Subgroups — C₁₁×#18042 #14595235

Order 2816.

630 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₁₁×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1593	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1587	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1579	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1566	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#1487	C₂	1	2	yes	maximal
8	C₁₁×#1451	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₁×Q₁₆	C₄	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
11	C₁₁×#446	—	2	4	no	—
12	C₁₁×#446	C₂²	1	4	yes	—
13	C₈×Q₈×C₁₁	C₂²	1	4	yes	—
14	C₄×C₁₁×Q₁₆	C₄	1	2	yes	—
15	C₄×C₁₁×Q₁₆	C₄	1	1	yes	characteristic
16	C₄×C₁₁×Q₁₆	C₄	1	1	yes	characteristic
17	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
18	C₄×C₁₁×Q₁₆	C₂²	1	2	yes	—
19	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
20	C₁₁×#431	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×#107	C₄	1	1	yes	characteristic
22	C₁₁×#423	—	2	2	no	—
23	C₁₁×#423	C₂²	1	2	yes	—
24	C₂×C₁₁×#103	C₄	1	2	yes	—
25	C₄×C₁₁×M₁₆	—	2	2	no	—
26	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
28	C₁₁×#334	C₂²	1	2	yes	—
29	C₁₁×#334	C₂²	1	2	yes	—
30	C₁₁×Q₈⋊C₈	C₂²	1	4	yes	—
31	C₁₁×Q₈⋊C₈	C₂²	1	4	yes	—
32	C₁₁×#322	C₂²	1	2	yes	—
33	C₁₁×#322	C₂²	1	2	yes	—
34	C₂²×Q₈×C₁₁	C₂×C₄	1	2	yes	—
35	C₂×C₁₁×Q₁₆	—	2	4	no	—
36	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
37	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
38	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₁×M₁₆	—	2	2	no	—
40	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
41	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₄×Q₈×C₁₁	—	2	2	no	—
44	C₄×Q₈×C₁₁	—	2	2	no	—
45	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
46	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
47	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
48	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
49	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
50	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₁	—	2	2	no	—
52	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
53	C₁₁×#107	C₂×C₄	1	2	yes	—
54	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
55	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
56	C₁₁×C₄⋊C₈	—	2	4	no	—
57	C₁₁×C₄⋊C₈	—	2	4	no	—
58	C₁₁×C₄⋊C₈	—	2	2	no	—
59	C₁₁×C₄⋊C₈	—	2	1	no	—
60	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
61	C₁₁×#103	C₂×C₄	1	2	yes	—
62	C₁₁×#103	C₂×C₄	1	2	yes	—
63	C₁₁×#103	C₂×C₄	1	2	yes	—
64	C₁₁×#103	C₂×C₄	1	2	yes	—
65	C₁₁×C₂²⋊C₈	—	2	1	no	—
66	C₁₁×#97	—	2	4	no	—
67	C₁₁×#97	D₄	1	2	yes	—
68	C₄×C₈×C₁₁	—	2	4	no	—
69	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
70	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
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	#18042	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂×Q₈×C₁₁	—	2	2	no	—
77	C₂×Q₈×C₁₁	—	2	4	no	—
78	C₂×Q₈×C₁₁	—	4	2	no	—
79	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
80	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₁	—	2	2	no	—
82	C₂²×C₄×C₁₁	—	2	2	no	—
83	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
86	C₁₁×Q₁₆	—	2	2	no	—
87	C₁₁×Q₁₆	—	2	4	no	—
88	C₁₁×Q₁₆	M₁₆	1	4	yes	complemented
89	C₁₁×M₁₆	—	2	4	no	—
90	C₁₁×M₁₆	—	4	4	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	1	no	—
95	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
100	C₁₁×C₄⋊C₄	—	2	2	no	—
101	C₁₁×C₄⋊C₄	—	2	2	no	—
102	C₁₁×C₄⋊C₄	—	2	2	no	—
103	C₁₁×C₄⋊C₄	—	2	2	no	—
104	C₁₁×C₄⋊C₄	—	2	2	no	—
105	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
106	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
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	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₁₁	#41	1	1	yes	characteristic
114	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
115	Q₈×M₁₆	C₂×C₁₁	1	2	yes	—
