Subgroups — C₁₁×#19195 #14596388

Order 2816.

638 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3246	C₂	1	2	yes	maximal
2	C₁₁×#3160	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2931	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1691	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1675	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1673	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₁×#335	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1550	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₁×#131	—	2	1	no	—
10	C₁₁×#533	C₂²	1	2	yes	—
11	C₁₁×#532	C₂²	1	1	yes	characteristic
12	C₁₁×#500	C₂²	1	1	yes	characteristic
13	C₁₁×#500	C₂²	1	1	yes	characteristic
14	C₁₁×#499	—	2	1	no	—
15	C₁₁×#499	—	2	1	no	—
16	C₁₁×#498	C₂²	1	2	yes	—
17	C₁₁×#476	C₂²	1	4	yes	—
18	C₁₁×#475	—	2	2	no	—
19	C₁₁×#465	—	2	4	no	—
20	C₁₁×#461	C₂²	1	4	yes	—
21	C₁₁×#460	—	2	2	no	—
22	C₁₁×#436	—	2	1	no	—
23	C₁₁×#436	C₂²	1	2	yes	—
24	C₈×D₄×C₁₁	—	2	1	no	—
25	C₈×D₄×C₁₁	C₂²	1	2	yes	—
26	C₁₁×#427	—	2	1	no	—
27	C₁₁×#427	—	2	1	no	—
28	C₁₁×#423	C₂²	1	1	yes	characteristic
29	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
30	C₁₁×#408	—	2	1	no	—
31	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
32	C₁₁×#335	C₂²	1	2	yes	—
33	C₁₁×#335	C₂²	1	2	yes	—
34	C₁₁×#333	C₂²	1	4	yes	—
35	C₁₁×#332	C₂²	1	4	yes	—
36	C₂×C₁₁×#41	—	2	1	no	—
37	C₂×C₁₁×SD₁₆	—	2	4	no	—
38	C₁₁×#131	—	4	4	no	—
39	C₂×C₁₁×M₁₆	—	2	1	no	—
40	C₂×C₁₁×M₁₆	—	2	2	no	—
41	C₂²×C₈×C₁₁	—	2	2	no	—
42	C₂²×C₈×C₁₁	—	2	2	no	—
43	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
45	C₁₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
46	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
47	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
48	C₁₁×#127	D₄	1	1	yes	characteristic
49	C₁₁×#125	—	2	2	no	—
50	C₁₁×#124	—	2	1	no	—
51	C₁₁×C₂²⋊Q₈	—	2	2	no	—
52	C₁₁×C₂²⋊Q₈	—	2	2	no	—
53	C₁₁×#121	—	2	1	no	—
54	C₁₁×#121	D₄	1	2	yes	—
55	C₄×Q₈×C₁₁	—	2	2	no	—
56	C₄×Q₈×C₁₁	—	2	2	no	—
57	C₄×D₄×C₁₁	—	2	1	no	—
58	C₄×D₄×C₁₁	C₂³	1	2	yes	—
59	C₁₁×#117	—	2	2	no	—
60	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
61	C₁₁×#107	—	2	1	no	—
62	C₁₁×#107	—	2	1	no	—
63	C₁₁×#107	—	2	1	no	—
64	C₁₁×#107	—	2	1	no	—
65	C₁₁×#106	—	2	2	no	—
66	C₁₁×#106	—	2	2	no	—
67	C₁₁×#106	—	2	4	no	—
68	C₁₁×C₄⋊C₈	—	2	2	no	—
69	C₁₁×C₄⋊C₈	—	2	1	no	—
70	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
71	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
72	C₁₁×#103	—	2	4	no	—
73	C₁₁×#102	—	2	4	no	—
74	C₁₁×C₂²⋊C₈	—	2	2	no	—
75	C₁₁×C₂²⋊C₈	—	2	2	no	—
76	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
77	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
78	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
79	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
80	#19195	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₁₁×#41	—	4	2	no	—
82	C₁₁×#41	—	4	2	no	—
83	C₂×Q₈×C₁₁	—	2	1	no	—
84	C₂×Q₈×C₁₁	—	2	2	no	—
