Subgroups — C₁₁×#10696 #14587889

Order 2816.

1078 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	C₂²×C₁₁×#97	C₂	1	2	yes	maximal
2	C₂²×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#336	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×#336	C₂	1	2	yes	maximal
5	C₄×C₁₁×#95	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
8	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₁₁	C₂²	1	2	yes	—
11	C₂×C₁₁×#97	—	2	4	no	—
12	C₂×C₁₁×#97	—	2	4	no	—
13	C₂×C₁₁×#97	C₄	1	8	yes	complemented
14	C₂×C₄×C₈×C₁₁	—	2	4	no	—
15	C₂×C₄×C₈×C₁₁	C₄	1	4	yes	complemented
16	C₂×C₁₁×#95	C₄	1	4	yes	—
17	C₁₁×#336	C₄	1	8	yes	complemented
18	C₁₁×#336	C₄	1	4	yes	complemented
19	C₂³×C₄×C₁₁	C₂×C₄	1	4	yes	—
20	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
21	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
22	C₂²×C₈×C₁₁	—	2	2	no	—
23	C₂²×C₈×C₁₁	—	2	2	no	—
24	C₂²×C₈×C₁₁	—	2	2	no	—
25	C₂²×C₈×C₁₁	—	2	1	no	—
26	C₂²×C₈×C₁₁	—	2	2	no	—
27	C₂²×C₈×C₁₁	—	2	1	no	—
28	C₂²×C₈×C₁₁	—	2	2	no	—
29	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
30	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
31	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
32	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
33	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
34	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
35	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
36	C₂²×C₈×C₁₁	D₄	1	4	yes	—
37	C₂²×C₈×C₁₁	D₄	1	2	yes	—
38	C₂²×C₈×C₁₁	Q₈	1	2	yes	—
39	C₂×C₄²×C₁₁	—	2	2	no	—
40	C₂×C₄²×C₁₁	—	2	2	no	—
41	C₂×C₄²×C₁₁	—	2	2	no	—
42	C₂×C₄²×C₁₁	—	2	2	no	—
43	C₂×C₄²×C₁₁	—	2	2	no	—
44	C₂×C₄²×C₁₁	—	2	2	no	—
45	C₂×C₄²×C₁₁	C₂×C₄	1	4	yes	—
46	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₁₁	C₂×C₄	1	4	yes	—
49	C₁₁×#97	—	2	16	no	—
50	C₄×C₈×C₁₁	—	2	8	no	—
51	C₁₁×#95	—	2	8	no	—
52	#10696	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	—	2	4	no	—
55	C₂²×C₄×C₁₁	—	2	4	no	—
56	C₂²×C₄×C₁₁	—	2	4	no	—
57	C₂²×C₄×C₁₁	—	2	4	no	—
58	C₂²×C₄×C₁₁	—	2	8	no	—
59	C₂²×C₄×C₁₁	—	2	8	no	—
60	C₂²×C₄×C₁₁	C₄²	1	8	yes	—
61	C₂²×C₄×C₁₁	C₄²	1	4	yes	—
62	C₂²×C₄×C₁₁	M₁₆	1	8	yes	—
63	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
65	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
67	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
68	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
70	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
71	C₂²×C₄×C₁₁	#41	1	2	yes	—
72	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
73	C₂×C₈×C₁₁	—	2	2	no	—
74	C₂×C₈×C₁₁	—	2	4	no	—
75	C₂×C₈×C₁₁	—	2	2	no	—
76	C₂×C₈×C₁₁	—	2	4	no	—
77	C₂×C₈×C₁₁	—	2	4	no	—
78	C₂×C₈×C₁₁	—	2	4	no	—
79	C₂×C₈×C₁₁	—	2	4	no	—
80	C₂×C₈×C₁₁	—	2	4	no	—
81	C₂×C₈×C₁₁	—	2	4	no	—
82	C₂×C₈×C₁₁	—	2	4	no	—
83	C₂×C₈×C₁₁	C₄²	1	4	yes	—
84	C₂×C₈×C₁₁	C₄²	1	8	yes	—
85	C₂×C₈×C₁₁	C₄²	1	4	yes	—
86	C₂×C₈×C₁₁	C₂²⋊C₄	1	4	yes	—
87	C₂×C₈×C₁₁	C₂²⋊C₄	1	8	yes	—
88	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
89	C₂×C₈×C₁₁	C₄⋊C₄	1	8	yes	—
90	C₄²×C₁₁	—	2	2	no	—
91	C₄²×C₁₁	—	2	4	no	—
