Subgroups — C₅₃×#8597 #27216109

Order 13568.

546 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×M₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#1797	C₂	1	2	yes	maximal
3	C₂×C₅₃×#335	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#1277	C₂	1	2	yes	maximal, complemented
6	C₂²×M₁₆×C₅₃	C₄	1	1	yes	characteristic
7	C₂²×M₁₆×C₅₃	C₄	1	1	yes	characteristic
8	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	—
10	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	—
11	C₂×C₂²⋊C₈×C₅₃	—	2	2	no	—
12	C₄×M₁₆×C₅₃	—	2	2	no	—
13	C₄×M₁₆×C₅₃	—	2	2	no	—
14	C₂×#97×C₅₃	C₄	1	1	yes	characteristic
15	C₂×#97×C₅₃	C₄	1	1	yes	characteristic
16	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
18	C₅₃×#336	—	2	2	no	—
19	C₅₃×#335	—	2	2	no	—
20	C₅₃×#334	—	2	2	no	—
21	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₅₃	Q₈	1	1	yes	characteristic
24	C₂×M₁₆×C₅₃	—	2	2	no	—
25	C₂×M₁₆×C₅₃	—	2	2	no	—
26	C₂×M₁₆×C₅₃	—	2	2	no	—
27	C₂×M₁₆×C₅₃	—	2	2	no	—
28	C₂×M₁₆×C₅₃	—	2	2	no	—
29	C₂×M₁₆×C₅₃	C₈	1	4	yes	complemented
30	C₂²×C₈×C₅₃	—	2	2	no	—
31	C₂²×C₈×C₅₃	—	2	2	no	—
32	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₅₃	—	2	1	no	—
37	C₂×C₄²×C₅₃	—	2	1	no	—
38	C₂×C₄²×C₅₃	—	2	1	no	—
39	C₂×C₄²×C₅₃	—	2	1	no	—
40	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₅₃	Q₈	1	1	yes	characteristic
43	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
44	C₄⋊C₈×C₅₃	—	2	2	no	—
45	C₄⋊C₈×C₅₃	—	2	2	no	—
46	C₄⋊C₈×C₅₃	—	2	2	no	—
47	C₄⋊C₈×C₅₃	—	2	2	no	—
48	C₂²⋊C₈×C₅₃	—	4	4	no	—
49	#97×C₅₃	—	2	2	no	—
50	#97×C₅₃	—	2	2	no	—
51	C₄×C₈×C₅₃	—	2	1	no	—
52	C₄×C₈×C₅₃	—	2	1	no	—
53	C₄×C₈×C₅₃	D₄	1	2	yes	—
54	C₄×C₈×C₅₃	D₄	1	2	yes	—
55	C₂⁴×C₅₃	C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₅₃	—	2	1	no	—
57	C₂²×C₄×C₅₃	—	2	1	no	—
58	C₂²×C₄×C₅₃	—	2	1	no	—
59	C₂²×C₄×C₅₃	—	2	1	no	—
60	C₂²×C₄×C₅₃	—	2	1	no	—
61	C₂²×C₄×C₅₃	—	2	1	no	—
62	C₂²×C₄×C₅₃	—	2	1	no	—
63	C₂²×C₄×C₅₃	—	2	1	no	—
64	C₂²×C₄×C₅₃	—	2	2	no	—
65	C₂²×C₄×C₅₃	—	2	2	no	—
66	C₂²×C₄×C₅₃	—	4	2	no	—
67	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₅₃	C₂×C₈	1	2	yes	—
71	C₂²×C₄×C₅₃	M₁₆	1	2	yes	—
72	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
75	M₁₆×C₅₃	—	2	8	no	—
76	M₁₆×C₅₃	—	2	8	no	—
77	C₂×C₈×C₅₃	—	2	1	no	—
78	C₂×C₈×C₅₃	—	2	1	no	—
79	C₂×C₈×C₅₃	—	2	1	no	—
