Subgroups — #27540884

Order 13568.

668 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20287854	C₂	1	2	yes	maximal, complemented
2	#20286515	C₂	1	1	yes	maximal, characteristic, complemented
3	#20276964	C₂	1	1	yes	maximal, characteristic, complemented
4	#20276833	C₂	1	2	yes	maximal, complemented
5	#20276791	C₂	1	1	yes	maximal, characteristic, complemented
6	#20276788	C₂	1	1	yes	maximal, characteristic, complemented
7	#20276672	C₂	1	2	yes	maximal, complemented
8	#20276670	C₂	1	2	yes	maximal, complemented
9	#20276594	C₂	1	1	yes	maximal, characteristic, complemented
10	#20276552	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3292	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811428	C₂²	1	2	yes	complemented
13	#16811425	—	2	1	no	—
14	#16811059	—	2	2	no	—
15	#16811059	C₂²	1	2	yes	complemented
16	#16811058	—	2	2	no	—
17	#16811058	C₂²	1	2	yes	complemented
18	#16811053	—	2	2	no	—
19	#16811053	C₂²	1	1	yes	characteristic
20	C₂×#13133158	—	2	2	no	—
21	C₂×#13133158	C₂²	1	2	yes	complemented
22	C₂×#13133158	C₂²	1	2	yes	complemented
23	#16811040	C₂²	1	2	yes	complemented
24	#16811000	C₂²	1	1	yes	characteristic, complemented
25	#16810894	—	2	1	no	—
26	#16810893	C₂²	1	2	yes	complemented
27	#16810792	—	2	2	no	—
28	#16810741	C₂²	1	1	yes	characteristic, complemented
29	#16810452	C₂²	1	1	yes	characteristic, complemented
30	#16810444	C₂²	1	1	yes	characteristic, complemented
31	#16810436	C₂²	1	2	yes	complemented
32	#16810435	C₂²	1	2	yes	complemented
33	#16810430	C₂²	1	1	yes	characteristic, complemented
34	#16810429	C₂²	1	1	yes	characteristic, complemented
35	#16810407	C₂²	1	2	yes	complemented
36	C₄×#11719908	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#576	—	2	1	no	—
38	C₅₃×#576	C₂²	1	2	yes	complemented
39	C₅₃×#493	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#472	—	2	1	no	—
41	C₅₃×#472	C₂²	1	2	yes	complemented
42	C₅₃×#453	—	2	2	no	—
43	C₅₃×#443	C₂²	1	1	yes	characteristic
44	C₅₃×#443	C₂²	1	1	yes	characteristic, complemented
45	#13133263	—	2	2	no	—
46	#13133245	—	2	2	no	—
47	#13133245	—	4	2	no	—
48	#13133244	—	4	2	no	—
49	#13133242	—	2	2	no	—
50	#13133240	—	4	1	no	—
51	#13133239	—	2	2	no	—
52	#13133239	C₂³	1	1	yes	characteristic
53	C₂×D₄₂₄	—	2	1	no	—
54	C₂×D₄₂₄	—	2	2	no	—
55	C₂×D₄₂₄	C₂³	1	2	yes	—
56	D₈×D₅₃	—	4	1	no	—
57	#13133223	—	2	1	no	—
58	#13133214	—	2	1	no	—
