Subgroups — Q₁₆×#4313 #14725228

Order 2816.

638 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#4313	C₂	1	2	yes	maximal
2	C₄×Q₁₆×D₁₁	C₂	1	1	yes	maximal, characteristic
3	#13067514	C₂	1	1	yes	maximal, characteristic, complemented
4	#13067512	C₂	1	1	yes	maximal, characteristic, complemented
5	#13067466	C₂	1	2	yes	maximal, complemented
6	#13067463	C₂	1	2	yes	maximal, complemented
7	Q₁₆×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#13067373	C₂	1	1	yes	maximal, characteristic
9	#13067043	C₂	1	2	yes	maximal
10	C₈×#4313	C₂	1	1	yes	maximal, characteristic
11	C₈×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₁₁	C₄	1	1	yes	characteristic
13	C₄×Q₈×D₁₁	C₂²	1	2	yes	—
14	C₈×Q₈×C₁₁	C₂²	1	2	yes	—
15	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
16	Q₁₆×Dic₁₁	C₄	1	1	yes	characteristic
17	C₄×#4326	C₂²	1	2	yes	—
18	Q₈×C₁₁⋊C₈	C₂²	1	2	yes	—
19	D₁₁×#107	C₄	1	1	yes	characteristic
20	#10622486	C₄	1	1	yes	characteristic
21	#10622450	—	2	2	no	—
22	#10622450	C₂²	1	2	yes	—
23	#10622444	—	2	2	no	—
24	#10622444	C₂²	1	2	yes	—
25	D₁₁×#103	C₄	1	2	yes	—
26	#10622403	C₄	1	2	yes	—
27	C₄×Dic₄₄	C₂²	1	1	yes	characteristic
28	C₄×#4313	—	2	2	no	—
29	C₄×#4313	C₂²	1	1	yes	characteristic
30	#10622298	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
32	#10622292	—	2	2	no	—
33	#10622292	C₂²	1	2	yes	—
34	C₁₁×#335	C₂²	1	1	yes	characteristic
35	C₁₁×Q₈⋊C₈	C₂²	1	2	yes	—
36	C₈²×C₁₁	C₂²	1	1	yes	characteristic
37	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
38	#10622122	C₂²	1	2	yes	—
39	#10622117	C₂²	1	2	yes	—
40	#10622096	C₂²	1	1	yes	characteristic
41	#10622094	C₂²	1	2	yes	—
42	#10622093	C₂²	1	1	yes	characteristic
43	#10622092	C₂²	1	1	yes	characteristic
44	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×Q₈×D₁₁	C₂×C₄	1	2	yes	—
46	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
47	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
48	Q₈×Dic₁₁	C₂×C₄	1	2	yes	—
49	C₂×#4326	C₂×C₄	1	2	yes	—
50	Q₁₆×D₁₁	—	2	4	no	—
51	C₂×Dic₄₄	C₂×C₄	1	1	yes	characteristic
52	C₂×#4313	—	2	2	no	—
53	C₂×#4313	D₄	1	1	yes	characteristic
54	C₂×#4313	D₄	1	1	yes	characteristic
55	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
57	C₄⋊C₄×D₁₁	—	2	2	no	—
58	C₄⋊C₄×D₁₁	C₂×C₄	1	2	yes	—
59	#66940	—	2	2	no	—
60	#66940	C₂×C₄	1	2	yes	—
61	C₄²×D₁₁	—	2	2	no	—
62	C₄²×D₁₁	C₂³	1	1	yes	characteristic
63	C₄×Dic₂₂	—	2	2	no	—
64	C₄×Dic₂₂	C₂³	1	2	yes	—
65	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
66	C₁₁×C₄⋊C₈	—	2	2	no	—
