Subgroups — #32152193

Order 18176.

524 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22598853	C₂	1	1	yes	maximal, characteristic, complemented
2	#443×D₇₁	C₂	1	1	yes	maximal, characteristic
3	#22590517	C₂	1	1	yes	maximal, characteristic, complemented
4	#22590516	C₂	1	1	yes	maximal, characteristic, complemented
5	#22590513	C₂	1	1	yes	maximal, characteristic, complemented
6	#22590510	C₂	1	2	yes	maximal, complemented
7	#22590509	C₂	1	2	yes	maximal, complemented
8	#22590111	C₂	1	2	yes	maximal, complemented
9	#364×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#22590074	C₂	1	2	yes	maximal
11	C₇₁×#2231	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₇₁	C₂²	1	1	yes	characteristic
13	#131×D₇₁	—	2	1	no	—
14	#17986555	—	2	1	no	—
15	M₃₂×D₇₁	C₂²	1	2	yes	—
16	#17986403	—	2	1	no	—
17	#17986401	C₂²	1	1	yes	characteristic, complemented
18	#17986398	—	2	1	no	—
19	#17986396	C₂²	1	2	yes	complemented
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	#17986036	—	2	1	no	—
27	#17986034	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	#499×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	#14556151	Q₈	1	1	yes	characteristic, complemented
45	#14556150	C₂³	1	1	yes	characteristic
46	#14556149	—	2	1	no	—
47	#14556148	—	2	1	no	—
48	#14556147	Q₈	1	1	yes	characteristic, complemented
49	Q₁₆×D₇₁	Q₈	1	1	yes	characteristic, complemented
50	SD₁₆×D₇₁	—	2	1	no	—
51	D₈×D₇₁	Q₈	1	1	yes	characteristic, complemented
52	#14556136	—	2	1	no	—
53	#14556136	—	4	1	no	—
54	#14556135	—	2	1	no	—
55	#14556134	—	2	1	no	—
56	#14556134	—	4	1	no	—
57	M₁₆×D₇₁	—	2	1	no	—
58	M₁₆×D₇₁	—	4	1	no	—
59	C₂×C₈×D₇₁	—	4	1	no	—
60	C₂×C₈×D₇₁	D₄	1	1	yes	characteristic
61	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
62	#14556127	—	2	2	no	—
63	#14556120	—	2	1	no	—
64	#14556106	—	4	2	no	—
65	#14556093	—	4	2	no	—
66	#14556086	—	2	2	no	—
67	C₄²×D₇₁	D₄	1	1	yes	characteristic
68	#14556068	C₂³	1	2	yes	—
69	#14556067	—	2	2	no	—
70	C₁₆×D₇₁	—	2	2	no	—
71	#14556064	C₂³	1	1	yes	characteristic
72	#14556063	—	2	1	no	—
73	#14556062	—	2	1	no	—
74	#14556061	—	2	2	no	—
75	#14556060	C₂³	1	2	yes	—
76	#14556059	—	2	2	no	—
77	#14556056	—	2	1	no	—
78	#14556055	—	2	1	no	—
79	#14556054	—	2	1	no	—
80	C₄×C₇₁⋊C₈	D₄	1	1	yes	characteristic
81	C₈×Dic₇₁	D₄	1	1	yes	characteristic
82	C₈×Dic₇₁	C₂³	1	1	yes	characteristic
83	#135×C₇₁	C₂³	1	1	yes	characteristic
84	#131×C₇₁	—	2	1	no	—
85	#125×C₇₁	—	2	1	no	—
86	M₃₂×C₇₁	C₂³	1	2	yes	—
87	#108×C₇₁	C₂³	1	1	yes	characteristic
88	#107×C₇₁	—	2	1	no	—
