Subgroups — #27537673

Order 13568.

662 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic
2	C₁₆×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×#11719908	C₂	1	1	yes	maximal, characteristic, complemented
4	#20276534	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₆×C₂²⋊D₅₃	C₂	1	2	yes	maximal, complemented
6	#20276532	C₂	1	2	yes	maximal, complemented
7	#20276513	C₂	1	1	yes	maximal, characteristic, complemented
8	#20276512	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16810402	C₂	1	2	yes	maximal, complemented
10	C₂²⋊C₁₆×D₅₃	C₂	1	2	yes	maximal, complemented
11	D₄×C₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₅₃	C₂²	1	2	yes	—
13	C₄×D₄×D₅₃	C₄	1	1	yes	characteristic
14	C₂²×#11719908	C₂²	1	2	yes	complemented
15	C₂×C₁₆×D₅₃	C₂²	1	2	yes	complemented
16	C₂×C₁₆×D₅₃	C₂²	1	2	yes	complemented
17	C₈×D₂₁₂	C₂²	1	1	yes	characteristic
18	D₄×#88322	C₄	1	1	yes	characteristic
19	#16810688	C₄	1	1	yes	characteristic
20	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	—
21	#16810686	C₄	1	2	yes	—
22	C₄⋊C₈×D₅₃	C₄	1	1	yes	characteristic
23	C₂²⋊C₈×D₅₃	C₄	1	2	yes	—
24	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
25	C₄⋊#11719908	C₂²	1	1	yes	characteristic, complemented
26	#16810441	C₂²	1	1	yes	characteristic, complemented
27	#16810441	C₂²	1	1	yes	characteristic, complemented
28	C₂²⋊#11719908	C₂²	1	2	yes	complemented
29	#16810402	C₂²	1	1	yes	characteristic
30	#16810402	C₂²	1	1	yes	characteristic
31	#16810402	C₂²	1	2	yes	—
32	#16810402	C₂²	1	2	yes	complemented
33	#16810402	C₂²	1	2	yes	complemented
34	C₄×#11719908	C₂²	1	1	yes	characteristic, complemented
35	C₁₆×Dic₅₃	C₂²	1	2	yes	complemented
36	C₂²×C₁₆×C₅₃	C₂²	1	2	yes	complemented
37	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
38	C₅₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
40	C₄×C₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×D₄×D₅₃	C₈	1	1	yes	characteristic
42	C₂²×C₄×D₅₃	C₂×C₄	1	2	yes	—
43	C₂²×#88322	C₂×C₄	1	2	yes	—
44	C₂×C₈×D₅₃	—	4	2	no	—
45	C₂×C₈×D₅₃	—	4	2	no	—
46	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
48	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
49	C₂×C₈×D₅₃	C₂³	1	2	yes	—
50	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
51	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
52	D₄×Dic₅₃	C₈	1	1	yes	characteristic
53	#13133179	C₈	1	1	yes	characteristic
54	C₄×C₂²⋊D₅₃	C₂×C₄	1	2	yes	—
55	#13133177	C₈	1	2	yes	—
56	C₄⋊C₄×D₅₃	C₈	1	1	yes	characteristic
57	C₂²⋊C₄×D₅₃	C₈	1	2	yes	—
58	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
59	C₂×#11719908	—	4	2	no	—
60	C₂×#11719908	C₂³	1	1	yes	characteristic
61	C₂×#11719908	C₂³	1	2	yes	—
62	C₂×#11719908	C₂³	1	1	yes	characteristic
63	C₁₆×D₅₃	—	4	2	no	—
64	C₁₆×D₅₃	—	4	2	no	—
65	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