59	#13133163	D₄	1	1	yes	characteristic, complemented
60	#13133161	—	2	2	no	—
61	#13133161	D₄	1	1	yes	characteristic, complemented
62	#13133160	—	2	2	no	—
63	#13133160	D₄	1	1	yes	characteristic, complemented
64	#13133158	—	2	2	no	—
65	#13133158	—	2	2	no	—
66	#13133158	—	2	2	no	—
67	#13133158	—	2	2	no	—
68	#13133158	—	4	2	no	—
69	#13133158	D₄	1	1	yes	characteristic, complemented
70	#13133157	—	2	2	no	—
71	#13133157	C₂³	1	2	yes	—
72	C₂×#11719908	—	2	2	no	—
73	C₂×#11719908	C₂³	1	1	yes	characteristic
74	C₂×#11719908	C₂³	1	1	yes	characteristic
75	#13133153	C₂³	1	1	yes	characteristic
76	#13133145	—	2	1	no	—
77	#13133133	—	2	2	no	—
78	H(5,𝔽₂)×C₅₃	—	2	2	no	—
79	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
80	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
81	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
82	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
83	#135×C₅₃	—	2	2	no	—
84	#135×C₅₃	—	4	1	no	—
85	#135×C₅₃	D₄	1	1	yes	characteristic
86	#135×C₅₃	C₂³	1	1	yes	characteristic
87	C₂×D₈×C₅₃	—	2	1	no	—
88	C₂×D₈×C₅₃	—	2	2	no	—
89	C₂×D₈×C₅₃	—	4	1	no	—
90	C₂×D₈×C₅₃	C₂³	1	2	yes	—
91	#131×C₅₃	—	2	1	no	—
92	#131×C₅₃	C₂³	1	2	yes	—
93	#127×C₅₃	—	2	1	no	—
94	#108×C₅₃	D₄	1	1	yes	characteristic
95	#108×C₅₃	C₂³	1	1	yes	characteristic
96	#104×C₅₃	—	2	1	no	—
97	#104×C₅₃	D₄	1	2	yes	—
98	#100×C₅₃	—	2	2	no	—
99	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
100	#41×C₅₃	—	2	1	no	—
101	#41×C₅₃	—	4	2	no	—
102	#41×C₅₃	—	4	2	no	—
103	#41×C₅₃	C₂×D₄	1	2	yes	—
104	C₂×D₄×C₅₃	—	2	2	no	—
105	C₂×D₄×C₅₃	—	4	2	no	—
106	C₂×D₄×C₅₃	—	4	2	no	—
107	C₂×D₄×C₅₃	—	8	1	no	—
108	C₂×D₄×C₅₃	—	8	2	no	—
109	#11719949	—	4	2	no	—
110	D₄×D₅₃	—	4	2	no	—
111	D₄×D₅₃	—	8	2	no	—
112	#11719945	—	2	1	no	—
113	#11719945	—	4	2	no	—
114	C₂×D₂₁₂	—	2	2	no	—
115	C₂×D₂₁₂	—	4	2	no	—
116	C₂×D₂₁₂	—	8	1	no	—
117	Q₁₆×C₅₃	D₈	1	1	yes	characteristic
118	Q₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
119	SD₁₆×C₅₃	—	2	1	no	—
120	SD₁₆×C₅₃	—	4	2	no	—
121	SD₁₆×C₅₃	—	4	2	no	—
122	SD₁₆×C₅₃	D₈	1	2	yes	—
123	D₈×C₅₃	—	2	2	no	—
124	D₈×C₅₃	—	2	2	no	—
125	D₈×C₅₃	—	4	2	no	—
126	D₈×C₅₃	—	4	2	no	—
127	D₈×C₅₃	—	4	1	no	—
128	D₈×C₅₃	—	4	1	no	—
129	D₈×C₅₃	D₈	1	1	yes	characteristic
130	D₈×C₅₃	C₂×D₄	1	1	yes	characteristic
131	M₁₆×C₅₃	—	2	2	no	—
132	M₁₆×C₅₃	—	2	1	no	—
133	M₁₆×C₅₃	—	4	1	no	—
134	M₁₆×C₅₃	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₅₃	—	2	2	no	—
