Subgroups — C₁₁×#22240 #14599433

Order 2816.

750 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#446	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1984	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1984	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1917	C₂	1	4	yes	maximal
7	C₁₁×#1916	C₂	1	4	yes	maximal
8	C₁₁×#1831	C₂	1	1	yes	maximal, characteristic
9	C₁₁×#1744	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₁×C₄⋊Q₈	C₄	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₁₁×#446	—	2	4	no	—
14	C₈×Q₈×C₁₁	—	2	4	no	—
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×#97	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
23	C₁₁×#391	C₄	1	1	yes	characteristic
24	C₁₁×#391	C₄	1	1	yes	characteristic
25	C₁₁×#389	C₄	1	4	yes	—
26	C₁₁×#384	C₄	1	1	yes	characteristic
27	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
28	C₄³×C₁₁	C₂²	1	1	yes	characteristic
29	C₁₁×#336	C₂²	1	2	yes	—
30	C₁₁×#336	C₂²	1	4	yes	—
31	C₁₁×#336	C₂²	1	4	yes	—
32	C₁₁×#336	C₂²	1	4	yes	—
33	C₁₁×#336	C₂²	1	2	yes	—
34	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
35	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
37	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
38	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
39	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
41	C₁₁×C₄⋊Q₈	—	2	4	no	—
42	C₄×Q₈×C₁₁	—	2	2	no	—
43	C₄×Q₈×C₁₁	—	2	2	no	—
44	C₄×Q₈×C₁₁	—	2	2	no	—
45	C₄×Q₈×C₁₁	—	2	2	no	—
46	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
47	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
48	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
56	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
57	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
58	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
59	C₁₁×C₄⋊C₈	—	2	4	no	—
60	C₁₁×C₄⋊C₈	—	2	4	no	—
61	C₁₁×C₄⋊C₈	—	2	2	no	—
62	C₁₁×C₄⋊C₈	—	2	2	no	—
63	C₁₁×#97	—	2	4	no	—
64	C₄×C₈×C₁₁	—	2	4	no	—
65	C₄×C₈×C₁₁	—	2	2	no	—
66	C₄×C₈×C₁₁	D₄	1	4	yes	—
67	C₁₁×#95	C₂×C₄	1	4	yes	—
68	C₁₁×#95	C₂×C₄	1	4	yes	—
69	#22240	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂×Q₈×C₁₁	—	2	2	no	—
71	C₂×Q₈×C₁₁	—	2	2	no	—
72	C₂×Q₈×C₁₁	—	2	2	no	—
73	C₂×Q₈×C₁₁	—	2	2	no	—
74	C₂×Q₈×C₁₁	—	2	2	no	—
75	C₂×Q₈×C₁₁	M₁₆	1	4	yes	—
76	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
85	C₂×C₈×C₁₁	—	2	2	no	—
86	C₂×C₈×C₁₁	—	2	2	no	—
87	C₂×C₈×C₁₁	—	2	2	no	—
88	C₂×C₈×C₁₁	—	2	2	no	—
89	C₂×C₈×C₁₁	—	2	2	no	—
90	C₂×C₈×C₁₁	—	2	4	no	—
91	C₂×C₈×C₁₁	—	2	4	no	—
92	C₂×C₈×C₁₁	—	2	2	no	—
93	C₂×C₈×C₁₁	—	2	2	no	—
94	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
95	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
96	C₁₁×C₄⋊C₄	—	2	4	no	—
97	C₁₁×C₄⋊C₄	—	2	2	no	—
98	C₁₁×C₄⋊C₄	—	2	2	no	—
99	C₁₁×C₄⋊C₄	—	2	4	no	—
100	C₁₁×C₄⋊C₄	—	2	8	no	—
101	C₁₁×C₄⋊C₄	—	2	8	no	—
102	C₄²×C₁₁	—	2	2	no	—
103	C₄²×C₁₁	—	2	4	no	—
104	C₄²×C₁₁	—	2	2	no	—
105	C₄²×C₁₁	—	2	2	no	—
106	C₄²×C₁₁	—	2	2	no	—
107	C₄²×C₁₁	—	2	2	no	—
108	C₄²×C₁₁	—	2	2	no	—
109	C₄²×C₁₁	—	2	2	no	—
110	C₄²×C₁₁	—	2	2	no	—
111	C₄²×C₁₁	C₂×D₄	1	2	yes	—
112	C₄²×C₁₁	#41	1	2	yes	—
113	C₂×#446	C₂×C₁₁	1	1	yes	characteristic
114	C₂×C₈×Q₈	C₂×C₁₁	1	1	yes	characteristic
115	C₄×C₄⋊Q₈	C₂×C₁₁	1	1	yes	characteristic
116	#1984	C₂×C₁₁	1	1	yes	characteristic
117	#1984	C₂×C₁₁	1	1	yes	characteristic
118	#1917	C₂×C₁₁	1	4	yes	—
119	#1916	C₂×C₁₁	1	4	yes	—
120	#1831	C₂×C₁₁	1	1	yes	characteristic
121	#1744	C₂×C₁₁	1	1	yes	characteristic
122	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
123	Q₈×C₁₁	—	2	8	no	—
124	Q₈×C₁₁	—	4	4	no	—
125	C₂×C₄×C₁₁	—	2	2	no	—
126	C₂×C₄×C₁₁	—	2	2	no	—
