Subgroups — #28313912

Order 13568.

814 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	#20291526	C₂	1	2	yes	maximal
2	#20289939	C₂	1	1	yes	maximal, characteristic, complemented
3	#20289938	C₂	1	1	yes	maximal, characteristic, complemented
4	#20289935	C₂	1	1	yes	maximal, characteristic, complemented
5	#20289934	C₂	1	1	yes	maximal, characteristic, complemented
6	#20289923	C₂	1	2	yes	maximal, complemented
7	#20289919	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×#11719936	C₂	1	2	yes	maximal, complemented
9	C₈×#11719940	C₂	1	2	yes	maximal, complemented
10	C₈×D₅₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#20283137	C₂	1	1	yes	maximal, characteristic
12	#16811675	C₄	1	4	yes	—
13	#16811656	C₄	1	4	yes	—
14	#16811655	C₄	1	4	yes	—
15	#16811653	C₄	1	4	yes	—
16	#16811642	C₂²	1	2	yes	—
17	#16811641	C₂²	1	2	yes	—
18	#16811640	C₂²	1	2	yes	—
19	C₄×#11719936	C₂²	1	2	yes	—
20	C₄×#11719940	C₂²	1	2	yes	—
21	C₄×D₅₃⋊C₈	C₂²	1	2	yes	—
22	#88324⋊C₈	C₂²	1	2	yes	—
23	#88324⋊C₈	C₂²	1	2	yes	—
24	#88324⋊C₈	C₂²	1	2	yes	—
25	#88324⋊C₈	C₂²	1	2	yes	—
26	#16811464	C₂²	1	1	yes	characteristic
27	#16811464	C₂²	1	1	yes	characteristic
28	C₈×#88324	C₂²	1	2	yes	—
29	C₈×#88324	C₂²	1	1	yes	characteristic
30	C₈×#88324	C₂²	1	1	yes	characteristic
31	C₈×#88324	C₂²	1	2	yes	—
32	C₂×#13133225	C₄	1	1	yes	characteristic
33	C₂×#13133223	C₄	1	1	yes	characteristic
34	#16811091	C₂²	1	1	yes	characteristic
35	#16810580	C₄	1	1	yes	characteristic
36	#16810580	C₄	1	1	yes	characteristic
37	#16810579	C₄	1	1	yes	characteristic
38	#16810577	C₄	1	1	yes	characteristic
39	#16810577	C₄	1	1	yes	characteristic
40	#16810575	C₂²	1	1	yes	characteristic
41	#16810575	C₂²	1	1	yes	characteristic
42	M₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
43	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
46	C₅₃×#405	C₄	1	1	yes	characteristic
47	C₂×#11719936	C₂×C₄	1	4	yes	—
48	C₂×#11719940	C₂×C₄	1	4	yes	—
49	C₂×D₅₃⋊C₈	C₂×C₄	1	4	yes	—
50	#13133284	C₂×C₄	1	4	yes	—
51	#13133284	C₂×C₄	1	4	yes	—
52	C₄⋊#88324	C₂×C₄	1	4	yes	—
53	#13133274	C₂×C₄	1	4	yes	—
54	#13133274	C₂×C₄	1	4	yes	—
55	C₂²⋊#88324	C₂×C₄	1	4	yes	—
56	#13133272	C₂×C₄	1	4	yes	—
57	#13133272	C₂×C₄	1	4	yes	—
58	C₄×#88324	C₂×C₄	1	4	yes	—
59	C₄×#88324	C₂³	1	2	yes	—
60	C₄×#88324	C₂³	1	2	yes	—
61	C₄×#88324	C₂³	1	2	yes	—
62	C₄×#88324	C₂³	1	2	yes	—
63	C₂×#11719945	C₂×C₄	1	1	yes	characteristic
64	#13133225	—	2	4	no	—
65	#13133223	—	2	4	no	—
66	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
67	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
68	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
69	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
70	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