85	C₂×Q₈×C₁₁	—	2	2	no	—
86	C₂×D₄×C₁₁	—	2	2	no	—
87	C₂×D₄×C₁₁	—	2	1	no	—
88	C₂×D₄×C₁₁	—	2	1	no	—
89	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₁₁	—	2	2	no	—
91	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
94	C₁₁×SD₁₆	—	8	4	no	—
95	C₁₁×M₁₆	—	4	4	no	—
96	C₁₁×M₁₆	—	4	2	no	—
97	C₂×C₈×C₁₁	—	2	2	no	—
98	C₂×C₈×C₁₁	—	2	2	no	—
99	C₂×C₈×C₁₁	—	2	4	no	—
100	C₂×C₈×C₁₁	—	4	4	no	—
101	C₂×C₈×C₁₁	—	8	2	no	—
102	C₂×C₈×C₁₁	SD₁₆	1	4	yes	complemented
103	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
104	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
105	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
106	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
107	C₁₁×C₄⋊C₄	—	2	1	no	—
108	C₁₁×C₄⋊C₄	—	2	2	no	—
109	C₁₁×C₄⋊C₄	—	2	2	no	—
110	C₁₁×C₄⋊C₄	—	2	2	no	—
111	C₁₁×C₄⋊C₄	—	2	2	no	—
112	C₁₁×C₄⋊C₄	—	4	2	no	—
113	C₁₁×C₄⋊C₄	—	4	2	no	—
114	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
115	C₁₁×C₂²⋊C₄	—	2	2	no	—
116	C₁₁×C₂²⋊C₄	—	2	2	no	—
117	C₁₁×C₂²⋊C₄	—	4	2	no	—
118	C₄²×C₁₁	—	4	2	no	—
119	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₁₁	#41	1	1	yes	characteristic
122	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
123	#3246	C₂×C₁₁	1	2	yes	—
124	#3160	C₂×C₁₁	1	1	yes	characteristic, complemented
125	#2931	C₂×C₁₁	1	1	yes	characteristic
126	#1691	C₂×C₁₁	1	4	yes	complemented
127	#1675	C₂×C₁₁	1	2	yes	complemented
128	#1673	C₂×C₁₁	1	2	yes	complemented
129	C₂×#335	C₂×C₁₁	1	1	yes	characteristic, complemented
130	#1550	C₂×C₁₁	1	2	yes	complemented
131	C₂³×C₁₁	—	2	2	no	—
132	C₂³×C₁₁	#121	1	1	yes	characteristic
133	Q₈×C₁₁	—	4	2	no	—
134	Q₈×C₁₁	—	4	2	no	—
135	Q₈×C₁₁	—	4	2	no	—
136	Q₈×C₁₁	—	8	2	no	—
137	D₄×C₁₁	—	2	2	no	—
138	D₄×C₁₁	—	2	2	no	—
139	D₄×C₁₁	—	4	2	no	—
140	D₄×C₁₁	—	4	4	no	—
141	D₄×C₁₁	—	4	2	no	—
142	C₂×C₄×C₁₁	—	2	1	no	—
143	C₂×C₄×C₁₁	—	2	1	no	—
144	C₂×C₄×C₁₁	—	2	2	no	—
145	C₂×C₄×C₁₁	—	4	1	no	—
146	C₂×C₄×C₁₁	—	4	2	no	—
147	C₂×C₄×C₁₁	—	4	2	no	—
148	C₂×C₄×C₁₁	—	4	2	no	—
149	C₂×C₄×C₁₁	—	4	2	no	—
150	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
151	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
152	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
153	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
154	C₂×C₄×C₁₁	#137	1	2	yes	—
155	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
158	C₈×C₁₁	—	2	1	no	—
159	C₈×C₁₁	—	2	1	no	—
160	C₈×C₁₁	—	4	2	no	—
161	C₈×C₁₁	—	4	4	no	—
162	C₈×C₁₁	C₂×SD₁₆	1	2	yes	—
163	C₈×C₁₁	C₂×SD₁₆	1	2	yes	—
164	C₂×#131	—	2	1	no	—
165	#533	C₂²×C₁₁	1	2	yes	—
166	#532	C₂²×C₁₁	1	1	yes	characteristic
167	#500	C₂²×C₁₁	1	1	yes	characteristic
168	#500	C₂²×C₁₁	1	1	yes	characteristic
169	#499	—	2	1	no	—
170	#499	—	2	1	no	—
171	#498	C₂²×C₁₁	1	2	yes	—
172	#476	C₂²×C₁₁	1	4	yes	—
173	#475	—	2	2	no	—
174	#465	—	2	4	no	—
175	#461	C₂²×C₁₁	1	4	yes	—
176	#460	—	2	2	no	—
177	#436	—	2	1	no	—
178	#436	C₂²×C₁₁	1	2	yes	—
179	C₈×D₄	—	2	1	no	—
180	C₈×D₄	C₂²×C₁₁	1	2	yes	—
181	#427	—	2	1	no	—
182	#427	—	2	1	no	—
