Subgroups — C₁₁×#18084 #14595277

Order 2816.

652 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3169	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2979	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1589	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1586	C₂	1	4	yes	maximal, complemented
5	C₈×C₁₁×D₈	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1484	C₂	1	2	yes	maximal, complemented
8	C₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#532	C₂²	1	2	yes	—
10	C₁₁×#500	C₄	1	1	yes	characteristic
11	C₁₁×#493	C₄	1	1	yes	characteristic
12	C₁₁×#486	C₄	1	2	yes	—
13	C₁₁×#466	C₄	1	2	yes	—
14	C₁₁×#466	C₄	1	2	yes	—
15	C₄×C₁₁×D₈	C₂²	1	2	yes	—
16	C₄×C₁₁×D₈	C₂²	1	2	yes	—
17	C₁₁×#436	—	2	2	no	—
18	C₁₁×#436	C₂²	1	4	yes	—
19	C₈×D₄×C₁₁	—	2	2	no	—
20	C₈×D₄×C₁₁	C₂²	1	4	yes	—
21	C₁₁×#431	C₂²	1	2	yes	—
22	C₁₁×#431	C₂²	1	1	yes	characteristic
23	C₁₁×#408	—	2	4	no	—
24	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
26	C₁₁×#335	C₂²	1	1	yes	characteristic
27	C₁₁×#335	C₂²	1	1	yes	characteristic
28	C₁₁×#334	C₂²	1	2	yes	—
29	C₁₁×D₄⋊C₈	C₂²	1	4	yes	—
30	C₁₁×D₄⋊C₈	C₂²	1	4	yes	—
31	C₁₁×#322	C₂²	1	2	yes	—
32	C₈²×C₁₁	C₂²	1	2	yes	—
33	C₂×C₁₁×#41	—	2	2	no	—
34	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
35	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
36	C₂×C₁₁×M₁₆	—	2	1	no	—
37	C₂×C₁₁×M₁₆	—	2	4	no	—
38	C₂²×C₈×C₁₁	—	2	4	no	—
39	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
41	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
42	C₁₁×#127	C₂×C₄	1	2	yes	—
43	C₁₁×#124	—	2	2	no	—
44	C₁₁×#121	—	2	2	no	—
45	C₁₁×#121	C₂×C₄	1	4	yes	—
46	C₄×D₄×C₁₁	—	2	2	no	—
47	C₄×D₄×C₁₁	C₂³	1	4	yes	—
48	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
49	C₁₁×#107	C₂×C₄	1	2	yes	—
50	C₁₁×#107	C₂×C₄	1	2	yes	—
51	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
52	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
53	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
54	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
55	C₁₁×#102	C₂×C₄	1	4	yes	—
56	C₁₁×#102	C₂×C₄	1	4	yes	—
57	C₁₁×C₂²⋊C₈	—	2	2	no	—
58	C₁₁×C₂²⋊C₈	—	2	4	no	—
59	C₁₁×C₂²⋊C₈	—	2	4	no	—
60	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
61	C₁₁×#97	—	2	1	no	—
62	C₄×C₈×C₁₁	—	2	2	no	—
63	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
64	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
65	C₄×C₈×C₁₁	C₂³	1	2	yes	—
66	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
68	C₄×C₈×C₁₁	C₂³	1	2	yes	—
69	#18084	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₁₁×#41	—	8	2	no	—
71	C₁₁×#41	—	8	2	no	—
72	C₂×Q₈×C₁₁	—	2	2	no	—
73	C₂×D₄×C₁₁	—	2	4	no	—
74	C₂×D₄×C₁₁	—	2	2	no	—
75	C₂×D₄×C₁₁	—	2	2	no	—
76	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
77	C₂²×C₄×C₁₁	—	2	4	no	—
78	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
81	C₁₁×D₈	—	2	4	no	—
82	C₁₁×D₈	—	4	2	no	—
83	C₁₁×M₁₆	—	2	4	no	—
84	C₁₁×M₁₆	—	8	4	no	—
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	—	4	1	no	—
90	C₂×C₈×C₁₁	—	8	4	no	—
91	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
96	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
97	C₁₁×C₄⋊C₄	—	2	2	no	—
98	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
99	C₁₁×C₂²⋊C₄	—	2	4	no	—
100	C₁₁×C₂²⋊C₄	—	2	4	no	—
101	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₁₁	#41	1	1	yes	characteristic
104	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
105	#3169	C₂×C₁₁	1	1	yes	characteristic
106	#2979	C₂×C₁₁	1	2	yes	complemented
107	#1589	C₂×C₁₁	1	2	yes	complemented
108	#1586	C₂×C₁₁	1	4	yes	complemented
109	C₈×D₈	C₂×C₁₁	1	2	yes	complemented
110	#1564	C₂×C₁₁	1	1	yes	characteristic, complemented
111	#1484	C₂×C₁₁	1	2	yes	complemented
112	C₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