89	#106×C₇₁	C₂³	1	2	yes	—
90	#104×C₇₁	—	2	1	no	—
91	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
92	#11765866	—	2	1	no	—
93	#11765865	—	2	1	no	—
94	#11765865	—	4	1	no	—
95	#11765864	—	2	1	no	—
96	#11765864	—	4	1	no	—
97	C₂×Dic₁₄₂	—	4	2	no	—
98	Q₈×D₇₁	—	2	1	no	—
99	D₄×D₇₁	—	2	1	no	—
100	D₄×D₇₁	—	4	1	no	—
101	C₂×C₄×D₇₁	—	2	1	no	—
102	C₂×C₄×D₇₁	—	4	1	no	—
103	C₂×C₄×D₇₁	C₂×D₄	1	1	yes	characteristic
104	Dic₂₈₄	C₂×Q₈	1	1	yes	characteristic
105	#11765855	—	2	1	no	—
106	#11765854	—	2	1	no	—
107	#11765853	—	2	1	no	—
108	#11765852	—	2	1	no	—
109	D₅₆₈	C₂×Q₈	1	1	yes	characteristic
110	#11765850	—	2	1	no	—
111	#11765849	—	2	1	no	—
112	#11765849	—	4	1	no	—
113	#11765848	—	4	1	no	—
114	#11765848	—	4	1	no	—
115	#11765848	—	4	1	no	—
116	C₂×C₇₁⋊C₈	—	4	1	no	—
117	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
118	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
119	C₈×D₇₁	—	4	1	no	—
120	C₈×D₇₁	—	4	1	no	—
121	C₈×D₇₁	—	4	1	no	—
122	C₈×D₇₁	SD₁₆	1	1	yes	characteristic
123	C₈×D₇₁	SD₁₆	1	1	yes	characteristic
124	C₈×D₇₁	SD₁₆	1	1	yes	characteristic
125	C₈×D₇₁	SD₁₆	1	1	yes	characteristic
126	C₈×D₇₁	C₂×Q₈	1	1	yes	characteristic
127	C₈×D₇₁	C₂×Q₈	1	1	yes	characteristic
128	C₈×D₇₁	#41	1	1	yes	characteristic
129	C₈×D₇₁	#41	1	1	yes	characteristic
130	C₄⋊Dic₇₁	—	2	2	no	—
131	Dic₇₁⋊C₄	—	4	2	no	—
132	Dic₇₁⋊C₄	—	4	2	no	—
133	(C₂×D₇₁)⋊C₄	—	4	2	no	—
134	C₄×Dic₇₁	—	2	1	no	—
135	C₄×Dic₇₁	—	4	2	no	—
136	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
137	C₇₁⋊C₁₆	—	2	2	no	—
138	#41×C₇₁	—	2	1	no	—
139	Q₁₆×C₇₁	C₂×Q₈	1	1	yes	characteristic
140	SD₁₆×C₇₁	—	2	1	no	—
141	D₈×C₇₁	C₂×Q₈	1	1	yes	characteristic
142	M₁₆×C₇₁	—	2	1	no	—
143	M₁₆×C₇₁	—	4	1	no	—
144	C₂×C₈×C₇₁	—	4	1	no	—
145	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
147	C₄⋊C₄×C₇₁	—	2	2	no	—
148	C₄⋊C₄×C₇₁	—	4	2	no	—
149	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
150	C₁₆×C₇₁	—	2	2	no	—
151	C₂²×D₇₁	—	4	1	no	—
152	C₂²×D₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
153	Q₈×C₇₁	—	2	1	no	—
154	D₄×C₇₁	—	2	1	no	—
155	D₄×C₇₁	—	4	1	no	—
156	C₂×C₄×C₇₁	—	2	1	no	—
157	C₂×C₄×C₇₁	—	4	1	no	—
158	C₂×C₄×C₇₁	—	4	2	no	—
159	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
160	C₂²⋊D₇₁	—	4	1	no	—
161	C₂²⋊D₇₁	—	4	1	no	—
162	C₂²⋊D₇₁	—	4	1	no	—
163	C₂×Dic₇₁	—	2	1	no	—
164	C₂×Dic₇₁	—	4	1	no	—
165	C₂×Dic₇₁	—	4	2	no	—
166	C₂×Dic₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
167	D₂₈₄	—	2	1	no	—
168	D₂₈₄	—	4	1	no	—
169	C₄×D₇₁	—	4	2	no	—
170	C₄×D₇₁	—	4	1	no	—
171	C₄×D₇₁	—	4	1	no	—
172	C₄×D₇₁	—	4	1	no	—
