Subgroups — #27273775

Order 13568.

666 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16810676	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#11719917	C₂	1	1	yes	maximal, characteristic
3	#20272564	C₂	1	4	yes	maximal, complemented
4	C₂×C₅₃×#431	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11719917	C₄	1	2	yes	—
6	#16810676	—	2	1	no	—
7	#16810676	—	2	1	no	—
8	#16810676	—	2	1	no	—
9	#16810676	—	2	1	no	—
10	C₂×C₄⋊#88322	C₂²	1	2	yes	—
11	C₂×C₂²⋊#88322	C₄	1	2	yes	—
12	C₄×#11719917	—	2	1	no	—
13	C₄×#11719917	—	2	1	no	—
14	C₄×#11719917	C₄	1	2	yes	—
15	C₄×#11719917	C₂²	1	2	yes	—
16	C₂×#13133128	—	2	1	no	—
17	C₂×C₄×#88322	—	2	1	no	—
18	C₂×C₄×#88322	C₄	1	2	yes	—
19	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
20	C₅₃×#431	—	2	1	no	—
21	C₅₃×#431	—	2	1	no	—
22	C₅₃×#431	C₄	1	2	yes	—
23	C₅₃×#431	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₅₃	—	2	1	no	—
25	C₂×C₂²⋊C₈×C₅₃	C₄	1	2	yes	—
26	C₂×C₄×C₈×C₅₃	—	2	1	no	—
27	C₂×#11719917	—	2	2	no	—
28	C₂×#11719917	—	2	4	no	—
29	C₂×#11719917	C₈	1	8	yes	complemented
30	C₂×#11719917	C₂×C₄	1	4	yes	—
31	C₂²×#88322	—	2	2	no	—
32	C₂²×#88322	C₂×C₄	1	4	yes	—
33	C₄⋊#88322	—	2	2	no	—
34	C₄⋊#88322	—	2	2	no	—
35	C₂²⋊#88322	—	2	2	no	—
36	C₂²⋊#88322	—	2	2	no	—
37	#13133128	—	2	2	no	—
38	#13133128	—	2	2	no	—
39	C₄×#88322	—	2	2	no	—
40	C₄×#88322	—	2	2	no	—
41	C₄×#88322	—	2	2	no	—
42	C₄×#88322	—	2	2	no	—
43	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₈×C₅₃	—	2	2	no	—
47	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₅₃	Q₈	1	1	yes	characteristic
57	C₂×C₄²×C₅₃	Q₈	1	1	yes	characteristic
58	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
59	C₄⋊C₈×C₅₃	—	2	2	no	—
60	C₄⋊C₈×C₅₃	—	2	2	no	—
61	C₂²⋊C₈×C₅₃	—	2	2	no	—
62	C₂²⋊C₈×C₅₃	C₂×C₄	1	4	yes	—
63	C₄×C₈×C₅₃	—	2	2	no	—
64	C₄×C₈×C₅₃	—	2	2	no	—
65	C₂⁴×C₅₃	C₄²	1	1	yes	characteristic
66	C₂²×C₄×C₅₃	—	4	2	no	—
67	C₂²×C₄×C₅₃	—	4	2	no	—
68	C₂²×C₄×C₅₃	C₄²	1	1	yes	characteristic
69	C₂²×C₄×C₅₃	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₅₃	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅₃	C₂×C₈	1	4	yes	—
84	C₂²×C₄×C₅₃	M₁₆	1	4	yes	—
85	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₈×C₅₃	—	2	4	no	—
89	C₂×C₈×C₅₃	—	4	4	no	—
90	C₄²×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
91	C₄²×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₄²×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
93	C₄²×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₄²×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
95	C₄²×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
96	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
97	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₅₃	C₂×Q₈	1	1	yes	characteristic
106	#11719917	—	2	8	no	—
107	#11719917	—	2	4	no	—
108	#11719917	C₂×C₈	1	8	yes	complemented