92	C₄²×C₁₁	—	2	2	no	—
93	C₄²×C₁₁	—	2	4	no	—
94	C₄²×C₁₁	—	2	4	no	—
95	C₄²×C₁₁	—	2	4	no	—
96	C₄²×C₁₁	—	2	4	no	—
97	C₂²×#97	C₂×C₁₁	1	2	yes	—
98	C₂²×C₄×C₈	C₂×C₁₁	1	1	yes	characteristic
99	C₂×#336	C₂×C₁₁	1	2	yes	—
100	C₂×#336	C₂×C₁₁	1	1	yes	characteristic
101	C₄×#95	C₂×C₁₁	1	1	yes	characteristic
102	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
103	C₂³×C₁₁	C₂×C₄²	1	2	yes	—
104	C₂³×C₁₁	C₄×D₄	1	2	yes	—
105	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
106	C₂³×C₁₁	C₄×Q₈	1	1	yes	characteristic
107	C₂³×C₁₁	C₂×M₁₆	1	4	yes	—
108	C₂³×C₁₁	#131	1	4	yes	—
109	C₂×C₄×C₁₁	—	2	4	no	—
110	C₂×C₄×C₁₁	—	2	4	no	—
111	C₂×C₄×C₁₁	—	2	16	no	—
112	C₂×C₄×C₁₁	—	2	8	no	—
113	C₂×C₄×C₁₁	—	2	8	no	—
114	C₂×C₄×C₁₁	—	2	8	no	—
115	C₂×C₄×C₁₁	—	4	8	no	—
116	C₂×C₄×C₁₁	—	4	8	no	—
117	C₂×C₄×C₁₁	#97	1	8	yes	complemented
118	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
119	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
120	C₂×C₄×C₁₁	C₂×C₄²	1	2	yes	—
121	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
123	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
125	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
126	C₂×C₄×C₁₁	#117	1	2	yes	—
127	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
128	C₂×C₄×C₁₁	#117	1	2	yes	—
129	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
130	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
131	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
132	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
133	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
134	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
135	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
136	C₈×C₁₁	—	2	4	no	—
137	C₈×C₁₁	—	2	8	no	—
138	C₈×C₁₁	#95	1	8	yes	complemented
139	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
140	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
141	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
142	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
143	C₂²×C₄²	C₂²×C₁₁	1	2	yes	—
144	C₂×#97	—	2	4	no	—
145	C₂×#97	—	2	4	no	—
146	C₂×#97	C₄×C₁₁	1	8	yes	complemented
147	C₂×C₄×C₈	—	2	4	no	—
148	C₂×C₄×C₈	C₄×C₁₁	1	4	yes	complemented
149	C₂×#95	C₄×C₁₁	1	4	yes	—
150	#336	C₄×C₁₁	1	8	yes	complemented
151	#336	C₄×C₁₁	1	4	yes	complemented
152	C₂²×C₁₁	C₄³	1	1	yes	characteristic
153	C₂²×C₁₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₁₁	C₄×C₂²⋊C₄	1	2	yes	—
155	C₂²×C₁₁	C₄×C₄⋊C₄	1	1	yes	characteristic
156	C₂²×C₁₁	C₄×C₄⋊C₄	1	2	yes	—
157	C₂²×C₁₁	C₂×#97	1	2	yes	—
158	C₂²×C₁₁	C₄×M₁₆	1	4	yes	—
159	C₂²×C₁₁	#405	1	2	yes	—
160	C₂²×C₁₁	#405	1	4	yes	—
161	C₂²×C₁₁	#435	1	8	yes	—
162	C₂²×C₁₁	#436	1	4	yes	—
163	C₂²×C₁₁	#446	1	4	yes	—
164	C₄×C₁₁	—	2	8	no	—
165	C₄×C₁₁	—	4	8	no	—
166	C₄×C₁₁	C₂×#95	1	1	yes	characteristic
167	C₄×C₁₁	#376	1	1	yes	characteristic
168	C₄×C₁₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
169	C₄×C₁₁	C₄×C₂²⋊C₄	1	2	yes	—
170	C₄×C₁₁	C₄×C₄⋊C₄	1	1	yes	characteristic
171	C₄×C₁₁	C₄×C₄⋊C₄	1	2	yes	—
172	C₂³×C₄	C₂×C₄×C₁₁	1	4	yes	—
