Subgroups — C₁₁×#11393 #14588586

Order 2816.

850 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3458	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1740	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1735	C₂	1	2	yes	maximal
4	C₁₁×#1733	C₂	1	2	yes	maximal
5	C₁₁×#1729	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₁₁×#544	—	2	4	no	—
9	C₁₁×#544	C₄	1	4	yes	complemented
10	C₁₁×#543	—	2	2	no	—
11	C₁₁×#533	—	2	4	no	—
12	C₁₁×#533	—	2	2	no	—
13	C₂×C₁₁×#117	C₂²	1	2	yes	—
14	C₂×C₁₁×#117	C₂²	1	2	yes	—
15	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
16	C₁₁×#342	—	2	2	no	—
17	C₁₁×#340	—	2	4	no	—
18	C₁₁×#339	—	2	4	no	—
19	C₁₁×#336	—	2	2	no	—
20	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
21	C₂×C₁₁×M₁₆	—	2	1	no	—
22	C₂×C₁₁×M₁₆	—	2	2	no	—
23	C₂×C₁₁×M₁₆	—	2	2	no	—
24	C₂×C₁₁×M₁₆	Q₈	1	2	yes	complemented
25	C₂²×C₈×C₁₁	—	2	1	no	—
26	C₂²×C₈×C₁₁	—	2	1	no	—
27	C₂²×C₈×C₁₁	—	2	2	no	—
28	C₂²×C₈×C₁₁	—	2	1	no	—
29	C₂²×C₈×C₁₁	—	2	2	no	—
30	C₂²×C₈×C₁₁	Q₈	1	2	yes	complemented
31	C₁₁×C₄⋊Q₈	—	2	4	no	—
32	C₁₁×C₄⋊Q₈	—	2	8	no	—
33	C₁₁×#125	—	2	4	no	—
34	C₁₁×#125	—	2	8	no	—
35	C₁₁×C₂²⋊Q₈	—	2	16	no	—
36	C₁₁×C₂²⋊Q₈	—	2	8	no	—
37	C₄×Q₈×C₁₁	—	2	8	no	—
38	C₁₁×#117	—	2	2	no	—
39	C₁₁×#117	—	2	2	no	—
40	C₁₁×#117	—	2	2	no	—
41	C₁₁×#117	—	2	2	no	—
42	C₁₁×#117	—	2	2	no	—
43	C₁₁×#117	—	2	2	no	—
44	C₁₁×#117	—	2	2	no	—
45	C₁₁×#117	C₂×C₄	1	4	yes	—
46	C₁₁×#117	D₄	1	4	yes	—
47	C₁₁×#117	Q₈	1	4	yes	complemented
48	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
49	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×C₁₁×C₄⋊C₄	D₄	1	4	yes	—
51	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
52	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
53	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
54	C₂×C₄²×C₁₁	—	2	2	no	—
55	C₂×C₄²×C₁₁	—	2	2	no	—
56	C₂×C₄²×C₁₁	D₄	1	2	yes	—
57	#11393	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
59	C₂×Q₈×C₁₁	—	2	8	no	—
60	C₂²×C₄×C₁₁	—	2	4	no	—
61	C₂²×C₄×C₁₁	—	4	2	no	—
62	C₂²×C₄×C₁₁	C₂²⋊C₄	1	4	yes	—
63	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
65	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
66	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
68	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
69	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
70	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
71	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
72	C₂²×C₄×C₁₁	#41	1	2	yes	—
73	C₁₁×M₁₆	—	2	4	no	—
74	C₁₁×M₁₆	—	4	2	no	—
75	C₂×C₈×C₁₁	—	2	4	no	—
76	C₂×C₈×C₁₁	—	2	2	no	—
77	C₂×C₈×C₁₁	—	2	2	no	—
78	C₂×C₈×C₁₁	—	4	1	no	—
79	C₂×C₈×C₁₁	—	4	1	no	—
80	C₂×C₈×C₁₁	—	4	2	no	—
81	C₂×C₈×C₁₁	—	4	1	no	—
82	C₂×C₈×C₁₁	—	4	1	no	—
83	C₁₁×C₄⋊C₄	—	2	16	no	—
84	C₁₁×C₄⋊C₄	—	2	8	no	—
85	C₁₁×C₄⋊C₄	—	2	4	no	—
