Subgroups — C₁₁×#11244 #14588437

Order 2816.

670 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#430	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#344	C₂	1	2	yes	maximal
4	C₂×C₁₁×#339	C₂	1	2	yes	maximal
5	C₂×C₁₁×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
7	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
8	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×#117	C₂²	1	2	yes	—
10	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
11	C₁₁×#430	—	2	4	no	—
12	C₂×C₁₁×#108	—	2	2	no	—
13	C₁₁×#423	—	2	2	no	—
14	C₁₁×#423	C₄	1	4	yes	complemented
15	C₂×C₁₁×C₄⋊C₈	—	2	2	no	—
16	C₁₁×#344	—	2	4	no	—
17	C₁₁×#339	—	2	4	no	—
18	C₁₁×H(3,ℤ/4)	—	2	2	no	—
19	C₂³×C₄×C₁₁	—	2	1	no	—
20	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
21	C₂×C₁₁×M₁₆	—	2	2	no	—
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	—	2	2	no	—
31	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
32	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
33	C₂×C₁₁×M₁₆	D₄	1	4	yes	—
34	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
35	C₂²×C₈×C₁₁	—	2	1	no	—
36	C₂²×C₈×C₁₁	—	2	2	no	—
37	C₂²×C₈×C₁₁	D₄	1	2	yes	—
38	C₁₁×#117	—	2	2	no	—
39	C₁₁×#117	—	2	2	no	—
40	C₁₁×#117	—	2	2	no	—
41	C₁₁×#117	Q₈	1	4	yes	—
42	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
43	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
44	C₂×C₄²×C₁₁	—	2	1	no	—
45	C₂×C₄²×C₁₁	—	2	1	no	—
46	C₂×C₄²×C₁₁	—	2	1	no	—
47	C₂×C₄²×C₁₁	—	2	2	no	—
48	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₁₁	D₄	1	2	yes	—
50	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
51	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
52	C₁₁×#108	—	2	8	no	—
53	C₁₁×C₄⋊C₈	—	2	8	no	—
54	#11244	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₂⁴×C₁₁	#41	1	1	yes	characteristic
56	C₂²×C₄×C₁₁	—	2	1	no	—
57	C₂²×C₄×C₁₁	—	2	2	no	—
58	C₂²×C₄×C₁₁	—	2	2	no	—
59	C₂²×C₄×C₁₁	—	2	1	no	—
60	C₂²×C₄×C₁₁	—	4	4	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	—	2	4	no	—
76	C₁₁×M₁₆	—	2	4	no	—
77	C₁₁×M₁₆	—	4	2	no	—
78	C₁₁×M₁₆	—	4	2	no	—
79	C₁₁×M₁₆	—	4	2	no	—
80	C₂×C₈×C₁₁	—	2	2	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	—	4	1	no	—
85	C₂×C₈×C₁₁	—	4	2	no	—
86	C₂×C₈×C₁₁	—	4	1	no	—
87	C₂×C₈×C₁₁	—	4	2	no	—
88	C₂×C₈×C₁₁	C₂²⋊C₄	1	4	yes	—
89	C₁₁×C₄⋊C₄	—	2	4	no	—
90	C₁₁×C₄⋊C₄	—	4	2	no	—
91	C₁₁×C₂²⋊C₄	—	2	4	no	—
92	C₁₁×C₂²⋊C₄	—	4	2	no	—
93	C₄²×C₁₁	—	2	2	no	—
94	C₄²×C₁₁	—	2	2	no	—
95	C₄²×C₁₁	—	2	1	no	—
96	C₄²×C₁₁	—	2	1	no	—
97	C₄²×C₁₁	—	2	4	no	—
98	C₄²×C₁₁	—	4	2	no	—
99	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
100	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
101	C₂×#430	C₂×C₁₁	1	1	yes	characteristic
102	C₂×#423	C₂×C₁₁	1	1	yes	characteristic
103	C₂×#344	C₂×C₁₁	1	2	yes	—
104	C₂×#339	C₂×C₁₁	1	2	yes	—
105	C₂×H(3,ℤ/4)	C₂×C₁₁	1	1	yes	characteristic
106	C₂³×C₁₁	—	4	2	no	—
107	C₂³×C₁₁	#117	1	1	yes	characteristic
108	C₂³×C₁₁	#121	1	1	yes	characteristic
109	C₂³×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
110	C₂³×C₁₁	C₂²⋊Q₈	1	2	yes	—
111	C₂³×C₁₁	#126	1	2	yes	—
112	C₂×C₄×C₁₁	—	2	4	no	—
113	C₂×C₄×C₁₁	—	2	2	no	—
114	C₂×C₄×C₁₁	—	2	2	no	—
115	C₂×C₄×C₁₁	—	4	4	no	—
116	C₂×C₄×C₁₁	—	4	4	no	—
117	C₂×C₄×C₁₁	—	4	2	no	—
118	C₂×C₄×C₁₁	—	4	4	no	—
119	C₂×C₄×C₁₁	—	8	4	no	—
