Subgroups — C₁₁×#18063 #14595256

Order 2816.

648 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2991	C₂	1	2	yes	maximal, complemented
2	C₄×C₁₁×#135	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1594	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1583	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1579	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1566	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1489	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×#135	C₄	1	1	yes	characteristic
10	C₄×C₁₁×#41	C₂²	1	2	yes	—
11	C₈×Q₈×C₁₁	C₂²	1	4	yes	—
12	C₄×C₁₁×Q₁₆	C₄	1	1	yes	characteristic
13	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
14	C₄×C₁₁×SD₁₆	C₄	1	2	yes	—
15	C₄×C₁₁×SD₁₆	C₂²	1	2	yes	—
16	C₄×C₁₁×D₈	C₄	1	1	yes	characteristic
17	C₄×C₁₁×D₈	C₂²	1	1	yes	characteristic
18	C₁₁×#436	—	2	4	no	—
19	C₁₁×#436	C₂²	1	4	yes	—
20	C₁₁×#431	—	2	2	no	—
21	C₁₁×#431	C₂²	1	1	yes	characteristic
22	C₁₁×#427	C₄	1	1	yes	characteristic
23	C₁₁×#423	—	2	2	no	—
24	C₁₁×#423	C₂²	1	2	yes	—
25	C₁₁×#416	C₄	1	2	yes	—
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×D₄⋊C₈	C₂²	1	4	yes	—
32	C₁₁×#322	C₂²	1	2	yes	—
33	C₁₁×#322	C₂²	1	2	yes	—
34	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
35	C₁₁×#135	—	2	4	no	—
36	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
37	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
38	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₁×M₁₆	—	2	1	no	—
40	C₂×C₁₁×M₁₆	—	2	2	no	—
41	C₂×C₁₁×M₁₆	—	2	4	no	—
42	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
44	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
45	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
46	C₄×D₄×C₁₁	—	2	2	no	—
47	C₄×D₄×C₁₁	—	2	2	no	—
48	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₁₁	C₂³	1	2	yes	—
50	C₁₁×#117	—	2	2	no	—
51	C₁₁×#117	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₁	—	2	2	no	—
53	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
54	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
55	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
56	C₁₁×#106	C₂×C₄	1	2	yes	—
57	C₁₁×C₄⋊C₈	—	2	4	no	—
58	C₁₁×C₄⋊C₈	—	2	2	no	—
59	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
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×#102	C₂×C₄	1	2	yes	—
64	C₁₁×#102	C₂×C₄	1	2	yes	—
65	C₁₁×C₂²⋊C₈	—	2	4	no	—
66	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
67	C₁₁×#97	—	2	1	no	—
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	#18063	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₁₁×#41	—	2	4	no	—
77	C₁₁×#41	—	4	2	no	—
78	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
79	C₂×D₄×C₁₁	—	2	2	no	—
80	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₁	—	2	2	no	—
82	C₂²×C₄×C₁₁	—	2	2	no	—
83	C₂²×C₄×C₁₁	—	2	2	no	—
84	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
87	C₁₁×Q₁₆	M₁₆	1	4	yes	complemented
88	C₁₁×SD₁₆	—	2	4	no	—
89	C₁₁×D₈	—	2	2	no	—
90	C₁₁×M₁₆	—	4	2	no	—
91	C₁₁×M₁₆	—	8	2	no	—
92	C₁₁×M₁₆	—	8	4	no	—
93	C₂×C₈×C₁₁	—	2	2	no	—
94	C₂×C₈×C₁₁	—	2	4	no	—
95	C₂×C₈×C₁₁	—	2	2	no	—
96	C₂×C₈×C₁₁	—	4	1	no	—
97	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
102	C₁₁×C₄⋊C₄	—	2	2	no	—
103	C₁₁×C₄⋊C₄	—	2	2	no	—
104	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
105	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
106	C₁₁×C₂²⋊C₄	—	2	2	no	—
107	C₁₁×C₂²⋊C₄	—	2	2	no	—
108	C₁₁×C₂²⋊C₄	—	2	2	no	—
109	C₄²×C₁₁	—	2	2	no	—
110	C₄²×C₁₁	—	2	2	no	—
111	C₄²×C₁₁	—	2	2	no	—
112	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₁₁	#41	1	1	yes	characteristic
115	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
116	#2991	C₂×C₁₁	1	2	yes	complemented
117	C₄×#135	C₂×C₁₁	1	1	yes	characteristic
118	#1594	C₂×C₁₁	1	2	yes	complemented
119	#1583	C₂×C₁₁	1	4	yes	complemented
