Subgroups — C₁₁×#19188 #14596381

Order 2816.

714 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	C₁₁×#3226	C₂	1	2	yes	maximal
2	C₂×C₁₁×#494	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2931	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1689	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1669	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1546	C₂	1	2	yes	maximal, complemented
8	C₂²×C₁₁×Q₁₆	—	2	1	no	—
9	C₂²×C₁₁×Q₁₆	—	2	1	no	—
10	C₂×C₁₁×#131	—	2	1	no	—
11	C₁₁×#532	C₂²	1	1	yes	characteristic
12	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
13	C₁₁×#500	—	2	2	no	—
14	C₁₁×#494	—	2	1	no	—
15	C₁₁×#494	—	2	1	no	—
16	C₁₁×#494	C₂²	1	2	yes	—
17	C₁₁×#494	C₂²	1	2	yes	—
18	C₁₁×#486	—	2	2	no	—
19	C₁₁×#480	—	2	4	no	—
20	C₁₁×#474	C₂²	1	8	yes	—
21	C₁₁×#436	—	2	1	no	—
22	C₁₁×#436	C₂²	1	2	yes	—
23	C₈×D₄×C₁₁	—	2	1	no	—
24	C₈×D₄×C₁₁	C₂²	1	2	yes	—
25	C₁₁×#431	C₂²	1	2	yes	—
26	C₁₁×#423	C₂²	1	1	yes	characteristic
27	C₁₁×#408	—	2	1	no	—
28	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
29	C₁₁×#335	C₂²	1	2	yes	—
30	C₁₁×#334	C₂²	1	2	yes	—
31	C₁₁×#332	C₂²	1	8	yes	—
32	C₂×C₁₁×#41	—	2	1	no	—
33	C₂²×Q₈×C₁₁	—	2	2	no	—
34	C₂×C₁₁×Q₁₆	—	2	2	no	—
35	C₂×C₁₁×Q₁₆	—	2	2	no	—
36	C₂×C₁₁×Q₁₆	—	2	2	no	—
37	C₂×C₁₁×Q₁₆	—	2	2	no	—
38	C₂×C₁₁×Q₁₆	—	4	4	no	—
39	C₂×C₁₁×Q₁₆	—	4	4	no	—
40	C₁₁×#131	—	4	4	no	—
41	C₂×C₁₁×M₁₆	—	2	1	no	—
42	C₂×C₁₁×M₁₆	—	2	2	no	—
43	C₂²×C₈×C₁₁	—	2	2	no	—
44	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
46	C₁₁×C₄⋊Q₈	—	2	2	no	—
47	C₁₁×C₄⋊Q₈	—	2	2	no	—
48	C₁₁×C₄⋊Q₈	—	2	2	no	—
49	C₁₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
50	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
51	C₁₁×#127	D₄	1	1	yes	characteristic
52	C₁₁×#124	—	2	1	no	—
53	C₁₁×#121	—	2	1	no	—
54	C₁₁×#121	D₄	1	2	yes	—
55	C₄×D₄×C₁₁	—	2	1	no	—
56	C₄×D₄×C₁₁	C₂³	1	2	yes	—
57	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
59	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
60	C₁₁×#107	—	2	8	no	—
61	C₁₁×C₄⋊C₈	—	2	1	no	—
62	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
63	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
64	C₁₁×#102	—	2	8	no	—
65	C₁₁×C₂²⋊C₈	—	2	2	no	—
66	C₁₁×C₂²⋊C₈	—	2	2	no	—
67	C₁₁×C₂²⋊C₈	—	2	2	no	—
68	C₄×C₈×C₁₁	—	2	2	no	—
69	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
70	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
71	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
72	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
73	#19188	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₁₁×#41	—	4	2	no	—
75	C₁₁×#41	—	4	2	no	—
76	C₂×Q₈×C₁₁	—	2	1	no	—
77	C₂×Q₈×C₁₁	—	2	4	no	—
78	C₂×Q₈×C₁₁	—	4	2	no	—
79	C₂×Q₈×C₁₁	—	4	4	no	—
80	C₂×Q₈×C₁₁	—	4	4	no	—
81	C₂×D₄×C₁₁	—	2	2	no	—
82	C₂×D₄×C₁₁	—	2	1	no	—
83	C₂×D₄×C₁₁	—	2	1	no	—
