Subgroups — #27355601

Order 13568.

786 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₈×D₅₃	C₂	1	1	yes	maximal, characteristic
2	D₄×#11719912	C₂	1	2	yes	maximal, complemented
3	#20273630	C₂	1	1	yes	maximal, characteristic, complemented
4	#20273628	C₂	1	1	yes	maximal, characteristic, complemented
5	#20273579	C₂	1	2	yes	maximal, complemented
6	#20273576	C₂	1	2	yes	maximal, complemented
7	#20273539	C₂	1	1	yes	maximal, characteristic, complemented
8	#20273469	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273138	C₂	1	2	yes	maximal, complemented
10	#20273001	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1580	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₅₃	C₄	1	1	yes	characteristic
13	C₂²×#11719912	—	2	2	no	—
14	C₄×D₄×D₅₃	C₂²	1	2	yes	—
15	C₄×D₄₂₄	C₂²	1	1	yes	characteristic
16	D₈×Dic₅₃	C₄	1	1	yes	characteristic
17	#16810705	C₄	1	1	yes	characteristic
18	C₄×#11719922	C₂²	1	2	yes	—
19	#16810703	C₄	1	2	yes	—
20	#16810702	C₂²	1	2	yes	complemented
21	#16810700	C₂²	1	2	yes	complemented
22	#16810694	—	2	2	no	—
23	#16810691	—	2	2	no	—
24	D₄×#88322	C₂²	1	2	yes	complemented
25	#16810674	C₂²	1	1	yes	characteristic
26	#107×D₅₃	C₄	1	1	yes	characteristic
27	#16810645	C₂²	1	2	yes	—
28	#102×D₅₃	C₄	1	2	yes	—
29	#16810585	—	2	2	no	—
30	C₄×#11719912	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
32	#16810374	C₂²	1	1	yes	characteristic, complemented
33	#16810373	C₂²	1	2	yes	complemented
34	#16810352	C₂²	1	2	yes	complemented
35	D₄⋊#88322	C₂²	1	2	yes	complemented
36	#16810350	C₂²	1	2	yes	complemented
37	#16810345	C₂²	1	1	yes	characteristic, complemented
38	#16810344	C₂²	1	1	yes	characteristic, complemented
39	#16810344	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
42	C₅₃×#334	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×D₄⋊C₈	C₂²	1	2	yes	complemented
44	C₅₃×#322	C₂²	1	1	yes	characteristic, complemented
45	C₂×D₄×D₅₃	C₂×C₄	1	2	yes	—
46	C₂²×C₄×D₅₃	—	2	2	no	—
47	C₂×D₄₂₄	C₂×C₄	1	1	yes	characteristic
48	C₂×#11719922	C₂×C₄	1	2	yes	—
49	D₈×D₅₃	—	2	4	no	—
50	C₂×#11719912	—	2	2	no	—
51	C₂×#11719912	—	2	2	no	—
52	C₂×#11719912	—	2	2	no	—
53	C₂×#11719912	—	4	8	no	—
54	C₂×#11719912	D₄	1	2	yes	—
55	C₂²×#88322	—	2	2	no	—
56	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
58	C₄×D₂₁₂	C₂³	1	2	yes	—
59	D₄×Dic₅₃	C₂×C₄	1	2	yes	—
60	#13133179	C₂×C₄	1	2	yes	—
61	C₄×C₂²⋊D₅₃	—	2	2	no	—
62	#13133177	—	2	2	no	—
63	C₄⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
64	C₂²⋊C₄×D₅₃	—	2	2	no	—
65	C₄²×D₅₃	C₂³	1	1	yes	characteristic
66	#13133151	C₂×C₄	1	1	yes	characteristic
67	#13133150	C₂×C₄	1	2	yes	—
68	C₄⋊#88322	C₂³	1	2	yes	—
69	#13133146	—	2	2	no	—
70	#13133146	—	2	1	no	—
71	#13133139	C₂×C₄	1	2	yes	—
72	#13133138	C₂×C₄	1	2	yes	—
