Subgroups — #27355834

Order 13568.

718 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283747	C₂	1	2	yes	maximal, complemented
2	C₄×D₈×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#20273629	C₂	1	1	yes	maximal, characteristic, complemented
4	#20273547	C₂	1	2	yes	maximal, complemented
5	#20273542	C₂	1	2	yes	maximal, complemented
6	#20273540	C₂	1	1	yes	maximal, characteristic, complemented
7	#20273538	C₂	1	1	yes	maximal, characteristic, complemented
8	#20273475	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273156	C₂	1	2	yes	maximal, complemented
10	#20273001	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1594	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₅₃	C₄	1	1	yes	characteristic
13	C₄×D₄×D₅₃	C₂²	1	2	yes	—
14	C₄×D₄₂₄	C₂²	1	1	yes	characteristic
15	D₈×Dic₅₃	C₄	1	1	yes	characteristic
16	#16810705	C₄	1	1	yes	characteristic
17	C₄×#11719922	C₂²	1	2	yes	—
18	#16810703	C₄	1	2	yes	—
19	#16810701	C₂²	1	2	yes	complemented
20	#16810697	—	2	2	no	—
21	#16810692	—	2	2	no	—
22	C₈×D₂₁₂	C₂²	1	2	yes	complemented
23	#16810688	C₂²	1	2	yes	complemented
24	#16810679	C₂²	1	2	yes	—
25	#16810674	C₂²	1	1	yes	characteristic
26	#107×D₅₃	C₄	1	1	yes	characteristic
27	#102×D₅₃	C₄	1	2	yes	—
28	#16810586	—	2	2	no	—
29	C₂²⋊C₈×D₅₃	—	2	2	no	—
30	C₄×#11719912	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
32	#16810375	C₂²	1	2	yes	complemented
33	#16810374	C₂²	1	1	yes	characteristic, 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	C₅₃×#436	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×#11719917	—	2	2	no	—
51	C₂×#11719912	—	2	1	no	—
52	C₂×C₈×D₅₃	—	2	2	no	—
53	C₂×C₈×D₅₃	—	2	2	no	—
54	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
56	C₄×D₂₁₂	C₂³	1	2	yes	—
57	D₄×Dic₅₃	C₂×C₄	1	2	yes	—
58	#13133179	C₂×C₄	1	2	yes	—
59	C₄×C₂²⋊D₅₃	—	2	2	no	—
60	#13133177	—	2	2	no	—
61	C₄⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
62	C₂²⋊C₄×D₅₃	—	2	2	no	—
63	C₄²×D₅₃	C₂³	1	1	yes	characteristic
64	#13133151	C₂×C₄	1	1	yes	characteristic
65	#13133150	C₂×C₄	1	2	yes	—
66	C₄⋊#88322	C₂³	1	2	yes	—
67	#13133146	D₄	1	2	yes	—
68	#13133139	C₂×C₄	1	2	yes	—
69	#13133138	C₂×C₄	1	2	yes	—
70	#13133137	C₂×C₄	1	2	yes	—
71	C₂²⋊#88322	—	2	2	no	—
72	#13133129	—	2	2	no	—
73	#13133129	—	2	2	no	—
74	#13133129	—	2	2	no	—
75	#13133129	D₄	1	2	yes	—
76	#13133127	—	2	2	no	—
77	#13133127	—	2	1	no	—
78	C₄×#88322	C₂³	1	1	yes	characteristic
79	C₄×#88322	C₂³	1	1	yes	characteristic
80	C₄×#88322	C₂³	1	1	yes	characteristic
81	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