127	C₂×C₄×C₁₁	—	2	2	no	—
128	C₂×C₄×C₁₁	—	2	2	no	—
129	C₂×C₄×C₁₁	—	2	2	no	—
130	C₂×C₄×C₁₁	—	2	2	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	—	2	2	no	—
137	C₂×C₄×C₁₁	—	2	4	no	—
138	C₂×C₄×C₁₁	—	2	4	no	—
139	C₂×C₄×C₁₁	—	2	2	no	—
140	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
141	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
142	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
143	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
144	C₂×C₄×C₁₁	#131	1	4	yes	—
145	C₂×C₄×C₁₁	#131	1	2	yes	—
146	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
148	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
149	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
150	C₈×C₁₁	—	2	2	no	—
151	C₈×C₁₁	—	2	2	no	—
152	C₈×C₁₁	—	4	2	no	—
153	C₈×C₁₁	—	4	2	no	—
154	C₈×C₁₁	—	4	2	no	—
155	C₂×C₄⋊Q₈	C₄×C₁₁	1	1	yes	characteristic
156	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
157	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
158	#446	—	2	4	no	—
159	C₈×Q₈	—	2	4	no	—
160	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
161	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
162	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
163	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
164	C₂×#97	C₂²×C₁₁	1	2	yes	—
165	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
166	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
167	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
168	#391	C₄×C₁₁	1	1	yes	characteristic
169	#391	C₄×C₁₁	1	1	yes	characteristic
170	#389	C₄×C₁₁	1	4	yes	—
171	#384	C₄×C₁₁	1	1	yes	characteristic
172	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
173	C₄³	C₂²×C₁₁	1	1	yes	characteristic
174	#336	C₂²×C₁₁	1	4	yes	—
175	#336	C₂²×C₁₁	1	2	yes	—
176	#336	C₂²×C₁₁	1	4	yes	—
177	#336	C₂²×C₁₁	1	4	yes	—
178	#336	C₂²×C₁₁	1	2	yes	—
179	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
180	C₂²×C₁₁	#519	1	2	yes	—
181	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
182	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
183	C₂²×C₁₁	C₂×#131	1	2	yes	—
184	C₄×C₁₁	—	2	4	no	—
185	C₄×C₁₁	—	2	2	no	—
186	C₄×C₁₁	—	2	4	no	—
187	C₄×C₁₁	—	4	2	no	—
188	C₄×C₁₁	—	4	2	no	—
189	C₄×C₁₁	—	4	2	no	—
190	C₄×C₁₁	—	4	2	no	—
191	C₄×C₁₁	#435	1	4	yes	—
192	C₄×C₁₁	#536	1	1	yes	characteristic
193	C₄×C₁₁	#536	1	1	yes	characteristic
194	C₄×C₁₁	#541	1	2	yes	—
195	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
196	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
197	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
198	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
199	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
200	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
201	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
202	C₄⋊Q₈	—	2	4	no	—
203	C₄×Q₈	—	2	2	no	—
204	C₄×Q₈	—	2	2	no	—
205	C₄×Q₈	—	2	2	no	—
206	C₄×Q₈	—	2	2	no	—
207	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
208	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
209	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
210	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
211	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
212	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
213	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
214	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
215	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
216	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
217	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
