Subgroups — C₁₁×#11239 #14588432

Order 2816.

682 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×#107	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#424	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#343	C₂	1	2	yes	maximal
4	C₂×C₁₁×#341	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1736	C₂	1	2	yes	maximal
6	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
7	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
8	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
10	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₁₁×#107	—	2	2	no	—
12	C₂×C₁₁×#107	—	2	4	no	—
13	C₁₁×#424	—	2	2	no	—
14	C₁₁×#424	C₄	1	4	yes	complemented
15	C₂×C₁₁×C₄⋊C₈	—	2	2	no	—
16	C₁₁×#343	—	2	4	no	—
17	C₁₁×#341	—	2	2	no	—
18	C₁₁×#340	—	2	4	no	—
19	C₂³×C₄×C₁₁	—	2	2	no	—
20	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
21	C₂×C₁₁×M₁₆	—	2	1	no	—
22	C₂×C₁₁×M₁₆	—	2	2	no	—
23	C₂×C₁₁×M₁₆	—	2	2	no	—
24	C₂×C₁₁×M₁₆	—	2	2	no	—
25	C₂×C₁₁×M₁₆	—	2	2	no	—
26	C₂×C₁₁×M₁₆	—	2	2	no	—
27	C₂×C₁₁×M₁₆	—	2	2	no	—
28	C₂×C₁₁×M₁₆	—	2	2	no	—
29	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
30	C₂×C₁₁×M₁₆	Q₈	1	4	yes	—
31	C₂²×C₈×C₁₁	—	2	2	no	—
32	C₂²×C₈×C₁₁	—	2	2	no	—
33	C₂²×C₈×C₁₁	—	2	2	no	—
34	C₂²×C₈×C₁₁	—	2	1	no	—
35	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₁₁	D₄	1	2	yes	—
37	C₂²×C₈×C₁₁	D₄	1	2	yes	—
38	C₁₁×#117	—	2	1	no	—
39	C₁₁×#117	—	2	1	no	—
40	C₁₁×#117	C₂×C₄	1	2	yes	—
41	C₁₁×#117	Q₈	1	2	yes	—
42	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
43	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
44	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
45	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
46	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
47	C₂×C₁₁×C₄⋊C₄	D₄	1	4	yes	—
48	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
49	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
50	C₂×C₄²×C₁₁	—	2	1	no	—
51	C₁₁×#107	—	2	8	no	—
52	C₁₁×C₄⋊C₈	—	2	8	no	—
53	#11239	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂⁴×C₁₁	#41	1	1	yes	characteristic
55	C₂²×C₄×C₁₁	—	2	2	no	—
56	C₂²×C₄×C₁₁	—	2	4	no	—
57	C₂²×C₄×C₁₁	—	4	2	no	—
58	C₂²×C₄×C₁₁	—	4	2	no	—
59	C₂²×C₄×C₁₁	—	8	4	no	—
60	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
65	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
66	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
67	C₂²×C₄×C₁₁	#41	1	2	yes	—
68	C₂²×C₄×C₁₁	#41	1	2	yes	—
69	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
70	C₁₁×M₁₆	—	2	4	no	—
71	C₁₁×M₁₆	—	2	4	no	—
72	C₁₁×M₁₆	—	2	4	no	—
73	C₁₁×M₁₆	—	4	2	no	—
74	C₁₁×M₁₆	—	4	2	no	—
75	C₁₁×M₁₆	—	4	2	no	—
76	C₂×C₈×C₁₁	—	2	2	no	—
77	C₂×C₈×C₁₁	—	2	4	no	—
78	C₂×C₈×C₁₁	—	2	2	no	—
79	C₂×C₈×C₁₁	—	2	4	no	—
