Subgroups — C₁₁×#17890 #14595083

Order 2816.

666 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2965	C₂	1	2	yes	maximal, complemented
2	C₄×C₁₁×#135	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1594	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1593	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1592	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1476	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₁×#322	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×#135	C₄	1	1	yes	characteristic
10	C₄×C₁₁×#41	C₂²	1	2	yes	—
11	C₁₁×#446	C₂²	1	4	yes	—
12	C₄×C₁₁×Q₁₆	C₄	1	1	yes	characteristic
13	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
14	C₄×C₁₁×SD₁₆	C₄	1	2	yes	—
15	C₄×C₁₁×SD₁₆	C₂²	1	2	yes	—
16	C₄×C₁₁×D₈	C₄	1	1	yes	characteristic
17	C₄×C₁₁×D₈	C₂²	1	1	yes	characteristic
18	C₁₁×#436	C₂²	1	4	yes	—
19	C₁₁×#435	—	2	4	no	—
20	C₁₁×#431	—	2	2	no	—
21	C₁₁×#431	C₂²	1	2	yes	—
22	C₁₁×#427	C₄	1	1	yes	characteristic
23	C₁₁×#416	C₄	1	2	yes	—
24	C₄×C₁₁×M₁₆	—	2	2	no	—
25	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
28	C₁₁×#335	C₂²	1	2	yes	—
29	C₁₁×#334	C₂²	1	2	yes	—
30	C₁₁×Q₈⋊C₈	C₂²	1	4	yes	—
31	C₁₁×D₄⋊C₈	C₂²	1	4	yes	—
32	C₁₁×#322	C₂²	1	2	yes	—
33	C₁₁×#322	C₂²	1	2	yes	—
34	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
35	C₁₁×#135	—	2	4	no	—
36	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
37	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
38	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₁×M₁₆	—	2	4	no	—
40	C₂²×C₈×C₁₁	—	2	1	no	—
41	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₁	D₄	1	2	yes	—
44	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
45	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
46	C₄×D₄×C₁₁	—	2	2	no	—
47	C₄×D₄×C₁₁	—	2	2	no	—
48	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₁₁	C₂³	1	2	yes	—
50	C₁₁×#117	—	2	2	no	—
51	C₁₁×#117	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₁	—	2	2	no	—
53	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
54	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
55	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
56	C₁₁×#106	C₂×C₄	1	2	yes	—
57	C₁₁×C₄⋊C₈	—	2	4	no	—
58	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
59	C₁₁×#103	C₂×C₄	1	2	yes	—
60	C₁₁×#103	C₂×C₄	1	2	yes	—
61	C₁₁×#102	C₂×C₄	1	2	yes	—
62	C₁₁×#102	C₂×C₄	1	2	yes	—
63	C₁₁×C₂²⋊C₈	—	2	2	no	—
64	C₁₁×C₂²⋊C₈	—	2	4	no	—
65	C₁₁×#97	—	2	4	no	—
66	C₄×C₈×C₁₁	—	2	2	no	—
67	C₄×C₈×C₁₁	—	2	1	no	—
68	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
69	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
70	C₄×C₈×C₁₁	D₄	1	2	yes	—
71	C₄×C₈×C₁₁	C₂³	1	2	yes	—
72	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
73	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₁₁	C₂³	1	2	yes	—
75	#17890	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₁₁×#41	—	2	4	no	—
77	C₁₁×#41	—	2	4	no	—
78	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
79	C₂×D₄×C₁₁	—	2	2	no	—
80	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₁	—	2	2	no	—
