Subgroups — C₁₁×#11376 #14588569

Order 2816.

654 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	C₂×C₁₁×#427	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#341	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#339	C₂	1	2	yes	maximal
4	C₁₁×#1729	C₂	1	2	yes	maximal
5	C₂×C₁₁×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
7	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×#117	C₂²	1	2	yes	—
10	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
11	C₁₁×#427	—	2	2	no	—
12	C₁₁×#427	—	2	2	no	—
13	C₂×C₁₁×#107	C₄	1	1	yes	characteristic, complemented
14	C₂×C₁₁×#107	C₄	1	1	yes	characteristic, complemented
15	C₂×C₁₁×#106	C₄	1	2	yes	complemented
16	C₁₁×#341	—	2	2	no	—
17	C₁₁×#339	—	2	4	no	—
18	C₁₁×#336	—	2	2	no	—
19	C₁₁×#336	—	2	4	no	—
20	C₂³×C₄×C₁₁	—	2	1	no	—
21	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
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	Q₈	1	4	yes	—
28	C₂²×C₈×C₁₁	—	2	2	no	—
29	C₂²×C₈×C₁₁	—	2	2	no	—
30	C₂²×C₈×C₁₁	—	2	1	no	—
31	C₂²×C₈×C₁₁	—	2	2	no	—
32	C₂²×C₈×C₁₁	—	2	1	no	—
33	C₂²×C₈×C₁₁	—	2	2	no	—
34	C₂²×C₈×C₁₁	—	2	2	no	—
35	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₁	D₄	1	2	yes	—
38	C₂²×C₈×C₁₁	D₄	1	2	yes	—
39	C₂²×C₈×C₁₁	D₄	1	2	yes	—
40	C₁₁×#117	—	2	2	no	—
41	C₁₁×#117	—	2	2	no	—
42	C₁₁×#117	—	2	2	no	—
43	C₁₁×#117	—	2	2	no	—
44	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
45	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
46	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
47	C₂×C₄²×C₁₁	—	2	2	no	—
48	C₂×C₄²×C₁₁	—	2	2	no	—
49	C₂×C₄²×C₁₁	—	2	1	no	—
50	C₂×C₄²×C₁₁	—	2	2	no	—
51	C₂×C₄²×C₁₁	D₄	1	2	yes	—
52	C₁₁×#107	—	2	2	no	—
53	C₁₁×#107	—	2	2	no	—
54	C₁₁×#106	—	2	4	no	—
55	#11376	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂⁴×C₁₁	#41	1	1	yes	characteristic
57	C₂²×C₄×C₁₁	—	2	4	no	—
58	C₂²×C₄×C₁₁	—	2	2	no	—
59	C₂²×C₄×C₁₁	—	2	2	no	—
60	C₂²×C₄×C₁₁	—	2	2	no	—
61	C₂²×C₄×C₁₁	—	4	2	no	—
62	C₂²×C₄×C₁₁	—	4	2	no	—
63	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
69	C₂²×C₄×C₁₁	#41	1	2	yes	—
70	C₂²×C₄×C₁₁	#41	1	2	yes	—
71	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
72	C₂²×C₄×C₁₁	#41	1	2	yes	—
73	C₁₁×M₁₆	—	2	4	no	—
74	C₁₁×M₁₆	—	2	4	no	—
75	C₁₁×M₁₆	—	4	2	no	—
76	C₁₁×M₁₆	—	4	2	no	—
77	C₂×C₈×C₁₁	—	2	2	no	—
78	C₂×C₈×C₁₁	—	2	2	no	—
79	C₂×C₈×C₁₁	—	2	2	no	—
80	C₂×C₈×C₁₁	—	2	4	no	—
81	C₂×C₈×C₁₁	—	2	2	no	—
82	C₂×C₈×C₁₁	—	2	2	no	—
83	C₂×C₈×C₁₁	—	2	4	no	—
84	C₂×C₈×C₁₁	—	2	4	no	—
85	C₂×C₈×C₁₁	—	4	1	no	—
86	C₂×C₈×C₁₁	—	4	2	no	—
87	C₂×C₈×C₁₁	—	4	1	no	—
88	C₂×C₈×C₁₁	—	4	2	no	—
89	C₂×C₈×C₁₁	—	4	2	no	—
90	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
91	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
92	C₁₁×C₄⋊C₄	—	2	2	no	—
93	C₁₁×C₄⋊C₄	—	2	2	no	—
94	C₁₁×C₄⋊C₄	—	2	2	no	—
95	C₁₁×C₄⋊C₄	—	2	2	no	—
96	C₁₁×C₂²⋊C₄	—	4	2	no	—
