Subgroups — #27375583

Order 13568.

710 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20287704	C₂	1	1	yes	maximal, characteristic, complemented
2	#20286948	C₂	1	2	yes	maximal, complemented
3	D₄×D₄₂₄	C₂	1	1	yes	maximal, characteristic
4	#20274321	C₂	1	1	yes	maximal, characteristic, complemented
5	#20274277	C₂	1	2	yes	maximal, complemented
6	#20274080	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274075	C₂	1	1	yes	maximal, characteristic, complemented
8	#20273897	C₂	1	2	yes	maximal, complemented
9	#20273828	C₂	1	2	yes	maximal, complemented
10	#20273601	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₄₂₄	—	2	1	no	—
13	#16811346	C₂²	1	2	yes	complemented
14	D₄×D₂₁₂	C₂²	1	2	yes	—
15	#16811007	—	2	1	no	—
16	#16811003	C₂²	1	1	yes	characteristic, complemented
17	#16811000	C₂²	1	1	yes	characteristic
18	#16810970	C₂²	1	2	yes	complemented
19	#16810970	C₂²	1	2	yes	complemented
20	#16810949	—	2	2	no	—
21	#16810903	C₂²	1	2	yes	—
22	#16810872	—	2	2	no	—
23	#16810859	—	2	1	no	—
24	#16810846	—	2	2	no	—
25	#16810829	C₂²	1	2	yes	complemented
26	#16810823	C₂²	1	2	yes	complemented
27	#16810819	C₂²	1	2	yes	—
28	#16810772	—	2	2	no	—
29	#16810759	—	2	2	no	—
30	C₄×Dic₂₁₂	—	2	1	no	—
31	C₄×D₄₂₄	C₂²	1	1	yes	characteristic
32	#16810702	C₂²	1	2	yes	complemented
33	#16810626	—	2	2	no	—
34	#16810376	C₂²	1	1	yes	characteristic, complemented
35	#16810370	C₂²	1	2	yes	complemented
36	#16810366	C₂²	1	2	yes	complemented
37	#16810352	C₂²	1	2	yes	complemented
38	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
40	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
41	C₅₃×#334	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₈²×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₂²×D₂₁₂	—	2	2	no	—
46	C₂×D₄×D₅₃	—	2	2	no	—
47	C₂×Dic₂₁₂	—	2	1	no	—
48	C₂×Dic₂₁₂	—	2	1	no	—
49	C₂×#11719913	—	2	2	no	—
50	C₂×#11719924	—	2	2	no	—
51	C₂×D₄₂₄	—	2	1	no	—
52	C₂×D₄₂₄	—	2	1	no	—
53	C₂×D₄₂₄	—	2	2	no	—
54	C₂×D₄₂₄	—	4	4	no	—
55	C₂×D₄₂₄	D₄	1	1	yes	characteristic
56	C₂×#11719912	—	2	2	no	—
57	#13133217	C₂³	1	2	yes	—
58	#13133214	C₂³	1	2	yes	—
59	#13133212	—	4	2	no	—
60	#13133205	—	2	2	no	—
61	#13133193	—	2	2	no	—
62	#13133192	—	2	2	no	—
63	#13133191	—	2	2	no	—
64	#13133187	—	4	2	no	—
65	C₄×Dic₁₀₆	—	2	2	no	—
66	C₄×D₂₁₂	C₂³	1	2	yes	—
67	#13133175	—	2	2	no	—
68	#13133151	D₄	1	1	yes	characteristic
69	#13133150	—	2	2	no	—
70	C₄⋊#88322	C₂³	1	2	yes	—
71	#13133142	—	2	2	no	—
72	#13133139	—	2	2	no	—
73	#13133139	—	2	2	no	—
74	#13133139	—	2	2	no	—
75	#13133139	—	4	2	no	—
76	#13133139	D₄	1	2	yes	—
77	#13133138	—	2	2	no	—
78	#13133137	—	2	2	no	—
79	#13133129	—	2	2	no	—
80	C₂×SD₁₆×C₅₃	D₄	1	1	yes	characteristic
