Subgroups — #32097405

Order 18176.

612 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22598852	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#17986116	C₂	1	1	yes	maximal, characteristic
3	#22589514	C₂	1	2	yes	maximal, complemented
4	#22589510	C₂	1	2	yes	maximal, complemented
5	#22589239	C₂	1	1	yes	maximal, characteristic
6	#22588464	C₂	1	1	yes	maximal, characteristic, complemented
7	#22588463	C₂	1	1	yes	maximal, characteristic, complemented
8	#22588392	C₂	1	2	yes	maximal, complemented
9	#22588384	C₂	1	2	yes	maximal, complemented
10	#22588220	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#1976	C₂	1	1	yes	maximal, characteristic
12	C₂×#14556135	C₂²	1	2	yes	—
13	#17986552	C₂²	1	2	yes	—
14	#17986403	—	2	1	no	—
15	#17986400	—	2	1	no	—
16	#17986399	—	2	1	no	—
17	#17986396	—	2	1	no	—
18	#17986116	—	2	1	no	—
19	#17986116	—	2	1	no	—
20	#17986116	—	2	1	no	—
21	#17986116	—	2	1	no	—
22	C₂×#14556064	C₂²	1	1	yes	characteristic
23	C₂×#14556063	C₂²	1	1	yes	characteristic
24	#17986037	C₂²	1	1	yes	characteristic
25	#17986035	C₂²	1	1	yes	characteristic
26	#17986035	C₂²	1	2	yes	—
27	#17986016	C₂²	1	2	yes	—
28	C₂×#14556055	C₂²	1	2	yes	—
29	#17985973	C₂²	1	2	yes	—
30	#17985954	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₇₁	C₂²	1	1	yes	characteristic
32	#17985770	C₂²	1	2	yes	—
33	#17985769	C₂²	1	2	yes	—
34	#17985760	C₂²	1	1	yes	characteristic
35	#17985758	C₂²	1	1	yes	characteristic
36	#17985755	C₂²	1	2	yes	—
37	#17985755	C₂²	1	2	yes	—
38	C₂×#135×C₇₁	C₂²	1	1	yes	characteristic
39	#427×C₇₁	C₂²	1	1	yes	characteristic
40	#421×C₇₁	C₂²	1	2	yes	—
41	#410×C₇₁	C₂²	1	2	yes	—
42	#405×C₇₁	C₂²	1	1	yes	characteristic
43	#14556135	—	2	2	no	—
44	#14556135	—	2	2	no	—
45	#14556135	—	2	2	no	—
46	#14556135	—	2	2	no	—
47	C₂×#11765849	—	2	2	no	—
48	C₂×#11765849	C₂³	1	1	yes	characteristic
49	C₂×#11765849	C₂³	1	2	yes	—
50	C₂²×C₇₁⋊C₈	—	2	2	no	—
51	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
52	#14556127	—	2	2	no	—
53	#14556119	—	2	2	no	—
54	#14556105	—	4	2	no	—
55	C₄×Dic₁₄₂	—	4	2	no	—
56	#14556087	C₂³	1	1	yes	characteristic
57	#14556087	C₂³	1	2	yes	—
58	C₂×C₄×Dic₇₁	C₂³	1	1	yes	characteristic
59	#14556064	—	2	1	no	—
60	#14556064	—	2	1	no	—
61	#14556063	—	2	1	no	—
62	#14556063	—	2	1	no	—
63	#14556062	—	2	1	no	—
64	#14556061	—	2	2	no	—
65	#14556061	—	2	1	no	—
66	#14556060	—	2	1	no	—
67	#14556059	—	2	2	no	—
68	#14556059	—	2	1	no	—
69	#14556055	—	2	2	no	—
70	#14556055	—	2	2	no	—
71	#14556055	—	4	2	no	—
72	#14556043	—	4	2	no	—
73	#14556038	—	2	1	no	—
74	C₈×Dic₇₁	—	2	1	no	—
75	C₈×Dic₇₁	D₄	1	1	yes	characteristic
76	C₈×Dic₇₁	D₄	1	1	yes	characteristic
77	C₈×Dic₇₁	D₄	1	1	yes	characteristic