97	C₁₁×C₂²⋊C₄	—	4	2	no	—
98	C₄²×C₁₁	—	2	4	no	—
99	C₄²×C₁₁	—	4	2	no	—
100	C₄²×C₁₁	—	4	1	no	—
101	C₄²×C₁₁	—	4	1	no	—
102	C₄²×C₁₁	—	4	2	no	—
103	C₂×#427	C₂×C₁₁	1	1	yes	characteristic
104	C₂×#341	C₂×C₁₁	1	1	yes	characteristic
105	C₂×#339	C₂×C₁₁	1	2	yes	—
106	#1729	C₂×C₁₁	1	2	yes	—
107	C₂×#336	C₂×C₁₁	1	1	yes	characteristic
108	C₂³×C₁₁	—	2	2	no	—
109	C₂³×C₁₁	—	2	2	no	—
110	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
111	C₂³×C₁₁	#121	1	1	yes	characteristic
112	C₂³×C₁₁	#124	1	1	yes	characteristic
113	C₂³×C₁₁	#125	1	2	yes	—
114	C₂³×C₁₁	#126	1	2	yes	—
115	C₂×C₄×C₁₁	—	2	4	no	—
116	C₂×C₄×C₁₁	—	4	8	no	—
117	C₂×C₄×C₁₁	—	4	2	no	—
118	C₂×C₄×C₁₁	—	4	2	no	—
119	C₂×C₄×C₁₁	—	4	2	no	—
120	C₂×C₄×C₁₁	—	4	2	no	—
121	C₂×C₄×C₁₁	—	4	4	no	—
122	C₂×C₄×C₁₁	—	4	4	no	—
123	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₁₁	#117	1	2	yes	—
125	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
126	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
127	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
128	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
129	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
130	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
131	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
132	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
133	C₂×C₄×C₁₁	#123	1	2	yes	—
134	C₂×C₄×C₁₁	#123	1	2	yes	—
135	C₂×C₄×C₁₁	#123	1	2	yes	—
136	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
137	C₂×C₄×C₁₁	#125	1	2	yes	—
138	C₂×C₄×C₁₁	#126	1	2	yes	—
139	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
140	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
141	C₈×C₁₁	—	2	2	no	—
142	C₈×C₁₁	—	2	2	no	—
143	C₈×C₁₁	—	4	2	no	—
144	C₈×C₁₁	—	4	4	no	—
145	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
146	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
147	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
148	C₂×#117	C₂²×C₁₁	1	2	yes	—
149	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
150	#427	—	2	2	no	—
151	#427	—	2	2	no	—
152	C₂×#107	C₄×C₁₁	1	1	yes	characteristic, complemented
153	C₂×#107	C₄×C₁₁	1	1	yes	characteristic, complemented
154	C₂×#106	C₄×C₁₁	1	2	yes	complemented
155	#341	—	2	2	no	—
156	#339	—	2	4	no	—
157	#336	—	2	2	no	—
158	#336	—	2	4	no	—
159	C₂²×C₁₁	—	2	4	no	—
160	C₂²×C₁₁	—	2	4	no	—
161	C₂²×C₁₁	—	2	1	no	—
162	C₂²×C₁₁	—	2	1	no	—
163	C₂²×C₁₁	—	2	1	no	—
164	C₂²×C₁₁	—	2	1	no	—
165	C₂²×C₁₁	#387	1	2	yes	—
166	C₂²×C₁₁	#390	1	1	yes	characteristic
167	C₂²×C₁₁	#397	1	1	yes	characteristic
168	C₂²×C₁₁	#398	1	1	yes	characteristic
169	C₂²×C₁₁	#400	1	2	yes	—
170	C₂²×C₁₁	#443	1	2	yes	—
171	C₂²×C₁₁	#444	1	2	yes	—
172	C₄×C₁₁	—	4	4	no	—
173	C₄×C₁₁	—	8	2	no	—
174	C₄×C₁₁	—	8	2	no	—
175	C₄×C₁₁	#381	1	1	yes	characteristic
176	C₄×C₁₁	#387	1	2	yes	—
