Subgroups — #27540882

Order 13568.

668 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20287853	C₂	1	1	yes	maximal, characteristic, complemented
2	#20286512	C₂	1	2	yes	maximal, complemented
3	#20276963	C₂	1	1	yes	maximal, characteristic, complemented
4	#20276835	C₂	1	1	yes	maximal, characteristic, complemented
5	#20276832	C₂	1	1	yes	maximal, characteristic, complemented
6	#20276789	C₂	1	2	yes	maximal, complemented
7	#20276672	C₂	1	2	yes	maximal, complemented
8	#20276669	C₂	1	2	yes	maximal, complemented
9	#20276596	C₂	1	1	yes	maximal, characteristic, complemented
10	#20276550	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3415	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811426	—	2	2	no	—
13	#16811425	C₂²	1	2	yes	complemented
14	#16811060	—	2	2	no	—
15	#16811058	C₂²	1	2	yes	complemented
16	#16811056	—	2	1	no	—
17	C₂×D₈₄₈	C₂²	1	1	yes	characteristic, complemented
18	C₂×#13133158	C₂²	1	2	yes	complemented
19	D₁₆×D₅₃	—	2	1	no	—
20	#16811039	C₂²	1	1	yes	characteristic, complemented
21	#16810998	C₂²	1	2	yes	complemented
22	#16810893	C₂²	1	2	yes	complemented
23	#16810891	—	2	2	no	—
24	#16810890	C₂²	1	2	yes	complemented
25	#16810791	—	2	2	no	—
26	#16810789	—	2	2	no	—
27	#16810740	C₂²	1	2	yes	complemented
28	#16810738	C₂²	1	1	yes	characteristic
29	#16810453	C₂²	1	1	yes	characteristic, complemented
30	#16810443	C₂²	1	1	yes	characteristic, complemented
31	#16810437	C₂²	1	2	yes	complemented
32	#16810436	C₂²	1	2	yes	complemented
33	#16810430	C₂²	1	2	yes	complemented
34	#16810408	C₂²	1	1	yes	characteristic, complemented
35	#16810407	C₂²	1	1	yes	characteristic, complemented
36	C₁₆×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#576	C₂²	1	2	yes	complemented
38	C₅₃×#509	—	2	2	no	—
39	C₅₃×#509	C₂²	1	2	yes	complemented
40	C₅₃×#508	—	2	1	no	—
41	C₅₃×#508	C₂²	1	1	yes	characteristic
42	C₂×D₁₆×C₅₃	—	2	1	no	—
43	C₂×D₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
44	C₅₃×#504	C₂²	1	1	yes	characteristic, complemented
45	#13133263	—	2	2	no	—
46	#13133244	—	4	2	no	—
47	#13133243	—	2	2	no	—
48	#13133243	—	4	2	no	—
49	#13133242	—	2	2	no	—
50	#13133242	—	2	2	no	—
51	#13133242	—	4	2	no	—
52	#13133240	—	2	2	no	—
53	#13133237	—	4	2	no	—
54	#13133237	D₄	1	1	yes	characteristic
55	C₂×D₄₂₄	C₂³	1	2	yes	—
56	C₂×#11719922	—	2	2	no	—
57	C₂×#11719922	—	4	2	no	—
58	D₈×D₅₃	—	2	2	no	—
59	#13133224	—	2	2	no	—
60	#13133223	C₂³	1	1	yes	characteristic
61	#13133213	—	2	2	no	—
62	#13133160	—	2	2	no	—
63	D₈₄₈	—	2	1	no	—
64	D₈₄₈	—	2	1	no	—
65	#13133158	—	2	2	no	—
66	#13133158	—	4	2	no	—
67	#13133157	C₂³	1	1	yes	characteristic
68	#13133156	—	2	1	no	—
69	C₂×#11719908	C₂³	1	1	yes	characteristic
70	C₁₆×D₅₃	—	2	1	no	—
71	#13133153	C₂³	1	2	yes	—
72	#13133152	D₄	1	1	yes	characteristic
73	#13133144	—	2	2	no	—
74	#13133144	D₄	1	1	yes	characteristic