78	C₈×Dic₇₁	D₄	1	1	yes	characteristic
79	C₂×#41×C₇₁	C₂³	1	2	yes	—
80	#135×C₇₁	—	2	1	no	—
81	#135×C₇₁	—	2	1	no	—
82	#135×C₇₁	—	2	1	no	—
83	#135×C₇₁	—	2	1	no	—
84	C₂×Q₁₆×C₇₁	Q₈	1	1	yes	characteristic, complemented
85	C₂×SD₁₆×C₇₁	Q₈	1	2	yes	complemented
86	C₂×D₈×C₇₁	Q₈	1	1	yes	characteristic, complemented
87	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
89	#117×C₇₁	C₂³	1	1	yes	characteristic
90	#117×C₇₁	C₂³	1	2	yes	—
91	#107×C₇₁	—	2	1	no	—
92	#106×C₇₁	—	2	1	no	—
93	#104×C₇₁	—	4	2	no	—
94	#99×C₇₁	—	4	2	no	—
95	#97×C₇₁	—	2	1	no	—
96	C₄×C₈×C₇₁	—	2	1	no	—
97	C₂×Dic₁₄₂	—	4	2	no	—
98	C₂²×Dic₇₁	—	2	1	no	—
99	#11765849	—	2	2	no	—
100	#11765849	—	2	1	no	—
101	#11765849	—	2	2	no	—
102	#11765849	—	2	1	no	—
103	#11765849	—	4	2	no	—
104	#11765849	—	4	2	no	—
105	C₂×C₇₁⋊C₈	—	2	1	no	—
106	C₂×C₇₁⋊C₈	—	2	2	no	—
107	C₂×C₇₁⋊C₈	—	4	2	no	—
108	C₂×C₇₁⋊C₈	—	4	2	no	—
109	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
110	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
111	C₂×C₇₁⋊C₈	#41	1	1	yes	characteristic
112	C₂×C₇₁⋊C₈	#41	1	1	yes	characteristic
113	C₂×C₇₁⋊C₈	#41	1	1	yes	characteristic
114	C₂×C₇₁⋊C₈	#41	1	1	yes	characteristic
115	C₄⋊Dic₇₁	—	2	2	no	—
116	C₄⋊Dic₇₁	—	2	1	no	—
117	C₄⋊Dic₇₁	—	4	2	no	—
118	Dic₇₁⋊C₄	—	4	2	no	—
119	Dic₇₁⋊C₄	—	4	2	no	—
120	C₂²⋊Dic₇₁	—	2	1	no	—
121	C₂²⋊Dic₇₁	—	2	2	no	—
122	C₄×Dic₇₁	—	2	1	no	—
123	C₄×Dic₇₁	—	2	1	no	—
124	C₄×Dic₇₁	—	2	2	no	—
125	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
126	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
127	#41×C₇₁	—	2	2	no	—
128	#41×C₇₁	—	2	2	no	—
129	#41×C₇₁	—	2	2	no	—
130	#41×C₇₁	—	2	2	no	—
131	C₂×Q₈×C₇₁	C₂×Q₈	1	2	yes	—
132	C₂×D₄×C₇₁	—	2	2	no	—
133	C₂×D₄×C₇₁	C₂×Q₈	1	2	yes	—
134	C₂²×C₄×C₇₁	—	2	2	no	—
135	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
136	Q₁₆×C₇₁	—	2	1	no	—
137	Q₁₆×C₇₁	—	2	1	no	—
138	SD₁₆×C₇₁	—	2	2	no	—
139	SD₁₆×C₇₁	—	2	2	no	—
140	D₈×C₇₁	—	2	1	no	—
141	D₈×C₇₁	—	2	1	no	—
142	M₁₆×C₇₁	—	2	1	no	—
143	M₁₆×C₇₁	—	2	1	no	—
144	C₂×C₈×C₇₁	—	2	1	no	—
145	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₇₁	C₂×Q₈	1	1	yes	characteristic
148	C₂×C₈×C₇₁	C₂×Q₈	1	1	yes	characteristic
149	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
150	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
151	C₄⋊C₄×C₇₁	—	2	2	no	—
152	C₄⋊C₄×C₇₁	—	2	1	no	—
153	C₂²⋊C₄×C₇₁	—	2	1	no	—
154	C₂²⋊C₄×C₇₁	—	2	2	no	—
155	C₄²×C₇₁	—	2	1	no	—
156	C₄²×C₇₁	—	2	2	no	—
157	C₂³×C₇₁	—	2	2	no	—
158	C₂³×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
159	Q₈×C₇₁	—	2	2	no	—
160	Q₈×C₇₁	—	2	2	no	—
161	D₄×C₇₁	—	2	2	no	—
162	D₄×C₇₁	—	2	2	no	—
163	D₄×C₇₁	—	4	2	no	—
164	D₄×C₇₁	—	4	2	no	—
165	C₂×C₄×C₇₁	—	2	2	no	—
166	C₂×C₄×C₇₁	—	4	2	no	—
