Subgroups — #27277938

Order 13568.

520 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16810645	C₂	1	1	yes	maximal, characteristic
2	#20274692	C₂	1	1	yes	maximal, characteristic
3	C₄×#13133129	C₂	1	1	yes	maximal, characteristic
4	C₂×#16810376	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16810375	C₂	1	1	yes	maximal, characteristic, complemented
6	#20272549	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11719912	—	2	1	no	—
9	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
10	#16810645	—	2	2	no	—
11	#16810645	—	2	2	no	—
12	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
14	C₂×#13133146	—	2	1	no	—
15	C₂×#13133129	—	2	1	no	—
16	C₂×#13133129	C₄	1	1	yes	characteristic
17	C₂×#13133129	C₄	1	1	yes	characteristic
18	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
19	#16810377	—	2	1	no	—
20	#16810377	C₄	1	1	yes	characteristic
21	#16810377	C₄	1	1	yes	characteristic
22	#16810376	—	2	2	no	—
23	#16810375	—	2	2	no	—
24	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₅₃	Q₈	1	1	yes	characteristic
30	C₂×#11719912	—	2	4	no	—
31	C₂×#11719912	—	4	2	no	—
32	C₂×#11719912	—	4	2	no	—
33	C₂²×#88322	—	2	1	no	—
34	C₂²×#88322	—	2	1	no	—
35	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
36	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
39	C₂×C₄×Dic₅₃	Q₈	1	1	yes	characteristic
40	C₄²×D₅₃	—	2	1	no	—
41	C₄²×D₅₃	—	2	1	no	—
42	C₄²×D₅₃	—	2	1	no	—
43	C₄²×D₅₃	—	2	1	no	—
44	C₄⋊#88322	—	2	1	no	—
45	C₄⋊#88322	—	2	1	no	—
46	C₄⋊#88322	—	2	1	no	—
47	C₄⋊#88322	D₄	1	2	yes	—
48	#13133146	—	2	4	no	—
49	#13133129	—	2	2	no	—
50	#13133129	—	2	2	no	—
51	#13133129	—	4	2	no	—
52	C₄×#88322	—	2	1	no	—
53	C₄×#88322	—	2	1	no	—
54	C₂²×C₈×C₅₃	—	2	1	no	—
55	C₂²×C₈×C₅₃	—	2	1	no	—
56	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
59	C₄⋊C₈×C₅₃	—	2	1	no	—
60	C₄⋊C₈×C₅₃	—	2	1	no	—
61	C₄⋊C₈×C₅₃	—	2	1	no	—
62	C₄⋊C₈×C₅₃	D₄	1	2	yes	—
63	C₄×C₈×C₅₃	—	2	1	no	—
64	C₄×C₈×C₅₃	—	2	1	no	—
65	C₂³×D₅₃	C₄⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
69	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
70	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
71	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
72	C₂×C₄×D₅₃	—	2	1	no	—
73	C₂×C₄×D₅₃	—	2	1	no	—
74	C₂×C₄×D₅₃	—	2	1	no	—
75	C₂×C₄×D₅₃	—	2	1	no	—
76	C₂×C₄×D₅₃	—	2	1	no	—
77	C₂×C₄×D₅₃	—	2	1	no	—
78	C₂×C₄×D₅₃	—	2	1	no	—
79	C₂×C₄×D₅₃	—	2	1	no	—
80	C₂×C₄×D₅₃	—	2	1	no	—
81	C₂×C₄×D₅₃	—	2	1	no	—
82	C₂×C₄×D₅₃	—	2	1	no	—
83	C₂×C₄×D₅₃	—	2	1	no	—
84	C₂×C₄×D₅₃	—	2	2	no	—
85	C₂×C₄×D₅₃	—	4	1	no	—