83	C₂×D₈×C₅₃	C₂×C₄	1	1	yes	characteristic
84	C₂×M₁₆×C₅₃	—	2	2	no	—
85	C₄×D₄×C₅₃	C₂³	1	2	yes	—
86	#107×C₅₃	C₂×C₄	1	1	yes	characteristic
87	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
88	#102×C₅₃	C₂×C₄	1	2	yes	—
89	C₂²⋊C₈×C₅₃	—	2	2	no	—
90	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₂³×D₅₃	—	2	2	no	—
94	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₅₃	—	2	2	no	—
96	C₂×C₂²⋊D₅₃	—	2	2	no	—
97	C₂²×Dic₅₃	—	2	2	no	—
98	D₄×D₅₃	—	2	4	no	—
99	D₄×D₅₃	—	4	2	no	—
100	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
101	C₂×C₄×D₅₃	—	2	2	no	—
102	C₂×C₄×D₅₃	—	2	2	no	—
103	C₂×C₄×D₅₃	—	2	2	no	—
104	C₂×C₄×D₅₃	—	8	2	no	—
105	C₂×C₄×D₅₃	—	8	2	no	—
106	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
108	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
109	D₈×C₅₃	—	2	2	no	—
110	M₁₆×C₅₃	—	8	2	no	—
111	C₂×C₈×C₅₃	—	2	2	no	—
112	C₂×C₈×C₅₃	—	2	1	no	—
113	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
116	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
117	C₂²⋊C₄×C₅₃	—	2	2	no	—
118	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
119	C₂²⋊Dic₅₃	—	2	2	no	—
120	#11719922	—	2	4	no	—
121	#11719921	—	2	2	no	—
122	#11719921	—	2	2	no	—
123	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
124	#11719919	—	2	2	no	—
125	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
127	C₄×Dic₅₃	#41	1	1	yes	characteristic
128	#11719917	—	8	2	no	—
129	C₂×#88322	—	2	2	no	—
130	C₂×#88322	—	2	1	no	—
131	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
132	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
133	C₂×#88322	C₂×D₄	1	2	yes	—
134	D₄₂₄	M₁₆	1	4	yes	complemented
135	#11719912	—	4	2	no	—
136	C₈×D₅₃	—	2	2	no	—
137	C₈×D₅₃	—	4	1	no	—
138	C₈×D₅₃	—	8	2	no	—
139	C₈×D₅₃	—	8	2	no	—
140	C₂³×C₅₃	—	2	2	no	—
141	C₂²×D₅₃	—	2	2	no	—
142	C₂²×D₅₃	—	4	4	no	—
143	C₂²×D₅₃	—	4	4	no	—
144	C₂²×D₅₃	—	8	2	no	—
145	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
146	D₄×C₅₃	—	2	2	no	—
147	D₄×C₅₃	—	2	2	no	—
148	C₂×C₄×C₅₃	—	2	2	no	—
149	C₂×C₄×C₅₃	—	4	2	no	—
150	C₂×C₄×C₅₃	—	4	2	no	—
151	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
154	C₂²⋊D₅₃	—	4	4	no	—
155	C₂×Dic₅₃	—	2	2	no	—
156	C₂×Dic₅₃	—	8	2	no	—
157	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
158	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
159	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
160	D₂₁₂	—	2	2	no	—
161	D₂₁₂	C₂×M₁₆	1	4	yes	—
162	C₄×D₅₃	—	2	2	no	—
163	C₄×D₅₃	—	2	1	no	—
164	C₄×D₅₃	—	2	1	no	—
165	C₄×D₅₃	—	2	2	no	—
166	C₄×D₅₃	—	4	2	no	—
