Subgroups — #29649494

Order 15616.

714 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21454929	C₂	1	2	yes	maximal, complemented
2	C₄×#14519800	C₂	1	1	yes	maximal, characteristic
3	#21444634	C₂	1	2	yes	maximal, complemented
4	#21444629	C₂	1	2	yes	maximal, complemented
5	Q₁₆×#92418	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×D₄₈₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#21444613	C₂	1	1	yes	maximal, characteristic, complemented
8	#335×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#21444205	C₂	1	2	yes	maximal, complemented
10	#21444101	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14519800	C₄	1	1	yes	characteristic
13	C₄×#11758226	C₂²	1	2	yes	—
14	Q₈×#92418	C₂²	1	2	yes	—
15	Q₁₆×Dic₆₁	C₄	1	1	yes	characteristic
16	C₄×#11758201	C₂²	1	2	yes	—
17	#16839847	C₄	1	2	yes	—
18	C₄×D₄₈₈	C₂²	1	1	yes	characteristic
19	#16839844	C₄	1	1	yes	characteristic
20	C₈×D₂₄₄	—	2	2	no	—
21	C₈×D₂₄₄	C₂²	1	2	yes	—
22	#16839827	—	2	2	no	—
23	#16839827	C₂²	1	2	yes	—
24	#16839813	—	2	2	no	—
25	#16839813	C₂²	1	1	yes	characteristic
26	#16839813	C₂²	1	1	yes	characteristic
27	#16839799	C₄	1	1	yes	characteristic
28	C₄⋊C₈×D₆₁	—	2	2	no	—
29	C₄⋊C₈×D₆₁	C₂²	1	2	yes	—
30	#16839757	C₄	1	2	yes	—
31	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
32	#16839515	C₂²	1	1	yes	characteristic
33	#16839514	C₂²	1	2	yes	—
34	Q₈⋊#92418	C₂²	1	2	yes	—
35	#16839491	C₂²	1	2	yes	—
36	#16839489	C₂²	1	2	yes	—
37	#16839484	C₂²	1	1	yes	characteristic
38	#16839484	C₂²	1	1	yes	characteristic
39	C₈×#92418	C₂²	1	1	yes	characteristic
40	C₈×Q₈×C₆₁	C₂²	1	2	yes	—
41	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
42	C₆₁×#335	C₂²	1	1	yes	characteristic
43	C₆₁×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₆₁	C₂²	1	1	yes	characteristic
45	C₂×#11758226	C₂×C₄	1	2	yes	—
46	#14519800	C₈	1	8	yes	complemented
47	C₂×#11758201	C₂×C₄	1	2	yes	—
48	C₂×D₄₈₈	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₆₁	—	2	2	no	—
50	C₂×C₈×D₆₁	—	2	2	no	—
51	C₂×C₈×D₆₁	—	2	2	no	—
52	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
54	Q₈×Dic₆₁	C₂×C₄	1	2	yes	—
55	C₄×D₂₄₄	—	2	2	no	—
56	C₄×D₂₄₄	C₂³	1	2	yes	—
57	#14519739	—	2	2	no	—
58	#14519739	C₂×C₄	1	2	yes	—
59	#14519735	—	2	2	no	—
60	#14519735	C₂×C₄	1	2	yes	—
61	C₄²×D₆₁	—	2	2	no	—
62	C₄²×D₆₁	C₂³	1	1	yes	characteristic
63	#14519711	C₂×C₄	1	1	yes	characteristic
64	#14519708	C₂×C₄	1	2	yes	—
65	C₄⋊#92418	—	2	2	no	—
66	C₄⋊#92418	C₂³	1	2	yes	—
67	#14519706	—	2	2	no	—
68	#14519706	—	2	1	no	—
69	#14519706	D₄	1	1	yes	characteristic
70	#14519706	D₄	1	1	yes	characteristic
