Subgroups — #27537704

Order 13568.

584 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283407	C₂	1	1	yes	maximal, characteristic
2	#20276543	C₂	1	2	yes	maximal, complemented
3	#20276538	C₂	1	2	yes	maximal, complemented
4	C₁₆×C₂²⋊D₅₃	C₂	1	2	yes	maximal, complemented
5	#20276532	C₂	1	2	yes	maximal, complemented
6	#20276519	C₂	1	2	yes	maximal, complemented
7	#20276329	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²⋊C₁₆×D₅₃	C₂	1	2	yes	maximal, complemented
9	C₅₃×#2113	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
11	#16811130	C₄	1	1	yes	characteristic
12	C₂×#13133157	C₂²	1	1	yes	characteristic, complemented
13	C₂²×#11719908	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₁₆×D₅₃	C₂²	1	2	yes	—
15	C₂×C₁₆×D₅₃	C₂²	1	2	yes	—
16	#16810692	C₄	1	2	yes	—
17	#16810692	C₄	1	2	yes	—
18	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	—
19	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	—
20	#16810651	C₄	1	1	yes	characteristic
21	#16810590	C₄	1	1	yes	characteristic
22	#16810586	C₄	1	1	yes	characteristic
23	#16810578	C₂²	1	1	yes	characteristic
24	#16810441	C₂²	1	2	yes	complemented
25	#16810441	C₂²	1	2	yes	complemented
26	C₂²⋊#11719908	C₂²	1	2	yes	—
27	C₂²⋊#11719908	C₂²	1	2	yes	complemented
28	#16810402	C₂²	1	2	yes	—
29	#16810402	C₂²	1	2	yes	—
30	#16810398	C₂²	1	2	yes	complemented
31	C₁₆×Dic₅₃	C₂²	1	2	yes	complemented
32	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×M₃₂×C₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₅₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
36	C₅₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
37	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
38	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
39	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
40	C₂×C₈×D₅₃	—	4	1	no	—
41	C₂×C₈×D₅₃	—	4	1	no	—
42	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
43	C₂×C₈×D₅₃	C₂³	1	2	yes	—
44	#13133198	C₈	1	1	yes	characteristic
45	#13133198	C₈	1	1	yes	characteristic
46	#13133193	C₈	1	2	yes	—
47	#13133188	C₈	1	2	yes	—
48	#13133185	C₈	1	1	yes	characteristic
49	#13133185	C₈	1	1	yes	characteristic
50	C₄×C₂²⋊D₅₃	C₂×C₄	1	2	yes	—
51	C₄×C₂²⋊D₅₃	C₂×C₄	1	2	yes	—
52	#13133176	C₂×C₄	1	1	yes	characteristic
53	#13133157	—	4	1	no	—
54	C₂×#11719908	—	4	1	no	—
55	C₂×#11719908	C₂³	1	2	yes	—
56	C₂×#11719908	C₂³	1	2	yes	—
57	C₁₆×D₅₃	—	4	2	no	—
58	C₁₆×D₅₃	—	4	2	no	—
59	#13133146	C₂×C₄	1	2	yes	—
60	#13133146	C₂×C₄	1	2	yes	—
61	C₂²⋊#88322	C₂×C₄	1	2	yes	—
62	C₂²⋊#88322	C₂×C₄	1	2	yes	—
