Subgroups — #2230×D₇₁ #32152178

Order 18176.

558 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#498×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#443×D₇₁	C₂	1	1	yes	maximal, characteristic
3	#22590512	C₂	1	1	yes	maximal, characteristic, complemented
4	#22590511	C₂	1	1	yes	maximal, characteristic, complemented
5	#22590510	C₂	1	2	yes	maximal, complemented
6	#22590509	C₂	1	2	yes	maximal, complemented
7	#22590508	C₂	1	1	yes	maximal, characteristic, complemented
8	#365×D₇₁	C₂	1	2	yes	maximal, complemented
9	#364×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#360×D₇₁	C₂	1	2	yes	maximal
11	C₇₁×#2230	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₇₁	C₂²	1	1	yes	characteristic
13	#131×D₇₁	—	2	1	no	—
14	C₄⋊Q₈×D₇₁	—	2	1	no	—
15	M₃₂×D₇₁	C₂²	1	2	yes	—
16	#17986397	C₂²	1	1	yes	characteristic, complemented
17	#17986396	—	2	1	no	—
18	#17986396	C₂²	1	2	yes	complemented
19	#17986395	—	2	1	no	—
20	#17986117	C₂²	1	1	yes	characteristic
21	#17986116	C₂²	1	1	yes	characteristic
22	#17986115	C₂²	1	1	yes	characteristic
23	#17986114	—	2	1	no	—
24	#17986113	—	2	1	no	—
25	#108×D₇₁	C₂²	1	1	yes	characteristic
26	#106×D₇₁	—	2	1	no	—
27	#106×D₇₁	C₂²	1	2	yes	—
28	#104×D₇₁	—	2	1	no	—
29	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
30	#17985823	C₂²	1	2	yes	complemented
31	#17985822	C₂²	1	2	yes	complemented
32	#17985821	C₂²	1	2	yes	complemented
33	#17985820	C₂²	1	1	yes	characteristic, complemented
34	#17985819	C₂²	1	2	yes	complemented
35	#17985810	C₂²	1	2	yes	—
36	#17985809	C₂²	1	2	yes	—
37	#17985808	C₂²	1	2	yes	—
38	#498×C₇₁	C₂²	1	1	yes	characteristic, complemented
39	#443×C₇₁	C₂²	1	1	yes	characteristic
40	#365×C₇₁	C₂²	1	2	yes	complemented
41	#364×C₇₁	C₂²	1	1	yes	characteristic, complemented
42	#360×C₇₁	C₂²	1	2	yes	—
43	#41×D₇₁	—	2	1	no	—
44	C₂×Q₈×D₇₁	—	4	1	no	—
45	#14556151	Q₈	1	1	yes	characteristic, complemented
46	#14556150	C₂³	1	1	yes	characteristic
47	#14556149	—	2	1	no	—
48	#14556148	—	2	1	no	—
49	#14556147	Q₈	1	1	yes	characteristic, complemented
50	Q₁₆×D₇₁	Q₈	1	1	yes	characteristic, complemented
51	SD₁₆×D₇₁	—	2	1	no	—
52	D₈×D₇₁	Q₈	1	1	yes	characteristic, complemented
53	#14556136	—	2	1	no	—
54	#14556136	—	4	1	no	—
55	#14556135	—	2	1	no	—
56	#14556134	—	2	1	no	—
57	#14556134	—	4	1	no	—
58	M₁₆×D₇₁	—	2	1	no	—
59	M₁₆×D₇₁	—	4	1	no	—
60	C₂×C₈×D₇₁	—	4	1	no	—
61	C₂×C₈×D₇₁	D₄	1	1	yes	characteristic