177	C₄×C₁₁	#391	1	1	yes	characteristic
178	C₄×C₁₁	#397	1	1	yes	characteristic
179	C₄×C₁₁	#398	1	1	yes	characteristic
180	C₄×C₁₁	#399	1	2	yes	—
181	C₂³×C₄	—	2	1	no	—
182	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
183	C₂×M₁₆	—	2	2	no	—
184	C₂×M₁₆	—	2	2	no	—
185	C₂×M₁₆	—	2	2	no	—
186	C₂×M₁₆	—	2	2	no	—
187	C₂×M₁₆	—	2	2	no	—
188	C₂×M₁₆	Q₈×C₁₁	1	4	yes	—
189	C₂²×C₈	—	2	2	no	—
190	C₂²×C₈	—	2	2	no	—
191	C₂²×C₈	—	2	1	no	—
192	C₂²×C₈	—	2	2	no	—
193	C₂²×C₈	—	2	1	no	—
194	C₂²×C₈	—	2	2	no	—
195	C₂²×C₈	—	2	2	no	—
196	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
197	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
198	C₂²×C₈	D₄×C₁₁	1	2	yes	—
199	C₂²×C₈	D₄×C₁₁	1	2	yes	—
200	C₂²×C₈	D₄×C₁₁	1	2	yes	—
201	#117	—	2	2	no	—
202	#117	—	2	2	no	—
203	#117	—	2	2	no	—
204	#117	—	2	2	no	—
205	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
206	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
207	C₂×C₂²⋊C₄	—	2	2	no	—
208	C₂×C₄²	—	2	2	no	—
209	C₂×C₄²	—	2	2	no	—
210	C₂×C₄²	—	2	2	no	—
211	C₂×C₄²	—	2	1	no	—
212	C₂×C₄²	D₄×C₁₁	1	2	yes	—
213	#107	—	2	2	no	—
214	#107	—	2	2	no	—
215	#106	—	2	4	no	—
216	C₂×C₁₁	—	2	1	no	—
217	C₂×C₁₁	—	2	1	no	—
218	C₂×C₁₁	—	2	2	no	—
219	C₂×C₁₁	#1445	1	1	yes	characteristic
220	C₂×C₁₁	#1922	1	4	yes	—
221	C₂×C₁₁	#1974	1	1	yes	characteristic
222	C₂×C₁₁	#1975	1	1	yes	characteristic
223	C₂⁴	C₁₁×#41	1	1	yes	characteristic
224	C₂²×C₄	—	2	4	no	—
225	C₂²×C₄	—	2	2	no	—
226	C₂²×C₄	—	2	2	no	—
227	C₂²×C₄	—	2	2	no	—
228	C₂²×C₄	—	4	2	no	—
229	C₂²×C₄	—	4	2	no	—
230	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
231	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
232	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
233	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
234	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
235	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
236	C₂²×C₄	C₁₁×#41	1	2	yes	—
237	C₂²×C₄	C₁₁×#41	1	2	yes	—
238	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
239	C₂²×C₄	C₁₁×#41	1	2	yes	—
240	M₁₆	—	2	4	no	—
241	M₁₆	—	2	4	no	—
242	M₁₆	—	4	2	no	—
243	M₁₆	—	4	2	no	—
244	C₂×C₈	—	2	2	no	—
245	C₂×C₈	—	2	2	no	—
246	C₂×C₈	—	2	2	no	—
247	C₂×C₈	—	2	2	no	—
248	C₂×C₈	—	2	4	no	—
249	C₂×C₈	—	2	2	no	—
250	C₂×C₈	—	2	4	no	—
251	C₂×C₈	—	2	4	no	—
252	C₂×C₈	—	4	1	no	—
253	C₂×C₈	—	4	2	no	—
254	C₂×C₈	—	4	1	no	—
255	C₂×C₈	—	4	2	no	—
256	C₂×C₈	—	4	2	no	—
257	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
258	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
259	C₄⋊C₄	—	2	2	no	—
260	C₄⋊C₄	—	2	2	no	—
261	C₄⋊C₄	—	2	2	no	—
262	C₄⋊C₄	—	2	2	no	—
263	C₂²⋊C₄	—	4	2	no	—
264	C₂²⋊C₄	—	4	2	no	—
265	C₄²	—	2	4	no	—
266	C₄²	—	4	2	no	—
267	C₄²	—	4	1	no	—
268	C₄²	—	4	1	no	—
269	C₄²	—	4	2	no	—
270	C₁₁	#11376	1	1	yes	characteristic, direct product factor, Sylow