71	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
76	#13133182	C₂×C₄	1	2	yes	—
77	#13133179	C₂×C₄	1	2	yes	—
78	#13133177	C₂×C₄	1	2	yes	—
79	#13133177	C₂×C₄	1	2	yes	—
80	#13133174	C₂×C₄	1	1	yes	characteristic
81	#13133174	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
83	C₄²×D₅₃	C₂³	1	1	yes	characteristic
84	C₄²×D₅₃	C₂³	1	1	yes	characteristic
85	#13133128	C₂×C₄	1	1	yes	characteristic
86	#13133128	C₂×C₄	1	1	yes	characteristic
87	#13133127	C₂×C₄	1	1	yes	characteristic
88	#13133127	C₂×C₄	1	1	yes	characteristic
89	C₄×#88322	C₂×C₄	1	1	yes	characteristic
90	C₄×#88322	C₂×C₄	1	1	yes	characteristic
91	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
94	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
95	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
96	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
97	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
98	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
99	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
100	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
101	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
102	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
103	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊D₅₃	C₄²	1	1	yes	characteristic
106	C₂×C₂²⋊D₅₃	C₄²	1	1	yes	characteristic
107	C₂²×Dic₅₃	C₂²×C₄	1	2	yes	—
108	#11719945	—	2	2	no	—
109	#11719945	—	2	2	no	—
110	C₂×D₂₁₂	C₄²	1	1	yes	characteristic
111	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
113	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
114	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×Dic₁₀₆	C₄²	1	1	yes	characteristic
116	#11719940	—	2	8	no	—
117	C₂×#88324	C₂²×C₄	1	4	yes	—
118	C₂×#88324	C₂²×C₄	1	4	yes	—
119	C₂×#88324	C₂²×C₄	1	4	yes	—
120	C₂×#88324	C₂²×C₄	1	4	yes	—
121	#11719936	—	2	8	no	—
122	D₅₃⋊C₈	—	2	8	no	—
123	M₁₆×C₅₃	—	2	2	no	—
124	C₂×C₈×C₅₃	—	2	2	no	—
125	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
129	C₄⋊C₄×C₅₃	C₄²	1	2	yes	—
130	C₂²⋊C₄×C₅₃	C₄²	1	2	yes	—
131	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
133	#11719921	C₄²	1	2	yes	—
134	#11719921	C₄²	1	2	yes	—
135	#11719919	C₄²	1	2	yes	—
136	#11719919	C₄²	1	2	yes	—
137	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
139	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
140	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
141	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
142	#11719917	—	2	2	no	—
143	C₂×#88322	—	2	2	no	—
144	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
145	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
146	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
147	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