113	C₂³×C₁₁	—	2	4	no	—
114	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
115	Q₈×C₁₁	—	8	2	no	—
116	D₄×C₁₁	—	2	4	no	—
117	D₄×C₁₁	—	2	4	no	—
118	D₄×C₁₁	—	4	4	no	—
119	D₄×C₁₁	—	8	2	no	—
120	D₄×C₁₁	—	8	4	no	—
121	C₂×C₄×C₁₁	—	2	1	no	—
122	C₂×C₄×C₁₁	—	2	1	no	—
123	C₂×C₄×C₁₁	—	2	1	no	—
124	C₂×C₄×C₁₁	—	2	1	no	—
125	C₂×C₄×C₁₁	—	2	2	no	—
126	C₂×C₄×C₁₁	—	2	4	no	—
127	C₂×C₄×C₁₁	—	4	4	no	—
128	C₂×C₄×C₁₁	—	4	4	no	—
129	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
130	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
131	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
132	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
135	C₈×C₁₁	—	2	4	no	—
136	C₈×C₁₁	—	2	1	no	—
137	C₈×C₁₁	—	2	1	no	—
138	C₈×C₁₁	—	2	1	no	—
139	C₈×C₁₁	—	2	2	no	—
140	C₈×C₁₁	—	2	2	no	—
141	C₈×C₁₁	—	4	2	no	—
142	C₈×C₁₁	—	4	2	no	—
143	C₈×C₁₁	#131	1	2	yes	—
144	#532	C₂²×C₁₁	1	2	yes	—
145	#500	C₄×C₁₁	1	1	yes	characteristic
146	#493	C₄×C₁₁	1	1	yes	characteristic
147	#486	C₄×C₁₁	1	2	yes	—
148	#466	C₄×C₁₁	1	2	yes	—
149	#466	C₄×C₁₁	1	2	yes	—
150	C₄×D₈	C₂²×C₁₁	1	2	yes	—
151	C₄×D₈	C₂²×C₁₁	1	2	yes	—
152	#436	—	2	2	no	—
153	#436	C₂²×C₁₁	1	4	yes	—
154	C₈×D₄	—	2	2	no	—
155	C₈×D₄	C₂²×C₁₁	1	4	yes	—
156	#431	C₂²×C₁₁	1	2	yes	—
157	#431	C₂²×C₁₁	1	1	yes	characteristic
158	#408	—	2	4	no	—
159	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
160	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
161	#335	C₂²×C₁₁	1	1	yes	characteristic
162	#335	C₂²×C₁₁	1	1	yes	characteristic
163	#334	C₂²×C₁₁	1	2	yes	—
164	D₄⋊C₈	C₂²×C₁₁	1	4	yes	—
165	D₄⋊C₈	C₂²×C₁₁	1	4	yes	—
166	#322	C₂²×C₁₁	1	2	yes	—
167	C₈²	C₂²×C₁₁	1	2	yes	—
168	C₂²×C₁₁	—	2	1	no	—
169	C₂²×C₁₁	—	2	1	no	—
170	C₂²×C₁₁	—	2	1	no	—
171	C₂²×C₁₁	—	4	4	no	—
172	C₂²×C₁₁	—	4	4	no	—
173	C₂²×C₁₁	—	4	4	no	—
174	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
175	C₄×C₁₁	—	2	1	no	—
176	C₄×C₁₁	—	2	1	no	—
177	C₄×C₁₁	—	2	1	no	—
178	C₄×C₁₁	—	4	4	no	—
179	C₄×C₁₁	#443	1	2	yes	—
180	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
181	C₄×C₁₁	#568	1	1	yes	characteristic
182	C₄×C₁₁	#576	1	1	yes	characteristic
183	C₄×C₁₁	#576	1	1	yes	characteristic
184	C₂×#41	—	2	2	no	—
185	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
186	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
187	C₂×M₁₆	—	2	1	no	—
188	C₂×M₁₆	—	2	4	no	—
189	C₂²×C₈	—	2	4	no	—
190	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
191	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
192	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
193	#127	C₂×C₄×C₁₁	1	2	yes	—
194	#124	—	2	2	no	—
195	#121	—	2	2	no	—
196	#121	C₂×C₄×C₁₁	1	4	yes	—
197	C₄×D₄	—	2	2	no	—
198	C₄×D₄	C₂³×C₁₁	1	4	yes	—
199	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
200	#107	C₂×C₄×C₁₁	1	2	yes	—
201	#107	C₂×C₄×C₁₁	1	2	yes	—
202	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
203	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
204	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
205	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
206	#102	C₂×C₄×C₁₁	1	4	yes	—
207	#102	C₂×C₄×C₁₁	1	4	yes	—
208	C₂²⋊C₈	—	2	2	no	—
209	C₂²⋊C₈	—	2	4	no	—
210	C₂²⋊C₈	—	2	4	no	—
211	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
212	#97	—	2	1	no	—
213	C₄×C₈	—	2	2	no	—
214	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
215	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
216	C₄×C₈	C₂³×C₁₁	1	2	yes	—
217	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
218	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
219	C₄×C₈	C₂³×C₁₁	1	2	yes	—
220	C₂×C₁₁	—	4	1	no	—
221	C₂×C₁₁	—	8	4	no	—
222	C₂×C₁₁	#2935	1	1	yes	characteristic
223	C₂×C₁₁	#2948	1	1	yes	characteristic
224	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
225	#41	—	8	2	no	—