84	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₁₁	—	2	2	no	—
86	C₂²×C₄×C₁₁	—	4	2	no	—
87	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
90	C₁₁×Q₁₆	—	4	4	no	—
91	C₁₁×Q₁₆	—	4	4	no	—
92	C₁₁×Q₁₆	—	4	4	no	—
93	C₁₁×Q₁₆	—	4	4	no	—
94	C₁₁×M₁₆	—	4	4	no	—
95	C₁₁×M₁₆	—	4	2	no	—
96	C₂×C₈×C₁₁	—	2	2	no	—
97	C₂×C₈×C₁₁	—	2	4	no	—
98	C₂×C₈×C₁₁	—	2	2	no	—
99	C₂×C₈×C₁₁	—	4	4	no	—
100	C₂×C₈×C₁₁	D₈	1	4	yes	—
101	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
102	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
103	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
104	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
105	C₁₁×C₄⋊C₄	—	2	1	no	—
106	C₁₁×C₄⋊C₄	—	2	4	no	—
107	C₁₁×C₄⋊C₄	—	2	4	no	—
108	C₁₁×C₄⋊C₄	—	4	2	no	—
109	C₁₁×C₄⋊C₄	—	4	2	no	—
110	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
111	C₁₁×C₂²⋊C₄	—	2	2	no	—
112	C₁₁×C₂²⋊C₄	—	2	2	no	—
113	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₁₁	#41	1	1	yes	characteristic
116	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
117	#3226	C₂×C₁₁	1	2	yes	—
118	C₂×#494	C₂×C₁₁	1	1	yes	characteristic, complemented
119	#2931	C₂×C₁₁	1	1	yes	characteristic
120	#1689	C₂×C₁₁	1	4	yes	complemented
121	#1669	C₂×C₁₁	1	4	yes	complemented
122	#1564	C₂×C₁₁	1	1	yes	characteristic, complemented
123	#1546	C₂×C₁₁	1	2	yes	complemented
124	C₂³×C₁₁	—	2	2	no	—
125	C₂³×C₁₁	#121	1	1	yes	characteristic
126	Q₈×C₁₁	—	4	2	no	—
127	Q₈×C₁₁	—	4	4	no	—
128	Q₈×C₁₁	—	4	4	no	—
129	Q₈×C₁₁	—	8	4	no	—
130	D₄×C₁₁	—	2	4	no	—
131	D₄×C₁₁	—	4	4	no	—
132	D₄×C₁₁	—	4	2	no	—
133	D₄×C₁₁	—	4	2	no	—
134	C₂×C₄×C₁₁	—	2	2	no	—
135	C₂×C₄×C₁₁	—	2	2	no	—
136	C₂×C₄×C₁₁	—	2	2	no	—
137	C₂×C₄×C₁₁	—	4	2	no	—
138	C₂×C₄×C₁₁	—	4	2	no	—
139	C₂×C₄×C₁₁	—	4	4	no	—
140	C₂×C₄×C₁₁	—	8	4	no	—
141	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
142	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
143	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
144	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
145	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
146	C₂×C₄×C₁₁	C₂²×D₄	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	—	4	2	no	—
152	C₈×C₁₁	—	4	4	no	—
153	C₈×C₁₁	C₂×D₈	1	2	yes	—
154	C₈×C₁₁	C₂×D₈	1	2	yes	—
155	C₂²×Q₁₆	—	2	1	no	—
156	C₂²×Q₁₆	—	2	1	no	—
157	C₂×#131	—	2	1	no	—
158	#532	C₂²×C₁₁	1	1	yes	characteristic
159	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
160	#500	—	2	2	no	—
161	#494	—	2	1	no	—
162	#494	—	2	1	no	—
163	#494	C₂²×C₁₁	1	2	yes	—
164	#494	C₂²×C₁₁	1	2	yes	—
165	#486	—	2	2	no	—
166	#480	—	2	4	no	—
167	#474	C₂²×C₁₁	1	8	yes	—
168	#436	—	2	1	no	—
169	#436	C₂²×C₁₁	1	2	yes	—
170	C₈×D₄	—	2	1	no	—
171	C₈×D₄	C₂²×C₁₁	1	2	yes	—
172	#431	C₂²×C₁₁	1	2	yes	—
173	#423	C₂²×C₁₁	1	1	yes	characteristic
174	#408	—	2	1	no	—
175	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
