Subgroups — #2170×D₇₁ #32150676

Order 18176.

662 conjugacy classes of subgroups.

The subgroup lattice has 430 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	#22590178	C₂	1	1	yes	maximal, characteristic, complemented
4	#22590177	C₂	1	1	yes	maximal, characteristic, complemented
5	#22590176	C₂	1	1	yes	maximal, characteristic, complemented
6	#22590175	C₂	1	2	yes	maximal, complemented
7	#22590174	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	C₄×C₁₆×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#2170	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	C₄×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
38	C₁₆×Dic₇₁	C₂²	1	1	yes	characteristic, complemented
39	C₁₆×Dic₇₁	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	C₄×C₁₆×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	1	yes	characteristic
79	C₁₆×D₇₁	D₄	1	1	yes	characteristic
80	C₁₆×D₇₁	D₄	1	1	yes	characteristic
81	C₁₆×D₇₁	D₄	1	1	yes	characteristic
82	#14556064	C₂×C₄	1	1	yes	characteristic
83	#14556063	C₂×C₄	1	2	yes	—
84	#14556056	C₂×C₄	1	2	yes	—
85	#14556055	C₂×C₄	1	2	yes	—
86	#14556054	C₂×C₄	1	2	yes	—
87	C₄×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₇₁	C₂³	1	1	yes	characteristic
90	#135×C₇₁	C₂×C₄	1	1	yes	characteristic
91	#131×C₇₁	C₂³	1	2	yes	—
92	M₃₂×C₇₁	—	2	2	no	—
93	M₃₂×C₇₁	C₂³	1	2	yes	—
94	C₂×C₁₆×C₇₁	—	2	2	no	—
95	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
96	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
97	#108×C₇₁	C₂×C₄	1	1	yes	characteristic
98	#104×C₇₁	C₂×C₄	1	2	yes	—
99	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
100	#11765866	C₂×C₈	1	2	yes	—
101	#11765865	—	2	2	no	—
102	#11765865	C₂²×C₄	1	2	yes	—
103	#11765864	—	2	2	no	—
104	#11765864	C₂×C₈	1	2	yes	—
105	Q₈×D₇₁	C₂×C₈	1	2	yes	—
106	D₄×D₇₁	—	2	2	no	—
107	D₄×D₇₁	C₂×C₈	1	2	yes	—
108	C₂×C₄×D₇₁	—	2	1	no	—
109	C₂×C₄×D₇₁	—	2	2	no	—
110	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
111	Dic₂₈₄	C₂×C₈	1	1	yes	characteristic
112	#11765855	C₂×C₈	1	2	yes	—
113	#11765854	C₂×C₈	1	2	yes	—
114	#11765853	C₂×C₈	1	2	yes	—
115	#11765852	C₂×C₈	1	2	yes	—
116	D₅₆₈	C₂×C₈	1	1	yes	characteristic
117	#11765850	C₂×C₈	1	2	yes	—
118	#11765849	—	2	2	no	—
119	#11765849	C₂²×C₄	1	2	yes	—
120	#11765848	—	2	2	no	—
121	#11765848	—	2	2	no	—
122	#11765848	—	2	2	no	—
123	C₂×C₇₁⋊C₈	—	2	2	no	—
124	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
126	C₈×D₇₁	—	2	2	no	—