73	#13133137	C₂×C₄	1	2	yes	—
74	C₂²⋊#88322	—	2	2	no	—
75	#13133129	—	2	2	no	—
76	#13133129	—	2	2	no	—
77	#13133129	—	2	1	no	—
78	#13133127	D₄	1	2	yes	—
79	C₄×#88322	C₂³	1	1	yes	characteristic
80	C₄×#88322	C₂³	1	1	yes	characteristic
81	C₄×#88322	C₂³	1	1	yes	characteristic
82	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
84	C₂×D₈×C₅₃	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₈×C₅₃	—	2	2	no	—
86	C₄×D₄×C₅₃	C₂³	1	2	yes	—
87	#107×C₅₃	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
89	#102×C₅₃	C₂×C₄	1	2	yes	—
90	C₂²⋊C₈×C₅₃	—	2	2	no	—
91	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
94	C₂³×D₅₃	—	2	2	no	—
95	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₅₃	—	2	2	no	—
97	C₂×C₂²⋊D₅₃	—	2	2	no	—
98	C₂²×Dic₅₃	—	2	2	no	—
99	D₄×D₅₃	—	2	4	no	—
100	D₄×D₅₃	—	4	2	no	—
101	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
102	C₂×C₄×D₅₃	—	2	2	no	—
103	C₂×C₄×D₅₃	—	2	2	no	—
104	C₂×C₄×D₅₃	—	2	2	no	—
105	C₂×C₄×D₅₃	—	4	4	no	—
106	C₂×C₄×D₅₃	—	4	4	no	—
107	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
110	D₈×C₅₃	M₁₆	1	4	yes	complemented
111	C₂×C₈×C₅₃	—	2	2	no	—
112	C₂×C₈×C₅₃	—	2	1	no	—
113	C₂×C₈×C₅₃	—	4	4	no	—
114	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
117	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
118	C₂²⋊C₄×C₅₃	—	2	2	no	—
119	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
120	C₂²⋊Dic₅₃	—	2	2	no	—
121	#11719922	—	2	4	no	—
122	#11719921	—	2	2	no	—
123	#11719921	—	2	2	no	—
124	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
125	#11719919	—	2	2	no	—
126	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
128	C₄×Dic₅₃	#41	1	1	yes	characteristic
129	C₂×#88322	—	2	2	no	—
130	C₂×#88322	—	2	1	no	—
131	C₂×#88322	—	4	4	no	—
132	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
133	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
134	C₂×#88322	C₂×D₄	1	2	yes	—
135	D₄₂₄	—	2	2	no	—
136	#11719912	—	2	4	no	—
137	#11719912	—	4	4	no	—
138	#11719912	—	4	4	no	—
139	#11719912	—	4	4	no	—
140	C₈×D₅₃	—	2	2	no	—
141	C₈×D₅₃	—	4	1	no	—
142	C₂³×C₅₃	—	2	2	no	—
143	C₂²×D₅₃	—	2	2	no	—
144	C₂²×D₅₃	—	4	4	no	—
145	C₂²×D₅₃	—	4	4	no	—
146	C₂²×D₅₃	—	8	2	no	—
147	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
148	D₄×C₅₃	—	2	2	no	—
149	D₄×C₅₃	C₂×M₁₆	1	4	yes	complemented
150	C₂×C₄×C₅₃	—	2	2	no	—
151	C₂×C₄×C₅₃	—	4	2	no	—
152	C₂×C₄×C₅₃	—	4	2	no	—
153	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
156	C₂²⋊D₅₃	—	4	4	no	—
157	C₂×Dic₅₃	—	2	2	no	—
158	C₂×Dic₅₃	—	4	4	no	—
159	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
160	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
161	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
162	D₂₁₂	—	2	2	no	—
163	D₂₁₂	—	2	2	no	—
164	C₄×D₅₃	—	2	1	no	—