176	#335	C₂²×C₁₁	1	2	yes	—
177	#334	C₂²×C₁₁	1	2	yes	—
178	#332	C₂²×C₁₁	1	8	yes	—
179	C₂²×C₁₁	—	2	1	no	—
180	C₂²×C₁₁	—	2	1	no	—
181	C₂²×C₁₁	—	4	2	no	—
182	C₂²×C₁₁	—	4	2	no	—
183	C₂²×C₁₁	—	4	2	no	—
184	C₂²×C₁₁	#459	1	2	yes	—
185	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
186	C₄×C₁₁	—	2	1	no	—
187	C₄×C₁₁	—	2	1	no	—
188	C₄×C₁₁	—	4	2	no	—
189	C₄×C₁₁	—	8	4	no	—
190	C₄×C₁₁	#459	1	2	yes	—
191	C₄×C₁₁	#473	1	2	yes	—
192	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
193	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₄×C₁₁	#578	1	2	yes	—
195	C₂×#41	—	2	1	no	—
196	C₂²×Q₈	—	2	2	no	—
197	C₂×Q₁₆	—	2	2	no	—
198	C₂×Q₁₆	—	2	2	no	—
199	C₂×Q₁₆	—	2	2	no	—
200	C₂×Q₁₆	—	2	2	no	—
201	C₂×Q₁₆	—	4	4	no	—
202	C₂×Q₁₆	—	4	4	no	—
203	#131	—	4	4	no	—
204	C₂×M₁₆	—	2	1	no	—
205	C₂×M₁₆	—	2	2	no	—
206	C₂²×C₈	—	2	2	no	—
207	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
208	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
209	C₄⋊Q₈	—	2	2	no	—
210	C₄⋊Q₈	—	2	2	no	—
211	C₄⋊Q₈	—	2	2	no	—
212	C₄⋊Q₈	D₄×C₁₁	1	1	yes	characteristic
213	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
214	#127	D₄×C₁₁	1	1	yes	characteristic
215	#124	—	2	1	no	—
216	#121	—	2	1	no	—
217	#121	D₄×C₁₁	1	2	yes	—
218	C₄×D₄	—	2	1	no	—
219	C₄×D₄	C₂³×C₁₁	1	2	yes	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
223	#107	—	2	8	no	—
224	C₄⋊C₈	—	2	1	no	—
225	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
226	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
227	#102	—	2	8	no	—
228	C₂²⋊C₈	—	2	2	no	—
229	C₂²⋊C₈	—	2	2	no	—
230	C₂²⋊C₈	—	2	2	no	—
231	C₄×C₈	—	2	2	no	—
232	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
233	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
234	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
235	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
236	C₂×C₁₁	—	2	2	no	—
237	C₂×C₁₁	—	8	2	no	—
238	C₂×C₁₁	C₂×#459	1	1	yes	characteristic
239	C₂×C₁₁	#3059	1	1	yes	characteristic
240	C₂×C₁₁	C₂×#473	1	1	yes	characteristic
241	#41	—	4	2	no	—
242	#41	—	4	2	no	—
243	C₂×Q₈	—	2	1	no	—
244	C₂×Q₈	—	2	4	no	—
245	C₂×Q₈	—	4	2	no	—
246	C₂×Q₈	—	4	4	no	—
247	C₂×Q₈	—	4	4	no	—
248	C₂×D₄	—	2	2	no	—
249	C₂×D₄	—	2	1	no	—
250	C₂×D₄	—	2	1	no	—
251	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
255	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
256	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
257	Q₁₆	—	4	4	no	—
258	Q₁₆	—	4	4	no	—
259	Q₁₆	—	4	4	no	—
260	Q₁₆	—	4	4	no	—
261	M₁₆	—	4	2	no	—
262	M₁₆	—	4	4	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	4	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	4	4	no	—
267	C₂×C₈	C₁₁×D₈	1	4	yes	—
268	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
269	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