62	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
63	#14556128	—	2	1	no	—
64	#14556127	—	2	2	no	—
65	#14556127	—	4	1	no	—
66	#14556126	—	4	1	no	—
67	C₄⋊C₄×D₇₁	—	2	2	no	—
68	C₄⋊C₄×D₇₁	—	4	1	no	—
69	C₄²×D₇₁	D₄	1	1	yes	characteristic
70	#14556068	C₂³	1	2	yes	—
71	#14556067	—	2	2	no	—
72	C₁₆×D₇₁	—	2	2	no	—
73	#14556064	C₂³	1	1	yes	characteristic
74	#14556063	—	2	1	no	—
75	#14556060	—	2	1	no	—
76	#14556060	C₂³	1	2	yes	—
77	#14556059	—	2	2	no	—
78	#14556059	—	2	2	no	—
79	#14556056	—	2	1	no	—
80	#14556055	—	2	1	no	—
81	#14556054	—	2	1	no	—
82	C₄×C₇₁⋊C₈	D₄	1	1	yes	characteristic
83	C₈×Dic₇₁	D₄	1	1	yes	characteristic
84	C₈×Dic₇₁	C₂³	1	1	yes	characteristic
85	#135×C₇₁	C₂³	1	1	yes	characteristic
86	#131×C₇₁	—	2	1	no	—
87	C₄⋊Q₈×C₇₁	—	2	1	no	—
88	M₃₂×C₇₁	C₂³	1	2	yes	—
89	#108×C₇₁	C₂³	1	1	yes	characteristic
90	#106×C₇₁	—	2	1	no	—
91	#106×C₇₁	C₂³	1	2	yes	—
92	#104×C₇₁	—	2	1	no	—
93	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
94	#11765866	—	2	1	no	—
95	#11765865	—	2	1	no	—
96	#11765865	—	4	1	no	—
97	#11765864	—	2	1	no	—
98	#11765864	—	4	1	no	—
99	C₂×Dic₁₄₂	—	4	2	no	—
100	C₂×Dic₁₄₂	—	4	1	no	—
101	Q₈×D₇₁	—	2	1	no	—
102	Q₈×D₇₁	—	8	4	no	—
103	D₄×D₇₁	—	2	1	no	—
104	D₄×D₇₁	—	4	1	no	—
105	C₂×C₄×D₇₁	—	2	1	no	—
106	C₂×C₄×D₇₁	—	4	1	no	—
107	C₂×C₄×D₇₁	—	4	2	no	—
108	C₂×C₄×D₇₁	C₂×D₄	1	1	yes	characteristic
109	Dic₂₈₄	C₂×Q₈	1	1	yes	characteristic, complemented
110	#11765855	—	2	1	no	—
111	#11765854	—	2	1	no	—
112	#11765853	—	2	1	no	—
113	#11765852	—	2	1	no	—
114	D₅₆₈	C₂×Q₈	1	1	yes	characteristic, complemented
115	#11765850	—	2	1	no	—
116	#11765849	—	2	1	no	—
117	#11765849	—	4	1	no	—
118	#11765848	—	4	1	no	—
119	#11765848	—	4	1	no	—
120	#11765848	—	4	1	no	—
121	C₂×C₇₁⋊C₈	—	4	1	no	—
122	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
123	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
124	C₈×D₇₁	—	4	1	no	—
125	C₈×D₇₁	—	4	1	no	—
126	C₈×D₇₁	—	4	1	no	—
127	C₈×D₇₁	SD₁₆	1	1	yes	characteristic
128	C₈×D₇₁	SD₁₆	1	1	yes	characteristic
129	C₈×D₇₁	SD₁₆	1	1	yes	characteristic
130	C₈×D₇₁	SD₁₆	1	1	yes	characteristic
131	C₈×D₇₁	C₂×Q₈	1	1	yes	characteristic
132	C₈×D₇₁	C₂×Q₈	1	1	yes	characteristic
133	C₈×D₇₁	#41	1	1	yes	characteristic
134	C₈×D₇₁	#41	1	1	yes	characteristic
135	C₄⋊Dic₇₁	—	2	2	no	—
136	C₄⋊Dic₇₁	—	4	1	no	—
137	Dic₇₁⋊C₄	—	4	2	no	—
138	Dic₇₁⋊C₄	—	4	2	no	—
139	C₄×Dic₇₁	—	2	1	no	—
140	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
141	C₇₁⋊C₁₆	—	2	2	no	—