75	#13133143	D₄	1	1	yes	characteristic
76	#13133134	—	2	2	no	—
77	#13133133	—	2	2	no	—
78	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
79	H(5,𝔽₂)×C₅₃	—	2	2	no	—
80	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
81	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
82	#135×C₅₃	—	2	2	no	—
83	#135×C₅₃	C₂³	1	2	yes	—
84	C₂×D₈×C₅₃	—	2	2	no	—
85	C₂×D₈×C₅₃	C₂³	1	2	yes	—
86	#131×C₅₃	C₂³	1	1	yes	characteristic
87	Q₃₂×C₅₃	D₄	1	1	yes	characteristic, complemented
88	SD₃₂×C₅₃	—	2	2	no	—
89	SD₃₂×C₅₃	D₄	1	2	yes	complemented
90	D₁₆×C₅₃	—	2	2	no	—
91	D₁₆×C₅₃	—	2	1	no	—
92	D₁₆×C₅₃	—	2	1	no	—
93	D₁₆×C₅₃	D₄	1	1	yes	characteristic, complemented
94	M₃₂×C₅₃	—	2	1	no	—
95	M₃₂×C₅₃	C₂³	1	1	yes	characteristic
96	C₂×C₁₆×C₅₃	—	2	1	no	—
97	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
98	#41×C₅₃	—	2	2	no	—
99	#41×C₅₃	—	4	2	no	—
100	#41×C₅₃	—	4	2	no	—
101	#41×C₅₃	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₅₃	—	2	2	no	—
103	C₂×D₄×C₅₃	—	4	2	no	—
104	C₂×D₄×C₅₃	—	4	2	no	—
105	C₂×D₄×C₅₃	—	8	2	no	—
106	C₂×C₂²⋊D₅₃	—	8	2	no	—
107	#11719949	—	4	2	no	—
108	D₄×D₅₃	—	4	2	no	—
109	D₄×D₅₃	—	8	2	no	—
110	#11719945	—	4	2	no	—
111	#11719945	C₂×D₄	1	1	yes	characteristic
112	C₂×D₂₁₂	—	2	2	no	—
113	C₂×D₂₁₂	—	4	2	no	—
114	Q₁₆×C₅₃	C₂×D₄	1	2	yes	—
115	SD₁₆×C₅₃	—	2	2	no	—
116	SD₁₆×C₅₃	—	4	2	no	—
117	D₈×C₅₃	—	2	2	no	—
118	D₈×C₅₃	—	2	2	no	—
119	D₈×C₅₃	—	4	2	no	—
120	D₈×C₅₃	C₂×D₄	1	2	yes	—
121	M₁₆×C₅₃	—	2	1	no	—
122	M₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₅₃	—	2	1	no	—
124	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
125	#11719925	D₈	1	1	yes	characteristic
126	#11719924	—	4	2	no	—
127	#11719924	—	4	2	no	—
128	#11719924	D₈	1	1	yes	characteristic
129	#11719923	—	4	2	no	—
130	#11719923	D₈	1	1	yes	characteristic
131	#11719922	—	4	2	no	—
132	#11719922	—	4	2	no	—
133	#11719922	—	4	2	no	—
134	#11719922	—	4	2	no	—
135	#11719922	—	4	2	no	—
136	#11719922	D₈	1	1	yes	characteristic
137	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
138	#11719917	—	2	2	no	—
139	#11719917	—	4	2	no	—
140	#11719917	C₂×D₄	1	1	yes	characteristic
141	C₂×#88322	—	4	2	no	—
142	C₂×#88322	C₂×D₄	1	1	yes	characteristic
143	D₄₂₄	—	2	2	no	—
144	D₄₂₄	—	2	2	no	—
145	#11719912	—	2	1	no	—
146	C₈×D₅₃	—	2	1	no	—
147	C₁₆×C₅₃	—	2	1	no	—
148	C₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
149	C₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
150	#11719908	—	2	1	no	—
151	#11719908	—	2	1	no	—
152	C₂³×C₅₃	—	4	2	no	—
153	C₂³×C₅₃	—	8	2	no	—
154	C₂²×D₅₃	—	4	2	no	—
155	C₂²×D₅₃	—	8	2	no	—
156	Q₈×C₅₃	—	2	2	no	—
157	Q₈×C₅₃	C₂×D₈	1	1	yes	characteristic
158	D₄×C₅₃	—	2	1	no	—
159	D₄×C₅₃	—	2	2	no	—
160	D₄×C₅₃	—	4	2	no	—
161	D₄×C₅₃	—	4	2	no	—
162	D₄×C₅₃	—	4	2	no	—
163	D₄×C₅₃	—	8	2	no	—
164	D₄×C₅₃	—	8	2	no	—