67	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
68	C₁₁×#103	C₂×C₄	1	2	yes	—
69	C₄×C₈×C₁₁	—	2	2	no	—
70	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
71	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
72	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
73	#66899	C₂×C₄	1	2	yes	—
74	(C₂×D₁₁)⋊C₈	—	2	1	no	—
75	#66882	C₂×C₄	1	1	yes	characteristic
76	#66880	C₂×C₄	1	2	yes	—
77	#66879	—	2	2	no	—
78	#66879	—	2	2	no	—
79	#66879	D₄	1	1	yes	characteristic
80	#66879	D₄	1	1	yes	characteristic
81	Dic₁₁⋊C₈	—	2	2	no	—
82	Dic₁₁⋊C₈	—	2	2	no	—
83	Dic₁₁⋊C₈	—	2	1	no	—
84	Dic₁₁⋊C₈	—	2	2	no	—
85	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
87	#66874	C₂×C₄	1	2	yes	—
88	#66871	C₂×C₄	1	2	yes	—
89	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
90	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
91	C₄×C₁₁⋊C₈	—	2	2	no	—
92	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
93	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
94	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
95	M₁₆×Q₁₆	—	11	1	no	maximal, Sylow
96	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
97	Q₈×D₁₁	—	2	4	no	—
98	Q₈×D₁₁	—	4	2	no	—
99	C₂×C₄×D₁₁	—	2	2	no	—
100	C₂×C₄×D₁₁	—	2	2	no	—
101	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×D₁₁	#41	1	1	yes	characteristic
104	C₂×Dic₂₂	—	2	2	no	—
105	C₂×Dic₂₂	C₂²×C₄	1	2	yes	—
106	C₁₁×Q₁₆	M₁₆	1	4	yes	complemented
107	C₂×C₈×C₁₁	—	2	2	no	—
108	C₂×C₈×C₁₁	—	2	1	no	—
109	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
113	C₁₁×C₄⋊C₄	—	2	2	no	—
114	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
115	C₄²×C₁₁	—	2	2	no	—
116	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
117	#4326	—	2	4	no	—
118	C₄⋊Dic₁₁	—	2	2	no	—
119	C₄⋊Dic₁₁	C₂²×C₄	1	2	yes	—
120	Dic₁₁⋊C₄	—	2	2	no	—
121	Dic₁₁⋊C₄	—	2	2	no	—
122	Dic₁₁⋊C₄	—	2	2	no	—
123	C₄×Dic₁₁	—	2	2	no	—
124	C₄×Dic₁₁	—	2	2	no	—
125	C₄×Dic₁₁	—	2	2	no	—
126	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
128	C₄×Dic₁₁	#41	1	1	yes	characteristic
129	C₂×C₁₁⋊C₈	—	2	2	no	—
130	C₂×C₁₁⋊C₈	—	2	1	no	—
131	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
134	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
135	Dic₄₄	—	2	2	no	—
136	#4313	—	2	2	no	—
137	#4313	—	4	4	no	—
138	#4313	Q₁₆	1	4	yes	direct product factor
139	C₈×D₁₁	—	2	2	no	—
140	C₈×D₁₁	—	4	1	no	—
141	Q₈×M₁₆	—	11	2	no	—
142	C₂×C₄×Q₁₆	—	11	1	no	—
143	#1591	—	11	1	no	—
144	#1591	—	11	1	no	—
145	#1584	—	11	2	no	—
146	#1584	—	11	2	no	—
147	C₈×Q₁₆	—	11	1	no	—
