Subgroups — D₄×D₅₃⋊C₁₆ #28328293

Order 13568.

806 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₅₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
2	#20291094	C₂	1	2	yes	maximal, complemented
3	#20291093	C₂	1	4	yes	maximal, complemented
4	D₄×#11719910	C₂	1	2	yes	maximal, complemented
5	D₅₃⋊(C₄⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
6	D₅₃⋊(C₂²⋊C₁₆)	C₂	1	2	yes	maximal, complemented
7	C₄×D₅₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic
9	C₂×D₅₃⋊C₁₆	—	2	8	no	—
10	C₂×D₅₃⋊C₁₆	C₂²	1	2	yes	—
11	C₂×D₅₃⋊C₁₆	C₂²	1	1	yes	characteristic
12	C₂×D₅₃⋊C₁₆	C₂²	1	1	yes	characteristic
13	C₂×D₅₃⋊C₁₆	C₂²	1	4	yes	complemented
14	C₂²×#11719910	C₂²	1	4	yes	complemented
15	#16811544	C₂²	1	2	yes	complemented
16	C₄⋊#11719910	C₂²	1	2	yes	complemented
17	#16811518	C₂²	1	4	yes	complemented
18	C₂²⋊#11719910	C₂²	1	4	yes	complemented
19	#16811509	C₂²	1	2	yes	complemented
20	C₄×#11719910	C₂²	1	2	yes	complemented
21	C₂²×C₈×D₅₃	C₂²	1	2	yes	—
22	C₄×D₄×D₅₃	C₄	1	1	yes	characteristic
23	C₈×D₂₁₂	C₄	1	1	yes	characteristic
24	D₄×#88322	C₂²	1	1	yes	characteristic
25	#16810688	C₂²	1	1	yes	characteristic
26	C₈×C₂²⋊D₅₃	C₄	1	2	yes	—
27	#16810686	C₂²	1	2	yes	—
28	C₄⋊C₈×D₅₃	C₄	1	1	yes	characteristic
29	C₂²⋊C₈×D₅₃	C₄	1	2	yes	—
30	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
31	C₈×D₄×C₅₃	C₄	1	1	yes	characteristic
32	D₅₃⋊C₁₆	—	2	4	no	—
33	D₅₃⋊C₁₆	—	2	2	no	—
34	D₅₃⋊C₁₆	—	2	8	no	—
35	D₅₃⋊C₁₆	D₄	1	4	yes	direct product factor
36	C₂×#11719910	—	2	8	no	—
37	C₂×#11719910	C₂³	1	4	yes	—
38	C₂×#11719910	C₂³	1	2	yes	—
39	C₂×#11719910	C₂³	1	2	yes	—
40	C₂×D₄×D₅₃	C₈	1	1	yes	characteristic
41	C₂²×C₄×D₅₃	C₂×C₄	1	2	yes	—
42	C₂²×#88322	C₂³	1	2	yes	—
43	C₂×C₈×D₅₃	—	2	4	no	—
44	C₂×C₈×D₅₃	—	2	4	no	—
45	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
47	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
48	C₂×C₈×D₅₃	C₂³	1	2	yes	—
49	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
50	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
51	D₄×Dic₅₃	C₈	1	1	yes	characteristic
52	#13133179	C₈	1	1	yes	characteristic
53	C₄×C₂²⋊D₅₃	C₂×C₄	1	2	yes	—
54	#13133177	C₈	1	2	yes	—
55	C₄⋊C₄×D₅₃	C₈	1	1	yes	characteristic
56	C₂²⋊C₄×D₅₃	C₈	1	2	yes	—
57	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
58	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
59	#13133146	C₂×C₄	1	2	yes	—
60	C₂²⋊#88322	C₂×C₄	1	2	yes	—
61	#13133129	C₂×C₄	1	2	yes	—
62	#13133129	C₂×C₄	1	2	yes	—
63	C₄×#88322	C₂³	1	1	yes	characteristic
64	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