120	#1579	C₂×C₁₁	1	2	yes	complemented
121	#1566	C₂×C₁₁	1	1	yes	characteristic, complemented
122	#1489	C₂×C₁₁	1	2	yes	complemented
123	#1451	C₂×C₁₁	1	1	yes	characteristic, complemented
124	C₂³×C₁₁	—	2	2	no	—
125	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
126	Q₈×C₁₁	—	2	2	no	—
127	Q₈×C₁₁	C₂×M₁₆	1	4	yes	—
128	D₄×C₁₁	—	2	2	no	—
129	D₄×C₁₁	—	2	2	no	—
130	D₄×C₁₁	—	4	4	no	—
131	C₂×C₄×C₁₁	—	2	2	no	—
132	C₂×C₄×C₁₁	—	2	1	no	—
133	C₂×C₄×C₁₁	—	2	1	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	2	no	—
138	C₂×C₄×C₁₁	—	4	4	no	—
139	C₂×C₄×C₁₁	—	4	2	no	—
140	C₂×C₄×C₁₁	—	4	2	no	—
141	C₂×C₄×C₁₁	—	4	4	no	—
142	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
148	C₈×C₁₁	—	2	1	no	—
149	C₈×C₁₁	—	2	1	no	—
150	C₈×C₁₁	—	2	1	no	—
151	C₈×C₁₁	—	2	4	no	—
152	C₈×C₁₁	—	4	2	no	—
153	C₈×C₁₁	—	4	4	no	—
154	C₈×C₁₁	C₂×M₁₆	1	2	yes	—
155	C₂×#135	C₄×C₁₁	1	1	yes	characteristic
156	C₄×#41	C₂²×C₁₁	1	2	yes	—
157	C₈×Q₈	C₂²×C₁₁	1	4	yes	—
158	C₄×Q₁₆	C₄×C₁₁	1	1	yes	characteristic
159	C₄×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
160	C₄×SD₁₆	C₄×C₁₁	1	2	yes	—
161	C₄×SD₁₆	C₂²×C₁₁	1	2	yes	—
162	C₄×D₈	C₄×C₁₁	1	1	yes	characteristic
163	C₄×D₈	C₂²×C₁₁	1	1	yes	characteristic
164	#436	—	2	4	no	—
165	#436	C₂²×C₁₁	1	4	yes	—
166	#431	—	2	2	no	—
167	#431	C₂²×C₁₁	1	1	yes	characteristic
168	#427	C₄×C₁₁	1	1	yes	characteristic
169	#423	—	2	2	no	—
170	#423	C₂²×C₁₁	1	2	yes	—
171	#416	C₄×C₁₁	1	2	yes	—
172	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
173	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
174	#334	C₂²×C₁₁	1	2	yes	—
175	#334	C₂²×C₁₁	1	2	yes	—
176	Q₈⋊C₈	C₂²×C₁₁	1	4	yes	—
177	D₄⋊C₈	C₂²×C₁₁	1	4	yes	—
178	#322	C₂²×C₁₁	1	2	yes	—
179	#322	C₂²×C₁₁	1	2	yes	—
180	C₂²×C₁₁	—	2	1	no	—
181	C₂²×C₁₁	—	2	1	no	—
182	C₂²×C₁₁	—	2	1	no	—
183	C₂²×C₁₁	—	4	2	no	—
184	C₂²×C₁₁	—	4	2	no	—
185	C₂²×C₁₁	—	4	2	no	—
186	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
187	C₄×C₁₁	—	2	1	no	—
188	C₄×C₁₁	—	2	4	no	—
189	C₄×C₁₁	—	2	1	no	—
190	C₄×C₁₁	—	2	1	no	—
191	C₄×C₁₁	—	4	2	no	—
192	C₄×C₁₁	—	4	2	no	—
193	C₄×C₁₁	#444	1	2	yes	—
194	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
195	C₄×C₁₁	#568	1	1	yes	characteristic
196	C₄×C₁₁	#577	1	2	yes	—
197	C₂×#41	C₂×C₄×C₁₁	1	2	yes	—
198	#135	—	2	4	no	—
199	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
200	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
201	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
202	C₂×M₁₆	—	2	1	no	—
203	C₂×M₁₆	—	2	2	no	—
204	C₂×M₁₆	—	2	4	no	—
205	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
206	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
207	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
208	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
209	C₄×D₄	—	2	2	no	—
210	C₄×D₄	—	2	2	no	—
211	C₄×D₄	C₂×C₄×C₁₁	1	2	yes	—
212	C₄×D₄	C₂³×C₁₁	1	2	yes	—
213	#117	—	2	2	no	—
214	#117	C₂×C₄×C₁₁	1	2	yes	—
215	C₂×C₄²	—	2	2	no	—
216	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
217	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
218	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
219	#106	C₂×C₄×C₁₁	1	2	yes	—
220	C₄⋊C₈	—	2	4	no	—
221	C₄⋊C₈	—	2	2	no	—
222	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
223	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
224	#103	C₂×C₄×C₁₁	1	2	yes	—
225	#103	C₂×C₄×C₁₁	1	2	yes	—
226	#102	C₂×C₄×C₁₁	1	2	yes	—
227	#102	C₂×C₄×C₁₁	1	2	yes	—
228	C₂²⋊C₈	—	2	4	no	—
229	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
230	#97	—	2	1	no	—
231	C₄×C₈	—	2	4	no	—
232	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
233	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
234	C₄×C₈	C₂³×C₁₁	1	2	yes	—
235	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
236	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
237	C₄×C₈	C₂³×C₁₁	1	2	yes	—
