Subgroups — #32152190

Order 18176.

524 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22598849	C₂	1	1	yes	maximal, characteristic, complemented
2	#443×D₇₁	C₂	1	1	yes	maximal, characteristic
3	#22590515	C₂	1	2	yes	maximal, complemented
4	#22590514	C₂	1	2	yes	maximal, complemented
5	#22590512	C₂	1	1	yes	maximal, characteristic, complemented
6	#22590511	C₂	1	1	yes	maximal, characteristic, complemented
7	#22590508	C₂	1	1	yes	maximal, characteristic, 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×#2230	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₇₁	C₂²	1	1	yes	characteristic
13	#131×D₇₁	—	2	1	no	—
14	#17986554	—	2	1	no	—
15	M₃₂×D₇₁	C₂²	1	2	yes	—
16	#17986402	—	2	1	no	—
17	#17986399	—	2	1	no	—
18	#17986399	C₂²	1	2	yes	complemented
19	#17986397	C₂²	1	1	yes	characteristic, 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	#17986034	—	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	#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	#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	#14556128	—	2	1	no	—
63	#14556119	—	2	2	no	—
64	#14556108	—	4	1	no	—
65	#14556104	—	4	1	no	—
66	Q₈×Dic₇₁	—	4	1	no	—
67	#14556093	—	4	1	no	—
68	#14556086	—	2	2	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	#14556061	—	2	2	no	—
76	#14556061	—	2	2	no	—
77	#14556060	—	2	1	no	—
78	#14556060	C₂³	1	2	yes	—
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	1	no	—
100	Q₈×D₇₁	—	2	1	no	—
101	D₄×D₇₁	—	2	1	no	—
102	D₄×D₇₁	—	4	1	no	—
103	C₂×C₄×D₇₁	—	2	1	no	—
104	C₂×C₄×D₇₁	—	4	1	no	—
105	C₂×C₄×D₇₁	C₂×D₄	1	1	yes	characteristic
106	Dic₂₈₄	C₂×Q₈	1	1	yes	characteristic
107	#11765855	—	2	1	no	—
108	#11765854	—	2	1	no	—
109	#11765853	—	2	1	no	—
110	#11765852	—	2	1	no	—
111	D₅₆₈	C₂×Q₈	1	1	yes	characteristic
112	#11765850	—	2	1	no	—
113	#11765849	—	2	1	no	—
114	#11765849	—	4	1	no	—
115	#11765848	—	4	1	no	—
116	#11765848	—	4	1	no	—
117	#11765848	—	4	1	no	—
118	C₂×C₇₁⋊C₈	—	4	1	no	—
119	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
120	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
121	C₈×D₇₁	—	4	1	no	—
122	C₈×D₇₁	—	4	1	no	—
123	C₈×D₇₁	—	4	1	no	—
124	C₈×D₇₁	SD₁₆	1	1	yes	characteristic
125	C₈×D₇₁	SD₁₆	1	1	yes	characteristic
126	C₈×D₇₁	SD₁₆	1	1	yes	characteristic
127	C₈×D₇₁	SD₁₆	1	1	yes	characteristic
128	C₈×D₇₁	C₂×Q₈	1	1	yes	characteristic
129	C₈×D₇₁	C₂×Q₈	1	1	yes	characteristic
130	C₈×D₇₁	#41	1	1	yes	characteristic
131	C₈×D₇₁	#41	1	1	yes	characteristic
132	C₄⋊Dic₇₁	—	2	2	no	—
133	C₄⋊Dic₇₁	—	4	2	no	—
134	C₄⋊Dic₇₁	—	4	1	no	—
135	Dic₇₁⋊C₄	—	4	2	no	—
136	(C₂×D₇₁)⋊C₄	—	4	2	no	—
137	C₄×Dic₇₁	—	2	1	no	—
138	C₄×Dic₇₁	—	4	2	no	—
139	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
140	C₇₁⋊C₁₆	—	2	2	no	—
141	#41×C₇₁	—	2	1	no	—
142	C₂×Q₈×C₇₁	—	4	1	no	—
143	Q₁₆×C₇₁	C₂×Q₈	1	1	yes	characteristic