165	D₄×C₅₃	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₅₃	—	2	1	no	—
167	C₂×C₄×C₅₃	—	4	2	no	—
168	C₂×C₄×C₅₃	—	8	2	no	—
169	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
170	C₂²⋊D₅₃	—	2	1	no	—
171	C₂²⋊D₅₃	—	8	2	no	—
172	C₂²⋊D₅₃	—	16	4	no	—
173	C₂×Dic₅₃	—	2	1	no	—
174	D₂₁₂	—	4	2	no	—
175	D₂₁₂	—	4	2	no	—
176	D₂₁₂	—	8	2	no	—
177	D₂₁₂	C₂×D₈	1	1	yes	characteristic
178	C₄×D₅₃	—	2	1	no	—
179	C₄×D₅₃	—	8	2	no	—
180	Dic₁₀₆	C₂×D₈	1	1	yes	characteristic
181	C₈×C₅₃	—	2	1	no	—
182	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
183	C₈×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
184	#88322	—	2	1	no	—
185	#88322	—	4	2	no	—
186	#88322	C₂×D₈	1	1	yes	characteristic
187	#88322	C₂×D₈	1	1	yes	characteristic
188	#33858	—	53	1	no	maximal, Sylow
189	C₂²×C₅₃	—	2	1	no	—
190	C₂²×C₅₃	—	4	2	no	—
191	C₂²×C₅₃	—	8	2	no	—
192	C₂²×C₅₃	—	16	2	no	—
193	C₂²×C₅₃	—	32	2	no	—
194	C₂²×C₅₃	#576	1	1	yes	characteristic
195	C₂×D₅₃	—	2	1	no	—
196	C₂×D₅₃	—	8	2	no	—
197	C₂×D₅₃	—	16	2	no	—
198	C₂×D₅₃	—	32	2	no	—
199	C₄×C₅₃	—	2	1	no	—
200	C₄×C₅₃	—	4	2	no	—
201	C₄×C₅₃	D₄²	1	1	yes	characteristic
202	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
203	Dic₅₃	—	2	2	no	—
204	Dic₅₃	—	2	1	no	—
205	#3415	—	53	1	no	—
206	#3415	D₅₃	1	1	yes	characteristic, complemented
207	#3292	—	53	2	no	—
208	#2246	—	53	1	no	—
209	#2221	—	53	1	no	—
210	#2221	—	53	1	no	—
211	#2213	—	53	2	no	—
212	#2192	—	53	2	no	—
213	#2192	—	53	2	no	—
214	#2178	—	53	1	no	—
215	#2170	—	53	1	no	—
216	C₂×C₅₃	—	2	1	no	—
217	C₂×C₅₃	—	4	1	no	—
218	C₂×C₅₃	—	8	2	no	—
219	C₂×C₅₃	—	16	2	no	—
220	C₂×C₅₃	D₄×D₈	1	1	yes	characteristic
221	D₅₃	—	4	1	no	—
222	D₅₃	—	16	2	no	—
223	#576	—	53	2	no	—
224	#576	—	106	2	no	—
225	#576	C₂×D₅₃	1	2	yes	complemented
226	#509	—	2	2	no	—
227	#509	—	53	2	no	—
228	#509	—	106	2	no	—
229	#509	C₂×D₅₃	1	2	yes	complemented
230	#508	—	2	1	no	—
231	#508	—	106	1	no	—
232	#508	C₂×D₅₃	1	1	yes	characteristic
233	C₂×D₁₆	—	2	1	no	—
234	C₂×D₁₆	—	53	2	no	—
235	C₂×D₁₆	—	53	1	no	—
236	C₂×D₁₆	—	106	1	no	—
237	C₂×D₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
238	#504	—	53	1	no	—
239	#504	C₂×D₅₃	1	1	yes	characteristic, complemented
240	#493	—	53	2	no	—
241	#472	—	53	2	no	—
242	#472	—	53	2	no	—
243	#472	—	106	2	no	—
244	#453	—	106	2	no	—
245	#453	—	106	2	no	—
246	#443	—	53	1	no	—
247	#443	—	53	2	no	—
248	#368	—	53	1	no	—
249	#364	—	53	1	no	—
250	#361	—	53	2	no	—
251	#361	—	53	2	no	—
252	#359	—	53	2	no	—
253	#350	—	53	1	no	—
254	#350	—	53	1	no	—
255	C₄×C₁₆	—	53	1	no	—
256	C₅₃	#33858	1	1	yes	characteristic, complemented, Sylow
257	H(5,𝔽₂)	—	2	2	no	—
258	H(5,𝔽₂)	—	106	2	no	—
259	AGL(1,ℤ/8)	—	2	2	no	—
260	AGL(1,ℤ/8)	—	4	2	no	—
261	AGL(1,ℤ/8)	—	106	2	no	—
262	AGL(1,ℤ/8)	—	106	2	no	—
263	AGL(1,ℤ/8)	—	106	2	no	—
264	AGL(1,ℤ/8)	—	212	2	no	—
265	AGL(1,ℤ/8)	—	212	2	no	—