82	C₂²×C₄×C₁₁	—	2	2	no	—
83	C₂²×C₄×C₁₁	—	2	2	no	—
84	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
87	C₁₁×Q₁₆	—	2	2	no	—
88	C₁₁×SD₁₆	—	2	4	no	—
89	C₁₁×D₈	—	2	2	no	—
90	C₁₁×M₁₆	—	4	8	no	—
91	C₂×C₈×C₁₁	—	2	2	no	—
92	C₂×C₈×C₁₁	—	2	4	no	—
93	C₂×C₈×C₁₁	—	2	2	no	—
94	C₂×C₈×C₁₁	—	4	2	no	—
95	C₂×C₈×C₁₁	—	4	2	no	—
96	C₂×C₈×C₁₁	M₁₆	1	4	yes	complemented
97	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
102	C₁₁×C₄⋊C₄	—	2	2	no	—
103	C₁₁×C₄⋊C₄	—	2	2	no	—
104	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
105	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
106	C₁₁×C₂²⋊C₄	—	2	2	no	—
107	C₁₁×C₂²⋊C₄	—	2	2	no	—
108	C₁₁×C₂²⋊C₄	—	2	2	no	—
109	C₄²×C₁₁	—	2	2	no	—
110	C₄²×C₁₁	—	2	2	no	—
111	C₄²×C₁₁	—	2	2	no	—
112	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₁₁	#41	1	1	yes	characteristic
115	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
116	#2965	C₂×C₁₁	1	2	yes	complemented
117	C₄×#135	C₂×C₁₁	1	1	yes	characteristic
118	#1594	C₂×C₁₁	1	2	yes	complemented
119	#1593	C₂×C₁₁	1	2	yes	complemented
120	#1592	C₂×C₁₁	1	4	yes	complemented
121	#1564	C₂×C₁₁	1	1	yes	characteristic, complemented
122	#1476	C₂×C₁₁	1	2	yes	complemented
123	C₂×#322	C₂×C₁₁	1	1	yes	characteristic, complemented
124	C₂³×C₁₁	—	2	2	no	—
125	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
126	Q₈×C₁₁	—	2	2	no	—
127	Q₈×C₁₁	—	2	2	no	—
128	D₄×C₁₁	—	2	2	no	—
129	D₄×C₁₁	—	2	2	no	—
130	D₄×C₁₁	—	4	4	no	—
131	C₂×C₄×C₁₁	—	2	2	no	—
132	C₂×C₄×C₁₁	—	2	2	no	—
133	C₂×C₄×C₁₁	—	2	2	no	—
134	C₂×C₄×C₁₁	—	2	2	no	—
135	C₂×C₄×C₁₁	—	2	2	no	—
136	C₂×C₄×C₁₁	—	4	4	no	—
137	C₂×C₄×C₁₁	—	4	4	no	—
138	C₂×C₄×C₁₁	—	4	4	no	—
139	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
140	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
143	C₂×C₄×C₁₁	#131	1	2	yes	—
144	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
147	C₈×C₁₁	—	2	1	no	—
148	C₈×C₁₁	—	2	1	no	—
149	C₈×C₁₁	—	2	4	no	—
150	C₈×C₁₁	—	4	2	no	—
151	C₈×C₁₁	—	4	4	no	—
152	C₈×C₁₁	C₂×M₁₆	1	2	yes	—
153	C₈×C₁₁	C₂×M₁₆	1	2	yes	—
154	C₂×#135	C₄×C₁₁	1	1	yes	characteristic
155	C₄×#41	C₂²×C₁₁	1	2	yes	—
156	#446	C₂²×C₁₁	1	4	yes	—
157	C₄×Q₁₆	C₄×C₁₁	1	1	yes	characteristic
158	C₄×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
159	C₄×SD₁₆	C₄×C₁₁	1	2	yes	—
160	C₄×SD₁₆	C₂²×C₁₁	1	2	yes	—
161	C₄×D₈	C₄×C₁₁	1	1	yes	characteristic
162	C₄×D₈	C₂²×C₁₁	1	1	yes	characteristic
163	#436	C₂²×C₁₁	1	4	yes	—
164	#435	—	2	4	no	—
165	#431	—	2	2	no	—
166	#431	C₂²×C₁₁	1	2	yes	—
167	#427	C₄×C₁₁	1	1	yes	characteristic
168	#416	C₄×C₁₁	1	2	yes	—
169	C₄×M₁₆	—	2	2	no	—
170	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
171	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
172	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
173	#335	C₂²×C₁₁	1	2	yes	—
174	#334	C₂²×C₁₁	1	2	yes	—
175	Q₈⋊C₈	C₂²×C₁₁	1	4	yes	—
176	D₄⋊C₈	C₂²×C₁₁	1	4	yes	—
177	#322	C₂²×C₁₁	1	2	yes	—
178	#322	C₂²×C₁₁	1	2	yes	—
179	C₂²×C₁₁	—	2	1	no	—
180	C₂²×C₁₁	—	2	1	no	—
181	C₂²×C₁₁	—	4	2	no	—
182	C₂²×C₁₁	—	4	2	no	—