86	C₁₁×C₄⋊C₄	—	2	4	no	—
87	C₁₁×C₄⋊C₄	—	2	4	no	—
88	C₁₁×C₄⋊C₄	—	4	2	no	—
89	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	8	yes	—
90	C₁₁×C₂²⋊C₄	—	2	4	no	—
91	C₁₁×C₂²⋊C₄	—	2	4	no	—
92	C₁₁×C₂²⋊C₄	—	2	4	no	—
93	C₁₁×C₂²⋊C₄	—	2	4	no	—
94	C₁₁×C₂²⋊C₄	—	4	2	no	—
95	C₄²×C₁₁	—	2	4	no	—
96	C₄²×C₁₁	—	2	2	no	—
97	C₄²×C₁₁	—	2	4	no	—
98	C₄²×C₁₁	—	2	2	no	—
99	C₄²×C₁₁	—	2	4	no	—
100	C₄²×C₁₁	—	4	2	no	—
101	#3458	C₂×C₁₁	1	1	yes	characteristic
102	#1740	C₂×C₁₁	1	1	yes	characteristic
103	#1735	C₂×C₁₁	1	2	yes	—
104	#1733	C₂×C₁₁	1	2	yes	—
105	#1729	C₂×C₁₁	1	1	yes	characteristic
106	C₂³×C₁₁	—	4	2	no	—
107	C₂³×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
108	C₂³×C₁₁	#120	1	2	yes	—
109	C₂³×C₁₁	C₂²⋊Q₈	1	2	yes	—
110	C₂³×C₁₁	#124	1	1	yes	characteristic
111	C₂³×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
112	Q₈×C₁₁	—	8	8	no	—
113	C₂×C₄×C₁₁	—	2	4	no	—
114	C₂×C₄×C₁₁	—	2	8	no	—
115	C₂×C₄×C₁₁	—	4	4	no	—
116	C₂×C₄×C₁₁	—	4	4	no	—
117	C₂×C₄×C₁₁	—	8	4	no	—
118	C₂×C₄×C₁₁	—	8	4	no	—
119	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
120	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
121	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
122	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
123	C₂×C₄×C₁₁	#120	1	1	yes	characteristic
124	C₂×C₄×C₁₁	#120	1	1	yes	characteristic
125	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
126	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
127	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
128	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
129	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
130	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
131	C₂×C₄×C₁₁	#124	1	2	yes	—
132	C₂×C₄×C₁₁	#124	1	2	yes	—
133	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
134	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
135	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
136	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
137	C₈×C₁₁	—	4	2	no	—
138	C₈×C₁₁	—	4	2	no	—
139	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
140	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
141	#544	—	2	4	no	—
142	#544	C₄×C₁₁	1	4	yes	complemented
143	#543	—	2	2	no	—
144	#533	—	2	4	no	—
145	#533	—	2	2	no	—
146	C₂×#117	C₂²×C₁₁	1	2	yes	—
147	C₂×#117	C₂²×C₁₁	1	2	yes	—
148	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
149	#342	—	2	2	no	—
150	#340	—	2	4	no	—
151	#339	—	2	4	no	—
152	#336	—	2	2	no	—
153	C₂²×C₁₁	—	2	2	no	—
154	C₂²×C₁₁	—	2	4	no	—
155	C₂²×C₁₁	—	4	2	no	—
156	C₂²×C₁₁	—	4	1	no	—
157	C₂²×C₁₁	—	4	1	no	—
158	C₂²×C₁₁	#379	1	1	yes	characteristic
159	C₂²×C₁₁	#391	1	1	yes	characteristic
160	C₂²×C₁₁	#391	1	1	yes	characteristic
161	C₂²×C₁₁	#393	1	2	yes	—
162	C₂²×C₁₁	#395	1	2	yes	—