71	#14519701	C₂×C₄	1	2	yes	—
72	#14519699	C₂×C₄	1	2	yes	—
73	#14519697	C₂×C₄	1	2	yes	—
74	#14519689	—	2	1	no	—
75	#14519689	—	2	2	no	—
76	#14519689	—	2	2	no	—
77	#14519689	D₄	1	1	yes	characteristic
78	#14519689	D₄	1	1	yes	characteristic
79	C₄×#92418	—	2	2	no	—
80	C₄×#92418	C₂³	1	1	yes	characteristic
81	C₄×#92418	C₂³	1	1	yes	characteristic
82	C₄×#92418	C₂³	1	1	yes	characteristic
83	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
85	C₂×Q₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
87	#107×C₆₁	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₈×C₆₁	—	2	2	no	—
89	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
90	#103×C₆₁	C₂×C₄	1	2	yes	—
91	C₄×C₈×C₆₁	—	2	2	no	—
92	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
95	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
96	#11758226	—	2	4	no	—
97	#11758226	C₂×C₈	1	8	yes	complemented
98	C₂×D₂₄₄	—	2	2	no	—
99	C₂×D₂₄₄	C₂²×C₄	1	2	yes	—
100	C₂×C₄×D₆₁	—	2	2	no	—
101	C₂×C₄×D₆₁	—	2	2	no	—
102	C₂×C₄×D₆₁	—	2	2	no	—
103	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
105	C₂×C₄×D₆₁	#41	1	1	yes	characteristic
106	Q₁₆×C₆₁	C₂×C₈	1	4	yes	complemented
107	C₂×C₈×C₆₁	—	2	2	no	—
108	C₂×C₈×C₆₁	—	2	1	no	—
109	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
113	C₄⋊C₄×C₆₁	—	2	2	no	—
114	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
115	C₄²×C₆₁	—	2	2	no	—
116	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
117	#11758201	C₂×C₈	1	8	yes	complemented
118	#11758198	—	2	2	no	—
119	#11758198	—	2	2	no	—
120	#11758198	—	2	2	no	—
121	C₄⋊Dic₆₁	—	2	2	no	—
122	C₄⋊Dic₆₁	C₂²×C₄	1	2	yes	—
123	C₄×Dic₆₁	—	2	2	no	—
124	C₄×Dic₆₁	—	2	2	no	—
125	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
127	C₄×Dic₆₁	#41	1	1	yes	characteristic
128	C₂×#92418	—	2	2	no	—
129	C₂×#92418	—	2	1	no	—
130	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
131	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
132	C₂×#92418	C₂×D₄	1	1	yes	characteristic
133	C₂×#92418	C₂×D₄	1	1	yes	characteristic
134	D₄₈₈	C₂×C₈	1	4	yes	complemented
135	C₈×D₆₁	—	2	2	no	—
136	C₈×D₆₁	—	8	2	no	—
137	C₈×D₆₁	—	8	2	no	—
138	C₈×D₆₁	—	8	2	no	—
139	C₈×D₆₁	C₂×C₈	1	4	yes	complemented
140	C₂²×D₆₁	—	2	2	no	—
141	C₂²×D₆₁	C₄×D₄	1	1	yes	characteristic
142	Q₈×C₆₁	—	2	2	no	—
143	Q₈×C₆₁	C₂²×C₈	1	4	yes	—
144	C₂×C₄×C₆₁	—	2	2	no	—
145	C₂×C₄×C₆₁	—	2	2	no	—
146	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
149	C₂×Dic₆₁	—	2	2	no	—
150	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
151	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