80	C₂×C₈×C₁₁	—	2	4	no	—
81	C₂×C₈×C₁₁	—	2	2	no	—
82	C₂×C₈×C₁₁	—	4	1	no	—
83	C₂×C₈×C₁₁	—	4	2	no	—
84	C₂×C₈×C₁₁	—	4	2	no	—
85	C₂×C₈×C₁₁	—	4	1	no	—
86	C₂×C₈×C₁₁	C₂²⋊C₄	1	4	yes	—
87	C₁₁×C₄⋊C₄	—	2	2	no	—
88	C₁₁×C₄⋊C₄	—	2	4	no	—
89	C₁₁×C₄⋊C₄	—	2	4	no	—
90	C₁₁×C₄⋊C₄	—	4	2	no	—
91	C₁₁×C₄⋊C₄	—	4	2	no	—
92	C₁₁×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
93	C₁₁×C₂²⋊C₄	—	2	2	no	—
94	C₁₁×C₂²⋊C₄	—	2	2	no	—
95	C₄²×C₁₁	—	2	2	no	—
96	C₄²×C₁₁	—	2	2	no	—
97	C₂²×#107	C₂×C₁₁	1	1	yes	characteristic
98	C₂×#424	C₂×C₁₁	1	1	yes	characteristic
99	C₂×#343	C₂×C₁₁	1	2	yes	—
100	C₂×#341	C₂×C₁₁	1	1	yes	characteristic
101	#1736	C₂×C₁₁	1	2	yes	—
102	C₂³×C₁₁	—	2	2	no	—
103	C₂³×C₁₁	—	2	2	no	—
104	C₂³×C₁₁	#117	1	1	yes	characteristic
105	C₂³×C₁₁	#121	1	1	yes	characteristic
106	C₂³×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
107	C₂³×C₁₁	#123	1	2	yes	—
108	C₂³×C₁₁	#125	1	2	yes	—
109	C₂×C₄×C₁₁	—	2	4	no	—
110	C₂×C₄×C₁₁	—	4	2	no	—
111	C₂×C₄×C₁₁	—	4	2	no	—
112	C₂×C₄×C₁₁	—	4	4	no	—
113	C₂×C₄×C₁₁	—	8	4	no	—
114	C₂×C₄×C₁₁	—	8	4	no	—
115	C₂×C₄×C₁₁	—	8	4	no	—
116	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
117	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
119	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
120	C₂×C₄×C₁₁	#120	1	1	yes	characteristic
121	C₂×C₄×C₁₁	#121	1	2	yes	—
122	C₂×C₄×C₁₁	#121	1	2	yes	—
123	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
124	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
125	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
126	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
127	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
128	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
129	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
130	C₂×C₄×C₁₁	#125	1	2	yes	—
131	C₂×C₄×C₁₁	#126	1	2	yes	—
132	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
133	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
134	C₈×C₁₁	—	2	4	no	—
135	C₈×C₁₁	—	4	2	no	—
136	C₈×C₁₁	—	4	4	no	—
137	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
138	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
139	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
140	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
141	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
142	C₂×#107	—	2	2	no	—
143	C₂×#107	—	2	4	no	—
144	#424	—	2	2	no	—
145	#424	C₄×C₁₁	1	4	yes	complemented
146	C₂×C₄⋊C₈	—	2	2	no	—
147	#343	—	2	4	no	—
148	#341	—	2	2	no	—
149	#340	—	2	4	no	—
150	C₂²×C₁₁	—	2	2	no	—
151	C₂²×C₁₁	—	2	2	no	—
152	C₂²×C₁₁	—	2	4	no	—
153	C₂²×C₁₁	—	2	2	no	—
154	C₂²×C₁₁	—	2	2	no	—
155	C₂²×C₁₁	#380	1	1	yes	characteristic
156	C₂²×C₁₁	#387	1	2	yes	—
157	C₂²×C₁₁	#394	1	1	yes	characteristic
