Subgroups — #27278018

Order 13568.

552 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16810688	C₂	1	1	yes	maximal, characteristic
2	#20275434	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13133137	C₂	1	1	yes	maximal, characteristic
4	C₂×#16810373	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16810352	C₂	1	1	yes	maximal, characteristic
6	#20272542	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₅₃	—	2	1	no	—
9	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
10	#16810688	—	2	2	no	—
11	#16810688	—	2	2	no	—
12	C₂×C₄⋊#88322	—	2	1	no	—
13	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
14	C₂×#13133137	C₄	1	1	yes	characteristic
15	C₂×#13133137	C₄	1	1	yes	characteristic
16	C₂×#13133129	—	2	1	no	—
17	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
18	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
19	#16810385	C₄	1	1	yes	characteristic
20	#16810385	C₄	1	1	yes	characteristic
21	#16810378	—	2	1	no	—
22	#16810373	—	2	2	no	—
23	#16810352	—	2	2	no	—
24	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
27	C₂²×D₂₁₂	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₅₃	—	2	1	no	—
29	C₂²×#88322	—	2	1	no	—
30	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
31	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
32	C₂²×#88322	D₄	1	1	yes	characteristic
33	C₂²×#88322	D₄	1	1	yes	characteristic
34	C₂×C₈×D₅₃	—	2	4	no	—
35	C₂×C₈×D₅₃	—	4	2	no	—
36	C₂×C₈×D₅₃	—	4	2	no	—
37	C₄×D₂₁₂	—	2	1	no	—
38	C₄×D₂₁₂	—	2	1	no	—
39	C₄×D₂₁₂	D₄	1	2	yes	—
40	C₄×D₂₁₂	Q₈	1	2	yes	—
41	C₂×C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
42	C₂×#11719921	—	2	1	no	—
43	C₄⋊#88322	—	2	1	no	—
44	C₄⋊#88322	—	2	1	no	—
45	C₄⋊#88322	—	4	2	no	—
46	#13133137	—	2	2	no	—
47	#13133137	C₈	1	4	yes	complemented
48	#13133129	—	2	4	no	—
49	C₄×#88322	—	2	1	no	—
50	C₄×#88322	—	2	1	no	—
51	C₄×#88322	—	2	1	no	—
52	C₄×#88322	—	2	1	no	—
53	C₂²×C₈×C₅₃	—	2	1	no	—
54	C₂²×C₈×C₅₃	—	2	1	no	—
55	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₅₃	—	2	1	no	—
58	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
59	C₄⋊C₈×C₅₃	—	2	1	no	—
60	C₄⋊C₈×C₅₃	D₄	1	2	yes	—
61	C₄×C₈×C₅₃	—	2	1	no	—
62	C₄×C₈×C₅₃	—	2	1	no	—
63	#95×C₅₃	—	2	1	no	—
64	C₂³×D₅₃	—	2	1	no	—
65	C₂²×C₄×C₅₃	—	2	1	no	—
66	C₂²×C₄×C₅₃	—	2	1	no	—
67	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
70	C₂²×Dic₅₃	—	2	1	no	—
71	C₂×D₂₁₂	—	2	1	no	—
72	C₂×D₂₁₂	—	2	1	no	—
73	C₂×D₂₁₂	—	2	1	no	—
74	C₂×D₂₁₂	C₄⋊C₄	1	2	yes	—
75	C₂×D₂₁₂	C₂×C₈	1	2	yes	—
76	C₂×D₂₁₂	M₁₆	1	2	yes	—
77	C₂×C₄×D₅₃	—	2	2	no	—