86	C₂×C₄×D₅₃	D₈	1	2	yes	—
87	C₂×C₄×D₅₃	Q₁₆	1	2	yes	—
88	C₂×C₈×C₅₃	—	2	1	no	—
89	C₂×C₈×C₅₃	—	2	1	no	—
90	C₂×C₈×C₅₃	—	2	1	no	—
91	C₂×C₈×C₅₃	—	2	2	no	—
92	C₂×C₈×C₅₃	—	2	1	no	—
93	C₂×C₈×C₅₃	—	2	1	no	—
94	C₂×C₈×C₅₃	—	4	1	no	—
95	C₂×C₈×C₅₃	—	4	1	no	—
96	C₂×C₈×C₅₃	—	4	1	no	—
97	C₂×C₈×C₅₃	—	4	1	no	—
98	C₂×C₈×C₅₃	—	4	1	no	—
99	C₂×C₈×C₅₃	M₁₆	1	2	yes	complemented
100	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
101	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₅₃	#41	1	1	yes	characteristic
103	C₄²×C₅₃	#41	1	1	yes	characteristic
104	C₄×Dic₅₃	—	2	1	no	—
105	C₄×Dic₅₃	—	2	1	no	—
106	C₄×Dic₅₃	—	2	1	no	—
107	C₄×Dic₅₃	—	2	1	no	—
108	C₄×Dic₅₃	—	2	1	no	—
109	C₄×Dic₅₃	—	2	1	no	—
110	C₂×#88322	—	2	1	no	—
111	C₂×#88322	—	2	1	no	—
112	C₂×#88322	—	2	1	no	—
113	C₂×#88322	—	2	2	no	—
114	C₂×#88322	—	2	1	no	—
115	C₂×#88322	—	2	1	no	—
116	C₂×#88322	—	4	1	no	—
117	C₂×#88322	—	4	1	no	—
118	C₂×#88322	—	4	1	no	—
119	C₂×#88322	—	4	1	no	—
120	C₂×#88322	—	4	1	no	—
121	C₂×#88322	M₁₆	1	2	yes	complemented
122	#11719912	—	4	8	no	—
123	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂²×D₅₃	—	2	1	no	—
125	C₂²×D₅₃	—	2	1	no	—
126	C₂²×D₅₃	—	2	1	no	—
127	C₂²×D₅₃	—	2	1	no	—
128	C₂²×D₅₃	—	2	1	no	—
129	C₂²×D₅₃	—	2	1	no	—
130	C₂²×D₅₃	#107	1	2	yes	—
131	C₂×C₄×C₅₃	—	2	1	no	—
132	C₂×C₄×C₅₃	—	2	1	no	—
133	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
135	C₂×C₄×C₅₃	#120	1	1	yes	characteristic
136	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
137	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
138	C₂×C₄×C₅₃	#123	1	1	yes	characteristic
139	C₂×C₄×C₅₃	C₂×M₁₆	1	1	yes	characteristic
140	C₂×C₄×C₅₃	C₂×M₁₆	1	1	yes	characteristic
141	C₂×C₄×C₅₃	#131	1	1	yes	characteristic
142	C₂×C₄×C₅₃	#131	1	1	yes	characteristic
143	C₂×C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
144	C₂×C₄×C₅₃	C₂×Q₁₆	1	1	yes	characteristic
145	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
146	C₂×C₄×C₅₃	#137	1	1	yes	characteristic
147	C₂×Dic₅₃	—	2	1	no	—
148	C₂×Dic₅₃	—	2	1	no	—
149	C₂×Dic₅₃	—	2	1	no	—
150	C₂×Dic₅₃	—	2	1	no	—
151	C₂×Dic₅₃	—	2	1	no	—
152	C₂×Dic₅₃	—	2	1	no	—
153	C₂×Dic₅₃	—	2	1	no	—
154	C₂×Dic₅₃	#107	1	2	yes	—
155	C₂×Dic₅₃	#108	1	2	yes	—
156	C₄×D₅₃	—	2	2	no	—
157	C₄×D₅₃	—	2	2	no	—
158	C₄×D₅₃	—	2	2	no	—
159	C₄×D₅₃	—	2	2	no	—
160	C₄×D₅₃	—	4	2	no	—
161	C₄×D₅₃	—	4	2	no	—
162	C₄×D₅₃	—	4	1	no	—
163	C₄×D₅₃	—	4	1	no	—
164	C₄×D₅₃	—	4	1	no	—
165	C₄×D₅₃	—	4	1	no	—
166	C₈×C₅₃	—	2	2	no	—
167	C₈×C₅₃	—	4	1	no	—
168	C₈×C₅₃	—	4	2	no	—
169	C₈×C₅₃	—	8	1	no	—
170	#88322	—	2	2	no	—
171	#88322	—	4	1	no	—