63	#13133129	C₂×C₄	1	2	yes	—
64	#13133129	C₂×C₄	1	2	yes	—
65	#13133127	C₂×C₄	1	2	yes	—
66	C₈×Dic₅₃	C₂³	1	2	yes	—
67	C₂×#41×C₅₃	C₂×C₄	1	1	yes	characteristic
68	#131×C₅₃	—	4	1	no	—
69	#131×C₅₃	—	4	1	no	—
70	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
71	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
72	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
76	M₃₂×C₅₃	—	4	1	no	—
77	C₂×C₁₆×C₅₃	—	4	1	no	—
78	C₂×C₁₆×C₅₃	C₂³	1	2	yes	—
79	C₂×C₁₆×C₅₃	C₂³	1	2	yes	—
80	C₂³×D₅₃	C₂×C₈	1	1	yes	characteristic
81	#41×C₅₃	—	4	1	no	—
82	#41×C₅₃	—	4	1	no	—
83	C₂×Q₈×C₅₃	C₂×C₈	1	1	yes	characteristic
84	C₂×D₄×C₅₃	C₂×C₈	1	1	yes	characteristic
85	C₂×D₄×C₅₃	C₂×C₈	1	1	yes	characteristic
86	C₂×D₄×C₅₃	C₂×C₈	1	1	yes	characteristic
87	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₂²⋊D₅₃	C₂×C₈	1	2	yes	—
91	C₂×C₂²⋊D₅₃	C₂×C₈	1	2	yes	—
92	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
93	C₂×C₄×D₅₃	—	4	1	no	—
94	C₂×C₄×D₅₃	—	4	1	no	—
95	C₂×C₄×D₅₃	C₂×C₈	1	2	yes	—
96	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
97	M₁₆×C₅₃	—	4	1	no	—
98	M₁₆×C₅₃	—	4	1	no	—
99	M₁₆×C₅₃	—	4	1	no	—
100	C₂×C₈×C₅₃	—	2	1	no	—
101	C₂×C₈×C₅₃	—	2	1	no	—
102	C₂×C₈×C₅₃	—	2	1	no	—
103	C₂×C₈×C₅₃	—	2	1	no	—
104	C₂×C₈×C₅₃	—	2	1	no	—
105	C₂×C₈×C₅₃	—	2	1	no	—
106	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
110	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
111	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
112	C₂²⋊Dic₅₃	C₂×C₈	1	2	yes	—
113	C₂²⋊Dic₅₃	C₂×C₈	1	2	yes	—
114	#11719921	C₂×C₈	1	2	yes	—
115	#11719921	C₂×C₈	1	2	yes	—
116	C₄⋊Dic₅₃	C₂×C₈	1	2	yes	—
117	#11719919	C₂×C₈	1	2	yes	—
118	#11719919	C₂×C₈	1	2	yes	—
119	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
120	#11719917	—	4	1	no	—
121	C₂×#88322	—	4	1	no	—
122	C₂×#88322	C₂²×C₄	1	2	yes	—
123	C₂×#88322	C₂²×C₄	1	2	yes	—
124	C₈×D₅₃	—	2	2	no	—
125	C₈×D₅₃	—	2	2	no	—
126	C₈×D₅₃	—	4	2	no	—
127	C₁₆×C₅₃	—	2	2	no	—
128	C₁₆×C₅₃	—	2	2	no	—
129	#11719908	—	2	2	no	—
130	#11719908	—	2	2	no	—
131	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
132	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
133	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
134	C₂²×D₅₃	—	2	4	no	—
135	C₂²×D₅₃	—	4	1	no	—
136	C₂²×D₅₃	C₂²×C₈	1	2	yes	—
137	Q₈×C₅₃	—	4	1	no	—
138	D₄×C₅₃	—	4	1	no	—
139	D₄×C₅₃	—	4	1	no	—
140	D₄×C₅₃	—	4	1	no	—
141	C₂×C₄×C₅₃	—	2	1	no	—
142	C₂×C₄×C₅₃	—	2	1	no	—
143	C₂×C₄×C₅₃	—	2	1	no	—
144	C₂×C₄×C₅₃	—	2	1	no	—
145	C₂×C₄×C₅₃	—	2	1	no	—
146	C₂×C₄×C₅₃	—	2	1	no	—