142	#41×C₇₁	—	2	1	no	—
143	C₂×Q₈×C₇₁	—	4	1	no	—
144	Q₁₆×C₇₁	C₂×Q₈	1	1	yes	characteristic, complemented
145	SD₁₆×C₇₁	—	2	1	no	—
146	D₈×C₇₁	C₂×Q₈	1	1	yes	characteristic, complemented
147	M₁₆×C₇₁	—	2	1	no	—
148	M₁₆×C₇₁	—	4	1	no	—
149	C₂×C₈×C₇₁	—	4	1	no	—
150	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
152	C₄⋊C₄×C₇₁	—	2	2	no	—
153	C₄⋊C₄×C₇₁	—	4	1	no	—
154	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
155	C₁₆×C₇₁	—	2	2	no	—
156	C₂²×D₇₁	—	4	1	no	—
157	C₂²×D₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
158	Q₈×C₇₁	—	2	1	no	—
159	Q₈×C₇₁	—	8	2	no	—
160	D₄×C₇₁	—	2	1	no	—
161	D₄×C₇₁	—	4	1	no	—
162	C₂×C₄×C₇₁	—	2	1	no	—
163	C₂×C₄×C₇₁	—	4	1	no	—
164	C₂×C₄×C₇₁	—	4	2	no	—
165	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
166	C₂²⋊D₇₁	—	4	1	no	—
167	C₂²⋊D₇₁	—	4	1	no	—
168	C₂²⋊D₇₁	—	4	1	no	—
169	C₂×Dic₇₁	—	2	1	no	—
170	C₂×Dic₇₁	—	4	1	no	—
171	C₂×Dic₇₁	—	4	2	no	—
172	C₂×Dic₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
173	D₂₈₄	—	2	1	no	—
174	D₂₈₄	—	4	1	no	—
175	C₄×D₇₁	—	2	4	no	—
176	C₄×D₇₁	—	4	1	no	—
177	C₄×D₇₁	—	4	1	no	—
178	C₄×D₇₁	—	4	1	no	—
179	C₄×D₇₁	—	8	4	no	—
180	C₄×D₇₁	C₂²⋊Q₈	1	1	yes	characteristic
181	C₄×D₇₁	C₂²⋊Q₈	1	1	yes	characteristic
182	C₄×D₇₁	C₂×SD₁₆	1	1	yes	characteristic
183	C₄×D₇₁	C₂×SD₁₆	1	1	yes	characteristic
184	Dic₁₄₂	—	2	1	no	—
185	Dic₁₄₂	—	4	1	no	—
186	Dic₁₄₂	—	8	4	no	—
187	Dic₁₄₂	—	8	2	no	—
188	C₈×C₇₁	—	4	1	no	—
189	C₈×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
190	C₈×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
191	C₈×C₇₁	C₂²×Q₈	1	1	yes	characteristic
192	C₈×C₇₁	C₂×#41	1	1	yes	characteristic
193	C₇₁⋊C₈	—	4	1	no	—
194	C₇₁⋊C₈	C₂²⋊Q₈	1	1	yes	characteristic
195	C₇₁⋊C₈	C₂²⋊Q₈	1	1	yes	characteristic
196	C₇₁⋊C₈	C₂×SD₁₆	1	1	yes	characteristic
197	C₇₁⋊C₈	C₂×SD₁₆	1	1	yes	characteristic
198	C₂²×C₇₁	—	4	1	no	—
199	C₂²×C₇₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
200	C₂×D₇₁	—	2	2	no	—
201	C₂×D₇₁	—	4	1	no	—
202	C₂×D₇₁	—	8	2	no	—
203	C₂×D₇₁	#476	1	1	yes	characteristic
204	C₂×D₇₁	#476	1	1	yes	characteristic
205	C₄×C₇₁	—	2	2	no	—
206	C₄×C₇₁	—	4	1	no	—
207	C₄×C₇₁	—	8	2	no	—
208	C₄×C₇₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
209	C₄×C₇₁	C₂²×SD₁₆	1	1	yes	characteristic
210	Dic₇₁	—	2	2	no	—
211	Dic₇₁	—	4	1	no	—
212	Dic₇₁	—	8	2	no	—
213	Dic₇₁	#476	1	1	yes	characteristic
214	Dic₇₁	#476	1	1	yes	characteristic
215	C₂×#2230	—	71	1	no	maximal, Sylow