173	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
174	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
175	C₂²×C₈	—	2	2	no	—
176	C₂²×C₈	—	2	2	no	—
177	C₂²×C₈	—	2	2	no	—
178	C₂²×C₈	—	2	1	no	—
179	C₂²×C₈	—	2	2	no	—
180	C₂²×C₈	—	2	1	no	—
181	C₂²×C₈	—	2	2	no	—
182	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	—
183	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	—
184	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	—
185	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
186	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	—
187	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
188	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	—
189	C₂²×C₈	D₄×C₁₁	1	4	yes	—
190	C₂²×C₈	D₄×C₁₁	1	2	yes	—
191	C₂²×C₈	Q₈×C₁₁	1	2	yes	—
192	C₂×C₄²	—	2	2	no	—
193	C₂×C₄²	—	2	2	no	—
194	C₂×C₄²	—	2	2	no	—
195	C₂×C₄²	—	2	2	no	—
196	C₂×C₄²	—	2	2	no	—
197	C₂×C₄²	—	2	2	no	—
198	C₂×C₄²	C₂×C₄×C₁₁	1	4	yes	—
199	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
200	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
201	C₂×C₄²	C₂×C₄×C₁₁	1	4	yes	—
202	#97	—	2	16	no	—
203	C₄×C₈	—	2	8	no	—
204	#95	—	2	8	no	—
205	C₂×C₁₁	C₄×#95	1	1	yes	characteristic
206	C₂×C₁₁	C₄×#97	1	1	yes	characteristic
207	C₂×C₁₁	#1726	1	1	yes	characteristic
208	C₂×C₁₁	#1752	1	2	yes	—
209	C₂×C₁₁	#1753	1	4	yes	—
210	C₂×C₁₁	#1770	1	2	yes	—
211	C₂×C₁₁	#1771	1	4	yes	—
212	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
213	C₂²×C₄	—	2	4	no	—
214	C₂²×C₄	—	2	4	no	—
215	C₂²×C₄	—	2	4	no	—
216	C₂²×C₄	—	2	4	no	—
217	C₂²×C₄	—	2	8	no	—
218	C₂²×C₄	—	2	8	no	—
219	C₂²×C₄	C₄²×C₁₁	1	8	yes	—
220	C₂²×C₄	C₄²×C₁₁	1	4	yes	—
221	C₂²×C₄	C₁₁×M₁₆	1	8	yes	—
222	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
223	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
224	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
225	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
226	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
227	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
228	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
229	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
230	C₂²×C₄	C₁₁×#41	1	2	yes	—
231	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
232	C₂×C₈	—	2	2	no	—
233	C₂×C₈	—	2	4	no	—
234	C₂×C₈	—	2	2	no	—
235	C₂×C₈	—	2	4	no	—
236	C₂×C₈	—	2	4	no	—
237	C₂×C₈	—	2	4	no	—
238	C₂×C₈	—	2	4	no	—
239	C₂×C₈	—	2	4	no	—
240	C₂×C₈	—	2	4	no	—
241	C₂×C₈	—	2	4	no	—
242	C₂×C₈	C₄²×C₁₁	1	4	yes	—
243	C₂×C₈	C₄²×C₁₁	1	8	yes	—
244	C₂×C₈	C₄²×C₁₁	1	4	yes	—
245	C₂×C₈	C₁₁×C₂²⋊C₄	1	4	yes	—
246	C₂×C₈	C₁₁×C₂²⋊C₄	1	8	yes	—
247	C₂×C₈	C₁₁×C₄⋊C₄	1	4	yes	—
248	C₂×C₈	C₁₁×C₄⋊C₄	1	8	yes	—
249	C₄²	—	2	2	no	—
250	C₄²	—	2	4	no	—
251	C₄²	—	2	2	no	—
252	C₄²	—	2	4	no	—
253	C₄²	—	2	4	no	—
254	C₄²	—	2	4	no	—
255	C₄²	—	2	4	no	—
256	C₁₁	#10696	1	1	yes	characteristic, direct product factor, Sylow
257	C₂³	C₂×C₄²×C₁₁	1	1	yes	characteristic
258	C₂³	C₂×C₄²×C₁₁	1	2	yes	—
259	C₂³	C₄×D₄×C₁₁	1	2	yes	—
260	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