81	C₂²×C₈×C₅₃	—	2	1	no	—
82	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
83	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
84	#106×C₅₃	D₄	1	1	yes	characteristic
85	C₄⋊C₈×C₅₃	—	2	1	no	—
86	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
88	#103×C₅₃	D₄	1	1	yes	characteristic
89	#102×C₅₃	D₄	1	1	yes	characteristic
90	C₂²⋊C₈×C₅₃	—	2	1	no	—
91	C₄×C₈×C₅₃	—	2	1	no	—
92	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
95	C₂³×D₅₃	—	4	2	no	—
96	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₅₃	—	2	1	no	—
99	C₂×C₂²⋊D₅₃	—	4	2	no	—
100	D₄×D₅₃	—	4	4	no	—
101	D₄×D₅₃	—	8	2	no	—
102	C₂×D₂₁₂	—	2	2	no	—
103	C₂×D₂₁₂	—	2	2	no	—
104	C₂×D₂₁₂	—	2	2	no	—
105	C₂×D₂₁₂	—	4	4	no	—
106	C₂×D₂₁₂	—	4	2	no	—
107	C₂×D₂₁₂	—	8	2	no	—
108	C₂×D₂₁₂	C₂×D₄	1	2	yes	—
109	C₂×C₄×D₅₃	—	2	2	no	—
110	C₂×Dic₁₀₆	—	2	2	no	—
111	SD₁₆×C₅₃	—	2	2	no	—
112	C₂×C₈×C₅₃	—	2	1	no	—
113	C₂×C₈×C₅₃	—	2	1	no	—
114	C₂×C₈×C₅₃	—	2	1	no	—
115	C₂×C₈×C₅₃	—	4	2	no	—
116	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
120	C₄⋊C₄×C₅₃	—	2	1	no	—
121	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
122	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
123	C₂²⋊C₄×C₅₃	—	2	1	no	—
124	C₄²×C₅₃	—	2	1	no	—
125	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
126	#11719924	—	8	2	no	—
127	#11719921	—	2	2	no	—
128	#11719921	—	4	2	no	—
129	#11719921	—	4	2	no	—
130	#11719921	—	4	2	no	—
131	C₄⋊Dic₅₃	—	2	2	no	—
132	C₄⋊Dic₅₃	—	2	2	no	—
133	C₄⋊Dic₅₃	C₂×D₄	1	2	yes	—
134	#11719919	—	4	2	no	—
135	C₄×Dic₅₃	—	4	2	no	—
136	C₂×#88322	—	2	2	no	—
137	Dic₂₁₂	—	4	2	no	—
138	Dic₂₁₂	—	8	1	no	—
139	D₄₂₄	—	2	2	no	—
140	D₄₂₄	—	4	4	no	—
141	D₄₂₄	—	4	2	no	—
142	D₄₂₄	—	8	1	no	—
143	#11719913	—	8	2	no	—
144	#11719912	—	8	2	no	—
145	C₂³×C₅₃	—	2	1	no	—
146	C₂²×D₅₃	—	2	2	no	—
147	C₂²×D₅₃	—	4	2	no	—
148	C₂²×D₅₃	—	8	4	no	—
149	C₂²×D₅₃	—	8	4	no	—
150	C₂²×D₅₃	—	16	2	no	—
151	Q₈×C₅₃	—	2	1	no	—
152	Q₈×C₅₃	—	2	1	no	—
153	D₄×C₅₃	—	2	1	no	—
154	D₄×C₅₃	#135	1	2	yes	—
155	C₂×C₄×C₅₃	—	2	1	no	—
156	C₂×C₄×C₅₃	—	2	1	no	—
157	C₂×C₄×C₅₃	—	2	1	no	—
158	C₂×C₄×C₅₃	—	4	1	no	—
159	C₂×C₄×C₅₃	—	4	1	no	—
160	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂²⋊D₅₃	—	8	4	no	—
164	C₂×Dic₅₃	—	2	2	no	—
165	C₂×Dic₅₃	—	4	2	no	—
166	D₂₁₂	—	2	2	no	—
167	D₂₁₂	—	2	2	no	—
168	D₂₁₂	—	4	2	no	—
169	D₂₁₂	—	4	2	no	—
170	D₂₁₂	—	4	2	no	—
171	D₂₁₂	—	4	2	no	—
172	D₂₁₂	—	8	2	no	—
173	D₂₁₂	—	8	4	no	—
174	C₄×D₅₃	—	4	2	no	—
175	C₄×D₅₃	—	4	2	no	—
176	Dic₁₀₆	—	4	2	no	—
177	Dic₁₀₆	—	4	2	no	—
178	C₈×C₅₃	—	2	1	no	—
179	C₈×C₅₃	—	2	1	no	—
180	C₈×C₅₃	—	2	1	no	—
181	C₈×C₅₃	—	4	1	no	—
182	C₈×C₅₃	—	4	1	no	—
183	C₈×C₅₃	—	4	1	no	—
184	C₈×C₅₃	AGL(1,ℤ/8)	1	2	yes	—
185	#88322	—	4	2	no	—