216	C₂×C₇₁	—	2	1	no	—
217	C₂×C₇₁	—	8	1	no	—
218	C₂×C₇₁	C₂×#476	1	1	yes	characteristic
219	D₇₁	—	2	1	no	—
220	D₇₁	—	8	1	no	—
221	D₇₁	#2230	1	2	yes	direct product factor
222	C₂×#498	—	71	1	no	—
223	C₂×#443	—	71	1	no	—
224	#2230	—	71	1	no	—
225	#2230	—	71	1	no	—
226	#2230	—	71	2	no	—
227	#2230	—	71	1	no	—
228	#2230	—	71	2	no	—
229	#2230	D₇₁	1	1	yes	characteristic, direct product factor
230	C₂×#365	—	71	2	no	—
231	C₂×#364	—	71	1	no	—
232	C₂×#360	—	71	2	no	—
233	C₇₁	C₂×#2230	1	1	yes	characteristic, complemented, Sylow
234	C₂×#135	—	71	1	no	—
235	C₂×#131	—	142	1	no	—
236	C₂×C₄⋊Q₈	—	142	1	no	—
237	C₂×M₃₂	—	71	2	no	—
238	#498	—	71	2	no	—
239	#498	—	71	1	no	—
240	#498	—	142	1	no	—
241	#498	—	142	1	no	—
242	#498	C₂×D₇₁	1	1	yes	characteristic, complemented
243	#443	—	71	1	no	—
244	#443	—	71	1	no	—
245	#443	—	71	1	no	—
246	#443	—	142	1	no	—
247	#443	—	142	1	no	—
248	#443	C₂×D₇₁	1	1	yes	characteristic
249	C₂×#108	—	71	1	no	—
250	C₂×#106	—	71	2	no	—
251	C₂×#106	—	142	1	no	—
252	C₂×#104	—	142	1	no	—
253	C₂×C₄×C₈	—	71	1	no	—
254	#365	—	71	2	no	—
255	#365	—	71	2	no	—
256	#365	—	71	2	no	—
257	#365	C₂×D₇₁	1	2	yes	complemented
258	#364	—	71	2	no	—
259	#364	—	71	1	no	—
260	#364	C₂×D₇₁	1	1	yes	characteristic, complemented
261	#360	—	71	2	no	—
262	#360	—	71	2	no	—
263	#360	—	71	2	no	—
264	#360	C₂×D₇₁	1	2	yes	—
265	C₂×#41	—	142	1	no	—
266	C₂²×Q₈	—	284	1	no	—
267	#135	—	71	1	no	—
268	#135	—	71	1	no	—
269	#135	—	71	1	no	—
270	#135	—	142	1	no	—
271	#135	—	142	1	no	—
272	#135	C₂²×D₇₁	1	1	yes	characteristic
273	C₂×Q₁₆	—	71	1	no	—
274	C₂×SD₁₆	—	142	1	no	—
275	C₂×D₈	—	71	1	no	—
276	#131	—	2	1	no	—
277	#131	—	284	1	no	—
278	#131	—	284	1	no	—
279	#131	—	142	1	no	—
280	#131	—	142	1	no	—
281	#131	—	142	1	no	—
282	C₂×M₁₆	—	284	1	no	—
283	C₂×M₁₆	—	142	1	no	—
284	C₂²×C₈	—	284	1	no	—
285	C₂²×C₈	—	71	1	no	—
286	C₂²×C₈	—	71	1	no	—
287	C₄⋊Q₈	—	2	1	no	—
288	C₄⋊Q₈	—	284	1	no	—
289	C₄⋊Q₈	—	284	1	no	—
290	C₄⋊Q₈	—	142	2	no	—
291	C₄⋊Q₈	—	142	1	no	—
292	C₂×C₄⋊C₄	—	284	1	no	—
293	C₂×C₄⋊C₄	—	142	2	no	—
294	C₂×C₄²	—	71	1	no	—
295	M₃₂	—	71	2	no	—
296	M₃₂	—	142	2	no	—
297	M₃₂	C₂²×D₇₁	1	2	yes	—
298	C₂×C₁₆	—	142	2	no	—
299	#108	—	71	1	no	—
300	#108	—	142	1	no	—
301	#108	C₂²×D₇₁	1	1	yes	characteristic
302	#106	—	2	1	no	—
303	#106	—	71	2	no	—
304	#106	—	142	2	no	—
305	#106	—	142	2	no	—
306	#106	—	142	1	no	—
307	#106	C₂²×D₇₁	1	2	yes	—
308	#104	—	2	1	no	—
309	#104	—	142	1	no	—
310	#104	—	142	1	no	—
