Subgroups — #28306923

Order 13568.

714 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13133287	C₂	1	1	yes	maximal, characteristic
2	C₂×#16811586	C₂	1	1	yes	maximal, characteristic
3	C₂×#16811506	C₂	1	2	yes	maximal
4	#20290409	C₂	1	2	yes	maximal
5	C₂×#108×D₅₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×#11719936	C₂²	1	2	yes	—
7	C₂×D₅₃⋊M₁₆	C₂²	1	1	yes	characteristic
8	C₂×#13133296	C₂²	1	1	yes	characteristic
9	C₂×#13133287	—	2	1	no	—
10	C₂×#13133287	—	2	1	no	—
11	C₂×#13133287	—	2	2	no	—
12	C₂×#13133287	C₄	1	4	yes	complemented
13	#16811586	—	2	2	no	—
14	#16811586	C₄	1	4	yes	—
15	C₂×#13133271	—	2	1	no	—
16	C₂×C₈×#6157	—	2	1	no	—
17	#16811506	—	2	4	no	—
18	#16811499	—	2	4	no	—
19	C₂×M₁₆×D₅₃	C₂²	1	2	yes	—
20	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
21	C₂×#13133153	C₄	1	1	yes	characteristic, complemented
22	C₂×#13133152	C₄	1	2	yes	complemented
23	#108×D₅₃	—	2	2	no	—
24	#108×D₅₃	—	2	2	no	—
25	C₂×#108×C₅₃	C₄	1	1	yes	characteristic, complemented
26	C₂×#11719936	—	2	2	no	—
27	C₂×#11719936	—	2	2	no	—
28	C₂×#11719936	—	2	2	no	—
29	C₂×#11719936	—	2	2	no	—
30	C₂×#11719936	—	2	2	no	—
31	C₂×#11719936	C₂×C₄	1	4	yes	—
32	C₂×#11719936	D₄	1	2	yes	—
33	D₅₃⋊M₁₆	—	2	1	no	—
34	D₅₃⋊M₁₆	—	2	1	no	—
35	D₅₃⋊M₁₆	C₂×C₄	1	2	yes	—
36	D₅₃⋊M₁₆	Q₈	1	2	yes	—
37	C₂×#11719940	—	2	1	no	—
38	C₂×D₅₃⋊C₈	—	2	1	no	—
39	C₂²×#88324	—	2	2	no	—
40	#13133296	—	2	1	no	—
41	#13133296	—	2	1	no	—
42	#13133296	C₂×C₄	1	2	yes	—
43	#13133296	D₄	1	2	yes	—
44	C₂×C₄⋊#6157	—	2	1	no	—
45	C₂×C₂²⋊#6157	Q₈	1	2	yes	—
46	C₂×C₄×#6157	—	2	1	no	—
47	#13133287	—	2	4	no	—
48	#13133287	—	2	4	no	—
49	#13133271	—	2	4	no	—
50	C₈×#6157	—	2	4	no	—
51	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
52	C₂×#11719917	C₂×C₄	1	2	yes	—
53	C₂×#11719912	—	2	2	no	—
54	M₁₆×D₅₃	—	2	2	no	—
55	M₁₆×D₅₃	—	2	2	no	—
56	M₁₆×D₅₃	—	2	2	no	—
57	M₁₆×D₅₃	—	2	2	no	—
58	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₅₃	—	2	2	no	—
60	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
61	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
62	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
63	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
64	C₂×C₈×D₅₃	D₄	1	2	yes	—
65	C₂×C₈×D₅₃	D₄	1	2	yes	—
66	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
67	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
68	#13133153	—	2	2	no	—
69	#13133152	—	2	4	no	—
70	C₂×M₁₆×C₅₃	C₂×C₄	1	2	yes	—
71	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
72	#108×C₅₃	—	2	2	no	—
73	C₂³×D₅₃	C₂×Q₈	1	1	yes	characteristic
74	C₂²×#6157	—	2	2	no	—
75	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
76	C₂²×Dic₅₃	#41	1	1	yes	characteristic