226	#41	—	8	2	no	—
227	C₂×Q₈	—	2	2	no	—
228	C₂×D₄	—	2	4	no	—
229	C₂×D₄	—	2	2	no	—
230	C₂×D₄	—	2	2	no	—
231	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
232	C₂²×C₄	—	2	4	no	—
233	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
234	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
235	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
236	D₈	—	2	4	no	—
237	D₈	—	4	2	no	—
238	M₁₆	—	2	4	no	—
239	M₁₆	—	8	4	no	—
240	C₂×C₈	—	2	2	no	—
241	C₂×C₈	—	2	2	no	—
242	C₂×C₈	—	2	2	no	—
243	C₂×C₈	—	2	2	no	—
244	C₂×C₈	—	4	1	no	—
245	C₂×C₈	—	8	4	no	—
246	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
247	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
248	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
249	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
250	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
251	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
252	C₄⋊C₄	—	2	2	no	—
253	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
254	C₂²⋊C₄	—	2	4	no	—
255	C₂²⋊C₄	—	2	4	no	—
256	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
257	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
258	C₄²	C₁₁×#41	1	1	yes	characteristic
259	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
260	C₁₁	#18084	1	1	yes	characteristic, direct product factor, Sylow
261	C₂³	—	2	4	no	—
262	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
263	Q₈	—	8	2	no	—
264	D₄	—	2	4	no	—
265	D₄	—	2	4	no	—
266	D₄	—	4	4	no	—
267	D₄	—	8	2	no	—
268	D₄	—	8	4	no	—
269	C₂×C₄	—	2	1	no	—
270	C₂×C₄	—	2	1	no	—
271	C₂×C₄	—	2	1	no	—
272	C₂×C₄	—	2	1	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	4	no	—
275	C₂×C₄	—	4	4	no	—
276	C₂×C₄	—	4	4	no	—
277	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
278	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
279	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
280	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
281	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
282	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
283	C₈	—	2	4	no	—
284	C₈	—	2	1	no	—
285	C₈	—	2	1	no	—
286	C₈	—	2	1	no	—
287	C₈	—	2	2	no	—
288	C₈	—	2	2	no	—
289	C₈	—	4	2	no	—
290	C₈	—	4	2	no	—
291	C₈	C₁₁×#131	1	2	yes	—
292	C₂²	—	2	1	no	—
293	C₂²	—	2	1	no	—
294	C₂²	—	2	1	no	—
295	C₂²	—	4	4	no	—
296	C₂²	—	4	4	no	—
297	C₂²	—	4	4	no	—
298	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
299	C₄	—	2	1	no	—
300	C₄	—	2	1	no	—
301	C₄	—	2	1	no	—
302	C₄	—	4	4	no	—
303	C₄	C₁₁×#443	1	2	yes	—
304	C₄	C₂×C₁₁×#131	1	1	yes	characteristic
305	C₄	C₁₁×#568	1	1	yes	characteristic
306	C₄	C₁₁×#576	1	1	yes	characteristic
307	C₄	C₁₁×#576	1	1	yes	characteristic
308	C₂	—	4	1	no	—
309	C₂	—	8	4	no	—
310	C₂	C₁₁×#2935	1	1	yes	characteristic
311	C₂	C₁₁×#2948	1	1	yes	characteristic
312	C₂	C₂×C₁₁×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₄²	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₁₁×#3169	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₁₁×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2979	C₂	semidirect
3. C₁₁×#1589	C₂	semidirect
4. C₁₁×#1586	C₂	semidirect
5. C₈×C₁₁×D₈	C₂	semidirect
6. C₁₁×#1564	C₂	semidirect
7. C₁₁×#1484	C₂	semidirect
8. C₈×C₁₁×M₁₆	C₂	semidirect
69. #18084	C₁₁	direct (N × H)
106. #2979	C₂×C₁₁	semidirect
107. #1589	C₂×C₁₁	semidirect
108. #1586	C₂×C₁₁	semidirect
109. C₈×D₈	C₂×C₁₁	semidirect
110. #1564	C₂×C₁₁	semidirect
111. #1484	C₂×C₁₁	semidirect
112. C₈×M₁₆	C₂×C₁₁	semidirect
260. C₁₁	#18084	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×#3169	2
C₁₁×#2979	2
C₁₁×#1589	2
C₁₁×#1586	2
C₈×C₁₁×D₈	2
C₁₁×#1564	2
C₁₁×#1484	2
C₈×C₁₁×M₁₆	2
#18084	11

Subgroups — C11×#18084 #14595277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#18084 #14595277