165	C₄×D₅₃	—	2	1	no	—
166	C₄×D₅₃	—	4	1	no	—
167	C₄×D₅₃	—	4	4	no	—
168	C₄×D₅₃	—	4	2	no	—
169	C₄×D₅₃	—	4	2	no	—
170	C₄×D₅₃	—	4	4	no	—
171	C₄×D₅₃	AGL(1,ℤ/8)	1	4	yes	—
172	C₈×C₅₃	—	2	1	no	—
173	C₈×C₅₃	—	2	2	no	—
174	C₈×C₅₃	—	4	1	no	—
175	C₈×C₅₃	—	4	2	no	—
176	C₈×C₅₃	C₂×M₁₆	1	2	yes	complemented
177	#88322	—	2	1	no	—
178	#88322	—	2	1	no	—
179	#88322	—	2	2	no	—
180	#88322	—	4	1	no	—
181	#88322	—	4	2	no	—
182	#18044	—	53	1	no	maximal, Sylow
183	C₂²×C₅₃	—	2	4	no	—
184	C₂²×C₅₃	—	4	2	no	—
185	C₂²×C₅₃	—	4	2	no	—
186	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
187	C₂×D₅₃	—	2	1	no	—
188	C₂×D₅₃	—	2	1	no	—
189	C₂×D₅₃	—	4	2	no	—
190	C₂×D₅₃	—	4	2	no	—
191	C₂×D₅₃	—	4	2	no	—
192	C₂×D₅₃	—	8	8	no	—
193	C₂×D₅₃	#442	1	2	yes	—
194	C₄×C₅₃	—	2	1	no	—
195	C₄×C₅₃	—	4	2	no	—
196	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
197	C₄×C₅₃	#568	1	1	yes	characteristic
198	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
199	Dic₅₃	—	2	1	no	—
200	Dic₅₃	—	2	1	no	—
201	Dic₅₃	—	4	2	no	—
202	Dic₅₃	#442	1	2	yes	—
203	C₂×C₄×D₈	—	53	1	no	—
204	D₄×M₁₆	—	53	2	no	—
205	#1594	—	53	1	no	—
206	#1594	—	53	1	no	—
207	#1586	—	53	2	no	—
208	#1586	—	53	2	no	—
209	#1580	—	53	1	no	—
210	#1580	D₅₃	1	1	yes	characteristic, complemented
211	#1566	—	53	1	no	—
212	#1486	—	53	2	no	—
213	#1451	—	53	1	no	—
214	C₂×C₅₃	—	4	4	no	—
215	C₂×C₅₃	D₄×M₁₆	1	1	yes	characteristic
216	C₂×C₅₃	C₂×#442	1	1	yes	characteristic
217	C₂×C₅₃	#2957	1	1	yes	characteristic
218	D₅₃	—	2	2	no	—
219	D₅₃	—	8	2	no	—
220	C₂²×D₈	—	53	1	no	—
221	C₂²×M₁₆	—	106	2	no	—
222	C₂×C₄×D₄	—	53	2	no	—
223	C₄×D₈	—	53	1	no	—
224	C₄×D₈	—	53	2	no	—
225	C₄×D₈	—	53	1	no	—
226	C₄×D₈	—	53	2	no	—
227	C₄×D₈	—	53	1	no	—
228	C₄×D₈	C₂×D₅₃	1	1	yes	characteristic
229	#436	—	53	2	no	—
230	#436	—	53	2	no	—
231	#435	—	106	2	no	—
232	#435	—	106	2	no	—
233	C₈×D₄	—	53	2	no	—
234	C₈×D₄	C₂×D₅₃	1	2	yes	complemented
235	#431	—	53	1	no	—
236	C₂×#107	—	53	1	no	—
237	#423	—	53	2	no	—
238	C₂×#102	—	53	2	no	—
239	#407	—	106	2	no	—
240	C₄×M₁₆	—	53	1	no	—
241	C₂×C₄×C₈	—	53	1	no	—
242	#334	—	53	2	no	—
243	#334	—	53	1	no	—
244	#334	C₂×D₅₃	1	1	yes	characteristic, complemented
245	D₄⋊C₈	—	53	2	no	—
246	D₄⋊C₈	—	53	2	no	—
247	D₄⋊C₈	—	53	2	no	—
248	D₄⋊C₈	C₂×D₅₃	1	2	yes	complemented
249	#322	—	53	1	no	—
250	#322	—	53	1	no	—
251	#322	—	53	1	no	—
252	#322	C₂×D₅₃	1	1	yes	characteristic, complemented
253	C₅₃	#18044	1	1	yes	characteristic, complemented, Sylow
254	C₂²×D₄	—	53	2	no	—
255	C₂³×C₄	—	106	2	no	—
256	C₂×D₈	—	53	2	no	—
257	C₂×D₈	—	53	1	no	—
258	C₂×D₈	—	106	4	no	—
259	C₂×D₈	C₄×D₅₃	1	1	yes	characteristic
260	C₂×M₁₆	—	53	2	no	—
261	C₂×M₁₆	—	106	2	no	—
262	C₂×M₁₆	—	106	2	no	—
263	C₂×M₁₆	—	106	2	no	—
264	C₂×M₁₆	—	212	8	no	—
265	C₂²×C₈	—	2	2	no	—
266	C₂²×C₈	—	53	1	no	—