271	C₂³	—	2	2	no	—
272	C₂³	—	2	2	no	—
273	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
274	C₂³	C₁₁×#121	1	1	yes	characteristic
275	C₂³	C₁₁×#124	1	1	yes	characteristic
276	C₂³	C₁₁×#125	1	2	yes	—
277	C₂³	C₁₁×#126	1	2	yes	—
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	4	8	no	—
280	C₂×C₄	—	4	2	no	—
281	C₂×C₄	—	4	2	no	—
282	C₂×C₄	—	4	2	no	—
283	C₂×C₄	—	4	2	no	—
284	C₂×C₄	—	4	4	no	—
285	C₂×C₄	—	4	4	no	—
286	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
287	C₂×C₄	C₁₁×#117	1	2	yes	—
288	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
289	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
290	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
291	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
292	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
293	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
294	C₂×C₄	C₁₁×#123	1	1	yes	characteristic
295	C₂×C₄	C₁₁×#123	1	1	yes	characteristic
296	C₂×C₄	C₁₁×#123	1	2	yes	—
297	C₂×C₄	C₁₁×#123	1	2	yes	—
298	C₂×C₄	C₁₁×#123	1	2	yes	—
299	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
300	C₂×C₄	C₁₁×#125	1	2	yes	—
301	C₂×C₄	C₁₁×#126	1	2	yes	—
302	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
303	C₂×C₄	C₁₁×C₄⋊Q₈	1	1	yes	characteristic
304	C₈	—	2	2	no	—
305	C₈	—	2	2	no	—
306	C₈	—	4	2	no	—
307	C₈	—	4	4	no	—
308	C₂²	—	2	4	no	—
309	C₂²	—	2	4	no	—
310	C₂²	—	2	1	no	—
311	C₂²	—	2	1	no	—
312	C₂²	—	2	1	no	—
313	C₂²	—	2	1	no	—
314	C₂²	C₁₁×#387	1	2	yes	—
315	C₂²	C₁₁×#390	1	1	yes	characteristic
316	C₂²	C₁₁×#397	1	1	yes	characteristic
317	C₂²	C₁₁×#398	1	1	yes	characteristic
318	C₂²	C₁₁×#400	1	2	yes	—
319	C₂²	C₁₁×#443	1	2	yes	—
320	C₂²	C₁₁×#444	1	2	yes	—
321	C₄	—	4	4	no	—
322	C₄	—	8	2	no	—
323	C₄	—	8	2	no	—
324	C₄	C₁₁×#381	1	1	yes	characteristic
325	C₄	C₁₁×#387	1	2	yes	—
326	C₄	C₁₁×#391	1	1	yes	characteristic
327	C₄	C₁₁×#397	1	1	yes	characteristic
328	C₄	C₁₁×#398	1	1	yes	characteristic
329	C₄	C₁₁×#399	1	2	yes	—
330	C₂	—	2	1	no	—
331	C₂	—	2	1	no	—
332	C₂	—	2	2	no	—
333	C₂	C₁₁×#1445	1	1	yes	characteristic
334	C₂	C₁₁×#1922	1	4	yes	—
335	C₂	C₁₁×#1974	1	1	yes	characteristic
336	C₂	C₁₁×#1975	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
socle	C₂³×C₁₁	C₄×D₄
prime radical	C₂⁴×C₁₁	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁ ◁ C₂³×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₂×C₁₁×#107	C₄	semidirect
14. C₂×C₁₁×#107	C₄	semidirect
15. C₂×C₁₁×#106	C₄	semidirect
55. #11376	C₁₁	direct (N × H)
152. C₂×#107	C₄×C₁₁	semidirect
153. C₂×#107	C₄×C₁₁	semidirect
154. C₂×#106	C₄×C₁₁	semidirect
270. C₁₁	#11376	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#427	2
C₂×C₁₁×#341	2
C₂×C₁₁×#339	2
C₁₁×#1729	2
C₂×C₁₁×#336	2
#11376	11

Subgroups — C11×#11376 #14588569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11376 #14588569