66	#13133146	C₂×C₄	1	2	yes	—
67	C₂²⋊#88322	C₂×C₄	1	2	yes	—
68	#13133129	C₂×C₄	1	2	yes	—
69	#13133129	C₂×C₄	1	2	yes	—
70	C₄×#88322	C₂×C₄	1	1	yes	characteristic
71	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
72	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
74	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₁₆×C₅₃	—	4	2	no	—
76	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
77	C₂×C₁₆×C₅₃	C₂³	1	2	yes	—
78	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
80	C₂²⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
81	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
82	C₂³×D₅₃	C₂×C₈	1	2	yes	—
83	C₂×D₄×C₅₃	C₂×C₈	1	1	yes	characteristic
84	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
85	C₂×C₂²⋊D₅₃	C₂×C₈	1	2	yes	—
86	C₂²×Dic₅₃	C₂×C₈	1	2	yes	—
87	D₄×D₅₃	C₁₆	1	8	yes	complemented
88	C₂×D₂₁₂	C₂×C₈	1	1	yes	characteristic
89	C₂×C₄×D₅₃	—	4	2	no	—
90	C₂×C₄×D₅₃	—	4	2	no	—
91	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
92	C₂×C₄×D₅₃	C₂×C₈	1	2	yes	—
93	C₂×C₄×D₅₃	C₂×C₈	1	2	yes	—
94	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
95	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
96	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₅₃	—	2	2	no	—
98	C₂×C₈×C₅₃	—	2	2	no	—
99	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
102	C₄⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
103	C₂²⋊C₄×C₅₃	C₂×C₈	1	2	yes	—
104	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²⋊Dic₅₃	C₂×C₈	1	2	yes	—
106	#11719921	C₂×C₈	1	2	yes	—
107	#11719921	C₂×C₈	1	2	yes	—
108	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
109	#11719919	C₂×C₈	1	2	yes	—
110	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
111	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
112	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×#88322	—	4	2	no	—
114	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
115	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
116	C₂×#88322	C₂²×C₄	1	2	yes	—
117	C₈×D₅₃	—	2	2	no	—
118	C₈×D₅₃	—	2	2	no	—
119	C₈×D₅₃	—	2	1	no	—
120	C₈×D₅₃	—	2	1	no	—
121	C₈×D₅₃	—	4	2	no	—
122	C₈×D₅₃	—	4	2	no	—
123	C₈×D₅₃	—	4	1	no	—
124	C₁₆×C₅₃	—	2	1	no	—
125	C₁₆×C₅₃	—	2	2	no	—
126	C₁₆×C₅₃	—	2	1	no	—
127	#11719908	—	2	1	no	—
128	#11719908	—	2	2	no	—
129	#11719908	—	2	1	no	—
130	C₂³×C₅₃	C₂²×C₈	1	2	yes	—
131	C₂²×D₅₃	—	4	2	no	—
132	C₂²×D₅₃	—	4	2	no	—
133	C₂²×D₅₃	C₂×C₁₆	1	8	yes	complemented
134	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
135	C₂²×D₅₃	C₂²×C₈	1	2	yes	—
136	D₄×C₅₃	C₂×C₁₆	1	4	yes	complemented
137	C₂×C₄×C₅₃	—	2	2	no	—
138	C₂×C₄×C₅₃	—	2	2	no	—
139	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
140	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
141	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
143	C₂²⋊D₅₃	C₂×C₁₆	1	8	yes	complemented