127	C₈×D₇₁	—	2	2	no	—
128	C₈×D₇₁	—	2	2	no	—
129	C₈×D₇₁	C₂×C₈	1	1	yes	characteristic
130	C₈×D₇₁	C₂×C₈	1	1	yes	characteristic
131	C₈×D₇₁	C₂×C₈	1	1	yes	characteristic
132	C₈×D₇₁	C₂×C₈	1	1	yes	characteristic
133	C₈×D₇₁	C₂×D₄	1	1	yes	characteristic
134	C₈×D₇₁	C₂×D₄	1	1	yes	characteristic
135	C₈×D₇₁	#41	1	1	yes	characteristic
136	C₈×D₇₁	#41	1	1	yes	characteristic
137	C₄×Dic₇₁	—	2	1	no	—
138	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
139	C₇₁⋊C₁₆	—	2	2	no	—
140	C₇₁⋊C₁₆	—	2	1	no	—
141	C₇₁⋊C₁₆	C₂×D₄	1	1	yes	characteristic
142	C₇₁⋊C₁₆	C₂×D₄	1	1	yes	characteristic
143	#41×C₇₁	C₂²×C₄	1	2	yes	—
144	Q₁₆×C₇₁	C₂×C₈	1	1	yes	characteristic
145	SD₁₆×C₇₁	C₂×C₈	1	2	yes	—
146	D₈×C₇₁	C₂×C₈	1	1	yes	characteristic
147	M₁₆×C₇₁	—	2	2	no	—
148	M₁₆×C₇₁	C₂²×C₄	1	2	yes	—
149	C₂×C₈×C₇₁	—	2	2	no	—
150	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
152	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
153	C₁₆×C₇₁	—	2	2	no	—
154	C₁₆×C₇₁	—	2	1	no	—
155	C₁₆×C₇₁	C₂×D₄	1	1	yes	characteristic
156	C₁₆×C₇₁	C₂×D₄	1	1	yes	characteristic
157	C₂²×D₇₁	—	2	2	no	—
158	C₂²×D₇₁	#131	1	1	yes	characteristic
159	Q₈×C₇₁	C₂²×C₈	1	2	yes	—
160	D₄×C₇₁	—	2	2	no	—
161	D₄×C₇₁	C₂²×C₈	1	2	yes	—
162	C₂×C₄×C₇₁	—	2	1	no	—
163	C₂×C₄×C₇₁	—	2	2	no	—
164	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
165	C₂²⋊D₇₁	—	2	2	no	—
166	C₂²⋊D₇₁	—	2	2	no	—
167	C₂²⋊D₇₁	—	2	2	no	—
168	C₂×Dic₇₁	—	2	1	no	—
169	C₂×Dic₇₁	—	2	2	no	—
170	C₂×Dic₇₁	#131	1	1	yes	characteristic
171	D₂₈₄	—	2	2	no	—
172	D₂₈₄	C₂²×C₈	1	2	yes	—
173	C₄×D₇₁	—	2	4	no	—
174	C₄×D₇₁	—	2	2	no	—
175	C₄×D₇₁	—	2	2	no	—
176	C₄×D₇₁	—	2	2	no	—
177	C₄×D₇₁	C₄×D₄	1	1	yes	characteristic
178	C₄×D₇₁	C₄×D₄	1	1	yes	characteristic
179	C₄×D₇₁	C₂²×C₈	1	1	yes	characteristic
180	C₄×D₇₁	C₂²×C₈	1	1	yes	characteristic
181	Dic₁₄₂	—	2	2	no	—
182	Dic₁₄₂	C₂²×C₈	1	2	yes	—
183	C₈×C₇₁	—	2	2	no	—
184	C₈×C₇₁	C₂²×C₈	1	1	yes	characteristic
185	C₈×C₇₁	C₂²×C₈	1	1	yes	characteristic
186	C₈×C₇₁	C₂²×D₄	1	1	yes	characteristic
187	C₈×C₇₁	C₂×#41	1	1	yes	characteristic
188	C₇₁⋊C₈	—	2	2	no	—
189	C₇₁⋊C₈	C₄×D₄	1	1	yes	characteristic
190	C₇₁⋊C₈	C₄×D₄	1	1	yes	characteristic
191	C₇₁⋊C₈	C₂²×C₈	1	1	yes	characteristic
192	C₇₁⋊C₈	C₂²×C₈	1	1	yes	characteristic
193	C₂²×C₇₁	—	2	2	no	—
194	C₂²×C₇₁	C₂×#131	1	1	yes	characteristic
195	C₂×D₇₁	—	2	2	no	—
196	C₂×D₇₁	—	2	2	no	—
197	C₂×D₇₁	—	4	4	no	—
198	C₂×D₇₁	C₈×D₄	1	1	yes	characteristic
199	C₂×D₇₁	C₈×D₄	1	1	yes	characteristic