172	#88322	—	4	2	no	—
173	#88322	—	8	1	no	—
174	#8832	—	53	1	no	maximal, Sylow
175	C₂²×C₅₃	#385	1	1	yes	characteristic
176	C₂²×C₅₃	#423	1	1	yes	characteristic
177	C₂²×C₅₃	#424	1	1	yes	characteristic
178	C₂²×C₅₃	C₂×#107	1	1	yes	characteristic
179	C₂²×C₅₃	#428	1	1	yes	characteristic
180	C₂²×C₅₃	C₂×#108	1	1	yes	characteristic
181	C₂²×C₅₃	#430	1	1	yes	characteristic
182	C₂×D₅₃	—	2	2	no	—
183	C₂×D₅₃	—	2	2	no	—
184	C₂×D₅₃	—	2	2	no	—
185	C₂×D₅₃	—	4	1	no	—
186	C₂×D₅₃	—	4	1	no	—
187	C₂×D₅₃	—	4	1	no	—
188	C₂×D₅₃	—	4	1	no	—
189	C₄×C₅₃	—	2	1	no	—
190	C₄×C₅₃	—	2	1	no	—
191	C₄×C₅₃	#435	1	1	yes	characteristic
192	C₄×C₅₃	#435	1	1	yes	characteristic
193	C₄×C₅₃	#436	1	1	yes	characteristic
194	C₄×C₅₃	#436	1	1	yes	characteristic
195	C₄×C₅₃	#447	1	1	yes	characteristic
196	C₄×C₅₃	#451	1	1	yes	characteristic
197	C₄×C₅₃	#480	1	1	yes	characteristic
198	C₄×C₅₃	#484	1	1	yes	characteristic
199	Dic₅₃	—	2	2	no	—
200	Dic₅₃	—	2	2	no	—
201	Dic₅₃	—	4	1	no	—
202	C₂×#423	—	53	1	no	—
203	#1797	—	53	1	no	—
204	C₄×C₂²⋊C₈	—	53	1	no	—
205	C₂×#335	—	53	1	no	—
206	C₂×#335	—	53	1	no	—
207	#1277	—	53	1	no	—
208	#1277	D₅₃	1	1	yes	characteristic, complemented
209	C₂×C₅₃	#1567	1	1	yes	characteristic
210	C₂×C₅₃	#1569	1	1	yes	characteristic
211	C₂×C₅₃	#1571	1	1	yes	characteristic
212	C₂×C₅₃	#1574	1	1	yes	characteristic
213	C₂×C₅₃	#1851	1	1	yes	characteristic
214	C₂×C₅₃	#1852	1	1	yes	characteristic
215	C₂×C₅₃	#1855	1	1	yes	characteristic
216	D₅₃	—	4	2	no	—
217	C₂²×M₁₆	—	106	1	no	—
218	C₂²×C₄²	—	53	1	no	—
219	#423	—	106	2	no	—
220	#423	—	106	2	no	—
221	C₂×C₄⋊C₈	—	53	1	no	—
222	C₂×C₄⋊C₈	—	53	1	no	—
223	C₂×C₄⋊C₈	—	106	1	no	—
224	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
226	C₂×C₂²⋊C₈	—	53	1	no	—
227	C₂×C₂²⋊C₈	—	53	1	no	—
228	C₂×C₂²⋊C₈	—	106	1	no	—
229	C₂×C₄×C₈	—	53	1	no	—
230	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
231	#336	—	53	1	no	—
232	#336	—	53	1	no	—
233	#336	—	106	1	no	—
234	#335	—	106	2	no	—
235	#335	—	106	2	no	—
236	C₅₃	#8832	1	1	yes	characteristic, complemented, Sylow
237	C₂³×C₄	—	53	1	no	—
238	C₂³×C₄	—	53	1	no	—
239	C₂³×C₄	—	53	1	no	—
240	C₂×M₁₆	—	106	4	no	—
241	C₂×M₁₆	—	212	2	no	—
242	C₂×M₁₆	—	212	2	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₂²×C₈	—	53	1	no	—
246	C₂²×C₈	—	53	1	no	—
247	C₂²×C₈	—	106	1	no	—
248	C₂²×C₈	—	106	1	no	—
249	C₂²×C₈	C₄×D₅₃	1	1	yes	characteristic
250	C₂²×C₈	C₄×D₅₃	1	1	yes	characteristic
251	C₂×C₄²	—	53	1	no	—
252	C₂×C₄²	—	53	1	no	—
253	C₂×C₄²	—	53	1	no	—
254	C₂×C₄²	—	106	1	no	—
255	C₂×C₄²	—	106	1	no	—
256	C₂×C₄²	—	106	1	no	—
257	C₂×C₄²	—	106	1	no	—