261	C₂³	C₄×Q₈×C₁₁	1	1	yes	characteristic
262	C₂³	C₂×C₁₁×M₁₆	1	4	yes	—
263	C₂³	C₁₁×#131	1	4	yes	—
264	C₂×C₄	—	2	4	no	—
265	C₂×C₄	—	2	4	no	—
266	C₂×C₄	—	2	16	no	—
267	C₂×C₄	—	2	8	no	—
268	C₂×C₄	—	2	8	no	—
269	C₂×C₄	—	2	8	no	—
270	C₂×C₄	—	4	8	no	—
271	C₂×C₄	—	4	8	no	—
272	C₂×C₄	C₁₁×#97	1	8	yes	complemented
273	C₂×C₄	C₂×C₄²×C₁₁	1	1	yes	characteristic
274	C₂×C₄	C₂×C₄²×C₁₁	1	1	yes	characteristic
275	C₂×C₄	C₂×C₄²×C₁₁	1	2	yes	—
276	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
278	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
279	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
280	C₂×C₄	C₁₁×#117	1	1	yes	characteristic
281	C₂×C₄	C₁₁×#117	1	2	yes	—
282	C₂×C₄	C₁₁×#117	1	1	yes	characteristic
283	C₂×C₄	C₁₁×#117	1	2	yes	—
284	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
285	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
286	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
287	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
288	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
289	C₂×C₄	C₄×Q₈×C₁₁	1	1	yes	characteristic
290	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
291	C₈	—	2	4	no	—
292	C₈	—	2	8	no	—
293	C₈	C₁₁×#95	1	8	yes	complemented
294	C₂²	C₄³×C₁₁	1	1	yes	characteristic
295	C₂²	C₄×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
296	C₂²	C₄×C₁₁×C₂²⋊C₄	1	2	yes	—
297	C₂²	C₄×C₁₁×C₄⋊C₄	1	1	yes	characteristic
298	C₂²	C₄×C₁₁×C₄⋊C₄	1	2	yes	—
299	C₂²	C₂×C₁₁×#97	1	2	yes	—
300	C₂²	C₄×C₁₁×M₁₆	1	4	yes	—
301	C₂²	C₁₁×#405	1	2	yes	—
302	C₂²	C₁₁×#405	1	4	yes	—
303	C₂²	C₁₁×#435	1	8	yes	—
304	C₂²	C₁₁×#436	1	4	yes	—
305	C₂²	C₁₁×#446	1	4	yes	—
306	C₄	—	2	8	no	—
307	C₄	—	4	8	no	—
308	C₄	C₂×C₁₁×#95	1	1	yes	characteristic
309	C₄	C₁₁×#376	1	1	yes	characteristic
310	C₄	C₄×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
311	C₄	C₄×C₁₁×C₂²⋊C₄	1	2	yes	—
312	C₄	C₄×C₁₁×C₄⋊C₄	1	1	yes	characteristic
313	C₄	C₄×C₁₁×C₄⋊C₄	1	2	yes	—
314	C₂	C₄×C₁₁×#95	1	1	yes	characteristic
315	C₂	C₄×C₁₁×#97	1	1	yes	characteristic
316	C₂	C₁₁×#1726	1	1	yes	characteristic
317	C₂	C₁₁×#1752	1	2	yes	—
318	C₂	C₁₁×#1753	1	4	yes	—
319	C₂	C₁₁×#1770	1	2	yes	—
320	C₂	C₁₁×#1771	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₁	C₂³
commutator	C₂²	C₄³×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
socle, prime radical	C₂⁴×C₁₁	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₂×C₁₁×#97	C₄	semidirect
15. C₂×C₄×C₈×C₁₁	C₄	semidirect
17. C₁₁×#336	C₄	semidirect
18. C₁₁×#336	C₄	semidirect
52. #10696	C₁₁	direct (N × H)
117. C₂×C₄×C₁₁	#97	semidirect
138. C₈×C₁₁	#95	semidirect
146. C₂×#97	C₄×C₁₁	semidirect
148. C₂×C₄×C₈	C₄×C₁₁	semidirect
150. #336	C₄×C₁₁	semidirect
151. #336	C₄×C₁₁	semidirect
256. C₁₁	#10696	direct (N × H)
272. C₂×C₄	C₁₁×#97	semidirect
293. C₈	C₁₁×#95	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₁×#97	2
C₂²×C₄×C₈×C₁₁	2
C₂×C₁₁×#336	2
C₄×C₁₁×#95	2
#10696	11

Subgroups — C11×#10696 #14587889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#10696 #14587889