152	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
153	D₂₄₄	—	2	8	no	—
154	D₂₄₄	—	2	2	no	—
155	D₂₄₄	C₂²×C₈	1	4	yes	—
156	C₄×D₆₁	—	2	1	no	—
157	C₄×D₆₁	—	2	1	no	—
158	C₄×D₆₁	—	2	8	no	—
159	C₄×D₆₁	—	4	1	no	—
160	C₄×D₆₁	—	4	2	no	—
161	C₄×D₆₁	—	4	2	no	—
162	C₄×D₆₁	—	8	2	no	—
163	C₄×D₆₁	C₂²×C₈	1	2	yes	—
164	C₄×D₆₁	#131	1	2	yes	—
165	C₈×C₆₁	—	2	1	no	—
166	C₈×C₆₁	—	2	1	no	—
167	C₈×C₆₁	—	2	1	no	—
168	C₈×C₆₁	—	4	1	no	—
169	C₈×C₆₁	—	4	2	no	—
170	C₈×C₆₁	C₂²×C₈	1	2	yes	—
171	#92418	—	2	1	no	—
172	#92418	—	2	1	no	—
173	#92418	—	2	1	no	—
174	#92418	—	4	1	no	—
175	#92418	—	4	2	no	—
176	#92418	C₂²×C₈	1	2	yes	—
177	#17857	—	61	1	no	maximal, Sylow
178	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
179	C₂×D₆₁	—	2	1	no	—
180	C₂×D₆₁	—	2	1	no	—
181	C₂×D₆₁	—	2	4	no	—
182	C₂×D₆₁	—	4	2	no	—
183	C₂×D₆₁	—	4	2	no	—
184	C₂×D₆₁	C₈×D₄	1	2	yes	—
185	C₄×C₆₁	—	2	4	no	—
186	C₄×C₆₁	—	2	1	no	—
187	C₄×C₆₁	—	4	2	no	—
188	C₄×C₆₁	C₂³×C₈	1	1	yes	characteristic
189	C₄×C₆₁	C₂×#131	1	1	yes	characteristic
190	C₄×C₆₁	#576	1	1	yes	characteristic
191	C₄×C₆₁	#578	1	1	yes	characteristic
192	Dic₆₁	—	2	1	no	—
193	Dic₆₁	—	2	1	no	—
194	Dic₆₁	—	4	2	no	—
195	Dic₆₁	C₈×D₄	1	2	yes	—
196	#2988	—	61	2	no	—
197	C₄×#135	—	61	1	no	—
198	SD₁₆⋊C₈	—	61	2	no	—
199	SD₁₆⋊C₈	—	61	2	no	—
200	C₈×Q₁₆	—	61	1	no	—
201	C₈×Q₁₆	D₆₁	1	1	yes	characteristic, complemented
202	C₈×D₈	—	61	1	no	—
203	C₈×D₈	—	61	1	no	—
204	C₂×#335	—	61	1	no	—
205	#1477	—	61	2	no	—
206	#1450	—	61	1	no	—
207	C₂×C₆₁	C₂×C₈×D₄	1	1	yes	characteristic
208	C₂×C₆₁	#2951	1	1	yes	characteristic
209	C₂×C₆₁	#2957	1	1	yes	characteristic
210	D₆₁	—	2	2	no	—
211	D₆₁	—	4	4	no	—
212	C₂×#135	—	61	1	no	—
213	C₄×#41	—	61	2	no	—
214	C₈×Q₈	—	61	2	no	—
215	C₈×Q₈	C₂×D₆₁	1	2	yes	—
216	C₄×Q₁₆	—	61	1	no	—
217	C₄×Q₁₆	C₂×D₆₁	1	1	yes	characteristic
218	C₄×SD₁₆	—	61	2	no	—
219	C₄×SD₁₆	—	61	2	no	—
220	C₄×D₈	—	61	1	no	—
221	C₄×D₈	—	61	1	no	—
222	C₈×D₄	—	61	2	no	—
223	C₈×D₄	—	61	2	no	—
224	C₈×D₄	—	122	2	no	—
225	C₈×D₄	—	122	2	no	—
226	#431	—	61	1	no	—
227	#431	—	61	1	no	—
228	#431	—	122	2	no	—
229	#427	—	61	1	no	—
230	C₂×C₄⋊C₈	—	61	2	no	—
231	C₂×C₄⋊C₈	—	122	2	no	—
232	#416	—	61	2	no	—
233	C₂×C₄×C₈	—	61	1	no	—
234	#335	—	61	2	no	—
235	#335	—	61	1	no	—
236	#335	C₂×D₆₁	1	1	yes	characteristic
237	Q₈⋊C₈	—	61	2	no	—
238	Q₈⋊C₈	C₂×D₆₁	1	2	yes	—
239	D₄⋊C₈	—	61	2	no	—
240	D₄⋊C₈	—	61	2	no	—
241	#322	—	61	1	no	—
242	#322	—	61	1	no	—
243	C₈²	—	61	1	no	—
244	C₈²	C₂×D₆₁	1	1	yes	characteristic
245	C₆₁	#17857	1	1	yes	characteristic, complemented, Sylow
246	C₂×#41	—	61	2	no	—
247	#135	—	61	8	no	—