183	#423	C₂²×C₁₁	1	1	yes	characteristic
184	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
185	#408	—	2	1	no	—
186	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
187	#335	C₂²×C₁₁	1	2	yes	—
188	#335	C₂²×C₁₁	1	2	yes	—
189	#333	C₂²×C₁₁	1	4	yes	—
190	#332	C₂²×C₁₁	1	4	yes	—
191	C₂²×C₁₁	—	2	1	no	—
192	C₂²×C₁₁	—	2	1	no	—
193	C₂²×C₁₁	—	4	2	no	—
194	C₂²×C₁₁	—	4	2	no	—
195	C₂²×C₁₁	—	4	2	no	—
196	C₂²×C₁₁	#461	1	2	yes	—
197	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
198	C₄×C₁₁	—	2	1	no	—
199	C₄×C₁₁	—	2	1	no	—
200	C₄×C₁₁	—	2	1	no	—
201	C₄×C₁₁	—	4	2	no	—
202	C₄×C₁₁	—	8	2	no	—
203	C₄×C₁₁	—	8	2	no	—
204	C₄×C₁₁	#461	1	2	yes	—
205	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
206	C₄×C₁₁	C₂×#137	1	1	yes	characteristic
207	C₄×C₁₁	#576	1	1	yes	characteristic
208	C₄×C₁₁	#578	1	1	yes	characteristic
209	C₂×#41	—	2	1	no	—
210	C₂×SD₁₆	—	2	4	no	—
211	#131	—	4	4	no	—
212	C₂×M₁₆	—	2	1	no	—
213	C₂×M₁₆	—	2	2	no	—
214	C₂²×C₈	—	2	2	no	—
215	C₂²×C₈	—	2	2	no	—
216	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
217	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
218	C₄⋊Q₈	D₄×C₁₁	1	1	yes	characteristic
219	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
220	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
221	#127	D₄×C₁₁	1	1	yes	characteristic
222	#125	—	2	2	no	—
223	#124	—	2	1	no	—
224	C₂²⋊Q₈	—	2	2	no	—
225	C₂²⋊Q₈	—	2	2	no	—
226	#121	—	2	1	no	—
227	#121	D₄×C₁₁	1	2	yes	—
228	C₄×Q₈	—	2	2	no	—
229	C₄×Q₈	—	2	2	no	—
230	C₄×D₄	—	2	1	no	—
231	C₄×D₄	C₂³×C₁₁	1	2	yes	—
232	#117	—	2	2	no	—
233	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
234	#107	—	2	1	no	—
235	#107	—	2	1	no	—
236	#107	—	2	1	no	—
237	#107	—	2	1	no	—
238	#106	—	2	2	no	—
239	#106	—	2	2	no	—
240	#106	—	2	4	no	—
241	C₄⋊C₈	—	2	2	no	—
242	C₄⋊C₈	—	2	1	no	—
243	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
244	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
245	#103	—	2	4	no	—
246	#102	—	2	4	no	—
247	C₂²⋊C₈	—	2	2	no	—
248	C₂²⋊C₈	—	2	2	no	—
249	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
250	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
251	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
252	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
253	C₂×C₁₁	—	2	2	no	—
254	C₂×C₁₁	—	8	2	no	—
255	C₂×C₁₁	C₂×#461	1	1	yes	characteristic
256	C₂×C₁₁	#3061	1	1	yes	characteristic
257	C₂×C₁₁	#3067	1	1	yes	characteristic
258	#41	—	4	2	no	—
259	#41	—	4	2	no	—
260	C₂×Q₈	—	2	1	no	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×D₄	—	2	2	no	—
264	C₂×D₄	—	2	1	no	—
265	C₂×D₄	—	2	1	no	—
266	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
270	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
271	SD₁₆	—	8	4	no	—
272	M₁₆	—	4	2	no	—
273	M₁₆	—	4	4	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	4	4	no	—
278	C₂×C₈	—	8	2	no	—
279	C₂×C₈	C₁₁×SD₁₆	1	4	yes	complemented
280	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