148	C₈×Q₁₆	D₁₁	1	1	yes	characteristic, complemented
149	#1567	—	11	1	no	—
150	#1487	—	11	2	no	—
151	C₈×M₁₆	—	11	1	no	—
152	C₂²×D₁₁	C₄×D₄	1	1	yes	characteristic
153	Q₈×C₁₁	—	2	2	no	—
154	Q₈×C₁₁	C₂×M₁₆	1	4	yes	—
155	C₂×C₄×C₁₁	—	2	2	no	—
156	C₂×C₄×C₁₁	—	2	2	no	—
157	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
160	C₂×Dic₁₁	—	2	2	no	—
161	C₂×Dic₁₁	—	2	2	no	—
162	C₂×Dic₁₁	C₄×D₄	1	1	yes	characteristic
163	C₂×Dic₁₁	C₄×D₄	1	1	yes	characteristic
164	C₂×Dic₁₁	C₄×D₄	1	1	yes	characteristic
165	C₄×D₁₁	—	2	1	no	—
166	C₄×D₁₁	—	2	1	no	—
167	C₄×D₁₁	—	4	1	no	—
168	C₄×D₁₁	—	4	4	no	—
169	C₄×D₁₁	—	8	2	no	—
170	C₄×D₁₁	C₂×Q₁₆	1	2	yes	—
171	C₄×D₁₁	#135	1	2	yes	—
172	Dic₂₂	—	2	2	no	—
173	Dic₂₂	—	2	2	no	—
174	Dic₂₂	—	4	4	no	—
175	C₈×C₁₁	—	2	1	no	—
176	C₈×C₁₁	—	2	1	no	—
177	C₈×C₁₁	—	4	1	no	—
178	C₈×C₁₁	—	4	2	no	—
179	C₈×C₁₁	C₂×M₁₆	1	2	yes	—
180	C₈×C₁₁	C₂×Q₁₆	1	2	yes	complemented
181	C₁₁⋊C₈	—	2	1	no	—
182	C₁₁⋊C₈	—	2	1	no	—
183	C₁₁⋊C₈	—	2	1	no	—
184	C₁₁⋊C₈	—	4	1	no	—
185	C₁₁⋊C₈	—	4	2	no	—
186	C₁₁⋊C₈	C₂×Q₁₆	1	2	yes	complemented
187	C₂²×Q₁₆	—	11	1	no	—
188	C₂×C₄×Q₈	—	11	2	no	—
189	#446	—	11	2	no	—
190	#446	—	11	2	no	—
191	#446	—	22	2	no	—
192	#446	—	22	2	no	—
193	C₈×Q₈	—	11	2	no	—
194	C₈×Q₈	C₂×D₁₁	1	2	yes	—
195	C₄×Q₁₆	—	11	1	no	—
196	C₄×Q₁₆	—	11	2	no	—
197	C₄×Q₁₆	—	11	1	no	—
198	C₄×Q₁₆	—	11	2	no	—
199	C₄×Q₁₆	—	11	1	no	—
200	C₄×Q₁₆	C₂×D₁₁	1	1	yes	characteristic
201	#431	—	11	1	no	—
202	C₂×#107	—	11	1	no	—
203	#423	—	11	2	no	—
204	#423	—	22	2	no	—
205	C₂×#103	—	11	2	no	—
206	C₄×M₁₆	—	11	1	no	—
207	C₄×M₁₆	—	22	2	no	—
208	C₂×C₄×C₈	—	11	1	no	—
209	#335	—	11	2	no	—
210	#335	—	11	1	no	—
211	#335	C₂×D₁₁	1	1	yes	characteristic
212	Q₈⋊C₈	—	11	2	no	—
213	Q₈⋊C₈	—	11	2	no	—
214	Q₈⋊C₈	—	11	2	no	—
215	Q₈⋊C₈	C₂×D₁₁	1	2	yes	—
216	#322	—	11	1	no	—
217	#322	—	11	1	no	—
218	C₈²	—	11	1	no	—
219	C₈²	C₂×D₁₁	1	1	yes	characteristic
220	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
221	C₂×D₁₁	—	2	1	no	—
222	C₂×D₁₁	—	2	1	no	—
223	C₂×D₁₁	C₄×Q₁₆	1	2	yes	—
224	C₄×C₁₁	—	2	4	no	—
225	C₄×C₁₁	—	2	1	no	—
226	C₄×C₁₁	—	4	2	no	—
227	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
228	C₄×C₁₁	#568	1	1	yes	characteristic
229	C₄×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
230	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
231	Dic₁₁	—	2	1	no	—
232	Dic₁₁	—	2	1	no	—
233	Dic₁₁	—	4	2	no	—
234	Dic₁₁	—	4	2	no	—
235	Dic₁₁	C₄×Q₁₆	1	2	yes	—
236	C₂²×Q₈	—	11	2	no	—
237	C₂×Q₁₆	—	11	2	no	—
238	C₂×Q₁₆	—	11	1	no	—
239	C₂×Q₁₆	—	22	4	no	—
240	C₂×Q₁₆	C₄×D₁₁	1	1	yes	characteristic