258	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	53	2	no	—
263	C₄⋊C₈	—	106	4	no	—
264	C₄⋊C₈	—	106	1	no	—
265	C₄⋊C₈	—	106	1	no	—
266	C₄⋊C₈	—	106	1	no	—
267	C₄⋊C₈	D₂₁₂	1	2	yes	—
268	C₂²⋊C₈	—	106	2	no	—
269	C₂²⋊C₈	—	106	2	no	—
270	C₂²⋊C₈	—	212	2	no	—
271	C₄×C₈	—	2	1	no	—
272	C₄×C₈	—	2	1	no	—
273	C₄×C₈	—	106	1	no	—
274	C₄×C₈	—	106	1	no	—
275	C₂⁴	—	53	1	no	—
276	C₂²×C₄	—	53	1	no	—
277	C₂²×C₄	—	53	1	no	—
278	C₂²×C₄	—	53	2	no	—
279	C₂²×C₄	—	53	2	no	—
280	C₂²×C₄	—	53	1	no	—
281	C₂²×C₄	—	106	2	no	—
282	C₂²×C₄	—	106	1	no	—
283	C₂²×C₄	—	106	1	no	—
284	C₂²×C₄	—	106	1	no	—
285	C₂²×C₄	—	106	1	no	—
286	C₂²×C₄	—	106	1	no	—
287	C₂²×C₄	—	106	1	no	—
288	C₂²×C₄	—	106	1	no	—
289	C₂²×C₄	—	106	1	no	—
290	C₂²×C₄	—	106	1	no	—
291	C₂²×C₄	—	106	1	no	—
292	C₂²×C₄	—	106	1	no	—
293	C₂²×C₄	—	106	1	no	—
294	C₂²×C₄	—	212	1	no	—
295	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
296	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
297	C₂²×C₄	Q₈×D₅₃	1	1	yes	characteristic
298	M₁₆	—	212	8	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	—	53	2	no	—
311	C₂×C₈	—	106	1	no	—
312	C₂×C₈	—	106	1	no	—
313	C₂×C₈	—	106	1	no	—
314	C₂×C₈	—	106	2	no	—
315	C₂×C₈	—	106	1	no	—
316	C₂×C₈	—	106	1	no	—
317	C₂×C₈	—	212	1	no	—
318	C₂×C₈	—	212	1	no	—
319	C₂×C₈	—	212	1	no	—
320	C₂×C₈	—	212	1	no	—
321	C₂×C₈	—	212	1	no	—
322	C₂×C₈	#11719912	1	2	yes	complemented
323	C₄²	—	106	1	no	—
324	C₄²	—	106	1	no	—
325	C₄²	—	106	1	no	—
326	C₄²	—	106	1	no	—
327	C₄²	—	106	1	no	—
328	C₄²	—	106	1	no	—
329	C₄²	C₂×D₂₁₂	1	1	yes	characteristic
330	C₄²	#11719945	1	1	yes	characteristic
331	C₄²	D₄×D₅₃	1	1	yes	characteristic
332	C₄²	#11719947	1	1	yes	characteristic
333	C₂³	—	53	2	no	—
334	C₂³	—	106	1	no	—
335	C₂³	—	106	1	no	—
336	C₂³	—	106	1	no	—
337	C₂³	—	106	1	no	—
338	C₂³	—	106	1	no	—
339	C₂³	—	106	1	no	—
340	C₂³	C₄⋊C₄×D₅₃	1	1	yes	characteristic
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	53	2	no	—
344	C₂×C₄	—	53	2	no	—
345	C₂×C₄	—	106	1	no	—
346	C₂×C₄	—	106	1	no	—
347	C₂×C₄	—	106	1	no	—
348	C₂×C₄	—	106	1	no	—
349	C₂×C₄	—	106	2	no	—
350	C₂×C₄	—	106	2	no	—
351	C₂×C₄	—	106	2	no	—
352	C₂×C₄	—	106	2	no	—
353	C₂×C₄	—	106	1	no	—
354	C₂×C₄	—	106	1	no	—
355	C₂×C₄	—	106	1	no	—
356	C₂×C₄	—	212	2	no	—
357	C₂×C₄	—	212	2	no	—
358	C₂×C₄	—	212	1	no	—
359	C₂×C₄	—	212	1	no	—
360	C₂×C₄	—	212	1	no	—
361	C₂×C₄	—	212	1	no	—
362	C₂×C₄	#13133177	1	1	yes	characteristic
363	C₂×C₄	C₄×D₂₁₂	1	1	yes	characteristic
364	C₂×C₄	#13133187	1	1	yes	characteristic
365	C₂×C₄	#13133195	1	1	yes	characteristic