311	#104	—	142	1	no	—
312	C₄×C₈	—	71	1	no	—
313	C₄×C₈	—	71	1	no	—
314	C₄×C₈	—	71	1	no	—
315	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
316	#41	—	2	1	no	—
317	#41	—	284	1	no	—
318	#41	—	284	1	no	—
319	#41	—	142	1	no	—
320	#41	—	142	1	no	—
321	#41	—	142	1	no	—
322	C₂×Q₈	—	4	1	no	—
323	C₂×Q₈	—	284	1	no	—
324	C₂×Q₈	—	284	2	no	—
325	C₂×Q₈	—	568	4	no	—
326	C₂×Q₈	—	142	1	no	—
327	C₂×D₄	—	284	1	no	—
328	C₂×D₄	—	142	1	no	—
329	C₂²×C₄	—	284	1	no	—
330	C₂²×C₄	—	284	2	no	—
331	C₂²×C₄	—	71	1	no	—
332	C₂²×C₄	—	142	1	no	—
333	Q₁₆	—	71	1	no	—
334	Q₁₆	—	142	1	no	—
335	Q₁₆	Q₈×D₇₁	1	1	yes	characteristic, complemented
336	SD₁₆	—	2	1	no	—
337	SD₁₆	—	142	1	no	—
338	SD₁₆	—	142	1	no	—
339	SD₁₆	—	142	1	no	—
340	D₈	—	71	1	no	—
341	D₈	—	142	1	no	—
342	D₈	Q₈×D₇₁	1	1	yes	characteristic, complemented
343	M₁₆	—	2	1	no	—
344	M₁₆	—	4	1	no	—
345	M₁₆	—	284	1	no	—
346	M₁₆	—	284	1	no	—
347	M₁₆	—	284	1	no	—
348	M₁₆	—	284	1	no	—
349	M₁₆	—	142	1	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	284	1	no	—
352	C₂×C₈	—	284	1	no	—
353	C₂×C₈	—	284	1	no	—
354	C₂×C₈	—	284	1	no	—
355	C₂×C₈	—	71	1	no	—
356	C₂×C₈	—	71	1	no	—
357	C₂×C₈	—	71	1	no	—
358	C₂×C₈	—	71	1	no	—
359	C₂×C₈	—	71	1	no	—
360	C₂×C₈	—	71	1	no	—
361	C₂×C₈	—	71	1	no	—
362	C₂×C₈	—	71	1	no	—
363	C₂×C₈	—	71	1	no	—
364	C₂×C₈	—	71	1	no	—
365	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
366	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	—	284	1	no	—
370	C₄⋊C₄	—	284	2	no	—
371	C₄⋊C₄	—	284	2	no	—
372	C₄⋊C₄	—	142	2	no	—
373	C₄²	—	71	1	no	—
374	C₄²	—	142	1	no	—
375	C₄²	D₄×D₇₁	1	1	yes	characteristic
376	C₁₆	—	2	2	no	—
377	C₁₆	—	142	2	no	—
378	C₂³	—	284	1	no	—
379	C₂³	—	71	1	no	—
380	Q₈	—	2	1	no	—
381	Q₈	—	8	2	no	—
382	Q₈	—	284	1	no	—
383	Q₈	—	568	2	no	—
384	Q₈	—	568	4	no	—
385	Q₈	—	142	1	no	—
386	D₄	—	2	1	no	—
387	D₄	—	4	1	no	—
388	D₄	—	284	1	no	—
389	D₄	—	284	1	no	—
390	D₄	—	284	1	no	—
391	D₄	—	284	1	no	—
392	D₄	—	142	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	284	1	no	—
397	C₂×C₄	—	284	1	no	—
398	C₂×C₄	—	284	1	no	—
399	C₂×C₄	—	284	1	no	—
400	C₂×C₄	—	284	2	no	—
401	C₂×C₄	—	568	4	no	—
402	C₂×C₄	—	71	1	no	—
403	C₂×C₄	—	71	1	no	—
404	C₂×C₄	—	71	1	no	—
405	C₂×C₄	—	71	1	no	—
406	C₂×C₄	—	71	1	no	—
407	C₂×C₄	—	142	4	no	—
408	C₂×C₄	—	142	1	no	—
409	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
410	C₈	—	4	1	no	—
411	C₈	—	284	1	no	—
412	C₈	—	71	1	no	—
413	C₈	—	71	1	no	—