281	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
282	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
283	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
284	C₄⋊C₄	—	2	1	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	4	2	no	—
290	C₄⋊C₄	—	4	2	no	—
291	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
292	C₂²⋊C₄	—	2	2	no	—
293	C₂²⋊C₄	—	2	2	no	—
294	C₂²⋊C₄	—	4	2	no	—
295	C₄²	—	4	2	no	—
296	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
297	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
298	C₄²	C₁₁×#41	1	1	yes	characteristic
299	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
300	C₁₁	#19195	1	1	yes	characteristic, direct product factor, Sylow
301	C₂³	—	2	2	no	—
302	C₂³	C₁₁×#121	1	1	yes	characteristic
303	Q₈	—	4	2	no	—
304	Q₈	—	4	2	no	—
305	Q₈	—	4	2	no	—
306	Q₈	—	8	2	no	—
307	D₄	—	2	2	no	—
308	D₄	—	2	2	no	—
309	D₄	—	4	2	no	—
310	D₄	—	4	4	no	—
311	D₄	—	4	2	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
321	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
322	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
323	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
324	C₂×C₄	C₁₁×#137	1	2	yes	—
325	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
326	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
327	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
328	C₈	—	2	1	no	—
329	C₈	—	2	1	no	—
330	C₈	—	4	2	no	—
331	C₈	—	4	4	no	—
332	C₈	C₂×C₁₁×SD₁₆	1	2	yes	—
333	C₈	C₂×C₁₁×SD₁₆	1	2	yes	—
334	C₂²	—	2	1	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	4	2	no	—
337	C₂²	—	4	2	no	—
338	C₂²	—	4	2	no	—
339	C₂²	C₁₁×#461	1	2	yes	—
340	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
341	C₄	—	2	1	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	1	no	—
344	C₄	—	4	2	no	—
345	C₄	—	8	2	no	—
346	C₄	—	8	2	no	—
347	C₄	C₁₁×#461	1	2	yes	—
348	C₄	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
349	C₄	C₂×C₁₁×#137	1	1	yes	characteristic
350	C₄	C₁₁×#576	1	1	yes	characteristic
351	C₄	C₁₁×#578	1	1	yes	characteristic
352	C₂	—	2	2	no	—
353	C₂	—	8	2	no	—
354	C₂	C₂×C₁₁×#461	1	1	yes	characteristic
355	C₂	C₁₁×#3061	1	1	yes	characteristic
356	C₂	C₁₁×#3067	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. C₁₁×#3160	C₂	semidirect
4. C₁₁×#1691	C₂	semidirect
5. C₁₁×#1675	C₂	semidirect
6. C₁₁×#1673	C₂	semidirect
7. C₂×C₁₁×#335	C₂	semidirect
8. C₁₁×#1550	C₂	semidirect
80. #19195	C₁₁	direct (N × H)
102. C₂×C₈×C₁₁	SD₁₆	semidirect
124. #3160	C₂×C₁₁	semidirect
126. #1691	C₂×C₁₁	semidirect
127. #1675	C₂×C₁₁	semidirect
128. #1673	C₂×C₁₁	semidirect
129. C₂×#335	C₂×C₁₁	semidirect
130. #1550	C₂×C₁₁	semidirect
279. C₂×C₈	C₁₁×SD₁₆	semidirect
300. C₁₁	#19195	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×#3246	2
C₁₁×#3160	2
C₁₁×#2931	2
C₁₁×#1691	2
C₁₁×#1675	2
C₁₁×#1673	2
C₂×C₁₁×#335	2
C₁₁×#1550	2
#19195	11

Subgroups — C11×#19195 #14596388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19195 #14596388