Subgroups — C₁₁×#11241 #14588434

Order 2816.

638 conjugacy classes of subgroups.

The subgroup lattice has 320 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×#424	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#344	C₂	1	2	yes	maximal
4	C₂×C₁₁×#341	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1733	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	2	yes	—
10	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
11	C₁₁×#427	—	2	4	no	—
12	C₂×C₁₁×#107	—	2	1	no	—
13	C₂×C₁₁×#106	—	2	1	no	—
14	C₁₁×#424	—	2	1	no	—
15	C₁₁×#424	—	2	1	no	—
16	C₁₁×#424	C₄	1	4	yes	complemented
17	C₂×C₁₁×C₄⋊C₈	—	2	2	no	—
18	C₁₁×#344	—	2	4	no	—
19	C₁₁×#341	—	2	2	no	—
20	C₁₁×#339	—	2	4	no	—
21	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
22	C₂×C₁₁×M₁₆	—	2	2	no	—
23	C₂×C₁₁×M₁₆	—	2	1	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	—	2	2	no	—
30	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
31	C₂×C₁₁×M₁₆	Q₈	1	4	yes	—
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	—	2	2	no	—
36	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
37	C₂²×C₈×C₁₁	D₄	1	2	yes	—
38	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
40	C₁₁×#117	—	2	1	no	—
41	C₁₁×#117	—	2	1	no	—
42	C₁₁×#117	—	2	2	no	—
43	C₁₁×#117	—	2	2	no	—
44	C₁₁×#117	—	2	2	no	—
45	C₁₁×#117	C₂×C₄	1	2	yes	—
46	C₁₁×#117	D₄	1	4	yes	—
47	C₁₁×#117	D₄	1	2	yes	—
48	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
49	C₂×C₁₁×C₄⋊C₄	Q₈	1	2	yes	—
50	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
51	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
52	C₂×C₄²×C₁₁	—	2	1	no	—
53	C₂×C₄²×C₁₁	—	2	2	no	—
54	C₁₁×#107	—	2	4	no	—
55	C₁₁×#106	—	2	4	no	—
56	C₁₁×C₄⋊C₈	—	2	4	no	—
57	C₁₁×C₄⋊C₈	—	2	4	no	—
58	#11241	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
59	C₂⁴×C₁₁	#41	1	1	yes	characteristic
60	C₂²×C₄×C₁₁	—	2	2	no	—
61	C₂²×C₄×C₁₁	—	4	2	no	—
62	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₁	C₂×D₄	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	2	yes	—
67	C₂²×C₄×C₁₁	C₂×Q₈	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	C₁₁×M₁₆	—	2	4	no	—
73	C₁₁×M₁₆	—	2	4	no	—
74	C₁₁×M₁₆	—	2	4	no	—
75	C₁₁×M₁₆	—	4	1	no	—
76	C₁₁×M₁₆	—	4	2	no	—
77	C₁₁×M₁₆	—	4	2	no	—
78	C₁₁×M₁₆	—	4	1	no	—
79	C₂×C₈×C₁₁	—	2	2	no	—
80	C₂×C₈×C₁₁	—	2	4	no	—
81	C₂×C₈×C₁₁	—	2	1	no	—
82	C₂×C₈×C₁₁	—	2	1	no	—
83	C₂×C₈×C₁₁	—	2	4	no	—
84	C₂×C₈×C₁₁	—	2	4	no	—
85	C₂×C₈×C₁₁	—	2	1	no	—
86	C₂×C₈×C₁₁	—	2	1	no	—
87	C₂×C₈×C₁₁	—	4	2	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	4	no	—
94	C₁₁×C₄⋊C₄	—	4	2	no	—
95	C₁₁×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
96	C₁₁×C₂²⋊C₄	—	2	2	no	—
97	C₁₁×C₂²⋊C₄	—	2	2	no	—
98	C₁₁×C₂²⋊C₄	—	2	4	no	—
99	C₁₁×C₂²⋊C₄	—	4	2	no	—
100	C₄²×C₁₁	—	2	2	no	—
101	C₄²×C₁₁	—	2	2	no	—
102	C₄²×C₁₁	—	2	4	no	—
103	C₄²×C₁₁	—	4	2	no	—
104	C₂×#427	C₂×C₁₁	1	1	yes	characteristic
105	C₂×#424	C₂×C₁₁	1	1	yes	characteristic
106	C₂×#344	C₂×C₁₁	1	2	yes	—
107	C₂×#341	C₂×C₁₁	1	1	yes	characteristic
108	#1733	C₂×C₁₁	1	2	yes	—
109	C₂³×C₁₁	—	4	2	no	—
110	C₂³×C₁₁	#117	1	1	yes	characteristic
111	C₂³×C₁₁	#121	1	1	yes	characteristic
112	C₂³×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
113	C₂³×C₁₁	#123	1	2	yes	—
114	C₂³×C₁₁	#125	1	2	yes	—
115	C₂×C₄×C₁₁	—	2	4	no	—
116	C₂×C₄×C₁₁	—	4	4	no	—
117	C₂×C₄×C₁₁	—	4	4	no	—
118	C₂×C₄×C₁₁	—	8	4	no	—
119	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
