Subgroups — C₁₁×#22672 #14599865

Order 2816.

1050 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#442	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₁×D₈	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2349	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1943	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1862	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1846	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1804	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
11	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
12	C₁₁×#442	—	2	8	no	—
13	C₄×C₁₁×D₈	C₄	1	8	yes	complemented
14	C₂×C₁₁×#107	C₂²	1	2	yes	—
15	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×#106	C₂²	1	2	yes	—
17	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×#102	C₂²	1	4	yes	—
19	C₂×C₁₁×#102	C₂²	1	2	yes	—
20	C₂×C₁₁×#97	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
22	C₁₁×#389	C₂²	1	4	yes	—
23	C₁₁×#385	—	2	4	no	—
24	C₁₁×#382	C₂²	1	2	yes	—
25	C₁₁×#380	—	2	2	no	—
26	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₁₁×#95	—	2	2	no	—
28	C₁₁×#340	C₂²	1	4	yes	—
29	C₁₁×#336	C₂²	1	2	yes	—
30	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
31	C₂³×C₄×C₁₁	—	2	2	no	—
32	C₂³×C₄×C₁₁	—	2	4	no	—
33	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	—
34	C₂×C₁₁×D₈	D₄	1	4	yes	—
35	C₂×C₁₁×D₈	Q₈	1	4	yes	—
36	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
37	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
39	C₄×D₄×C₁₁	—	2	8	no	—
40	C₄×D₄×C₁₁	—	2	4	no	—
41	C₄×D₄×C₁₁	—	4	4	no	—
42	C₄×D₄×C₁₁	C₂×C₄	1	8	yes	complemented
43	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
44	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
45	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
46	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
47	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
48	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
49	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
50	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
51	C₁₁×#107	—	4	2	no	—
52	C₁₁×#107	C₂×C₄	1	4	yes	complemented
53	C₁₁×#106	—	2	4	no	—
54	C₁₁×C₄⋊C₈	—	2	2	no	—
55	C₁₁×#102	—	2	8	no	—
56	C₁₁×#102	C₂×C₄	1	8	yes	complemented
57	C₁₁×#97	—	2	4	no	—
58	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	complemented
59	C₁₁×#95	—	2	2	no	—
60	C₁₁×#95	—	2	4	no	—
61	C₁₁×#95	—	2	2	no	—
62	C₁₁×#95	D₄	1	2	yes	—
63	#22672	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂⁴×C₁₁	—	2	2	no	—
65	C₂×D₄×C₁₁	—	2	2	no	—
66	C₂×D₄×C₁₁	—	2	2	no	—
67	C₂×D₄×C₁₁	—	2	2	no	—
68	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
69	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
70	C₂×D₄×C₁₁	C₂×Q₈	1	4	yes	—
71	C₂²×C₄×C₁₁	—	2	2	no	—
72	C₂²×C₄×C₁₁	—	2	8	no	—
73	C₂²×C₄×C₁₁	—	2	4	no	—
74	C₂²×C₄×C₁₁	—	4	8	no	—
75	C₂²×C₄×C₁₁	—	4	8	no	—
76	C₂²×C₄×C₁₁	—	8	4	no	—
77	C₂²×C₄×C₁₁	—	8	4	no	—
78	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
79	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
82	C₁₁×D₈	C₄⋊C₄	1	16	yes	complemented
83	C₂×C₈×C₁₁	—	2	2	no	—
