Subgroups — #32150912

Order 18176.

646 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22597257	C₂	1	1	yes	maximal, characteristic, complemented
2	#22597224	C₂	1	1	yes	maximal, characteristic, complemented
3	#22590239	C₂	1	4	yes	maximal, complemented
4	#22590232	C₂	1	4	yes	maximal, complemented
5	C₂×#17985822	C₂	1	1	yes	maximal, characteristic, complemented
6	#22590089	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#17985809	C₂	1	1	yes	maximal, characteristic, complemented
8	#22589944	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₁×#3414	C₂	1	1	yes	maximal, characteristic
10	#17986766	—	2	1	no	—
11	#17986482	—	2	1	no	—
12	C₂×#14556068	C₂²	1	1	yes	characteristic
13	#17986121	C₂²	1	4	yes	—
14	#17986116	—	2	2	no	—
15	#17986111	C₂²	1	2	yes	complemented
16	#17986106	C₂²	1	2	yes	complemented
17	SD₁₆×Dic₇₁	—	2	2	no	—
18	C₂×#14556064	C₂²	1	1	yes	characteristic
19	C₂×#14556060	C₂²	1	1	yes	characteristic
20	#17986016	—	2	1	no	—
21	#17986000	—	2	1	no	—
22	#17985954	C₂²	1	1	yes	characteristic
23	#17985822	C₂²	1	4	yes	complemented
24	#17985815	C₂²	1	2	yes	complemented
25	#17985812	C₂²	1	2	yes	complemented
26	#17985809	C₂²	1	4	yes	—
27	#17985776	C₂²	1	4	yes	complemented
28	C₂×#135×C₇₁	C₂²	1	1	yes	characteristic
29	C₂×#135×C₇₁	C₂²	1	1	yes	characteristic
30	#510×C₇₁	C₄	1	2	yes	complemented
31	#510×C₇₁	C₂²	1	2	yes	—
32	#509×C₇₁	C₄	1	2	yes	complemented
33	#509×C₇₁	C₂²	1	2	yes	—
34	#508×C₇₁	C₄	1	4	yes	complemented
35	C₂×M₃₂×C₇₁	C₂²	1	1	yes	characteristic
36	#14556135	—	2	4	no	—
37	#14556135	—	4	2	no	—
38	C₂×#11765849	—	2	1	no	—
39	C₂×#11765849	—	4	2	no	—
40	C₂×#11765849	D₄	1	1	yes	characteristic
41	Q₈×Dic₇₁	—	2	2	no	—
42	D₄×Dic₇₁	—	2	2	no	—
43	D₄×Dic₇₁	—	4	2	no	—
44	#14556087	—	4	1	no	—
45	#14556087	D₄	1	1	yes	characteristic
46	C₂×C₄⋊Dic₇₁	—	2	1	no	—
47	C₂×C₄⋊Dic₇₁	—	4	1	no	—
48	#14556068	—	2	1	no	—
49	#14556068	C₂³	1	2	yes	—
50	C₂×C₇₁⋊C₁₆	—	2	1	no	—
51	#14556064	—	2	1	no	—
52	#14556064	C₂³	1	2	yes	—
53	#14556060	—	2	1	no	—
54	#14556060	C₂³	1	2	yes	—
55	#14556055	—	2	4	no	—
56	#14556052	—	2	2	no	—
57	#14556049	—	2	2	no	—
58	#14556038	C₂³	1	2	yes	—
59	C₈×Dic₇₁	D₄	1	2	yes	—
60	C₂×#41×C₇₁	—	2	1	no	—
61	C₂×#41×C₇₁	—	2	1	no	—
62	#135×C₇₁	—	2	1	no	—
63	#135×C₇₁	—	2	1	no	—
64	#135×C₇₁	—	2	1	no	—
65	#135×C₇₁	—	2	1	no	—
66	#135×C₇₁	C₂×C₄	1	2	yes	—
67	#135×C₇₁	C₂×C₄	1	2	yes	—
68	#135×C₇₁	C₂×C₄	1	2	yes	complemented
69	#135×C₇₁	C₂³	1	2	yes	—
70	C₂×Q₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic, complemented
71	C₂×Q₁₆×C₇₁	C₂³	1	1	yes	characteristic
72	C₂×SD₁₆×C₇₁	—	2	1	no	—
73	C₂×SD₁₆×C₇₁	—	2	1	no	—
