1	2	yes	—
28	#17986113	C₄	1	2	yes	—
29	#108×D₇₁	C₄	1	1	yes	characteristic
30	#104×D₇₁	C₄	1	2	yes	—
31	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
32	#17985820	C₂²	1	1	yes	characteristic, complemented
33	#17985819	C₂²	1	2	yes	complemented
34	#17985784	C₂²	1	2	yes	complemented
35	#17985783	C₂²	1	2	yes	complemented
36	#17985782	C₂²	1	2	yes	complemented
37	#17985775	C₂²	1	1	yes	characteristic, complemented
38	#17985774	C₂²	1	1	yes	characteristic, complemented
39	#17985774	C₂²	1	1	yes	characteristic, complemented
40	#504×C₇₁	C₂²	1	2	yes	complemented
41	#443×C₇₁	C₂²	1	1	yes	characteristic
42	#364×C₇₁	C₂²	1	1	yes	characteristic, complemented
43	#350×C₇₁	C₂²	1	2	yes	complemented
44	#346×C₇₁	C₂²	1	1	yes	characteristic, complemented
45	#41×D₇₁	C₂×C₄	1	2	yes	—
46	#14556151	C₈	1	1	yes	characteristic
47	#14556150	C₂×C₄	1	1	yes	characteristic
48	#14556149	C₈	1	2	yes	—
49	#14556148	C₂×C₄	1	2	yes	—
50	#14556147	C₈	1	1	yes	characteristic
51	Q₁₆×D₇₁	C₈	1	1	yes	characteristic
52	SD₁₆×D₇₁	C₈	1	2	yes	—
53	D₈×D₇₁	C₈	1	1	yes	characteristic
54	#14556136	—	2	2	no	—
55	#14556136	C₂×C₄	1	2	yes	—
56	#14556135	C₂×C₄	1	2	yes	—
57	#14556134	—	2	2	no	—
58	#14556134	C₂³	1	2	yes	—
59	M₁₆×D₇₁	—	2	2	no	—
60	M₁₆×D₇₁	C₂×C₄	1	2	yes	—
61	C₂×C₈×D₇₁	—	2	2	no	—
62	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
64	C₄²×D₇₁	C₂×C₄	1	1	yes	characteristic
65	#14556068	—	2	2	no	—
66	#14556068	C₂³	1	2	yes	—
67	#14556067	—	2	2	no	—
68	#14556067	—	2	2	no	—
69	#14556067	—	2	2	no	—
70	C₂×C₇₁⋊C₁₆	—	2	2	no	—
71	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
72	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
73	C₁₆×D₇₁	—	2	2	no	—
74	C₁₆×D₇₁	—	2	1	no	—
75	C₁₆×D₇₁	—	2	1	no	—
76	C₁₆×D₇₁	—	2	2	no	—
77	C₁₆×D₇₁	—	2	2	no	—
78	C₁₆×D₇₁	D₄	1	2	yes	—
79	C₁₆×D₇₁	D₄	1	2	yes	—
80	#14556064	C₂×C₄	1	1	yes	characteristic
81	#14556063	C₂×C₄	1	2	yes	—
82	#14556056	C₂×C₄	1	2	yes	—
83	#14556055	C₂×C₄	1	2	yes	—
84	#14556054	C₂×C₄	1	2	yes	—
85	C₄×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₇₁	C₂³	1	1	yes	characteristic
88	#135×C₇₁	C₂×C₄	1	1	yes	characteristic
89	#131×C₇₁	C₂³	1	2	yes	—
90	M₃₂×C₇₁	—	2	2	no	—
91	M₃₂×C₇₁	C₂³	1	2	yes	—
92	C₂×C₁₆×C₇₁	—	2	2	no	—
93	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
94	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
95	#108×C₇₁	C₂×C₄	1	1	yes	characteristic
96	#104×C₇₁	C₂×C₄	1	2	yes	—
97	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
98	#11765866	C₂×C₈	1	2	yes	—
99	#11765865	—	2	2	no	—
100	#11765865	C₂²×C₄	1	2	yes	—
101	#11765864	—	2	2	no	—
102	#11765864	C₂×C₈	1	2	yes	—
103	Q₈×D₇₁	C₂×C₈	1	2	yes	—