84	C₂×C₈×C₁₁	—	2	2	no	—
85	C₂×C₈×C₁₁	—	2	1	no	—
86	C₂×C₈×C₁₁	—	2	1	no	—
87	C₂×C₈×C₁₁	—	2	2	no	—
88	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
89	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
90	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
91	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
92	C₁₁×C₄⋊C₄	—	2	2	no	—
93	C₁₁×C₄⋊C₄	—	2	4	no	—
94	C₁₁×C₄⋊C₄	—	2	4	no	—
95	C₁₁×C₄⋊C₄	—	4	2	no	—
96	C₁₁×C₄⋊C₄	—	8	4	no	—
97	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
98	C₁₁×C₂²⋊C₄	—	2	8	no	—
99	C₁₁×C₂²⋊C₄	—	4	8	no	—
100	C₄²×C₁₁	—	2	2	no	—
101	C₄²×C₁₁	—	2	2	no	—
102	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
103	C₄²×C₁₁	#41	1	2	yes	—
104	C₂×#442	C₂×C₁₁	1	2	yes	—
105	C₂×C₄×D₈	C₂×C₁₁	1	1	yes	characteristic
106	#2349	C₂×C₁₁	1	2	yes	complemented
107	#1943	C₂×C₁₁	1	2	yes	complemented
108	#1862	C₂×C₁₁	1	4	yes	complemented
109	#1846	C₂×C₁₁	1	1	yes	characteristic, complemented
110	#1804	C₂×C₁₁	1	2	yes	complemented
111	#1770	C₂×C₁₁	1	1	yes	characteristic, complemented
112	C₂³×C₁₁	—	2	4	no	—
113	C₂³×C₁₁	—	2	4	no	—
114	C₂³×C₁₁	—	2	4	no	—
115	C₂³×C₁₁	—	4	4	no	—
116	C₂³×C₁₁	—	4	4	no	—
117	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
118	D₄×C₁₁	—	2	4	no	—
119	D₄×C₁₁	—	2	4	no	—
120	D₄×C₁₁	—	2	4	no	—
121	D₄×C₁₁	C₂×C₄⋊C₄	1	8	yes	—
122	C₂×C₄×C₁₁	—	2	2	no	—
123	C₂×C₄×C₁₁	—	2	2	no	—
124	C₂×C₄×C₁₁	—	2	4	no	—
125	C₂×C₄×C₁₁	—	2	4	no	—
126	C₂×C₄×C₁₁	—	2	4	no	—
127	C₂×C₄×C₁₁	—	2	4	no	—
128	C₂×C₄×C₁₁	—	4	4	no	—
129	C₂×C₄×C₁₁	—	4	4	no	—
130	C₂×C₄×C₁₁	—	4	4	no	—
131	C₂×C₄×C₁₁	—	4	4	no	—
132	C₂×C₄×C₁₁	—	8	8	no	—
133	C₂×C₄×C₁₁	—	8	16	no	—
134	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
135	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
136	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
139	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
140	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
141	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
142	C₈×C₁₁	—	2	2	no	—
143	C₈×C₁₁	—	4	2	no	—
144	C₈×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
145	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
146	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
147	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
148	#442	—	2	8	no	—
149	C₄×D₈	C₄×C₁₁	1	8	yes	complemented
150	C₂×#107	C₂²×C₁₁	1	2	yes	—
151	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
152	C₂×#106	C₂²×C₁₁	1	2	yes	—
153	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
154	C₂×#102	C₂²×C₁₁	1	4	yes	—
155	C₂×#102	C₂²×C₁₁	1	2	yes	—
156	C₂×#97	C₂²×C₁₁	1	2	yes	—
157	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
158	#389	C₂²×C₁₁	1	4	yes	—
159	#385	—	2	4	no	—
160	#382	C₂²×C₁₁	1	2	yes	—
161	#380	—	2	2	no	—
162	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
163	C₂×#95	—	2	2	no	—
164	#340	C₂²×C₁₁	1	4	yes	—
165	#336	C₂²×C₁₁	1	2	yes	—
166	C₂²×C₁₁	—	2	8	no	—
167	C₂²×C₁₁	—	4	8	no	—
168	C₂²×C₁₁	—	4	4	no	—
169	C₂²×C₁₁	—	4	4	no	—
170	C₂²×C₁₁	—	4	8	no	—
171	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
172	C₂²×C₁₁	D₄²	1	1	yes	characteristic
