Subgroups — C₁₁×#18044 #14595237

Order 2816.

786 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₁×D₈	C₂	1	1	yes	maximal, characteristic
2	D₄×C₁₁×M₁₆	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1594	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1586	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1580	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1566	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1486	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₁×D₈	C₄	1	1	yes	characteristic
10	C₂²×C₁₁×M₁₆	—	2	2	no	—
11	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
12	C₄×C₁₁×D₈	C₄	1	2	yes	—
13	C₄×C₁₁×D₈	C₄	1	1	yes	characteristic
14	C₄×C₁₁×D₈	C₄	1	1	yes	characteristic
15	C₄×C₁₁×D₈	C₂²	1	1	yes	characteristic
16	C₄×C₁₁×D₈	C₂²	1	2	yes	—
17	C₄×C₁₁×D₈	C₂²	1	1	yes	characteristic
18	C₁₁×#436	C₂²	1	4	yes	complemented
19	C₁₁×#435	—	2	4	no	—
20	C₈×D₄×C₁₁	C₂²	1	4	yes	complemented
21	C₁₁×#431	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×#107	C₄	1	1	yes	characteristic
23	C₁₁×#423	C₂²	1	2	yes	—
24	C₂×C₁₁×#102	C₄	1	2	yes	—
25	C₁₁×#407	—	2	2	no	—
26	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
28	C₁₁×#334	C₂²	1	2	yes	complemented
29	C₁₁×#334	C₂²	1	2	yes	complemented
30	C₁₁×D₄⋊C₈	C₂²	1	4	yes	complemented
31	C₁₁×D₄⋊C₈	C₂²	1	4	yes	complemented
32	C₁₁×#322	C₂²	1	2	yes	complemented
33	C₁₁×#322	C₂²	1	2	yes	complemented
34	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₁	—	2	2	no	—
36	C₂×C₁₁×D₈	—	2	4	no	—
37	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
38	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
40	C₂×C₁₁×M₁₆	—	2	2	no	—
41	C₂×C₁₁×M₁₆	—	2	4	no	—
42	C₂×C₁₁×M₁₆	—	4	8	no	—
43	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
44	C₂²×C₈×C₁₁	—	2	4	no	—
45	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
47	C₄×D₄×C₁₁	—	2	2	no	—
48	C₄×D₄×C₁₁	—	2	2	no	—
49	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
50	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
51	C₄×D₄×C₁₁	C₂³	1	2	yes	—
52	C₄×D₄×C₁₁	C₂³	1	2	yes	—
53	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
55	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
56	C₁₁×#107	C₂×C₄	1	2	yes	—
57	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
58	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
59	C₁₁×C₄⋊C₈	—	2	2	no	—
60	C₁₁×C₄⋊C₈	—	2	1	no	—
61	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
62	C₁₁×#102	C₂×C₄	1	2	yes	—
63	C₁₁×#102	C₂×C₄	1	2	yes	—
64	C₁₁×#102	C₂×C₄	1	2	yes	—
65	C₁₁×#102	C₂×C₄	1	2	yes	—
66	C₁₁×C₂²⋊C₈	—	2	1	no	—
67	C₁₁×C₂²⋊C₈	—	2	4	no	—
68	C₁₁×C₂²⋊C₈	—	2	4	no	—
69	C₁₁×#97	D₄	1	2	yes	—
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	#18044	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂⁴×C₁₁	—	2	2	no	—
78	C₂×D₄×C₁₁	—	2	4	no	—
79	C₂×D₄×C₁₁	—	2	2	no	—
80	C₂×D₄×C₁₁	—	4	2	no	—
81	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
82	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₁	—	2	2	no	—
84	C₂²×C₄×C₁₁	—	2	2	no	—
85	C₂²×C₄×C₁₁	—	2	2	no	—
86	C₂²×C₄×C₁₁	—	2	2	no	—
87	C₂²×C₄×C₁₁	—	2	2	no	—
88	C₂²×C₄×C₁₁	—	4	4	no	—
89	C₂²×C₄×C₁₁	—	4	4	no	—
90	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