80	C₂×C₈×C₅₃	—	2	1	no	—
81	C₂×C₈×C₅₃	—	2	1	no	—
82	C₂×C₈×C₅₃	—	2	1	no	—
83	C₂×C₈×C₅₃	—	4	2	no	—
84	C₂×C₈×C₅₃	—	4	2	no	—
85	C₂×C₈×C₅₃	—	4	2	no	—
86	C₂×C₈×C₅₃	—	4	2	no	—
87	C₂×C₈×C₅₃	—	4	2	no	—
88	C₂×C₈×C₅₃	—	4	2	no	—
89	C₂×C₈×C₅₃	C₂²⋊C₄	1	2	yes	—
90	C₂×C₈×C₅₃	C₂²⋊C₄	1	2	yes	—
91	C₂×C₈×C₅₃	C₂×C₈	1	2	yes	—
92	C₂×C₈×C₅₃	C₂×C₈	1	2	yes	—
93	C₂×C₈×C₅₃	M₁₆	1	2	yes	—
94	C₂×C₈×C₅₃	M₁₆	1	2	yes	—
95	C₄²×C₅₃	—	2	1	no	—
96	C₄²×C₅₃	—	2	1	no	—
97	C₄²×C₅₃	—	2	1	no	—
98	C₄²×C₅₃	—	2	1	no	—
99	C₄²×C₅₃	—	2	1	no	—
100	C₄²×C₅₃	—	2	1	no	—
101	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₅₃	#41	1	1	yes	characteristic
104	C₄²×C₅₃	#41	1	1	yes	characteristic
105	C₂³×C₅₃	—	2	1	no	—
106	C₂³×C₅₃	—	2	1	no	—
107	C₂³×C₅₃	—	2	2	no	—
108	C₂³×C₅₃	—	2	2	no	—
109	C₂³×C₅₃	C₄⋊C₈	1	2	yes	—
110	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄×C₅₃	—	2	1	no	—
112	C₂×C₄×C₅₃	—	2	1	no	—
113	C₂×C₄×C₅₃	—	2	2	no	—
114	C₂×C₄×C₅₃	—	2	2	no	—
115	C₂×C₄×C₅₃	—	2	2	no	—
116	C₂×C₄×C₅₃	—	2	2	no	—
117	C₂×C₄×C₅₃	—	2	2	no	—
118	C₂×C₄×C₅₃	—	2	1	no	—
119	C₂×C₄×C₅₃	—	2	1	no	—
120	C₂×C₄×C₅₃	—	2	2	no	—
121	C₂×C₄×C₅₃	—	2	2	no	—
122	C₂×C₄×C₅₃	—	4	2	no	—
123	C₂×C₄×C₅₃	—	4	2	no	—
124	C₂×C₄×C₅₃	—	4	2	no	—
125	C₂×C₄×C₅₃	—	4	1	no	—
126	C₂×C₄×C₅₃	—	4	1	no	—
127	C₂×C₄×C₅₃	C₄⋊C₈	1	2	yes	—
128	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
130	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
131	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
132	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
133	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
134	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
135	C₂×C₄×C₅₃	C₂×M₁₆	1	1	yes	characteristic
136	C₂×C₄×C₅₃	C₂×M₁₆	1	1	yes	characteristic
137	C₂×C₄×C₅₃	C₂×M₁₆	1	1	yes	characteristic
138	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	2	yes	—
139	C₂×C₄×C₅₃	#137	1	2	yes	—
140	C₈×C₅₃	—	2	2	no	—
141	C₈×C₅₃	—	2	2	no	—
142	C₈×C₅₃	—	2	2	no	—
143	C₈×C₅₃	—	8	2	no	—
144	C₈×C₅₃	—	8	2	no	—
145	C₈×C₅₃	C₂²⋊C₈	1	4	yes	complemented
146	#8597	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂²×C₅₃	—	2	2	no	—
148	C₂²×C₅₃	—	2	4	no	—
149	C₂²×C₅₃	—	4	1	no	—
150	C₂²×C₅₃	—	4	1	no	—
151	C₂²×C₅₃	—	4	2	no	—
152	C₂²×C₅₃	#380	1	1	yes	characteristic
153	C₂²×C₅₃	C₂×C₄⋊C₈	1	1	yes	characteristic
154	C₂²×C₅₃	#423	1	1	yes	characteristic