78	C₂×C₄×D₅₃	—	2	2	no	—
79	C₂×C₄×D₅₃	—	4	1	no	—
80	C₂×C₄×D₅₃	—	4	1	no	—
81	C₂×C₄×D₅₃	—	4	1	no	—
82	C₂×C₄×D₅₃	—	4	1	no	—
83	C₂×C₈×C₅₃	—	2	2	no	—
84	C₂×C₈×C₅₃	—	2	2	no	—
85	C₂×C₈×C₅₃	—	4	1	no	—
86	C₂×C₈×C₅₃	—	4	1	no	—
87	C₂×C₈×C₅₃	—	4	1	no	—
88	C₂×C₈×C₅₃	—	4	1	no	—
89	C₄⋊C₄×C₅₃	—	2	1	no	—
90	C₄⋊C₄×C₅₃	—	2	1	no	—
91	C₄⋊C₄×C₅₃	—	2	1	no	—
92	C₄⋊C₄×C₅₃	C₂×C₈	1	2	yes	complemented
93	C₄²×C₅₃	—	4	1	no	—
94	C₄²×C₅₃	—	4	1	no	—
95	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
96	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
97	C₄²×C₅₃	C₂×Q₈	1	1	yes	characteristic
98	C₄²×C₅₃	#41	1	1	yes	characteristic
99	#11719921	—	2	2	no	—
100	#11719921	—	2	2	no	—
101	C₄⋊Dic₅₃	—	2	1	no	—
102	C₄⋊Dic₅₃	C₄⋊C₄	1	2	yes	—
103	C₂×#88322	—	2	1	no	—
104	C₂×#88322	—	2	1	no	—
105	C₂×#88322	—	2	1	no	—
106	C₂×#88322	—	2	1	no	—
107	C₂×#88322	—	2	1	no	—
108	C₂×#88322	—	2	1	no	—
109	C₂×#88322	—	2	1	no	—
110	C₂×#88322	—	2	1	no	—
111	C₂×#88322	—	2	1	no	—
112	C₂×#88322	—	2	1	no	—
113	C₂×#88322	—	4	1	no	—
114	C₂×#88322	—	4	1	no	—
115	C₂×#88322	—	4	1	no	—
116	C₂×#88322	C₂×C₈	1	2	yes	complemented
117	C₂×#88322	SD₁₆	1	2	yes	—
118	C₈×D₅₃	—	4	8	no	—
119	C₂³×C₅₃	C₄×D₄	1	1	yes	characteristic
120	C₂²×D₅₃	—	2	2	no	—
121	C₂²×D₅₃	—	2	2	no	—
122	C₂²×D₅₃	—	2	2	no	—
123	C₂²×D₅₃	—	4	1	no	—
124	C₂²×D₅₃	—	4	1	no	—
125	C₂²×D₅₃	—	4	1	no	—
126	C₂²×D₅₃	—	4	1	no	—
127	C₂×C₄×C₅₃	—	2	1	no	—
128	C₂×C₄×C₅₃	—	2	1	no	—
129	C₂×C₄×C₅₃	—	2	2	no	—
130	C₂×C₄×C₅₃	—	4	1	no	—
131	C₂×C₄×C₅₃	—	4	1	no	—
132	C₂×C₄×C₅₃	—	4	1	no	—
133	C₂×C₄×C₅₃	—	4	1	no	—
134	C₂×C₄×C₅₃	—	4	1	no	—
135	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
137	C₂×C₄×C₅₃	#120	1	1	yes	characteristic
138	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
139	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
140	C₂×C₄×C₅₃	#123	1	1	yes	characteristic
141	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₄×C₅₃	C₂×M₁₆	1	1	yes	characteristic
143	C₂×C₄×C₅₃	#131	1	1	yes	characteristic
144	C₂×C₄×C₅₃	#131	1	1	yes	characteristic
145	C₂×C₄×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
146	C₂×C₄×C₅₃	#135	1	1	yes	characteristic
147	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₂×Dic₅₃	—	2	2	no	—
150	C₂×Dic₅₃	—	4	1	no	—
151	C₂×Dic₅₃	—	4	1	no	—
152	D₂₁₂	—	2	2	no	—
153	D₂₁₂	—	2	2	no	—
154	D₂₁₂	—	2	2	no	—
155	D₂₁₂	C₄⋊C₈	1	4	yes	complemented
156	C₄×D₅₃	—	4	2	no	—
157	C₄×D₅₃	—	4	2	no	—
158	C₄×D₅₃	—	4	2	no	—
159	C₄×D₅₃	—	4	2	no	—
160	C₈×C₅₃	—	4	2	no	—
161	C₈×C₅₃	—	4	2	no	—
162	#88322	—	2	2	no	—
163	#88322	—	2	2	no	—