120	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
123	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
124	C₂×C₄×C₁₁	#120	1	1	yes	characteristic
125	C₂×C₄×C₁₁	#121	1	2	yes	—
126	C₂×C₄×C₁₁	#121	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	1	yes	characteristic
131	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
132	C₂×C₄×C₁₁	#123	1	2	yes	—
133	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
134	C₂×C₄×C₁₁	#125	1	2	yes	—
135	C₂×C₄×C₁₁	#125	1	2	yes	—
136	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
137	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
138	C₈×C₁₁	—	2	4	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	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
144	C₂×#117	C₂²×C₁₁	1	2	yes	—
145	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
146	#430	—	2	4	no	—
147	C₂×#108	—	2	2	no	—
148	#423	—	2	2	no	—
149	#423	C₄×C₁₁	1	4	yes	complemented
150	C₂×C₄⋊C₈	—	2	2	no	—
151	#344	—	2	4	no	—
152	#339	—	2	4	no	—
153	H(3,ℤ/4)	—	2	2	no	—
154	C₂²×C₁₁	—	2	2	no	—
155	C₂²×C₁₁	—	2	4	no	—
156	C₂²×C₁₁	—	4	1	no	—
157	C₂²×C₁₁	—	4	1	no	—
158	C₂²×C₁₁	—	4	2	no	—
159	C₂²×C₁₁	#380	1	1	yes	characteristic
160	C₂²×C₁₁	#387	1	2	yes	—
161	C₂²×C₁₁	#395	1	1	yes	characteristic
162	C₂²×C₁₁	#396	1	2	yes	—
163	C₂²×C₁₁	#400	1	1	yes	characteristic
164	C₄×C₁₁	—	2	4	no	—
165	C₄×C₁₁	—	4	2	no	—
166	C₄×C₁₁	—	8	4	no	—
167	C₄×C₁₁	#386	1	1	yes	characteristic
168	C₄×C₁₁	#389	1	2	yes	—
169	C₄×C₁₁	#391	1	1	yes	characteristic
170	C₄×C₁₁	#394	1	1	yes	characteristic
171	C₄×C₁₁	#398	1	2	yes	—
172	C₄×C₁₁	#398	1	1	yes	characteristic
173	C₂³×C₄	—	2	1	no	—
174	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
175	C₂×M₁₆	—	2	2	no	—
176	C₂×M₁₆	—	2	2	no	—
177	C₂×M₁₆	—	2	1	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	—	2	2	no	—
184	C₂×M₁₆	—	2	2	no	—
185	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
186	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
187	C₂×M₁₆	D₄×C₁₁	1	4	yes	—
188	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
189	C₂²×C₈	—	2	1	no	—
190	C₂²×C₈	—	2	2	no	—
191	C₂²×C₈	D₄×C₁₁	1	2	yes	—
192	#117	—	2	2	no	—
193	#117	—	2	2	no	—
194	#117	—	2	2	no	—
195	#117	Q₈×C₁₁	1	4	yes	—
196	C₂×C₄⋊C₄	—	2	2	no	—
197	C₂×C₂²⋊C₄	—	2	2	no	—
198	C₂×C₄²	—	2	1	no	—
199	C₂×C₄²	—	2	1	no	—
200	C₂×C₄²	—	2	1	no	—
201	C₂×C₄²	—	2	2	no	—
202	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
203	C₂×C₄²	D₄×C₁₁	1	2	yes	—
204	C₂×C₄²	Q₈×C₁₁	1	1	yes	characteristic
205	C₂×C₄²	Q₈×C₁₁	1	1	yes	characteristic
206	#108	—	2	8	no	—
207	C₄⋊C₈	—	2	8	no	—
208	C₂×C₁₁	—	2	1	no	—
209	C₂×C₁₁	—	2	2	no	—
210	C₂×C₁₁	—	2	2	no	—
211	C₂×C₁₁	—	2	1	no	—
212	C₂×C₁₁	#1441	1	1	yes	characteristic
213	C₂×C₁₁	#2102	1	2	yes	—
214	C₂⁴	C₁₁×#41	1	1	yes	characteristic
215	C₂²×C₄	—	2	1	no	—
216	C₂²×C₄	—	2	2	no	—
217	C₂²×C₄	—	2	2	no	—
218	C₂²×C₄	—	2	1	no	—
219	C₂²×C₄	—	4	4	no	—
220	C₂²×C₄	—	4	2	no	—
221	C₂²×C₄	C₂²×C₄×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	1	yes	characteristic
225	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
226	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
227	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
228	C₂²×C₄	C₁₁×#41	1	2	yes	—
229	C₂²×C₄	C₁₁×#41	1	2	yes	—