93	C₁₁×D₈	—	2	2	no	—
94	C₁₁×D₈	—	2	4	no	—
95	C₁₁×D₈	M₁₆	1	4	yes	complemented
96	C₁₁×M₁₆	—	2	4	no	—
97	C₁₁×M₁₆	—	4	8	no	—
98	C₁₁×M₁₆	—	4	4	no	—
99	C₂×C₈×C₁₁	—	2	2	no	—
100	C₂×C₈×C₁₁	—	2	4	no	—
101	C₂×C₈×C₁₁	—	2	2	no	—
102	C₂×C₈×C₁₁	—	4	1	no	—
103	C₂×C₈×C₁₁	—	4	8	no	—
104	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
109	C₁₁×C₄⋊C₄	—	2	2	no	—
110	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
111	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
112	C₁₁×C₂²⋊C₄	—	2	2	no	—
113	C₁₁×C₂²⋊C₄	—	2	2	no	—
114	C₁₁×C₂²⋊C₄	—	2	2	no	—
115	C₁₁×C₂²⋊C₄	—	2	2	no	—
116	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₁₁	#41	1	1	yes	characteristic
119	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
120	C₂×C₄×D₈	C₂×C₁₁	1	1	yes	characteristic
121	D₄×M₁₆	C₂×C₁₁	1	2	yes	complemented
122	#1594	C₂×C₁₁	1	2	yes	complemented
123	#1586	C₂×C₁₁	1	4	yes	complemented
124	#1580	C₂×C₁₁	1	2	yes	complemented
125	#1566	C₂×C₁₁	1	1	yes	characteristic, complemented
126	#1486	C₂×C₁₁	1	2	yes	complemented
127	#1451	C₂×C₁₁	1	1	yes	characteristic, complemented
128	C₂³×C₁₁	—	2	2	no	—
129	C₂³×C₁₁	—	2	2	no	—
130	C₂³×C₁₁	—	4	4	no	—
131	C₂³×C₁₁	—	4	4	no	—
132	C₂³×C₁₁	—	8	2	no	—
133	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
134	D₄×C₁₁	—	2	2	no	—
135	D₄×C₁₁	—	2	2	no	—
136	D₄×C₁₁	—	2	2	no	—
137	D₄×C₁₁	—	4	4	no	—
138	D₄×C₁₁	C₂×M₁₆	1	4	yes	complemented
139	C₂×C₄×C₁₁	—	2	1	no	—
140	C₂×C₄×C₁₁	—	2	1	no	—
141	C₂×C₄×C₁₁	—	2	2	no	—
142	C₂×C₄×C₁₁	—	2	2	no	—
143	C₂×C₄×C₁₁	—	4	1	no	—
144	C₂×C₄×C₁₁	—	4	4	no	—
145	C₂×C₄×C₁₁	—	4	2	no	—
146	C₂×C₄×C₁₁	—	4	2	no	—
147	C₂×C₄×C₁₁	—	4	2	no	—
148	C₂×C₄×C₁₁	—	4	2	no	—
149	C₂×C₄×C₁₁	—	4	4	no	—
150	C₂×C₄×C₁₁	—	4	4	no	—
151	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	4	yes	—
155	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
158	C₈×C₁₁	—	2	1	no	—
159	C₈×C₁₁	—	2	1	no	—
160	C₈×C₁₁	—	2	1	no	—
161	C₈×C₁₁	—	2	4	no	—
162	C₈×C₁₁	—	4	2	no	—
163	C₈×C₁₁	—	4	4	no	—
164	C₈×C₁₁	C₂×M₁₆	1	2	yes	complemented
165	C₂²×D₈	C₄×C₁₁	1	1	yes	characteristic
166	C₂²×M₁₆	—	2	2	no	—
167	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
168	C₄×D₈	C₄×C₁₁	1	2	yes	—
169	C₄×D₈	C₄×C₁₁	1	1	yes	characteristic
170	C₄×D₈	C₄×C₁₁	1	1	yes	characteristic
171	C₄×D₈	C₂²×C₁₁	1	1	yes	characteristic
172	C₄×D₈	C₂²×C₁₁	1	2	yes	—
173	C₄×D₈	C₂²×C₁₁	1	1	yes	characteristic
174	#436	C₂²×C₁₁	1	4	yes	complemented
175	#435	—	2	4	no	—
176	C₈×D₄	C₂²×C₁₁	1	4	yes	complemented
177	#431	C₂²×C₁₁	1	1	yes	characteristic
178	C₂×#107	C₄×C₁₁	1	1	yes	characteristic
179	#423	C₂²×C₁₁	1	2	yes	—
180	C₂×#102	C₄×C₁₁	1	2	yes	—
181	#407	—	2	2	no	—
182	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
183	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
184	#334	C₂²×C₁₁	1	2	yes	complemented
185	#334	C₂²×C₁₁	1	2	yes	complemented
186	D₄⋊C₈	C₂²×C₁₁	1	4	yes	complemented
187	D₄⋊C₈	C₂²×C₁₁	1	4	yes	complemented
188	#322	C₂²×C₁₁	1	2	yes	complemented
189	#322	C₂²×C₁₁	1	2	yes	complemented
190	C₂²×C₁₁	—	2	1	no	—
191	C₂²×C₁₁	—	2	1	no	—
192	C₂²×C₁₁	—	2	4	no	—
193	C₂²×C₁₁	—	4	2	no	—
194	C₂²×C₁₁	—	4	2	no	—
195	C₂²×C₁₁	—	4	2	no	—
196	C₂²×C₁₁	—	4	2	no	—
197	C₂²×C₁₁	—	4	2	no	—
198	C₂²×C₁₁	—	8	8	no	—
199	C₂²×C₁₁	#442	1	2	yes	—
