Subgroups — #32150874

Order 18176.

642 conjugacy classes of subgroups.

The subgroup lattice has 420 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	#22597252	C₂	1	2	yes	maximal, complemented
3	#22590224	C₂	1	2	yes	maximal, complemented
4	#22590223	C₂	1	2	yes	maximal, complemented
5	#22590222	C₂	1	1	yes	maximal, characteristic, complemented
6	#22590221	C₂	1	1	yes	maximal, characteristic, complemented
7	#22590220	C₂	1	1	yes	maximal, characteristic, complemented
8	#368×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#22590066	C₂	1	2	yes	maximal, complemented
10	#22589935	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#2178	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₇₁	C₂²	1	2	yes	—
13	#17986764	—	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×#14556067	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic
24	#17986119	—	2	2	no	—
25	#17986118	—	2	2	no	—
26	#17986117	C₂²	1	2	yes	complemented
27	#17986116	C₂²	1	2	yes	complemented
28	#17986115	C₂²	1	2	yes	complemented
29	#108×D₇₁	C₂²	1	2	yes	—
30	#17986014	—	2	2	no	—
31	#17985953	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	C₁₆×Dic₇₁	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	C₄×C₁₆×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	C₂×#11765848	—	4	2	no	—
60	C₂×#11765848	D₄	1	1	yes	characteristic
61	M₁₆×D₇₁	—	2	2	no	—
62	M₁₆×D₇₁	—	4	2	no	—
63	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
64	#14556085	D₄	1	1	yes	characteristic
65	Dic₅₆₈	C₂×C₄	1	1	yes	characteristic
66	#14556074	C₂×C₄	1	2	yes	—
67	#14556073	C₂×C₄	1	2	yes	—
68	#14556072	C₂×C₄	1	2	yes	—
69	#14556071	C₂×C₄	1	2	yes	—
70	D₁₁₃₆	C₂×C₄	1	1	yes	characteristic
71	#14556069	C₂×C₄	1	2	yes	—
72	#14556067	—	2	1	no	—
73	#14556067	—	2	1	no	—
74	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
75	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
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	#14556039	D₄	1	1	yes	characteristic
86	#14556038	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
91	SD₃₂×C₇₁	C₂×C₄	1	2	yes	—
92	D₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
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	—	4	2	no	—
107	C₂×C₄×D₇₁	C₂×D₄	1	1	yes	characteristic
108	Dic₂₈₄	C₂²×C₄	1	2	yes	—
109	#11765855	—	2	2	no	—
110	#11765854	—	2	2	no	—
111	#11765853	—	2	2	no	—
112	#11765852	—	2	2	no	—
113	D₅₆₈	C₂²×C₄	1	2	yes	—
114	#11765850	—	2	2	no	—
115	#11765849	—	2	2	no	—
116	#11765849	—	4	2	no	—
117	#11765848	—	4	2	no	—
118	#11765848	—	4	2	no	—
119	#11765848	—	4	2	no	—
120	#11765848	D₈	1	1	yes	characteristic
121	#11765848	D₈	1	1	yes	characteristic
122	#11765848	D₈	1	1	yes	characteristic
123	#11765848	D₈	1	1	yes	characteristic
124	C₂×C₇₁⋊C₈	—	4	2	no	—
125	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
126	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
127	C₈×D₇₁	—	4	2	no	—
128	C₈×D₇₁	—	4	2	no	—
129	C₈×D₇₁	—	4	2	no	—