173	C₂²×C₁₁	D₄×Q₈	1	1	yes	characteristic
174	C₂²×C₁₁	#575	1	2	yes	—
175	C₂²×C₁₁	#576	1	2	yes	—
176	C₄×C₁₁	—	2	2	no	—
177	C₄×C₁₁	—	2	2	no	—
178	C₄×C₁₁	—	4	4	no	—
179	C₄×C₁₁	—	4	4	no	—
180	C₄×C₁₁	—	8	4	no	—
181	C₄×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
182	C₄×C₁₁	#520	1	1	yes	characteristic
183	C₄×C₁₁	#547	1	1	yes	characteristic
184	C₄×C₁₁	#554	1	1	yes	characteristic
185	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
186	C₂³×C₄	—	2	2	no	—
187	C₂³×C₄	—	2	4	no	—
188	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	—
189	C₂×D₈	D₄×C₁₁	1	4	yes	—
190	C₂×D₈	Q₈×C₁₁	1	4	yes	—
191	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
192	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
193	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
194	C₄×D₄	—	2	8	no	—
195	C₄×D₄	—	2	4	no	—
196	C₄×D₄	—	4	4	no	—
197	C₄×D₄	C₂×C₄×C₁₁	1	8	yes	complemented
198	C₂×C₄⋊C₄	—	2	4	no	—
199	C₂×C₄⋊C₄	D₄×C₁₁	1	2	yes	—
200	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
201	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
202	C₂×C₂²⋊C₄	—	2	2	no	—
203	C₂×C₂²⋊C₄	—	2	4	no	—
204	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
205	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
206	#107	—	4	2	no	—
207	#107	C₂×C₄×C₁₁	1	4	yes	complemented
208	#106	—	2	4	no	—
209	C₄⋊C₈	—	2	2	no	—
210	#102	—	2	8	no	—
211	#102	C₂×C₄×C₁₁	1	8	yes	complemented
212	#97	—	2	4	no	—
213	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	complemented
214	#95	—	2	2	no	—
215	#95	—	2	4	no	—
216	#95	—	2	2	no	—
217	#95	D₄×C₁₁	1	2	yes	—
218	C₂×C₁₁	—	4	8	no	—
219	C₂×C₁₁	D₄×C₄⋊C₄	1	1	yes	characteristic
220	C₂×C₁₁	#2943	1	1	yes	characteristic
221	C₂×C₁₁	#2948	1	1	yes	characteristic
222	C₂×C₁₁	#3273	1	2	yes	—
223	C₂×C₁₁	#3389	1	2	yes	—
224	C₂⁴	—	2	2	no	—
225	C₂×D₄	—	2	2	no	—
226	C₂×D₄	—	2	2	no	—
227	C₂×D₄	—	2	2	no	—
228	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
229	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
230	C₂×D₄	C₂×Q₈×C₁₁	1	4	yes	—
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	2	8	no	—
233	C₂²×C₄	—	2	4	no	—
234	C₂²×C₄	—	4	8	no	—
235	C₂²×C₄	—	4	8	no	—
236	C₂²×C₄	—	8	4	no	—
237	C₂²×C₄	—	8	4	no	—
238	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
239	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
240	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
241	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
242	D₈	C₁₁×C₄⋊C₄	1	16	yes	complemented
243	C₂×C₈	—	2	1	no	—
244	C₂×C₈	—	2	1	no	—
245	C₂×C₈	—	2	2	no	—
246	C₂×C₈	—	2	2	no	—
247	C₂×C₈	—	2	2	no	—
248	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
249	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
250	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
251	C₂×C₈	C₂×Q₈×C₁₁	1	2	yes	—
252	C₄⋊C₄	—	2	2	no	—
253	C₄⋊C₄	—	2	4	no	—
254	C₄⋊C₄	—	2	4	no	—
255	C₄⋊C₄	—	4	2	no	—
256	C₄⋊C₄	—	8	4	no	—
257	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
258	C₂²⋊C₄	—	2	8	no	—
259	C₂²⋊C₄	—	4	8	no	—
260	C₄²	—	2	2	no	—
261	C₄²	—	2	2	no	—
262	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