230	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
231	M₁₆	—	2	4	no	—
232	M₁₆	—	2	4	no	—
233	M₁₆	—	2	4	no	—
234	M₁₆	—	2	4	no	—
235	M₁₆	—	2	4	no	—
236	M₁₆	—	4	2	no	—
237	M₁₆	—	4	2	no	—
238	M₁₆	—	4	2	no	—
239	C₂×C₈	—	2	2	no	—
240	C₂×C₈	—	2	2	no	—
241	C₂×C₈	—	2	2	no	—
242	C₂×C₈	—	2	4	no	—
243	C₂×C₈	—	4	1	no	—
244	C₂×C₈	—	4	2	no	—
245	C₂×C₈	—	4	1	no	—
246	C₂×C₈	—	4	2	no	—
247	C₂×C₈	C₁₁×C₂²⋊C₄	1	4	yes	—
248	C₄⋊C₄	—	2	4	no	—
249	C₄⋊C₄	—	4	2	no	—
250	C₂²⋊C₄	—	2	4	no	—
251	C₂²⋊C₄	—	4	2	no	—
252	C₄²	—	2	2	no	—
253	C₄²	—	2	2	no	—
254	C₄²	—	2	1	no	—
255	C₄²	—	2	1	no	—
256	C₄²	—	2	4	no	—
257	C₄²	—	4	2	no	—
258	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
259	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
260	C₁₁	#11244	1	1	yes	characteristic, direct product factor, Sylow
261	C₂³	—	4	2	no	—
262	C₂³	C₁₁×#117	1	1	yes	characteristic
263	C₂³	C₁₁×#121	1	1	yes	characteristic
264	C₂³	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
265	C₂³	C₁₁×C₂²⋊Q₈	1	2	yes	—
266	C₂³	C₁₁×#126	1	2	yes	—
267	C₂×C₄	—	2	4	no	—
268	C₂×C₄	—	2	2	no	—
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	4	4	no	—
271	C₂×C₄	—	4	4	no	—
272	C₂×C₄	—	4	2	no	—
273	C₂×C₄	—	4	4	no	—
274	C₂×C₄	—	8	4	no	—
275	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
277	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
278	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
279	C₂×C₄	C₁₁×#120	1	1	yes	characteristic
280	C₂×C₄	C₁₁×#121	1	2	yes	—
281	C₂×C₄	C₁₁×#121	1	2	yes	—
282	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
283	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
284	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
285	C₂×C₄	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
286	C₂×C₄	C₁₁×#123	1	1	yes	characteristic
287	C₂×C₄	C₁₁×#123	1	2	yes	—
288	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
289	C₂×C₄	C₁₁×#125	1	2	yes	—
290	C₂×C₄	C₁₁×#125	1	2	yes	—
291	C₂×C₄	C₁₁×C₄⋊Q₈	1	2	yes	—
292	C₂×C₄	C₁₁×C₄⋊Q₈	1	1	yes	characteristic
293	C₈	—	2	4	no	—
294	C₈	—	4	2	no	—
295	C₈	—	4	4	no	—
296	C₂²	—	2	2	no	—
297	C₂²	—	2	4	no	—
298	C₂²	—	4	1	no	—
299	C₂²	—	4	1	no	—
300	C₂²	—	4	2	no	—
301	C₂²	C₁₁×#380	1	1	yes	characteristic
302	C₂²	C₁₁×#387	1	2	yes	—
303	C₂²	C₁₁×#395	1	1	yes	characteristic
304	C₂²	C₁₁×#396	1	2	yes	—
305	C₂²	C₁₁×#400	1	1	yes	characteristic
306	C₄	—	2	4	no	—
307	C₄	—	4	2	no	—
308	C₄	—	8	4	no	—
309	C₄	C₁₁×#386	1	1	yes	characteristic
310	C₄	C₁₁×#389	1	2	yes	—
311	C₄	C₁₁×#391	1	1	yes	characteristic
312	C₄	C₁₁×#394	1	1	yes	characteristic
313	C₄	C₁₁×#398	1	2	yes	—
314	C₄	C₁₁×#398	1	1	yes	characteristic
315	C₂	—	2	1	no	—
316	C₂	—	2	2	no	—
317	C₂	—	2	2	no	—
318	C₂	—	2	1	no	—
319	C₂	C₁₁×#1441	1	1	yes	characteristic
320	C₂	C₁₁×#2102	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	#124
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
socle	C₂²×C₁₁	#400
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
14. C₁₁×#423	C₄	semidirect
54. #11244	C₁₁	direct (N × H)
149. #423	C₄×C₁₁	semidirect
260. C₁₁	#11244	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×#430	2
C₂×C₁₁×#423	2
C₂×C₁₁×#344	2
C₂×C₁₁×#339	2
C₂×C₁₁×H(3,ℤ/4)	2
#11244	11

Subgroups — C11×#11244 #14588437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11244 #14588437