116	C₂×C₄×Q₁₆	C₂×C₁₁	1	1	yes	characteristic
117	#1593	C₂×C₁₁	1	2	yes	complemented
118	#1587	C₂×C₁₁	1	4	yes	complemented
119	#1579	C₂×C₁₁	1	2	yes	complemented
120	#1566	C₂×C₁₁	1	1	yes	characteristic
121	#1487	C₂×C₁₁	1	2	yes	—
122	#1451	C₂×C₁₁	1	1	yes	characteristic
123	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
124	Q₈×C₁₁	—	2	2	no	—
125	Q₈×C₁₁	—	2	2	no	—
126	Q₈×C₁₁	—	2	2	no	—
127	Q₈×C₁₁	—	4	4	no	—
128	Q₈×C₁₁	C₂×M₁₆	1	4	yes	—
129	C₂×C₄×C₁₁	—	2	2	no	—
130	C₂×C₄×C₁₁	—	2	1	no	—
131	C₂×C₄×C₁₁	—	2	1	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	—	4	1	no	—
136	C₂×C₄×C₁₁	—	4	4	no	—
137	C₂×C₄×C₁₁	—	8	2	no	—
138	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
139	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
140	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₁₁	#137	1	4	yes	—
142	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
145	C₈×C₁₁	—	2	1	no	—
146	C₈×C₁₁	—	2	1	no	—
147	C₈×C₁₁	—	2	1	no	—
148	C₈×C₁₁	—	2	4	no	—
149	C₈×C₁₁	—	4	2	no	—
150	C₈×C₁₁	—	4	4	no	—
151	C₈×C₁₁	C₂×M₁₆	1	2	yes	—
152	C₂²×Q₁₆	C₄×C₁₁	1	1	yes	characteristic
153	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
154	#446	—	2	4	no	—
155	#446	C₂²×C₁₁	1	4	yes	—
156	C₈×Q₈	C₂²×C₁₁	1	4	yes	—
157	C₄×Q₁₆	C₄×C₁₁	1	2	yes	—
158	C₄×Q₁₆	C₄×C₁₁	1	1	yes	characteristic
159	C₄×Q₁₆	C₄×C₁₁	1	1	yes	characteristic
160	C₄×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
161	C₄×Q₁₆	C₂²×C₁₁	1	2	yes	—
162	C₄×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
163	#431	C₂²×C₁₁	1	1	yes	characteristic
164	C₂×#107	C₄×C₁₁	1	1	yes	characteristic
165	#423	—	2	2	no	—
166	#423	C₂²×C₁₁	1	2	yes	—
167	C₂×#103	C₄×C₁₁	1	2	yes	—
168	C₄×M₁₆	—	2	2	no	—
169	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
170	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
171	#334	C₂²×C₁₁	1	2	yes	—
172	#334	C₂²×C₁₁	1	2	yes	—
173	Q₈⋊C₈	C₂²×C₁₁	1	4	yes	—
174	Q₈⋊C₈	C₂²×C₁₁	1	4	yes	—
175	#322	C₂²×C₁₁	1	2	yes	—
176	#322	C₂²×C₁₁	1	2	yes	—
177	C₂²×C₁₁	—	2	1	no	—
178	C₂²×C₁₁	—	2	1	no	—
179	C₂²×C₁₁	#441	1	2	yes	—
180	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
181	C₄×C₁₁	—	2	1	no	—
182	C₄×C₁₁	—	2	4	no	—
183	C₄×C₁₁	—	2	1	no	—
184	C₄×C₁₁	—	2	1	no	—
185	C₄×C₁₁	—	4	2	no	—
186	C₄×C₁₁	—	4	2	no	—
187	C₄×C₁₁	—	4	2	no	—
188	C₄×C₁₁	#441	1	2	yes	—
189	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
190	C₄×C₁₁	#568	1	1	yes	characteristic
191	C₄×C₁₁	C₂×#137	1	2	yes	—
192	C₂²×Q₈	C₂×C₄×C₁₁	1	2	yes	—
193	C₂×Q₁₆	—	2	4	no	—
194	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
195	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
196	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
197	C₂×M₁₆	—	2	2	no	—
198	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
199	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
200	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
201	C₄×Q₈	—	2	2	no	—
202	C₄×Q₈	—	2	2	no	—
203	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
204	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
205	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
206	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
207	C₂×C₄⋊C₄	—	2	2	no	—
208	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
209	C₂×C₄²	—	2	2	no	—
210	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
211	#107	C₂×C₄×C₁₁	1	2	yes	—
212	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
213	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
214	C₄⋊C₈	—	2	4	no	—
215	C₄⋊C₈	—	2	4	no	—
216	C₄⋊C₈	—	2	2	no	—
217	C₄⋊C₈	—	2	1	no	—
218	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
219	#103	C₂×C₄×C₁₁	1	2	yes	—
220	#103	C₂×C₄×C₁₁	1	2	yes	—
221	#103	C₂×C₄×C₁₁	1	2	yes	—
222	#103	C₂×C₄×C₁₁	1	2	yes	—
223	C₂²⋊C₈	—	2	1	no	—
224	#97	—	2	4	no	—
225	#97	D₄×C₁₁	1	2	yes	—
226	C₄×C₈	—	2	4	no	—
227	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
