Subgroups — M₁₆×D₄₂₄ #27355516

Order 13568.

794 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₄₂₄	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₂₁₂	C₂	1	2	yes	maximal, complemented
3	#20273601	C₂	1	2	yes	maximal, complemented
4	#20273546	C₂	1	4	yes	maximal, complemented
5	C₈×D₄₂₄	C₂	1	2	yes	maximal, complemented
6	#20273474	C₂	1	1	yes	maximal, characteristic, complemented
7	#20273141	C₂	1	2	yes	maximal, complemented
8	C₈×M₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₄₂₄	C₄	1	1	yes	characteristic
10	C₂×M₁₆×D₅₃	—	2	2	no	—
11	C₂×C₄×D₂₁₂	C₂²	1	2	yes	—
12	C₄×D₄₂₄	C₄	1	2	yes	—
13	C₄×D₄₂₄	C₄	1	1	yes	characteristic
14	C₄×D₄₂₄	C₄	1	1	yes	characteristic
15	C₄×D₄₂₄	C₂²	1	1	yes	characteristic
16	C₄×D₄₂₄	C₂²	1	2	yes	—
17	C₄×D₄₂₄	C₂²	1	1	yes	characteristic
18	#16810702	C₂²	1	4	yes	complemented
19	#16810696	—	2	4	no	—
20	C₈×D₂₁₂	C₂²	1	4	yes	complemented
21	C₂×#13133151	C₄	1	1	yes	characteristic
22	#16810647	C₂²	1	2	yes	—
23	C₂×#13133139	C₄	1	2	yes	—
24	#16810586	—	2	2	no	—
25	#16810376	C₂²	1	2	yes	complemented
26	#16810376	C₂²	1	2	yes	complemented
27	#16810352	C₂²	1	4	yes	complemented
28	#16810352	C₂²	1	4	yes	complemented
29	C₅₃×#431	C₂²	1	1	yes	characteristic
30	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
32	C₅₃×#322	C₂²	1	2	yes	complemented
33	C₈²×C₅₃	C₂²	1	2	yes	complemented
34	C₂²×D₂₁₂	C₂×C₄	1	2	yes	—
35	C₂²×C₄×D₅₃	—	2	2	no	—
36	C₂×D₄₂₄	—	2	4	no	—
37	C₂×D₄₂₄	C₂×C₄	1	1	yes	characteristic
38	C₂×D₄₂₄	C₂×C₄	1	2	yes	—
39	C₂×D₄₂₄	C₂×C₄	1	1	yes	characteristic
40	C₂×#11719917	—	2	2	no	—
41	C₂×#11719912	—	2	4	no	—
42	M₁₆×D₅₃	—	4	8	no	—
43	C₂×C₈×D₅₃	—	2	4	no	—
44	C₄×D₂₁₂	—	2	2	no	—
45	C₄×D₂₁₂	—	2	2	no	—
46	C₄×D₂₁₂	C₂×C₄	1	2	yes	—
47	C₄×D₂₁₂	C₂×C₄	1	2	yes	—
48	C₄×D₂₁₂	C₂³	1	2	yes	—
49	C₄×D₂₁₂	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₅₃	C₂×C₄	1	2	yes	—
51	C₂×#11719921	—	2	2	no	—
52	#13133151	C₂×C₄	1	2	yes	—
53	#13133151	C₂×C₄	1	1	yes	characteristic
54	#13133151	C₂×C₄	1	1	yes	characteristic
55	C₄⋊#88322	—	2	2	no	—
56	C₄⋊#88322	C₂³	1	4	yes	—
57	#13133139	C₂×C₄	1	2	yes	—
58	#13133139	C₂×C₄	1	2	yes	—
59	#13133139	C₂×C₄	1	2	yes	—
60	#13133139	C₂×C₄	1	2	yes	—
61	#13133129	—	2	4	no	—
62	#13133129	—	2	4	no	—
63	C₂×M₁₆×C₅₃	D₄	1	1	yes	characteristic
64	C₂×M₁₆×C₅₃	D₄	1	1	yes	characteristic
65	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₅₃	—	2	1	no	—
69	C₂²⋊C₈×C₅₃	—	2	1	no	—
70	#97×C₅₃	D₄	1	2	yes	—
71	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