136	C₂×C₈×C₅₃	—	4	1	no	—
137	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
139	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
140	#11719924	—	4	2	no	—
141	#11719922	—	4	2	no	—
142	#11719917	—	2	1	no	—
143	Dic₂₁₂	C₂×D₄	1	1	yes	characteristic
144	D₄₂₄	—	2	2	no	—
145	D₄₂₄	—	2	2	no	—
146	D₄₂₄	—	4	2	no	—
147	D₄₂₄	—	4	1	no	—
148	D₄₂₄	—	4	1	no	—
149	D₄₂₄	C₂×D₄	1	1	yes	characteristic
150	#11719913	—	2	1	no	—
151	#11719913	—	4	2	no	—
152	#11719912	—	4	1	no	—
153	C₈×D₅₃	—	4	1	no	—
154	#11719908	—	2	2	no	—
155	#11719908	—	2	1	no	—
156	#11719908	C₂×D₄	1	1	yes	characteristic
157	#11719908	C₂×D₄	1	1	yes	characteristic
158	C₂³×C₅₃	—	4	2	no	—
159	C₂³×C₅₃	—	8	2	no	—
160	C₂²×D₅₃	—	4	2	no	—
161	C₂²×D₅₃	—	8	2	no	—
162	Q₈×C₅₃	—	2	1	no	—
163	Q₈×C₅₃	C₂×D₈	1	2	yes	—
164	D₄×C₅₃	—	2	2	no	—
165	D₄×C₅₃	—	2	1	no	—
166	D₄×C₅₃	—	4	1	no	—
167	D₄×C₅₃	—	4	2	no	—
168	D₄×C₅₃	—	4	2	no	—
169	D₄×C₅₃	—	8	2	no	—
170	D₄×C₅₃	—	8	2	no	—
171	D₄×C₅₃	—	16	2	no	—
172	D₄×C₅₃	C₂×D₈	1	2	yes	—
173	C₂×C₄×C₅₃	—	2	1	no	—
174	C₂×C₄×C₅₃	—	2	2	no	—
175	C₂×C₄×C₅₃	—	4	1	no	—
176	C₂×C₄×C₅₃	—	8	2	no	—
177	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
178	C₂²⋊D₅₃	—	4	1	no	—
179	C₂²⋊D₅₃	—	8	2	no	—
180	D₂₁₂	—	2	1	no	—
181	D₂₁₂	—	4	2	no	—
182	D₂₁₂	—	4	2	no	—
183	D₂₁₂	—	8	2	no	—
184	D₂₁₂	—	16	2	no	—
185	C₄×D₅₃	—	4	1	no	—
186	C₄×D₅₃	—	8	2	no	—
187	Dic₁₀₆	—	2	1	no	—
188	C₈×C₅₃	—	2	2	no	—
189	C₈×C₅₃	—	4	1	no	—
190	C₈×C₅₃	C₂×D₈	1	1	yes	characteristic
191	C₈×C₅₃	C₂×D₈	1	1	yes	characteristic
192	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
193	C₈×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
194	#88322	—	4	1	no	—
195	#33858	—	53	1	no	maximal, Sylow
196	C₂²×C₅₃	—	2	2	no	—
197	C₂²×C₅₃	—	4	1	no	—
198	C₂²×C₅₃	—	8	2	no	—
199	C₂²×C₅₃	—	16	2	no	—
200	C₂²×C₅₃	—	32	2	no	—
201	C₂²×C₅₃	#576	1	1	yes	characteristic
202	C₂×D₅₃	—	4	1	no	—
203	C₂×D₅₃	—	8	2	no	—
204	C₂×D₅₃	—	16	2	no	—
205	C₂×D₅₃	—	32	2	no	—
206	C₄×C₅₃	—	2	2	no	—
207	C₄×C₅₃	—	2	2	no	—
208	C₄×C₅₃	—	4	1	no	—
209	C₄×C₅₃	D₄²	1	1	yes	characteristic
210	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
211	Dic₅₃	—	4	1	no	—
212	#3415	—	53	2	no	—
213	#3292	—	53	1	no	—
214	#3292	D₅₃	1	1	yes	characteristic, complemented
215	#2246	—	53	1	no	—
216	#2221	—	53	2	no	—
217	#2213	—	53	1	no	—
218	#2213	—	53	1	no	—
219	#2192	—	53	2	no	—
220	#2192	—	53	2	no	—
221	#2178	—	53	1	no	—
222	#2170	—	53	1	no	—