104	D₄×D₇₁	—	2	2	no	—
105	D₄×D₇₁	C₂×C₈	1	2	yes	—
106	C₂×C₄×D₇₁	—	2	2	no	—
107	C₂×C₄×D₇₁	—	2	1	no	—
108	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
109	Dic₂₈₄	C₂×C₈	1	1	yes	characteristic
110	#11765855	C₂×C₈	1	2	yes	—
111	#11765854	C₂×C₈	1	2	yes	—
112	#11765853	C₂×C₈	1	2	yes	—
113	#11765852	C₂×C₈	1	2	yes	—
114	D₅₆₈	C₂×C₈	1	1	yes	characteristic
115	#11765850	C₂×C₈	1	2	yes	—
116	#11765849	—	2	2	no	—
117	#11765849	C₂²×C₄	1	2	yes	—
118	#11765848	—	2	2	no	—
119	#11765848	—	2	2	no	—
120	#11765848	—	2	2	no	—
121	C₂×C₇₁⋊C₈	—	2	2	no	—
122	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
124	C₈×D₇₁	—	2	2	no	—
125	C₈×D₇₁	—	2	2	no	—
126	C₈×D₇₁	—	2	2	no	—
127	C₈×D₇₁	C₂×C₈	1	1	yes	characteristic
128	C₈×D₇₁	C₂×C₈	1	1	yes	characteristic
129	C₈×D₇₁	C₂×C₈	1	1	yes	characteristic
130	C₈×D₇₁	C₂×C₈	1	1	yes	characteristic
131	C₈×D₇₁	C₂×D₄	1	1	yes	characteristic
132	C₈×D₇₁	C₂×D₄	1	1	yes	characteristic
133	C₈×D₇₁	#41	1	1	yes	characteristic
134	C₈×D₇₁	#41	1	1	yes	characteristic
135	C₄×Dic₇₁	—	2	1	no	—
136	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
137	C₇₁⋊C₁₆	—	2	2	no	—
138	C₇₁⋊C₁₆	—	2	1	no	—
139	C₇₁⋊C₁₆	C₂×D₄	1	2	yes	—
140	#41×C₇₁	C₂²×C₄	1	2	yes	—
141	Q₁₆×C₇₁	C₂×C₈	1	1	yes	characteristic
142	SD₁₆×C₇₁	C₂×C₈	1	2	yes	—
143	D₈×C₇₁	C₂×C₈	1	1	yes	characteristic
144	M₁₆×C₇₁	—	2	2	no	—
145	M₁₆×C₇₁	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₇₁	—	2	2	no	—
147	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
149	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
150	C₁₆×C₇₁	—	2	2	no	—
151	C₁₆×C₇₁	—	2	1	no	—
152	C₁₆×C₇₁	C₂×D₄	1	2	yes	—
153	C₂²×D₇₁	—	2	2	no	—
154	C₂²×D₇₁	#131	1	1	yes	characteristic
155	Q₈×C₇₁	C₂²×C₈	1	2	yes	—
156	D₄×C₇₁	—	2	2	no	—
157	D₄×C₇₁	C₂²×C₈	1	2	yes	—
158	C₂×C₄×C₇₁	—	2	2	no	—
159	C₂×C₄×C₇₁	—	2	1	no	—
160	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
161	C₂²⋊D₇₁	—	2	2	no	—
162	C₂²⋊D₇₁	—	2	2	no	—
163	C₂²⋊D₇₁	—	2	2	no	—
164	C₂×Dic₇₁	—	2	2	no	—
165	C₂×Dic₇₁	—	2	1	no	—
166	C₂×Dic₇₁	#131	1	1	yes	characteristic
167	D₂₈₄	—	2	2	no	—
168	D₂₈₄	C₂²×C₈	1	2	yes	—
169	C₄×D₇₁	—	2	2	no	—
170	C₄×D₇₁	—	2	2	no	—
171	C₄×D₇₁	—	2	2	no	—
172	C₄×D₇₁	—	4	2	no	—
173	C₄×D₇₁	C₄×D₄	1	1	yes	characteristic
174	C₄×D₇₁	C₄×D₄	1	1	yes	characteristic
175	C₄×D₇₁	C₂²×C₈	1	1	yes	characteristic
176	C₄×D₇₁	C₂²×C₈	1	1	yes	characteristic
177	Dic₁₄₂	—	2	2	no	—
178	Dic₁₄₂	C₂²×C₈	1	2	yes	—
179	C₈×C₇₁	—	2	2	no	—
180	C₈×C₇₁	C₂²×C₈	1	1	yes	characteristic
181	C₈×C₇₁	C₂²×C₈	1	1	yes	characteristic
182	C₈×C₇₁	C₂²×D₄	1	1	yes	characteristic
183	C₈×C₇₁	C₂×#41	1	1	yes	characteristic
184	C₇₁⋊C₈	—	2	2	no	—