77	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
80	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
83	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
84	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
85	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
86	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
87	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
88	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
89	C₂²⋊#6157	—	2	2	no	—
90	C₂²⋊#6157	C₄⋊C₄	1	4	yes	—
91	#11719940	—	2	2	no	—
92	#11719940	—	2	2	no	—
93	C₂×#88324	—	2	2	no	—
94	C₂×#88324	—	2	4	no	—
95	C₂×#88324	—	4	2	no	—
96	C₂×#88324	—	4	2	no	—
97	C₄⋊#6157	—	2	2	no	—
98	C₄⋊#6157	—	2	2	no	—
99	C₄×#6157	—	2	2	no	—
100	C₄×#6157	—	2	2	no	—
101	#11719936	—	2	2	no	—
102	#11719936	—	2	4	no	—
103	#11719936	—	2	4	no	—
104	#11719936	—	4	2	no	—
105	#11719936	—	4	2	no	—
106	#11719936	C₄⋊C₄	1	4	yes	—
107	D₅₃⋊C₈	—	2	2	no	—
108	D₅₃⋊C₈	—	2	2	no	—
109	M₁₆×C₅₃	—	2	2	no	—
110	M₁₆×C₅₃	—	2	2	no	—
111	C₂×C₈×C₅₃	—	2	2	no	—
112	C₂×C₈×C₅₃	C₄²	1	2	yes	—
113	C₂×C₈×C₅₃	C₂²⋊C₄	1	2	yes	—
114	C₂×C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
116	#11719917	—	2	2	no	—
117	#11719917	—	2	2	no	—
118	C₂×#88322	—	2	2	no	—
119	C₂×#88322	C₄²	1	2	yes	—
120	C₂×#88322	C₂²⋊C₄	1	2	yes	—
121	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
122	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
123	#11719912	—	4	2	no	—
124	#11719912	—	4	2	no	—
125	C₈×D₅₃	—	4	2	no	—
126	C₈×D₅₃	—	4	2	no	—
127	C₈×D₅₃	C₂²⋊C₄	1	2	yes	—
128	C₈×D₅₃	C₂²⋊C₄	1	2	yes	—
129	C₈×D₅₃	C₂²⋊C₄	1	2	yes	—
130	C₈×D₅₃	C₂²⋊C₄	1	2	yes	—
131	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
132	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
133	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
134	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
135	C₂³×C₅₃	C₄×Q₈	1	1	yes	characteristic
136	C₂²×D₅₃	—	4	2	no	—
137	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂²×D₅₃	C₄×Q₈	1	1	yes	characteristic
139	C₂²×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
140	C₂²×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂²×D₅₃	C₄⋊Q₈	1	1	yes	characteristic
142	C₂²×D₅₃	C₄⋊Q₈	1	1	yes	characteristic
143	C₂×#6157	—	2	4	no	—
144	C₂×#6157	—	4	4	no	—
145	C₂×C₄×C₅₃	C₂×C₄²	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	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₅₃	C₄×Q₈	1	1	yes	characteristic
151	C₂×Dic₅₃	#117	1	1	yes	characteristic
152	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
153	C₂×Dic₅₃	#121	1	1	yes	characteristic
154	C₂×Dic₅₃	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂×Dic₅₃	#124	1	1	yes	characteristic
