Subgroups — M₁₆×D₅₃⋊C₈ #28313741

Order 13568.

1046 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₃⋊#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₅₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#20289913	C₂	1	4	yes	maximal, complemented
4	M₁₆×#88324	C₂	1	4	yes	maximal, complemented
5	#20289909	C₂	1	2	yes	maximal, complemented
6	C₈×D₅₃⋊C₈	C₂	1	2	yes	maximal, complemented
7	C₄×M₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic
8	C₂²×D₅₃⋊C₈	C₄	1	2	yes	—
9	#16811642	C₄	1	2	yes	—
10	#16811641	C₂²	1	2	yes	—
11	#16811640	C₄	1	2	yes	—
12	#16811639	C₂²	1	2	yes	—
13	D₅₃⋊(C₄⋊C₈)	C₄	1	2	yes	—
14	D₅₃⋊(C₂²⋊C₈)	C₄	1	2	yes	—
15	C₄×D₅₃⋊C₈	C₄	1	2	yes	—
16	C₄×D₅₃⋊C₈	C₄	1	2	yes	—
17	C₄×D₅₃⋊C₈	C₂²	1	2	yes	—
18	C₄×D₅₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₄×D₅₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₄×D₅₃⋊C₈	C₂²	1	2	yes	—
21	C₂×C₄×#88324	C₄	1	2	yes	—
22	C₂×C₄×#88324	C₂²	1	2	yes	—
23	#16811464	C₂²	1	8	yes	complemented
24	C₈×#88324	C₂²	1	8	yes	complemented
25	C₂×M₁₆×D₅₃	C₄	1	2	yes	—
26	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
27	C₄×#11719917	C₄	1	1	yes	characteristic
28	#16810575	C₂²	1	2	yes	—
29	M₁₆×Dic₅₃	C₂²	1	2	yes	—
30	C₄×#11719912	C₄	1	2	yes	—
31	#97×D₅₃	C₄	1	2	yes	—
32	C₄×C₈×D₅₃	C₂²	1	2	yes	—
33	C₄×M₁₆×C₅₃	C₄	1	1	yes	characteristic
34	C₂×D₅₃⋊C₈	—	2	8	no	—
35	C₂×D₅₃⋊C₈	C₂×C₄	1	2	yes	—
36	C₂×D₅₃⋊C₈	C₂×C₄	1	4	yes	—
37	C₂×D₅₃⋊C₈	C₂×C₄	1	4	yes	—
38	C₂×D₅₃⋊C₈	C₂×C₄	1	2	yes	—
39	C₂²×#88324	C₂×C₄	1	4	yes	—
40	#13133284	C₂×C₄	1	4	yes	—
41	C₄⋊#88324	C₂×C₄	1	4	yes	—
42	#13133274	C₂×C₄	1	4	yes	—
43	C₂²⋊#88324	C₂×C₄	1	4	yes	—
44	C₄×#88324	C₂×C₄	1	2	yes	—
45	C₄×#88324	C₂×C₄	1	4	yes	—
46	C₄×#88324	C₂×C₄	1	2	yes	—
47	C₄×#88324	C₂×C₄	1	4	yes	—
48	C₄×#88324	C₂×C₄	1	4	yes	—
49	C₄×#88324	C₂³	1	2	yes	—
50	C₄×#88324	C₂³	1	2	yes	—
51	C₄×#88324	C₂³	1	4	yes	—
52	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
55	C₂×#11719917	C₂×C₄	1	2	yes	—
56	C₂×#11719912	C₂×C₄	1	4	yes	—
57	M₁₆×D₅₃	C₈	1	16	yes	complemented
58	C₂×C₈×D₅₃	C₂×C₄	1	4	yes	—
59	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
62	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
63	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
65	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
66	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
67	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₅₃	C₂³	1	1	yes	characteristic
69	C₄²×D₅₃	C₂³	1	1	yes	characteristic
70	#13133128	C₂×C₄	1	2	yes	—
71	#13133127	C₂×C₄	1	4	yes	—
72	C₄×#88322	C₂×C₄	1	2	yes	—
73	C₈×Dic₅₃	C₂³	1	4	yes	—
74	C₂×M₁₆×C₅₃	C₂×C₄	1	2	yes	—
75	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