173	C₄×D₇₁	C₂²⋊Q₈	1	1	yes	characteristic
174	C₄×D₇₁	C₂²⋊Q₈	1	1	yes	characteristic
175	C₄×D₇₁	C₂×SD₁₆	1	1	yes	characteristic
176	C₄×D₇₁	C₂×SD₁₆	1	1	yes	characteristic
177	Dic₁₄₂	—	2	1	no	—
178	Dic₁₄₂	—	4	1	no	—
179	Dic₁₄₂	—	8	4	no	—
180	C₈×C₇₁	—	4	1	no	—
181	C₈×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
182	C₈×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
183	C₈×C₇₁	C₂²×Q₈	1	1	yes	characteristic
184	C₈×C₇₁	C₂×#41	1	1	yes	characteristic
185	C₇₁⋊C₈	—	4	1	no	—
186	C₇₁⋊C₈	C₂²⋊Q₈	1	1	yes	characteristic
187	C₇₁⋊C₈	C₂²⋊Q₈	1	1	yes	characteristic
188	C₇₁⋊C₈	C₂×SD₁₆	1	1	yes	characteristic
189	C₇₁⋊C₈	C₂×SD₁₆	1	1	yes	characteristic
190	C₂²×C₇₁	—	4	1	no	—
191	C₂²×C₇₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
192	C₂×D₇₁	—	4	1	no	—
193	C₂×D₇₁	—	4	1	no	—
194	C₂×D₇₁	—	8	2	no	—
195	C₂×D₇₁	#476	1	1	yes	characteristic
196	C₂×D₇₁	#476	1	1	yes	characteristic
197	C₄×C₇₁	—	4	1	no	—
198	C₄×C₇₁	—	4	1	no	—
199	C₄×C₇₁	—	8	2	no	—
200	C₄×C₇₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
201	C₄×C₇₁	C₂²×SD₁₆	1	1	yes	characteristic
202	Dic₇₁	—	2	2	no	—
203	Dic₇₁	—	4	1	no	—
204	Dic₇₁	—	8	2	no	—
205	Dic₇₁	#476	1	1	yes	characteristic
206	Dic₇₁	#476	1	1	yes	characteristic
207	#33637	—	71	1	no	maximal, Sylow
208	C₂×C₇₁	—	2	1	no	—
209	C₂×C₇₁	—	8	1	no	—
210	C₂×C₇₁	C₂×#476	1	1	yes	characteristic
211	D₇₁	—	2	1	no	—
212	D₇₁	—	2	1	no	—
213	D₇₁	—	8	1	no	—
214	#3160	—	71	1	no	—
215	C₂×#443	—	71	1	no	—
216	#2231	—	71	1	no	—
217	#2231	—	71	1	no	—
218	#2231	—	71	1	no	—
219	#2231	D₇₁	1	1	yes	characteristic, complemented
220	#2230	—	71	2	no	—
221	#2230	—	71	2	no	—
222	#2155	—	71	2	no	—
223	C₂×#364	—	71	1	no	—
224	#2145	—	71	2	no	—
225	C₇₁	#33637	1	1	yes	characteristic, complemented, Sylow
226	C₂×#135	—	71	1	no	—
227	C₂×#131	—	142	1	no	—
228	#533	—	142	1	no	—
229	C₂×M₃₂	—	71	2	no	—
230	#500	—	142	1	no	—
231	#499	—	71	1	no	—
232	#499	—	142	1	no	—
233	#499	C₂×D₇₁	1	1	yes	characteristic, complemented
234	#498	—	71	2	no	—
235	#443	—	71	1	no	—
236	#443	—	71	1	no	—
237	#443	—	71	1	no	—
238	#443	—	142	1	no	—
239	#443	—	142	1	no	—
240	#443	C₂×D₇₁	1	1	yes	characteristic
241	C₂×#108	—	71	1	no	—
242	#427	—	71	2	no	—
243	#427	—	142	1	no	—
244	C₂×#104	—	142	1	no	—
245	C₂×C₄×C₈	—	71	1	no	—
246	#365	—	71	2	no	—
247	#365	—	71	2	no	—
248	#365	—	71	2	no	—
249	#365	C₂×D₇₁	1	2	yes	complemented
250	#364	—	71	2	no	—
251	#364	—	71	1	no	—
252	#364	C₂×D₇₁	1	1	yes	characteristic, complemented
253	#360	—	71	2	no	—
254	#360	—	71	2	no	—
255	#360	—	71	2	no	—
256	#360	C₂×D₇₁	1	2	yes	—