267	C₂²×C₈	—	53	1	no	—
268	C₂²×C₈	—	106	2	no	—
269	C₄×D₄	—	53	2	no	—
270	C₄×D₄	—	53	2	no	—
271	C₄×D₄	—	53	2	no	—
272	C₄×D₄	—	106	2	no	—
273	C₄×D₄	—	106	2	no	—
274	C₄×D₄	C₂²×D₅₃	1	2	yes	—
275	C₂×C₄⋊C₄	—	53	2	no	—
276	C₂×C₂²⋊C₄	—	106	2	no	—
277	C₂×C₄²	—	53	1	no	—
278	#107	—	53	1	no	—
279	#107	—	53	2	no	—
280	#107	C₄×D₅₃	1	1	yes	characteristic
281	C₄⋊C₈	—	53	2	no	—
282	C₄⋊C₈	—	106	2	no	—
283	C₄⋊C₈	—	106	1	no	—
284	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
285	#102	—	53	2	no	—
286	#102	—	53	2	no	—
287	#102	—	53	2	no	—
288	#102	C₄×D₅₃	1	2	yes	—
289	C₂²⋊C₈	—	2	2	no	—
290	C₂²⋊C₈	—	106	2	no	—
291	C₂²⋊C₈	—	106	1	no	—
292	C₂²⋊C₈	—	106	2	no	—
293	C₂²⋊C₈	—	106	2	no	—
294	#97	—	53	2	no	—
295	C₄×C₈	—	53	1	no	—
296	C₄×C₈	—	53	1	no	—
297	C₄×C₈	—	53	1	no	—
298	C₄×C₈	—	53	1	no	—
299	C₄×C₈	—	53	1	no	—
300	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
301	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
302	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
303	C₂⁴	—	106	2	no	—
304	C₂×D₄	—	53	2	no	—
305	C₂×D₄	—	106	2	no	—
306	C₂×D₄	—	106	4	no	—
307	C₂×D₄	—	212	2	no	—
308	C₂×D₄	C₂×C₄×D₅₃	1	2	yes	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	53	1	no	—
311	C₂²×C₄	—	53	1	no	—
312	C₂²×C₄	—	53	1	no	—
313	C₂²×C₄	—	106	2	no	—
314	C₂²×C₄	—	106	2	no	—
315	C₂²×C₄	—	106	2	no	—
316	C₂²×C₄	—	106	2	no	—
317	C₂²×C₄	—	212	4	no	—
318	C₂²×C₄	—	212	4	no	—
319	D₈	—	106	4	no	—
320	D₈	—	106	2	no	—
321	D₈	#11719912	1	4	yes	complemented
322	M₁₆	—	106	4	no	—
323	M₁₆	—	212	4	no	—
324	M₁₆	—	212	4	no	—
325	M₁₆	—	212	4	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	4	4	no	—
329	C₂×C₈	—	53	1	no	—
330	C₂×C₈	—	53	1	no	—
331	C₂×C₈	—	53	2	no	—
332	C₂×C₈	—	106	2	no	—
333	C₂×C₈	—	106	2	no	—
334	C₂×C₈	—	106	1	no	—
335	C₂×C₈	—	212	1	no	—
336	C₂×C₈	—	212	4	no	—
337	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
338	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
339	C₂×C₈	D₄×D₅₃	1	2	yes	—
340	C₄⋊C₄	—	53	2	no	—
341	C₄⋊C₄	—	106	2	no	—
342	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	—	106	2	no	—
345	C₂²⋊C₄	—	106	2	no	—
346	C₂²⋊C₄	—	106	2	no	—
347	C₄²	—	53	1	no	—
348	C₄²	—	53	1	no	—
349	C₄²	—	53	1	no	—
350	C₄²	C₂³×D₅₃	1	1	yes	characteristic
351	C₂³	—	2	2	no	—
352	C₂³	—	53	1	no	—
353	C₂³	—	106	2	no	—
354	C₂³	—	424	2	no	—
355	C₂³	—	212	4	no	—
356	C₂³	—	212	4	no	—
357	D₄	—	2	2	no	—
358	D₄	—	106	2	no	—
359	D₄	—	106	2	no	—
360	D₄	—	212	4	no	—
361	D₄	C₂×#11719912	1	4	yes	complemented
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	53	1	no	—
366	C₂×C₄	—	53	4	no	—
367	C₂×C₄	—	53	1	no	—
368	C₂×C₄	—	53	1	no	—
369	C₂×C₄	—	106	1	no	—
370	C₂×C₄	—	106	1	no	—
371	C₂×C₄	—	106	2	no	—
372	C₂×C₄	—	212	1	no	—
373	C₂×C₄	—	212	4	no	—
374	C₂×C₄	—	212	4	no	—