147	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
148	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
149	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
150	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
151	C₂²⋊D₅₃	—	2	4	no	—
152	C₂²⋊D₅₃	—	2	4	no	—
153	C₂×Dic₅₃	—	4	1	no	—
154	C₂×Dic₅₃	C₂²×C₈	1	2	yes	—
155	C₂×Dic₅₃	C₂²×C₈	1	2	yes	—
156	C₂×Dic₅₃	C₂²×C₈	1	2	yes	—
157	C₄×D₅₃	—	2	2	no	—
158	C₄×D₅₃	—	2	2	no	—
159	C₄×D₅₃	—	4	2	no	—
160	C₈×C₅₃	—	2	1	no	—
161	C₈×C₅₃	—	2	1	no	—
162	C₈×C₅₃	—	2	1	no	—
163	C₈×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
164	C₈×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
165	#88322	—	2	2	no	—
166	#88322	—	2	2	no	—
167	#33491	—	53	1	no	maximal, Sylow
168	C₂²×C₅₃	—	2	2	no	—
169	C₂²×C₅₃	—	2	2	no	—
170	C₂²×C₅₃	—	2	2	no	—
171	C₂²×C₅₃	—	2	1	no	—
172	C₂²×C₅₃	—	2	1	no	—
173	C₂²×C₅₃	—	2	1	no	—
174	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
175	C₂×D₅₃	—	2	2	no	—
176	C₂×D₅₃	—	2	2	no	—
177	C₂×D₅₃	—	4	4	no	—
178	C₂×D₅₃	#504	1	4	yes	—
179	C₄×C₅₃	—	2	1	no	—
180	C₄×C₅₃	—	2	1	no	—
181	C₄×C₅₃	—	2	1	no	—
182	C₄×C₅₃	#518	1	1	yes	characteristic
183	C₄×C₅₃	#568	1	1	yes	characteristic
184	Dic₅₃	—	2	2	no	—
185	Dic₅₃	—	2	2	no	—
186	Dic₅₃	—	2	2	no	—
187	#2929	—	53	1	no	—
188	#2168	—	53	2	no	—
189	#2168	—	53	2	no	—
190	D₄×C₁₆	—	53	2	no	—
191	D₄×C₁₆	—	53	2	no	—
192	#2164	—	53	2	no	—
193	#2113	—	53	1	no	—
194	#2113	D₅₃	1	1	yes	characteristic, complemented
195	C₂×C₂²⋊C₁₆	—	53	2	no	—
196	C₂×C₅₃	—	4	1	no	—
197	C₂×C₅₃	—	4	1	no	—
198	C₂×C₅₃	—	4	1	no	—
199	C₂×C₅₃	#2972	1	1	yes	characteristic
200	C₂×C₅₃	C₂×#504	1	2	yes	—
201	D₅₃	—	2	4	no	—
202	C₂×#131	C₂×D₅₃	1	1	yes	characteristic
203	C₂³×C₈	—	53	1	no	—
204	#525	—	53	1	no	—
205	C₂×M₃₂	—	53	1	no	—
206	C₂×M₃₂	C₂×D₅₃	1	1	yes	characteristic, complemented
207	C₂²×C₁₆	—	53	1	no	—
208	C₂²×C₁₆	—	53	2	no	—
209	C₂²×C₁₆	—	53	2	no	—
210	C₂²×C₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
211	#435	—	53	2	no	—
212	#435	—	53	2	no	—
213	C₈×D₄	—	53	2	no	—
214	C₈×D₄	—	53	2	no	—
215	#424	—	53	1	no	—
216	#408	—	53	1	no	—
217	#407	—	53	1	no	—
218	#405	—	53	1	no	—
219	C₄⋊C₁₆	—	53	2	no	—
220	C₄⋊C₁₆	—	53	2	no	—
221	C₂²⋊C₁₆	—	53	2	no	—
222	C₂²⋊C₁₆	—	53	2	no	—
223	C₂²⋊C₁₆	—	53	2	no	—
224	C₂²⋊C₁₆	—	53	2	no	—
225	C₂²⋊C₁₆	C₂×D₅₃	1	2	yes	—
226	C₂²⋊C₁₆	C₂×D₅₃	1	2	yes	complemented
227	#346	—	53	2	no	—
228	C₄×C₁₆	—	53	2	no	—
229	C₅₃	#33491	1	1	yes	characteristic, complemented, Sylow
230	C₂×#41	C₄×D₅₃	1	1	yes	characteristic
231	C₂³×C₄	—	53	1	no	—
232	#131	—	4	1	no	—