200	C₄×C₇₁	—	2	2	no	—
201	C₄×C₇₁	—	2	2	no	—
202	C₄×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
203	C₄×C₇₁	C₂³×C₈	1	1	yes	characteristic
204	Dic₇₁	—	2	2	no	—
205	Dic₇₁	—	2	2	no	—
206	Dic₇₁	C₈×D₄	1	1	yes	characteristic
207	Dic₇₁	C₈×D₄	1	1	yes	characteristic
208	C₂×#2170	—	71	1	no	maximal, Sylow
209	C₂×C₇₁	—	2	1	no	—
210	C₂×C₇₁	—	4	2	no	—
211	C₂×C₇₁	C₂×C₈×D₄	1	1	yes	characteristic
212	D₇₁	—	2	1	no	—
213	D₇₁	—	4	2	no	—
214	D₇₁	#2170	1	2	yes	direct product factor
215	C₂×#504	—	71	2	no	—
216	C₂×#443	—	71	1	no	—
217	#2170	—	71	2	no	—
218	#2170	—	71	1	no	—
219	#2170	—	71	1	no	—
220	#2170	—	71	2	no	—
221	#2170	—	71	1	no	—
222	#2170	D₇₁	1	1	yes	characteristic, direct product factor
223	C₂×#364	—	71	1	no	—
224	C₂×#350	—	71	2	no	—
225	C₂×C₄×C₁₆	—	71	1	no	—
226	C₇₁	C₂×#2170	1	1	yes	characteristic, complemented, Sylow
227	C₂×#135	—	71	1	no	—
228	C₂×#131	—	71	2	no	—
229	#504	—	71	2	no	—
230	#504	—	71	2	no	—
231	#504	—	71	2	no	—
232	#504	—	142	2	no	—
233	#504	—	142	2	no	—
234	#504	C₂×D₇₁	1	2	yes	complemented
235	C₂×M₃₂	—	71	2	no	—
236	C₂×M₃₂	—	142	2	no	—
237	C₂²×C₁₆	—	71	1	no	—
238	C₂²×C₁₆	—	71	1	no	—
239	C₂²×C₁₆	—	142	2	no	—
240	#443	—	71	1	no	—
241	#443	—	71	2	no	—
242	#443	—	71	1	no	—
243	#443	—	71	2	no	—
244	#443	—	71	1	no	—
245	#443	C₂×D₇₁	1	1	yes	characteristic
246	C₂×#108	—	71	1	no	—
247	C₂×#104	—	71	2	no	—
248	C₂×C₄×C₈	—	71	1	no	—
249	#364	—	71	2	no	—
250	#364	—	71	1	no	—
251	#364	C₂×D₇₁	1	1	yes	characteristic, complemented
252	#350	—	71	2	no	—
253	#350	—	71	2	no	—
254	#350	—	71	2	no	—
255	#350	C₂×D₇₁	1	2	yes	complemented
256	C₄×C₁₆	—	71	1	no	—
257	C₄×C₁₆	—	71	1	no	—
258	C₄×C₁₆	—	71	1	no	—
259	C₄×C₁₆	C₂×D₇₁	1	1	yes	characteristic, complemented
260	C₂×#41	—	71	2	no	—
261	#135	—	71	2	no	—
262	#135	—	71	1	no	—
263	#135	—	71	2	no	—
264	#135	—	71	1	no	—
265	#135	—	71	1	no	—
266	#135	C₄×D₇₁	1	1	yes	characteristic
267	C₂×Q₁₆	—	71	1	no	—
268	C₂×SD₁₆	—	71	2	no	—
269	C₂×D₈	—	71	1	no	—
270	#131	—	71	2	no	—
271	#131	—	71	2	no	—
272	#131	—	71	2	no	—
273	#131	—	142	2	no	—
274	#131	—	142	2	no	—
275	#131	C₂²×D₇₁	1	2	yes	—
276	C₂×M₁₆	—	71	2	no	—
277	C₂×M₁₆	—	142	2	no	—
278	C₂²×C₈	—	71	1	no	—
279	C₂²×C₈	—	71	1	no	—
280	C₂²×C₈	—	142	2	no	—
281	C₂×C₄²	—	71	1	no	—
282	M₃₂	—	2	2	no	—
283	M₃₂	—	71	2	no	—
284	M₃₂	—	142	2	no	—
285	M₃₂	—	142	2	no	—
286	M₃₂	—	142	2	no	—
287	M₃₂	—	142	2	no	—
288	M₃₂	C₂²×D₇₁	1	2	yes	—
289	C₂×C₁₆	—	2	2	no	—
