Subgroups — C₁₁×M₁₆×Q₁₆ #14595231

Order 2816.

638 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₄²	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂³×C₁₁	C₄×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₄×C₁₁×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1591	C₂	semidirect
4. C₁₁×#1584	C₂	semidirect
5. C₈×C₁₁×Q₁₆	C₂	semidirect
76. M₁₆×Q₁₆	C₁₁	direct (N × H)
89. C₁₁×Q₁₆	M₁₆	direct (N × H)
92. C₁₁×M₁₆	Q₁₆	direct (N × H)
120. #1591	C₂×C₁₁	semidirect
121. #1584	C₂×C₁₁	semidirect
122. C₈×Q₁₆	C₂×C₁₁	semidirect
156. C₈×C₁₁	C₂×Q₁₆	semidirect
256. Q₁₆	C₁₁×M₁₆	direct (N × H)
259. M₁₆	C₁₁×Q₁₆	direct (N × H)
285. C₁₁	M₁₆×Q₁₆	direct (N × H)
316. C₈	C₂×C₁₁×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
Q₈×C₁₁×M₁₆	2
C₂×C₄×C₁₁×Q₁₆	2
C₁₁×#1591	2
C₁₁×#1584	2
C₈×C₁₁×Q₁₆	2
C₁₁×#1567	2
C₁₁×#1487	2
C₈×C₁₁×M₁₆	2
M₁₆×Q₁₆	11

Subgroups — C11×M16×Q16 #14595231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×M₁₆×Q₁₆ #14595231