164	#88322	—	4	1	no	—
165	#88322	—	4	1	no	—
166	#88322	—	8	1	no	—
167	#8845	—	53	1	no	maximal, Sylow
168	C₂²×C₅₃	#385	1	1	yes	characteristic
169	C₂²×C₅₃	C₈×D₄	1	1	yes	characteristic
170	C₂²×C₅₃	#435	1	1	yes	characteristic
171	C₂²×C₅₃	C₄×SD₁₆	1	1	yes	characteristic
172	C₂²×C₅₃	#442	1	1	yes	characteristic
173	C₂²×C₅₃	#443	1	1	yes	characteristic
174	C₂²×C₅₃	#444	1	1	yes	characteristic
175	C₂×D₅₃	—	2	4	no	—
176	C₂×D₅₃	—	4	2	no	—
177	C₂×D₅₃	—	4	2	no	—
178	C₂×D₅₃	—	4	2	no	—
179	C₂×D₅₃	—	4	2	no	—
180	C₂×D₅₃	—	4	2	no	—
181	C₂×D₅₃	—	4	2	no	—
182	C₄×C₅₃	—	2	1	no	—
183	C₄×C₅₃	—	2	1	no	—
184	C₄×C₅₃	—	4	2	no	—
185	C₄×C₅₃	—	8	1	no	—
186	C₄×C₅₃	C₂×C₄⋊C₈	1	1	yes	characteristic
187	C₄×C₅₃	#424	1	1	yes	characteristic
188	C₄×C₅₃	C₈×D₄	1	1	yes	characteristic
189	C₄×C₅₃	#435	1	1	yes	characteristic
190	C₄×C₅₃	#449	1	1	yes	characteristic
191	C₄×C₅₃	#450	1	1	yes	characteristic
192	C₄×C₅₃	#476	1	1	yes	characteristic
193	C₄×C₅₃	#478	1	1	yes	characteristic
194	Dic₅₃	—	4	2	no	—
195	C₂×C₈×D₄	—	53	1	no	—
196	#1939	—	53	1	no	—
197	C₄×#102	—	53	1	no	—
198	C₂×#334	—	53	1	no	—
199	C₂×D₄⋊C₈	—	53	1	no	—
200	#1279	D₅₃	1	1	yes	characteristic, complemented
201	#1273	—	53	1	no	—
202	C₂×C₅₃	C₈×SD₁₆	1	1	yes	characteristic
203	C₂×C₅₃	#1580	1	1	yes	characteristic
204	C₂×C₅₃	#1582	1	1	yes	characteristic
205	C₂×C₅₃	#1586	1	1	yes	characteristic
206	C₂×C₅₃	#1850	1	1	yes	characteristic
207	C₂×C₅₃	#1864	1	1	yes	characteristic
208	C₂×C₅₃	#1866	1	1	yes	characteristic
209	D₅₃	—	4	4	no	—
210	C₂³×C₈	—	106	1	no	—
211	C₂×C₄×D₄	—	53	1	no	—
212	C₈×D₄	—	106	2	no	—
213	C₈×D₄	—	106	2	no	—
214	C₂×C₄⋊C₈	—	53	1	no	—
215	C₂×C₄⋊C₈	—	106	1	no	—
216	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
217	C₂×#102	—	53	1	no	—
218	C₂×#102	—	53	1	no	—
219	C₂×C₂²⋊C₈	—	106	1	no	—
220	C₂×C₄×C₈	—	53	1	no	—
221	C₂×C₄×C₈	—	53	1	no	—
222	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
223	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
224	#340	—	53	1	no	—
225	#340	—	53	1	no	—
226	#336	—	106	1	no	—
227	#334	—	106	2	no	—
228	D₄⋊C₈	—	106	2	no	—
229	C₅₃	#8845	1	1	yes	characteristic, complemented, Sylow
230	C₂²×D₄	—	53	1	no	—
231	C₂³×C₄	—	106	1	no	—
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	—	2	1	no	—
234	C₂²×C₈	—	53	1	no	—
235	C₂²×C₈	—	53	1	no	—
236	C₂²×C₈	—	53	1	no	—
237	C₂²×C₈	—	53	1	no	—
238	C₂²×C₈	—	106	4	no	—
239	C₂²×C₈	—	106	1	no	—
240	C₂²×C₈	—	212	2	no	—
241	C₂²×C₈	—	212	2	no	—
242	C₄×D₄	—	53	2	no	—
243	C₄×D₄	—	53	2	no	—
244	C₄×D₄	—	106	1	no	—
245	C₄×D₄	—	106	1	no	—