248	C₂×Q₁₆	C₄×D₆₁	1	1	yes	characteristic
249	C₂×SD₁₆	—	61	2	no	—
250	C₂×D₈	—	61	1	no	—
251	C₂²×C₈	—	61	1	no	—
252	C₂²×C₈	—	61	1	no	—
253	C₂²×C₈	—	122	2	no	—
254	C₂²×C₈	—	122	2	no	—
255	C₂²×C₈	—	122	2	no	—
256	C₄×Q₈	—	61	2	no	—
257	C₄×Q₈	C₂²×D₆₁	1	2	yes	—
258	C₄×D₄	—	61	2	no	—
259	C₄×D₄	—	61	2	no	—
260	C₄×D₄	—	122	2	no	—
261	C₄×D₄	—	122	2	no	—
262	#117	—	61	2	no	—
263	#117	—	122	2	no	—
264	C₂×C₄²	—	61	1	no	—
265	C₂×C₄²	—	122	2	no	—
266	#107	—	61	1	no	—
267	#107	C₄×D₆₁	1	1	yes	characteristic
268	#106	—	61	2	no	—
269	C₄⋊C₈	—	2	2	no	—
270	C₄⋊C₈	—	61	1	no	—
271	C₄⋊C₈	—	61	1	no	—
272	C₄⋊C₈	—	61	2	no	—
273	C₄⋊C₈	—	122	2	no	—
274	C₄⋊C₈	—	122	2	no	—
275	C₄⋊C₈	—	122	1	no	—
276	C₄⋊C₈	C₂²×D₆₁	1	2	yes	—
277	#103	—	61	2	no	—
278	#103	C₄×D₆₁	1	2	yes	—
279	#102	—	61	2	no	—
280	#102	—	61	2	no	—
281	C₂²⋊C₈	—	61	1	no	—
282	C₂²⋊C₈	—	61	1	no	—
283	C₂²⋊C₈	—	122	2	no	—
284	C₂²⋊C₈	—	122	1	no	—
285	C₂²⋊C₈	—	122	2	no	—
286	C₄×C₈	—	2	2	no	—
287	C₄×C₈	—	61	1	no	—
288	C₄×C₈	—	61	1	no	—
289	C₄×C₈	—	61	1	no	—
290	C₄×C₈	—	61	1	no	—
291	C₄×C₈	—	61	1	no	—
292	C₄×C₈	—	122	2	no	—
293	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
294	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
295	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
296	#41	—	61	8	no	—
297	#41	—	122	4	no	—
298	C₂×Q₈	C₂×C₄×D₆₁	1	2	yes	—
299	C₂×D₄	—	61	2	no	—
300	C₂×D₄	—	122	2	no	—
301	C₂²×C₄	—	61	1	no	—
302	C₂²×C₄	—	61	1	no	—
303	C₂²×C₄	—	61	1	no	—
304	C₂²×C₄	—	122	2	no	—
305	C₂²×C₄	—	122	2	no	—
306	C₂²×C₄	—	122	2	no	—
307	Q₁₆	C₈×D₆₁	1	4	yes	complemented
308	SD₁₆	—	61	8	no	—
309	D₈	—	61	4	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	61	1	no	—
313	C₂×C₈	—	61	4	no	—
314	C₂×C₈	—	61	1	no	—
315	C₂×C₈	—	61	1	no	—
316	C₂×C₈	—	61	1	no	—
317	C₂×C₈	—	122	2	no	—
318	C₂×C₈	—	122	2	no	—
319	C₂×C₈	—	122	1	no	—
320	C₂×C₈	—	488	2	no	—
321	C₂×C₈	—	488	2	no	—
322	C₂×C₈	—	488	2	no	—
323	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
324	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
325	C₂×C₈	D₄×D₆₁	1	1	yes	characteristic
326	C₂×C₈	D₄×D₆₁	1	1	yes	characteristic
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	61	2	no	—
329	C₄⋊C₄	—	122	2	no	—
330	C₄⋊C₄	C₂×C₄×D₆₁	1	2	yes	—
331	C₂²⋊C₄	—	122	2	no	—
332	C₂²⋊C₄	—	122	2	no	—
333	C₂²⋊C₄	—	122	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	61	1	no	—
336	C₄²	—	61	1	no	—
337	C₄²	—	61	1	no	—
338	C₄²	—	122	2	no	—
339	C₄²	—	122	2	no	—
340	C₄²	C₂³×D₆₁	1	1	yes	characteristic
341	C₂³	—	61	1	no	—
342	C₂³	—	122	2	no	—
343	Q₈	—	2	2	no	—
344	Q₈	C₂×C₈×D₆₁	1	4	yes	—
345	D₄	—	61	4	no	—