65	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
67	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
68	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
69	C₂²⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
70	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
71	C₂³×D₅₃	C₂×C₈	1	2	yes	—
72	C₂×D₄×C₅₃	C₂×C₈	1	1	yes	characteristic
73	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
74	C₂×C₂²⋊D₅₃	C₂×C₈	1	2	yes	—
75	C₂²×Dic₅₃	C₂×C₈	1	2	yes	—
76	D₄×D₅₃	C₁₆	1	8	yes	complemented
77	C₂×D₂₁₂	C₂×C₈	1	1	yes	characteristic
78	C₂×C₄×D₅₃	—	2	4	no	—
79	C₂×C₄×D₅₃	—	2	4	no	—
80	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
81	C₂×C₄×D₅₃	C₂×C₈	1	2	yes	—
82	C₂×C₄×D₅₃	C₂×C₈	1	2	yes	—
83	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
84	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
85	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₈×C₅₃	—	2	4	no	—
87	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
89	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
90	C₄⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
91	C₂²⋊C₄×C₅₃	C₂×C₈	1	2	yes	—
92	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²⋊Dic₅₃	C₂×C₈	1	2	yes	—
94	#11719921	C₂×C₈	1	2	yes	—
95	#11719921	C₂×C₈	1	2	yes	—
96	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
97	#11719919	C₂×C₈	1	2	yes	—
98	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
99	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
100	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×#88322	—	2	2	no	—
102	C₂×#88322	—	2	2	no	—
103	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
104	C₂×#88322	C₂²×C₄	1	2	yes	—
105	C₂×#88322	C₂⁴	1	1	yes	characteristic
106	C₈×D₅₃	—	2	4	no	—
107	C₈×D₅₃	—	2	2	no	—
108	C₈×D₅₃	—	2	4	no	—
109	C₈×D₅₃	—	2	2	no	—
110	C₈×D₅₃	—	2	2	no	—
111	C₈×D₅₃	C₂×D₄	1	2	yes	—
112	C₈×D₅₃	#41	1	2	yes	—
113	#11719910	—	2	4	no	—
114	#11719910	—	2	2	no	—
115	#11719910	C₂×D₄	1	4	yes	complemented
116	C₂³×C₅₃	C₂²×C₈	1	2	yes	—
117	C₂²×D₅₃	—	2	4	no	—
118	C₂²×D₅₃	—	2	4	no	—
119	C₂²×D₅₃	C₂×C₁₆	1	8	yes	complemented
120	C₂²×D₅₃	C₂²×C₈	1	2	yes	—
121	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
122	D₄×C₅₃	C₂×C₁₆	1	4	yes	complemented
123	C₂×C₄×C₅₃	—	2	2	no	—
124	C₂×C₄×C₅₃	—	2	2	no	—
125	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
126	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
127	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
128	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
129	C₂²⋊D₅₃	C₂×C₁₆	1	8	yes	complemented
130	C₂×Dic₅₃	—	2	4	no	—
131	C₂×Dic₅₃	C₂²×C₈	1	2	yes	—