266	AGL(1,ℤ/8)	—	212	2	no	—
267	#135	—	2	2	no	—
268	#135	—	53	1	no	—
269	#135	—	106	2	no	—
270	#135	—	212	2	no	—
271	#135	C₂²×D₅₃	1	2	yes	—
272	C₂×D₈	—	2	2	no	—
273	C₂×D₈	—	53	2	no	—
274	C₂×D₈	—	106	2	no	—
275	C₂×D₈	—	106	2	no	—
276	C₂×D₈	—	212	2	no	—
277	C₂×D₈	C₂²×D₅₃	1	2	yes	—
278	#131	—	53	1	no	—
279	#131	—	106	2	no	—
280	#131	C₂²×D₅₃	1	1	yes	characteristic
281	#127	—	106	2	no	—
282	Q₃₂	C₂²⋊D₅₃	1	1	yes	characteristic, complemented
283	SD₃₂	—	2	2	no	—
284	SD₃₂	—	106	2	no	—
285	SD₃₂	C₂²⋊D₅₃	1	2	yes	complemented
286	D₁₆	—	2	2	no	—
287	D₁₆	—	2	1	no	—
288	D₁₆	—	2	1	no	—
289	D₁₆	—	106	2	no	—
290	D₁₆	—	106	1	no	—
291	D₁₆	—	106	1	no	—
292	D₁₆	—	212	2	no	—
293	D₁₆	C₂²⋊D₅₃	1	1	yes	characteristic, complemented
294	M₃₂	—	2	1	no	—
295	M₃₂	—	53	1	no	—
296	M₃₂	—	106	1	no	—
297	M₃₂	C₂²×D₅₃	1	1	yes	characteristic
298	C₂×C₁₆	—	2	1	no	—
299	C₂×C₁₆	—	53	1	no	—
300	C₂×C₁₆	—	106	1	no	—
301	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
302	#108	—	53	1	no	—
303	#108	—	53	2	no	—
304	#104	—	53	1	no	—
305	#104	—	53	1	no	—
306	#104	—	106	2	no	—
307	#100	—	106	2	no	—
308	#100	—	106	2	no	—
309	C₄×C₈	—	53	1	no	—
310	#41	—	2	2	no	—
311	#41	—	4	2	no	—
312	#41	—	4	2	no	—
313	#41	—	53	1	no	—
314	#41	—	212	2	no	—
315	#41	—	212	2	no	—
316	#41	D₄×D₅₃	1	1	yes	characteristic
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	—	8	2	no	—
321	C₂×D₄	—	106	2	no	—
322	C₂×D₄	—	424	2	no	—
323	C₂×D₄	—	424	2	no	—
324	C₂×D₄	—	212	2	no	—
325	C₂×D₄	—	212	2	no	—
326	Q₁₆	—	53	1	no	—
327	Q₁₆	C₂×C₂²⋊D₅₃	1	2	yes	—
328	SD₁₆	—	2	2	no	—
329	SD₁₆	—	4	2	no	—
330	SD₁₆	—	53	1	no	—
331	SD₁₆	—	53	1	no	—
332	SD₁₆	—	212	2	no	—
333	SD₁₆	—	212	2	no	—
334	SD₁₆	—	212	2	no	—
335	D₈	—	2	2	no	—
336	D₈	—	2	2	no	—
337	D₈	—	4	2	no	—
338	D₈	—	53	1	no	—
339	D₈	—	106	2	no	—
340	D₈	—	106	2	no	—
341	D₈	—	212	2	no	—
342	D₈	—	212	2	no	—
343	D₈	—	212	2	no	—
344	D₈	—	212	2	no	—
345	D₈	—	212	2	no	—
346	D₈	C₂×C₂²⋊D₅₃	1	2	yes	—
347	M₁₆	—	2	1	no	—
348	M₁₆	—	53	1	no	—
349	M₁₆	—	106	1	no	—
350	M₁₆	—	106	2	no	—
351	M₁₆	—	212	2	no	—
352	M₁₆	D₄×D₅₃	1	1	yes	characteristic
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	53	1	no	—
355	C₂×C₈	—	106	1	no	—
356	C₂×C₈	—	212	2	no	—
357	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
358	C₄²	—	53	1	no	—
359	C₁₆	—	2	1	no	—
360	C₁₆	—	106	1	no	—
361	C₁₆	—	106	1	no	—
362	C₁₆	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
363	C₁₆	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
364	C₂³	—	4	2	no	—
365	C₂³	—	8	2	no	—
366	C₂³	—	424	2	no	—
367	C₂³	—	212	2	no	—
368	Q₈	—	2	2	no	—
369	Q₈	—	53	1	no	—
370	Q₈	D₈×D₅₃	1	1	yes	characteristic
371	D₄	—	2	1	no	—
372	D₄	—	2	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	8	2	no	—
377	D₄	—	8	2	no	—
378	D₄	—	53	1	no	—
379	D₄	—	848	4	no	—
380	D₄	—	106	1	no	—
381	D₄	—	424	2	no	—
382	D₄	—	424	2	no	—