144	SD₁₆×C₇₁	—	2	1	no	—
145	D₈×C₇₁	C₂×Q₈	1	1	yes	characteristic
146	M₁₆×C₇₁	—	2	1	no	—
147	M₁₆×C₇₁	—	4	1	no	—
148	C₂×C₈×C₇₁	—	4	1	no	—
149	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
151	C₄⋊C₄×C₇₁	—	2	2	no	—
152	C₄⋊C₄×C₇₁	—	4	1	no	—
153	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
154	C₁₆×C₇₁	—	2	2	no	—
155	C₂²×D₇₁	—	4	1	no	—
156	C₂²×D₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
157	Q₈×C₇₁	—	2	1	no	—
158	Q₈×C₇₁	—	8	2	no	—
159	D₄×C₇₁	—	2	1	no	—
160	D₄×C₇₁	—	4	1	no	—
161	C₂×C₄×C₇₁	—	2	1	no	—
162	C₂×C₄×C₇₁	—	4	1	no	—
163	C₂×C₄×C₇₁	—	4	2	no	—
164	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
165	C₂²⋊D₇₁	—	4	1	no	—
166	C₂²⋊D₇₁	—	4	1	no	—
167	C₂²⋊D₇₁	—	4	1	no	—
168	C₂×Dic₇₁	—	2	1	no	—
169	C₂×Dic₇₁	—	4	1	no	—
170	C₂×Dic₇₁	—	4	2	no	—
171	C₂×Dic₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
172	D₂₈₄	—	2	1	no	—
173	D₂₈₄	—	4	1	no	—
174	C₄×D₇₁	—	4	2	no	—
175	C₄×D₇₁	—	4	1	no	—
176	C₄×D₇₁	—	4	1	no	—
177	C₄×D₇₁	—	4	1	no	—
178	C₄×D₇₁	C₂²⋊Q₈	1	1	yes	characteristic
179	C₄×D₇₁	C₂²⋊Q₈	1	1	yes	characteristic
180	C₄×D₇₁	C₂×SD₁₆	1	1	yes	characteristic
181	C₄×D₇₁	C₂×SD₁₆	1	1	yes	characteristic
182	Dic₁₄₂	—	2	1	no	—
183	Dic₁₄₂	—	4	1	no	—
184	Dic₁₄₂	—	8	2	no	—
185	C₈×C₇₁	—	4	1	no	—
186	C₈×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
187	C₈×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
188	C₈×C₇₁	C₂²×Q₈	1	1	yes	characteristic
189	C₈×C₇₁	C₂×#41	1	1	yes	characteristic
190	C₇₁⋊C₈	—	4	1	no	—
191	C₇₁⋊C₈	C₂²⋊Q₈	1	1	yes	characteristic
192	C₇₁⋊C₈	C₂²⋊Q₈	1	1	yes	characteristic
193	C₇₁⋊C₈	C₂×SD₁₆	1	1	yes	characteristic
194	C₇₁⋊C₈	C₂×SD₁₆	1	1	yes	characteristic
195	C₂²×C₇₁	—	4	1	no	—
196	C₂²×C₇₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₂×D₇₁	—	4	1	no	—
198	C₂×D₇₁	—	4	1	no	—
199	C₂×D₇₁	—	8	2	no	—
200	C₂×D₇₁	#476	1	1	yes	characteristic
201	C₂×D₇₁	#476	1	1	yes	characteristic
202	C₄×C₇₁	—	2	2	no	—
203	C₄×C₇₁	—	4	1	no	—
204	C₄×C₇₁	—	8	2	no	—
205	C₄×C₇₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
206	C₄×C₇₁	C₂²×SD₁₆	1	1	yes	characteristic
207	Dic₇₁	—	4	1	no	—
208	Dic₇₁	—	4	1	no	—
209	Dic₇₁	—	8	2	no	—
210	Dic₇₁	#476	1	1	yes	characteristic
211	Dic₇₁	#476	1	1	yes	characteristic
212	#33637	—	71	1	no	maximal, Sylow
213	C₂×C₇₁	—	2	1	no	—
214	C₂×C₇₁	—	8	1	no	—
215	C₂×C₇₁	C₂×#476	1	1	yes	characteristic
216	D₇₁	—	2	1	no	—
217	D₇₁	—	2	1	no	—
218	D₇₁	—	8	1	no	—
219	#3160	—	71	1	no	—
220	C₂×#443	—	71	1	no	—
221	#2231	—	71	2	no	—
222	#2231	—	71	2	no	—
223	#2230	—	71	1	no	—
224	#2230	—	71	1	no	—
225	#2230	—	71	1	no	—
226	#2230	D₇₁	1	1	yes	characteristic, complemented
227	#2155	—	71	2	no	—
228	C₂×#364	—	71	1	no	—
229	#2145	—	71	2	no	—
230	C₇₁	#33637	1	1	yes	characteristic, complemented, Sylow
231	C₂×#135	—	71	1	no	—
232	C₂×#131	—	142	1	no	—
233	#533	—	142	1	no	—
234	C₂×M₃₂	—	71	2	no	—