109	C₂×#88322	—	2	8	no	—
110	C₂×#88322	—	2	4	no	—
111	C₂×#88322	—	2	4	no	—
112	C₂×#88322	—	4	4	no	—
113	C₂³×C₅₃	—	4	1	no	—
114	C₂³×C₅₃	—	4	1	no	—
115	C₂³×C₅₃	#95	1	1	yes	characteristic
116	C₂³×C₅₃	#95	1	1	yes	characteristic
117	C₂³×C₅₃	C₄×C₈	1	2	yes	—
118	C₂³×C₅₃	#97	1	2	yes	—
119	C₂³×C₅₃	C₂×C₄²	1	1	yes	characteristic
120	C₂×C₄×C₅₃	—	2	2	no	—
121	C₂×C₄×C₅₃	—	2	2	no	—
122	C₂×C₄×C₅₃	—	2	2	no	—
123	C₂×C₄×C₅₃	—	2	2	no	—
124	C₂×C₄×C₅₃	—	2	2	no	—
125	C₂×C₄×C₅₃	—	2	2	no	—
126	C₂×C₄×C₅₃	—	4	1	no	—
127	C₂×C₄×C₅₃	—	4	1	no	—
128	C₂×C₄×C₅₃	—	4	1	no	—
129	C₂×C₄×C₅₃	—	4	1	no	—
130	C₂×C₄×C₅₃	—	4	1	no	—
131	C₂×C₄×C₅₃	—	4	1	no	—
132	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
133	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
134	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
135	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
136	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
137	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
138	C₂×C₄×C₅₃	C₄×C₈	1	2	yes	—
139	C₂×C₄×C₅₃	#97	1	2	yes	—
140	C₂×C₄×C₅₃	C₂²⋊C₈	1	4	yes	—
141	C₂×C₄×C₅₃	C₂²⋊C₈	1	4	yes	—
142	C₂×C₄×C₅₃	C₄⋊C₈	1	4	yes	—
143	C₂×C₄×C₅₃	C₄⋊C₈	1	4	yes	—
144	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
151	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
152	C₈×C₅₃	—	4	4	no	—
153	#88322	—	2	8	no	—
154	#88322	—	4	4	no	—
155	#7932	—	53	1	no	maximal, Sylow
156	C₂²×C₅₃	—	2	1	no	—
157	C₂²×C₅₃	—	2	1	no	—
158	C₂²×C₅₃	—	2	1	no	—
159	C₂²×C₅₃	—	2	1	no	—
160	C₂²×C₅₃	—	2	1	no	—
161	C₂²×C₅₃	—	2	1	no	—
162	C₂²×C₅₃	—	4	2	no	—
163	C₂²×C₅₃	—	4	2	no	—
164	C₂²×C₅₃	#336	1	2	yes	—
165	C₂²×C₅₃	#336	1	2	yes	—
166	C₂²×C₅₃	C₂×#95	1	1	yes	characteristic
167	C₂²×C₅₃	C₂×C₄×C₈	1	1	yes	characteristic
168	C₂²×C₅₃	C₂×#97	1	1	yes	characteristic
169	C₄×C₅₃	—	2	1	no	—
170	C₄×C₅₃	—	2	1	no	—
171	C₄×C₅₃	—	2	1	no	—
172	C₄×C₅₃	—	2	1	no	—
173	C₄×C₅₃	—	2	1	no	—
174	C₄×C₅₃	—	2	1	no	—
175	C₄×C₅₃	#336	1	2	yes	—
176	C₄×C₅₃	#336	1	2	yes	—
177	C₄×C₅₃	#344	1	2	yes	—
178	C₄×C₅₃	C₂×C₂²⋊C₈	1	2	yes	—
179	C₄×C₅₃	#413	1	2	yes	—
180	C₄×C₅₃	C₂×C₄⋊C₈	1	2	yes	—
181	C₂×#431	—	53	1	no	—
182	C₂×#431	D₅₃	1	1	yes	characteristic
183	C₂×C₄×M₁₆	—	53	1	no	—
184	#1283	—	53	4	no	—
185	C₂×C₅₃	—	2	2	no	—
186	C₂×C₅₃	—	2	2	no	—
187	C₂×C₅₃	—	2	1	no	—
188	C₂×C₅₃	—	2	1	no	—
189	C₂×C₅₃	C₂×#336	1	1	yes	characteristic
190	C₂×C₅₃	#1742	1	1	yes	characteristic
191	C₂×C₅₃	C₂×#344	1	1	yes	characteristic
192	C₂²×M₁₆	—	53	2	no	—
193	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic
194	#431	—	2	1	no	—
195	#431	—	2	1	no	—
196	#431	—	106	1	no	—
197	#431	—	106	1	no	—
198	#431	—	106	1	no	—
199	#431	—	106	1	no	—
200	#431	Dic₅₃	1	2	yes	—
201	#431	C₂×D₅₃	1	2	yes	—
202	C₂×C₄⋊C₈	—	2	1	no	—
203	C₂×C₄⋊C₈	—	53	2	no	—
204	C₂×C₂²⋊C₈	—	53	2	no	—
205	C₂×C₂²⋊C₈	Dic₅₃	1	2	yes	—
206	C₄×M₁₆	—	53	2	no	—