223	C₂×C₅₃	—	2	1	no	—
224	C₂×C₅₃	—	4	2	no	—
225	C₂×C₅₃	—	8	1	no	—
226	C₂×C₅₃	—	16	2	no	—
227	C₂×C₅₃	D₄×D₈	1	1	yes	characteristic
228	D₅₃	—	8	1	no	—
229	D₅₃	—	16	2	no	—
230	#576	—	2	1	no	—
231	#576	—	53	2	no	—
232	#576	—	106	1	no	—
233	#576	C₂×D₅₃	1	2	yes	complemented
234	#509	—	53	2	no	—
235	#509	—	53	2	no	—
236	#509	—	106	2	no	—
237	#509	—	106	2	no	—
238	#508	—	53	1	no	—
239	#508	—	106	2	no	—
240	C₂×D₁₆	—	53	2	no	—
241	C₂×D₁₆	—	53	2	no	—
242	C₂×D₁₆	—	106	2	no	—
243	#504	—	53	2	no	—
244	#493	—	53	1	no	—
245	#493	C₂×D₅₃	1	1	yes	characteristic, complemented
246	#472	—	2	1	no	—
247	#472	—	53	2	no	—
248	#472	—	106	1	no	—
249	#472	C₂×D₅₃	1	2	yes	complemented
250	#453	—	2	2	no	—
251	#453	—	106	2	no	—
252	#443	—	53	1	no	—
253	#443	C₂×D₅₃	1	1	yes	characteristic
254	#443	C₂×D₅₃	1	1	yes	characteristic, complemented
255	#368	—	53	1	no	—
256	#364	—	53	1	no	—
257	#361	—	53	2	no	—
258	#361	—	53	2	no	—
259	#359	—	53	1	no	—
260	#359	—	53	1	no	—
261	#350	—	53	2	no	—
262	C₄×C₁₆	—	53	1	no	—
263	C₅₃	#33858	1	1	yes	characteristic, complemented, Sylow
264	H(5,𝔽₂)	—	2	2	no	—
265	H(5,𝔽₂)	—	106	2	no	—
266	AGL(1,ℤ/8)	—	2	2	no	—
267	AGL(1,ℤ/8)	—	2	2	no	—
268	AGL(1,ℤ/8)	—	4	2	no	—
269	AGL(1,ℤ/8)	—	4	2	no	—
270	AGL(1,ℤ/8)	—	106	2	no	—
271	AGL(1,ℤ/8)	—	106	2	no	—
272	AGL(1,ℤ/8)	—	212	2	no	—
273	AGL(1,ℤ/8)	—	212	2	no	—
274	#135	—	2	2	no	—
275	#135	—	4	1	no	—
276	#135	—	53	1	no	—
277	#135	—	106	2	no	—
278	#135	—	212	1	no	—
279	#135	C₂²⋊D₅₃	1	1	yes	characteristic
280	#135	C₂²×D₅₃	1	1	yes	characteristic
281	C₂×D₈	—	2	2	no	—
282	C₂×D₈	—	2	1	no	—
283	C₂×D₈	—	4	1	no	—
284	C₂×D₈	—	53	2	no	—
285	C₂×D₈	—	106	2	no	—
286	C₂×D₈	—	106	1	no	—
287	C₂×D₈	—	212	1	no	—
288	C₂×D₈	C₂²×D₅₃	1	2	yes	—
289	#131	—	2	1	no	—
290	#131	—	106	1	no	—
291	#131	C₂²×D₅₃	1	2	yes	—
292	#127	—	2	1	no	—
293	#127	—	106	1	no	—
294	Q₃₂	—	53	1	no	—
295	SD₃₂	—	53	1	no	—
296	SD₃₂	—	53	1	no	—
297	SD₃₂	—	106	2	no	—
298	SD₃₂	—	106	2	no	—
299	D₁₆	—	53	1	no	—
300	D₁₆	—	106	2	no	—
301	D₁₆	—	106	2	no	—
302	D₁₆	—	106	2	no	—
303	D₁₆	—	106	2	no	—
304	D₁₆	—	212	2	no	—
305	M₃₂	—	53	2	no	—
306	M₃₂	—	106	2	no	—
307	C₂×C₁₆	—	53	1	no	—
308	C₂×C₁₆	—	53	1	no	—
309	C₂×C₁₆	—	106	2	no	—
310	#108	—	53	1	no	—
311	#108	C₂²⋊D₅₃	1	1	yes	characteristic
312	#108	C₂²×D₅₃	1	1	yes	characteristic
313	#104	—	2	1	no	—
314	#104	—	106	1	no	—
315	#104	C₂²⋊D₅₃	1	2	yes	—
316	#100	—	2	2	no	—