290	C₂×C₁₆	—	71	1	no	—
291	C₂×C₁₆	—	71	1	no	—
292	C₂×C₁₆	—	71	1	no	—
293	C₂×C₁₆	—	71	1	no	—
294	C₂×C₁₆	—	71	1	no	—
295	C₂×C₁₆	—	71	1	no	—
296	C₂×C₁₆	—	142	2	no	—
297	C₂×C₁₆	—	142	1	no	—
298	C₂×C₁₆	—	142	1	no	—
299	C₂×C₁₆	—	142	2	no	—
300	C₂×C₁₆	—	142	2	no	—
301	C₂×C₁₆	—	142	2	no	—
302	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
303	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
304	#108	—	71	2	no	—
305	#108	—	71	1	no	—
306	#108	C₄×D₇₁	1	1	yes	characteristic
307	#104	—	71	2	no	—
308	#104	—	71	2	no	—
309	#104	—	71	2	no	—
310	#104	C₄×D₇₁	1	2	yes	—
311	C₄×C₈	—	71	1	no	—
312	C₄×C₈	—	71	1	no	—
313	C₄×C₈	—	71	1	no	—
314	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
315	#41	—	71	2	no	—
316	#41	—	71	2	no	—
317	#41	—	71	2	no	—
318	#41	—	142	2	no	—
319	#41	—	142	2	no	—
320	#41	C₂×C₄×D₇₁	1	2	yes	—
321	C₂×Q₈	—	71	2	no	—
322	C₂×D₄	—	71	2	no	—
323	C₂×D₄	—	142	2	no	—
324	C₂²×C₄	—	71	1	no	—
325	C₂²×C₄	—	142	2	no	—
326	C₂²×C₄	—	142	1	no	—
327	Q₁₆	—	71	2	no	—
328	Q₁₆	—	71	1	no	—
329	Q₁₆	C₈×D₇₁	1	1	yes	characteristic
330	SD₁₆	—	71	2	no	—
331	SD₁₆	—	71	2	no	—
332	SD₁₆	—	71	2	no	—
333	SD₁₆	C₈×D₇₁	1	2	yes	—
334	D₈	—	71	2	no	—
335	D₈	—	71	1	no	—
336	D₈	C₈×D₇₁	1	1	yes	characteristic
337	M₁₆	—	2	2	no	—
338	M₁₆	—	71	2	no	—
339	M₁₆	—	142	2	no	—
340	M₁₆	—	142	2	no	—
341	M₁₆	—	142	2	no	—
342	M₁₆	—	142	2	no	—
343	M₁₆	C₂×C₄×D₇₁	1	2	yes	—
344	C₂×C₈	—	2	2	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	—	71	1	no	—
350	C₂×C₈	—	71	1	no	—
351	C₂×C₈	—	71	1	no	—
352	C₂×C₈	—	71	1	no	—
353	C₂×C₈	—	71	1	no	—
354	C₂×C₈	—	71	1	no	—
355	C₂×C₈	—	142	2	no	—
356	C₂×C₈	—	142	2	no	—
357	C₂×C₈	—	142	2	no	—
358	C₂×C₈	—	142	2	no	—
359	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
360	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
361	C₄²	—	71	1	no	—
362	C₄²	—	142	1	no	—
363	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
364	C₁₆	—	2	2	no	—
365	C₁₆	—	2	1	no	—
366	C₁₆	—	71	1	no	—
367	C₁₆	—	71	1	no	—
368	C₁₆	—	142	2	no	—
369	C₁₆	—	142	1	no	—
370	C₁₆	D₄×D₇₁	1	1	yes	characteristic
371	C₁₆	D₄×D₇₁	1	1	yes	characteristic
372	C₂³	—	71	1	no	—
373	C₂³	—	142	2	no	—
374	Q₈	—	71	2	no	—
375	Q₈	—	142	2	no	—
376	Q₈	C₂×C₈×D₇₁	1	2	yes	—
377	D₄	—	2	2	no	—
378	D₄	—	71	2	no	—
379	D₄	—	142	2	no	—
380	D₄	—	142	2	no	—
381	D₄	—	142	2	no	—
382	D₄	—	142	2	no	—
383	D₄	C₂×C₈×D₇₁	1	2	yes	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	71	1	no	—
387	C₂×C₄	—	71	1	no	—