238	C₂×C₁₁	—	4	1	no	—
239	C₂×C₁₁	—	8	2	no	—
240	C₂×C₁₁	D₄×M₁₆	1	1	yes	characteristic
241	C₂×C₁₁	#2952	1	1	yes	characteristic
242	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
243	#41	—	2	4	no	—
244	#41	—	4	2	no	—
245	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
246	C₂×D₄	—	2	2	no	—
247	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
252	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
253	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
254	Q₁₆	C₁₁×M₁₆	1	4	yes	complemented
255	SD₁₆	—	2	4	no	—
256	D₈	—	2	2	no	—
257	M₁₆	—	4	2	no	—
258	M₁₆	—	8	4	no	—
259	M₁₆	—	8	2	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	4	1	no	—
264	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
265	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
266	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
267	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
268	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	—	2	2	no	—
271	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
272	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
273	C₂²⋊C₄	—	2	2	no	—
274	C₂²⋊C₄	—	2	2	no	—
275	C₂²⋊C₄	—	2	2	no	—
276	C₄²	—	2	2	no	—
277	C₄²	—	2	2	no	—
278	C₄²	—	2	2	no	—
279	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
280	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
281	C₄²	C₁₁×#41	1	1	yes	characteristic
282	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
283	C₁₁	#18063	1	1	yes	characteristic, direct product factor, Sylow
284	C₂³	—	2	2	no	—
285	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
286	Q₈	—	2	2	no	—
287	Q₈	C₂×C₁₁×M₁₆	1	4	yes	—
288	D₄	—	2	2	no	—
289	D₄	—	2	2	no	—
290	D₄	—	4	4	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	4	4	no	—
299	C₂×C₄	—	4	2	no	—
300	C₂×C₄	—	4	2	no	—
301	C₂×C₄	—	4	4	no	—
302	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
303	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
304	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
305	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
306	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
307	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
308	C₈	—	2	1	no	—
309	C₈	—	2	1	no	—
310	C₈	—	2	1	no	—
311	C₈	—	2	4	no	—
312	C₈	—	4	2	no	—
313	C₈	—	4	4	no	—
314	C₈	C₂×C₁₁×M₁₆	1	2	yes	—
315	C₂²	—	2	1	no	—
316	C₂²	—	2	1	no	—
317	C₂²	—	2	1	no	—
318	C₂²	—	4	2	no	—
319	C₂²	—	4	2	no	—
320	C₂²	—	4	2	no	—
321	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
322	C₄	—	2	1	no	—
323	C₄	—	2	4	no	—
324	C₄	—	2	1	no	—
325	C₄	—	2	1	no	—
326	C₄	—	4	2	no	—
327	C₄	—	4	2	no	—
328	C₄	C₁₁×#444	1	2	yes	—
329	C₄	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
330	C₄	C₁₁×#568	1	1	yes	characteristic
331	C₄	C₁₁×#577	1	2	yes	—
332	C₂	—	4	1	no	—
333	C₂	—	8	2	no	—
334	C₂	D₄×C₁₁×M₁₆	1	1	yes	characteristic
335	C₂	C₁₁×#2952	1	1	yes	characteristic
336	C₂	C₂×C₁₁×#444	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	C₂×C₁₁×#135	C₄
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
1. C₁₁×#2991	C₂	semidirect
3. C₁₁×#1594	C₂	semidirect
4. C₁₁×#1583	C₂	semidirect
5. C₁₁×#1579	C₂	semidirect
6. C₁₁×#1566	C₂	semidirect
7. C₁₁×#1489	C₂	semidirect
8. C₁₁×#1451	C₂	semidirect
75. #18063	C₁₁	direct (N × H)
87. C₁₁×Q₁₆	M₁₆	semidirect
116. #2991	C₂×C₁₁	semidirect
118. #1594	C₂×C₁₁	semidirect
119. #1583	C₂×C₁₁	semidirect
120. #1579	C₂×C₁₁	semidirect
121. #1566	C₂×C₁₁	semidirect
122. #1489	C₂×C₁₁	semidirect
123. #1451	C₂×C₁₁	semidirect
254. Q₁₆	C₁₁×M₁₆	semidirect
283. C₁₁	#18063	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×#2991	2
C₄×C₁₁×#135	2
C₁₁×#1594	2
C₁₁×#1583	2
C₁₁×#1579	2
C₁₁×#1566	2
C₁₁×#1489	2
C₁₁×#1451	2
#18063	11

Subgroups — C11×#18063 #14595256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#18063 #14595256