317	#100	—	106	2	no	—
318	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
319	#41	—	2	1	no	—
320	#41	—	4	2	no	—
321	#41	—	4	2	no	—
322	#41	—	106	1	no	—
323	#41	—	212	2	no	—
324	#41	—	212	2	no	—
325	#41	C₂×C₂²⋊D₅₃	1	2	yes	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	8	1	no	—
330	C₂×D₄	—	8	2	no	—
331	C₂×D₄	—	106	2	no	—
332	C₂×D₄	—	424	1	no	—
333	C₂×D₄	—	424	2	no	—
334	C₂×D₄	—	212	2	no	—
335	C₂×D₄	—	212	2	no	—
336	Q₁₆	—	53	1	no	—
337	Q₁₆	#11719922	1	1	yes	characteristic
338	Q₁₆	D₄×D₅₃	1	1	yes	characteristic
339	SD₁₆	—	2	1	no	—
340	SD₁₆	—	4	2	no	—
341	SD₁₆	—	4	2	no	—
342	SD₁₆	—	106	1	no	—
343	SD₁₆	—	212	2	no	—
344	SD₁₆	—	212	2	no	—
345	SD₁₆	#11719922	1	2	yes	—
346	D₈	—	2	2	no	—
347	D₈	—	2	2	no	—
348	D₈	—	4	2	no	—
349	D₈	—	4	2	no	—
350	D₈	—	4	1	no	—
351	D₈	—	4	1	no	—
352	D₈	—	53	1	no	—
353	D₈	—	106	2	no	—
354	D₈	—	106	2	no	—
355	D₈	—	212	2	no	—
356	D₈	—	212	2	no	—
357	D₈	—	212	1	no	—
358	D₈	—	212	1	no	—
359	D₈	#11719922	1	1	yes	characteristic
360	D₈	D₄×D₅₃	1	1	yes	characteristic
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	1	no	—
363	M₁₆	—	4	1	no	—
364	M₁₆	—	106	1	no	—
365	M₁₆	—	212	1	no	—
366	M₁₆	C₂×C₂²⋊D₅₃	1	2	yes	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	4	1	no	—
369	C₂×C₈	—	212	1	no	—
370	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
371	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
372	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
373	C₁₆	—	53	1	no	—
374	C₁₆	—	53	1	no	—
375	C₁₆	—	106	2	no	—
376	C₁₆	—	106	1	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	8	2	no	—
379	C₂³	—	424	2	no	—
380	C₂³	—	212	2	no	—
381	Q₈	—	2	1	no	—
382	Q₈	—	106	1	no	—
383	Q₈	C₂×#11719922	1	2	yes	—
384	D₄	—	2	2	no	—
385	D₄	—	2	1	no	—
386	D₄	—	4	1	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	8	2	no	—
390	D₄	—	8	2	no	—
391	D₄	—	16	2	no	—
392	D₄	—	848	2	no	—
393	D₄	—	106	1	no	—
394	D₄	—	424	2	no	—
395	D₄	—	424	2	no	—
396	D₄	—	212	1	no	—
397	D₄	—	212	2	no	—
398	D₄	—	212	2	no	—
399	D₄	C₂×#11719922	1	2	yes	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	8	2	no	—
404	C₂×C₄	—	424	2	no	—
405	C₂×C₄	—	212	1	no	—
406	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
407	C₈	—	2	2	no	—
408	C₈	—	4	1	no	—
409	C₈	—	212	1	no	—
410	C₈	C₂×#11719922	1	1	yes	characteristic
411	C₈	C₂×#11719922	1	1	yes	characteristic
412	C₈	C₂×D₄×D₅₃	1	1	yes	characteristic