235	#500	—	142	1	no	—
236	#499	—	71	2	no	—
237	#499	—	142	1	no	—
238	#498	—	71	1	no	—
239	#498	C₂×D₇₁	1	1	yes	characteristic, complemented
240	#443	—	71	1	no	—
241	#443	—	71	1	no	—
242	#443	—	71	1	no	—
243	#443	—	142	1	no	—
244	#443	—	142	1	no	—
245	#443	C₂×D₇₁	1	1	yes	characteristic
246	C₂×#108	—	71	1	no	—
247	#427	—	71	2	no	—
248	#427	—	142	1	no	—
249	C₂×#104	—	142	1	no	—
250	C₂×C₄×C₈	—	71	1	no	—
251	#365	—	71	2	no	—
252	#365	—	71	2	no	—
253	#365	—	71	2	no	—
254	#365	C₂×D₇₁	1	2	yes	complemented
255	#364	—	71	2	no	—
256	#364	—	71	1	no	—
257	#364	C₂×D₇₁	1	1	yes	characteristic, complemented
258	#360	—	71	2	no	—
259	#360	—	71	2	no	—
260	#360	—	71	2	no	—
261	#360	C₂×D₇₁	1	2	yes	—
262	C₂×#41	—	142	1	no	—
263	#135	—	71	1	no	—
264	#135	—	71	1	no	—
265	#135	—	71	1	no	—
266	#135	—	142	1	no	—
267	#135	—	142	1	no	—
268	#135	C₂²×D₇₁	1	1	yes	characteristic
269	C₂×Q₁₆	—	71	1	no	—
270	C₂×SD₁₆	—	142	1	no	—
271	C₂×D₈	—	71	1	no	—
272	#131	—	2	1	no	—
273	#131	—	284	1	no	—
274	#131	—	284	1	no	—
275	#131	—	142	1	no	—
276	#131	—	142	1	no	—
277	#131	—	142	1	no	—
278	C₂×M₁₆	—	284	1	no	—
279	C₂×M₁₆	—	142	1	no	—
280	C₂²×C₈	—	284	1	no	—
281	C₂²×C₈	—	71	1	no	—
282	C₂²×C₈	—	71	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	142	1	no	—
285	#125	—	142	2	no	—
286	C₂²⋊Q₈	—	284	1	no	—
287	C₂²⋊Q₈	—	284	1	no	—
288	C₄×Q₈	—	284	1	no	—
289	C₄×Q₈	—	284	1	no	—
290	#117	—	142	2	no	—
291	C₂×C₄²	—	71	1	no	—
292	M₃₂	—	71	2	no	—
293	M₃₂	—	142	2	no	—
294	M₃₂	C₂²×D₇₁	1	2	yes	—
295	C₂×C₁₆	—	142	2	no	—
296	#108	—	71	1	no	—
297	#108	—	142	1	no	—
298	#108	C₂²×D₇₁	1	1	yes	characteristic
299	#107	—	142	2	no	—
300	#107	—	142	2	no	—
301	#106	—	2	1	no	—
302	#106	—	71	2	no	—
303	#106	—	142	1	no	—
304	#106	C₂²×D₇₁	1	2	yes	—
305	#104	—	2	1	no	—
306	#104	—	142	1	no	—
307	#104	—	142	1	no	—
308	#104	—	142	1	no	—
309	C₄×C₈	—	71	1	no	—
310	C₄×C₈	—	71	1	no	—
311	C₄×C₈	—	71	1	no	—
312	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
313	#41	—	2	1	no	—
314	#41	—	284	1	no	—
315	#41	—	284	1	no	—
316	#41	—	142	1	no	—
317	#41	—	142	1	no	—
318	#41	—	142	1	no	—
319	C₂×Q₈	—	4	1	no	—
320	C₂×Q₈	—	284	1	no	—
321	C₂×Q₈	—	142	1	no	—
322	C₂×D₄	—	284	1	no	—
323	C₂×D₄	—	142	1	no	—
324	C₂²×C₄	—	284	1	no	—
325	C₂²×C₄	—	71	1	no	—
326	C₂²×C₄	—	142	1	no	—
327	Q₁₆	—	71	1	no	—
328	Q₁₆	—	142	1	no	—
329	Q₁₆	Q₈×D₇₁	1	1	yes	characteristic
330	SD₁₆	—	2	1	no	—
331	SD₁₆	—	142	1	no	—
332	SD₁₆	—	142	1	no	—
333	SD₁₆	—	142	1	no	—
334	D₈	—	71	1	no	—
335	D₈	—	142	1	no	—
336	D₈	Q₈×D₇₁	1	1	yes	characteristic
337	M₁₆	—	2	1	no	—
338	M₁₆	—	4	1	no	—
339	M₁₆	—	284	1	no	—
340	M₁₆	—	284	1	no	—
341	M₁₆	—	284	1	no	—
342	M₁₆	—	284	1	no	—
343	M₁₆	—	142	1	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	—	284	1	no	—
346	C₂×C₈	—	284	1	no	—
347	C₂×C₈	—	284	1	no	—