132	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
133	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
134	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
135	D₂₁₂	C₂×C₁₆	1	4	yes	complemented
136	C₄×D₅₃	—	2	4	no	—
137	C₄×D₅₃	—	2	2	no	—
138	C₄×D₅₃	—	2	2	no	—
139	C₄×D₅₃	—	2	2	no	—
140	C₄×D₅₃	—	2	4	no	—
141	C₄×D₅₃	C₂×C₁₆	1	4	yes	complemented
142	C₄×D₅₃	C₄×D₄	1	2	yes	—
143	C₄×D₅₃	#131	1	2	yes	—
144	C₈×C₅₃	—	2	2	no	—
145	C₈×C₅₃	—	2	1	no	—
146	C₈×C₅₃	C₄×D₄	1	2	yes	—
147	#88322	—	2	2	no	—
148	#88322	—	2	1	no	—
149	#88322	C₂²×D₄	1	1	yes	characteristic
150	#88322	C₂×#41	1	1	yes	characteristic
151	C₂×D₄×C₁₆	—	53	1	no	maximal, Sylow
152	C₂²×C₅₃	—	2	2	no	—
153	C₂²×C₅₃	—	2	2	no	—
154	C₂²×C₅₃	C₂²×C₁₆	1	4	yes	complemented
155	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
156	C₂×D₅₃	—	2	2	no	—
157	C₂×D₅₃	—	2	2	no	—
158	C₂×D₅₃	—	2	16	no	—
159	C₂×D₅₃	C₈×D₄	1	2	yes	—
160	C₂×D₅₃	C₂²×C₁₆	1	2	yes	—
161	C₂×D₅₃	C₂²×C₁₆	1	4	yes	complemented
162	C₂×D₅₃	#504	1	2	yes	—
163	C₄×C₅₃	—	2	1	no	—
164	C₄×C₅₃	—	2	2	no	—
165	C₄×C₅₃	C₂²×C₁₆	1	2	yes	complemented
166	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
167	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
168	Dic₅₃	—	2	1	no	—
169	Dic₅₃	—	2	2	no	—
170	Dic₅₃	C₈×D₄	1	2	yes	—
171	Dic₅₃	C₂²×C₁₆	1	2	yes	complemented
172	C₂³×C₁₆	—	53	2	no	—
173	C₂×C₈×D₄	—	53	1	no	—
174	D₄×C₁₆	—	53	2	no	—
175	D₄×C₁₆	—	53	4	no	—
176	D₄×C₁₆	—	53	2	no	—
177	C₂×C₄⋊C₁₆	—	53	1	no	—
178	C₂×C₂²⋊C₁₆	—	53	2	no	—
179	C₂×C₄×C₁₆	—	53	1	no	—
180	C₂×C₅₃	—	2	4	no	—
181	C₂×C₅₃	C₂×C₈×D₄	1	1	yes	characteristic
182	C₂×C₅₃	C₂³×C₁₆	1	1	yes	characteristic
183	C₂×C₅₃	C₂×#504	1	1	yes	characteristic
184	D₅₃	—	2	4	no	—
185	D₅₃	D₄×C₁₆	1	4	yes	complemented
186	C₂³×C₈	—	53	2	no	—
187	C₂×C₄×D₄	—	53	1	no	—
188	C₂²×C₁₆	—	53	1	no	—
189	C₂²×C₁₆	—	53	1	no	—
190	C₂²×C₁₆	—	53	2	no	—
191	C₂²×C₁₆	—	53	4	no	—
192	C₂²×C₁₆	—	53	4	no	—
193	C₂²×C₁₆	—	106	8	no	—
194	C₈×D₄	—	53	2	no	—
195	C₈×D₄	—	53	1	no	—
196	C₈×D₄	—	53	1	no	—
197	C₈×D₄	—	53	2	no	—
198	C₈×D₄	—	53	1	no	—
199	C₈×D₄	#6157	1	1	yes	characteristic
200	C₂×C₄⋊C₈	—	53	1	no	—
201	C₂×C₂²⋊C₈	—	53	2	no	—
202	C₂×C₄×C₈	—	53	1	no	—
203	C₄⋊C₁₆	—	53	2	no	—
204	C₄⋊C₁₆	—	53	2	no	—
205	C₂²⋊C₁₆	—	53	4	no	—
206	C₂²⋊C₁₆	—	53	4	no	—
207	C₄×C₁₆	—	53	2	no	—
208	C₄×C₁₆	—	53	2	no	—
209	C₅₃	C₂×D₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
210	C₂²×D₄	—	53	1	no	—
211	C₂³×C₄	—	53	2	no	—
212	C₂²×C₈	—	53	1	no	—
213	C₂²×C₈	—	53	2	no	—
214	C₂²×C₈	—	53	2	no	—
215	C₂²×C₈	—	53	2	no	—
216	C₂²×C₈	—	53	1	no	—
217	C₂²×C₈	—	53	2	no	—