74	C₂×D₈×C₇₁	C₂×C₄	1	1	yes	characteristic, complemented
75	C₂×D₈×C₇₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
77	Q₃₂×C₇₁	C₂×C₄	1	4	yes	complemented
78	SD₃₂×C₇₁	C₂×C₄	1	4	yes	complemented
79	SD₃₂×C₇₁	C₂×C₄	1	4	yes	complemented
80	D₁₆×C₇₁	C₂×C₄	1	4	yes	complemented
81	M₃₂×C₇₁	C₂×C₄	1	2	yes	complemented
82	M₃₂×C₇₁	C₂³	1	2	yes	—
83	C₂×C₁₆×C₇₁	C₂×C₄	1	2	yes	complemented
84	C₂²×Dic₇₁	—	4	2	no	—
85	C₂²×Dic₇₁	—	4	1	no	—
86	#11765849	—	2	1	no	—
87	#11765849	—	2	1	no	—
88	#11765849	—	2	2	no	—
89	#11765849	—	4	4	no	—
90	#11765849	—	4	1	no	—
91	C₂×C₇₁⋊C₈	—	4	4	no	—
92	C₂×C₇₁⋊C₈	—	4	1	no	—
93	C₂×C₇₁⋊C₈	C₂×D₄	1	2	yes	—
94	C₄⋊Dic₇₁	—	2	1	no	—
95	C₄⋊Dic₇₁	—	2	2	no	—
96	C₄⋊Dic₇₁	—	4	2	no	—
97	C₄⋊Dic₇₁	—	4	1	no	—
98	C₂²⋊Dic₇₁	—	2	1	no	—
99	C₂²⋊Dic₇₁	—	4	2	no	—
100	C₄×Dic₇₁	—	4	2	no	—
101	C₄×Dic₇₁	C₂×D₄	1	2	yes	—
102	C₇₁⋊C₁₆	—	2	2	no	—
103	#41×C₇₁	—	2	2	no	—
104	#41×C₇₁	—	2	2	no	—
105	#41×C₇₁	—	2	2	no	—
106	#41×C₇₁	—	2	2	no	—
107	#41×C₇₁	—	4	1	no	—
108	#41×C₇₁	—	4	1	no	—
109	#41×C₇₁	—	4	1	no	—
110	#41×C₇₁	—	4	1	no	—
111	C₂×Q₈×C₇₁	—	2	1	no	—
112	C₂×Q₈×C₇₁	—	2	1	no	—
113	C₂×D₄×C₇₁	—	2	1	no	—
114	C₂×D₄×C₇₁	—	2	1	no	—
115	C₂×D₄×C₇₁	—	4	1	no	—
116	C₂×D₄×C₇₁	—	4	1	no	—
117	C₂²×C₄×C₇₁	—	4	1	no	—
118	C₂²×C₄×C₇₁	—	4	1	no	—
119	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
120	Q₁₆×C₇₁	—	2	1	no	—
121	Q₁₆×C₇₁	—	2	1	no	—
122	Q₁₆×C₇₁	C₂²×C₄	1	2	yes	—
123	Q₁₆×C₇₁	C₂²×C₄	1	2	yes	—
124	SD₁₆×C₇₁	—	2	2	no	—
125	SD₁₆×C₇₁	—	2	2	no	—
126	SD₁₆×C₇₁	—	2	2	no	—
127	SD₁₆×C₇₁	—	2	2	no	—
128	D₈×C₇₁	—	2	1	no	—
129	D₈×C₇₁	—	2	1	no	—
130	D₈×C₇₁	C₂²×C₄	1	2	yes	—
131	D₈×C₇₁	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
136	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
137	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
138	C₁₆×C₇₁	C₂²×C₄	1	4	yes	—
139	C₂³×C₇₁	—	4	1	no	—
140	C₂³×C₇₁	—	4	1	no	—
141	C₂³×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
142	Q₈×C₇₁	—	2	2	no	—
143	Q₈×C₇₁	—	2	2	no	—
144	Q₈×C₇₁	—	4	1	no	—
145	Q₈×C₇₁	—	4	1	no	—
146	D₄×C₇₁	—	2	2	no	—
147	D₄×C₇₁	—	2	2	no	—
148	D₄×C₇₁	—	4	2	no	—
149	D₄×C₇₁	—	4	2	no	—
150	D₄×C₇₁	—	4	2	no	—
151	D₄×C₇₁	—	4	2	no	—
152	D₄×C₇₁	—	4	1	no	—
153	D₄×C₇₁	—	4	1	no	—
154	C₂×C₄×C₇₁	—	4	1	no	—
155	C₂×C₄×C₇₁	—	4	1	no	—
156	C₂×C₄×C₇₁	—	4	2	no	—
157	C₂×C₄×C₇₁	—	4	2	no	—
158	C₂×C₄×C₇₁	—	4	2	no	—
159	C₂×C₄×C₇₁	—	4	2	no	—
160	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
166	C₂×Dic₇₁	—	2	2	no	—
167	C₂×Dic₇₁	—	4	2	no	—
168	C₂×Dic₇₁	—	16	2	no	—
169	C₂×Dic₇₁	—	16	1	no	—
170	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
171	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