122	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
123	C₂×C₄×C₁₁	#120	1	1	yes	characteristic
124	C₂×C₄×C₁₁	#121	1	2	yes	—
125	C₂×C₄×C₁₁	#121	1	2	yes	—
126	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
127	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
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	1	yes	characteristic
131	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
132	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
133	C₂×C₄×C₁₁	#125	1	2	yes	—
134	C₂×C₄×C₁₁	#126	1	2	yes	—
135	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
136	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
137	C₈×C₁₁	—	2	2	no	—
138	C₈×C₁₁	—	2	2	no	—
139	C₈×C₁₁	—	4	2	no	—
140	C₈×C₁₁	—	4	4	no	—
141	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
142	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
143	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
144	C₂×#117	C₂²×C₁₁	1	2	yes	—
145	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
146	#427	—	2	4	no	—
147	C₂×#107	—	2	1	no	—
148	C₂×#106	—	2	1	no	—
149	#424	—	2	1	no	—
150	#424	—	2	1	no	—
151	#424	C₄×C₁₁	1	4	yes	complemented
152	C₂×C₄⋊C₈	—	2	2	no	—
153	#344	—	2	4	no	—
154	#341	—	2	2	no	—
155	#339	—	2	4	no	—
156	C₂²×C₁₁	—	2	2	no	—
157	C₂²×C₁₁	—	2	2	no	—
158	C₂²×C₁₁	—	2	2	no	—
159	C₂²×C₁₁	—	4	2	no	—
160	C₂²×C₁₁	—	4	2	no	—
161	C₂²×C₁₁	#380	1	1	yes	characteristic
162	C₂²×C₁₁	#387	1	2	yes	—
163	C₂²×C₁₁	#394	1	1	yes	characteristic
164	C₂²×C₁₁	#398	1	2	yes	—
165	C₂²×C₁₁	#398	1	1	yes	characteristic
166	C₄×C₁₁	—	4	4	no	—
167	C₄×C₁₁	—	8	4	no	—
168	C₄×C₁₁	#386	1	1	yes	characteristic
169	C₄×C₁₁	#389	1	2	yes	—
170	C₄×C₁₁	#391	1	1	yes	characteristic
171	C₄×C₁₁	#395	1	1	yes	characteristic
172	C₄×C₁₁	#396	1	2	yes	—
173	C₄×C₁₁	#400	1	1	yes	characteristic
174	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
175	C₂×M₁₆	—	2	2	no	—
176	C₂×M₁₆	—	2	1	no	—
177	C₂×M₁₆	—	2	2	no	—
178	C₂×M₁₆	—	2	2	no	—
179	C₂×M₁₆	—	2	2	no	—
180	C₂×M₁₆	—	2	2	no	—
181	C₂×M₁₆	—	2	2	no	—
182	C₂×M₁₆	—	2	2	no	—
183	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
184	C₂×M₁₆	Q₈×C₁₁	1	4	yes	—
185	C₂²×C₈	—	2	2	no	—
186	C₂²×C₈	—	2	2	no	—
187	C₂²×C₈	—	2	1	no	—
188	C₂²×C₈	—	2	2	no	—
189	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
190	C₂²×C₈	D₄×C₁₁	1	2	yes	—
191	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
192	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
193	#117	—	2	1	no	—
194	#117	—	2	1	no	—
195	#117	—	2	2	no	—
196	#117	—	2	2	no	—
197	#117	—	2	2	no	—
198	#117	C₂×C₄×C₁₁	1	2	yes	—
199	#117	D₄×C₁₁	1	4	yes	—
200	#117	D₄×C₁₁	1	2	yes	—
201	C₂×C₄⋊C₄	—	2	2	no	—
202	C₂×C₄⋊C₄	Q₈×C₁₁	1	2	yes	—
203	C₂×C₂²⋊C₄	—	2	1	no	—
204	C₂×C₂²⋊C₄	—	2	2	no	—
205	C₂×C₄²	—	2	1	no	—
206	C₂×C₄²	—	2	2	no	—
207	#107	—	2	4	no	—
208	#106	—	2	4	no	—
209	C₄⋊C₈	—	2	4	no	—
210	C₄⋊C₈	—	2	4	no	—
211	C₂×C₁₁	—	2	1	no	—
212	C₂×C₁₁	—	2	2	no	—
213	C₂×C₁₁	—	2	2	no	—
214	C₂×C₁₁	—	2	1	no	—
215	C₂×C₁₁	#1441	1	1	yes	characteristic
216	C₂×C₁₁	#1814	1	2	yes	—
217	C₂⁴	C₁₁×#41	1	1	yes	characteristic
218	C₂²×C₄	—	2	2	no	—
219	C₂²×C₄	—	4	2	no	—
220	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
221	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
222	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
223	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
224	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
225	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