167	C₂×C₄×C₇₁	—	4	2	no	—
168	C₂×C₄×C₇₁	—	4	2	no	—
169	C₂×C₄×C₇₁	—	4	1	no	—
170	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₇₁	C₂²×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×Dic₇₁	—	2	1	no	—
177	C₂×Dic₇₁	—	2	1	no	—
178	C₂×Dic₇₁	—	4	2	no	—
179	C₂×Dic₇₁	—	4	2	no	—
180	C₂×Dic₇₁	—	4	1	no	—
181	Dic₁₄₂	—	8	4	no	—
182	C₈×C₇₁	—	4	1	no	—
183	C₈×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
184	C₈×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
185	C₈×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
186	C₈×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
187	C₇₁⋊C₈	—	4	2	no	—
188	C₇₁⋊C₈	—	4	1	no	—
189	C₇₁⋊C₈	#124	1	1	yes	characteristic
190	C₇₁⋊C₈	#124	1	1	yes	characteristic
191	C₇₁⋊C₈	#124	1	1	yes	characteristic
192	C₇₁⋊C₈	#124	1	1	yes	characteristic
193	C₂²×C₇₁	—	4	1	no	—
194	C₂²×C₇₁	—	4	2	no	—
195	C₂²×C₇₁	—	8	2	no	—
196	C₂²×C₇₁	#535	1	1	yes	characteristic
197	C₂²×C₇₁	#554	1	1	yes	characteristic
198	C₂²×C₇₁	#555	1	1	yes	characteristic
199	C₄×C₇₁	—	4	2	no	—
200	C₄×C₇₁	—	8	2	no	—
201	C₄×C₇₁	—	8	1	no	—
202	C₄×C₇₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
203	C₄×C₇₁	C₂×#124	1	1	yes	characteristic
204	C₄×C₇₁	#554	1	1	yes	characteristic
205	C₄×C₇₁	#555	1	1	yes	characteristic
206	Dic₇₁	—	2	2	no	—
207	Dic₇₁	—	4	1	no	—
208	Dic₇₁	—	8	2	no	—
209	Dic₇₁	—	8	1	no	—
210	#29154	—	71	1	no	maximal, Sylow
211	C₂×C₇₁	—	2	1	no	—
212	C₂×C₇₁	—	2	1	no	—
213	C₂×C₇₁	—	2	1	no	—
214	C₂×C₇₁	—	8	2	no	—
215	C₂×C₇₁	#2563	1	1	yes	characteristic
216	#3160	—	71	1	no	—
217	C₂×#443	—	71	1	no	—
218	#2031	—	71	2	no	—
219	#2031	—	71	2	no	—
220	#1976	—	71	1	no	—
221	#1976	D₇₁	1	1	yes	characteristic
222	#1833	—	71	1	no	—
223	#1833	—	71	1	no	—
224	#1814	—	71	2	no	—
225	#1812	—	71	2	no	—
226	#1772	—	71	1	no	—
227	C₇₁	#29154	1	1	yes	characteristic, complemented, Sylow
228	C₂×#135	C₂×D₇₁	1	1	yes	characteristic
229	C₂×#131	—	71	2	no	—
230	#533	—	71	2	no	—
231	#500	—	142	1	no	—
232	#499	—	142	1	no	—
233	#499	—	142	1	no	—
234	#498	—	142	1	no	—
235	#443	—	142	1	no	—
236	#443	—	142	1	no	—
237	#443	—	142	1	no	—
238	#443	—	142	1	no	—
239	C₂×#108	—	71	1	no	—
240	C₂×#108	—	71	1	no	—
241	#427	—	71	1	no	—
242	#427	—	71	1	no	—
243	#427	—	71	2	no	—
244	#427	C₂×D₇₁	1	1	yes	characteristic
245	#421	—	71	2	no	—
246	#421	C₂×D₇₁	1	2	yes	—
247	C₂×#104	—	71	2	no	—
248	#410	—	71	2	no	—
249	#410	C₂×D₇₁	1	2	yes	—
250	#405	—	71	1	no	—
251	#405	C₂×D₇₁	1	1	yes	characteristic
252	C₂×C₄×C₈	—	71	1	no	—
253	#344	—	71	2	no	—
254	#344	—	71	2	no	—
255	#339	—	71	1	no	—
256	#339	—	71	1	no	—
257	H(3,ℤ/4)	—	71	2	no	—
258	H(3,ℤ/4)	—	71	2	no	—
259	C₂×#41	C₂²×D₇₁	1	2	yes	—
260	#135	—	2	1	no	—
261	#135	—	2	1	no	—