130	C₈×D₇₁	C₂²×C₄	1	1	yes	characteristic
131	C₈×D₇₁	C₂²×C₄	1	1	yes	characteristic
132	C₈×D₇₁	#41	1	1	yes	characteristic
133	C₈×D₇₁	#41	1	1	yes	characteristic
134	Dic₇₁⋊C₄	—	2	1	no	—
135	(C₂×D₇₁)⋊C₄	—	2	1	no	—
136	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
137	C₇₁⋊C₁₆	—	2	1	no	—
138	C₇₁⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
139	C₇₁⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
140	#41×C₇₁	—	2	2	no	—
141	Q₁₆×C₇₁	C₂²×C₄	1	2	yes	—
142	SD₁₆×C₇₁	—	2	2	no	—
143	D₈×C₇₁	C₂²×C₄	1	2	yes	—
144	M₁₆×C₇₁	—	2	2	no	—
145	M₁₆×C₇₁	—	4	2	no	—
146	C₂×C₈×C₇₁	—	4	2	no	—
147	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
149	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
150	C₁₆×C₇₁	—	2	1	no	—
151	C₁₆×C₇₁	C₂²×C₄	1	1	yes	characteristic
152	C₁₆×C₇₁	C₂²×C₄	1	1	yes	characteristic
153	C₂²×D₇₁	—	4	2	no	—
154	C₂²×D₇₁	#135	1	1	yes	characteristic
155	Q₈×C₇₁	—	2	2	no	—
156	D₄×C₇₁	—	2	2	no	—
157	D₄×C₇₁	—	4	2	no	—
158	C₂×C₄×C₇₁	—	2	1	no	—
159	C₂×C₄×C₇₁	—	4	2	no	—
160	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
161	C₂²⋊D₇₁	—	4	2	no	—
162	C₂²⋊D₇₁	—	4	2	no	—
163	C₂²⋊D₇₁	—	4	2	no	—
164	C₂×Dic₇₁	—	2	1	no	—
165	C₂×Dic₇₁	—	4	2	no	—
166	C₂×Dic₇₁	#135	1	1	yes	characteristic
167	D₂₈₄	—	2	2	no	—
168	D₂₈₄	—	4	2	no	—
169	C₄×D₇₁	—	4	2	no	—
170	C₄×D₇₁	—	4	2	no	—
171	C₄×D₇₁	—	4	2	no	—
172	C₄×D₇₁	C₄×D₄	1	1	yes	characteristic
173	C₄×D₇₁	C₄×D₄	1	1	yes	characteristic
174	C₄×D₇₁	C₂×D₈	1	1	yes	characteristic
175	C₄×D₇₁	C₂×D₈	1	1	yes	characteristic
176	Dic₁₄₂	—	2	2	no	—
177	Dic₁₄₂	—	4	2	no	—
178	C₈×C₇₁	—	4	2	no	—
179	C₈×C₇₁	C₂×D₈	1	1	yes	characteristic
180	C₈×C₇₁	C₂×D₈	1	1	yes	characteristic
181	C₈×C₇₁	C₂³×C₄	1	1	yes	characteristic
182	C₈×C₇₁	C₂×#41	1	1	yes	characteristic
183	C₇₁⋊C₈	—	4	2	no	—
184	C₇₁⋊C₈	C₄×D₄	1	1	yes	characteristic
185	C₇₁⋊C₈	C₄×D₄	1	1	yes	characteristic
186	C₇₁⋊C₈	C₂×D₈	1	1	yes	characteristic
187	C₇₁⋊C₈	C₂×D₈	1	1	yes	characteristic
188	C₂²×C₇₁	—	4	2	no	—
189	C₂²×C₇₁	C₂×#135	1	1	yes	characteristic
190	C₂×D₇₁	—	4	1	no	—
191	C₂×D₇₁	—	4	2	no	—
192	C₂×D₇₁	—	16	2	no	—
193	C₂×D₇₁	C₄×D₈	1	1	yes	characteristic
194	C₂×D₇₁	C₄×D₈	1	1	yes	characteristic
195	C₄×C₇₁	—	4	1	no	—
196	C₄×C₇₁	—	4	2	no	—
197	C₄×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
198	C₄×C₇₁	C₂²×D₈	1	1	yes	characteristic
199	Dic₇₁	—	4	1	no	—
200	Dic₇₁	—	4	2	no	—
201	Dic₇₁	C₄×D₈	1	1	yes	characteristic
202	Dic₇₁	C₄×D₈	1	1	yes	characteristic
203	#33465	—	71	1	no	maximal, Sylow
204	C₂×C₇₁	—	2	1	no	—
205	C₂×C₇₁	—	8	2	no	—
206	C₂×C₇₁	C₂×C₄×D₈	1	1	yes	characteristic
207	D₇₁	—	2	1	no	—
208	D₇₁	—	2	1	no	—
209	D₇₁	—	8	2	no	—
210	C₂×#508	—	71	1	no	—
211	#2957	—	71	2	no	—
212	#2179	—	71	2	no	—
213	#2179	—	71	2	no	—
214	#2178	—	71	1	no	—
215	#2178	—	71	1	no	—
216	#2178	—	71	1	no	—
217	#2178	D₇₁	1	1	yes	characteristic, complemented
218	C₂×#368	—	71	1	no	—
219	#2143	—	71	2	no	—
220	#2108	—	71	1	no	—
221	C₇₁	#33465	1	1	yes	characteristic, complemented, Sylow
222	C₂×#135	—	71	2	no	—