72	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
73	C₄×C₈×C₅₃	C₂³	1	2	yes	—
74	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
76	C₄×C₈×C₅₃	C₂³	1	2	yes	—
77	C₂³×D₅₃	—	2	2	no	—
78	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
81	C₂²×Dic₅₃	—	2	2	no	—
82	C₂×D₂₁₂	—	2	4	no	—
83	C₂×D₂₁₂	—	2	2	no	—
84	C₂×D₂₁₂	—	4	2	no	—
85	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
86	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
87	C₂×C₄×D₅₃	—	2	2	no	—
88	C₂×C₄×D₅₃	—	2	2	no	—
89	C₂×C₄×D₅₃	—	2	2	no	—
90	C₂×C₄×D₅₃	—	2	2	no	—
91	C₂×C₄×D₅₃	—	4	4	no	—
92	C₂×C₄×D₅₃	—	4	4	no	—
93	M₁₆×C₅₃	—	2	2	no	—
94	M₁₆×C₅₃	D₈	1	4	yes	complemented
95	C₂×C₈×C₅₃	—	2	2	no	—
96	C₂×C₈×C₅₃	—	2	2	no	—
97	C₂×C₈×C₅₃	—	4	1	no	—
98	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
104	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₅₃	#41	1	1	yes	characteristic
107	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
108	#11719921	—	2	2	no	—
109	#11719921	—	2	2	no	—
110	#11719921	—	2	2	no	—
111	#11719921	—	2	2	no	—
112	C₄⋊Dic₅₃	—	2	2	no	—
113	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
114	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
115	#11719917	—	4	4	no	—
116	C₂×#88322	—	2	4	no	—
117	D₄₂₄	—	2	4	no	—
118	D₄₂₄	—	2	2	no	—
119	D₄₂₄	M₁₆	1	4	yes	direct product factor
120	#11719912	—	4	8	no	—
121	C₈×D₅₃	—	4	8	no	—
122	C₂³×C₅₃	C₄×D₄	1	1	yes	characteristic
123	C₂²×D₅₃	—	2	2	no	—
124	C₂²×D₅₃	—	2	2	no	—
125	C₂²×D₅₃	—	4	4	no	—
126	C₂²×D₅₃	—	4	4	no	—
127	C₂²×D₅₃	—	8	2	no	—
128	C₂×C₄×C₅₃	—	2	1	no	—
129	C₂×C₄×C₅₃	—	2	1	no	—
130	C₂×C₄×C₅₃	—	4	1	no	—
131	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
132	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
133	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₅₃	C₂×D₈	1	2	yes	—
135	C₂×C₄×C₅₃	#135	1	2	yes	—
136	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
139	C₂×Dic₅₃	—	2	2	no	—
140	C₂×Dic₅₃	—	2	2	no	—
141	C₂×Dic₅₃	—	4	4	no	—
142	D₂₁₂	—	2	2	no	—
143	D₂₁₂	—	2	2	no	—
144	D₂₁₂	—	2	2	no	—
145	D₂₁₂	—	4	4	no	—
146	D₂₁₂	C₂×M₁₆	1	4	yes	complemented
147	C₄×D₅₃	—	4	2	no	—
148	C₄×D₅₃	—	4	2	no	—
149	C₄×D₅₃	—	4	2	no	—
150	C₄×D₅₃	—	4	2	no	—
151	C₄×D₅₃	—	4	4	no	—
152	C₄×D₅₃	—	4	4	no	—
153	C₈×C₅₃	—	2	1	no	—
154	C₈×C₅₃	—	2	1	no	—
155	C₈×C₅₃	—	2	1	no	—
156	C₈×C₅₃	—	2	2	no	—
157	C₈×C₅₃	—	4	2	no	—
158	C₈×C₅₃	C₂×M₁₆	1	2	yes	complemented
159	C₈×C₅₃	C₂×D₈	1	4	yes	complemented
160	#88322	—	4	4	no	—
