Subgroups — #2179×D₇₁ #32150854

Order 18176.

654 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#508×D₇₁	C₂	1	1	yes	maximal, characteristic
2	#443×D₇₁	C₂	1	2	yes	maximal, complemented
3	#22590227	C₂	1	1	yes	maximal, characteristic, complemented
4	#22590226	C₂	1	1	yes	maximal, characteristic, complemented
5	#22590225	C₂	1	1	yes	maximal, characteristic, complemented
6	#22590224	C₂	1	2	yes	maximal, complemented
7	#22590223	C₂	1	2	yes	maximal, complemented
8	#368×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#359×D₇₁	C₂	1	2	yes	maximal, complemented
10	#346×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#2179	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₇₁	C₂²	1	2	yes	—
13	#131×D₇₁	—	2	2	no	—
14	#17986432	C₄	1	1	yes	characteristic, complemented
15	#17986431	C₂²	1	1	yes	characteristic
16	#17986430	C₄	1	2	yes	complemented
17	#17986429	C₂²	1	2	yes	—
18	#17986428	C₄	1	1	yes	characteristic, complemented
19	Q₃₂×D₇₁	C₄	1	1	yes	characteristic, complemented
20	SD₃₂×D₇₁	C₄	1	2	yes	complemented
21	D₁₆×D₇₁	C₄	1	1	yes	characteristic, complemented
22	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic
24	#17986117	C₂²	1	2	yes	complemented
25	#17986116	C₂²	1	2	yes	complemented
26	#17986115	C₂²	1	2	yes	complemented
27	#17986114	—	2	2	no	—
28	#17986113	—	2	2	no	—
29	#108×D₇₁	C₂²	1	2	yes	—
30	#104×D₇₁	—	2	2	no	—
31	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
32	#17985829	C₂²	1	1	yes	characteristic, complemented
33	#17985828	C₂²	1	2	yes	complemented
34	#17985807	C₂²	1	2	yes	complemented
35	#17985806	C₂²	1	2	yes	complemented
36	#17985805	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	#508×C₇₁	C₂²	1	1	yes	characteristic
41	#443×C₇₁	C₂²	1	2	yes	complemented
42	#368×C₇₁	C₂²	1	1	yes	characteristic, complemented
43	#359×C₇₁	C₂²	1	2	yes	complemented
44	#346×C₇₁	C₂²	1	1	yes	characteristic, complemented
45	#41×D₇₁	—	2	2	no	—
46	#14556151	C₂×C₄	1	2	yes	—
47	#14556150	C₂³	1	2	yes	—
48	#14556149	—	2	2	no	—
49	#14556148	—	2	2	no	—
50	#14556147	C₂×C₄	1	2	yes	—
51	Q₁₆×D₇₁	C₂×C₄	1	2	yes	—
52	SD₁₆×D₇₁	—	2	2	no	—
53	D₈×D₇₁	C₂×C₄	1	2	yes	—
54	#14556136	—	2	2	no	—
55	#14556136	—	4	2	no	—
56	#14556135	—	2	2	no	—
57	#14556134	—	2	2	no	—
58	#14556134	—	4	2	no	—
59	M₁₆×D₇₁	—	2	2	no	—
60	M₁₆×D₇₁	—	4	2	no	—
61	C₂×C₈×D₇₁	—	4	2	no	—
62	C₂×C₈×D₇₁	D₄	1	1	yes	characteristic
63	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