183	C₂²×C₁₁	—	4	2	no	—
184	C₂²×C₁₁	#436	1	2	yes	—
185	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
186	C₄×C₁₁	—	2	1	no	—
187	C₄×C₁₁	—	2	1	no	—
188	C₄×C₁₁	—	4	2	no	—
189	C₄×C₁₁	—	4	2	no	—
190	C₄×C₁₁	—	4	2	no	—
191	C₄×C₁₁	#436	1	2	yes	—
192	C₄×C₁₁	#444	1	2	yes	—
193	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
194	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
195	C₄×C₁₁	#575	1	2	yes	—
196	C₂×#41	C₂×C₄×C₁₁	1	2	yes	—
197	#135	—	2	4	no	—
198	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
199	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
200	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
201	C₂×M₁₆	—	2	4	no	—
202	C₂²×C₈	—	2	1	no	—
203	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
204	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
205	C₂²×C₈	D₄×C₁₁	1	2	yes	—
206	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
207	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
208	C₄×D₄	—	2	2	no	—
209	C₄×D₄	—	2	2	no	—
210	C₄×D₄	C₂×C₄×C₁₁	1	2	yes	—
211	C₄×D₄	C₂³×C₁₁	1	2	yes	—
212	#117	—	2	2	no	—
213	#117	C₂×C₄×C₁₁	1	2	yes	—
214	C₂×C₄²	—	2	2	no	—
215	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
216	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
217	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
218	#106	C₂×C₄×C₁₁	1	2	yes	—
219	C₄⋊C₈	—	2	4	no	—
220	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
221	#103	C₂×C₄×C₁₁	1	2	yes	—
222	#103	C₂×C₄×C₁₁	1	2	yes	—
223	#102	C₂×C₄×C₁₁	1	2	yes	—
224	#102	C₂×C₄×C₁₁	1	2	yes	—
225	C₂²⋊C₈	—	2	2	no	—
226	C₂²⋊C₈	—	2	4	no	—
227	#97	—	2	4	no	—
228	C₄×C₈	—	2	2	no	—
229	C₄×C₈	—	2	1	no	—
230	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
231	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
232	C₄×C₈	D₄×C₁₁	1	2	yes	—
233	C₄×C₈	C₂³×C₁₁	1	2	yes	—
234	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
235	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
236	C₄×C₈	C₂³×C₁₁	1	2	yes	—
237	C₂×C₁₁	—	2	2	no	—
238	C₂×C₁₁	—	8	2	no	—
239	C₂×C₁₁	C₂×#436	1	1	yes	characteristic
240	C₂×C₁₁	#2943	1	1	yes	characteristic
241	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
242	#41	—	2	4	no	—
243	#41	—	2	4	no	—
244	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
245	C₂×D₄	—	2	2	no	—
246	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
251	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
252	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
253	Q₁₆	—	2	2	no	—
254	SD₁₆	—	2	4	no	—
255	D₈	—	2	2	no	—
256	M₁₆	—	4	8	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	4	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	4	2	no	—
261	C₂×C₈	—	4	2	no	—
262	C₂×C₈	C₁₁×M₁₆	1	4	yes	complemented
263	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
264	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
265	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
266	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
267	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