167	C₄×D₅₃	—	4	2	no	—
168	C₄×D₅₃	—	8	2	no	—
169	C₄×D₅₃	—	8	2	no	—
170	C₈×C₅₃	—	2	1	no	—
171	C₈×C₅₃	—	2	2	no	—
172	C₈×C₅₃	—	4	1	no	—
173	C₈×C₅₃	—	4	2	no	—
174	C₈×C₅₃	C₂×M₁₆	1	2	yes	—
175	#88322	—	2	1	no	—
176	#88322	—	2	1	no	—
177	#88322	—	2	2	no	—
178	#88322	—	4	1	no	—
179	#88322	—	4	2	no	—
180	#18064	—	53	1	no	maximal, Sylow
181	C₂²×C₅₃	—	4	2	no	—
182	C₂²×C₅₃	—	4	2	no	—
183	C₂²×C₅₃	—	4	2	no	—
184	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
185	C₂×D₅₃	—	2	1	no	—
186	C₂×D₅₃	—	2	1	no	—
187	C₂×D₅₃	—	2	4	no	—
188	C₂×D₅₃	—	4	2	no	—
189	C₂×D₅₃	—	4	2	no	—
190	C₂×D₅₃	—	8	8	no	—
191	C₂×D₅₃	#444	1	2	yes	—
192	C₄×C₅₃	—	2	1	no	—
193	C₄×C₅₃	—	4	2	no	—
194	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
195	C₄×C₅₃	#568	1	1	yes	characteristic
196	C₄×C₅₃	#576	1	2	yes	—
197	Dic₅₃	—	2	1	no	—
198	Dic₅₃	—	2	1	no	—
199	Dic₅₃	—	2	1	no	—
200	Dic₅₃	—	4	2	no	—
201	#2974	—	53	2	no	—
202	C₂×C₄×D₈	—	53	1	no	—
203	#1594	—	53	1	no	—
204	#1594	D₅₃	1	1	yes	characteristic, complemented
205	#1581	—	53	2	no	—
206	#1581	—	53	2	no	—
207	#1580	—	53	1	no	—
208	#1580	—	53	1	no	—
209	#1568	—	53	1	no	—
210	#1490	—	53	2	no	—
211	#1451	—	53	1	no	—
212	C₂×C₅₃	—	8	2	no	—
213	C₂×C₅₃	D₄×M₁₆	1	1	yes	characteristic
214	C₂×C₅₃	#2948	1	1	yes	characteristic
215	C₂×C₅₃	C₂×#444	1	1	yes	characteristic
216	D₅₃	—	2	2	no	—
217	D₅₃	—	4	4	no	—
218	C₂²×D₈	—	53	1	no	—
219	C₂×C₄×D₄	—	53	2	no	—
220	C₄×D₈	—	53	1	no	—
221	C₄×D₈	—	53	2	no	—
222	C₄×D₈	—	53	1	no	—
223	C₄×D₈	—	53	2	no	—
224	C₄×D₈	—	53	1	no	—
225	C₄×D₈	C₂×D₅₃	1	1	yes	characteristic
226	#436	—	53	2	no	—
227	#436	C₂×D₅₃	1	2	yes	complemented
228	#435	—	106	2	no	—
229	#435	—	106	2	no	—
230	C₈×D₄	—	53	2	no	—
231	C₈×D₄	—	53	2	no	—
232	#432	—	53	2	no	—
233	#431	—	53	1	no	—
234	C₂×#107	—	53	1	no	—
235	C₂×#102	—	53	2	no	—
236	#407	—	106	2	no	—
237	C₂×C₂²⋊C₈	—	106	2	no	—
238	C₄×M₁₆	—	53	1	no	—
239	C₂×C₄×C₈	—	53	1	no	—
240	#335	—	53	2	no	—
241	#334	—	53	1	no	—
242	#334	C₂×D₅₃	1	1	yes	characteristic, complemented
243	D₄⋊C₈	—	53	2	no	—
244	D₄⋊C₈	—	53	2	no	—
245	D₄⋊C₈	—	53	2	no	—
246	D₄⋊C₈	C₂×D₅₃	1	2	yes	complemented
247	#322	—	53	1	no	—
248	#322	—	53	1	no	—
249	#322	—	53	1	no	—
250	#322	C₂×D₅₃	1	1	yes	characteristic, complemented
251	C₅₃	#18064	1	1	yes	characteristic, complemented, Sylow
252	C₂²×D₄	—	53	2	no	—
253	C₂³×C₄	—	106	2	no	—
254	C₂×D₈	—	53	2	no	—
255	C₂×D₈	—	53	1	no	—
256	C₂×D₈	—	106	4	no	—
257	C₂×D₈	C₄×D₅₃	1	1	yes	characteristic
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	—	106	1	no	—
260	C₂×M₁₆	—	106	2	no	—