218	C₂²×C₈	—	106	4	no	—
219	C₂²×C₈	—	106	4	no	—
220	C₂²×C₈	C₂×#6157	1	2	yes	—
221	C₄×D₄	—	53	1	no	—
222	C₄×D₄	—	53	2	no	—
223	C₄×D₄	—	53	1	no	—
224	C₄×D₄	—	53	2	no	—
225	C₄×D₄	—	53	1	no	—
226	C₄×D₄	C₂×#6157	1	1	yes	characteristic
227	C₂×C₄⋊C₄	—	53	1	no	—
228	C₂×C₂²⋊C₄	—	53	2	no	—
229	C₂×C₄²	—	53	1	no	—
230	C₂×C₁₆	—	53	2	no	—
231	C₂×C₁₆	—	53	4	no	—
232	C₂×C₁₆	—	53	2	no	—
233	C₂×C₁₆	—	53	4	no	—
234	C₂×C₁₆	—	106	8	no	—
235	C₂×C₁₆	—	106	8	no	—
236	C₂×C₁₆	—	106	2	no	—
237	C₂×C₁₆	—	106	4	no	—
238	C₄⋊C₈	—	53	2	no	—
239	C₄⋊C₈	—	53	1	no	—
240	C₄⋊C₈	C₂×#6157	1	1	yes	characteristic
241	C₂²⋊C₈	—	53	2	no	—
242	C₂²⋊C₈	—	53	2	no	—
243	C₂²⋊C₈	—	53	2	no	—
244	C₂²⋊C₈	C₂×#6157	1	2	yes	—
245	C₄×C₈	—	53	1	no	—
246	C₄×C₈	—	53	1	no	—
247	C₄×C₈	—	53	1	no	—
248	C₄×C₈	C₂×#6157	1	1	yes	characteristic
249	C₂⁴	—	53	2	no	—
250	C₂×D₄	—	53	2	no	—
251	C₂×D₄	—	53	8	no	—
252	C₂×D₄	—	53	1	no	—
253	C₂×D₄	D₅₃⋊C₈	1	1	yes	characteristic
254	C₂²×C₄	—	53	1	no	—
255	C₂²×C₄	—	53	1	no	—
256	C₂²×C₄	—	53	2	no	—
257	C₂²×C₄	—	53	1	no	—
258	C₂²×C₄	—	53	2	no	—
259	C₂²×C₄	—	53	2	no	—
260	C₂²×C₄	—	53	2	no	—
261	C₂²×C₄	—	106	4	no	—
262	C₂²×C₄	—	106	4	no	—
263	C₂²×C₄	C₂²×#6157	1	2	yes	—
264	C₂×C₈	—	2	4	no	—
265	C₂×C₈	—	53	1	no	—
266	C₂×C₈	—	53	2	no	—
267	C₂×C₈	—	53	2	no	—
268	C₂×C₈	—	53	1	no	—
269	C₂×C₈	—	53	2	no	—
270	C₂×C₈	—	106	2	no	—
271	C₂×C₈	—	106	2	no	—
272	C₂×C₈	—	106	4	no	—
273	C₂×C₈	—	106	2	no	—
274	C₂×C₈	—	106	2	no	—
275	C₂×C₈	—	106	2	no	—
276	C₂×C₈	—	106	4	no	—
277	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
278	C₂×C₈	C₂²×#6157	1	2	yes	—
279	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
280	C₄⋊C₄	—	53	2	no	—
281	C₄⋊C₄	—	53	1	no	—
282	C₄⋊C₄	D₅₃⋊C₈	1	1	yes	characteristic
283	C₂²⋊C₄	—	53	2	no	—
284	C₂²⋊C₄	—	53	2	no	—
285	C₂²⋊C₄	—	53	2	no	—
286	C₂²⋊C₄	D₅₃⋊C₈	1	2	yes	—
287	C₄²	—	53	1	no	—
288	C₄²	—	53	1	no	—
289	C₄²	—	53	1	no	—
290	C₄²	C₂²×#6157	1	1	yes	characteristic
291	C₁₆	—	53	4	no	—
292	C₁₆	—	106	4	no	—
293	C₁₆	—	106	2	no	—
294	C₂³	—	53	1	no	—
295	C₂³	—	53	8	no	—
296	C₂³	—	53	2	no	—
297	C₂³	—	106	4	no	—
298	C₂³	—	106	4	no	—
299	C₂³	C₂×D₅₃⋊C₈	1	2	yes	—
300	D₄	—	53	8	no	—
301	D₄	—	53	4	no	—
302	D₄	D₅₃⋊C₁₆	1	4	yes	direct product factor
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	53	1	no	—
306	C₂×C₄	—	53	1	no	—
307	C₂×C₄	—	53	4	no	—
308	C₂×C₄	—	53	2	no	—
309	C₂×C₄	—	53	2	no	—
310	C₂×C₄	—	53	1	no	—
311	C₂×C₄	—	53	2	no	—
312	C₂×C₄	—	106	4	no	—
313	C₂×C₄	—	106	2	no	—
314	C₂×C₄	—	106	4	no	—
315	C₂×C₄	—	106	4	no	—
316	C₂×C₄	—	106	2	no	—
317	C₂×C₄	—	106	2	no	—