155	C₂²×C₅₃	#428	1	2	yes	—
156	C₂²×C₅₃	#430	1	2	yes	—
157	C₄×C₅₃	—	2	2	no	—
158	C₄×C₅₃	—	2	1	no	—
159	C₄×C₅₃	—	2	1	no	—
160	C₄×C₅₃	—	4	1	no	—
161	C₄×C₅₃	—	4	1	no	—
162	C₄×C₅₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
163	C₄×C₅₃	#407	1	1	yes	characteristic
164	C₄×C₅₃	#431	1	1	yes	characteristic
165	C₄×C₅₃	#432	1	1	yes	characteristic
166	C₄×C₅₃	#468	1	2	yes	—
167	C₄×C₅₃	#469	1	1	yes	characteristic
168	C₄×C₅₃	#470	1	1	yes	characteristic
169	C₂×C₄×M₁₆	C₂×C₅₃	1	1	yes	characteristic
170	#1797	C₂×C₅₃	1	2	yes	—
171	C₂×#335	C₂×C₅₃	1	1	yes	characteristic, complemented
172	C₂×#334	C₂×C₅₃	1	1	yes	characteristic, complemented
173	#1277	C₂×C₅₃	1	2	yes	complemented
174	C₂×C₅₃	—	4	2	no	—
175	C₂×C₅₃	#1565	1	2	yes	—
176	C₂×C₅₃	#1569	1	2	yes	—
177	C₂×C₅₃	#1797	1	1	yes	characteristic
178	C₂×C₅₃	#1809	1	1	yes	characteristic
179	C₂×C₅₃	#1811	1	1	yes	characteristic
180	C₂²×M₁₆	C₄×C₅₃	1	1	yes	characteristic
181	C₂²×M₁₆	C₄×C₅₃	1	1	yes	characteristic
182	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
183	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	—
184	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	—
185	C₂×C₂²⋊C₈	—	2	2	no	—
186	C₄×M₁₆	—	2	2	no	—
187	C₄×M₁₆	—	2	2	no	—
188	C₂×#97	C₄×C₅₃	1	1	yes	characteristic
189	C₂×#97	C₄×C₅₃	1	1	yes	characteristic
190	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
191	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
192	#336	—	2	2	no	—
193	#335	—	2	2	no	—
194	#334	—	2	2	no	—
195	C₅₃	#8597	1	1	yes	characteristic, direct product factor, Sylow
196	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
197	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
198	C₂³×C₄	Q₈×C₅₃	1	1	yes	characteristic
199	C₂×M₁₆	—	2	2	no	—
200	C₂×M₁₆	—	2	2	no	—
201	C₂×M₁₆	—	2	2	no	—
202	C₂×M₁₆	—	2	2	no	—
203	C₂×M₁₆	—	2	2	no	—
204	C₂×M₁₆	C₈×C₅₃	1	4	yes	complemented
205	C₂²×C₈	—	2	2	no	—
206	C₂²×C₈	—	2	2	no	—
207	C₂²×C₈	C₂×C₄×C₅₃	1	1	yes	characteristic
208	C₂²×C₈	C₂×C₄×C₅₃	1	1	yes	characteristic
209	C₂²×C₈	C₂×C₄×C₅₃	1	1	yes	characteristic
210	C₂²×C₈	C₂×C₄×C₅₃	1	1	yes	characteristic
211	C₂×C₄²	—	2	1	no	—
212	C₂×C₄²	—	2	1	no	—
213	C₂×C₄²	—	2	1	no	—
214	C₂×C₄²	—	2	1	no	—
215	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