366	C₂×C₄	#13133197	1	1	yes	characteristic
367	C₂×C₄	#13133199	1	1	yes	characteristic
368	C₂×C₄	M₁₆×D₅₃	1	1	yes	characteristic
369	C₂×C₄	C₂×#11719912	1	1	yes	characteristic
370	C₂×C₄	#13133223	1	1	yes	characteristic
371	C₂×C₄	#13133225	1	1	yes	characteristic
372	C₂×C₄	D₈×D₅₃	1	1	yes	characteristic
373	C₂×C₄	Q₁₆×D₅₃	1	1	yes	characteristic
374	C₂×C₄	#13133244	1	1	yes	characteristic
375	C₂×C₄	#13133246	1	1	yes	characteristic
376	C₈	—	2	2	no	—
377	C₈	—	4	2	no	—
378	C₈	—	4	1	no	—
379	C₈	—	8	1	no	—
380	C₈	—	106	2	no	—
381	C₈	—	424	1	no	—
382	C₈	—	212	2	no	—
383	C₈	—	212	1	no	—
384	C₂²	—	106	2	no	—
385	C₂²	—	106	2	no	—
386	C₂²	—	106	2	no	—
387	C₂²	—	212	1	no	—
388	C₂²	—	212	1	no	—
389	C₂²	—	212	1	no	—
390	C₂²	—	212	1	no	—
391	C₂²	#16810497	1	1	yes	characteristic
392	C₂²	#16810645	1	1	yes	characteristic
393	C₂²	#16810648	1	1	yes	characteristic
394	C₂²	#107×D₅₃	1	1	yes	characteristic
395	C₂²	#16810662	1	1	yes	characteristic
396	C₂²	#108×D₅₃	1	1	yes	characteristic
397	C₂²	#16810670	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	106	2	no	—
401	C₄	—	106	2	no	—
402	C₄	—	212	1	no	—
403	C₄	#16810691	1	1	yes	characteristic
404	C₄	#16810696	1	1	yes	characteristic
405	C₄	#16810698	1	1	yes	characteristic
406	C₄	#16810702	1	1	yes	characteristic
407	C₄	#16810758	1	1	yes	characteristic
408	C₄	#16810780	1	1	yes	characteristic
409	C₄	#16810935	1	1	yes	characteristic
410	C₄	#16810957	1	1	yes	characteristic
411	C₂	—	212	2	no	—
412	C₂	#20273472	1	1	yes	characteristic
413	C₂	#20273479	1	1	yes	characteristic
414	C₂	#20273488	1	1	yes	characteristic
415	C₂	#20273502	1	1	yes	characteristic
416	C₂	#20274899	1	1	yes	characteristic
417	C₂	#20274904	1	1	yes	characteristic
418	C₂	#20274921	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₅₃
commutator	C₂²×C₄×C₅₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₃
Fitting	C₅₃×#1277	C₂
socle	C₂³×C₅₃	C₂×C₄⋊C₄
prime radical	C₂³×D₅₃	C₄⋊C₄
cosocle	C₂×C₄²×C₅₃	C₂³
hypercenter	#1277	D₅₃
hypocenter	C₅₃	#8832
LCS	G ▷ C₂²×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

Complements

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

N	H ≅ G/N	type
4. C₂×#16810376	C₂	semidirect
5. C₂×#16810375	C₂	semidirect
6. #20272549	C₂	semidirect
7. C₅₃×#1277	C₂	semidirect
99. C₂×C₈×C₅₃	M₁₆	semidirect
121. C₂×#88322	M₁₆	semidirect
208. #1277	D₅₃	semidirect
236. C₅₃	#8832	semidirect
322. C₂×C₈	#11719912	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16810645	2
#20274692	2
C₄×#13133129	2
C₂×#16810376	2
C₂×#16810375	2
#20272549	2
C₅₃×#1277	2
#8832	53