76	#97×C₅₃	C₂×C₄	1	2	yes	—
77	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	—
78	C₂³×D₅₃	C₄²	1	1	yes	characteristic
79	C₂²×C₄×C₅₃	C₄²	1	1	yes	characteristic
80	C₂²×C₄×C₅₃	C₄²	1	1	yes	characteristic
81	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×Dic₅₃	C₄²	1	1	yes	characteristic
83	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₄×D₅₃	—	2	4	no	—
86	C₂×C₄×D₅₃	—	2	4	no	—
87	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
88	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
89	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
90	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
91	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
92	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
93	C₂×C₄×D₅₃	C₂×C₈	1	8	yes	—
94	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×#88324	—	2	8	no	—
101	C₂×#88324	C₂²×C₄	1	4	yes	—
102	C₂×#88324	C₂²×C₄	1	8	yes	—
103	C₂×#88324	C₂²×C₄	1	4	yes	—
104	D₅₃⋊C₈	—	2	4	no	—
105	D₅₃⋊C₈	—	2	8	no	—
106	D₅₃⋊C₈	—	2	8	no	—
107	D₅₃⋊C₈	M₁₆	1	8	yes	direct product factor
108	M₁₆×C₅₃	C₂×C₈	1	8	yes	complemented
109	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
110	C₄²×C₅₃	C₄²	1	1	yes	characteristic
111	C₄²×C₅₃	C₄²	1	1	yes	characteristic
112	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
114	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
115	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
116	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
117	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
118	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
119	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
120	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
121	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
122	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
123	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
124	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
126	#11719917	C₂×C₈	1	8	yes	complemented
127	C₂×#88322	C₂²×C₄	1	4	yes	—
128	#11719912	C₂×C₈	1	16	yes	complemented
129	C₈×D₅₃	C₂×C₈	1	16	yes	complemented
130	C₂³×C₅₃	C₂×C₄²	1	1	yes	characteristic
131	C₂²×D₅₃	—	2	2	no	—
132	C₂²×D₅₃	—	2	2	no	—
133	C₂²×D₅₃	C₄×C₈	1	4	yes	—
134	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
135	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
136	C₂×C₄×C₅₃	—	2	2	no	—
137	C₂×C₄×C₅₃	—	2	2	no	—
138	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
139	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
140	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
141	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