246	C₂×C₄⋊C₄	—	53	1	no	—
247	C₂×C₄⋊C₄	C₄×D₅₃	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₄×D₅₃	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	—	106	1	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
252	C₄⋊C₈	—	2	1	no	—
253	C₄⋊C₈	—	106	1	no	—
254	C₄⋊C₈	—	106	1	no	—
255	C₄⋊C₈	—	212	2	no	—
256	C₄⋊C₈	D₂₁₂	1	2	yes	—
257	#102	—	53	4	no	—
258	#102	—	106	2	no	—
259	C₂²⋊C₈	—	106	4	no	—
260	C₄×C₈	—	2	1	no	—
261	C₄×C₈	—	2	1	no	—
262	C₄×C₈	—	106	1	no	—
263	C₄×C₈	—	106	1	no	—
264	C₄×C₈	—	106	1	no	—
265	C₄×C₈	—	106	1	no	—
266	#95	—	2	1	no	—
267	C₂⁴	—	106	1	no	—
268	C₂×D₄	—	53	2	no	—
269	C₂×D₄	—	53	2	no	—
270	C₂×D₄	—	53	2	no	—
271	C₂×D₄	—	106	1	no	—
272	C₂×D₄	—	106	1	no	—
273	C₂×D₄	—	106	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	106	1	no	—
277	C₂²×C₄	—	106	2	no	—
278	C₂²×C₄	—	106	2	no	—
279	C₂²×C₄	—	212	1	no	—
280	C₂²×C₄	—	212	1	no	—
281	C₂²×C₄	—	212	1	no	—
282	C₂²×C₄	—	212	1	no	—
283	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
284	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
285	C₂²×C₄	#11719947	1	1	yes	characteristic
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	4	1	no	—
289	C₂×C₈	—	4	1	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	53	2	no	—
293	C₂×C₈	—	53	2	no	—
294	C₂×C₈	—	106	1	no	—
295	C₂×C₈	—	106	1	no	—
296	C₂×C₈	—	106	1	no	—
297	C₂×C₈	—	106	1	no	—
298	C₂×C₈	—	106	1	no	—
299	C₂×C₈	—	106	1	no	—
300	C₂×C₈	—	106	1	no	—
301	C₂×C₈	—	106	1	no	—
302	C₂×C₈	—	106	1	no	—
303	C₂×C₈	—	106	1	no	—
304	C₂×C₈	—	212	8	no	—
305	C₂×C₈	—	212	1	no	—
306	C₂×C₈	—	212	1	no	—
307	C₂×C₈	—	212	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	53	2	no	—
312	C₄⋊C₄	—	106	1	no	—
313	C₄⋊C₄	C₈×D₅₃	1	2	yes	complemented
314	C₂²⋊C₄	—	106	2	no	—
315	C₂²⋊C₄	—	106	2	no	—
316	C₄²	—	4	1	no	—
317	C₄²	—	4	1	no	—
318	C₄²	C₂×D₂₁₂	1	1	yes	characteristic
319	C₄²	#11719945	1	1	yes	characteristic
320	C₄²	D₄×D₅₃	1	1	yes	characteristic
321	C₄²	Q₈×D₅₃	1	1	yes	characteristic
322	C₂³	—	106	2	no	—
323	C₂³	—	106	2	no	—
324	C₂³	—	106	2	no	—
325	C₂³	—	212	1	no	—
326	C₂³	—	212	1	no	—
327	C₂³	—	212	1	no	—
328	C₂³	—	212	1	no	—
329	C₂³	#13133177	1	1	yes	characteristic
330	D₄	—	53	4	no	—
331	D₄	—	106	2	no	—
332	D₄	—	106	2	no	—
333	D₄	—	106	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	106	2	no	—
343	C₂×C₄	—	212	1	no	—
344	C₂×C₄	—	212	1	no	—
345	C₂×C₄	—	212	2	no	—
346	C₂×C₄	—	212	2	no	—
347	C₂×C₄	—	212	2	no	—
348	C₂×C₄	—	212	2	no	—
349	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
350	C₂×C₄	C₄×D₂₁₂	1	1	yes	characteristic