163	C₄×C₁₁	—	4	4	no	—
164	C₄×C₁₁	—	4	8	no	—
165	C₄×C₁₁	—	8	4	no	—
166	C₄×C₁₁	#391	1	2	yes	—
167	C₄×C₁₁	#391	1	2	yes	—
168	C₄×C₁₁	#393	1	1	yes	characteristic
169	C₄×C₁₁	#393	1	1	yes	characteristic
170	C₄×C₁₁	#395	1	1	yes	characteristic
171	C₄×C₁₁	#395	1	1	yes	characteristic
172	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
173	C₂×M₁₆	—	2	1	no	—
174	C₂×M₁₆	—	2	2	no	—
175	C₂×M₁₆	—	2	2	no	—
176	C₂×M₁₆	Q₈×C₁₁	1	2	yes	complemented
177	C₂²×C₈	—	2	1	no	—
178	C₂²×C₈	—	2	2	no	—
179	C₂²×C₈	—	2	1	no	—
180	C₂²×C₈	—	2	1	no	—
181	C₂²×C₈	—	2	2	no	—
182	C₂²×C₈	Q₈×C₁₁	1	2	yes	complemented
183	C₄⋊Q₈	—	2	4	no	—
184	C₄⋊Q₈	—	2	8	no	—
185	#125	—	2	4	no	—
186	#125	—	2	8	no	—
187	C₂²⋊Q₈	—	2	16	no	—
188	C₂²⋊Q₈	—	2	8	no	—
189	C₄×Q₈	—	2	8	no	—
190	#117	—	2	2	no	—
191	#117	—	2	2	no	—
192	#117	—	2	2	no	—
193	#117	—	2	2	no	—
194	#117	—	2	2	no	—
195	#117	—	2	2	no	—
196	#117	—	2	2	no	—
197	#117	C₂×C₄×C₁₁	1	4	yes	—
198	#117	D₄×C₁₁	1	4	yes	—
199	#117	Q₈×C₁₁	1	4	yes	complemented
200	C₂×C₄⋊C₄	—	2	2	no	—
201	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
202	C₂×C₄⋊C₄	D₄×C₁₁	1	4	yes	—
203	C₂×C₂²⋊C₄	—	2	2	no	—
204	C₂×C₂²⋊C₄	—	2	2	no	—
205	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
206	C₂×C₄²	—	2	2	no	—
207	C₂×C₄²	—	2	2	no	—
208	C₂×C₄²	D₄×C₁₁	1	2	yes	—
209	C₂×C₁₁	—	2	2	no	—
210	C₂×C₁₁	—	2	1	no	—
211	C₂×C₁₁	—	2	1	no	—
212	C₂×C₁₁	—	2	2	no	—
213	C₂×C₁₁	#1446	1	1	yes	characteristic
214	C₂×C₁₁	#1794	1	2	yes	—
215	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
216	C₂×Q₈	—	2	8	no	—
217	C₂²×C₄	—	2	4	no	—
218	C₂²×C₄	—	4	2	no	—
219	C₂²×C₄	C₁₁×C₂²⋊C₄	1	4	yes	—
220	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
221	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
222	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
223	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
224	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
225	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
226	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
227	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
228	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
229	C₂²×C₄	C₁₁×#41	1	2	yes	—
230	M₁₆	—	2	4	no	—
231	M₁₆	—	4	2	no	—
232	C₂×C₈	—	2	4	no	—
233	C₂×C₈	—	2	2	no	—
234	C₂×C₈	—	2	2	no	—
235	C₂×C₈	—	4	1	no	—
236	C₂×C₈	—	4	1	no	—
237	C₂×C₈	—	4	2	no	—
238	C₂×C₈	—	4	1	no	—
239	C₂×C₈	—	4	1	no	—
240	C₄⋊C₄	—	2	16	no	—
241	C₄⋊C₄	—	2	8	no	—
242	C₄⋊C₄	—	2	4	no	—
243	C₄⋊C₄	—	2	4	no	—
244	C₄⋊C₄	—	2	4	no	—
245	C₄⋊C₄	—	4	2	no	—
246	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	8	yes	—
247	C₂²⋊C₄	—	2	4	no	—
248	C₂²⋊C₄	—	2	4	no	—
249	C₂²⋊C₄	—	2	4	no	—
250	C₂²⋊C₄	—	2	4	no	—
251	C₂²⋊C₄	—	4	2	no	—
252	C₄²	—	2	4	no	—
253	C₄²	—	2	4	no	—
254	C₄²	—	2	2	no	—
255	C₄²	—	2	2	no	—
256	C₄²	—	2	4	no	—