142	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
143	C₂×C₄×C₅₃	C₂²×C₈	1	4	yes	—
144	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
145	C₂×Dic₅₃	—	2	2	no	—
146	C₂×Dic₅₃	—	2	2	no	—
147	C₂×Dic₅₃	C₄×C₈	1	4	yes	—
148	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
149	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
150	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
151	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
152	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
153	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
154	C₄×D₅₃	—	2	2	no	—
155	C₄×D₅₃	—	2	2	no	—
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	C₄×C₈	1	4	yes	—
161	C₄×D₅₃	C₄×C₈	1	4	yes	—
162	C₄×D₅₃	C₂²×C₈	1	4	yes	—
163	C₄×D₅₃	C₂²×C₈	1	4	yes	—
164	C₄×D₅₃	C₂×M₁₆	1	4	yes	—
165	C₄×D₅₃	#131	1	4	yes	—
166	#88324	—	2	4	no	—
167	#88324	—	2	8	no	—
168	#88324	C₂×M₁₆	1	8	yes	complemented
169	C₈×C₅₃	C₂²×C₈	1	8	yes	complemented
170	#88322	C₂²×C₈	1	8	yes	complemented
171	C₂×C₈×M₁₆	—	53	1	no	maximal, Sylow
172	C₂²×C₅₃	—	2	1	no	—
173	C₂²×C₅₃	—	2	1	no	—
174	C₂²×C₅₃	C₂×C₄×C₈	1	2	yes	—
175	C₂²×C₅₃	C₂²×C₄²	1	1	yes	characteristic
176	C₂×D₅₃	—	2	1	no	—
177	C₂×D₅₃	—	2	1	no	—
178	C₂×D₅₃	—	2	8	no	—
179	C₂×D₅₃	C₂×C₄×C₈	1	2	yes	—
180	C₂×D₅₃	C₂×C₄×C₈	1	2	yes	—
181	C₂×D₅₃	C₄×M₁₆	1	2	yes	—
182	C₂×D₅₃	#405	1	2	yes	—
183	C₄×C₅₃	—	2	1	no	—
184	C₄×C₅₃	—	2	1	no	—
185	C₄×C₅₃	C₂×C₄×C₈	1	2	yes	—
186	C₄×C₅₃	C₄×M₁₆	1	2	yes	—
187	C₄×C₅₃	#405	1	2	yes	—
188	C₄×C₅₃	C₂³×C₈	1	2	yes	—
189	Dic₅₃	—	2	1	no	—
190	Dic₅₃	—	2	1	no	—
191	Dic₅₃	C₂×C₄×C₈	1	2	yes	—
192	Dic₅₃	C₂×C₄×C₈	1	2	yes	—
193	Dic₅₃	C₂²×M₁₆	1	2	yes	—
194	Dic₅₃	C₂×#131	1	2	yes	—
195	C₂×#431	—	53	1	no	—
196	C₂×C₄×M₁₆	—	53	1	no	—
197	C₂²×C₄×C₈	—	53	1	no	—
198	C₈×M₁₆	—	53	4	no	—
199	C₈×M₁₆	—	53	4	no	—
200	C₂×#322	—	53	2	no	—
201	C₂×C₈²	—	53	2	no	—
202	C₂×C₅₃	—	2	2	no	—
203	C₂×C₅₃	C₂²×C₄×C₈	1	1	yes	characteristic
204	C₂×C₅₃	C₂×C₄×M₁₆	1	1	yes	characteristic
205	C₂×C₅₃	C₂×#405	1	1	yes	characteristic
206	D₅₃	—	2	2	no	—
207	D₅₃	C₈×M₁₆	1	4	yes	complemented
208	C₂²×M₁₆	—	53	2	no	—
209	C₂³×C₈	—	53	2	no	—
210	C₂²×C₄²	—	53	1	no	—
211	#431	—	53	2	no	—
212	#431	—	53	2	no	—
213	#431	—	53	2	no	—
214	#431	—	53	2	no	—
215	C₂×C₄⋊C₈	—	53	2	no	—
216	C₂×C₂²⋊C₈	—	53	2	no	—
217	C₄×M₁₆	—	53	2	no	—
218	C₄×M₁₆	—	53	1	no	—
219	C₄×M₁₆	—	53	2	no	—
220	C₄×M₁₆	—	53	2	no	—
221	C₄×M₁₆	#6157	1	1	yes	characteristic
222	C₂×#97	—	53	2	no	—
223	C₂×C₄×C₈	—	53	2	no	—
224	C₂×C₄×C₈	—	53	2	no	—
225	C₂×C₄×C₈	—	53	2	no	—
226	C₂×C₄×C₈	—	53	2	no	—
227	C₂×C₄×C₈	—	53	1	no	—
228	C₂×C₄×C₈	—	53	1	no	—
229	C₂×C₄×C₈	—	53	2	no	—
230	C₂×C₄×C₈	—	53	2	no	—
231	C₂×C₄×C₈	—	53	2	no	—