64	C₄²×D₇₁	D₄	1	1	yes	characteristic
65	Dic₅₆₈	C₂×C₄	1	1	yes	characteristic, complemented
66	#14556074	C₂×C₄	1	2	yes	complemented
67	#14556073	C₂×C₄	1	2	yes	complemented
68	#14556072	C₂×C₄	1	2	yes	complemented
69	#14556071	C₂×C₄	1	2	yes	complemented
70	D₁₁₃₆	C₂×C₄	1	1	yes	characteristic, complemented
71	#14556069	C₂×C₄	1	2	yes	complemented
72	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
73	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
74	C₁₆×D₇₁	—	2	1	no	—
75	C₁₆×D₇₁	—	2	1	no	—
76	C₁₆×D₇₁	C₂×C₄	1	1	yes	characteristic
77	C₁₆×D₇₁	C₂×C₄	1	1	yes	characteristic
78	C₁₆×D₇₁	C₂×C₄	1	1	yes	characteristic
79	C₁₆×D₇₁	C₂×C₄	1	1	yes	characteristic
80	#14556064	C₂³	1	2	yes	—
81	#14556063	—	2	2	no	—
82	#14556056	—	2	2	no	—
83	#14556055	—	2	2	no	—
84	#14556054	—	2	2	no	—
85	C₄×C₇₁⋊C₈	D₄	1	1	yes	characteristic
86	C₈×Dic₇₁	D₄	1	1	yes	characteristic
87	C₈×Dic₇₁	C₂³	1	1	yes	characteristic
88	#135×C₇₁	C₂³	1	2	yes	—
89	#131×C₇₁	—	2	2	no	—
90	Q₃₂×C₇₁	C₂×C₄	1	1	yes	characteristic, complemented
91	SD₃₂×C₇₁	C₂×C₄	1	2	yes	complemented
92	D₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic, complemented
93	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
94	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
95	#108×C₇₁	C₂³	1	2	yes	—
96	#104×C₇₁	—	2	2	no	—
97	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
98	#11765866	—	2	2	no	—
99	#11765865	—	2	2	no	—
100	#11765865	—	4	2	no	—
101	#11765864	—	2	2	no	—
102	#11765864	—	4	2	no	—
103	Q₈×D₇₁	—	2	2	no	—
104	D₄×D₇₁	—	2	2	no	—
105	D₄×D₇₁	—	4	2	no	—
106	C₂×C₄×D₇₁	—	2	1	no	—
107	C₂×C₄×D₇₁	—	4	2	no	—
108	C₂×C₄×D₇₁	C₂×D₄	1	1	yes	characteristic
109	Dic₂₈₄	C₂²×C₄	1	2	yes	—
110	#11765855	—	2	2	no	—
111	#11765854	—	2	2	no	—
112	#11765853	—	2	2	no	—
113	#11765852	—	2	2	no	—
114	D₅₆₈	C₂²×C₄	1	2	yes	—
115	#11765850	—	2	2	no	—
116	#11765849	—	2	2	no	—
117	#11765849	—	4	2	no	—
118	#11765848	—	4	2	no	—
119	#11765848	—	4	2	no	—
120	#11765848	—	4	2	no	—
121	C₂×C₇₁⋊C₈	—	4	2	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	2	no	—
125	C₈×D₇₁	—	4	2	no	—
126	C₈×D₇₁	—	4	2	no	—
127	C₈×D₇₁	D₈	1	2	yes	—
128	C₈×D₇₁	D₈	1	2	yes	—
129	C₈×D₇₁	C₂²×C₄	1	1	yes	characteristic
130	C₈×D₇₁	C₂²×C₄	1	1	yes	characteristic
131	C₈×D₇₁	#41	1	1	yes	characteristic
132	C₈×D₇₁	#41	1	1	yes	characteristic
133	C₄×Dic₇₁	—	2	1	no	—
134	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