156	C₂×Dic₅₃	#125	1	1	yes	characteristic
157	C₄×D₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₄×D₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₄×D₅₃	#117	1	1	yes	characteristic
163	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
164	C₄×D₅₃	C₄×Q₈	1	1	yes	characteristic
165	C₄×D₅₃	#121	1	1	yes	characteristic
166	C₄×D₅₃	#121	1	1	yes	characteristic
167	C₄×D₅₃	#121	1	1	yes	characteristic
168	C₄×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
169	C₄×D₅₃	#124	1	1	yes	characteristic
170	C₄×D₅₃	#125	1	1	yes	characteristic
171	C₄×D₅₃	#127	1	1	yes	characteristic
172	C₄×D₅₃	C₄⋊Q₈	1	1	yes	characteristic
173	#88324	—	2	4	no	—
174	#88324	—	4	4	no	—
175	C₈×C₅₃	—	4	2	no	—
176	C₈×C₅₃	#95	1	2	yes	—
177	C₈×C₅₃	#95	1	2	yes	—
178	#88322	—	4	2	no	—
179	#88322	#95	1	2	yes	—
180	#88322	#95	1	2	yes	—
181	#10873	—	53	1	no	maximal, Sylow
182	C₂²×C₅₃	—	2	2	no	—
183	C₂²×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
184	C₂²×C₅₃	#389	1	1	yes	characteristic
185	C₂²×C₅₃	#391	1	1	yes	characteristic
186	C₂×D₅₃	—	2	2	no	—
187	C₂×D₅₃	—	2	2	no	—
188	C₂×D₅₃	—	4	1	no	—
189	C₂×D₅₃	—	4	1	no	—
190	C₂×D₅₃	—	4	1	no	—
191	C₂×D₅₃	—	4	1	no	—
192	C₂×D₅₃	#380	1	1	yes	characteristic
193	C₂×D₅₃	#384	1	1	yes	characteristic
194	C₂×D₅₃	#389	1	1	yes	characteristic
195	C₂×D₅₃	#391	1	1	yes	characteristic
196	#6157	—	4	4	no	—
197	C₄×C₅₃	C₂×#95	1	1	yes	characteristic
198	C₄×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
199	C₄×C₅₃	#389	1	1	yes	characteristic
200	C₄×C₅₃	#390	1	1	yes	characteristic
201	Dic₅₃	#380	1	1	yes	characteristic
202	Dic₅₃	#382	1	1	yes	characteristic
203	Dic₅₃	#389	1	1	yes	characteristic
204	Dic₅₃	#390	1	1	yes	characteristic
205	C₂²×#108	—	53	1	no	—
206	C₂²×#108	—	53	1	no	—
207	C₂×#405	—	53	1	no	—
208	C₂×#344	—	53	2	no	—
209	#1738	—	53	2	no	—
210	C₂×C₅₃	—	2	1	no	—
211	C₂×C₅₃	—	2	1	no	—
212	C₂×C₅₃	C₄⋊#95	1	1	yes	characteristic
213	C₂×C₅₃	#1953	1	2	yes	—
214	D₅₃	—	2	1	no	—
215	D₅₃	—	2	1	no	—
216	D₅₃	—	2	1	no	—
217	D₅₃	—	2	1	no	—
218	C₂²×M₁₆	—	53	1	no	—
219	C₂²×M₁₆	—	53	2	no	—
220	C₂²×M₁₆	—	53	2	no	—
221	C₂³×C₈	—	53	1	no	—
222	C₂×#117	—	53	1	no	—
223	C₂×#108	—	53	4	no	—
224	C₂×#108	—	53	2	no	—
225	C₂×#108	—	53	1	no	—
226	C₂×#108	—	106	2	no	—
227	C₂×#108	—	106	2	no	—
228	C₂×#108	—	106	1	no	—
229	C₂×#108	—	106	1	no	—
230	C₂×#108	—	106	2	no	—
231	C₂×#108	#6157	1	1	yes	characteristic, complemented
232	#405	—	53	4	no	—
233	#405	—	106	2	no	—
234	C₂×#97	—	106	1	no	—
235	C₂×C₄×C₈	—	106	1	no	—
236	#344	—	106	4	no	—
237	#341	—	106	4	no	—
238	C₅₃	#10873	1	1	yes	characteristic, complemented, Sylow
239	C₂³×C₄	—	53	1	no	—
240	C₂×M₁₆	—	53	2	no	—
241	C₂×M₁₆	—	53	2	no	—