375	C₂×C₄	—	212	4	no	—
376	C₂×C₄	—	212	2	no	—
377	C₂×C₄	—	212	2	no	—
378	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
379	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
380	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
381	C₈	—	2	1	no	—
382	C₈	—	2	2	no	—
383	C₈	—	4	1	no	—
384	C₈	—	4	2	no	—
385	C₈	—	106	1	no	—
386	C₈	—	106	1	no	—
387	C₈	—	106	2	no	—
388	C₈	—	212	1	no	—
389	C₈	—	212	2	no	—
390	C₈	C₂×#11719912	1	2	yes	complemented
391	C₂²	—	2	4	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	53	2	no	—
395	C₂²	—	106	1	no	—
396	C₂²	—	106	1	no	—
397	C₂²	—	424	8	no	—
398	C₂²	—	212	2	no	—
399	C₂²	—	212	2	no	—
400	C₂²	—	212	2	no	—
401	C₂²	C₄×D₄×D₅₃	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	4	2	no	—
404	C₄	—	53	2	no	—
405	C₄	—	106	1	no	—
406	C₄	—	106	1	no	—
407	C₄	—	212	2	no	—
408	C₄	C₂²×#11719912	1	1	yes	characteristic
409	C₄	#16811388	1	1	yes	characteristic
410	C₄	AGL(1,ℤ/8)×D₅₃	1	2	yes	—
411	C₂	—	4	4	no	—
412	C₂	—	106	2	no	—
413	C₂	—	424	2	no	—
414	C₂	D₄×#11719912	1	1	yes	characteristic
415	C₂	#442×D₅₃	1	1	yes	characteristic
416	C₂	#20283629	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1580	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	C₂×D₈×D₅₃	C₄
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	#1580	D₅₃
hypocenter	C₅₃	#18044
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1580

Complements

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

N	H ≅ G/N	type
2. D₄×#11719912	C₂	semidirect
3. #20273630	C₂	semidirect
4. #20273628	C₂	semidirect
5. #20273579	C₂	semidirect
6. #20273576	C₂	semidirect
7. #20273539	C₂	semidirect
8. #20273469	C₂	semidirect
9. #20273138	C₂	semidirect
10. #20273001	C₂	semidirect
11. C₅₃×#1580	C₂	semidirect
20. #16810702	C₂²	semidirect
21. #16810700	C₂²	semidirect
24. D₄×#88322	C₂²	semidirect
32. #16810374	C₂²	semidirect
33. #16810373	C₂²	semidirect
34. #16810352	C₂²	semidirect
35. D₄⋊#88322	C₂²	semidirect
36. #16810350	C₂²	semidirect
37. #16810345	C₂²	semidirect
38. #16810344	C₂²	semidirect
39. #16810344	C₂²	semidirect
41. C₈×D₄×C₅₃	C₂²	semidirect
42. C₅₃×#334	C₂²	semidirect
43. C₅₃×D₄⋊C₈	C₂²	semidirect
44. C₅₃×#322	C₂²	semidirect
110. D₈×C₅₃	M₁₆	semidirect
149. D₄×C₅₃	C₂×M₁₆	semidirect
176. C₈×C₅₃	C₂×M₁₆	semidirect
210. #1580	D₅₃	semidirect
234. C₈×D₄	C₂×D₅₃	semidirect
244. #334	C₂×D₅₃	semidirect
248. D₄⋊C₈	C₂×D₅₃	semidirect
252. #322	C₂×D₅₃	semidirect
253. C₅₃	#18044	semidirect
321. D₈	#11719912	semidirect
361. D₄	C₂×#11719912	semidirect
390. C₈	C₂×#11719912	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₈×D₅₃	2
D₄×#11719912	2
#20273630	2
#20273628	2
#20273579	2
#20273576	2
#20273539	2
#20273469	2
#20273138	2
#20273001	2
C₅₃×#1580	2
#18044	53