148	#11719912	—	2	2	no	—
149	#11719912	—	2	2	no	—
150	#11719912	—	2	2	no	—
151	#11719912	—	2	2	no	—
152	C₈×D₅₃	—	2	2	no	—
153	C₈×D₅₃	—	2	2	no	—
154	C₈×D₅₃	M₁₆	1	4	yes	complemented
155	C₈×D₅₃	M₁₆	1	4	yes	complemented
156	C₂³×C₅₃	C₂×C₄²	1	1	yes	characteristic
157	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
158	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₅₃	—	2	1	no	—
160	C₂×C₄×C₅₃	—	2	1	no	—
161	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
163	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
164	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
165	C₂²⋊D₅₃	—	2	2	no	—
166	C₂²⋊D₅₃	—	2	2	no	—
167	C₂×Dic₅₃	—	2	4	no	—
168	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
169	C₂×Dic₅₃	C₂×C₄²	1	2	yes	—
170	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
171	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
172	D₂₁₂	—	2	2	no	—
173	C₄×D₅₃	—	2	1	no	—
174	C₄×D₅₃	—	2	1	no	—
175	C₄×D₅₃	—	2	4	no	—
176	C₄×D₅₃	—	2	4	no	—
177	C₄×D₅₃	C₂×M₁₆	1	2	yes	—
178	C₄×D₅₃	C₂×M₁₆	1	2	yes	—
179	Dic₁₀₆	—	2	2	no	—
180	#88324	—	2	4	no	—
181	#88324	—	2	4	no	—
182	#88324	—	2	4	no	—
183	#88324	#131	1	8	yes	complemented
184	C₈×C₅₃	—	2	1	no	—
185	C₈×C₅₃	—	2	1	no	—
186	C₈×C₅₃	C₂×M₁₆	1	2	yes	—
187	C₈×C₅₃	C₂×M₁₆	1	2	yes	—
188	#88322	—	2	1	no	—
189	#88322	—	2	1	no	—
190	#88322	C₂×M₁₆	1	2	yes	—
191	#88322	C₂×M₁₆	1	2	yes	—
192	#17335	—	53	1	no	maximal, Sylow
193	C₂²×C₅₃	—	2	1	no	—
194	C₂²×C₅₃	—	2	2	no	—
195	C₂²×C₅₃	C₂²×C₄²	1	1	yes	characteristic
196	C₂×D₅₃	—	2	2	no	—
197	C₂×D₅₃	—	2	1	no	—
198	C₂×D₅₃	—	2	2	no	—
199	C₂×D₅₃	C₄×M₁₆	1	2	yes	—
200	C₄×C₅₃	—	2	1	no	—
201	C₄×C₅₃	—	2	2	no	—
202	C₄×C₅₃	—	2	2	no	—
203	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
204	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
205	Dic₅₃	—	2	1	no	—
206	Dic₅₃	—	2	2	no	—
207	Dic₅₃	C₄×M₁₆	1	2	yes	—
208	Dic₅₃	C₂×#131	1	4	yes	—
209	#2965	—	53	2	no	—
210	C₄×#131	—	53	1	no	—
211	#1455	—	53	1	no	—
212	#1455	—	53	1	no	—
213	#1453	—	53	1	no	—
214	#1453	—	53	1	no	—
215	#1451	—	53	2	no	—
216	#1450	—	53	1	no	—
217	C₈×M₁₆	—	53	2	no	—
218	C₈×M₁₆	—	53	2	no	—
219	C₂×C₈²	—	53	1	no	—
220	C₂×C₅₃	—	4	1	no	—
221	C₂×C₅₃	C₂×C₄×M₁₆	1	1	yes	characteristic
222	C₂×C₅₃	C₄×#131	1	2	yes	—
223	D₅₃	—	2	2	no	—
224	D₅₃	—	4	1	no	—
225	C₂×#131	—	53	1	no	—
226	C₂×#131	—	53	1	no	—
227	C₄×#41	—	53	1	no	—
228	#446	—	53	4	no	—
229	#436	—	53	4	no	—
230	#435	—	53	4	no	—
231	#435	—	53	4	no	—
232	#431	—	53	2	no	—
233	#431	—	53	2	no	—
234	#431	—	53	2	no	—
235	#405	—	53	1	no	—
236	#405	—	53	1	no	—
237	#405	—	53	1	no	—
238	#405	—	53	1	no	—
239	#405	—	53	1	no	—
240	#405	#6157	1	1	yes	characteristic
241	C₄×M₁₆	—	53	2	no	—
242	C₄×M₁₆	—	53	2	no	—
243	C₄×M₁₆	—	53	1	no	—
244	C₄×M₁₆	—	53	1	no	—