241	C₂×M₁₆	—	11	1	no	—
242	C₂×M₁₆	—	11	1	no	—
243	C₂×M₁₆	—	22	2	no	—
244	C₂²×C₈	—	11	1	no	—
245	C₂²×C₈	—	11	1	no	—
246	C₄×Q₈	—	11	2	no	—
247	C₄×Q₈	—	11	2	no	—
248	C₄×Q₈	—	11	2	no	—
249	C₄×Q₈	—	22	2	no	—
250	C₄×Q₈	—	22	2	no	—
251	C₄×Q₈	C₂²×D₁₁	1	2	yes	—
252	C₂×C₄⋊C₄	—	11	2	no	—
253	C₂×C₄⋊C₄	—	22	2	no	—
254	C₂×C₄²	—	11	1	no	—
255	C₂×C₄²	—	22	2	no	—
256	#107	—	11	1	no	—
257	#107	—	11	2	no	—
258	#107	C₄×D₁₁	1	1	yes	characteristic
259	C₄⋊C₈	—	2	2	no	—
260	C₄⋊C₈	—	11	2	no	—
261	C₄⋊C₈	—	22	2	no	—
262	C₄⋊C₈	—	22	2	no	—
263	C₄⋊C₈	—	22	1	no	—
264	C₄⋊C₈	—	22	2	no	—
265	C₄⋊C₈	—	22	2	no	—
266	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
267	#103	—	11	2	no	—
268	#103	—	11	2	no	—
269	#103	—	11	2	no	—
270	#103	C₄×D₁₁	1	2	yes	—
271	C₂²⋊C₈	—	22	1	no	—
272	#97	—	11	1	no	—
273	#97	—	11	1	no	—
274	#97	—	22	2	no	—
275	#97	—	22	2	no	—
276	C₄×C₈	—	2	2	no	—
277	C₄×C₈	—	11	1	no	—
278	C₄×C₈	—	11	1	no	—
279	C₄×C₈	—	11	1	no	—
280	C₄×C₈	—	11	1	no	—
281	C₄×C₈	—	11	1	no	—
282	C₄×C₈	—	22	2	no	—
283	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
284	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
285	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
286	C₂×C₁₁	D₄×M₁₆	1	1	yes	characteristic
287	C₂×C₁₁	C₂×C₄×Q₁₆	1	1	yes	characteristic
288	C₂×C₁₁	#2957	1	1	yes	characteristic
289	D₁₁	—	2	2	no	—
290	C₂×Q₈	—	11	2	no	—
291	C₂×Q₈	—	22	2	no	—
292	C₂×Q₈	—	22	4	no	—
293	C₂×Q₈	—	44	2	no	—
294	C₂×Q₈	C₂×C₄×D₁₁	1	2	yes	—
295	C₂²×C₄	—	11	1	no	—
296	C₂²×C₄	—	11	1	no	—
297	C₂²×C₄	—	11	1	no	—
298	C₂²×C₄	—	22	2	no	—
299	C₂²×C₄	—	22	2	no	—
300	Q₁₆	—	22	4	no	—
301	Q₁₆	—	22	2	no	—
302	Q₁₆	#4313	1	4	yes	direct product factor
303	M₁₆	—	11	4	no	—
304	M₁₆	—	22	2	no	—
305	M₁₆	—	44	4	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	11	1	no	—
309	C₂×C₈	—	11	1	no	—
310	C₂×C₈	—	11	1	no	—
311	C₂×C₈	—	11	1	no	—
312	C₂×C₈	—	22	2	no	—
313	C₂×C₈	—	22	2	no	—
314	C₂×C₈	—	22	1	no	—
315	C₂×C₈	—	44	1	no	—
316	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
317	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
318	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
319	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	11	2	no	—
322	C₄⋊C₄	—	22	2	no	—
323	C₄⋊C₄	—	22	2	no	—
324	C₄⋊C₄	—	22	2	no	—
325	C₄⋊C₄	—	22	2	no	—
326	C₄⋊C₄	C₂×C₄×D₁₁	1	2	yes	—
327	C₄²	—	2	2	no	—
328	C₄²	—	11	1	no	—
329	C₄²	—	11	1	no	—
330	C₄²	—	11	1	no	—
331	C₄²	—	22	2	no	—
332	C₄²	—	22	2	no	—
333	C₄²	—	22	2	no	—
334	C₄²	C₂³×D₁₁	1	1	yes	characteristic