257	C₄²	—	4	2	no	—
258	C₁₁	#11393	1	1	yes	characteristic, direct product factor, Sylow
259	C₂³	—	4	2	no	—
260	C₂³	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
261	C₂³	C₁₁×#120	1	2	yes	—
262	C₂³	C₁₁×C₂²⋊Q₈	1	2	yes	—
263	C₂³	C₁₁×#124	1	1	yes	characteristic
264	C₂³	C₁₁×C₄⋊Q₈	1	1	yes	characteristic
265	Q₈	—	8	8	no	—
266	C₂×C₄	—	2	4	no	—
267	C₂×C₄	—	2	8	no	—
268	C₂×C₄	—	4	4	no	—
269	C₂×C₄	—	4	4	no	—
270	C₂×C₄	—	8	4	no	—
271	C₂×C₄	—	8	4	no	—
272	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
273	C₂×C₄	C₄×Q₈×C₁₁	1	1	yes	characteristic
274	C₂×C₄	C₄×Q₈×C₁₁	1	1	yes	characteristic
275	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
276	C₂×C₄	C₁₁×#120	1	1	yes	characteristic
277	C₂×C₄	C₁₁×#120	1	1	yes	characteristic
278	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
279	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
280	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
281	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
282	C₂×C₄	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
283	C₂×C₄	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
284	C₂×C₄	C₁₁×#124	1	2	yes	—
285	C₂×C₄	C₁₁×#124	1	2	yes	—
286	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
287	C₂×C₄	C₁₁×C₄⋊Q₈	1	2	yes	—
288	C₂×C₄	C₁₁×C₄⋊Q₈	1	2	yes	—
289	C₂×C₄	C₁₁×C₄⋊Q₈	1	1	yes	characteristic
290	C₈	—	4	2	no	—
291	C₈	—	4	2	no	—
292	C₂²	—	2	2	no	—
293	C₂²	—	2	4	no	—
294	C₂²	—	4	2	no	—
295	C₂²	—	4	1	no	—
296	C₂²	—	4	1	no	—
297	C₂²	C₁₁×#379	1	1	yes	characteristic
298	C₂²	C₁₁×#391	1	1	yes	characteristic
299	C₂²	C₁₁×#391	1	1	yes	characteristic
300	C₂²	C₁₁×#393	1	2	yes	—
301	C₂²	C₁₁×#395	1	2	yes	—
302	C₄	—	4	4	no	—
303	C₄	—	4	8	no	—
304	C₄	—	8	4	no	—
305	C₄	C₁₁×#391	1	2	yes	—
306	C₄	C₁₁×#391	1	2	yes	—
307	C₄	C₁₁×#393	1	1	yes	characteristic
308	C₄	C₁₁×#393	1	1	yes	characteristic
309	C₄	C₁₁×#395	1	1	yes	characteristic
310	C₄	C₁₁×#395	1	1	yes	characteristic
311	C₂	—	2	2	no	—
312	C₂	—	2	1	no	—
313	C₂	—	2	1	no	—
314	C₂	—	2	2	no	—
315	C₂	C₁₁×#1446	1	1	yes	characteristic
316	C₂	C₁₁×#1794	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	#120
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
socle	C₂²×C₁₁	#379
prime radical	C₂⁴×C₁₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₁₁×#544	C₄	semidirect
24. C₂×C₁₁×M₁₆	Q₈	semidirect
30. C₂²×C₈×C₁₁	Q₈	semidirect
47. C₁₁×#117	Q₈	semidirect
57. #11393	C₁₁	direct (N × H)
142. #544	C₄×C₁₁	semidirect
176. C₂×M₁₆	Q₈×C₁₁	semidirect
182. C₂²×C₈	Q₈×C₁₁	semidirect
199. #117	Q₈×C₁₁	semidirect
258. C₁₁	#11393	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×#3458	2
C₁₁×#1740	2
C₁₁×#1735	2
C₁₁×#1733	2
C₁₁×#1729	2
#11393	11

Subgroups — C11×#11393 #14588586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11393 #14588586