223	#568	—	142	2	no	—
224	#508	—	71	2	no	—
225	#508	—	71	1	no	—
226	#508	—	71	2	no	—
227	#508	—	71	1	no	—
228	#508	—	71	1	no	—
229	#508	C₂×D₇₁	1	1	yes	characteristic
230	C₂×Q₃₂	—	71	1	no	—
231	C₂×SD₃₂	—	71	2	no	—
232	C₂×D₁₆	—	71	1	no	—
233	C₂×M₃₂	—	71	1	no	—
234	C₂²×C₁₆	—	71	1	no	—
235	#444	—	142	2	no	—
236	#444	—	142	2	no	—
237	#443	—	71	2	no	—
238	#443	—	71	2	no	—
239	#443	—	71	2	no	—
240	#443	C₂×D₇₁	1	2	yes	complemented
241	C₂×#108	—	71	2	no	—
242	#421	—	142	2	no	—
243	#405	—	71	1	no	—
244	#368	—	71	1	no	—
245	#368	—	71	2	no	—
246	#368	C₂×D₇₁	1	1	yes	characteristic, complemented
247	#359	—	71	2	no	—
248	#359	—	71	2	no	—
249	#359	—	71	2	no	—
250	#359	C₂×D₇₁	1	2	yes	complemented
251	#346	—	71	1	no	—
252	#346	—	71	1	no	—
253	C₄×C₁₆	—	71	1	no	—
254	C₄×C₁₆	C₂×D₇₁	1	1	yes	characteristic, complemented
255	C₂×#41	—	142	2	no	—
256	#135	—	71	2	no	—
257	#135	—	71	2	no	—
258	#135	—	71	2	no	—
259	#135	—	142	2	no	—
260	#135	—	142	2	no	—
261	#135	C₂²×D₇₁	1	2	yes	—
262	C₂×Q₁₆	—	71	2	no	—
263	C₂×SD₁₆	—	142	2	no	—
264	C₂×D₈	—	71	2	no	—
265	#131	—	2	2	no	—
266	#131	—	284	2	no	—
267	#131	—	284	2	no	—
268	#131	—	142	2	no	—
269	#131	—	142	2	no	—
270	#131	—	142	2	no	—
271	C₂×M₁₆	—	284	2	no	—
272	C₂×M₁₆	—	284	2	no	—
273	C₂×M₁₆	—	71	1	no	—
274	C₂×M₁₆	—	142	2	no	—
275	C₂²×C₈	—	71	1	no	—
276	#117	—	71	1	no	—
277	Q₃₂	—	71	2	no	—
278	Q₃₂	—	71	1	no	—
279	Q₃₂	C₄×D₇₁	1	1	yes	characteristic
280	SD₃₂	—	71	2	no	—
281	SD₃₂	—	71	2	no	—
282	SD₃₂	—	71	2	no	—
283	SD₃₂	C₄×D₇₁	1	2	yes	—
284	D₁₆	—	71	2	no	—
285	D₁₆	—	71	1	no	—
286	D₁₆	C₄×D₇₁	1	1	yes	characteristic
287	M₃₂	—	142	1	no	—
288	M₃₂	—	142	1	no	—
289	C₂×C₁₆	—	71	1	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	C₂²×D₇₁	1	1	yes	characteristic
296	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
297	#108	—	71	2	no	—
298	#108	—	142	2	no	—
299	#108	C₂²×D₇₁	1	2	yes	—
300	#104	—	2	2	no	—
301	#104	—	142	2	no	—
302	#104	—	142	2	no	—
303	#104	—	142	2	no	—
304	#97	—	71	1	no	—
305	#97	—	71	1	no	—
306	C₄×C₈	—	71	1	no	—
307	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
308	#41	—	2	2	no	—
309	#41	—	284	2	no	—
310	#41	—	284	2	no	—
311	#41	—	142	2	no	—
312	#41	—	142	2	no	—
313	#41	—	142	2	no	—
314	C₂×Q₈	—	142	2	no	—
315	C₂×D₄	—	284	2	no	—
316	C₂×D₄	—	142	2	no	—
317	C₂²×C₄	—	284	2	no	—
318	C₂²×C₄	—	71	1	no	—
319	Q₁₆	—	71	2	no	—
320	Q₁₆	—	142	2	no	—
321	Q₁₆	C₂×C₄×D₇₁	1	2	yes	—
322	SD₁₆	—	2	2	no	—
323	SD₁₆	—	142	2	no	—
324	SD₁₆	—	142	2	no	—
325	SD₁₆	—	142	2	no	—
326	D₈	—	71	2	no	—
327	D₈	—	142	2	no	—
328	D₈	C₂×C₄×D₇₁	1	2	yes	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	4	2	no	—
331	M₁₆	—	284	2	no	—
332	M₁₆	—	284	2	no	—
333	M₁₆	—	284	2	no	—
334	M₁₆	—	284	2	no	—
335	M₁₆	—	71	1	no	—
336	M₁₆	—	71	1	no	—
337	M₁₆	—	71	1	no	—
338	M₁₆	—	71	1	no	—
339	M₁₆	—	142	2	no	—
340	C₂×C₈	—	4	2	no	—
341	C₂×C₈	—	284	2	no	—
342	C₂×C₈	—	284	2	no	—
343	C₂×C₈	—	284	2	no	—
344	C₂×C₈	—	284	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	D₄×D₇₁	1	1	yes	characteristic