144	C₂×Dic₅₃	—	4	2	no	—
145	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
146	C₂×Dic₅₃	C₂²×C₈	1	2	yes	—
147	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
148	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
149	D₂₁₂	C₂×C₁₆	1	4	yes	complemented
150	C₄×D₅₃	—	2	1	no	—
151	C₄×D₅₃	—	2	2	no	—
152	C₄×D₅₃	—	2	1	no	—
153	C₄×D₅₃	—	2	2	no	—
154	C₄×D₅₃	—	4	2	no	—
155	C₄×D₅₃	—	4	2	no	—
156	C₄×D₅₃	—	4	1	no	—
157	C₄×D₅₃	C₂×C₁₆	1	4	yes	complemented
158	C₈×C₅₃	—	2	2	no	—
159	C₈×C₅₃	—	2	1	no	—
160	C₈×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
161	C₈×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
162	#88322	—	2	1	no	—
163	#88322	—	2	2	no	—
164	#88322	—	2	1	no	—
165	#33486	—	53	1	no	maximal, Sylow
166	C₂²×C₅₃	—	2	2	no	—
167	C₂²×C₅₃	—	2	2	no	—
168	C₂²×C₅₃	C₂²×C₁₆	1	4	yes	—
169	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
170	C₂×D₅₃	—	2	1	no	—
171	C₂×D₅₃	—	2	2	no	—
172	C₂×D₅₃	—	2	1	no	—
173	C₂×D₅₃	—	2	2	no	—
174	C₂×D₅₃	—	4	8	no	—
175	C₂×D₅₃	C₂²×C₁₆	1	2	yes	—
176	C₂×D₅₃	C₂²×C₁₆	1	4	yes	—
177	C₄×C₅₃	—	2	1	no	—
178	C₄×C₅₃	—	2	2	no	—
179	C₄×C₅₃	C₂²×C₁₆	1	2	yes	—
180	C₄×C₅₃	#518	1	1	yes	characteristic
181	C₄×C₅₃	#568	1	1	yes	characteristic
182	Dic₅₃	—	2	1	no	—
183	Dic₅₃	—	2	1	no	—
184	Dic₅₃	—	2	2	no	—
185	Dic₅₃	C₂²×C₁₆	1	2	yes	—
186	C₂×C₈×D₄	—	53	1	no	—
187	D₄×C₁₆	—	53	2	no	—
188	D₄×C₁₆	—	53	1	no	—
189	D₄×C₁₆	—	53	1	no	—
190	D₄×C₁₆	—	53	2	no	—
191	D₄×C₁₆	—	53	1	no	—
192	D₄×C₁₆	D₅₃	1	1	yes	characteristic, complemented
193	#2162	—	53	1	no	—
194	#2162	—	53	1	no	—
195	C₂×C₂²⋊C₁₆	—	53	2	no	—
196	C₂×C₂²⋊C₁₆	—	53	2	no	—
197	C₂×C₅₃	—	2	4	no	—
198	C₂×C₅₃	#2972	1	1	yes	characteristic
199	C₂×C₅₃	C₂³×C₁₆	1	1	yes	characteristic
200	C₂×C₅₃	#3407	1	1	yes	characteristic
201	D₅₃	—	2	2	no	—
202	D₅₃	—	2	4	no	—
203	C₂³×C₈	—	53	2	no	—
204	C₂×C₄×D₄	—	53	1	no	—
205	C₂²×C₁₆	—	53	2	no	—
206	C₂²×C₁₆	—	53	2	no	—
207	C₂²×C₁₆	—	53	2	no	—
208	C₂²×C₁₆	C₂×D₅₃	1	2	yes	complemented
209	C₈×D₄	—	53	2	no	—
210	C₈×D₄	—	53	1	no	—
211	C₈×D₄	—	53	1	no	—
212	C₈×D₄	—	53	2	no	—
213	C₈×D₄	—	53	1	no	—
214	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic
215	C₂×C₄⋊C₈	—	53	1	no	—
216	C₂×C₂²⋊C₈	—	53	2	no	—
217	C₂×C₄×C₈	—	53	1	no	—
218	C₄⋊C₁₆	—	53	1	no	—
219	C₄⋊C₁₆	—	53	1	no	—
220	C₄⋊C₁₆	—	53	1	no	—
221	C₄⋊C₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
222	C₂²⋊C₁₆	—	53	2	no	—
223	C₂²⋊C₁₆	—	53	2	no	—
224	C₂²⋊C₁₆	—	53	1	no	—
225	C₂²⋊C₁₆	—	53	1	no	—
226	C₂²⋊C₁₆	—	53	2	no	—
227	C₂²⋊C₁₆	—	53	2	no	—
228	C₂²⋊C₁₆	C₂×D₅₃	1	2	yes	complemented
229	C₄×C₁₆	—	53	2	no	—
230	C₄×C₁₆	—	53	1	no	—
231	C₄×C₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
232	C₅₃	#33486	1	1	yes	characteristic, complemented, Sylow
233	C₂²×D₄	—	53	1	no	—
234	C₂³×C₄	—	53	2	no	—
235	C₂²×C₈	—	53	2	no	—
236	C₂²×C₈	—	53	1	no	—