232	#322	—	53	8	no	—
233	C₈²	—	53	8	no	—
234	C₅₃	C₂×C₈×M₁₆	1	1	yes	characteristic, complemented, Sylow
235	C₂³×C₄	—	53	1	no	—
236	C₂³×C₄	—	53	1	no	—
237	C₂³×C₄	—	53	1	no	—
238	C₂×M₁₆	—	53	2	no	—
239	C₂×M₁₆	—	53	16	no	—
240	C₂×M₁₆	—	53	4	no	—
241	C₂×M₁₆	C₂×#6157	1	2	yes	—
242	C₂²×C₈	—	53	2	no	—
243	C₂²×C₈	—	53	4	no	—
244	C₂²×C₈	—	53	4	no	—
245	C₂²×C₈	—	53	4	no	—
246	C₂²×C₈	—	53	2	no	—
247	C₂²×C₈	—	53	4	no	—
248	C₂²×C₈	—	106	8	no	—
249	C₂×C₄²	—	53	1	no	—
250	C₂×C₄²	—	53	1	no	—
251	C₂×C₄²	—	53	1	no	—
252	C₂×C₄²	—	53	1	no	—
253	C₂×C₄²	—	53	1	no	—
254	C₂×C₄²	—	53	1	no	—
255	C₂×C₄²	—	53	1	no	—
256	C₂×C₄²	—	53	1	no	—
257	C₂×C₄²	—	53	1	no	—
258	C₂×C₄²	—	53	1	no	—
259	C₂×C₄²	—	53	1	no	—
260	C₂×C₄²	C₂×#6157	1	1	yes	characteristic
261	C₄⋊C₈	—	53	4	no	—
262	C₄⋊C₈	—	53	4	no	—
263	C₂²⋊C₈	—	53	4	no	—
264	C₂²⋊C₈	—	53	4	no	—
265	#97	—	53	4	no	—
266	#97	—	53	2	no	—
267	#97	C₂×#6157	1	2	yes	—
268	C₄×C₈	—	53	2	no	—
269	C₄×C₈	—	53	4	no	—
270	C₄×C₈	—	53	2	no	—
271	C₄×C₈	—	53	2	no	—
272	C₄×C₈	—	53	4	no	—
273	C₄×C₈	—	53	4	no	—
274	C₄×C₈	—	53	2	no	—
275	C₄×C₈	—	53	4	no	—
276	C₄×C₈	—	53	4	no	—
277	C₄×C₈	—	53	2	no	—
278	C₄×C₈	C₂×#6157	1	2	yes	—
279	C₂⁴	—	53	1	no	—
280	C₂²×C₄	—	53	1	no	—
281	C₂²×C₄	—	53	1	no	—
282	C₂²×C₄	—	53	1	no	—
283	C₂²×C₄	—	53	1	no	—
284	C₂²×C₄	—	53	1	no	—
285	C₂²×C₄	—	53	8	no	—
286	C₂²×C₄	—	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	—	106	4	no	—
297	C₂²×C₄	—	106	4	no	—
298	C₂²×C₄	C₄×#6157	1	1	yes	characteristic
299	C₂²×C₄	C₄×#6157	1	1	yes	characteristic
300	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
301	M₁₆	—	53	8	no	—
302	M₁₆	—	53	16	no	—
303	M₁₆	D₅₃⋊C₈	1	8	yes	direct product factor
304	C₂×C₈	—	53	4	no	—
305	C₂×C₈	—	53	8	no	—
306	C₂×C₈	—	53	4	no	—
307	C₂×C₈	—	53	16	no	—
308	C₂×C₈	—	53	4	no	—
309	C₂×C₈	—	53	8	no	—
310	C₂×C₈	—	106	8	no	—
311	C₂×C₈	—	106	8	no	—
312	C₂×C₈	—	106	4	no	—
313	C₂×C₈	—	106	8	no	—
314	C₂×C₈	C₂²×#6157	1	4	yes	—
315	C₄²	—	53	1	no	—
316	C₄²	—	53	1	no	—
317	C₄²	—	53	1	no	—
318	C₄²	—	53	1	no	—
319	C₄²	—	53	1	no	—
320	C₄²	—	53	1	no	—
321	C₄²	—	53	1	no	—
322	C₄²	—	53	1	no	—
323	C₄²	—	53	1	no	—
324	C₄²	—	53	1	no	—
325	C₄²	—	53	1	no	—
326	C₄²	—	53	1	no	—
327	C₄²	C₄×#6157	1	1	yes	characteristic
328	C₄²	C₄×#6157	1	1	yes	characteristic
329	C₄²	C₂²×#6157	1	1	yes	characteristic
330	C₄²	C₂²×#6157	1	1	yes	characteristic
331	C₂³	—	53	1	no	—
332	C₂³	—	53	4	no	—
333	C₂³	—	53	1	no	—
334	C₂³	—	106	2	no	—
335	C₂³	—	106	2	no	—
336	C₂³	C₂×C₄×#6157	1	1	yes	characteristic
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	53	4	no	—
340	C₂×C₄	—	53	1	no	—
341	C₂×C₄	—	53	1	no	—
342	C₂×C₄	—	53	1	no	—
343	C₂×C₄	—	53	1	no	—
344	C₂×C₄	—	53	4	no	—