186	#19900	—	53	1	no	maximal, Sylow
187	C₂²×C₅₃	—	2	2	no	—
188	C₂²×C₅₃	—	4	1	no	—
189	C₂²×C₅₃	—	4	1	no	—
190	C₂²×C₅₃	D₄²	1	1	yes	characteristic
191	C₂×D₅₃	—	4	2	no	—
192	C₂×D₅₃	—	4	2	no	—
193	C₂×D₅₃	—	4	2	no	—
194	C₂×D₅₃	—	8	2	no	—
195	C₂×D₅₃	—	8	2	no	—
196	C₂×D₅₃	—	8	2	no	—
197	C₂×D₅₃	—	16	8	no	—
198	C₄×C₅₃	—	2	1	no	—
199	C₄×C₅₃	—	4	1	no	—
200	C₄×C₅₃	—	4	1	no	—
201	C₄×C₅₃	—	4	1	no	—
202	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
203	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
204	C₄×C₅₃	#576	1	1	yes	characteristic
205	C₄×C₅₃	#576	1	1	yes	characteristic
206	Dic₅₃	—	4	2	no	—
207	Dic₅₃	—	8	2	no	—
208	#3393	—	53	1	no	—
209	#3324	—	53	2	no	—
210	D₄×D₈	—	53	1	no	—
211	#1709	—	53	1	no	—
212	#1701	—	53	2	no	—
213	#1669	—	53	1	no	—
214	#1668	—	53	1	no	—
215	#1639	—	53	2	no	—
216	#1628	—	53	2	no	—
217	#1589	—	53	1	no	—
218	C₈×SD₁₆	D₅₃	1	1	yes	characteristic, complemented
219	C₂×C₅₃	—	4	2	no	—
220	C₂×C₅₃	#3274	1	1	yes	characteristic
221	C₂×C₅₃	#3280	1	1	yes	characteristic
222	C₂×C₅₃	#3290	1	1	yes	characteristic
223	D₅₃	—	8	2	no	—
224	D₅₃	—	16	2	no	—
225	C₂²×D₈	—	106	1	no	—
226	#556	—	53	2	no	—
227	D₄²	—	53	2	no	—
228	#495	—	106	1	no	—
229	#494	—	53	1	no	—
230	#493	—	53	1	no	—
231	#486	—	53	2	no	—
232	#486	—	53	2	no	—
233	#482	—	106	2	no	—
234	#474	—	53	2	no	—
235	#468	—	106	2	no	—
236	#466	—	106	1	no	—
237	#464	—	106	2	no	—
238	#461	—	53	2	no	—
239	#460	—	53	2	no	—
240	#459	—	53	2	no	—
241	#450	—	106	2	no	—
242	#447	—	106	2	no	—
243	C₈×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
244	C₄×Q₁₆	—	106	1	no	—
245	C₄×SD₁₆	C₂×D₅₃	1	1	yes	characteristic
246	C₄×D₈	—	53	1	no	—
247	#436	—	53	2	no	—
248	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic
249	#418	—	106	2	no	—
250	#335	—	53	1	no	—
251	#334	C₂×D₅₃	1	1	yes	characteristic, complemented
252	#332	—	53	2	no	—
253	#331	—	53	2	no	—
254	Q₈⋊C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
255	D₄⋊C₈	—	53	2	no	—
256	D₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
257	C₈²	C₂×D₅₃	1	1	yes	characteristic, complemented
258	C₅₃	#19900	1	1	yes	characteristic, complemented, Sylow
259	C₂²×D₄	—	106	2	no	—
260	C₂²×D₄	—	106	2	no	—
261	C₂×Q₁₆	—	106	1	no	—
262	C₂×Q₁₆	—	106	1	no	—
263	C₂×SD₁₆	—	106	2	no	—
264	C₂×SD₁₆	—	106	2	no	—
265	C₂×SD₁₆	D₂₁₂	1	1	yes	characteristic
266	C₂×D₈	—	53	1	no	—
267	C₂×D₈	—	106	2	no	—
268	C₂×D₈	—	106	1	no	—
269	C₂×D₈	—	106	1	no	—
270	C₂×D₈	—	212	4	no	—
271	C₂×M₁₆	—	106	2	no	—
272	C₂²×C₈	—	2	1	no	—
273	C₄⋊Q₈	—	53	2	no	—
274	#127	—	53	2	no	—
275	#126	—	212	2	no	—
276	#124	—	106	2	no	—
277	C₂²⋊Q₈	—	106	2	no	—
278	#121	—	106	2	no	—
279	#121	—	106	2	no	—
280	#120	—	212	2	no	—