351	C₂×C₄	#13133187	1	1	yes	characteristic
352	C₂×C₄	#13133195	1	1	yes	characteristic
353	C₂×C₄	#13133197	1	1	yes	characteristic
354	C₂×C₄	#13133199	1	1	yes	characteristic
355	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
356	C₂×C₄	M₁₆×D₅₃	1	1	yes	characteristic
357	C₂×C₄	#13133223	1	1	yes	characteristic
358	C₂×C₄	#13133225	1	1	yes	characteristic
359	C₂×C₄	SD₁₆×D₅₃	1	1	yes	characteristic
360	C₂×C₄	#13133240	1	1	yes	characteristic
361	C₂×C₄	#13133241	1	1	yes	characteristic
362	C₂×C₄	#13133244	1	1	yes	characteristic
363	C₈	—	4	2	no	—
364	C₈	—	4	2	no	—
365	C₈	—	106	2	no	—
366	C₈	—	106	2	no	—
367	C₈	—	424	1	no	—
368	C₈	—	212	1	no	—
369	C₈	—	212	1	no	—
370	C₂²	—	106	4	no	—
371	C₂²	—	212	2	no	—
372	C₂²	—	212	2	no	—
373	C₂²	—	212	2	no	—
374	C₂²	—	212	2	no	—
375	C₂²	—	212	2	no	—
376	C₂²	—	212	2	no	—
377	C₂²	#16810497	1	1	yes	characteristic
378	C₂²	#16810686	1	1	yes	characteristic
379	C₂²	#16810697	1	1	yes	characteristic
380	C₂²	#16810708	1	1	yes	characteristic
381	C₂²	#16810732	1	1	yes	characteristic
382	C₂²	#16810737	1	1	yes	characteristic
383	C₂²	#16810742	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	4	2	no	—
387	C₄	—	8	1	no	—
388	C₄	—	212	2	no	—
389	C₄	C₄⋊C₈×D₅₃	1	1	yes	characteristic
390	C₄	#16810648	1	1	yes	characteristic
391	C₄	C₈×D₂₁₂	1	1	yes	characteristic
392	C₄	#16810696	1	1	yes	characteristic
393	C₄	#16810771	1	1	yes	characteristic
394	C₄	#16810775	1	1	yes	characteristic
395	C₄	#16810912	1	1	yes	characteristic
396	C₄	#16810926	1	1	yes	characteristic
397	C₂	—	212	4	no	—
398	C₂	#20273512	1	1	yes	characteristic
399	C₂	#20273536	1	1	yes	characteristic
400	C₂	#20273554	1	1	yes	characteristic
401	C₂	#20273582	1	1	yes	characteristic
402	C₂	#20274894	1	1	yes	characteristic
403	C₂	#20274977	1	1	yes	characteristic
404	C₂	#20274991	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₅₃
Fitting	C₅₃×#1279	C₂
socle	C₂³×C₅₃	C₄×D₄
prime radical	C₂²×D₂₁₂	C₂×C₄
cosocle	C₂×C₄²×C₅₃	C₂³
hypercenter	#1279	D₅₃
hypocenter	C₅₃	#8845
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
2. #20275434	C₂	semidirect
4. C₂×#16810373	C₂	semidirect
6. #20272542	C₂	semidirect
7. C₅₃×#1279	C₂	semidirect
47. #13133137	C₈	semidirect
92. C₄⋊C₄×C₅₃	C₂×C₈	semidirect
116. C₂×#88322	C₂×C₈	semidirect
155. D₂₁₂	C₄⋊C₈	semidirect
200. #1279	D₅₃	semidirect
229. C₅₃	#8845	semidirect
313. C₄⋊C₄	C₈×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16810688	2
#20275434	2
C₄×#13133137	2
C₂×#16810373	2
C₂×#16810352	2
#20272542	2
C₅₃×#1279	2
#8845	53