345	C₂×C₄	—	53	4	no	—
346	C₂×C₄	—	53	4	no	—
347	C₂×C₄	—	53	4	no	—
348	C₂×C₄	—	53	4	no	—
349	C₂×C₄	—	53	4	no	—
350	C₂×C₄	—	53	1	no	—
351	C₂×C₄	—	53	1	no	—
352	C₂×C₄	—	106	2	no	—
353	C₂×C₄	—	106	2	no	—
354	C₂×C₄	—	106	2	no	—
355	C₂×C₄	—	106	2	no	—
356	C₂×C₄	—	106	2	no	—
357	C₂×C₄	—	106	2	no	—
358	C₂×C₄	—	106	2	no	—
359	C₂×C₄	—	106	2	no	—
360	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
362	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
364	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
365	C₂×C₄	C₂×D₅₃⋊C₈	1	4	yes	—
366	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
367	C₈	—	53	8	no	—
368	C₈	—	53	8	no	—
369	C₈	—	106	8	no	—
370	C₈	—	106	4	no	—
371	C₈	C₂×D₅₃⋊C₈	1	8	yes	complemented
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	53	2	no	—
375	C₂²	—	53	2	no	—
376	C₂²	—	53	2	no	—
377	C₂²	—	53	2	no	—
378	C₂²	—	106	8	no	—
379	C₂²	—	106	1	no	—
380	C₂²	—	106	1	no	—
381	C₂²	C₄×D₅₃⋊C₈	1	2	yes	—
382	C₂²	C₂²×C₄×#6157	1	1	yes	characteristic
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	53	2	no	—
386	C₄	—	53	2	no	—
387	C₄	—	53	2	no	—
388	C₄	—	53	2	no	—
389	C₄	—	106	1	no	—
390	C₄	—	106	1	no	—
391	C₄	C₄×D₅₃⋊C₈	1	2	yes	—
392	C₄	M₁₆×#6157	1	2	yes	—
393	C₄	#16811589	1	2	yes	—
394	C₄	C₂²×D₅₃⋊C₈	1	2	yes	—
395	C₂	—	2	2	no	—
396	C₂	—	53	4	no	—
397	C₂	—	106	2	no	—
398	C₂	C₂×C₄×D₅₃⋊C₈	1	1	yes	characteristic
399	C₂	C₂×M₁₆×#6157	1	1	yes	characteristic
400	C₂	C₂×#16811589	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×#6157
commutator	C₂×C₅₃	C₂²×C₄×C₈
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₄×M₁₆×C₅₃	C₄
socle	C₂²×C₅₃	C₂²×C₄²
prime radical	C₂³×D₅₃	C₄²
cosocle	C₄×Dic₅₃	C₂⁴
hypercenter	C₄×M₁₆	#6157
hypocenter	C₅₃	C₂×C₈×M₁₆
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄² ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #20289913	C₂	semidirect
4. M₁₆×#88324	C₂	semidirect
5. #20289909	C₂	semidirect
6. C₈×D₅₃⋊C₈	C₂	semidirect
23. #16811464	C₂²	semidirect
24. C₈×#88324	C₂²	semidirect
57. M₁₆×D₅₃	C₈	semidirect
107. D₅₃⋊C₈	M₁₆	direct (N × H)
108. M₁₆×C₅₃	C₂×C₈	semidirect
126. #11719917	C₂×C₈	semidirect
128. #11719912	C₂×C₈	semidirect
129. C₈×D₅₃	C₂×C₈	semidirect
168. #88324	C₂×M₁₆	semidirect
169. C₈×C₅₃	C₂²×C₈	semidirect
170. #88322	C₂²×C₈	semidirect
207. D₅₃	C₈×M₁₆	semidirect
234. C₅₃	C₂×C₈×M₁₆	semidirect
303. M₁₆	D₅₃⋊C₈	direct (N × H)
371. C₈	C₂×D₅₃⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
D₅₃⋊#431	2
C₂×C₄×D₅₃⋊C₈	2
#20289913	2
M₁₆×#88324	2
#20289909	2
C₈×D₅₃⋊C₈	2
C₄×M₁₆×D₅₃	2
C₂×C₈×M₁₆	53

Subgroups — M16×D53⋊C8 #28313741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×D₅₃⋊C₈ #28313741