245	C₄×M₁₆	—	53	1	no	—
246	C₂×C₄×C₈	—	53	2	no	—
247	C₂×C₄×C₈	—	53	1	no	—
248	C₂×C₄×C₈	—	53	1	no	—
249	C₂×C₄×C₈	—	53	1	no	—
250	#322	—	53	2	no	—
251	#322	—	53	2	no	—
252	#322	—	53	2	no	—
253	#322	—	53	2	no	—
254	#322	—	53	1	no	—
255	#322	—	53	1	no	—
256	C₈²	—	53	2	no	—
257	C₈²	—	53	1	no	—
258	C₈²	—	53	1	no	—
259	C₈²	—	53	2	no	—
260	C₅₃	#17335	1	1	yes	characteristic, complemented, Sylow
261	C₂×#41	—	53	1	no	—
262	#131	—	106	4	no	—
263	#131	—	106	4	no	—
264	C₂×M₁₆	—	53	4	no	—
265	C₂×M₁₆	—	53	4	no	—
266	C₂×M₁₆	—	53	1	no	—
267	C₂×M₁₆	—	53	1	no	—
268	C₂×M₁₆	—	53	1	no	—
269	C₂×M₁₆	—	53	1	no	—
270	C₂×M₁₆	—	53	1	no	—
271	C₂×M₁₆	C₂×#6157	1	1	yes	characteristic
272	C₂²×C₈	—	53	1	no	—
273	C₂²×C₈	—	53	1	no	—
274	C₂²×C₈	—	53	4	no	—
275	C₂²×C₈	—	53	1	no	—
276	C₂²×C₈	—	53	1	no	—
277	C₂²×C₈	—	53	1	no	—
278	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
279	C₄×Q₈	—	53	2	no	—
280	C₄×D₄	—	53	2	no	—
281	C₄×D₄	—	53	2	no	—
282	C₄×D₄	—	53	2	no	—
283	#117	—	53	1	no	—
284	#117	—	53	1	no	—
285	#117	C₂×#6157	1	1	yes	characteristic
286	C₂×C₄²	—	53	1	no	—
287	C₂×C₄²	—	53	1	no	—
288	C₂×C₄²	—	53	1	no	—
289	C₄⋊C₈	—	53	4	no	—
290	C₄⋊C₈	—	53	4	no	—
291	C₄⋊C₈	—	53	4	no	—
292	C₂²⋊C₈	—	53	4	no	—
293	C₂²⋊C₈	—	53	4	no	—
294	C₂²⋊C₈	—	53	4	no	—
295	#97	—	53	4	no	—
296	#97	—	53	4	no	—
297	#97	—	53	1	no	—
298	#97	—	53	1	no	—
299	#97	—	53	1	no	—
300	#97	—	53	1	no	—
301	#97	C₂×#6157	1	1	yes	characteristic
302	#97	C₂×#6157	1	1	yes	characteristic
303	C₄×C₈	—	53	2	no	—
304	C₄×C₈	—	53	2	no	—
305	C₄×C₈	—	53	2	no	—
306	C₄×C₈	—	53	2	no	—
307	C₄×C₈	—	53	4	no	—
308	C₄×C₈	—	53	1	no	—
309	C₄×C₈	—	53	1	no	—
310	C₄×C₈	—	53	1	no	—
311	C₄×C₈	—	53	1	no	—
312	C₄×C₈	—	53	1	no	—
313	C₄×C₈	—	53	1	no	—
314	C₄×C₈	—	53	1	no	—
315	C₄×C₈	—	53	1	no	—
316	C₄×C₈	C₂×#6157	1	1	yes	characteristic
317	C₄×C₈	C₂×#6157	1	1	yes	characteristic
318	#41	—	106	2	no	—
319	#41	—	106	2	no	—
320	C₂×Q₈	—	53	1	no	—
321	C₂×D₄	—	53	1	no	—
322	C₂×D₄	—	53	1	no	—
323	C₂×D₄	—	53	1	no	—
324	C₂²×C₄	—	53	1	no	—
325	C₂²×C₄	—	53	2	no	—
326	C₂²×C₄	—	53	2	no	—
327	C₂²×C₄	—	53	2	no	—
328	C₂²×C₄	—	53	1	no	—
329	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
330	M₁₆	—	2	2	no	—
331	M₁₆	—	106	2	no	—
332	M₁₆	—	106	2	no	—
333	M₁₆	—	106	2	no	—
334	M₁₆	—	106	2	no	—
335	M₁₆	—	106	8	no	—
336	M₁₆	—	106	8	no	—
337	M₁₆	—	106	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	53	4	no	—
340	C₂×C₈	—	53	1	no	—
341	C₂×C₈	—	53	1	no	—
342	C₂×C₈	—	53	4	no	—
343	C₂×C₈	—	53	4	no	—
344	C₂×C₈	—	53	4	no	—
345	C₂×C₈	—	53	4	no	—
346	C₂×C₈	—	53	4	no	—
347	C₂×C₈	—	53	1	no	—
348	C₂×C₈	—	53	1	no	—
349	C₂×C₈	—	106	2	no	—
350	C₂×C₈	—	106	2	no	—
351	C₂×C₈	—	106	8	no	—
352	C₂×C₈	—	106	2	no	—
353	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