226	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
227	C₂²×C₄	C₁₁×#41	1	2	yes	—
228	C₂²×C₄	C₁₁×#41	1	2	yes	—
229	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
230	M₁₆	—	2	4	no	—
231	M₁₆	—	2	4	no	—
232	M₁₆	—	2	4	no	—
233	M₁₆	—	4	1	no	—
234	M₁₆	—	4	2	no	—
235	M₁₆	—	4	2	no	—
236	M₁₆	—	4	1	no	—
237	C₂×C₈	—	2	4	no	—
238	C₂×C₈	—	2	1	no	—
239	C₂×C₈	—	2	1	no	—
240	C₂×C₈	—	2	4	no	—
241	C₂×C₈	—	2	1	no	—
242	C₂×C₈	—	2	1	no	—
243	C₂×C₈	—	2	2	no	—
244	C₂×C₈	—	2	4	no	—
245	C₂×C₈	—	4	2	no	—
246	C₂×C₈	—	4	2	no	—
247	C₂×C₈	—	4	2	no	—
248	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
249	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
250	C₄⋊C₄	—	2	2	no	—
251	C₄⋊C₄	—	2	4	no	—
252	C₄⋊C₄	—	4	2	no	—
253	C₄⋊C₄	C₁₁×C₄⋊C₄	1	4	yes	—
254	C₂²⋊C₄	—	2	2	no	—
255	C₂²⋊C₄	—	2	2	no	—
256	C₂²⋊C₄	—	2	4	no	—
257	C₂²⋊C₄	—	4	2	no	—
258	C₄²	—	2	2	no	—
259	C₄²	—	2	2	no	—
260	C₄²	—	2	4	no	—
261	C₄²	—	4	2	no	—
262	C₁₁	#11241	1	1	yes	characteristic, direct product factor, Sylow
263	C₂³	—	4	2	no	—
264	C₂³	C₁₁×#117	1	1	yes	characteristic
265	C₂³	C₁₁×#121	1	1	yes	characteristic
266	C₂³	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
267	C₂³	C₁₁×#123	1	2	yes	—
268	C₂³	C₁₁×#125	1	2	yes	—
269	C₂×C₄	—	2	4	no	—
270	C₂×C₄	—	4	4	no	—
271	C₂×C₄	—	4	4	no	—
272	C₂×C₄	—	8	4	no	—
273	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
275	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
276	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
277	C₂×C₄	C₁₁×#120	1	1	yes	characteristic
278	C₂×C₄	C₁₁×#121	1	2	yes	—
279	C₂×C₄	C₁₁×#121	1	2	yes	—
280	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
281	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
282	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
283	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
284	C₂×C₄	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
285	C₂×C₄	C₁₁×#123	1	1	yes	characteristic
286	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
287	C₂×C₄	C₁₁×#125	1	2	yes	—
288	C₂×C₄	C₁₁×#126	1	2	yes	—
289	C₂×C₄	C₁₁×C₄⋊Q₈	1	2	yes	—
290	C₂×C₄	C₁₁×C₄⋊Q₈	1	1	yes	characteristic
291	C₈	—	2	2	no	—
292	C₈	—	2	2	no	—
293	C₈	—	4	2	no	—
294	C₈	—	4	4	no	—
295	C₂²	—	2	2	no	—
296	C₂²	—	2	2	no	—
297	C₂²	—	2	2	no	—
298	C₂²	—	4	2	no	—
299	C₂²	—	4	2	no	—
300	C₂²	C₁₁×#380	1	1	yes	characteristic
301	C₂²	C₁₁×#387	1	2	yes	—
302	C₂²	C₁₁×#394	1	1	yes	characteristic
303	C₂²	C₁₁×#398	1	2	yes	—
304	C₂²	C₁₁×#398	1	1	yes	characteristic
305	C₄	—	4	4	no	—
306	C₄	—	8	4	no	—
307	C₄	C₁₁×#386	1	1	yes	characteristic
308	C₄	C₁₁×#389	1	2	yes	—
309	C₄	C₁₁×#391	1	1	yes	characteristic
310	C₄	C₁₁×#395	1	1	yes	characteristic
311	C₄	C₁₁×#396	1	2	yes	—
312	C₄	C₁₁×#400	1	1	yes	characteristic
313	C₂	—	2	1	no	—
314	C₂	—	2	2	no	—
315	C₂	—	2	2	no	—
316	C₂	—	2	1	no	—
317	C₂	C₁₁×#1441	1	1	yes	characteristic
318	C₂	C₁₁×#1814	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	#121
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
socle	C₂²×C₁₁	#380
prime radical	C₂⁴×C₁₁	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
16. C₁₁×#424	C₄	semidirect
58. #11241	C₁₁	direct (N × H)
151. #424	C₄×C₁₁	semidirect
262. C₁₁	#11241	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×#424	2
C₂×C₁₁×#344	2
C₂×C₁₁×#341	2
C₁₁×#1733	2
#11241	11

Subgroups — C11×#11241 #14588434

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11241 #14588434