262	#135	—	2	1	no	—
263	#135	—	2	1	no	—
264	C₂×Q₁₆	Dic₁₄₂	1	1	yes	characteristic, complemented
265	C₂×SD₁₆	Dic₁₄₂	1	2	yes	complemented
266	C₂×D₈	Dic₁₄₂	1	1	yes	characteristic, complemented
267	#131	—	142	2	no	—
268	#131	—	142	2	no	—
269	#131	—	142	2	no	—
270	#131	—	142	2	no	—
271	C₂×M₁₆	—	71	2	no	—
272	C₂×M₁₆	—	71	1	no	—
273	C₂×M₁₆	—	142	2	no	—
274	C₂×M₁₆	C₂²×D₇₁	1	1	yes	characteristic
275	C₂²×C₈	—	71	1	no	—
276	C₂²×C₈	—	142	2	no	—
277	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
278	C₄⋊Q₈	—	142	2	no	—
279	#125	—	142	2	no	—
280	C₂²⋊Q₈	—	284	2	no	—
281	C₄×Q₈	—	284	2	no	—
282	#117	—	71	2	no	—
283	#117	—	71	1	no	—
284	#117	C₂²×D₇₁	1	2	yes	—
285	#117	C₂²×D₇₁	1	1	yes	characteristic
286	C₂×C₄²	—	71	1	no	—
287	#108	—	142	1	no	—
288	#108	—	142	1	no	—
289	#108	—	142	1	no	—
290	#108	—	142	1	no	—
291	#107	—	2	1	no	—
292	#107	—	142	1	no	—
293	#107	—	142	2	no	—
294	#107	—	142	1	no	—
295	#106	—	2	1	no	—
296	#106	—	142	1	no	—
297	#106	—	142	2	no	—
298	#106	—	142	1	no	—
299	#104	—	4	2	no	—
300	#104	—	284	2	no	—
301	#104	—	142	2	no	—
302	#104	—	142	2	no	—
303	#99	—	4	2	no	—
304	#99	—	284	2	no	—
305	#97	—	2	1	no	—
306	#97	—	142	1	no	—
307	C₄×C₈	—	2	1	no	—
308	C₄×C₈	—	71	1	no	—
309	C₄×C₈	—	71	1	no	—
310	C₄×C₈	—	71	1	no	—
311	C₄×C₈	—	71	1	no	—
312	C₄×C₈	—	142	1	no	—
313	#41	—	2	2	no	—
314	#41	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	C₂×Q₈	—	284	2	no	—
318	C₂×Q₈	C₂×Dic₁₄₂	1	2	yes	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	C₂×Dic₁₄₂	1	2	yes	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	142	1	no	—
323	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
324	Q₁₆	—	2	1	no	—
325	Q₁₆	—	2	1	no	—
326	SD₁₆	—	2	2	no	—
327	SD₁₆	—	2	2	no	—
328	D₈	—	2	1	no	—
329	D₈	—	2	1	no	—
330	M₁₆	—	2	1	no	—
331	M₁₆	—	2	1	no	—
332	M₁₆	—	284	2	no	—
333	M₁₆	—	284	2	no	—
334	M₁₆	—	142	2	no	—
335	M₁₆	—	142	1	no	—
336	M₁₆	—	142	2	no	—
337	M₁₆	—	142	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	284	2	no	—
340	C₂×C₈	—	284	2	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	—	142	2	no	—
348	C₂×C₈	—	142	1	no	—
349	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
350	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
351	C₂×C₈	C₂×Dic₁₄₂	1	1	yes	characteristic
352	C₂×C₈	C₂×Dic₁₄₂	1	1	yes	characteristic
353	C₂×C₈	#11765864	1	1	yes	characteristic
354	C₂×C₈	#11765864	1	1	yes	characteristic
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	284	2	no	—
358	C₄⋊C₄	—	284	2	no	—
359	C₄⋊C₄	—	284	2	no	—
360	C₄⋊C₄	—	142	2	no	—
361	C₄⋊C₄	—	142	1	no	—
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₂²⋊C₄	—	142	1	no	—
365	C₂²⋊C₄	—	142	2	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	71	1	no	—