242	C₂×M₁₆	—	53	2	no	—
243	C₂×M₁₆	—	53	4	no	—
244	C₂×M₁₆	—	53	2	no	—
245	C₂×M₁₆	—	106	2	no	—
246	C₂×M₁₆	—	106	1	no	—
247	C₂×M₁₆	—	106	1	no	—
248	C₂×M₁₆	—	106	1	no	—
249	C₂×M₁₆	—	106	2	no	—
250	C₂×M₁₆	—	106	2	no	—
251	C₂×M₁₆	—	106	2	no	—
252	C₂×M₁₆	—	106	2	no	—
253	C₂×M₁₆	—	106	2	no	—
254	C₂×M₁₆	—	106	2	no	—
255	C₂×M₁₆	—	106	2	no	—
256	C₂×M₁₆	—	106	2	no	—
257	C₂×M₁₆	—	106	2	no	—
258	C₂×M₁₆	C₂×#6157	1	2	yes	—
259	C₂²×C₈	—	53	1	no	—
260	C₂²×C₈	—	53	2	no	—
261	C₂²×C₈	—	53	2	no	—
262	C₂²×C₈	—	53	1	no	—
263	C₂²×C₈	—	53	1	no	—
264	C₂²×C₈	—	53	1	no	—
265	C₂²×C₈	—	53	1	no	—
266	C₂²×C₈	—	53	2	no	—
267	C₂²×C₈	—	53	2	no	—
268	C₂²×C₈	—	106	2	no	—
269	C₂²×C₈	—	106	1	no	—
270	C₂²×C₈	—	106	2	no	—
271	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
272	#117	—	53	2	no	—
273	#117	—	53	2	no	—
274	#117	—	106	1	no	—
275	#117	—	106	1	no	—
276	C₂×C₄⋊C₄	—	106	1	no	—
277	C₂×C₂²⋊C₄	—	53	2	no	—
278	C₂×C₄²	—	106	1	no	—
279	#108	—	2	2	no	—
280	#108	—	106	4	no	—
281	#108	—	106	4	no	—
282	#108	—	106	4	no	—
283	#108	—	106	2	no	—
284	#97	—	106	4	no	—
285	C₄×C₈	—	106	4	no	—
286	C₂⁴	—	53	1	no	—
287	C₂²×C₄	—	53	1	no	—
288	C₂²×C₄	—	53	1	no	—
289	C₂²×C₄	—	53	1	no	—
290	C₂²×C₄	—	53	1	no	—
291	C₂²×C₄	—	53	1	no	—
292	C₂²×C₄	—	53	1	no	—
293	C₂²×C₄	—	53	1	no	—
294	C₂²×C₄	—	53	1	no	—
295	C₂²×C₄	—	53	1	no	—
296	C₂²×C₄	—	53	1	no	—
297	C₂²×C₄	—	53	1	no	—
298	C₂²×C₄	—	53	1	no	—
299	C₂²×C₄	—	53	1	no	—
300	C₂²×C₄	—	106	2	no	—
301	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
302	M₁₆	—	2	2	no	—
303	M₁₆	—	2	2	no	—
304	M₁₆	—	53	4	no	—
305	M₁₆	—	106	2	no	—
306	M₁₆	—	106	2	no	—
307	M₁₆	—	106	2	no	—
308	M₁₆	—	106	4	no	—
309	M₁₆	—	106	4	no	—
310	M₁₆	—	106	2	no	—
311	M₁₆	—	106	2	no	—
312	M₁₆	—	212	2	no	—
313	M₁₆	—	212	2	no	—
314	M₁₆	—	212	2	no	—
315	M₁₆	—	212	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	53	2	no	—
318	C₂×C₈	—	53	2	no	—
319	C₂×C₈	—	53	1	no	—
320	C₂×C₈	—	53	1	no	—
321	C₂×C₈	—	53	2	no	—
322	C₂×C₈	—	53	2	no	—
323	C₂×C₈	—	53	2	no	—
324	C₂×C₈	—	53	2	no	—
325	C₂×C₈	—	53	2	no	—
326	C₂×C₈	—	53	2	no	—
327	C₂×C₈	—	53	2	no	—
328	C₂×C₈	—	53	2	no	—
329	C₂×C₈	—	106	2	no	—
330	C₂×C₈	—	106	2	no	—
331	C₂×C₈	—	106	2	no	—
332	C₂×C₈	—	106	4	no	—
333	C₂×C₈	—	106	2	no	—
334	C₂×C₈	—	212	2	no	—
335	C₂×C₈	—	212	2	no	—
336	C₂×C₈	—	212	2	no	—
337	C₂×C₈	—	212	2	no	—
338	C₂×C₈	C₄×#6157	1	2	yes	—
339	C₂×C₈	C₄⋊#6157	1	1	yes	characteristic
340	C₂×C₈	C₄⋊#6157	1	1	yes	characteristic
341	C₂×C₈	C₂²⋊#6157	1	2	yes	—
342	C₄⋊C₄	—	106	2	no	—
343	C₄⋊C₄	—	106	2	no	—
344	C₂²⋊C₄	—	53	4	no	—
345	C₂²⋊C₄	—	106	2	no	—
346	C₄²	—	106	2	no	—
347	C₄²	—	106	2	no	—
348	C₂³	—	53	1	no	—
349	C₂³	—	53	1	no	—
350	C₂³	—	53	1	no	—