172	C₈×C₇₁	C₂³×C₄	1	1	yes	characteristic
173	C₈×C₇₁	C₂×#41	1	1	yes	characteristic
174	C₇₁⋊C₈	—	2	2	no	—
175	C₇₁⋊C₈	—	4	2	no	—
176	C₂²×C₇₁	—	4	1	no	—
177	C₂²×C₇₁	—	4	2	no	—
178	C₂²×C₇₁	—	4	2	no	—
179	C₂²×C₇₁	—	8	1	no	—
180	C₂²×C₇₁	—	8	1	no	—
181	C₂²×C₇₁	—	16	1	no	—
182	C₂²×C₇₁	#442	1	1	yes	characteristic
183	C₂²×C₇₁	#442	1	1	yes	characteristic
184	C₂²×C₇₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₄×C₇₁	—	4	2	no	—
186	C₄×C₇₁	—	4	2	no	—
187	C₄×C₇₁	#442	1	1	yes	characteristic
188	C₄×C₇₁	#442	1	1	yes	characteristic
189	C₄×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
190	C₄×C₇₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
191	Dic₇₁	—	4	2	no	—
192	Dic₇₁	—	8	2	no	—
193	#33469	—	71	1	no	maximal, Sylow
194	C₂×C₇₁	—	2	1	no	—
195	C₂×C₇₁	—	2	1	no	—
196	C₂×C₇₁	—	2	1	no	—
197	C₂×C₇₁	—	8	2	no	—
198	C₂×C₇₁	—	8	2	no	—
199	C₂×C₇₁	C₂×#442	1	1	yes	characteristic
200	#3414	D₇₁	1	1	yes	characteristic
201	#2957	—	71	1	no	—
202	#2952	—	71	1	no	—
203	AGL(1,ℤ/16)	—	71	4	no	—
204	#2180	—	71	4	no	—
205	C₂×#365	—	71	1	no	—
206	#2148	—	71	1	no	—
207	C₂×#360	—	71	1	no	—
208	#2110	—	71	1	no	—
209	C₇₁	#33469	1	1	yes	characteristic, complemented, Sylow
210	C₂×#135	C₂×D₇₁	1	1	yes	characteristic
211	C₂×#135	C₂×D₇₁	1	1	yes	characteristic
212	#568	—	142	1	no	—
213	#520	—	142	1	no	—
214	#510	Dic₇₁	1	2	yes	complemented
215	#510	C₂×D₇₁	1	2	yes	—
216	#509	Dic₇₁	1	2	yes	complemented
217	#509	C₂×D₇₁	1	2	yes	—
218	#508	Dic₇₁	1	4	yes	complemented
219	C₂×M₃₂	—	71	1	no	—
220	C₂×M₃₂	C₂×D₇₁	1	1	yes	characteristic
221	#444	—	71	4	no	—
222	#443	—	142	2	no	—
223	#442	—	71	2	no	—
224	#441	—	71	2	no	—
225	C₄×SD₁₆	—	142	2	no	—
226	C₂×#108	—	71	1	no	—
227	C₂×#106	—	71	1	no	—
228	#421	—	142	1	no	—
229	#417	—	142	1	no	—
230	#405	—	71	1	no	—
231	#365	—	71	4	no	—
232	#362	—	71	2	no	—
233	#361	—	71	2	no	—
234	#360	—	71	4	no	—
235	#347	—	71	4	no	—
236	C₂×#41	—	2	1	no	—
237	C₂×#41	—	2	1	no	—
238	#135	—	2	1	no	—
239	#135	—	2	1	no	—
240	#135	—	2	1	no	—
241	#135	—	2	1	no	—
242	#135	C₂×Dic₇₁	1	2	yes	—
243	#135	C₂×Dic₇₁	1	2	yes	—
244	#135	C₂×Dic₇₁	1	2	yes	complemented
245	#135	C₂²×D₇₁	1	2	yes	—
246	C₂×Q₁₆	C₂×Dic₇₁	1	1	yes	characteristic, complemented
247	C₂×Q₁₆	C₂²×D₇₁	1	1	yes	characteristic
248	C₂×SD₁₆	—	2	1	no	—
249	C₂×SD₁₆	—	2	1	no	—
250	C₂×D₈	C₂×Dic₇₁	1	1	yes	characteristic, complemented
251	C₂×D₈	C₂²×D₇₁	1	1	yes	characteristic
252	#131	—	284	2	no	—
253	#131	—	142	4	no	—
254	C₂×M₁₆	—	284	2	no	—
255	C₂×M₁₆	—	71	1	no	—
256	C₂×M₁₆	—	142	1	no	—
257	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
258	C₄×Q₈	—	142	2	no	—
259	C₄×D₄	—	284	2	no	—
260	C₄×D₄	—	142	2	no	—