346	D₄	—	122	8	no	—
347	D₄	—	122	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	61	1	no	—
351	C₂×C₄	—	61	2	no	—
352	C₂×C₄	—	61	2	no	—
353	C₂×C₄	—	61	1	no	—
354	C₂×C₄	—	61	1	no	—
355	C₂×C₄	—	122	8	no	—
356	C₂×C₄	—	122	1	no	—
357	C₂×C₄	—	122	1	no	—
358	C₂×C₄	—	122	2	no	—
359	C₂×C₄	—	488	2	no	—
360	C₂×C₄	—	244	1	no	—
361	C₂×C₄	—	244	2	no	—
362	C₂×C₄	—	244	2	no	—
363	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
364	C₂×C₄	C₂×D₄×D₆₁	1	1	yes	characteristic
365	C₂×C₄	#41×D₆₁	1	1	yes	characteristic
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	—	2	1	no	—
369	C₈	—	4	1	no	—
370	C₈	—	4	2	no	—
371	C₈	—	61	2	no	—
372	C₈	—	122	1	no	—
373	C₈	—	122	1	no	—
374	C₈	—	122	1	no	—
375	C₈	—	244	1	no	—
376	C₈	—	244	2	no	—
377	C₈	C₂×C₈×D₆₁	1	2	yes	—
378	C₂²	—	61	2	no	—
379	C₂²	—	122	1	no	—
380	C₂²	—	122	1	no	—
381	C₂²	—	122	4	no	—
382	C₂²	—	244	2	no	—
383	C₂²	—	244	2	no	—
384	C₂²	C₄×D₄×D₆₁	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	2	4	no	—
387	C₄	—	4	2	no	—
388	C₄	—	61	2	no	—
389	C₄	—	122	1	no	—
390	C₄	—	122	1	no	—
391	C₄	—	244	2	no	—
392	C₄	C₂²×C₈×D₆₁	1	1	yes	characteristic
393	C₄	#131×D₆₁	1	1	yes	characteristic
394	C₄	#16840564	1	1	yes	characteristic
395	C₄	#16840575	1	1	yes	characteristic
396	C₂	—	122	2	no	—
397	C₂	—	244	4	no	—
398	C₂	C₈×D₄×D₆₁	1	1	yes	characteristic
399	C₂	#21454694	1	1	yes	characteristic
400	C₂	#21454731	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₁
commutator	C₄×C₆₁	C₂³×C₈
Frattini	C₄²	C₂³×D₆₁
Fitting	C₈×Q₁₆×C₆₁	C₂
socle	C₂²×C₆₁	C₂×C₄×D₄
prime radical	C₂×#14519800	C₄
cosocle	C₄²×C₆₁	C₂⁴
hypercenter	C₈×Q₁₆	D₆₁
hypocenter	C₆₁	#17857
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×Q₁₆

Complements

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

N	H ≅ G/N	type
1. #21454929	C₂	semidirect
3. #21444634	C₂	semidirect
4. #21444629	C₂	semidirect
5. Q₁₆×#92418	C₂	semidirect
6. C₈×D₄₈₈	C₂	semidirect
7. #21444613	C₂	semidirect
8. #335×D₆₁	C₂	semidirect
9. #21444205	C₂	semidirect
10. #21444101	C₂	semidirect
11. C₈×Q₁₆×C₆₁	C₂	semidirect
46. #14519800	C₈	semidirect
97. #11758226	C₂×C₈	semidirect
106. Q₁₆×C₆₁	C₂×C₈	semidirect
117. #11758201	C₂×C₈	semidirect
134. D₄₈₈	C₂×C₈	semidirect
139. C₈×D₆₁	C₂×C₈	semidirect
201. C₈×Q₁₆	D₆₁	semidirect
245. C₆₁	#17857	semidirect
307. Q₁₆	C₈×D₆₁	semidirect

Maximal subgroups

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

subgroup	index
#21454929	2
C₄×#14519800	2
#21444634	2
#21444629	2
Q₁₆×#92418	2
C₈×D₄₈₈	2
#21444613	2
#335×D₆₁	2
#21444205	2
#21444101	2
C₈×Q₁₆×C₆₁	2
#17857	61