414	C₈	—	71	1	no	—
415	C₈	—	71	1	no	—
416	C₈	SD₁₆×D₇₁	1	1	yes	characteristic
417	C₈	SD₁₆×D₇₁	1	1	yes	characteristic
418	C₈	C₂×Q₈×D₇₁	1	1	yes	characteristic
419	C₈	#41×D₇₁	1	1	yes	characteristic
420	C₂²	—	4	1	no	—
421	C₂²	—	284	1	no	—
422	C₂²	—	568	2	no	—
423	C₂²	—	71	1	no	—
424	C₂²	—	71	1	no	—
425	C₂²	—	142	2	no	—
426	C₂²	AGL(1,ℤ/8)×D₇₁	1	1	yes	characteristic
427	C₄	—	2	2	no	—
428	C₄	—	4	1	no	—
429	C₄	—	8	2	no	—
430	C₄	—	284	1	no	—
431	C₄	—	568	2	no	—
432	C₄	—	71	1	no	—
433	C₄	—	71	1	no	—
434	C₄	—	142	2	no	—
435	C₄	C₂²⋊Q₈×D₇₁	1	1	yes	characteristic
436	C₄	C₂×SD₁₆×D₇₁	1	1	yes	characteristic
437	C₂	—	2	1	no	—
438	C₂	—	8	1	no	—
439	C₂	—	568	1	no	—
440	C₂	—	71	2	no	—
441	C₂	—	142	1	no	—
442	C₂	#476×D₇₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#476×D₇₁
commutator, cosocle	C₂×C₈×C₇₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₁
Fitting	C₇₁×#2230	C₂
socle	C₂×C₇₁	C₂×#476
prime radical	#135×D₇₁	C₂²
hypercenter	#2230	D₇₁
hypocenter	C₇₁	C₂×#2230
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2230

Complements

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

N	H ≅ G/N	type
1. #498×D₇₁	C₂	semidirect
3. #22590512	C₂	semidirect
4. #22590511	C₂	semidirect
5. #22590510	C₂	semidirect
6. #22590509	C₂	semidirect
7. #22590508	C₂	semidirect
8. #365×D₇₁	C₂	semidirect
9. #364×D₇₁	C₂	semidirect
11. C₇₁×#2230	C₂	semidirect
16. #17986397	C₂²	semidirect
18. #17986396	C₂²	semidirect
30. #17985823	C₂²	semidirect
31. #17985822	C₂²	semidirect
32. #17985821	C₂²	semidirect
33. #17985820	C₂²	semidirect
34. #17985819	C₂²	semidirect
38. #498×C₇₁	C₂²	semidirect
40. #365×C₇₁	C₂²	semidirect
41. #364×C₇₁	C₂²	semidirect
45. #14556151	Q₈	semidirect
49. #14556147	Q₈	semidirect
50. Q₁₆×D₇₁	Q₈	semidirect
52. D₈×D₇₁	Q₈	semidirect
109. Dic₂₈₄	C₂×Q₈	semidirect
114. D₅₆₈	C₂×Q₈	semidirect
144. Q₁₆×C₇₁	C₂×Q₈	semidirect
146. D₈×C₇₁	C₂×Q₈	semidirect
221. D₇₁	#2230	direct (N × H)
229. #2230	D₇₁	direct (N × H)
233. C₇₁	C₂×#2230	semidirect
242. #498	C₂×D₇₁	semidirect
257. #365	C₂×D₇₁	semidirect
260. #364	C₂×D₇₁	semidirect
335. Q₁₆	Q₈×D₇₁	semidirect
342. D₈	Q₈×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
#498×D₇₁	2
#443×D₇₁	2
#22590512	2
#22590511	2
#22590510	2
#22590509	2
#22590508	2
#365×D₇₁	2
#364×D₇₁	2
#360×D₇₁	2
C₇₁×#2230	2
C₂×#2230	71

Subgroups — #2230×D71 #32152178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2230×D₇₁ #32152178