261	C₂²×C₈	—	53	1	no	—
262	C₂²×C₈	—	53	1	no	—
263	C₂²×C₈	—	106	2	no	—
264	C₂²×C₈	—	106	2	no	—
265	C₄×D₄	—	53	2	no	—
266	C₄×D₄	—	53	2	no	—
267	C₄×D₄	—	53	2	no	—
268	C₄×D₄	—	106	2	no	—
269	C₄×D₄	—	106	2	no	—
270	C₄×D₄	C₂²×D₅₃	1	2	yes	—
271	C₂×C₄⋊C₄	—	53	2	no	—
272	C₂×C₂²⋊C₄	—	106	2	no	—
273	C₂×C₄²	—	53	1	no	—
274	#107	—	53	1	no	—
275	#107	—	53	2	no	—
276	#107	C₄×D₅₃	1	1	yes	characteristic
277	C₄⋊C₈	—	53	2	no	—
278	C₄⋊C₈	—	53	2	no	—
279	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
280	#102	—	53	2	no	—
281	#102	—	53	2	no	—
282	#102	—	53	2	no	—
283	#102	C₄×D₅₃	1	2	yes	—
284	C₂²⋊C₈	—	2	2	no	—
285	C₂²⋊C₈	—	53	2	no	—
286	C₂²⋊C₈	—	106	2	no	—
287	C₂²⋊C₈	—	106	2	no	—
288	C₂²⋊C₈	—	106	2	no	—
289	C₂²⋊C₈	—	106	2	no	—
290	#97	—	106	1	no	—
291	#97	—	106	2	no	—
292	C₄×C₈	—	53	1	no	—
293	C₄×C₈	—	53	1	no	—
294	C₄×C₈	—	53	1	no	—
295	C₄×C₈	—	53	1	no	—
296	C₄×C₈	—	53	1	no	—
297	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
299	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
300	C₂⁴	—	106	2	no	—
301	C₂×D₄	—	53	2	no	—
302	C₂×D₄	—	106	2	no	—
303	C₂×D₄	—	106	4	no	—
304	C₂×D₄	—	212	2	no	—
305	C₂×D₄	C₂×C₄×D₅₃	1	2	yes	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	53	1	no	—
308	C₂²×C₄	—	53	1	no	—
309	C₂²×C₄	—	53	1	no	—
310	C₂²×C₄	—	106	2	no	—
311	C₂²×C₄	—	106	2	no	—
312	C₂²×C₄	—	106	2	no	—
313	C₂²×C₄	—	106	2	no	—
314	C₂²×C₄	—	424	2	no	—
315	C₂²×C₄	—	424	2	no	—
316	D₈	—	2	2	no	—
317	D₈	—	53	4	no	—
318	D₈	—	106	4	no	—
319	M₁₆	—	8	2	no	—
320	M₁₆	—	424	2	no	—
321	M₁₆	—	212	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	53	1	no	—
325	C₂×C₈	—	53	1	no	—
326	C₂×C₈	—	53	2	no	—
327	C₂×C₈	—	106	2	no	—
328	C₂×C₈	—	106	2	no	—
329	C₂×C₈	—	106	1	no	—
330	C₂×C₈	—	424	2	no	—
331	C₂×C₈	—	424	2	no	—
332	C₂×C₈	—	212	1	no	—
333	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
335	C₂×C₈	D₄×D₅₃	1	2	yes	—
336	C₄⋊C₄	—	53	2	no	—
337	C₄⋊C₄	—	106	2	no	—
338	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	106	2	no	—
341	C₂²⋊C₄	—	106	2	no	—
342	C₂²⋊C₄	—	106	2	no	—
343	C₄²	—	53	1	no	—
344	C₄²	—	53	1	no	—
345	C₄²	—	53	1	no	—
346	C₄²	C₂³×D₅₃	1	1	yes	characteristic
347	C₂³	—	2	2	no	—
348	C₂³	—	53	1	no	—
349	C₂³	—	106	2	no	—
350	C₂³	—	424	2	no	—
351	C₂³	—	212	4	no	—
352	C₂³	—	212	4	no	—
353	D₄	—	2	2	no	—
354	D₄	—	2	2	no	—
355	D₄	—	53	4	no	—
356	D₄	—	106	2	no	—
357	D₄	—	212	4	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	53	1	no	—
362	C₂×C₄	—	53	1	no	—
363	C₂×C₄	—	53	1	no	—
364	C₂×C₄	—	106	2	no	—
365	C₂×C₄	—	106	1	no	—
366	C₂×C₄	—	106	1	no	—