233	#131	—	4	1	no	—
234	C₂×M₁₆	—	53	1	no	—
235	C₂×M₁₆	C₄×D₅₃	1	1	yes	characteristic
236	C₂×M₁₆	C₄×D₅₃	1	1	yes	characteristic
237	C₂×M₁₆	C₄×D₅₃	1	1	yes	characteristic
238	C₂²×C₈	—	53	1	no	—
239	C₂²×C₈	—	53	2	no	—
240	C₂²×C₈	—	53	2	no	—
241	C₂²×C₈	—	212	1	no	—
242	C₂²×C₈	—	212	1	no	—
243	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
244	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
245	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
246	#123	—	53	1	no	—
247	#123	—	53	1	no	—
248	C₂²⋊Q₈	—	53	2	no	—
249	#121	—	53	2	no	—
250	#120	—	53	1	no	—
251	#120	—	53	1	no	—
252	C₄×D₄	—	53	2	no	—
253	C₄×D₄	—	53	2	no	—
254	#117	—	53	1	no	—
255	M₃₂	—	4	1	no	—
256	M₃₂	—	212	1	no	—
257	C₂×C₁₆	—	4	1	no	—
258	C₂×C₁₆	—	53	2	no	—
259	C₂×C₁₆	—	53	2	no	—
260	C₂×C₁₆	—	212	2	no	—
261	C₂×C₁₆	—	212	2	no	—
262	C₂×C₁₆	—	212	1	no	—
263	C₂×C₁₆	C₂²×D₅₃	1	2	yes	—
264	C₂×C₁₆	C₂²×D₅₃	1	2	yes	—
265	C₄⋊C₈	—	53	2	no	—
266	C₄⋊C₈	—	53	2	no	—
267	C₂²⋊C₈	—	53	2	no	—
268	C₂²⋊C₈	—	53	2	no	—
269	C₂²⋊C₈	—	53	2	no	—
270	C₂²⋊C₈	—	53	2	no	—
271	#97	—	53	2	no	—
272	C₄×C₈	—	53	2	no	—
273	C₂⁴	—	53	1	no	—
274	#41	—	4	1	no	—
275	#41	—	4	1	no	—
276	C₂×Q₈	C₈×D₅₃	1	1	yes	characteristic
277	C₂×D₄	—	53	2	no	—
278	C₂×D₄	—	53	2	no	—
279	C₂×D₄	C₈×D₅₃	1	1	yes	characteristic
280	C₂×D₄	C₈×D₅₃	1	1	yes	characteristic
281	C₂×D₄	C₈×D₅₃	1	1	yes	characteristic
282	C₂²×C₄	—	53	1	no	—
283	C₂²×C₄	—	53	2	no	—
284	C₂²×C₄	—	53	2	no	—
285	C₂²×C₄	—	212	1	no	—
286	C₂²×C₄	—	212	1	no	—
287	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
290	M₁₆	—	4	1	no	—
291	M₁₆	—	4	1	no	—
292	M₁₆	—	4	1	no	—
293	M₁₆	—	212	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	53	2	no	—
301	C₂×C₈	—	53	2	no	—
302	C₂×C₈	—	106	2	no	—
303	C₂×C₈	—	106	2	no	—
304	C₂×C₈	—	212	2	no	—
305	C₂×C₈	—	212	1	no	—
306	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
307	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
308	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
309	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
310	C₄⋊C₄	—	53	2	no	—
311	C₄⋊C₄	—	53	2	no	—
312	C₄⋊C₄	—	53	2	no	—
313	C₂²⋊C₄	—	53	1	no	—
314	C₂²⋊C₄	—	53	1	no	—
315	C₂²⋊C₄	—	53	2	no	—
316	C₂²⋊C₄	—	53	2	no	—
317	C₂²⋊C₄	—	53	2	no	—
318	C₂²⋊C₄	—	53	2	no	—
319	C₄²	—	53	2	no	—
320	C₁₆	—	2	2	no	—
321	C₁₆	—	2	2	no	—
322	C₁₆	—	106	2	no	—
323	C₁₆	—	106	2	no	—
324	C₂³	—	53	2	no	—
325	C₂³	—	106	4	no	—
326	C₂³	—	212	1	no	—
327	C₂³	C₂×C₈×D₅₃	1	1	yes	characteristic
328	C₂³	C₂×C₈×D₅₃	1	1	yes	characteristic
329	C₂³	C₂×C₈×D₅₃	1	1	yes	characteristic