335	C₁₁	M₁₆×Q₁₆	1	1	yes	characteristic, complemented, Sylow
336	C₂³	—	11	1	no	—
337	Q₈	—	2	2	no	—
338	Q₈	—	22	2	no	—
339	Q₈	—	22	2	no	—
340	Q₈	—	44	4	no	—
341	Q₈	C₂×#4313	1	4	yes	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	11	1	no	—
345	C₂×C₄	—	11	2	no	—
346	C₂×C₄	—	11	2	no	—
347	C₂×C₄	—	11	1	no	—
348	C₂×C₄	—	11	1	no	—
349	C₂×C₄	—	22	1	no	—
350	C₂×C₄	—	22	1	no	—
351	C₂×C₄	—	22	2	no	—
352	C₂×C₄	—	22	2	no	—
353	C₂×C₄	—	44	1	no	—
354	C₂×C₄	—	44	4	no	—
355	C₂×C₄	—	88	2	no	—
356	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
357	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
358	C₂×C₄	#41×D₁₁	1	1	yes	characteristic
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	4	1	no	—
362	C₈	—	4	2	no	—
363	C₈	—	11	2	no	—
364	C₈	—	22	1	no	—
365	C₈	—	22	1	no	—
366	C₈	—	22	1	no	—
367	C₈	—	44	1	no	—
368	C₈	—	44	2	no	—
369	C₈	C₂×#4313	1	2	yes	—
370	C₈	Q₁₆×D₁₁	1	2	yes	complemented
371	C₂²	—	11	2	no	—
372	C₂²	—	22	1	no	—
373	C₂²	—	22	1	no	—
374	C₂²	C₄×D₄×D₁₁	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	2	4	no	—
377	C₄	—	4	2	no	—
378	C₄	—	11	2	no	—
379	C₄	—	22	1	no	—
380	C₄	—	22	1	no	—
381	C₄	—	44	2	no	—
382	C₄	—	44	2	no	—
383	C₄	C₂²×#4313	1	1	yes	characteristic
384	C₄	#10623281	1	1	yes	characteristic
385	C₄	C₂×Q₁₆×D₁₁	1	1	yes	characteristic
386	C₄	D₁₁×#135	1	1	yes	characteristic
387	C₂	—	22	2	no	—
388	C₂	D₄×#4313	1	1	yes	characteristic
389	C₂	C₄×Q₁₆×D₁₁	1	1	yes	characteristic
390	C₂	#13077528	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₈×C₁₁×Q₁₆	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂²×D₁₁	C₄×D₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₈×Q₁₆	D₁₁
hypocenter	C₁₁	M₁₆×Q₁₆
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×Q₁₆

Complements

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

N	H ≅ G/N	type
3. #13067514	C₂	semidirect
4. #13067512	C₂	semidirect
5. #13067466	C₂	semidirect
6. #13067463	C₂	semidirect
7. Q₁₆×C₁₁⋊C₈	C₂	semidirect
11. C₈×C₁₁×Q₁₆	C₂	semidirect
106. C₁₁×Q₁₆	M₁₆	semidirect
138. #4313	Q₁₆	direct (N × H)
148. C₈×Q₁₆	D₁₁	semidirect
180. C₈×C₁₁	C₂×Q₁₆	semidirect
186. C₁₁⋊C₈	C₂×Q₁₆	semidirect
302. Q₁₆	#4313	direct (N × H)
335. C₁₁	M₁₆×Q₁₆	semidirect
370. C₈	Q₁₆×D₁₁	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#4313	2
C₄×Q₁₆×D₁₁	2
#13067514	2
#13067512	2
#13067466	2
#13067463	2
Q₁₆×C₁₁⋊C₈	2
#13067373	2
#13067043	2
C₈×#4313	2
C₈×C₁₁×Q₁₆	2
M₁₆×Q₁₆	11

Subgroups — Q16×#4313 #14725228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₁₆×#4313 #14725228