367	C₂×C₄	—	106	2	no	—
368	C₂×C₄	—	106	2	no	—
369	C₂×C₄	—	424	2	no	—
370	C₂×C₄	—	424	2	no	—
371	C₂×C₄	—	424	2	no	—
372	C₂×C₄	—	212	2	no	—
373	C₂×C₄	—	212	2	no	—
374	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
375	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
376	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
377	C₈	—	2	1	no	—
378	C₈	—	2	2	no	—
379	C₈	—	4	1	no	—
380	C₈	—	4	2	no	—
381	C₈	—	106	1	no	—
382	C₈	—	106	1	no	—
383	C₈	—	106	2	no	—
384	C₈	—	212	1	no	—
385	C₈	—	212	2	no	—
386	C₈	M₁₆×D₅₃	1	2	yes	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	53	2	no	—
391	C₂²	—	106	1	no	—
392	C₂²	—	106	1	no	—
393	C₂²	—	106	4	no	—
394	C₂²	—	424	8	no	—
395	C₂²	—	212	2	no	—
396	C₂²	—	212	2	no	—
397	C₂²	C₄×D₄×D₅₃	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	4	2	no	—
400	C₄	—	106	1	no	—
401	C₄	—	106	1	no	—
402	C₄	—	106	1	no	—
403	C₄	—	212	2	no	—
404	C₄	C₂×M₁₆×D₅₃	1	1	yes	characteristic
405	C₄	#16811388	1	1	yes	characteristic
406	C₄	#16811427	1	2	yes	—
407	C₂	—	8	2	no	—
408	C₂	—	106	2	no	—
409	C₂	—	212	4	no	—
410	C₂	#20283451	1	1	yes	characteristic
411	C₂	#20283564	1	1	yes	characteristic
412	C₂	#444×D₅₃	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×#1594	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	C₂×D₈×D₅₃	C₄
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	#1594	D₅₃
hypocenter	C₅₃	#18064
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1594

Complements

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

N	H ≅ G/N	type
1. #20283747	C₂	semidirect
3. #20273629	C₂	semidirect
4. #20273547	C₂	semidirect
5. #20273542	C₂	semidirect
6. #20273540	C₂	semidirect
7. #20273538	C₂	semidirect
8. #20273475	C₂	semidirect
9. #20273156	C₂	semidirect
10. #20273001	C₂	semidirect
11. C₅₃×#1594	C₂	semidirect
19. #16810701	C₂²	semidirect
22. C₈×D₂₁₂	C₂²	semidirect
23. #16810688	C₂²	semidirect
32. #16810375	C₂²	semidirect
33. #16810374	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. C₅₃×#436	C₂²	semidirect
42. C₅₃×#334	C₂²	semidirect
43. C₅₃×D₄⋊C₈	C₂²	semidirect
44. C₅₃×#322	C₂²	semidirect
134. D₄₂₄	M₁₆	semidirect
204. #1594	D₅₃	semidirect
227. #436	C₂×D₅₃	semidirect
242. #334	C₂×D₅₃	semidirect
246. D₄⋊C₈	C₂×D₅₃	semidirect
250. #322	C₂×D₅₃	semidirect
251. C₅₃	#18064	semidirect

Maximal subgroups

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

subgroup	index
#20283747	2
C₄×D₈×D₅₃	2
#20273629	2
#20273547	2
#20273542	2
#20273540	2
#20273538	2
#20273475	2
#20273156	2
#20273001	2
C₅₃×#1594	2
#18064	53