218	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
219	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
220	C₄⋊C₈	—	2	4	no	—
221	C₄⋊C₈	—	2	4	no	—
222	C₄⋊C₈	—	2	2	no	—
223	C₄⋊C₈	—	2	2	no	—
224	#97	—	2	4	no	—
225	C₄×C₈	—	2	4	no	—
226	C₄×C₈	—	2	2	no	—
227	C₄×C₈	D₄×C₁₁	1	4	yes	—
228	#95	C₂×C₄×C₁₁	1	4	yes	—
229	#95	C₂×C₄×C₁₁	1	4	yes	—
230	C₂×C₁₁	#2327	1	1	yes	characteristic
231	C₂×C₁₁	C₂×#435	1	1	yes	characteristic
232	C₂×C₁₁	#2931	1	1	yes	characteristic
233	C₂×C₁₁	#2984	1	2	yes	—
234	C₂×C₁₁	#2986	1	2	yes	—
235	C₂×Q₈	—	2	2	no	—
236	C₂×Q₈	—	2	2	no	—
237	C₂×Q₈	—	2	2	no	—
238	C₂×Q₈	—	2	2	no	—
239	C₂×Q₈	—	2	2	no	—
240	C₂×Q₈	C₁₁×M₁₆	1	4	yes	—
241	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
242	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
243	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
244	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
245	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
246	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
247	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
248	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
249	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	2	4	no	—
256	C₂×C₈	—	2	4	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
260	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
261	C₄⋊C₄	—	2	4	no	—
262	C₄⋊C₄	—	2	2	no	—
263	C₄⋊C₄	—	2	2	no	—
264	C₄⋊C₄	—	2	4	no	—
265	C₄⋊C₄	—	2	8	no	—
266	C₄⋊C₄	—	2	8	no	—
267	C₄²	—	2	2	no	—
268	C₄²	—	2	4	no	—
269	C₄²	—	2	2	no	—
270	C₄²	—	2	2	no	—
271	C₄²	—	2	2	no	—
272	C₄²	—	2	2	no	—
273	C₄²	—	2	2	no	—
274	C₄²	—	2	2	no	—
275	C₄²	—	2	2	no	—
276	C₄²	C₂×D₄×C₁₁	1	2	yes	—
277	C₄²	C₁₁×#41	1	2	yes	—
278	C₁₁	#22240	1	1	yes	characteristic, direct product factor, Sylow
279	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
280	Q₈	—	2	8	no	—
281	Q₈	—	4	4	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	2	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	4	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
298	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
299	C₂×C₄	C₂×C₁₁×M₁₆	1	4	yes	—
300	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
301	C₂×C₄	C₁₁×#131	1	4	yes	—
302	C₂×C₄	C₁₁×#131	1	2	yes	—
303	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
304	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
305	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
306	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
307	C₈	—	2	2	no	—
308	C₈	—	2	2	no	—
309	C₈	—	4	2	no	—
310	C₈	—	4	2	no	—
311	C₈	—	4	2	no	—
312	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
313	C₂²	C₁₁×#519	1	2	yes	—
314	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
315	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
316	C₂²	C₂×C₁₁×#131	1	2	yes	—
317	C₄	—	2	4	no	—
318	C₄	—	2	2	no	—
319	C₄	—	2	4	no	—
320	C₄	—	4	2	no	—
321	C₄	—	4	2	no	—
322	C₄	—	4	2	no	—
323	C₄	—	4	2	no	—
324	C₄	C₁₁×#435	1	4	yes	—
325	C₄	C₁₁×#536	1	1	yes	characteristic
326	C₄	C₁₁×#536	1	1	yes	characteristic
327	C₄	C₁₁×#541	1	2	yes	—
328	C₂	C₁₁×#2327	1	1	yes	characteristic
329	C₂	C₂×C₁₁×#435	1	1	yes	characteristic
330	C₂	C₁₁×#2931	1	1	yes	characteristic
331	C₂	C₁₁×#2984	1	2	yes	—
332	C₂	C₁₁×#2986	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
69. #22240	C₁₁	direct (N × H)
278. C₁₁	#22240	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×#446	2
C₂×C₈×Q₈×C₁₁	2
C₄×C₁₁×C₄⋊Q₈	2
C₁₁×#1984	2
C₁₁×#1917	2
C₁₁×#1916	2
C₁₁×#1831	2
C₁₁×#1744	2
#22240	11

Subgroups — C11×#22240 #14599433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22240 #14599433