257	C₂×#41	—	142	1	no	—
258	#135	—	71	1	no	—
259	#135	—	71	1	no	—
260	#135	—	71	1	no	—
261	#135	—	142	1	no	—
262	#135	—	142	1	no	—
263	#135	C₂²×D₇₁	1	1	yes	characteristic
264	C₂×Q₁₆	—	71	1	no	—
265	C₂×SD₁₆	—	142	1	no	—
266	C₂×D₈	—	71	1	no	—
267	#131	—	2	1	no	—
268	#131	—	284	1	no	—
269	#131	—	284	1	no	—
270	#131	—	142	1	no	—
271	#131	—	142	1	no	—
272	#131	—	142	1	no	—
273	C₂×M₁₆	—	284	1	no	—
274	C₂×M₁₆	—	142	1	no	—
275	C₂²×C₈	—	284	1	no	—
276	C₂²×C₈	—	71	1	no	—
277	C₂²×C₈	—	71	1	no	—
278	C₄⋊Q₈	—	142	2	no	—
279	#125	—	2	1	no	—
280	#125	—	142	1	no	—
281	C₂²⋊Q₈	—	284	2	no	—
282	C₄×Q₈	—	284	2	no	—
283	#117	—	142	2	no	—
284	C₂×C₄²	—	71	1	no	—
285	M₃₂	—	71	2	no	—
286	M₃₂	—	142	2	no	—
287	M₃₂	C₂²×D₇₁	1	2	yes	—
288	C₂×C₁₆	—	142	2	no	—
289	#108	—	71	1	no	—
290	#108	—	142	1	no	—
291	#108	C₂²×D₇₁	1	1	yes	characteristic
292	#107	—	2	1	no	—
293	#107	—	142	2	no	—
294	#107	—	142	1	no	—
295	#106	—	71	2	no	—
296	#106	—	142	2	no	—
297	#106	C₂²×D₇₁	1	2	yes	—
298	#104	—	2	1	no	—
299	#104	—	142	1	no	—
300	#104	—	142	1	no	—
301	#104	—	142	1	no	—
302	C₄×C₈	—	71	1	no	—
303	C₄×C₈	—	71	1	no	—
304	C₄×C₈	—	71	1	no	—
305	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
306	#41	—	2	1	no	—
307	#41	—	284	1	no	—
308	#41	—	284	1	no	—
309	#41	—	142	1	no	—
310	#41	—	142	1	no	—
311	#41	—	142	1	no	—
312	C₂×Q₈	—	284	2	no	—
313	C₂×Q₈	—	142	1	no	—
314	C₂×D₄	—	284	1	no	—
315	C₂×D₄	—	142	1	no	—
316	C₂²×C₄	—	284	1	no	—
317	C₂²×C₄	—	71	1	no	—
318	C₂²×C₄	—	142	1	no	—
319	Q₁₆	—	71	1	no	—
320	Q₁₆	—	142	1	no	—
321	Q₁₆	Q₈×D₇₁	1	1	yes	characteristic
322	SD₁₆	—	2	1	no	—
323	SD₁₆	—	142	1	no	—
324	SD₁₆	—	142	1	no	—
325	SD₁₆	—	142	1	no	—
326	D₈	—	71	1	no	—
327	D₈	—	142	1	no	—
328	D₈	Q₈×D₇₁	1	1	yes	characteristic
329	M₁₆	—	2	1	no	—
330	M₁₆	—	4	1	no	—
331	M₁₆	—	284	1	no	—
332	M₁₆	—	284	1	no	—
333	M₁₆	—	284	1	no	—
334	M₁₆	—	284	1	no	—
335	M₁₆	—	142	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	284	1	no	—
338	C₂×C₈	—	284	1	no	—
339	C₂×C₈	—	284	1	no	—
340	C₂×C₈	—	284	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	—	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	—	2	2	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄⋊C₄	—	284	2	no	—
356	C₄⋊C₄	—	284	2	no	—
357	C₄⋊C₄	—	142	2	no	—
358	C₂²⋊C₄	—	284	2	no	—
359	C₄²	—	284	2	no	—
360	C₄²	—	71	1	no	—
361	C₄²	—	142	1	no	—
362	C₄²	D₄×D₇₁	1	1	yes	characteristic
363	C₁₆	—	2	2	no	—
364	C₁₆	—	142	2	no	—
365	C₂³	—	284	1	no	—
366	C₂³	—	71	1	no	—
367	Q₈	—	2	1	no	—
368	Q₈	—	284	1	no	—
369	Q₈	—	568	4	no	—
370	Q₈	—	142	1	no	—