158	C₂²×C₁₁	#398	1	2	yes	—
159	C₂²×C₁₁	#398	1	1	yes	characteristic
160	C₂²×C₁₁	#472	1	2	yes	—
161	C₂²×C₁₁	#473	1	2	yes	—
162	C₄×C₁₁	—	4	4	no	—
163	C₄×C₁₁	—	8	4	no	—
164	C₄×C₁₁	#386	1	1	yes	characteristic
165	C₄×C₁₁	#389	1	2	yes	—
166	C₄×C₁₁	#391	1	1	yes	characteristic
167	C₄×C₁₁	#395	1	1	yes	characteristic
168	C₄×C₁₁	#396	1	2	yes	—
169	C₄×C₁₁	#400	1	1	yes	characteristic
170	C₂³×C₄	—	2	2	no	—
171	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
172	C₂×M₁₆	—	2	1	no	—
173	C₂×M₁₆	—	2	2	no	—
174	C₂×M₁₆	—	2	2	no	—
175	C₂×M₁₆	—	2	2	no	—
176	C₂×M₁₆	—	2	2	no	—
177	C₂×M₁₆	—	2	2	no	—
178	C₂×M₁₆	—	2	2	no	—
179	C₂×M₁₆	—	2	2	no	—
180	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
181	C₂×M₁₆	Q₈×C₁₁	1	4	yes	—
182	C₂²×C₈	—	2	2	no	—
183	C₂²×C₈	—	2	2	no	—
184	C₂²×C₈	—	2	2	no	—
185	C₂²×C₈	—	2	1	no	—
186	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
187	C₂²×C₈	D₄×C₁₁	1	2	yes	—
188	C₂²×C₈	D₄×C₁₁	1	2	yes	—
189	#117	—	2	1	no	—
190	#117	—	2	1	no	—
191	#117	C₂×C₄×C₁₁	1	2	yes	—
192	#117	Q₈×C₁₁	1	2	yes	—
193	C₂×C₄⋊C₄	—	2	2	no	—
194	C₂×C₄⋊C₄	—	2	2	no	—
195	C₂×C₄⋊C₄	—	2	2	no	—
196	C₂×C₄⋊C₄	—	2	2	no	—
197	C₂×C₄⋊C₄	—	2	2	no	—
198	C₂×C₄⋊C₄	D₄×C₁₁	1	4	yes	—
199	C₂×C₄⋊C₄	D₄×C₁₁	1	2	yes	—
200	C₂×C₂²⋊C₄	—	2	1	no	—
201	C₂×C₄²	—	2	1	no	—
202	#107	—	2	8	no	—
203	C₄⋊C₈	—	2	8	no	—
204	C₂×C₁₁	—	2	2	no	—
205	C₂×C₁₁	—	2	2	no	—
206	C₂×C₁₁	#1441	1	1	yes	characteristic
207	C₂×C₁₁	#1816	1	2	yes	—
208	C₂×C₁₁	#2045	1	1	yes	characteristic
209	C₂×C₁₁	#2047	1	1	yes	characteristic
210	C₂×C₁₁	#2089	1	2	yes	—
211	C₂⁴	C₁₁×#41	1	1	yes	characteristic
212	C₂²×C₄	—	2	2	no	—
213	C₂²×C₄	—	2	4	no	—
214	C₂²×C₄	—	4	2	no	—
215	C₂²×C₄	—	4	2	no	—
216	C₂²×C₄	—	8	4	no	—
217	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
218	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
219	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
220	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
221	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
222	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
223	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
224	C₂²×C₄	C₁₁×#41	1	2	yes	—
225	C₂²×C₄	C₁₁×#41	1	2	yes	—
226	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
227	M₁₆	—	2	4	no	—
228	M₁₆	—	2	4	no	—
229	M₁₆	—	2	4	no	—
230	M₁₆	—	4	2	no	—
231	M₁₆	—	4	2	no	—
232	M₁₆	—	4	2	no	—
233	C₂×C₈	—	2	4	no	—
234	C₂×C₈	—	2	2	no	—
235	C₂×C₈	—	2	4	no	—
236	C₂×C₈	—	2	2	no	—
237	C₂×C₈	—	2	2	no	—
238	C₂×C₈	—	2	4	no	—
239	C₂×C₈	—	4	1	no	—
240	C₂×C₈	—	4	2	no	—
241	C₂×C₈	—	4	2	no	—
242	C₂×C₈	—	4	1	no	—
243	C₂×C₈	C₁₁×C₂²⋊C₄	1	4	yes	—
244	C₄⋊C₄	—	2	2	no	—
245	C₄⋊C₄	—	2	4	no	—
246	C₄⋊C₄	—	2	4	no	—
247	C₄⋊C₄	—	4	2	no	—
248	C₄⋊C₄	—	4	2	no	—
249	C₄⋊C₄	C₁₁×C₄⋊C₄	1	4	yes	—