351	C₂³	—	53	1	no	—
352	C₂³	—	53	1	no	—
353	C₂³	—	53	1	no	—
354	C₂³	—	212	2	no	—
355	C₂³	Q₈×#6157	1	1	yes	characteristic
356	C₂×C₄	—	53	1	no	—
357	C₂×C₄	—	53	1	no	—
358	C₂×C₄	—	53	1	no	—
359	C₂×C₄	—	53	1	no	—
360	C₂×C₄	—	53	1	no	—
361	C₂×C₄	—	53	1	no	—
362	C₂×C₄	—	53	1	no	—
363	C₂×C₄	—	53	1	no	—
364	C₂×C₄	—	53	1	no	—
365	C₂×C₄	—	53	1	no	—
366	C₂×C₄	—	53	1	no	—
367	C₂×C₄	—	53	1	no	—
368	C₂×C₄	—	53	1	no	—
369	C₂×C₄	—	53	1	no	—
370	C₂×C₄	—	53	1	no	—
371	C₂×C₄	—	53	1	no	—
372	C₂×C₄	—	53	1	no	—
373	C₂×C₄	—	53	1	no	—
374	C₂×C₄	—	53	1	no	—
375	C₂×C₄	—	53	1	no	—
376	C₂×C₄	—	53	1	no	—
377	C₂×C₄	—	53	1	no	—
378	C₂×C₄	—	106	4	no	—
379	C₂×C₄	—	212	4	no	—
380	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
381	C₂×C₄	C₂×C₂²⋊#6157	1	1	yes	characteristic
382	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
383	C₂×C₄	D₄×#6157	1	1	yes	characteristic
384	C₂×C₄	D₄×#6157	1	1	yes	characteristic
385	C₂×C₄	Q₈×#6157	1	1	yes	characteristic
386	C₈	—	4	2	no	—
387	C₈	—	53	2	no	—
388	C₈	—	53	2	no	—
389	C₈	—	106	4	no	—
390	C₈	—	212	4	no	—
391	C₈	—	212	2	no	—
392	C₈	(C₂×#6157)⋊C₄	1	2	yes	—
393	C₈	(C₂×#6157)⋊C₄	1	2	yes	—
394	C₂²	—	2	2	no	—
395	C₂²	—	53	1	no	—
396	C₂²	—	53	1	no	—
397	C₂²	—	53	1	no	—
398	C₂²	—	53	1	no	—
399	C₂²	—	106	2	no	—
400	C₂²	—	106	2	no	—
401	C₂²	—	212	1	no	—
402	C₂²	—	212	1	no	—
403	C₂²	—	212	1	no	—
404	C₂²	—	212	1	no	—
405	C₂²	C₄⋊C₄×#6157	1	1	yes	characteristic
406	C₂²	#16811574	1	1	yes	characteristic
407	C₂²	(C₂×#6157)⋊Q₈	1	1	yes	characteristic
408	C₄	—	53	1	no	—
409	C₄	—	53	1	no	—
410	C₄	—	53	1	no	—
411	C₄	—	53	1	no	—
412	C₄	—	212	4	no	—
413	C₄	C₂×(C₂×#6157)⋊C₄	1	1	yes	characteristic
414	C₄	C₄⋊C₄×#6157	1	1	yes	characteristic
415	C₄	#16811574	1	1	yes	characteristic
416	C₄	#16811575	1	1	yes	characteristic
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	106	1	no	—
420	C₂	—	106	1	no	—
421	C₂	—	106	1	no	—
422	C₂	—	106	1	no	—
423	C₂	#20289892	1	1	yes	characteristic
424	C₂	#20290834	1	2	yes	—

	subgroup	G/H
center	C₂²	#16811574
commutator	C₂×C₄×C₅₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×#6157
Fitting	C₂×#108×C₅₃	C₄
socle	C₂²×C₅₃	#389
prime radical	C₂³×D₅₃	C₂×Q₈
cosocle	C₂²×C₄×D₅₃	C₂³
hypercenter	C₂×#108	#6157
hypocenter	C₅₃	#10873
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

Complements

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

N	H ≅ G/N	type
12. C₂×#13133287	C₄	semidirect
21. C₂×#13133153	C₄	semidirect
22. C₂×#13133152	C₄	semidirect
25. C₂×#108×C₅₃	C₄	semidirect
231. C₂×#108	#6157	semidirect
238. C₅₃	#10873	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13133287	2
C₂×#16811586	2
C₂×#16811506	2
#20290409	2
C₂×#108×D₅₃	2
#10873	53