261	#117	—	284	1	no	—
262	#117	—	71	1	no	—
263	C₂×C₄⋊C₄	—	284	1	no	—
264	C₂×C₄⋊C₄	—	142	1	no	—
265	Q₃₂	C₂×Dic₇₁	1	4	yes	complemented
266	SD₃₂	C₂×Dic₇₁	1	4	yes	complemented
267	SD₃₂	C₂×Dic₇₁	1	4	yes	complemented
268	D₁₆	C₂×Dic₇₁	1	4	yes	complemented
269	M₃₂	—	71	2	no	—
270	M₃₂	—	142	1	no	—
271	M₃₂	C₂×Dic₇₁	1	2	yes	complemented
272	M₃₂	C₂²×D₇₁	1	2	yes	—
273	C₂×C₁₆	—	142	1	no	—
274	C₂×C₁₆	C₂×Dic₇₁	1	2	yes	complemented
275	#108	—	71	2	no	—
276	#108	—	142	1	no	—
277	#106	—	71	2	no	—
278	#106	—	142	1	no	—
279	#104	—	142	4	no	—
280	#103	—	142	2	no	—
281	#102	—	142	2	no	—
282	#97	—	71	2	no	—
283	C₄×C₈	—	71	2	no	—
284	#41	—	2	2	no	—
285	#41	—	2	2	no	—
286	#41	—	2	2	no	—
287	#41	—	2	2	no	—
288	#41	—	4	1	no	—
289	#41	—	4	1	no	—
290	#41	—	4	1	no	—
291	#41	—	4	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	284	1	no	—
301	C₂²×C₄	—	284	2	no	—
302	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
303	Q₁₆	—	2	1	no	—
304	Q₁₆	—	2	1	no	—
305	Q₁₆	C₂²×Dic₇₁	1	2	yes	—
306	Q₁₆	C₂²×Dic₇₁	1	2	yes	—
307	SD₁₆	—	2	2	no	—
308	SD₁₆	—	2	2	no	—
309	SD₁₆	—	2	2	no	—
310	SD₁₆	—	2	2	no	—
311	D₈	—	2	1	no	—
312	D₈	—	2	1	no	—
313	D₈	C₂²×Dic₇₁	1	2	yes	—
314	D₈	C₂²×Dic₇₁	1	2	yes	—
315	M₁₆	—	284	1	no	—
316	M₁₆	—	284	4	no	—
317	M₁₆	—	142	2	no	—
318	M₁₆	—	142	1	no	—
319	M₁₆	—	142	1	no	—
320	C₂×C₈	—	284	1	no	—
321	C₂×C₈	—	284	4	no	—
322	C₂×C₈	—	71	2	no	—
323	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
324	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
325	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
326	C₂×C₈	#11765864	1	1	yes	characteristic
327	C₂×C₈	#11765864	1	1	yes	characteristic
328	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
329	C₄⋊C₄	—	284	2	no	—
330	C₄⋊C₄	—	284	1	no	—
331	C₄⋊C₄	—	142	2	no	—
332	C₄⋊C₄	—	142	1	no	—
333	C₂²⋊C₄	—	284	2	no	—
334	C₂²⋊C₄	—	142	1	no	—
335	C₄²	—	284	2	no	—
336	C₄²	—	71	2	no	—
337	C₁₆	—	142	2	no	—
338	C₁₆	C₂²×Dic₇₁	1	4	yes	—
339	C₂³	—	4	1	no	—
340	C₂³	—	4	1	no	—
341	C₂³	#14556152	1	1	yes	characteristic
342	Q₈	—	2	2	no	—
343	Q₈	—	2	2	no	—
344	Q₈	—	4	1	no	—
345	Q₈	—	4	1	no	—
346	D₄	—	2	2	no	—
347	D₄	—	2	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	1	no	—
353	D₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	284	2	no	—
361	C₂×C₄	—	1136	2	no	—
362	C₂×C₄	—	1136	1	no	—
363	C₂×C₄	—	142	2	no	—
364	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
365	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
366	C₂×C₄	#14556152	1	1	yes	characteristic
367	C₂×C₄	#14556152	1	1	yes	characteristic
368	C₂×C₄	#14556152	1	1	yes	characteristic
369	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