413	C₈	#13133262	1	1	yes	characteristic
414	C₂²	—	2	2	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	16	2	no	—
418	C₂²	—	32	2	no	—
419	C₂²	—	848	2	no	—
420	C₂²	—	1696	2	no	—
421	C₂²	—	424	2	no	—
422	C₂²	—	212	1	no	—
423	C₂²	#16811426	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	4	1	no	—
427	C₄	—	212	1	no	—
428	C₄	D₄×C₂²⋊D₅₃	1	1	yes	characteristic
429	C₄	C₂²×#11719922	1	1	yes	characteristic
430	C₂	—	2	1	no	—
431	C₂	—	4	2	no	—
432	C₂	—	8	1	no	—
433	C₂	—	16	2	no	—
434	C₂	—	848	2	no	—
435	C₂	—	424	1	no	—
436	C₂	D₄×#11719922	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#11719922
commutator, cosocle	C₂×C₈×C₅₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₅₃×#3292	C₂
socle	C₂×C₅₃	D₄×D₈
hypercenter	#3292	D₅₃
hypocenter	C₅₃	#33858
LCS	G ▷ C₂×C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #443 ◁ #3292

Complements

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

N	H ≅ G/N	type
1. #20287854	C₂	semidirect
2. #20286515	C₂	semidirect
3. #20276964	C₂	semidirect
4. #20276833	C₂	semidirect
5. #20276791	C₂	semidirect
6. #20276788	C₂	semidirect
7. #20276672	C₂	semidirect
8. #20276670	C₂	semidirect
9. #20276594	C₂	semidirect
10. #20276552	C₂	semidirect
11. C₅₃×#3292	C₂	semidirect
12. #16811428	C₂²	semidirect
15. #16811059	C₂²	semidirect
17. #16811058	C₂²	semidirect
21. C₂×#13133158	C₂²	semidirect
22. C₂×#13133158	C₂²	semidirect
23. #16811040	C₂²	semidirect
24. #16811000	C₂²	semidirect
26. #16810893	C₂²	semidirect
28. #16810741	C₂²	semidirect
29. #16810452	C₂²	semidirect
30. #16810444	C₂²	semidirect
31. #16810436	C₂²	semidirect
32. #16810435	C₂²	semidirect
33. #16810430	C₂²	semidirect
34. #16810429	C₂²	semidirect
35. #16810407	C₂²	semidirect
36. C₄×#11719908	C₂²	semidirect
38. C₅₃×#576	C₂²	semidirect
39. C₅₃×#493	C₂²	semidirect
41. C₅₃×#472	C₂²	semidirect
44. C₅₃×#443	C₂²	semidirect
59. #13133163	D₄	semidirect
61. #13133161	D₄	semidirect
63. #13133160	D₄	semidirect
69. #13133158	D₄	semidirect
214. #3292	D₅₃	semidirect
233. #576	C₂×D₅₃	semidirect
245. #493	C₂×D₅₃	semidirect
249. #472	C₂×D₅₃	semidirect
254. #443	C₂×D₅₃	semidirect
263. C₅₃	#33858	semidirect

Maximal subgroups

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

subgroup	index
#20287854	2
#20286515	2
#20276964	2
#20276833	2
#20276791	2
#20276788	2
#20276672	2
#20276670	2
#20276594	2
#20276552	2
C₅₃×#3292	2
#33858	53