371	D₄	—	2	1	no	—
372	D₄	—	4	1	no	—
373	D₄	—	284	1	no	—
374	D₄	—	284	1	no	—
375	D₄	—	284	1	no	—
376	D₄	—	284	1	no	—
377	D₄	—	142	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	284	1	no	—
382	C₂×C₄	—	284	1	no	—
383	C₂×C₄	—	284	2	no	—
384	C₂×C₄	—	284	1	no	—
385	C₂×C₄	—	284	1	no	—
386	C₂×C₄	—	284	2	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	—	71	1	no	—
392	C₂×C₄	—	142	1	no	—
393	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
394	C₈	—	4	1	no	—
395	C₈	—	284	1	no	—
396	C₈	—	71	1	no	—
397	C₈	—	71	1	no	—
398	C₈	—	71	1	no	—
399	C₈	—	71	1	no	—
400	C₈	SD₁₆×D₇₁	1	1	yes	characteristic
401	C₈	SD₁₆×D₇₁	1	1	yes	characteristic
402	C₈	C₂×Q₈×D₇₁	1	1	yes	characteristic
403	C₈	#41×D₇₁	1	1	yes	characteristic
404	C₂²	—	4	1	no	—
405	C₂²	—	284	1	no	—
406	C₂²	—	284	1	no	—
407	C₂²	—	568	2	no	—
408	C₂²	—	71	1	no	—
409	C₂²	—	71	1	no	—
410	C₂²	AGL(1,ℤ/8)×D₇₁	1	1	yes	characteristic
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	8	2	no	—
414	C₄	—	284	1	no	—
415	C₄	—	568	2	no	—
416	C₄	—	71	1	no	—
417	C₄	—	71	1	no	—
418	C₄	—	142	2	no	—
419	C₄	C₂²⋊Q₈×D₇₁	1	1	yes	characteristic
420	C₄	C₂×SD₁₆×D₇₁	1	1	yes	characteristic
421	C₂	—	2	1	no	—
422	C₂	—	8	1	no	—
423	C₂	—	568	1	no	—
424	C₂	—	142	1	no	—
425	C₂	—	142	1	no	—
426	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×#2231	C₂
socle	C₂×C₇₁	C₂×#476
prime radical	#135×D₇₁	C₂²
hypercenter	#2231	D₇₁
hypocenter	C₇₁	#33637
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2231

Complements

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

N	H ≅ G/N	type
1. #22598853	C₂	semidirect
3. #22590517	C₂	semidirect
4. #22590516	C₂	semidirect
5. #22590513	C₂	semidirect
6. #22590510	C₂	semidirect
7. #22590509	C₂	semidirect
8. #22590111	C₂	semidirect
9. #364×D₇₁	C₂	semidirect
11. C₇₁×#2231	C₂	semidirect
17. #17986401	C₂²	semidirect
19. #17986396	C₂²	semidirect
30. #17985823	C₂²	semidirect
31. #17985822	C₂²	semidirect
32. #17985821	C₂²	semidirect
33. #17985820	C₂²	semidirect
34. #17985819	C₂²	semidirect
38. #499×C₇₁	C₂²	semidirect
40. #365×C₇₁	C₂²	semidirect
41. #364×C₇₁	C₂²	semidirect
44. #14556151	Q₈	semidirect
48. #14556147	Q₈	semidirect
49. Q₁₆×D₇₁	Q₈	semidirect
51. D₈×D₇₁	Q₈	semidirect
219. #2231	D₇₁	semidirect
225. C₇₁	#33637	semidirect
233. #499	C₂×D₇₁	semidirect
249. #365	C₂×D₇₁	semidirect
252. #364	C₂×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
#22598853	2
#443×D₇₁	2
#22590517	2
#22590516	2
#22590513	2
#22590510	2
#22590509	2
#22590111	2
#364×D₇₁	2
#22590074	2
C₇₁×#2231	2
#33637	71