352	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
353	C₄⋊C₄	—	142	1	no	—
354	C₂²⋊C₄	—	142	1	no	—
355	C₄²	—	71	1	no	—
356	C₄²	D₄×D₇₁	1	1	yes	characteristic
357	C₁₆	—	2	1	no	—
358	C₁₆	—	71	1	no	—
359	C₁₆	—	71	1	no	—
360	C₁₆	—	142	1	no	—
361	C₁₆	C₂×C₄×D₇₁	1	1	yes	characteristic
362	C₁₆	C₂×C₄×D₇₁	1	1	yes	characteristic
363	C₂³	—	284	2	no	—
364	C₂³	—	71	1	no	—
365	Q₈	—	2	2	no	—
366	Q₈	—	284	2	no	—
367	Q₈	—	142	2	no	—
368	D₄	—	2	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	284	2	no	—
371	D₄	—	284	2	no	—
372	D₄	—	284	2	no	—
373	D₄	—	284	2	no	—
374	D₄	—	142	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	284	2	no	—
378	C₂×C₄	—	284	2	no	—
379	C₂×C₄	—	284	2	no	—
380	C₂×C₄	—	284	2	no	—
381	C₂×C₄	—	71	1	no	—
382	C₂×C₄	—	71	1	no	—
383	C₂×C₄	—	71	1	no	—
384	C₂×C₄	—	71	1	no	—
385	C₂×C₄	—	71	1	no	—
386	C₂×C₄	—	142	1	no	—
387	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
388	C₈	—	4	2	no	—
389	C₈	—	284	2	no	—
390	C₈	—	71	1	no	—
391	C₈	—	71	1	no	—
392	C₈	—	71	1	no	—
393	C₈	—	71	1	no	—
394	C₈	D₈×D₇₁	1	1	yes	characteristic
395	C₈	D₈×D₇₁	1	1	yes	characteristic
396	C₈	C₂²×C₄×D₇₁	1	1	yes	characteristic
397	C₈	#41×D₇₁	1	1	yes	characteristic
398	C₂²	—	4	2	no	—
399	C₂²	—	284	1	no	—
400	C₂²	—	284	2	no	—
401	C₂²	—	71	1	no	—
402	C₂²	—	71	1	no	—
403	C₂²	—	1136	2	no	—
404	C₂²	#135×D₇₁	1	1	yes	characteristic
405	C₄	—	4	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	284	1	no	—
408	C₄	—	284	2	no	—
409	C₄	—	71	1	no	—
410	C₄	—	71	1	no	—
411	C₄	C₄×D₄×D₇₁	1	1	yes	characteristic
412	C₄	C₂×D₈×D₇₁	1	1	yes	characteristic
413	C₂	—	2	1	no	—
414	C₂	—	8	2	no	—
415	C₂	—	568	2	no	—
416	C₂	—	142	1	no	—
417	C₂	—	142	1	no	—
418	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×#2178	C₂
socle	C₂×C₇₁	C₂×C₄×D₈
prime radical	#508×D₇₁	C₂
cosocle	C₂×C₈×C₇₁	C₂⁴
hypercenter	#2178	D₇₁
hypocenter	C₇₁	#33465
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #2178

Complements

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

N	H ≅ G/N	type
2. #22597252	C₂	semidirect
3. #22590224	C₂	semidirect
4. #22590223	C₂	semidirect
5. #22590222	C₂	semidirect
6. #22590221	C₂	semidirect
7. #22590220	C₂	semidirect
8. #368×D₇₁	C₂	semidirect
9. #22590066	C₂	semidirect
10. #22589935	C₂	semidirect
11. C₇₁×#2178	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
26. #17986117	C₂²	semidirect
27. #17986116	C₂²	semidirect
28. #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. C₁₆×Dic₇₁	C₂²	semidirect
41. #443×C₇₁	C₂²	semidirect
42. #368×C₇₁	C₂²	semidirect
43. #359×C₇₁	C₂²	semidirect
44. C₄×C₁₆×C₇₁	C₂²	semidirect
217. #2178	D₇₁	semidirect
221. C₇₁	#33465	semidirect
240. #443	C₂×D₇₁	semidirect
246. #368	C₂×D₇₁	semidirect
250. #359	C₂×D₇₁	semidirect
254. 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
#508×D₇₁	2
#22597252	2
#22590224	2
#22590223	2
#22590222	2
#22590221	2
#22590220	2
#368×D₇₁	2
#22590066	2
#22589935	2
C₇₁×#2178	2
#33465	71