216	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
217	C₂×C₄²	Q₈×C₅₃	1	1	yes	characteristic
218	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
219	C₄⋊C₈	—	2	2	no	—
220	C₄⋊C₈	—	2	2	no	—
221	C₄⋊C₈	—	2	2	no	—
222	C₄⋊C₈	—	2	2	no	—
223	C₂²⋊C₈	—	4	4	no	—
224	#97	—	2	2	no	—
225	#97	—	2	2	no	—
226	C₄×C₈	—	2	1	no	—
227	C₄×C₈	—	2	1	no	—
228	C₄×C₈	D₄×C₅₃	1	2	yes	—
229	C₄×C₈	D₄×C₅₃	1	2	yes	—
230	C₂⁴	C₄⋊C₄×C₅₃	1	1	yes	characteristic
231	C₂²×C₄	—	2	1	no	—
232	C₂²×C₄	—	2	1	no	—
233	C₂²×C₄	—	2	1	no	—
234	C₂²×C₄	—	2	1	no	—
235	C₂²×C₄	—	2	1	no	—
236	C₂²×C₄	—	2	1	no	—
237	C₂²×C₄	—	2	1	no	—
238	C₂²×C₄	—	2	1	no	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	4	2	no	—
242	C₂²×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
243	C₂²×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
244	C₂²×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
245	C₂²×C₄	C₂×C₈×C₅₃	1	2	yes	—
246	C₂²×C₄	M₁₆×C₅₃	1	2	yes	—
247	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
248	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
249	C₂²×C₄	C₂×Q₈×C₅₃	1	1	yes	characteristic
250	M₁₆	—	2	8	no	—
251	M₁₆	—	2	8	no	—
252	C₂×C₈	—	2	1	no	—
253	C₂×C₈	—	2	1	no	—
254	C₂×C₈	—	2	1	no	—
255	C₂×C₈	—	2	1	no	—
256	C₂×C₈	—	2	1	no	—
257	C₂×C₈	—	2	1	no	—
258	C₂×C₈	—	4	2	no	—
259	C₂×C₈	—	4	2	no	—
260	C₂×C₈	—	4	2	no	—
261	C₂×C₈	—	4	2	no	—
262	C₂×C₈	—	4	2	no	—
263	C₂×C₈	—	4	2	no	—
264	C₂×C₈	C₂²⋊C₄×C₅₃	1	2	yes	—
265	C₂×C₈	C₂²⋊C₄×C₅₃	1	2	yes	—
266	C₂×C₈	C₂×C₈×C₅₃	1	2	yes	—
267	C₂×C₈	C₂×C₈×C₅₃	1	2	yes	—
268	C₂×C₈	M₁₆×C₅₃	1	2	yes	—
269	C₂×C₈	M₁₆×C₅₃	1	2	yes	—
270	C₄²	—	2	1	no	—
271	C₄²	—	2	1	no	—
272	C₄²	—	2	1	no	—
273	C₄²	—	2	1	no	—
274	C₄²	—	2	1	no	—
275	C₄²	—	2	1	no	—
276	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
277	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
278	C₄²	#41×C₅₃	1	1	yes	characteristic
279	C₄²	#41×C₅₃	1	1	yes	characteristic
280	C₂³	—	2	1	no	—
281	C₂³	—	2	1	no	—
282	C₂³	—	2	2	no	—
283	C₂³	—	2	2	no	—
284	C₂³	C₄⋊C₈×C₅₃	1	2	yes	—
285	C₂³	C₂×C₄⋊C₄×C₅₃	1	1	yes	characteristic
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	1	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	4	2	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	—	4	2	no	—
300	C₂×C₄	—	4	1	no	—
301	C₂×C₄	—	4	1	no	—
302	C₂×C₄	C₄⋊C₈×C₅₃	1	2	yes	—