207	C₄×M₁₆	—	53	2	no	—
208	C₄×M₁₆	—	106	1	no	—
209	C₄×M₁₆	—	106	1	no	—
210	C₂×#97	—	106	1	no	—
211	C₂×C₄×C₈	—	2	1	no	—
212	C₂×C₄×C₈	—	53	2	no	—
213	C₂×C₄×C₈	—	106	1	no	—
214	C₅₃	#7932	1	1	yes	characteristic, complemented, Sylow
215	C₂³×C₄	C₄×D₅₃	1	1	yes	characteristic
216	C₂³×C₄	C₄×D₅₃	1	1	yes	characteristic
217	C₂³×C₄	C₂×Dic₅₃	1	1	yes	characteristic
218	C₂×M₁₆	—	53	4	no	—
219	C₂×M₁₆	—	53	8	no	—
220	C₂×M₁₆	—	106	4	no	—
221	C₂×M₁₆	—	106	2	no	—
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	—	53	4	no	—
224	C₂²×C₈	—	106	2	no	—
225	C₂×C₄²	Dic₁₀₆	1	1	yes	characteristic
226	C₂×C₄²	Dic₁₀₆	1	1	yes	characteristic
227	C₂×C₄²	C₄×D₅₃	1	1	yes	characteristic
228	C₂×C₄²	C₄×D₅₃	1	1	yes	characteristic
229	C₂×C₄²	D₂₁₂	1	1	yes	characteristic
230	C₂×C₄²	D₂₁₂	1	1	yes	characteristic
231	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
232	C₂×C₄²	C₂²⋊D₅₃	1	1	yes	characteristic
233	C₂×C₄²	C₂²⋊D₅₃	1	1	yes	characteristic
234	C₂×C₄²	C₂²⋊D₅₃	1	1	yes	characteristic
235	C₂×C₄²	C₂²⋊D₅₃	1	1	yes	characteristic
236	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
237	C₄⋊C₈	—	2	2	no	—
238	C₄⋊C₈	—	2	2	no	—
239	C₄⋊C₈	—	106	2	no	—
240	C₄⋊C₈	—	106	2	no	—
241	C₂²⋊C₈	—	2	2	no	—
242	C₂²⋊C₈	—	106	2	no	—
243	C₂²⋊C₈	—	106	2	no	—
244	C₂²⋊C₈	C₂×Dic₅₃	1	4	yes	—
245	#97	—	106	2	no	—
246	#97	—	106	2	no	—
247	C₄×C₈	—	2	2	no	—
248	C₄×C₈	—	2	2	no	—
249	C₄×C₈	—	106	2	no	—
250	C₄×C₈	—	106	2	no	—
251	C₄×C₈	—	106	2	no	—
252	C₄×C₈	—	106	2	no	—
253	C₂⁴	C₄×Dic₅₃	1	1	yes	characteristic
254	C₂²×C₄	—	4	2	no	—
255	C₂²×C₄	—	4	2	no	—
256	C₂²×C₄	C₈×D₅₃	1	4	yes	—
257	C₂²×C₄	#11719912	1	4	yes	—
258	C₂²×C₄	C₄×Dic₅₃	1	1	yes	characteristic
259	C₂²×C₄	C₄×Dic₅₃	1	1	yes	characteristic
260	C₂²×C₄	C₄×Dic₅₃	1	1	yes	characteristic
261	C₂²×C₄	#11719919	1	1	yes	characteristic
262	C₂²×C₄	#11719919	1	1	yes	characteristic
263	C₂²×C₄	#11719919	1	1	yes	characteristic
264	C₂²×C₄	#11719919	1	1	yes	characteristic
265	C₂²×C₄	C₄⋊Dic₅₃	1	1	yes	characteristic
266	C₂²×C₄	C₄⋊Dic₅₃	1	1	yes	characteristic
267	C₂²×C₄	#11719921	1	1	yes	characteristic
268	C₂²×C₄	#11719921	1	1	yes	characteristic
269	C₂²×C₄	#11719921	1	1	yes	characteristic
270	C₂²×C₄	#11719921	1	1	yes	characteristic
271	C₂²×C₄	C₂²⋊Dic₅₃	1	1	yes	characteristic
272	C₂²×C₄	C₂²⋊Dic₅₃	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
275	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
276	M₁₆	—	53	8	no	—
277	M₁₆	—	106	8	no	—
278	M₁₆	—	106	4	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	4	4	no	—
281	C₂×C₈	—	106	8	no	—
282	C₂×C₈	—	106	4	no	—
283	C₂×C₈	—	106	4	no	—
284	C₂×C₈	—	212	4	no	—
285	C₄²	#11719919	1	1	yes	characteristic
286	C₄²	#11719919	1	1	yes	characteristic
287	C₄²	#11719919	1	1	yes	characteristic
288	C₄²	#11719919	1	1	yes	characteristic
289	C₄²	C₄⋊Dic₅₃	1	1	yes	characteristic
290	C₄²	C₄⋊Dic₅₃	1	1	yes	characteristic