237	C₂²×C₈	—	53	2	no	—
238	C₂²×C₈	—	53	2	no	—
239	C₂²×C₈	—	53	2	no	—
240	C₂²×C₈	—	53	1	no	—
241	C₂²×C₈	—	212	2	no	—
242	C₂²×C₈	—	212	2	no	—
243	C₂²×C₈	C₂²×D₅₃	1	2	yes	—
244	C₄×D₄	—	53	1	no	—
245	C₄×D₄	—	53	2	no	—
246	C₄×D₄	—	53	1	no	—
247	C₄×D₄	—	53	2	no	—
248	C₄×D₄	—	53	1	no	—
249	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
250	C₂×C₄⋊C₄	—	53	1	no	—
251	C₂×C₂²⋊C₄	—	53	2	no	—
252	C₂×C₄²	—	53	1	no	—
253	C₂×C₁₆	—	4	2	no	—
254	C₂×C₁₆	—	53	1	no	—
255	C₂×C₁₆	—	53	2	no	—
256	C₂×C₁₆	—	53	1	no	—
257	C₂×C₁₆	—	212	2	no	—
258	C₂×C₁₆	—	212	2	no	—
259	C₂×C₁₆	—	212	2	no	—
260	C₂×C₁₆	C₂²×D₅₃	1	2	yes	—
261	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
262	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
263	C₄⋊C₈	—	53	2	no	—
264	C₄⋊C₈	—	53	1	no	—
265	C₄⋊C₈	C₄×D₅₃	1	1	yes	characteristic
266	C₂²⋊C₈	—	53	2	no	—
267	C₂²⋊C₈	—	53	2	no	—
268	C₂²⋊C₈	—	53	2	no	—
269	C₂²⋊C₈	C₄×D₅₃	1	2	yes	—
270	C₄×C₈	—	53	1	no	—
271	C₄×C₈	—	53	1	no	—
272	C₄×C₈	—	53	1	no	—
273	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
274	C₂⁴	—	53	2	no	—
275	C₂×D₄	—	53	2	no	—
276	C₂×D₄	—	53	8	no	—
277	C₂×D₄	—	53	1	no	—
278	C₂×D₄	C₈×D₅₃	1	1	yes	characteristic
279	C₂²×C₄	—	53	1	no	—
280	C₂²×C₄	—	53	2	no	—
281	C₂²×C₄	—	53	2	no	—
282	C₂²×C₄	—	53	1	no	—
283	C₂²×C₄	—	53	1	no	—
284	C₂²×C₄	—	53	2	no	—
285	C₂²×C₄	—	53	2	no	—
286	C₂²×C₄	—	212	2	no	—
287	C₂²×C₄	—	212	2	no	—
288	C₂²×C₄	C₂×C₄×D₅₃	1	2	yes	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	53	1	no	—
292	C₂×C₈	—	53	1	no	—
293	C₂×C₈	—	53	2	no	—
294	C₂×C₈	—	106	2	no	—
295	C₂×C₈	—	106	1	no	—
296	C₂×C₈	—	106	2	no	—
297	C₂×C₈	—	106	1	no	—
298	C₂×C₈	—	212	2	no	—
299	C₂×C₈	—	212	2	no	—
300	C₂×C₈	—	212	1	no	—
301	C₂×C₈	—	212	2	no	—
302	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
303	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
304	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
305	C₄⋊C₄	—	53	2	no	—
306	C₄⋊C₄	—	53	1	no	—
307	C₄⋊C₄	C₈×D₅₃	1	1	yes	characteristic
308	C₂²⋊C₄	—	53	2	no	—
309	C₂²⋊C₄	—	53	2	no	—
310	C₂²⋊C₄	—	53	2	no	—
311	C₂²⋊C₄	C₈×D₅₃	1	2	yes	—
312	C₄²	—	53	1	no	—
313	C₄²	—	53	1	no	—
314	C₄²	—	53	1	no	—
315	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
316	C₁₆	—	2	1	no	—
317	C₁₆	—	2	2	no	—
318	C₁₆	—	2	1	no	—
319	C₁₆	—	106	1	no	—
320	C₁₆	—	106	2	no	—
321	C₁₆	—	106	1	no	—
322	C₂³	—	53	2	no	—
323	C₂³	—	53	1	no	—
324	C₂³	—	53	8	no	—
325	C₂³	—	212	2	no	—
326	C₂³	—	212	2	no	—
327	C₂³	C₂×C₈×D₅₃	1	2	yes	—
328	D₄	—	53	8	no	—
329	D₄	—	53	4	no	—
330	D₄	C₁₆×D₅₃	1	4	yes	complemented
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	53	1	no	—
334	C₂×C₄	—	53	4	no	—
335	C₂×C₄	—	53	1	no	—
336	C₂×C₄	—	53	1	no	—
337	C₂×C₄	—	53	2	no	—
338	C₂×C₄	—	106	1	no	—
339	C₂×C₄	—	106	2	no	—
340	C₂×C₄	—	106	1	no	—
341	C₂×C₄	—	106	2	no	—
342	C₂×C₄	—	212	1	no	—