200	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
201	C₄×C₁₁	—	2	1	no	—
202	C₄×C₁₁	—	2	1	no	—
203	C₄×C₁₁	—	2	1	no	—
204	C₄×C₁₁	—	4	2	no	—
205	C₄×C₁₁	—	4	2	no	—
206	C₄×C₁₁	#442	1	2	yes	—
207	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
208	C₄×C₁₁	#568	1	1	yes	characteristic
209	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
210	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
211	C₂³×C₄	—	2	2	no	—
212	C₂×D₈	—	2	4	no	—
213	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
214	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
215	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
216	C₂×M₁₆	—	2	2	no	—
217	C₂×M₁₆	—	2	4	no	—
218	C₂×M₁₆	—	4	8	no	—
219	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
220	C₂²×C₈	—	2	4	no	—
221	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
222	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
223	C₄×D₄	—	2	2	no	—
224	C₄×D₄	—	2	2	no	—
225	C₄×D₄	C₂×C₄×C₁₁	1	2	yes	—
226	C₄×D₄	C₂×C₄×C₁₁	1	2	yes	—
227	C₄×D₄	C₂³×C₁₁	1	2	yes	—
228	C₄×D₄	C₂³×C₁₁	1	2	yes	—
229	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
230	C₂×C₂²⋊C₄	—	2	2	no	—
231	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
232	#107	C₂×C₄×C₁₁	1	2	yes	—
233	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
234	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
235	C₄⋊C₈	—	2	2	no	—
236	C₄⋊C₈	—	2	1	no	—
237	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
238	#102	C₂×C₄×C₁₁	1	2	yes	—
239	#102	C₂×C₄×C₁₁	1	2	yes	—
240	#102	C₂×C₄×C₁₁	1	2	yes	—
241	#102	C₂×C₄×C₁₁	1	2	yes	—
242	C₂²⋊C₈	—	2	1	no	—
243	C₂²⋊C₈	—	2	4	no	—
244	C₂²⋊C₈	—	2	4	no	—
245	#97	D₄×C₁₁	1	2	yes	—
246	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
247	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
248	C₄×C₈	C₂³×C₁₁	1	2	yes	—
249	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
250	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
251	C₄×C₈	C₂³×C₁₁	1	2	yes	—
252	C₂×C₁₁	—	2	2	no	—
253	C₂×C₁₁	—	4	4	no	—
254	C₂×C₁₁	—	8	2	no	—
255	C₂×C₁₁	D₄×M₁₆	1	1	yes	characteristic
256	C₂×C₁₁	C₂×#442	1	1	yes	characteristic
257	C₂×C₁₁	#2957	1	1	yes	characteristic
258	C₂⁴	—	2	2	no	—
259	C₂×D₄	—	2	4	no	—
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	—	4	2	no	—
262	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
263	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	4	4	no	—
270	C₂²×C₄	—	4	4	no	—
271	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
273	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
274	D₈	—	2	4	no	—
275	D₈	—	2	2	no	—
276	D₈	C₁₁×M₁₆	1	4	yes	complemented
277	M₁₆	—	2	4	no	—
278	M₁₆	—	4	8	no	—
279	M₁₆	—	4	4	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	4	1	no	—
284	C₂×C₈	—	4	8	no	—
285	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
286	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
287	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
288	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
289	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
292	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
293	C₂²⋊C₄	—	2	2	no	—
294	C₂²⋊C₄	—	2	2	no	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	2	2	no	—