291	C₄²	#11719921	1	1	yes	characteristic
292	C₄²	#11719921	1	1	yes	characteristic
293	C₄²	#11719921	1	1	yes	characteristic
294	C₄²	#11719921	1	1	yes	characteristic
295	C₄²	C₂²⋊Dic₅₃	1	1	yes	characteristic
296	C₄²	C₂²⋊Dic₅₃	1	1	yes	characteristic
297	C₄²	C₂×Dic₁₀₆	1	1	yes	characteristic
298	C₄²	C₂×D₂₁₂	1	1	yes	characteristic
299	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
300	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
301	C₂³	—	4	1	no	—
302	C₂³	—	4	1	no	—
303	C₂³	#13133124	1	1	yes	characteristic
304	C₂³	#13133124	1	1	yes	characteristic
305	C₂³	C₈×Dic₅₃	1	2	yes	—
306	C₂³	#13133127	1	2	yes	—
307	C₂³	C₂×C₄×Dic₅₃	1	1	yes	characteristic
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	#13133124	1	1	yes	characteristic
321	C₂×C₄	#13133124	1	1	yes	characteristic
322	C₂×C₄	#13133124	1	1	yes	characteristic
323	C₂×C₄	#13133124	1	1	yes	characteristic
324	C₂×C₄	#13133124	1	1	yes	characteristic
325	C₂×C₄	#13133124	1	1	yes	characteristic
326	C₂×C₄	C₈×Dic₅₃	1	2	yes	—
327	C₂×C₄	#13133127	1	2	yes	—
328	C₂×C₄	#13133129	1	4	yes	—
329	C₂×C₄	#13133129	1	4	yes	—
330	C₂×C₄	#13133146	1	4	yes	—
331	C₂×C₄	#13133146	1	4	yes	—
332	C₂×C₄	C₂×#11719921	1	1	yes	characteristic
333	C₂×C₄	C₂×#11719921	1	1	yes	characteristic
334	C₂×C₄	C₂×C₂²⋊Dic₅₃	1	1	yes	characteristic
335	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
336	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
337	C₂×C₄	C₂×C₄⋊Dic₅₃	1	1	yes	characteristic
338	C₂×C₄	C₂×C₈×D₅₃	1	2	yes	—
339	C₂×C₄	C₂×#11719912	1	2	yes	—
340	C₈	—	4	4	no	—
341	C₈	—	106	8	no	—
342	C₈	—	212	4	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	4	2	no	—
351	C₂²	#16810377	1	2	yes	—
352	C₂²	#16810377	1	2	yes	—
353	C₂²	C₂×#13133124	1	1	yes	characteristic
354	C₂²	C₂×C₈×Dic₅₃	1	1	yes	characteristic
355	C₂²	C₂×#13133127	1	1	yes	characteristic
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	#16810377	1	2	yes	—
363	C₄	#16810377	1	2	yes	—
364	C₄	#16810393	1	2	yes	—
365	C₄	C₂×#13133129	1	2	yes	—
366	C₄	#16810605	1	2	yes	—
367	C₄	C₂×#13133146	1	2	yes	—
368	C₂	—	2	1	no	—
369	C₂	—	2	1	no	—
370	C₂	—	2	2	no	—
371	C₂	—	2	2	no	—
372	C₂	C₂×#16810377	1	1	yes	characteristic
373	C₂	#20274453	1	1	yes	characteristic
374	C₂	C₂×#16810393	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	#11719921
commutator	C₂²×C₅₃	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₅₃
Fitting	C₂×C₅₃×#431	C₂
socle	C₂²×C₅₃	C₂×#95
prime radical	C₂⁴×C₅₃	C₄²
cosocle	C₂×C₄²×C₅₃	C₂³
hypercenter	C₂×#431	D₅₃
hypocenter	C₅₃	#7932
LCS	G ▷ C₂²×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #20272564	C₂	semidirect
29. C₂×#11719917	C₈	semidirect
108. #11719917	C₂×C₈	semidirect
214. C₅₃	#7932	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16810676	2
C₂×C₄×#11719917	2
#20272564	2
C₂×C₅₃×#431	2
#7932	53