161	M₁₆×D₈	—	53	1	no	maximal, Sylow
162	C₂²×C₅₃	—	2	1	no	—
163	C₂²×C₅₃	—	2	1	no	—
164	C₂²×C₅₃	C₄×D₈	1	2	yes	—
165	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
166	C₂×D₅₃	—	2	4	no	—
167	C₂×D₅₃	—	4	2	no	—
168	C₂×D₅₃	—	4	2	no	—
169	C₂×D₅₃	—	4	2	no	—
170	C₂×D₅₃	—	4	2	no	—
171	C₂×D₅₃	—	4	2	no	—
172	C₂×D₅₃	—	8	8	no	—
173	C₄×C₅₃	—	2	1	no	—
174	C₄×C₅₃	—	2	1	no	—
175	C₄×C₅₃	—	2	1	no	—
176	C₄×C₅₃	C₄×D₈	1	2	yes	—
177	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
178	C₄×C₅₃	#568	1	1	yes	characteristic
179	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
180	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
181	Dic₅₃	—	4	2	no	—
182	Dic₅₃	—	4	2	no	—
183	C₂×C₄×D₈	—	53	1	no	—
184	D₄×M₁₆	—	53	2	no	—
185	#1589	—	53	2	no	—
186	#1581	—	53	4	no	—
187	C₈×D₈	—	53	2	no	—
188	#1567	—	53	1	no	—
189	#1486	—	53	2	no	—
190	C₈×M₁₆	D₅₃	1	1	yes	characteristic, complemented
191	C₂×C₅₃	—	2	2	no	—
192	C₂×C₅₃	D₄×M₁₆	1	1	yes	characteristic
193	C₂×C₅₃	C₂×C₄×D₈	1	1	yes	characteristic
194	C₂×C₅₃	#2957	1	1	yes	characteristic
195	D₅₃	—	4	4	no	—
196	D₅₃	—	8	2	no	—
197	C₂²×D₈	—	53	1	no	—
198	C₂²×M₁₆	—	106	2	no	—
199	C₂×C₄×D₄	—	53	2	no	—
200	C₄×D₈	—	53	1	no	—
201	C₄×D₈	—	53	2	no	—
202	C₄×D₈	—	53	1	no	—
203	C₄×D₈	—	53	1	no	—
204	C₄×D₈	—	53	2	no	—
205	C₄×D₈	—	53	1	no	—
206	#436	—	53	4	no	—
207	#435	—	106	4	no	—
208	C₈×D₄	—	53	4	no	—
209	#431	C₂×D₅₃	1	1	yes	characteristic
210	C₂×#107	—	53	1	no	—
211	#423	—	53	2	no	—
212	C₂×#102	—	53	2	no	—
213	#407	—	106	2	no	—
214	C₄×M₁₆	C₂×D₅₃	1	1	yes	characteristic
215	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
216	#335	—	53	2	no	—
217	#335	—	53	2	no	—
218	D₄⋊C₈	—	53	4	no	—
219	D₄⋊C₈	—	53	4	no	—
220	#322	C₂×D₅₃	1	2	yes	complemented
221	C₈²	C₂×D₅₃	1	2	yes	complemented
222	C₅₃	M₁₆×D₈	1	1	yes	characteristic, complemented, Sylow
223	C₂²×D₄	—	53	2	no	—
224	C₂³×C₄	—	106	2	no	—
225	C₂×D₈	—	53	1	no	—
226	C₂×D₈	—	53	2	no	—
227	C₂×D₈	—	53	1	no	—
228	C₂×D₈	—	106	4	no	—
229	C₂×M₁₆	—	106	2	no	—
230	C₂×M₁₆	—	106	4	no	—
231	C₂×M₁₆	—	212	8	no	—
232	C₂×M₁₆	D₂₁₂	1	1	yes	characteristic
233	C₂×M₁₆	D₂₁₂	1	1	yes	characteristic
234	C₂²×C₈	—	106	4	no	—
235	C₂²×C₈	C₄×D₅₃	1	1	yes	characteristic
236	C₂²×C₈	C₄×D₅₃	1	1	yes	characteristic
237	C₄×D₄	—	53	2	no	—
238	C₄×D₄	—	53	2	no	—
239	C₄×D₄	—	53	2	no	—
240	C₄×D₄	—	53	2	no	—
241	C₄×D₄	—	106	2	no	—
242	C₄×D₄	—	106	2	no	—
243	C₂×C₄⋊C₄	—	53	2	no	—
244	C₂×C₂²⋊C₄	—	106	2	no	—
245	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