135	C₇₁⋊C₁₆	—	2	1	no	—
136	C₇₁⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
137	C₇₁⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
138	#41×C₇₁	—	2	2	no	—
139	Q₁₆×C₇₁	C₂²×C₄	1	2	yes	—
140	SD₁₆×C₇₁	—	2	2	no	—
141	D₈×C₇₁	C₂²×C₄	1	2	yes	—
142	M₁₆×C₇₁	—	2	2	no	—
143	M₁₆×C₇₁	—	4	2	no	—
144	C₂×C₈×C₇₁	—	4	2	no	—
145	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
147	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
148	C₁₆×C₇₁	—	2	1	no	—
149	C₁₆×C₇₁	C₂²×C₄	1	1	yes	characteristic
150	C₁₆×C₇₁	C₂²×C₄	1	1	yes	characteristic
151	C₂²×D₇₁	—	4	2	no	—
152	C₂²×D₇₁	#135	1	1	yes	characteristic
153	Q₈×C₇₁	—	2	2	no	—
154	D₄×C₇₁	—	2	2	no	—
155	D₄×C₇₁	—	4	2	no	—
156	C₂×C₄×C₇₁	—	2	1	no	—
157	C₂×C₄×C₇₁	—	4	2	no	—
158	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
159	C₂²⋊D₇₁	—	4	2	no	—
160	C₂²⋊D₇₁	—	4	2	no	—
161	C₂²⋊D₇₁	—	4	2	no	—
162	C₂×Dic₇₁	—	2	1	no	—
163	C₂×Dic₇₁	—	4	2	no	—
164	C₂×Dic₇₁	#135	1	1	yes	characteristic
165	D₂₈₄	—	2	2	no	—
166	D₂₈₄	—	4	2	no	—
167	C₄×D₇₁	—	4	2	no	—
168	C₄×D₇₁	—	4	2	no	—
169	C₄×D₇₁	—	4	2	no	—
170	C₄×D₇₁	—	4	2	no	—
171	C₄×D₇₁	C₄×D₄	1	1	yes	characteristic
172	C₄×D₇₁	C₄×D₄	1	1	yes	characteristic
173	C₄×D₇₁	C₂×D₈	1	1	yes	characteristic
174	C₄×D₇₁	C₂×D₈	1	1	yes	characteristic
175	Dic₁₄₂	—	2	2	no	—
176	Dic₁₄₂	—	4	2	no	—
177	C₈×C₇₁	—	4	2	no	—
178	C₈×C₇₁	C₂×D₈	1	2	yes	—
179	C₈×C₇₁	C₂³×C₄	1	1	yes	characteristic
180	C₈×C₇₁	C₂×#41	1	1	yes	characteristic
181	C₇₁⋊C₈	—	4	2	no	—
182	C₇₁⋊C₈	C₄×D₄	1	1	yes	characteristic
183	C₇₁⋊C₈	C₄×D₄	1	1	yes	characteristic
184	C₇₁⋊C₈	C₂×D₈	1	2	yes	—
185	C₂²×C₇₁	—	4	2	no	—
186	C₂²×C₇₁	C₂×#135	1	1	yes	characteristic
187	C₂×D₇₁	—	2	2	no	—
188	C₂×D₇₁	—	4	2	no	—
189	C₂×D₇₁	—	8	4	no	—
190	C₂×D₇₁	C₄×D₈	1	1	yes	characteristic
191	C₂×D₇₁	C₄×D₈	1	1	yes	characteristic
192	C₄×C₇₁	—	4	1	no	—
193	C₄×C₇₁	—	4	2	no	—
194	C₄×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
195	C₄×C₇₁	C₂²×D₈	1	1	yes	characteristic
196	Dic₇₁	—	4	1	no	—
197	Dic₇₁	—	4	2	no	—
198	Dic₇₁	C₄×D₈	1	1	yes	characteristic
199	Dic₇₁	C₄×D₈	1	1	yes	characteristic
200	C₂×#2179	—	71	1	no	maximal, Sylow
201	C₂×C₇₁	—	2	1	no	—
202	C₂×C₇₁	—	8	2	no	—
203	C₂×C₇₁	C₂×C₄×D₈	1	1	yes	characteristic
204	D₇₁	—	2	1	no	—
205	D₇₁	—	8	2	no	—
206	D₇₁	#2179	1	2	yes	direct product factor
207	C₂×#508	—	71	1	no	—
208	C₂×#443	—	71	2	no	—
209	#2179	—	71	1	no	—
210	#2179	—	71	2	no	—
211	#2179	—	71	1	no	—