185	C₇₁⋊C₈	C₄×D₄	1	1	yes	characteristic
186	C₇₁⋊C₈	C₄×D₄	1	1	yes	characteristic
187	C₇₁⋊C₈	C₂²×C₈	1	1	yes	characteristic
188	C₇₁⋊C₈	C₂²×C₈	1	1	yes	characteristic
189	C₂²×C₇₁	—	2	2	no	—
190	C₂²×C₇₁	C₂×#131	1	1	yes	characteristic
191	C₂×D₇₁	—	2	2	no	—
192	C₂×D₇₁	—	2	2	no	—
193	C₂×D₇₁	—	4	4	no	—
194	C₂×D₇₁	C₈×D₄	1	1	yes	characteristic
195	C₂×D₇₁	C₈×D₄	1	1	yes	characteristic
196	C₄×C₇₁	—	2	2	no	—
197	C₄×C₇₁	—	4	1	no	—
198	C₄×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
199	C₄×C₇₁	C₂³×C₈	1	1	yes	characteristic
200	Dic₇₁	—	2	2	no	—
201	Dic₇₁	—	4	1	no	—
202	Dic₇₁	C₈×D₄	1	1	yes	characteristic
203	Dic₇₁	C₈×D₄	1	1	yes	characteristic
204	C₂×#2171	—	71	1	no	maximal, Sylow
205	C₂×C₇₁	—	2	1	no	—
206	C₂×C₇₁	—	4	2	no	—
207	C₂×C₇₁	C₂×C₈×D₄	1	1	yes	characteristic
208	D₇₁	—	2	1	no	—
209	D₇₁	—	4	2	no	—
210	D₇₁	#2171	1	2	yes	direct product factor
211	C₂×#504	—	71	2	no	—
212	C₂×#443	—	71	1	no	—
213	#2171	—	71	2	no	—
214	#2171	—	71	1	no	—
215	#2171	—	71	1	no	—
216	#2171	—	71	2	no	—
217	#2171	—	71	1	no	—
218	#2171	D₇₁	1	1	yes	characteristic, direct product factor
219	C₂×#364	—	71	1	no	—
220	C₂×#350	—	71	2	no	—
221	C₂×#346	—	71	1	no	—
222	C₇₁	C₂×#2171	1	1	yes	characteristic, complemented, Sylow
223	C₂×#135	—	71	1	no	—
224	C₂×#131	—	71	2	no	—
225	#504	—	71	2	no	—
226	#504	—	71	2	no	—
227	#504	—	71	2	no	—
228	#504	—	142	2	no	—
229	#504	—	142	2	no	—
230	#504	C₂×D₇₁	1	2	yes	complemented
231	C₂×M₃₂	—	71	2	no	—
232	C₂×M₃₂	—	142	2	no	—
233	C₂²×C₁₆	—	71	1	no	—
234	C₂²×C₁₆	—	71	1	no	—
235	C₂²×C₁₆	—	142	2	no	—
236	#443	—	71	1	no	—
237	#443	—	71	2	no	—
238	#443	—	71	1	no	—
239	#443	—	71	2	no	—
240	#443	—	71	1	no	—
241	#443	C₂×D₇₁	1	1	yes	characteristic
242	C₂×#108	—	71	1	no	—
243	C₂×#104	—	71	2	no	—
244	C₂×C₄×C₈	—	71	1	no	—
245	#364	—	71	2	no	—
246	#364	—	71	1	no	—
247	#364	C₂×D₇₁	1	1	yes	characteristic, complemented
248	#350	—	71	2	no	—
249	#350	—	71	2	no	—
250	#350	—	71	2	no	—
251	#350	C₂×D₇₁	1	2	yes	complemented
252	#346	—	71	1	no	—
253	#346	—	71	1	no	—
254	#346	—	71	1	no	—
255	#346	C₂×D₇₁	1	1	yes	characteristic, complemented
256	C₂×#41	—	71	2	no	—
257	#135	—	71	2	no	—
258	#135	—	71	1	no	—
259	#135	—	71	2	no	—
260	#135	—	71	1	no	—
261	#135	—	71	1	no	—
262	#135	C₄×D₇₁	1	1	yes	characteristic
263	C₂×Q₁₆	—	71	1	no	—
264	C₂×SD₁₆	—	71	2	no	—
265	C₂×D₈	—	71	1	no	—
266	#131	—	71	2	no	—
267	#131	—	71	2	no	—
268	#131	—	71	2	no	—
269	#131	—	142	2	no	—
270	#131	—	142	2	no	—
271	#131	C₂²×D₇₁	1	2	yes	—
272	C₂×M₁₆	—	71	2	no	—
273	C₂×M₁₆	—	142	2	no	—
274	C₂²×C₈	—	71	1	no	—
275	C₂²×C₈	—	71	1	no	—
276	C₂²×C₈	—	142	2	no	—
277	C₂×C₄²	—	71	1	no	—
278	M₃₂	—	2	2	no	—