281	C₄×Q₈	—	106	2	no	—
282	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
283	C₄×D₄	—	53	2	no	—
284	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
285	#117	—	106	2	no	—
286	#107	—	53	1	no	—
287	#107	—	106	2	no	—
288	#106	D₂₁₂	1	1	yes	characteristic
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	53	2	no	—
291	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
292	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
293	#103	—	106	2	no	—
294	#103	D₂₁₂	1	1	yes	characteristic
295	#102	—	53	2	no	—
296	#102	—	106	2	no	—
297	#102	—	106	2	no	—
298	#102	—	106	2	no	—
299	#102	—	106	2	no	—
300	#102	—	106	2	no	—
301	#102	—	212	2	no	—
302	#102	D₂₁₂	1	1	yes	characteristic
303	C₂²⋊C₈	—	2	1	no	—
304	C₂²⋊C₈	—	106	2	no	—
305	C₄×C₈	—	2	1	no	—
306	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
307	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
308	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
309	C₂⁴	—	212	2	no	—
310	C₂×Q₈	—	106	2	no	—
311	C₂×Q₈	C₂×D₂₁₂	1	1	yes	characteristic
312	C₂×D₄	—	53	2	no	—
313	C₂×D₄	—	106	2	no	—
314	C₂×D₄	—	106	2	no	—
315	C₂×D₄	—	106	2	no	—
316	C₂×D₄	—	424	2	no	—
317	C₂×D₄	—	424	2	no	—
318	C₂×D₄	—	212	2	no	—
319	C₂×D₄	—	212	4	no	—
320	C₂×D₄	—	212	2	no	—
321	C₂×D₄	—	212	4	no	—
322	C₂×D₄	C₂×D₂₁₂	1	1	yes	characteristic
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	106	2	no	—
325	Q₁₆	—	424	1	no	—
326	Q₁₆	—	212	2	no	—
327	SD₁₆	—	2	2	no	—
328	SD₁₆	—	424	2	no	—
329	SD₁₆	—	424	2	no	—
330	D₈	—	106	2	no	—
331	D₈	—	424	1	no	—
332	D₈	—	212	4	no	—
333	D₈	—	212	2	no	—
334	M₁₆	—	424	2	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	4	2	no	—
339	C₂×C₈	—	106	2	no	—
340	C₂×C₈	C₂×D₂₁₂	1	1	yes	characteristic
341	C₂×C₈	C₂×D₂₁₂	1	1	yes	characteristic
342	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
343	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	53	2	no	—
346	C₄⋊C₄	—	106	2	no	—
347	C₄⋊C₄	—	106	2	no	—
348	C₄⋊C₄	—	212	2	no	—
349	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
350	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
351	C₂²⋊C₄	—	2	1	no	—
352	C₂²⋊C₄	—	106	2	no	—
353	C₂²⋊C₄	—	212	2	no	—
354	C₂²⋊C₄	—	212	2	no	—
355	C₂²⋊C₄	—	212	2	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	212	2	no	—
358	C₄²	C₂³×D₅₃	1	1	yes	characteristic
359	C₂³	—	2	1	no	—
360	C₂³	—	848	2	no	—
361	C₂³	—	106	2	no	—
362	C₂³	—	424	4	no	—
363	C₂³	—	424	4	no	—
364	C₂³	—	212	2	no	—
365	Q₈	—	2	1	no	—
366	Q₈	—	2	1	no	—
367	Q₈	—	212	2	no	—
368	Q₈	—	212	2	no	—
369	D₄	—	2	1	no	—
370	D₄	—	106	2	no	—
371	D₄	—	106	2	no	—
372	D₄	—	424	2	no	—
373	D₄	—	424	4	no	—
374	D₄	—	424	4	no	—
375	D₄	—	212	2	no	—
376	D₄	—	212	2	no	—
377	D₄	—	212	2	no	—