383	D₄	—	212	2	no	—
384	D₄	—	212	2	no	—
385	D₄	D₈×D₅₃	1	1	yes	characteristic
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	8	2	no	—
389	C₂×C₄	—	106	1	no	—
390	C₂×C₄	—	106	1	no	—
391	C₂×C₄	—	424	2	no	—
392	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	53	1	no	—
395	C₈	—	53	1	no	—
396	C₈	—	106	1	no	—
397	C₈	—	212	2	no	—
398	C₈	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
399	C₈	#13133262	1	1	yes	characteristic
400	C₂²	—	2	1	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	16	2	no	—
404	C₂²	—	32	2	no	—
405	C₂²	—	848	2	no	—
406	C₂²	—	106	1	no	—
407	C₂²	—	1696	2	no	—
408	C₂²	—	424	2	no	—
409	C₂²	#16811424	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	4	2	no	—
412	C₄	—	106	2	no	—
413	C₄	—	106	1	no	—
414	C₄	D₄×C₂²⋊D₅₃	1	1	yes	characteristic
415	C₄	C₂×D₈×D₅₃	1	1	yes	characteristic
416	C₂	—	2	1	no	—
417	C₂	—	4	1	no	—
418	C₂	—	8	2	no	—
419	C₂	—	16	2	no	—
420	C₂	—	848	2	no	—
421	C₂	—	212	1	no	—
422	C₂	D₈×C₂²⋊D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×C₂²⋊D₅₃
commutator, cosocle	C₂×C₈×C₅₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₅₃×#3415	C₂
socle	C₂×C₅₃	D₄×D₈
hypercenter	#3415	D₅₃
hypocenter	C₅₃	#33858
LCS	G ▷ C₂×C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #3415

Complements

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

N	H ≅ G/N	type
1. #20287853	C₂	semidirect
2. #20286512	C₂	semidirect
3. #20276963	C₂	semidirect
4. #20276835	C₂	semidirect
5. #20276832	C₂	semidirect
6. #20276789	C₂	semidirect
7. #20276672	C₂	semidirect
8. #20276669	C₂	semidirect
9. #20276596	C₂	semidirect
10. #20276550	C₂	semidirect
11. C₅₃×#3415	C₂	semidirect
13. #16811425	C₂²	semidirect
15. #16811058	C₂²	semidirect
17. C₂×D₈₄₈	C₂²	semidirect
18. C₂×#13133158	C₂²	semidirect
20. #16811039	C₂²	semidirect
21. #16810998	C₂²	semidirect
22. #16810893	C₂²	semidirect
24. #16810890	C₂²	semidirect
27. #16810740	C₂²	semidirect
29. #16810453	C₂²	semidirect
30. #16810443	C₂²	semidirect
31. #16810437	C₂²	semidirect
32. #16810436	C₂²	semidirect
33. #16810430	C₂²	semidirect
34. #16810408	C₂²	semidirect
35. #16810407	C₂²	semidirect
36. C₁₆×Dic₅₃	C₂²	semidirect
37. C₅₃×#576	C₂²	semidirect
39. C₅₃×#509	C₂²	semidirect
43. C₂×D₁₆×C₅₃	C₂²	semidirect
44. C₅₃×#504	C₂²	semidirect
87. Q₃₂×C₅₃	D₄	semidirect
89. SD₃₂×C₅₃	D₄	semidirect
93. D₁₆×C₅₃	D₄	semidirect
206. #3415	D₅₃	semidirect
225. #576	C₂×D₅₃	semidirect
229. #509	C₂×D₅₃	semidirect
237. C₂×D₁₆	C₂×D₅₃	semidirect
239. #504	C₂×D₅₃	semidirect
256. C₅₃	#33858	semidirect
282. Q₃₂	C₂²⋊D₅₃	semidirect
285. SD₃₂	C₂²⋊D₅₃	semidirect
293. D₁₆	C₂²⋊D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20287853	2
#20286512	2
#20276963	2
#20276835	2
#20276832	2
#20276789	2
#20276672	2
#20276669	2
#20276596	2
#20276550	2
C₅₃×#3415	2
#33858	53