212	#2179	—	71	2	no	—
213	#2179	—	71	1	no	—
214	#2179	D₇₁	1	1	yes	characteristic, direct product factor
215	C₂×#368	—	71	1	no	—
216	C₂×#359	—	71	2	no	—
217	C₂×#346	—	71	1	no	—
218	C₇₁	C₂×#2179	1	1	yes	characteristic, complemented, Sylow
219	C₂×#135	—	71	2	no	—
220	C₂×#131	—	142	2	no	—
221	#508	—	71	2	no	—
222	#508	—	71	1	no	—
223	#508	—	71	2	no	—
224	#508	—	71	1	no	—
225	#508	—	71	1	no	—
226	#508	C₂×D₇₁	1	1	yes	characteristic
227	C₂×Q₃₂	—	71	1	no	—
228	C₂×SD₃₂	—	71	2	no	—
229	C₂×D₁₆	—	71	1	no	—
230	C₂²×C₁₆	—	71	1	no	—
231	C₂²×C₁₆	—	71	1	no	—
232	#443	—	71	2	no	—
233	#443	—	71	2	no	—
234	#443	—	71	2	no	—
235	#443	—	142	2	no	—
236	#443	—	142	2	no	—
237	#443	C₂×D₇₁	1	2	yes	complemented
238	C₂×#108	—	71	2	no	—
239	C₂×#104	—	142	2	no	—
240	C₂×C₄×C₈	—	71	1	no	—
241	#368	—	71	1	no	—
242	#368	—	71	2	no	—
243	#368	C₂×D₇₁	1	1	yes	characteristic, complemented
244	#359	—	71	2	no	—
245	#359	—	71	2	no	—
246	#359	—	71	2	no	—
247	#359	C₂×D₇₁	1	2	yes	complemented
248	#346	—	71	1	no	—
249	#346	—	71	1	no	—
250	#346	—	71	1	no	—
251	#346	C₂×D₇₁	1	1	yes	characteristic, complemented
252	C₂×#41	—	142	2	no	—
253	#135	—	71	2	no	—
254	#135	—	71	2	no	—
255	#135	—	71	2	no	—
256	#135	—	142	2	no	—
257	#135	—	142	2	no	—
258	#135	C₂²×D₇₁	1	2	yes	—
259	C₂×Q₁₆	—	71	2	no	—
260	C₂×SD₁₆	—	142	2	no	—
261	C₂×D₈	—	71	2	no	—
262	#131	—	2	2	no	—
263	#131	—	284	2	no	—
264	#131	—	284	2	no	—
265	#131	—	142	2	no	—
266	#131	—	142	2	no	—
267	#131	—	142	2	no	—
268	C₂×M₁₆	—	284	2	no	—
269	C₂×M₁₆	—	142	2	no	—
270	C₂²×C₈	—	284	2	no	—
271	C₂²×C₈	—	71	1	no	—
272	C₂²×C₈	—	71	1	no	—
273	C₂×C₄²	—	71	1	no	—
274	Q₃₂	—	71	2	no	—
275	Q₃₂	—	71	1	no	—
276	Q₃₂	C₄×D₇₁	1	1	yes	characteristic, complemented
277	SD₃₂	—	71	2	no	—
278	SD₃₂	—	71	2	no	—
279	SD₃₂	—	71	2	no	—
280	SD₃₂	C₄×D₇₁	1	2	yes	complemented
281	D₁₆	—	71	2	no	—
282	D₁₆	—	71	1	no	—
283	D₁₆	C₄×D₇₁	1	1	yes	characteristic, complemented
284	C₂×C₁₆	—	71	1	no	—
285	C₂×C₁₆	—	71	1	no	—
286	C₂×C₁₆	—	71	1	no	—
287	C₂×C₁₆	—	71	1	no	—
288	C₂×C₁₆	—	71	1	no	—
289	C₂×C₁₆	—	71	1	no	—
290	C₂×C₁₆	—	142	1	no	—
291	C₂×C₁₆	—	142	1	no	—
292	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
293	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
294	#108	—	71	2	no	—
295	#108	—	142	2	no	—
296	#108	C₂²×D₇₁	1	2	yes	—
297	#104	—	2	2	no	—
298	#104	—	142	2	no	—
299	#104	—	142	2	no	—
300	#104	—	142	2	no	—
301	C₄×C₈	—	71	1	no	—