250	C₂²⋊C₄	—	2	2	no	—
251	C₂²⋊C₄	—	2	2	no	—
252	C₄²	—	2	2	no	—
253	C₄²	—	2	2	no	—
254	C₁₁	#11239	1	1	yes	characteristic, direct product factor, Sylow
255	C₂³	—	2	2	no	—
256	C₂³	—	2	2	no	—
257	C₂³	C₁₁×#117	1	1	yes	characteristic
258	C₂³	C₁₁×#121	1	1	yes	characteristic
259	C₂³	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
260	C₂³	C₁₁×#123	1	2	yes	—
261	C₂³	C₁₁×#125	1	2	yes	—
262	C₂×C₄	—	2	4	no	—
263	C₂×C₄	—	4	2	no	—
264	C₂×C₄	—	4	2	no	—
265	C₂×C₄	—	4	4	no	—
266	C₂×C₄	—	8	4	no	—
267	C₂×C₄	—	8	4	no	—
268	C₂×C₄	—	8	4	no	—
269	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
271	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
272	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
273	C₂×C₄	C₁₁×#120	1	1	yes	characteristic
274	C₂×C₄	C₁₁×#121	1	2	yes	—
275	C₂×C₄	C₁₁×#121	1	2	yes	—
276	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
277	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
278	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
279	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
280	C₂×C₄	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
281	C₂×C₄	C₁₁×#123	1	1	yes	characteristic
282	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
283	C₂×C₄	C₁₁×#125	1	2	yes	—
284	C₂×C₄	C₁₁×#126	1	2	yes	—
285	C₂×C₄	C₁₁×C₄⋊Q₈	1	2	yes	—
286	C₂×C₄	C₁₁×C₄⋊Q₈	1	1	yes	characteristic
287	C₈	—	2	4	no	—
288	C₈	—	4	2	no	—
289	C₈	—	4	4	no	—
290	C₂²	—	2	2	no	—
291	C₂²	—	2	2	no	—
292	C₂²	—	2	2	no	—
293	C₂²	—	2	2	no	—
294	C₂²	—	2	4	no	—
295	C₂²	C₁₁×#380	1	1	yes	characteristic
296	C₂²	C₁₁×#387	1	2	yes	—
297	C₂²	C₁₁×#394	1	1	yes	characteristic
298	C₂²	C₁₁×#398	1	2	yes	—
299	C₂²	C₁₁×#398	1	1	yes	characteristic
300	C₂²	C₁₁×#472	1	2	yes	—
301	C₂²	C₁₁×#473	1	2	yes	—
302	C₄	—	4	4	no	—
303	C₄	—	8	4	no	—
304	C₄	C₁₁×#386	1	1	yes	characteristic
305	C₄	C₁₁×#389	1	2	yes	—
306	C₄	C₁₁×#391	1	1	yes	characteristic
307	C₄	C₁₁×#395	1	1	yes	characteristic
308	C₄	C₁₁×#396	1	2	yes	—
309	C₄	C₁₁×#400	1	1	yes	characteristic
310	C₂	—	2	2	no	—
311	C₂	—	2	2	no	—
312	C₂	C₁₁×#1441	1	1	yes	characteristic
313	C₂	C₁₁×#1816	1	2	yes	—
314	C₂	C₁₁×#2045	1	1	yes	characteristic
315	C₂	C₁₁×#2047	1	1	yes	characteristic
316	C₂	C₁₁×#2089	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	#121
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₂⁴×C₁₁	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
14. C₁₁×#424	C₄	semidirect
53. #11239	C₁₁	direct (N × H)
145. #424	C₄×C₁₁	semidirect
254. C₁₁	#11239	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₁×#107	2
C₂×C₁₁×#424	2
C₂×C₁₁×#343	2
C₂×C₁₁×#341	2
C₁₁×#1736	2
#11239	11

Subgroups — C11×#11239 #14588432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11239 #14588432