303	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
304	C₂×C₄	#117×C₅₃	1	1	yes	characteristic
305	C₂×C₄	#121×C₅₃	1	1	yes	characteristic
306	C₂×C₄	#121×C₅₃	1	1	yes	characteristic
307	C₂×C₄	C₂²⋊Q₈×C₅₃	1	1	yes	characteristic
308	C₂×C₄	C₂²⋊Q₈×C₅₃	1	1	yes	characteristic
309	C₂×C₄	C₂²×C₈×C₅₃	1	1	yes	characteristic
310	C₂×C₄	C₂×M₁₆×C₅₃	1	1	yes	characteristic
311	C₂×C₄	C₂×M₁₆×C₅₃	1	1	yes	characteristic
312	C₂×C₄	C₂×M₁₆×C₅₃	1	1	yes	characteristic
313	C₂×C₄	AGL(1,ℤ/8)×C₅₃	1	2	yes	—
314	C₂×C₄	#137×C₅₃	1	2	yes	—
315	C₈	—	2	2	no	—
316	C₈	—	2	2	no	—
317	C₈	—	2	2	no	—
318	C₈	—	8	2	no	—
319	C₈	—	8	2	no	—
320	C₈	C₂²⋊C₈×C₅₃	1	4	yes	complemented
321	C₂²	—	2	2	no	—
322	C₂²	—	2	4	no	—
323	C₂²	—	4	1	no	—
324	C₂²	—	4	1	no	—
325	C₂²	—	4	2	no	—
326	C₂²	C₅₃×#380	1	1	yes	characteristic
327	C₂²	C₂×C₄⋊C₈×C₅₃	1	1	yes	characteristic
328	C₂²	C₅₃×#423	1	1	yes	characteristic
329	C₂²	C₅₃×#428	1	2	yes	—
330	C₂²	C₅₃×#430	1	2	yes	—
331	C₄	—	2	2	no	—
332	C₄	—	2	1	no	—
333	C₄	—	2	1	no	—
334	C₄	—	4	1	no	—
335	C₄	—	4	1	no	—
336	C₄	C₂×C₂²⋊C₈×C₅₃	1	1	yes	characteristic
337	C₄	C₅₃×#407	1	1	yes	characteristic
338	C₄	C₅₃×#431	1	1	yes	characteristic
339	C₄	C₅₃×#432	1	1	yes	characteristic
340	C₄	C₅₃×#468	1	2	yes	—
341	C₄	C₅₃×#469	1	1	yes	characteristic
342	C₄	C₅₃×#470	1	1	yes	characteristic
343	C₂	—	4	2	no	—
344	C₂	C₅₃×#1565	1	2	yes	—
345	C₂	C₅₃×#1569	1	2	yes	—
346	C₂	C₅₃×#1797	1	1	yes	characteristic
347	C₂	C₅₃×#1809	1	1	yes	characteristic
348	C₂	C₅₃×#1811	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₅₃
Frattini, cosocle	C₂×C₄²	C₂³×C₅₃
socle	C₂³×C₅₃	C₂×C₄⋊C₄
prime radical	C₂⁴×C₅₃	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ C₂²×C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₅₃×#335	C₂	semidirect
4. C₂×C₅₃×#334	C₂	semidirect
5. C₅₃×#1277	C₂	semidirect
29. C₂×M₁₆×C₅₃	C₈	semidirect
145. C₈×C₅₃	C₂²⋊C₈	semidirect
146. #8597	C₅₃	direct (N × H)
171. C₂×#335	C₂×C₅₃	semidirect
172. C₂×#334	C₂×C₅₃	semidirect
173. #1277	C₂×C₅₃	semidirect
195. C₅₃	#8597	direct (N × H)
204. C₂×M₁₆	C₈×C₅₃	semidirect
320. C₈	C₂²⋊C₈×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×M₁₆×C₅₃	2
C₅₃×#1797	2
C₂×C₅₃×#335	2
C₂×C₅₃×#334	2
C₅₃×#1277	2
#8597	53

Subgroups — C53×#8597 #27216109

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#8597 #27216109