388	C₂×C₄	—	71	1	no	—
389	C₂×C₄	—	71	1	no	—
390	C₂×C₄	—	71	1	no	—
391	C₂×C₄	—	142	2	no	—
392	C₂×C₄	—	142	2	no	—
393	C₂×C₄	—	142	4	no	—
394	C₂×C₄	—	142	2	no	—
395	C₂×C₄	—	142	1	no	—
396	C₂×C₄	—	142	2	no	—
397	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	71	1	no	—
400	C₈	—	71	1	no	—
401	C₈	—	71	1	no	—
402	C₈	—	71	1	no	—
403	C₈	—	142	2	no	—
404	C₈	C₂×C₈×D₇₁	1	1	yes	characteristic
405	C₈	C₂×C₈×D₇₁	1	1	yes	characteristic
406	C₈	C₂×D₄×D₇₁	1	1	yes	characteristic
407	C₈	#41×D₇₁	1	1	yes	characteristic
408	C₂²	—	2	2	no	—
409	C₂²	—	284	4	no	—
410	C₂²	—	71	1	no	—
411	C₂²	—	71	1	no	—
412	C₂²	—	142	2	no	—
413	C₂²	—	142	2	no	—
414	C₂²	#131×D₇₁	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	71	1	no	—
418	C₄	—	71	1	no	—
419	C₄	—	142	2	no	—
420	C₄	—	142	2	no	—
421	C₄	C₄×D₄×D₇₁	1	1	yes	characteristic
422	C₄	C₂²×C₈×D₇₁	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	4	2	no	—
425	C₂	—	284	2	no	—
426	C₂	—	71	2	no	—
427	C₂	—	142	1	no	—
428	C₂	C₈×D₄×D₇₁	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₄×D₇₁
commutator	C₄×C₇₁	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₇₁
Fitting	C₇₁×#2170	C₂
socle	C₂×C₇₁	C₂×C₈×D₄
prime radical	#135×D₇₁	C₄
cosocle	C₂×C₈×C₇₁	C₂⁴
hypercenter	#2170	D₇₁
hypocenter	C₇₁	C₂×#2170
LCS	G ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ #2170

Complements

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

N	H ≅ G/N	type
1. #504×D₇₁	C₂	semidirect
3. #22590178	C₂	semidirect
4. #22590177	C₂	semidirect
5. #22590176	C₂	semidirect
6. #22590175	C₂	semidirect
7. #22590174	C₂	semidirect
8. #364×D₇₁	C₂	semidirect
9. #350×D₇₁	C₂	semidirect
10. C₄×C₁₆×D₇₁	C₂	semidirect
11. C₇₁×#2170	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. C₄×C₇₁⋊C₁₆	C₂²	semidirect
38. C₁₆×Dic₇₁	C₂²	semidirect
39. C₁₆×Dic₇₁	C₂²	semidirect
40. #504×C₇₁	C₂²	semidirect
42. #364×C₇₁	C₂²	semidirect
43. #350×C₇₁	C₂²	semidirect
44. C₄×C₁₆×C₇₁	C₂²	semidirect
214. D₇₁	#2170	direct (N × H)
222. #2170	D₇₁	direct (N × H)
226. C₇₁	C₂×#2170	semidirect
234. #504	C₂×D₇₁	semidirect
251. #364	C₂×D₇₁	semidirect
255. #350	C₂×D₇₁	semidirect
259. C₄×C₁₆	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
#22590178	2
#22590177	2
#22590176	2
#22590175	2
#22590174	2
#364×D₇₁	2
#350×D₇₁	2
C₄×C₁₆×D₇₁	2
C₇₁×#2170	2
C₂×#2170	71

Subgroups — #2170×D71 #32150676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2170×D₇₁ #32150676