263	C₄²	C₁₁×#41	1	2	yes	—
264	C₁₁	#22672	1	1	yes	characteristic, direct product factor, Sylow
265	C₂³	—	2	4	no	—
266	C₂³	—	2	4	no	—
267	C₂³	—	2	4	no	—
268	C₂³	—	4	4	no	—
269	C₂³	—	4	4	no	—
270	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
271	D₄	—	2	4	no	—
272	D₄	—	2	4	no	—
273	D₄	—	2	4	no	—
274	D₄	C₂×C₁₁×C₄⋊C₄	1	8	yes	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	4	no	—
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	4	no	—
281	C₂×C₄	—	4	4	no	—
282	C₂×C₄	—	4	4	no	—
283	C₂×C₄	—	4	4	no	—
284	C₂×C₄	—	4	4	no	—
285	C₂×C₄	—	8	8	no	—
286	C₂×C₄	—	8	16	no	—
287	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
288	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
289	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
290	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
291	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
292	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
293	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
294	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
295	C₈	—	2	2	no	—
296	C₈	—	4	2	no	—
297	C₈	C₂×C₁₁×C₄⋊C₄	1	4	yes	—
298	C₂²	—	2	8	no	—
299	C₂²	—	4	4	no	—
300	C₂²	—	4	4	no	—
301	C₂²	—	4	8	no	—
302	C₂²	—	4	8	no	—
303	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
304	C₂²	D₄²×C₁₁	1	1	yes	characteristic
305	C₂²	D₄×Q₈×C₁₁	1	1	yes	characteristic
306	C₂²	C₁₁×#575	1	2	yes	—
307	C₂²	C₁₁×#576	1	2	yes	—
308	C₄	—	2	2	no	—
309	C₄	—	2	2	no	—
310	C₄	—	4	4	no	—
311	C₄	—	4	4	no	—
312	C₄	—	8	4	no	—
313	C₄	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
314	C₄	C₁₁×#520	1	1	yes	characteristic
315	C₄	C₁₁×#547	1	1	yes	characteristic
316	C₄	C₁₁×#554	1	1	yes	characteristic
317	C₂	—	4	8	no	—
318	C₂	D₄×C₁₁×C₄⋊C₄	1	1	yes	characteristic
319	C₂	C₁₁×#2943	1	1	yes	characteristic
320	C₂	C₁₁×#2948	1	1	yes	characteristic
321	C₂	C₁₁×#3273	1	2	yes	—
322	C₂	C₁₁×#3389	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂²×C₁₁×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₄×C₁₁×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#2349	C₂	semidirect
4. C₁₁×#1943	C₂	semidirect
5. C₁₁×#1862	C₂	semidirect
6. C₁₁×#1846	C₂	semidirect
7. C₁₁×#1804	C₂	semidirect
8. C₁₁×#1770	C₂	semidirect
13. C₄×C₁₁×D₈	C₄	semidirect
42. C₄×D₄×C₁₁	C₂×C₄	semidirect
52. C₁₁×#107	C₂×C₄	semidirect
56. C₁₁×#102	C₂×C₄	semidirect
58. C₄×C₈×C₁₁	C₂×C₄	semidirect
63. #22672	C₁₁	direct (N × H)
82. C₁₁×D₈	C₄⋊C₄	semidirect
106. #2349	C₂×C₁₁	semidirect
107. #1943	C₂×C₁₁	semidirect
108. #1862	C₂×C₁₁	semidirect
109. #1846	C₂×C₁₁	semidirect
110. #1804	C₂×C₁₁	semidirect
111. #1770	C₂×C₁₁	semidirect
149. C₄×D₈	C₄×C₁₁	semidirect
197. C₄×D₄	C₂×C₄×C₁₁	semidirect
207. #107	C₂×C₄×C₁₁	semidirect
211. #102	C₂×C₄×C₁₁	semidirect
213. C₄×C₈	C₂×C₄×C₁₁	semidirect
242. D₈	C₁₁×C₄⋊C₄	semidirect
264. C₁₁	#22672	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×#442	2
C₂×C₄×C₁₁×D₈	2
C₁₁×#2349	2
C₁₁×#1943	2
C₁₁×#1862	2
C₁₁×#1846	2
C₁₁×#1804	2
C₁₁×#1770	2
#22672	11

Subgroups — C11×#22672 #14599865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22672 #14599865