279	M₃₂	—	71	2	no	—
280	M₃₂	—	142	2	no	—
281	M₃₂	—	142	2	no	—
282	M₃₂	—	142	2	no	—
283	M₃₂	—	142	2	no	—
284	M₃₂	C₂²×D₇₁	1	2	yes	—
285	C₂×C₁₆	—	2	2	no	—
286	C₂×C₁₆	—	71	1	no	—
287	C₂×C₁₆	—	71	2	no	—
288	C₂×C₁₆	—	71	2	no	—
289	C₂×C₁₆	—	71	1	no	—
290	C₂×C₁₆	—	142	2	no	—
291	C₂×C₁₆	—	142	1	no	—
292	C₂×C₁₆	—	142	1	no	—
293	C₂×C₁₆	—	142	2	no	—
294	C₂×C₁₆	—	142	2	no	—
295	C₂×C₁₆	—	142	2	no	—
296	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
297	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
298	#108	—	71	2	no	—
299	#108	—	71	1	no	—
300	#108	C₄×D₇₁	1	1	yes	characteristic
301	#104	—	71	2	no	—
302	#104	—	71	2	no	—
303	#104	—	71	2	no	—
304	#104	C₄×D₇₁	1	2	yes	—
305	C₄×C₈	—	71	1	no	—
306	C₄×C₈	—	71	1	no	—
307	C₄×C₈	—	71	1	no	—
308	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
309	#41	—	71	2	no	—
310	#41	—	71	2	no	—
311	#41	—	71	2	no	—
312	#41	—	142	2	no	—
313	#41	—	142	2	no	—
314	#41	C₂×C₄×D₇₁	1	2	yes	—
315	C₂×Q₈	—	71	2	no	—
316	C₂×D₄	—	71	2	no	—
317	C₂×D₄	—	142	2	no	—
318	C₂²×C₄	—	71	1	no	—
319	C₂²×C₄	—	142	1	no	—
320	C₂²×C₄	—	142	2	no	—
321	Q₁₆	—	71	2	no	—
322	Q₁₆	—	71	1	no	—
323	Q₁₆	C₈×D₇₁	1	1	yes	characteristic
324	SD₁₆	—	71	2	no	—
325	SD₁₆	—	71	2	no	—
326	SD₁₆	—	71	2	no	—
327	SD₁₆	C₈×D₇₁	1	2	yes	—
328	D₈	—	71	2	no	—
329	D₈	—	71	1	no	—
330	D₈	C₈×D₇₁	1	1	yes	characteristic
331	M₁₆	—	2	2	no	—
332	M₁₆	—	71	2	no	—
333	M₁₆	—	142	2	no	—
334	M₁₆	—	142	2	no	—
335	M₁₆	—	142	2	no	—
336	M₁₆	—	142	2	no	—
337	M₁₆	C₂×C₄×D₇₁	1	2	yes	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	71	1	no	—
340	C₂×C₈	—	71	1	no	—
341	C₂×C₈	—	71	1	no	—
342	C₂×C₈	—	71	1	no	—
343	C₂×C₈	—	71	1	no	—
344	C₂×C₈	—	71	1	no	—
345	C₂×C₈	—	71	1	no	—
346	C₂×C₈	—	71	1	no	—
347	C₂×C₈	—	71	1	no	—
348	C₂×C₈	—	71	1	no	—
349	C₂×C₈	—	142	2	no	—
350	C₂×C₈	—	142	2	no	—
351	C₂×C₈	—	142	2	no	—
352	C₂×C₈	—	142	2	no	—
353	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
354	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
355	C₄²	—	71	1	no	—
356	C₄²	—	142	1	no	—
357	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
358	C₁₆	—	2	2	no	—
359	C₁₆	—	2	1	no	—
360	C₁₆	—	71	2	no	—
361	C₁₆	—	142	2	no	—
362	C₁₆	—	142	1	no	—
363	C₁₆	D₄×D₇₁	1	2	yes	—
364	C₂³	—	71	1	no	—
365	C₂³	—	142	2	no	—
366	Q₈	—	71	2	no	—
367	Q₈	—	142	2	no	—
368	Q₈	C₂×C₈×D₇₁	1	2	yes	—
369	D₄	—	2	2	no	—
370	D₄	—	71	2	no	—
371	D₄	—	142	2	no	—
372	D₄	—	142	2	no	—
373	D₄	—	142	2	no	—
374	D₄	—	142	2	no	—
375	D₄	C₂×C₈×D₇₁	1	2	yes	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	284	2	no	—
379	C₂×C₄	—	71	1	no	—
380	C₂×C₄	—	71	1	no	—
381	C₂×C₄	—	71	1	no	—