343	C₂×C₄	—	212	2	no	—
344	C₂×C₄	—	212	2	no	—
345	C₂×C₄	—	212	2	no	—
346	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
347	C₂×C₄	C₂×C₈×D₅₃	1	2	yes	—
348	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
349	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
350	C₈	—	2	2	no	—
351	C₈	—	2	1	no	—
352	C₈	—	106	2	no	—
353	C₈	—	106	1	no	—
354	C₈	—	106	1	no	—
355	C₈	#13133262	1	1	yes	characteristic
356	C₈	#13133263	1	1	yes	characteristic
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	53	2	no	—
360	C₂²	—	53	4	no	—
361	C₂²	—	106	1	no	—
362	C₂²	—	106	2	no	—
363	C₂²	—	106	1	no	—
364	C₂²	—	106	2	no	—
365	C₂²	—	212	8	no	—
366	C₂²	C₂×C₁₆×D₅₃	1	4	yes	—
367	C₂²	C₂²×C₈×D₅₃	1	1	yes	characteristic
368	C₄	—	2	1	no	—
369	C₄	—	2	2	no	—
370	C₄	—	53	2	no	—
371	C₄	—	106	1	no	—
372	C₄	—	106	1	no	—
373	C₄	—	106	2	no	—
374	C₄	C₂×C₁₆×D₅₃	1	2	yes	—
375	C₄	#16811095	1	1	yes	characteristic
376	C₄	#16811388	1	1	yes	characteristic
377	C₂	—	2	4	no	—
378	C₂	—	106	2	no	—
379	C₂	—	106	4	no	—
380	C₂	#20283736	1	1	yes	characteristic
381	C₂	C₂²×C₁₆×D₅₃	1	1	yes	characteristic
382	C₂	#20287816	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₅₃
commutator	C₂×C₅₃	C₂³×C₁₆
Fitting	D₄×C₁₆×C₅₃	C₂
socle	C₂²×C₅₃	C₂³×C₈
prime radical	C₂×D₄×D₅₃	C₈
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	D₄×C₁₆	D₅₃
hypocenter	C₅₃	#33486
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ D₄×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₁₆×D₂₁₂	C₂	semidirect
3. D₄×#11719908	C₂	semidirect
4. #20276534	C₂	semidirect
5. C₁₆×C₂²⋊D₅₃	C₂	semidirect
6. #20276532	C₂	semidirect
7. #20276513	C₂	semidirect
8. #20276512	C₂	semidirect
9. C₂×#16810402	C₂	semidirect
10. C₂²⋊C₁₆×D₅₃	C₂	semidirect
11. D₄×C₁₆×C₅₃	C₂	semidirect
14. C₂²×#11719908	C₂²	semidirect
15. C₂×C₁₆×D₅₃	C₂²	semidirect
16. C₂×C₁₆×D₅₃	C₂²	semidirect
25. C₄⋊#11719908	C₂²	semidirect
26. #16810441	C₂²	semidirect
27. #16810441	C₂²	semidirect
28. C₂²⋊#11719908	C₂²	semidirect
32. #16810402	C₂²	semidirect
33. #16810402	C₂²	semidirect
34. C₄×#11719908	C₂²	semidirect
35. C₁₆×Dic₅₃	C₂²	semidirect
36. C₂²×C₁₆×C₅₃	C₂²	semidirect
38. C₅₃×C₄⋊C₁₆	C₂²	semidirect
39. C₅₃×C₂²⋊C₁₆	C₂²	semidirect
40. C₄×C₁₆×C₅₃	C₂²	semidirect
87. D₄×D₅₃	C₁₆	semidirect
133. C₂²×D₅₃	C₂×C₁₆	semidirect
136. D₄×C₅₃	C₂×C₁₆	semidirect
143. C₂²⋊D₅₃	C₂×C₁₆	semidirect
149. D₂₁₂	C₂×C₁₆	semidirect
157. C₄×D₅₃	C₂×C₁₆	semidirect
192. D₄×C₁₆	D₅₃	semidirect
208. C₂²×C₁₆	C₂×D₅₃	semidirect
221. C₄⋊C₁₆	C₂×D₅₃	semidirect
228. C₂²⋊C₁₆	C₂×D₅₃	semidirect
231. C₄×C₁₆	C₂×D₅₃	semidirect
232. C₅₃	#33486	semidirect
330. D₄	C₁₆×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₈×D₄×D₅₃	2
C₁₆×D₂₁₂	2
D₄×#11719908	2
#20276534	2
C₁₆×C₂²⋊D₅₃	2
#20276532	2
#20276513	2
#20276512	2
C₂×#16810402	2
C₂²⋊C₁₆×D₅₃	2
D₄×C₁₆×C₅₃	2
#33486	53