246	#107	—	53	2	no	—
247	#107	—	53	1	no	—
248	#107	—	53	1	no	—
249	C₄⋊C₈	—	2	1	no	—
250	C₄⋊C₈	—	53	4	no	—
251	C₄⋊C₈	—	106	2	no	—
252	#102	—	53	2	no	—
253	#102	—	53	2	no	—
254	#102	—	53	2	no	—
255	#102	—	53	2	no	—
256	C₂²⋊C₈	—	2	1	no	—
257	C₂²⋊C₈	—	106	4	no	—
258	C₂²⋊C₈	—	106	4	no	—
259	#97	D₂₁₂	1	2	yes	—
260	C₄×C₈	C₄×D₅₃	1	1	yes	characteristic
261	C₄×C₈	C₄×D₅₃	1	1	yes	characteristic
262	C₄×C₈	C₂²×D₅₃	1	2	yes	—
263	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
264	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
265	C₄×C₈	C₂²×D₅₃	1	2	yes	—
266	C₂⁴	—	106	2	no	—
267	C₂×D₄	—	53	2	no	—
268	C₂×D₄	—	53	2	no	—
269	C₂×D₄	—	106	4	no	—
270	C₂×D₄	—	106	2	no	—
271	C₂×D₄	—	212	2	no	—
272	C₂²×C₄	—	106	2	no	—
273	C₂²×C₄	—	106	2	no	—
274	C₂²×C₄	—	106	2	no	—
275	C₂²×C₄	—	106	2	no	—
276	C₂²×C₄	—	106	2	no	—
277	C₂²×C₄	—	212	4	no	—
278	C₂²×C₄	—	212	4	no	—
279	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
281	C₂²×C₄	#11719945	1	1	yes	characteristic
282	D₈	—	53	4	no	—
283	D₈	—	106	4	no	—
284	D₈	—	106	2	no	—
285	M₁₆	—	2	2	no	—
286	M₁₆	—	212	4	no	—
287	M₁₆	—	212	8	no	—
288	M₁₆	D₄₂₄	1	4	yes	direct product factor
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	106	4	no	—
293	C₂×C₈	—	212	8	no	—
294	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
295	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
296	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
297	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
298	C₂×C₈	C₂×D₂₁₂	1	2	yes	—
299	C₂×C₈	C₂×D₂₁₂	1	2	yes	—
300	C₄⋊C₄	—	53	2	no	—
301	C₄⋊C₄	—	53	2	no	—
302	C₄⋊C₄	—	106	2	no	—
303	C₂²⋊C₄	—	106	2	no	—
304	C₂²⋊C₄	—	106	2	no	—
305	C₂²⋊C₄	—	106	2	no	—
306	C₂²⋊C₄	—	106	2	no	—
307	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
308	C₄²	C₂×D₂₁₂	1	1	yes	characteristic
309	C₄²	#11719945	1	1	yes	characteristic
310	C₄²	C₂³×D₅₃	1	1	yes	characteristic
311	C₂³	—	106	2	no	—
312	C₂³	—	106	2	no	—
313	C₂³	—	424	2	no	—
314	C₂³	—	212	4	no	—
315	C₂³	—	212	4	no	—
316	C₂³	C₄×D₂₁₂	1	1	yes	characteristic
317	D₄	—	53	4	no	—
318	D₄	—	106	2	no	—
319	D₄	—	106	2	no	—
320	D₄	—	106	2	no	—
321	D₄	—	212	4	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	106	2	no	—
326	C₂×C₄	—	106	2	no	—
327	C₂×C₄	—	212	4	no	—
328	C₂×C₄	—	212	2	no	—
329	C₂×C₄	—	212	2	no	—
330	C₂×C₄	—	212	2	no	—
331	C₂×C₄	—	212	2	no	—
332	C₂×C₄	—	212	4	no	—
333	C₂×C₄	—	212	4	no	—
334	C₂×C₄	C₄×D₂₁₂	1	1	yes	characteristic
335	C₂×C₄	C₄×D₂₁₂	1	1	yes	characteristic