270	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
271	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
272	C₄⋊C₄	—	2	1	no	—
273	C₄⋊C₄	—	2	4	no	—
274	C₄⋊C₄	—	2	4	no	—
275	C₄⋊C₄	—	4	2	no	—
276	C₄⋊C₄	—	4	2	no	—
277	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
278	C₂²⋊C₄	—	2	2	no	—
279	C₂²⋊C₄	—	2	2	no	—
280	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
281	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
282	C₄²	C₁₁×#41	1	1	yes	characteristic
283	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
284	C₁₁	#19188	1	1	yes	characteristic, direct product factor, Sylow
285	C₂³	—	2	2	no	—
286	C₂³	C₁₁×#121	1	1	yes	characteristic
287	Q₈	—	4	2	no	—
288	Q₈	—	4	4	no	—
289	Q₈	—	4	4	no	—
290	Q₈	—	8	4	no	—
291	D₄	—	2	4	no	—
292	D₄	—	4	4	no	—
293	D₄	—	4	2	no	—
294	D₄	—	4	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	—	4	2	no	—
300	C₂×C₄	—	4	4	no	—
301	C₂×C₄	—	8	4	no	—
302	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
303	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
304	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
305	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
306	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
307	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
308	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
309	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
310	C₈	—	2	1	no	—
311	C₈	—	2	1	no	—
312	C₈	—	4	2	no	—
313	C₈	—	4	4	no	—
314	C₈	C₂×C₁₁×D₈	1	2	yes	—
315	C₈	C₂×C₁₁×D₈	1	2	yes	—
316	C₂²	—	2	1	no	—
317	C₂²	—	2	1	no	—
318	C₂²	—	4	2	no	—
319	C₂²	—	4	2	no	—
320	C₂²	—	4	2	no	—
321	C₂²	C₁₁×#459	1	2	yes	—
322	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
323	C₄	—	2	1	no	—
324	C₄	—	2	1	no	—
325	C₄	—	4	2	no	—
326	C₄	—	8	4	no	—
327	C₄	C₁₁×#459	1	2	yes	—
328	C₄	C₁₁×#473	1	2	yes	—
329	C₄	C₂²×C₁₁×D₈	1	1	yes	characteristic
330	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
331	C₄	C₁₁×#578	1	2	yes	—
332	C₂	—	2	2	no	—
333	C₂	—	8	2	no	—
334	C₂	C₂×C₁₁×#459	1	1	yes	characteristic
335	C₂	C₁₁×#3059	1	1	yes	characteristic
336	C₂	C₂×C₁₁×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₁₁×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#494	C₂	semidirect
4. C₁₁×#1689	C₂	semidirect
5. C₁₁×#1669	C₂	semidirect
6. C₁₁×#1564	C₂	semidirect
7. C₁₁×#1546	C₂	semidirect
73. #19188	C₁₁	direct (N × H)
118. C₂×#494	C₂×C₁₁	semidirect
120. #1689	C₂×C₁₁	semidirect
121. #1669	C₂×C₁₁	semidirect
122. #1564	C₂×C₁₁	semidirect
123. #1546	C₂×C₁₁	semidirect
284. C₁₁	#19188	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#3226	2
C₂×C₁₁×#494	2
C₁₁×#2931	2
C₁₁×#1689	2
C₁₁×#1669	2
C₁₁×#1564	2
C₁₁×#1546	2
#19188	11

Subgroups — C11×#19188 #14596381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19188 #14596381