302	C₄×C₈	—	71	1	no	—
303	C₄×C₈	—	71	1	no	—
304	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
305	#41	—	2	2	no	—
306	#41	—	284	2	no	—
307	#41	—	284	2	no	—
308	#41	—	142	2	no	—
309	#41	—	142	2	no	—
310	#41	—	142	2	no	—
311	C₂×Q₈	—	142	2	no	—
312	C₂×D₄	—	284	2	no	—
313	C₂×D₄	—	142	2	no	—
314	C₂²×C₄	—	284	2	no	—
315	C₂²×C₄	—	71	1	no	—
316	C₂²×C₄	—	142	1	no	—
317	Q₁₆	—	71	2	no	—
318	Q₁₆	—	142	2	no	—
319	Q₁₆	C₂×C₄×D₇₁	1	2	yes	—
320	SD₁₆	—	2	2	no	—
321	SD₁₆	—	142	2	no	—
322	SD₁₆	—	142	2	no	—
323	SD₁₆	—	142	2	no	—
324	D₈	—	71	2	no	—
325	D₈	—	142	2	no	—
326	D₈	C₂×C₄×D₇₁	1	2	yes	—
327	M₁₆	—	2	2	no	—
328	M₁₆	—	4	2	no	—
329	M₁₆	—	284	2	no	—
330	M₁₆	—	284	2	no	—
331	M₁₆	—	284	2	no	—
332	M₁₆	—	284	2	no	—
333	M₁₆	—	142	2	no	—
334	C₂×C₈	—	4	2	no	—
335	C₂×C₈	—	284	2	no	—
336	C₂×C₈	—	284	2	no	—
337	C₂×C₈	—	284	2	no	—
338	C₂×C₈	—	284	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	2	no	—
346	C₂×C₈	—	71	2	no	—
347	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
348	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
349	C₄²	—	71	1	no	—
350	C₄²	—	142	1	no	—
351	C₄²	D₄×D₇₁	1	1	yes	characteristic
352	C₁₆	—	2	1	no	—
353	C₁₆	—	71	1	no	—
354	C₁₆	—	71	1	no	—
355	C₁₆	—	142	1	no	—
356	C₁₆	C₂×C₄×D₇₁	1	1	yes	characteristic
357	C₁₆	C₂×C₄×D₇₁	1	1	yes	characteristic
358	C₂³	—	284	2	no	—
359	C₂³	—	71	1	no	—
360	Q₈	—	2	2	no	—
361	Q₈	—	284	2	no	—
362	Q₈	—	142	2	no	—
363	D₄	—	2	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	284	2	no	—
366	D₄	—	284	2	no	—
367	D₄	—	284	2	no	—
368	D₄	—	284	2	no	—
369	D₄	—	142	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	284	2	no	—
373	C₂×C₄	—	284	2	no	—
374	C₂×C₄	—	284	2	no	—
375	C₂×C₄	—	284	2	no	—
376	C₂×C₄	—	284	2	no	—
377	C₂×C₄	—	71	1	no	—
378	C₂×C₄	—	71	1	no	—
379	C₂×C₄	—	71	1	no	—
380	C₂×C₄	—	71	1	no	—
381	C₂×C₄	—	71	1	no	—
382	C₂×C₄	—	142	1	no	—
383	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
384	C₈	—	4	2	no	—
385	C₈	—	284	2	no	—
386	C₈	—	71	1	no	—
387	C₈	—	71	1	no	—
388	C₈	—	71	2	no	—
389	C₈	D₈×D₇₁	1	2	yes	—
390	C₈	C₂²×C₄×D₇₁	1	1	yes	characteristic
391	C₈	#41×D₇₁	1	1	yes	characteristic
392	C₂²	—	4	2	no	—
393	C₂²	—	284	2	no	—
394	C₂²	—	568	4	no	—
395	C₂²	—	71	1	no	—
396	C₂²	—	71	1	no	—
397	C₂²	—	142	2	no	—
398	C₂²	#135×D₇₁	1	1	yes	characteristic
399	C₄	—	4	1	no	—
400	C₄	—	4	2	no	—
401	C₄	—	284	1	no	—
402	C₄	—	284	2	no	—
403	C₄	—	71	1	no	—