370	C₈	—	284	2	no	—
371	C₈	—	142	2	no	—
372	C₈	D₄×Dic₇₁	1	1	yes	characteristic
373	C₈	D₄×Dic₇₁	1	1	yes	characteristic
374	C₈	C₂³×Dic₇₁	1	1	yes	characteristic
375	C₈	C₂×#11765864	1	1	yes	characteristic
376	C₂²	—	4	1	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	8	1	no	—
380	C₂²	—	8	1	no	—
381	C₂²	—	16	1	no	—
382	C₂²	#17986111	1	1	yes	characteristic
383	C₂²	#17986111	1	1	yes	characteristic
384	C₂²	C₂×#14556152	1	1	yes	characteristic
385	C₄	—	4	2	no	—
386	C₄	—	4	2	no	—
387	C₄	—	284	2	no	—
388	C₄	—	568	2	no	—
389	C₄	#17986111	1	1	yes	characteristic
390	C₄	#17986111	1	1	yes	characteristic
391	C₄	C₂×D₄×Dic₇₁	1	1	yes	characteristic
392	C₄	C₂×#14556152	1	1	yes	characteristic
393	C₂	—	2	1	no	—
394	C₂	—	2	1	no	—
395	C₂	—	2	1	no	—
396	C₂	—	8	2	no	—
397	C₂	—	8	2	no	—
398	C₂	C₂×#17986111	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#17986111
commutator	C₈×C₇₁	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₇₁
Fitting, prime radical	C₇₁×#3414	C₂
socle	C₂×C₇₁	C₂×#442
cosocle	C₂×C₈×C₇₁	C₂⁴
hypercenter	#3414	D₇₁
hypocenter	C₇₁	#33469
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #3414

Complements

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

N	H ≅ G/N	type
1. #22597257	C₂	semidirect
2. #22597224	C₂	semidirect
3. #22590239	C₂	semidirect
4. #22590232	C₂	semidirect
5. C₂×#17985822	C₂	semidirect
6. #22590089	C₂	semidirect
7. C₂×#17985809	C₂	semidirect
8. #22589944	C₂	semidirect
15. #17986111	C₂²	semidirect
16. #17986106	C₂²	semidirect
23. #17985822	C₂²	semidirect
24. #17985815	C₂²	semidirect
25. #17985812	C₂²	semidirect
27. #17985776	C₂²	semidirect
30. #510×C₇₁	C₄	semidirect
32. #509×C₇₁	C₄	semidirect
34. #508×C₇₁	C₄	semidirect
68. #135×C₇₁	C₂×C₄	semidirect
70. C₂×Q₁₆×C₇₁	C₂×C₄	semidirect
74. C₂×D₈×C₇₁	C₂×C₄	semidirect
77. Q₃₂×C₇₁	C₂×C₄	semidirect
78. SD₃₂×C₇₁	C₂×C₄	semidirect
79. SD₃₂×C₇₁	C₂×C₄	semidirect
80. D₁₆×C₇₁	C₂×C₄	semidirect
81. M₃₂×C₇₁	C₂×C₄	semidirect
83. C₂×C₁₆×C₇₁	C₂×C₄	semidirect
209. C₇₁	#33469	semidirect
214. #510	Dic₇₁	semidirect
216. #509	Dic₇₁	semidirect
218. #508	Dic₇₁	semidirect
244. #135	C₂×Dic₇₁	semidirect
246. C₂×Q₁₆	C₂×Dic₇₁	semidirect
250. C₂×D₈	C₂×Dic₇₁	semidirect
265. Q₃₂	C₂×Dic₇₁	semidirect
266. SD₃₂	C₂×Dic₇₁	semidirect
267. SD₃₂	C₂×Dic₇₁	semidirect
268. D₁₆	C₂×Dic₇₁	semidirect
271. M₃₂	C₂×Dic₇₁	semidirect
274. C₂×C₁₆	C₂×Dic₇₁	semidirect

Maximal subgroups

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

subgroup	index
#22597257	2
#22597224	2
#22590239	2
#22590232	2
C₂×#17985822	2
#22590089	2
C₂×#17985809	2
#22589944	2
C₇₁×#3414	2
#33469	71