228	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
229	C₄×C₈	C₂³×C₁₁	1	2	yes	—
230	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
231	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
232	C₄×C₈	C₂³×C₁₁	1	2	yes	—
233	C₂×C₁₁	—	2	2	no	—
234	C₂×C₁₁	D₄×M₁₆	1	1	yes	characteristic
235	C₂×C₁₁	C₂×#441	1	1	yes	characteristic
236	C₂×C₁₁	#2957	1	1	yes	characteristic
237	C₂×Q₈	—	2	2	no	—
238	C₂×Q₈	—	2	4	no	—
239	C₂×Q₈	—	4	2	no	—
240	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
241	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
245	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
246	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
247	Q₁₆	—	2	4	no	—
248	Q₁₆	—	2	2	no	—
249	Q₁₆	C₁₁×M₁₆	1	4	yes	complemented
250	M₁₆	—	2	4	no	—
251	M₁₆	—	4	4	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	4	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	4	1	no	—
256	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
257	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
258	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
259	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
260	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
261	C₄⋊C₄	—	2	2	no	—
262	C₄⋊C₄	—	2	2	no	—
263	C₄⋊C₄	—	2	2	no	—
264	C₄⋊C₄	—	2	2	no	—
265	C₄⋊C₄	—	2	2	no	—
266	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
267	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
268	C₄²	—	2	2	no	—
269	C₄²	—	2	2	no	—
270	C₄²	—	2	2	no	—
271	C₄²	—	2	2	no	—
272	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
273	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
274	C₄²	C₁₁×#41	1	1	yes	characteristic
275	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
276	C₁₁	#18042	1	1	yes	characteristic, direct product factor, Sylow
277	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
278	Q₈	—	2	2	no	—
279	Q₈	—	2	2	no	—
280	Q₈	—	2	2	no	—
281	Q₈	—	4	4	no	—
282	Q₈	C₂×C₁₁×M₁₆	1	4	yes	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	1	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	4	1	no	—
290	C₂×C₄	—	4	4	no	—
291	C₂×C₄	—	8	2	no	—
292	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
293	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
294	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
295	C₂×C₄	C₁₁×#137	1	4	yes	—
296	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
297	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
298	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
299	C₈	—	2	1	no	—
300	C₈	—	2	1	no	—
301	C₈	—	2	1	no	—
302	C₈	—	2	4	no	—
303	C₈	—	4	2	no	—
304	C₈	—	4	4	no	—
305	C₈	C₂×C₁₁×M₁₆	1	2	yes	—
306	C₂²	—	2	1	no	—
307	C₂²	—	2	1	no	—
308	C₂²	C₁₁×#441	1	2	yes	—
309	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
310	C₄	—	2	1	no	—
311	C₄	—	2	4	no	—
312	C₄	—	2	1	no	—
313	C₄	—	2	1	no	—
314	C₄	—	4	2	no	—
315	C₄	—	4	2	no	—
316	C₄	—	4	2	no	—
317	C₄	C₁₁×#441	1	2	yes	—
318	C₄	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
319	C₄	C₁₁×#568	1	1	yes	characteristic
320	C₄	C₂×C₁₁×#137	1	2	yes	—
321	C₂	—	2	2	no	—
322	C₂	D₄×C₁₁×M₁₆	1	1	yes	characteristic
323	C₂	C₂×C₁₁×#441	1	1	yes	characteristic
324	C₂	C₁₁×#2957	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	C₂³×C₁₁	C₄×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₄×C₁₁×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1593	C₂	semidirect
4. C₁₁×#1587	C₂	semidirect
5. C₁₁×#1579	C₂	semidirect
75. #18042	C₁₁	direct (N × H)
88. C₁₁×Q₁₆	M₁₆	semidirect
117. #1593	C₂×C₁₁	semidirect
118. #1587	C₂×C₁₁	semidirect
119. #1579	C₂×C₁₁	semidirect
249. Q₁₆	C₁₁×M₁₆	semidirect
276. C₁₁	#18042	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×C₁₁×M₁₆	2
C₂×C₄×C₁₁×Q₁₆	2
C₁₁×#1593	2
C₁₁×#1587	2
C₁₁×#1579	2
C₁₁×#1566	2
C₁₁×#1487	2
C₁₁×#1451	2
#18042	11

Subgroups — C11×#18042 #14595235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#18042 #14595235