354	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
355	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
356	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
357	C₄⋊C₄	—	53	2	no	—
358	C₄⋊C₄	—	53	2	no	—
359	C₄⋊C₄	C₄×#6157	1	2	yes	—
360	C₂²⋊C₄	—	53	2	no	—
361	C₂²⋊C₄	—	53	2	no	—
362	C₂²⋊C₄	C₄×#6157	1	2	yes	—
363	C₄²	—	53	2	no	—
364	C₄²	—	53	2	no	—
365	C₄²	—	53	2	no	—
366	C₄²	—	53	1	no	—
367	C₄²	—	53	1	no	—
368	C₄²	C₂²×#6157	1	1	yes	characteristic
369	C₄²	C₂²×#6157	1	1	yes	characteristic
370	C₂³	—	53	1	no	—
371	C₂³	—	53	1	no	—
372	C₂³	C₂×C₄×#6157	1	1	yes	characteristic
373	Q₈	—	106	2	no	—
374	D₄	—	106	2	no	—
375	D₄	—	106	2	no	—
376	D₄	—	106	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	53	1	no	—
380	C₂×C₄	—	53	2	no	—
381	C₂×C₄	—	53	2	no	—
382	C₂×C₄	—	53	2	no	—
383	C₂×C₄	—	53	2	no	—
384	C₂×C₄	—	53	1	no	—
385	C₂×C₄	—	106	4	no	—
386	C₂×C₄	—	106	4	no	—
387	C₂×C₄	—	106	4	no	—
388	C₂×C₄	—	106	1	no	—
389	C₂×C₄	—	106	1	no	—
390	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
391	C₂×C₄	C₂×C₄×#6157	1	2	yes	—
392	C₂×C₄	C₂×C₄×#6157	1	2	yes	—
393	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	53	8	no	—
397	C₈	—	53	2	no	—
398	C₈	—	53	2	no	—
399	C₈	—	106	4	no	—
400	C₈	—	106	4	no	—
401	C₈	—	106	4	no	—
402	C₈	—	106	1	no	—
403	C₈	—	106	1	no	—
404	C₈	D₅₃⋊M₁₆	1	2	yes	—
405	C₈	D₅₃⋊M₁₆	1	2	yes	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	53	2	no	—
409	C₂²	—	106	2	no	—
410	C₂²	—	106	1	no	—
411	C₂²	—	106	2	no	—
412	C₂²	C₂²×C₄×#6157	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	53	2	no	—
417	C₄	—	53	4	no	—
418	C₄	—	106	1	no	—
419	C₄	—	106	2	no	—
420	C₄	C₂×D₅₃⋊M₁₆	1	1	yes	characteristic
421	C₄	C₂×D₅₃⋊M₁₆	1	1	yes	characteristic
422	C₂	—	4	1	no	—
423	C₂	—	106	2	no	—
424	C₂	—	212	1	no	—
425	C₂	C₄×D₅₃⋊M₁₆	1	1	yes	characteristic
426	C₂	#131×#6157	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂²×#6157
commutator, socle	C₂²×C₅₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₅₃×#405	C₄
prime radical	C₂×#11719945	C₂×C₄
cosocle	C₄×Dic₅₃	C₂⁴
hypercenter	#405	#6157
hypocenter	C₅₃	#17335
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
2. #20289939	C₂	semidirect
3. #20289938	C₂	semidirect
4. #20289935	C₂	semidirect
5. #20289934	C₂	semidirect
6. #20289923	C₂	semidirect
7. #20289919	C₂	semidirect
8. C₈×#11719936	C₂	semidirect
9. C₈×#11719940	C₂	semidirect
10. C₈×D₅₃⋊C₈	C₂	semidirect
154. C₈×D₅₃	M₁₆	semidirect
155. C₈×D₅₃	M₁₆	semidirect
183. #88324	#131	semidirect
260. C₅₃	#17335	semidirect

Maximal subgroups

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

subgroup	index
#20291526	2
#20289939	2
#20289938	2
#20289935	2
#20289934	2
#20289923	2
#20289919	2
C₈×#11719936	2
C₈×#11719940	2
C₈×D₅₃⋊C₈	2
#20283137	2
#17335	53