297	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
298	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
299	C₄²	C₁₁×#41	1	1	yes	characteristic
300	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
301	C₁₁	#18044	1	1	yes	characteristic, direct product factor, Sylow
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	4	4	no	—
305	C₂³	—	4	4	no	—
306	C₂³	—	8	2	no	—
307	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
308	D₄	—	2	2	no	—
309	D₄	—	2	2	no	—
310	D₄	—	2	2	no	—
311	D₄	—	4	4	no	—
312	D₄	C₂×C₁₁×M₁₆	1	4	yes	complemented
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
326	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
327	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
328	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	4	yes	—
329	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
330	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
331	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
332	C₈	—	2	1	no	—
333	C₈	—	2	1	no	—
334	C₈	—	2	1	no	—
335	C₈	—	2	4	no	—
336	C₈	—	4	2	no	—
337	C₈	—	4	4	no	—
338	C₈	C₂×C₁₁×M₁₆	1	2	yes	complemented
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	2	no	—
346	C₂²	—	4	2	no	—
347	C₂²	—	8	8	no	—
348	C₂²	C₁₁×#442	1	2	yes	—
349	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	2	no	—
355	C₄	C₁₁×#442	1	2	yes	—
356	C₄	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
357	C₄	C₁₁×#568	1	1	yes	characteristic
358	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	2	yes	—
359	C₂	—	2	2	no	—
360	C₂	—	4	4	no	—
361	C₂	—	8	2	no	—
362	C₂	D₄×C₁₁×M₁₆	1	1	yes	characteristic
363	C₂	C₂×C₁₁×#442	1	1	yes	characteristic
364	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	C₂²×C₁₁×D₈	C₄
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
2. D₄×C₁₁×M₁₆	C₂	semidirect
3. C₁₁×#1594	C₂	semidirect
4. C₁₁×#1586	C₂	semidirect
5. C₁₁×#1580	C₂	semidirect
6. C₁₁×#1566	C₂	semidirect
7. C₁₁×#1486	C₂	semidirect
8. C₁₁×#1451	C₂	semidirect
18. C₁₁×#436	C₂²	semidirect
20. C₈×D₄×C₁₁	C₂²	semidirect
28. C₁₁×#334	C₂²	semidirect
29. C₁₁×#334	C₂²	semidirect
30. C₁₁×D₄⋊C₈	C₂²	semidirect
31. C₁₁×D₄⋊C₈	C₂²	semidirect
32. C₁₁×#322	C₂²	semidirect
33. C₁₁×#322	C₂²	semidirect
76. #18044	C₁₁	direct (N × H)
95. C₁₁×D₈	M₁₆	semidirect
121. D₄×M₁₆	C₂×C₁₁	semidirect
122. #1594	C₂×C₁₁	semidirect
123. #1586	C₂×C₁₁	semidirect
124. #1580	C₂×C₁₁	semidirect
125. #1566	C₂×C₁₁	semidirect
126. #1486	C₂×C₁₁	semidirect
127. #1451	C₂×C₁₁	semidirect
138. D₄×C₁₁	C₂×M₁₆	semidirect
164. C₈×C₁₁	C₂×M₁₆	semidirect
174. #436	C₂²×C₁₁	semidirect
176. C₈×D₄	C₂²×C₁₁	semidirect
184. #334	C₂²×C₁₁	semidirect
185. #334	C₂²×C₁₁	semidirect
186. D₄⋊C₈	C₂²×C₁₁	semidirect
187. D₄⋊C₈	C₂²×C₁₁	semidirect
188. #322	C₂²×C₁₁	semidirect
189. #322	C₂²×C₁₁	semidirect
276. D₈	C₁₁×M₁₆	semidirect
301. C₁₁	#18044	direct (N × H)
312. D₄	C₂×C₁₁×M₁₆	semidirect
338. C₈	C₂×C₁₁×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₁₁×D₈	2
D₄×C₁₁×M₁₆	2
C₁₁×#1594	2
C₁₁×#1586	2
C₁₁×#1580	2
C₁₁×#1566	2
C₁₁×#1486	2
C₁₁×#1451	2
#18044	11

Subgroups — C11×#18044 #14595237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#18044 #14595237