330	Q₈	—	4	1	no	—
331	D₄	—	4	1	no	—
332	D₄	—	4	1	no	—
333	D₄	—	4	1	no	—
334	D₄	—	106	4	no	—
335	D₄	—	106	4	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	53	2	no	—
343	C₂×C₄	—	53	2	no	—
344	C₂×C₄	—	53	2	no	—
345	C₂×C₄	—	106	2	no	—
346	C₂×C₄	—	106	2	no	—
347	C₂×C₄	—	212	2	no	—
348	C₂×C₄	—	212	1	no	—
349	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
350	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
351	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
352	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
353	C₈	—	2	1	no	—
354	C₈	—	2	1	no	—
355	C₈	—	2	1	no	—
356	C₈	—	106	2	no	—
357	C₈	—	106	2	no	—
358	C₈	#13133262	1	1	yes	characteristic
359	C₈	#13133262	1	1	yes	characteristic
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	53	4	no	—
367	C₂²	—	106	2	no	—
368	C₂²	—	106	2	no	—
369	C₂²	—	212	4	no	—
370	C₂²	C₂²×C₈×D₅₃	1	1	yes	characteristic
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	106	2	no	—
375	C₄	—	106	2	no	—
376	C₄	—	106	2	no	—
377	C₄	#16811096	1	1	yes	characteristic
378	C₄	#16811389	1	1	yes	characteristic
379	C₂	—	4	1	no	—
380	C₂	—	4	1	no	—
381	C₂	—	4	1	no	—
382	C₂	—	106	4	no	—
383	C₂	#20283737	1	1	yes	characteristic
384	C₂	#504×D₅₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₅₃
commutator, socle	C₂²×C₅₃	C₂³×C₈
Fitting	C₅₃×#2113	C₂
prime radical	#16811130	C₄
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	#2113	D₅₃
hypocenter	C₅₃	#33491
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ #2113

Complements

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

N	H ≅ G/N	type
2. #20276543	C₂	semidirect
3. #20276538	C₂	semidirect
4. C₁₆×C₂²⋊D₅₃	C₂	semidirect
5. #20276532	C₂	semidirect
6. #20276519	C₂	semidirect
7. #20276329	C₂	semidirect
8. C₂²⋊C₁₆×D₅₃	C₂	semidirect
9. C₅₃×#2113	C₂	semidirect
12. C₂×#13133157	C₂²	semidirect
13. C₂²×#11719908	C₂²	semidirect
24. #16810441	C₂²	semidirect
25. #16810441	C₂²	semidirect
27. C₂²⋊#11719908	C₂²	semidirect
30. #16810398	C₂²	semidirect
31. C₁₆×Dic₅₃	C₂²	semidirect
33. C₂×M₃₂×C₅₃	C₂²	semidirect
34. C₂²×C₁₆×C₅₃	C₂²	semidirect
36. C₅₃×C₂²⋊C₁₆	C₂²	semidirect
194. #2113	D₅₃	semidirect
206. C₂×M₃₂	C₂×D₅₃	semidirect
210. C₂²×C₁₆	C₂×D₅₃	semidirect
226. C₂²⋊C₁₆	C₂×D₅₃	semidirect
229. C₅₃	#33491	semidirect

Maximal subgroups

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

subgroup	index
#20283407	2
#20276543	2
#20276538	2
C₁₆×C₂²⋊D₅₃	2
#20276532	2
#20276519	2
#20276329	2
C₂²⋊C₁₆×D₅₃	2
C₅₃×#2113	2
#33491	53