382	C₂×C₄	—	71	1	no	—
383	C₂×C₄	—	71	1	no	—
384	C₂×C₄	—	142	2	no	—
385	C₂×C₄	—	142	2	no	—
386	C₂×C₄	—	142	1	no	—
387	C₂×C₄	—	142	2	no	—
388	C₂×C₄	—	142	2	no	—
389	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
390	C₈	—	2	2	no	—
391	C₈	—	71	1	no	—
392	C₈	—	71	1	no	—
393	C₈	—	71	1	no	—
394	C₈	—	71	1	no	—
395	C₈	—	142	2	no	—
396	C₈	C₂×C₈×D₇₁	1	1	yes	characteristic
397	C₈	C₂×C₈×D₇₁	1	1	yes	characteristic
398	C₈	C₂×D₄×D₇₁	1	1	yes	characteristic
399	C₈	#41×D₇₁	1	1	yes	characteristic
400	C₂²	—	2	2	no	—
401	C₂²	—	284	4	no	—
402	C₂²	—	71	1	no	—
403	C₂²	—	71	1	no	—
404	C₂²	—	142	2	no	—
405	C₂²	—	142	2	no	—
406	C₂²	#131×D₇₁	1	1	yes	characteristic
407	C₄	—	2	2	no	—
408	C₄	—	4	1	no	—
409	C₄	—	284	1	no	—
410	C₄	—	71	1	no	—
411	C₄	—	71	1	no	—
412	C₄	—	142	2	no	—
413	C₄	C₄×D₄×D₇₁	1	1	yes	characteristic
414	C₄	C₂²×C₈×D₇₁	1	1	yes	characteristic
415	C₂	—	2	1	no	—
416	C₂	—	4	2	no	—
417	C₂	—	284	2	no	—
418	C₂	—	71	2	no	—
419	C₂	—	142	1	no	—
420	C₂	C₈×D₄×D₇₁	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₄×D₇₁
commutator	C₄×C₇₁	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₇₁
Fitting	C₇₁×#2171	C₂
socle	C₂×C₇₁	C₂×C₈×D₄
prime radical	#135×D₇₁	C₄
cosocle	C₂×C₈×C₇₁	C₂⁴
hypercenter	#2171	D₇₁
hypocenter	C₇₁	C₂×#2171
LCS	G ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ #2171

Complements

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

N	H ≅ G/N	type
1. #504×D₇₁	C₂	semidirect
3. #22590183	C₂	semidirect
4. #22590182	C₂	semidirect
5. #22590181	C₂	semidirect
6. #22590180	C₂	semidirect
7. #22590179	C₂	semidirect
8. #364×D₇₁	C₂	semidirect
9. #350×D₇₁	C₂	semidirect
10. #346×D₇₁	C₂	semidirect
11. C₇₁×#2171	C₂	semidirect
15. #17986417	C₂²	semidirect
16. #17986416	C₂²	semidirect
18. #17986415	C₂²	semidirect
32. #17985820	C₂²	semidirect
33. #17985819	C₂²	semidirect
34. #17985784	C₂²	semidirect
35. #17985783	C₂²	semidirect
36. #17985782	C₂²	semidirect
37. #17985775	C₂²	semidirect
38. #17985774	C₂²	semidirect
39. #17985774	C₂²	semidirect
40. #504×C₇₁	C₂²	semidirect
42. #364×C₇₁	C₂²	semidirect
43. #350×C₇₁	C₂²	semidirect
44. #346×C₇₁	C₂²	semidirect
210. D₇₁	#2171	direct (N × H)
218. #2171	D₇₁	direct (N × H)
222. C₇₁	C₂×#2171	semidirect
230. #504	C₂×D₇₁	semidirect
247. #364	C₂×D₇₁	semidirect
251. #350	C₂×D₇₁	semidirect
255. #346	C₂×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
#504×D₇₁	2
#443×D₇₁	2
#22590183	2
#22590182	2
#22590181	2
#22590180	2
#22590179	2
#364×D₇₁	2
#350×D₇₁	2
#346×D₇₁	2
C₇₁×#2171	2
C₂×#2171	71

Subgroups — #2171×D71 #32150682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2171×D₇₁ #32150682