348	C₂×C₈	—	284	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	—	71	1	no	—
356	C₂×C₈	—	71	1	no	—
357	C₂×C₈	—	71	1	no	—
358	C₂×C₈	—	71	1	no	—
359	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
360	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	—	284	1	no	—
364	C₄⋊C₄	—	284	2	no	—
365	C₄⋊C₄	—	284	2	no	—
366	C₄⋊C₄	—	142	2	no	—
367	C₂²⋊C₄	—	284	2	no	—
368	C₄²	—	284	2	no	—
369	C₄²	—	71	1	no	—
370	C₄²	—	142	1	no	—
371	C₄²	D₄×D₇₁	1	1	yes	characteristic
372	C₁₆	—	2	2	no	—
373	C₁₆	—	142	2	no	—
374	C₂³	—	284	1	no	—
375	C₂³	—	71	1	no	—
376	Q₈	—	2	1	no	—
377	Q₈	—	8	2	no	—
378	Q₈	—	284	1	no	—
379	Q₈	—	568	2	no	—
380	Q₈	—	142	1	no	—
381	D₄	—	2	1	no	—
382	D₄	—	4	1	no	—
383	D₄	—	284	1	no	—
384	D₄	—	284	1	no	—
385	D₄	—	284	1	no	—
386	D₄	—	284	1	no	—
387	D₄	—	142	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	284	2	no	—
392	C₂×C₄	—	284	1	no	—
393	C₂×C₄	—	284	1	no	—
394	C₂×C₄	—	284	1	no	—
395	C₂×C₄	—	284	1	no	—
396	C₂×C₄	—	284	2	no	—
397	C₂×C₄	—	71	1	no	—
398	C₂×C₄	—	71	1	no	—
399	C₂×C₄	—	71	1	no	—
400	C₂×C₄	—	71	1	no	—
401	C₂×C₄	—	71	1	no	—
402	C₂×C₄	—	142	1	no	—
403	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
404	C₈	—	4	1	no	—
405	C₈	—	284	1	no	—
406	C₈	—	71	1	no	—
407	C₈	—	71	1	no	—
408	C₈	—	71	1	no	—
409	C₈	—	71	1	no	—
410	C₈	SD₁₆×D₇₁	1	1	yes	characteristic
411	C₈	SD₁₆×D₇₁	1	1	yes	characteristic
412	C₈	C₂×Q₈×D₇₁	1	1	yes	characteristic
413	C₈	#41×D₇₁	1	1	yes	characteristic
414	C₂²	—	4	1	no	—
415	C₂²	—	284	1	no	—
416	C₂²	—	284	1	no	—
417	C₂²	—	568	2	no	—
418	C₂²	—	71	1	no	—
419	C₂²	—	71	1	no	—
420	C₂²	AGL(1,ℤ/8)×D₇₁	1	1	yes	characteristic
421	C₄	—	2	2	no	—
422	C₄	—	4	1	no	—
423	C₄	—	8	2	no	—
424	C₄	—	284	1	no	—
425	C₄	—	284	1	no	—
426	C₄	—	568	2	no	—
427	C₄	—	71	1	no	—
428	C₄	—	71	1	no	—
429	C₄	C₂²⋊Q₈×D₇₁	1	1	yes	characteristic
430	C₄	C₂×SD₁₆×D₇₁	1	1	yes	characteristic
431	C₂	—	2	1	no	—
432	C₂	—	8	1	no	—
433	C₂	—	568	1	no	—
434	C₂	—	142	1	no	—
435	C₂	—	142	1	no	—
436	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	#33637
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. #22598849	C₂	semidirect
3. #22590515	C₂	semidirect
4. #22590514	C₂	semidirect
5. #22590512	C₂	semidirect
6. #22590511	C₂	semidirect
7. #22590508	C₂	semidirect
8. #22590111	C₂	semidirect
9. #364×D₇₁	C₂	semidirect
11. C₇₁×#2230	C₂	semidirect
18. #17986399	C₂²	semidirect
19. #17986397	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
44. #14556151	Q₈	semidirect
48. #14556147	Q₈	semidirect
49. Q₁₆×D₇₁	Q₈	semidirect
51. D₈×D₇₁	Q₈	semidirect
226. #2230	D₇₁	semidirect
230. C₇₁	#33637	semidirect
239. #498	C₂×D₇₁	semidirect
254. #365	C₂×D₇₁	semidirect
257. #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
#22598849	2
#443×D₇₁	2
#22590515	2
#22590514	2
#22590512	2
#22590511	2
#22590508	2
#22590111	2
#364×D₇₁	2
#22590074	2
C₇₁×#2230	2
#33637	71