268	C₄⋊C₄	—	2	2	no	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
271	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
272	C₂²⋊C₄	—	2	2	no	—
273	C₂²⋊C₄	—	2	2	no	—
274	C₂²⋊C₄	—	2	2	no	—
275	C₄²	—	2	2	no	—
276	C₄²	—	2	2	no	—
277	C₄²	—	2	2	no	—
278	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
279	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
280	C₄²	C₁₁×#41	1	1	yes	characteristic
281	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
282	C₁₁	#17890	1	1	yes	characteristic, direct product factor, Sylow
283	C₂³	—	2	2	no	—
284	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
285	Q₈	—	2	2	no	—
286	Q₈	—	2	2	no	—
287	D₄	—	2	2	no	—
288	D₄	—	2	2	no	—
289	D₄	—	4	4	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	4	4	no	—
296	C₂×C₄	—	4	4	no	—
297	C₂×C₄	—	4	4	no	—
298	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
299	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
300	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
301	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
302	C₂×C₄	C₁₁×#131	1	2	yes	—
303	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
304	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
305	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
306	C₈	—	2	1	no	—
307	C₈	—	2	1	no	—
308	C₈	—	2	4	no	—
309	C₈	—	4	2	no	—
310	C₈	—	4	4	no	—
311	C₈	C₂×C₁₁×M₁₆	1	2	yes	—
312	C₈	C₂×C₁₁×M₁₆	1	2	yes	—
313	C₂²	—	2	1	no	—
314	C₂²	—	2	1	no	—
315	C₂²	—	4	2	no	—
316	C₂²	—	4	2	no	—
317	C₂²	—	4	2	no	—
318	C₂²	C₁₁×#436	1	2	yes	—
319	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
320	C₄	—	2	1	no	—
321	C₄	—	2	1	no	—
322	C₄	—	4	2	no	—
323	C₄	—	4	2	no	—
324	C₄	—	4	2	no	—
325	C₄	C₁₁×#436	1	2	yes	—
326	C₄	C₁₁×#444	1	2	yes	—
327	C₄	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
328	C₄	C₂×C₁₁×#131	1	1	yes	characteristic
329	C₄	C₁₁×#575	1	2	yes	—
330	C₂	—	2	2	no	—
331	C₂	—	8	2	no	—
332	C₂	C₂×C₁₁×#436	1	1	yes	characteristic
333	C₂	C₁₁×#2943	1	1	yes	characteristic
334	C₂	C₂×C₁₁×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₁₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₄²	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×C₁₁×#135	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#2965	C₂	semidirect
3. C₁₁×#1594	C₂	semidirect
4. C₁₁×#1593	C₂	semidirect
5. C₁₁×#1592	C₂	semidirect
6. C₁₁×#1564	C₂	semidirect
7. C₁₁×#1476	C₂	semidirect
8. C₂×C₁₁×#322	C₂	semidirect
75. #17890	C₁₁	direct (N × H)
96. C₂×C₈×C₁₁	M₁₆	semidirect
116. #2965	C₂×C₁₁	semidirect
118. #1594	C₂×C₁₁	semidirect
119. #1593	C₂×C₁₁	semidirect
120. #1592	C₂×C₁₁	semidirect
121. #1564	C₂×C₁₁	semidirect
122. #1476	C₂×C₁₁	semidirect
123. C₂×#322	C₂×C₁₁	semidirect
262. C₂×C₈	C₁₁×M₁₆	semidirect
282. C₁₁	#17890	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×#2965	2
C₄×C₁₁×#135	2
C₁₁×#1594	2
C₁₁×#1593	2
C₁₁×#1592	2
C₁₁×#1564	2
C₁₁×#1476	2
C₂×C₁₁×#322	2
#17890	11

Subgroups — C11×#17890 #14595083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#17890 #14595083