318	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
319	C₂×C₄	C₂×D₅₃⋊C₈	1	2	yes	—
320	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
321	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
322	C₈	—	2	2	no	—
323	C₈	—	2	1	no	—
324	C₈	—	53	1	no	—
325	C₈	—	53	1	no	—
326	C₈	—	106	2	no	—
327	C₈	—	106	1	no	—
328	C₈	D₄×#6157	1	2	yes	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	53	2	no	—
332	C₂²	—	53	2	no	—
333	C₂²	—	53	2	no	—
334	C₂²	—	53	4	no	—
335	C₂²	—	106	16	no	—
336	C₂²	—	106	2	no	—
337	C₂²	—	106	2	no	—
338	C₂²	C₂×D₅₃⋊C₁₆	1	4	yes	complemented
339	C₂²	C₂²×D₅₃⋊C₈	1	1	yes	characteristic
340	C₄	—	2	2	no	—
341	C₄	—	2	1	no	—
342	C₄	—	53	2	no	—
343	C₄	—	53	2	no	—
344	C₄	—	106	2	no	—
345	C₄	—	106	1	no	—
346	C₄	C₂×D₅₃⋊C₁₆	1	2	yes	complemented
347	C₄	C₂×D₄×#6157	1	1	yes	characteristic
348	C₄	D₅₃⋊#131	1	1	yes	characteristic
349	C₂	—	2	4	no	—
350	C₂	—	53	4	no	—
351	C₂	—	106	4	no	—
352	C₂	D₄×D₅₃⋊C₈	1	1	yes	characteristic
353	C₂	C₂²×D₅₃⋊C₁₆	1	1	yes	characteristic
354	C₂	D₅₃⋊#504	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×#6157
commutator	C₂×C₅₃	C₂³×C₁₆
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₈×D₄×C₅₃	C₄
socle	C₂²×C₅₃	C₂³×C₈
prime radical	C₂×D₄×D₅₃	C₈
cosocle	C₂×#88322	C₂⁴
hypercenter	C₈×D₄	#6157
hypocenter	C₅₃	C₂×D₄×C₁₆
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×D₅₃⋊C₁₆	C₂	semidirect
2. #20291094	C₂	semidirect
3. #20291093	C₂	semidirect
4. D₄×#11719910	C₂	semidirect
5. D₅₃⋊(C₄⋊C₁₆)	C₂	semidirect
6. D₅₃⋊(C₂²⋊C₁₆)	C₂	semidirect
7. C₄×D₅₃⋊C₁₆	C₂	semidirect
13. C₂×D₅₃⋊C₁₆	C₂²	semidirect
14. C₂²×#11719910	C₂²	semidirect
15. #16811544	C₂²	semidirect
16. C₄⋊#11719910	C₂²	semidirect
17. #16811518	C₂²	semidirect
18. C₂²⋊#11719910	C₂²	semidirect
19. #16811509	C₂²	semidirect
20. C₄×#11719910	C₂²	semidirect
35. D₅₃⋊C₁₆	D₄	direct (N × H)
76. D₄×D₅₃	C₁₆	semidirect
115. #11719910	C₂×D₄	semidirect
119. C₂²×D₅₃	C₂×C₁₆	semidirect
122. D₄×C₅₃	C₂×C₁₆	semidirect
129. C₂²⋊D₅₃	C₂×C₁₆	semidirect
135. D₂₁₂	C₂×C₁₆	semidirect
141. C₄×D₅₃	C₂×C₁₆	semidirect
154. C₂²×C₅₃	C₂²×C₁₆	semidirect
161. C₂×D₅₃	C₂²×C₁₆	semidirect
165. C₄×C₅₃	C₂²×C₁₆	semidirect
171. Dic₅₃	C₂²×C₁₆	semidirect
185. D₅₃	D₄×C₁₆	semidirect
209. C₅₃	C₂×D₄×C₁₆	semidirect
302. D₄	D₅₃⋊C₁₆	direct (N × H)
338. C₂²	C₂×D₅₃⋊C₁₆	semidirect
346. C₄	C₂×D₅₃⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₅₃⋊C₁₆	2
#20291094	2
#20291093	2
D₄×#11719910	2
D₅₃⋊(C₄⋊C₁₆)	2
D₅₃⋊(C₂²⋊C₁₆)	2
C₄×D₅₃⋊C₁₆	2
C₈×D₄×D₅₃	2
C₂×D₄×C₁₆	53

Subgroups — D4×D53⋊C16 #28328293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×D₅₃⋊C₁₆ #28328293