336	C₂×C₄	C₄×D₂₁₂	1	1	yes	characteristic
337	C₂×C₄	C₂×D₄₂₄	1	2	yes	—
338	C₂×C₄	#13133239	1	2	yes	—
339	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
341	C₂×C₄	C₂×#11719945	1	1	yes	characteristic
342	C₈	—	2	1	no	—
343	C₈	—	2	1	no	—
344	C₈	—	2	1	no	—
345	C₈	—	2	2	no	—
346	C₈	—	4	2	no	—
347	C₈	—	212	4	no	—
348	C₈	M₁₆×D₅₃	1	2	yes	complemented
349	C₈	C₂×D₄₂₄	1	4	yes	complemented
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	106	4	no	—
353	C₂²	—	424	8	no	—
354	C₂²	—	212	2	no	—
355	C₂²	—	212	2	no	—
356	C₂²	—	212	2	no	—
357	C₂²	—	212	2	no	—
358	C₂²	—	212	2	no	—
359	C₂²	C₄×D₄₂₄	1	2	yes	—
360	C₂²	C₂×C₄×D₂₁₂	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	212	2	no	—
365	C₄	—	212	2	no	—
366	C₄	C₄×D₄₂₄	1	2	yes	—
367	C₄	C₂×M₁₆×D₅₃	1	1	yes	characteristic
368	C₄	#16811389	1	1	yes	characteristic
369	C₄	C₂²×D₄₂₄	1	1	yes	characteristic
370	C₄	C₂×#13133239	1	1	yes	characteristic
371	C₂	—	2	2	no	—
372	C₂	—	424	2	no	—
373	C₂	—	212	4	no	—
374	C₂	M₁₆×D₂₁₂	1	1	yes	characteristic
375	C₂	C₂×C₄×D₄₂₄	1	1	yes	characteristic
376	C₂	#20283633	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₁₂
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₄²	C₂³×D₅₃
Fitting	C₈×M₁₆×C₅₃	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	C₂²×D₄₂₄	C₄
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	C₈×M₁₆	D₅₃
hypocenter	C₅₃	M₁₆×D₈
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
2. M₁₆×D₂₁₂	C₂	semidirect
3. #20273601	C₂	semidirect
4. #20273546	C₂	semidirect
5. C₈×D₄₂₄	C₂	semidirect
6. #20273474	C₂	semidirect
7. #20273141	C₂	semidirect
8. C₈×M₁₆×C₅₃	C₂	semidirect
18. #16810702	C₂²	semidirect
20. C₈×D₂₁₂	C₂²	semidirect
25. #16810376	C₂²	semidirect
26. #16810376	C₂²	semidirect
27. #16810352	C₂²	semidirect
28. #16810352	C₂²	semidirect
32. C₅₃×#322	C₂²	semidirect
33. C₈²×C₅₃	C₂²	semidirect
94. M₁₆×C₅₃	D₈	semidirect
119. D₄₂₄	M₁₆	direct (N × H)
146. D₂₁₂	C₂×M₁₆	semidirect
158. C₈×C₅₃	C₂×M₁₆	semidirect
159. C₈×C₅₃	C₂×D₈	semidirect
190. C₈×M₁₆	D₅₃	semidirect
220. #322	C₂×D₅₃	semidirect
221. C₈²	C₂×D₅₃	semidirect
222. C₅₃	M₁₆×D₈	semidirect
288. M₁₆	D₄₂₄	direct (N × H)
348. C₈	M₁₆×D₅₃	semidirect
349. C₈	C₂×D₄₂₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₄₂₄	2
M₁₆×D₂₁₂	2
#20273601	2
#20273546	2
C₈×D₄₂₄	2
#20273474	2
#20273141	2
C₈×M₁₆×C₅₃	2
M₁₆×D₈	53

Subgroups — M16×D424 #27355516

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×D₄₂₄ #27355516