404	C₄	—	71	1	no	—
405	C₄	C₄×D₄×D₇₁	1	1	yes	characteristic
406	C₄	C₂×D₈×D₇₁	1	1	yes	characteristic
407	C₂	—	2	1	no	—
408	C₂	—	8	2	no	—
409	C₂	—	568	2	no	—
410	C₂	—	71	2	no	—
411	C₂	—	142	1	no	—
412	C₂	C₄×D₈×D₇₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₈×D₇₁
commutator	C₈×C₇₁	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₇₁
Fitting	C₇₁×#2179	C₂
socle	C₂×C₇₁	C₂×C₄×D₈
prime radical	#508×D₇₁	C₂
cosocle	C₂×C₈×C₇₁	C₂⁴
hypercenter	#2179	D₇₁
hypocenter	C₇₁	C₂×#2179
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #2179

Complements

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

N	H ≅ G/N	type
2. #443×D₇₁	C₂	semidirect
3. #22590227	C₂	semidirect
4. #22590226	C₂	semidirect
5. #22590225	C₂	semidirect
6. #22590224	C₂	semidirect
7. #22590223	C₂	semidirect
8. #368×D₇₁	C₂	semidirect
9. #359×D₇₁	C₂	semidirect
10. #346×D₇₁	C₂	semidirect
11. C₇₁×#2179	C₂	semidirect
14. #17986432	C₄	semidirect
16. #17986430	C₄	semidirect
18. #17986428	C₄	semidirect
19. Q₃₂×D₇₁	C₄	semidirect
20. SD₃₂×D₇₁	C₄	semidirect
21. D₁₆×D₇₁	C₄	semidirect
24. #17986117	C₂²	semidirect
25. #17986116	C₂²	semidirect
26. #17986115	C₂²	semidirect
32. #17985829	C₂²	semidirect
33. #17985828	C₂²	semidirect
34. #17985807	C₂²	semidirect
35. #17985806	C₂²	semidirect
36. #17985805	C₂²	semidirect
37. #17985775	C₂²	semidirect
38. #17985774	C₂²	semidirect
39. #17985774	C₂²	semidirect
41. #443×C₇₁	C₂²	semidirect
42. #368×C₇₁	C₂²	semidirect
43. #359×C₇₁	C₂²	semidirect
44. #346×C₇₁	C₂²	semidirect
65. Dic₅₆₈	C₂×C₄	semidirect
66. #14556074	C₂×C₄	semidirect
67. #14556073	C₂×C₄	semidirect
68. #14556072	C₂×C₄	semidirect
69. #14556071	C₂×C₄	semidirect
70. D₁₁₃₆	C₂×C₄	semidirect
71. #14556069	C₂×C₄	semidirect
90. Q₃₂×C₇₁	C₂×C₄	semidirect
91. SD₃₂×C₇₁	C₂×C₄	semidirect
92. D₁₆×C₇₁	C₂×C₄	semidirect
206. D₇₁	#2179	direct (N × H)
214. #2179	D₇₁	direct (N × H)
218. C₇₁	C₂×#2179	semidirect
237. #443	C₂×D₇₁	semidirect
243. #368	C₂×D₇₁	semidirect
247. #359	C₂×D₇₁	semidirect
251. #346	C₂×D₇₁	semidirect
276. Q₃₂	C₄×D₇₁	semidirect
280. SD₃₂	C₄×D₇₁	semidirect
283. D₁₆	C₄×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
#508×D₇₁	2
#443×D₇₁	2
#22590227	2
#22590226	2
#22590225	2
#22590224	2
#22590223	2
#368×D₇₁	2
#359×D₇₁	2
#346×D₇₁	2
C₇₁×#2179	2
C₂×#2179	71

Subgroups — #2179×D71 #32150854

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2179×D₇₁ #32150854