378	D₄	—	212	2	no	—
379	D₄	#13133239	1	2	yes	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	106	2	no	—
386	C₂×C₄	—	212	2	no	—
387	C₂×C₄	—	212	2	no	—
388	C₂×C₄	—	212	2	no	—
389	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
390	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
391	C₂×C₄	#13133263	1	1	yes	characteristic
392	C₈	—	2	1	no	—
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	4	1	no	—
396	C₈	—	4	1	no	—
397	C₈	—	4	1	no	—
398	C₈	—	212	2	no	—
399	C₈	#13133244	1	2	yes	—
400	C₂²	—	2	2	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	848	8	no	—
404	C₂²	—	424	2	no	—
405	C₂²	—	424	2	no	—
406	C₂²	—	424	2	no	—
407	C₂²	—	212	2	no	—
408	C₂²	—	212	2	no	—
409	C₂²	—	212	2	no	—
410	C₂²	D₄×D₂₁₂	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	1	no	—
415	C₄	—	424	2	no	—
416	C₄	—	212	2	no	—
417	C₄	C₂×#13133239	1	1	yes	characteristic
418	C₄	C₂×#13133244	1	1	yes	characteristic
419	C₄	#16811425	1	1	yes	characteristic
420	C₄	#16811428	1	1	yes	characteristic
421	C₂	—	4	2	no	—
422	C₂	—	848	2	no	—
423	C₂	—	424	2	no	—
424	C₂	#20286336	1	1	yes	characteristic
425	C₂	#20286402	1	1	yes	characteristic
426	C₂	#20286502	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₁₂
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₈×SD₁₆×C₅₃	C₂
socle	C₂²×C₅₃	D₄²
prime radical	D₄×D₄₂₄	C₂
hypercenter	C₈×SD₁₆	D₅₃
hypocenter	C₅₃	#19900
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈×SD₁₆

Complements

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

N	H ≅ G/N	type
1. #20287704	C₂	semidirect
2. #20286948	C₂	semidirect
4. #20274321	C₂	semidirect
5. #20274277	C₂	semidirect
6. #20274080	C₂	semidirect
7. #20274075	C₂	semidirect
8. #20273897	C₂	semidirect
9. #20273828	C₂	semidirect
10. #20273601	C₂	semidirect
11. C₈×SD₁₆×C₅₃	C₂	semidirect
13. #16811346	C₂²	semidirect
16. #16811003	C₂²	semidirect
18. #16810970	C₂²	semidirect
19. #16810970	C₂²	semidirect
25. #16810829	C₂²	semidirect
26. #16810823	C₂²	semidirect
32. #16810702	C₂²	semidirect
34. #16810376	C₂²	semidirect
35. #16810370	C₂²	semidirect
36. #16810366	C₂²	semidirect
37. #16810352	C₂²	semidirect
38. C₈×Q₈×C₅₃	C₂²	semidirect
41. C₅₃×#334	C₂²	semidirect
42. C₅₃×Q₈⋊C₈	C₂²	semidirect
44. C₈²×C₅₃	C₂²	semidirect
218. C₈×SD₁₆	D₅₃	semidirect
243. C₈×Q₈	C₂×D₅₃	semidirect
251. #334	C₂×D₅₃	semidirect
254. Q₈⋊C₈	C₂×D₅₃	semidirect
257. C₈²	C₂×D₅₃	semidirect
258. C₅₃	#19900	semidirect

Maximal subgroups

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

subgroup	index
#20287704	2
#20286948	2
D₄×D₄₂₄	2
#20274321	2
#20274277	2
#20274080	2
#20274075	2
#20273897	2
#20273828	2
#20273601	2
C₈×SD₁₆×C₅₃	2
#19900	53