369	C₄²	—	71	1	no	—
370	C₄²	—	142	1	no	—
371	C₄²	—	142	2	no	—
372	C₄²	—	142	1	no	—
373	C₂³	—	2	2	no	—
374	C₂³	#14556173	1	1	yes	characteristic
375	Q₈	—	2	2	no	—
376	Q₈	—	2	2	no	—
377	Q₈	—	568	4	no	—
378	D₄	—	2	2	no	—
379	D₄	—	2	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	284	2	no	—
388	C₂×C₄	—	284	2	no	—
389	C₂×C₄	—	284	1	no	—
390	C₂×C₄	—	142	1	no	—
391	C₂×C₄	—	142	1	no	—
392	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
393	C₂×C₄	C₂²×Dic₁₄₂	1	1	yes	characteristic
394	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
395	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
396	C₂×C₄	C₂×#11765864	1	1	yes	characteristic
397	C₂×C₄	#14556173	1	1	yes	characteristic
398	C₈	—	4	1	no	—
399	C₈	—	284	1	no	—
400	C₈	—	284	2	no	—
401	C₈	—	71	1	no	—
402	C₈	—	71	1	no	—
403	C₈	—	71	1	no	—
404	C₈	—	71	1	no	—
405	C₈	#14556105	1	1	yes	characteristic
406	C₈	#14556105	1	1	yes	characteristic
407	C₈	#14556105	1	1	yes	characteristic
408	C₈	#14556105	1	1	yes	characteristic
409	C₂²	—	4	1	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	#17986562	1	1	yes	characteristic
413	C₂²	#17986708	1	1	yes	characteristic
414	C₂²	#17986713	1	1	yes	characteristic
415	C₄	—	4	2	no	—
416	C₄	—	8	2	no	—
417	C₄	—	8	1	no	—
418	C₄	—	284	1	no	—
419	C₄	—	568	2	no	—
420	C₄	—	568	1	no	—
421	C₄	—	142	2	no	—
422	C₄	C₂×#14556105	1	1	yes	characteristic
423	C₄	#124×D₇₁	1	1	yes	characteristic
424	C₄	#17986708	1	1	yes	characteristic
425	C₄	#17986713	1	1	yes	characteristic
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	8	2	no	—
430	C₂	#22593511	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#17986713
commutator, cosocle	C₂²×C₄×C₇₁	C₂⁴
Frattini	C₂²×C₄	C₂³×D₇₁
Fitting	C₇₁×#1976	C₂
socle	C₂×C₇₁	#2563
prime radical	C₂×#135×C₇₁	C₂²
hypercenter	#1976	D₇₁
hypocenter	C₇₁	#29154
LCS	G ▷ C₂²×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1976

Complements

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

N	H ≅ G/N	type
1. #22598852	C₂	semidirect
3. #22589514	C₂	semidirect
4. #22589510	C₂	semidirect
6. #22588464	C₂	semidirect
7. #22588463	C₂	semidirect
8. #22588392	C₂	semidirect
9. #22588384	C₂	semidirect
10. #22588220	C₂	semidirect
84. C₂×Q₁₆×C₇₁	Q₈	semidirect
85. C₂×SD₁₆×C₇₁	Q₈	semidirect
86. C₂×D₈×C₇₁	Q₈	semidirect
227. C₇₁	#29154	semidirect
264. C₂×Q₁₆	Dic₁₄₂	semidirect
265. C₂×SD₁₆	Dic₁₄₂	semidirect
266. C₂×D₈	Dic₁₄₂	semidirect

Maximal subgroups

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

subgroup	index
#22598852	2
C₂×#17986116	2
#22589514	2
#22589510	2
#22589239	2
#22588464	2
#22588463	2
#22588392	2
#22588384	2
#22588220	2
C₇₁×#1976	2
#29154	71