Subgroups — C₁₁×#10672 #14587865

Order 2816.

510 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	C₁₁×#1957	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1957	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1957	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1845	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1844	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1834	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1273	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×#107	—	2	2	no	—
10	C₂×C₁₁×#106	—	2	2	no	—
11	C₂×C₁₁×#102	—	2	2	no	—
12	C₂×C₁₁×#102	—	2	2	no	—
13	C₂×C₁₁×#102	—	2	2	no	—
14	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
17	C₁₁×#384	C₂²	1	1	yes	characteristic
18	C₁₁×#384	C₂²	1	1	yes	characteristic
19	C₁₁×#384	C₂²	1	1	yes	characteristic
20	C₁₁×#340	—	2	2	no	—
21	C₂²×D₄×C₁₁	—	2	1	no	—
22	C₂²×D₄×C₁₁	—	2	1	no	—
23	C₂²×D₄×C₁₁	—	2	1	no	—
24	C₂²×C₈×C₁₁	D₄	1	2	yes	—
25	C₂²×C₈×C₁₁	D₄	1	2	yes	—
26	C₂²×C₈×C₁₁	D₄	1	2	yes	—
27	C₁₁×#127	—	2	1	no	—
28	C₁₁×#127	—	2	1	no	—
29	C₁₁×#127	—	2	1	no	—
30	C₁₁×#127	Q₈	1	2	yes	—
31	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
32	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
33	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
34	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
35	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
36	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
37	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
38	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
39	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
40	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
41	C₁₁×#107	—	4	4	no	—
42	C₁₁×#106	—	4	4	no	—
43	C₁₁×#102	—	4	4	no	—
44	C₁₁×#102	—	4	4	no	—
45	C₁₁×#102	—	4	4	no	—
46	C₄×C₈×C₁₁	—	2	1	no	—
47	C₄×C₈×C₁₁	—	2	1	no	—
48	C₄×C₈×C₁₁	—	2	1	no	—
49	C₄×C₈×C₁₁	—	2	1	no	—
50	C₄×C₈×C₁₁	—	2	1	no	—
51	C₄×C₈×C₁₁	—	2	1	no	—
52	#10672	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂⁴×C₁₁	—	4	1	no	—
54	C₂×D₄×C₁₁	—	2	2	no	—
55	C₂×D₄×C₁₁	—	2	2	no	—
56	C₂×D₄×C₁₁	—	2	2	no	—
57	C₂×D₄×C₁₁	—	4	1	no	—
58	C₂×D₄×C₁₁	—	4	1	no	—
59	C₂×D₄×C₁₁	—	4	1	no	—
60	C₂×D₄×C₁₁	—	4	2	no	—
61	C₂×D₄×C₁₁	—	4	2	no	—
62	C₂×D₄×C₁₁	—	4	2	no	—
63	C₂×D₄×C₁₁	—	4	2	no	—
64	C₂×D₄×C₁₁	—	4	2	no	—
65	C₂×D₄×C₁₁	—	4	2	no	—
66	C₂²×C₄×C₁₁	—	4	1	no	—
67	C₂²×C₄×C₁₁	—	4	1	no	—
68	C₂²×C₄×C₁₁	—	4	1	no	—
69	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₁₁	—	2	2	no	—
73	C₂×C₈×C₁₁	—	2	2	no	—
74	C₂×C₈×C₁₁	—	2	2	no	—
75	C₂×C₈×C₁₁	—	2	2	no	—
76	C₂×C₈×C₁₁	—	2	2	no	—
77	C₂×C₈×C₁₁	—	2	2	no	—
78	C₂×C₈×C₁₁	—	2	2	no	—
79	C₂×C₈×C₁₁	D₈	1	4	yes	—
80	C₂×C₈×C₁₁	SD₁₆	1	4	yes	—
81	C₁₁×C₄⋊C₄	—	4	2	no	—
82	C₁₁×C₄⋊C₄	—	4	2	no	—
83	C₁₁×C₄⋊C₄	—	4	2	no	—
84	C₁₁×C₄⋊C₄	—	4	2	no	—
85	C₁₁×C₄⋊C₄	—	4	2	no	—
86	C₁₁×C₄⋊C₄	—	4	2	no	—
87	C₁₁×C₄⋊C₄	—	4	2	no	—
88	C₁₁×C₄⋊C₄	—	4	2	no	—
89	C₁₁×C₄⋊C₄	—	4	2	no	—
90	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
91	C₄²×C₁₁	#41	1	1	yes	characteristic
92	C₄²×C₁₁	#41	1	1	yes	characteristic
93	C₄²×C₁₁	#41	1	1	yes	characteristic
94	#1957	C₂×C₁₁	1	1	yes	characteristic
95	#1957	C₂×C₁₁	1	1	yes	characteristic
96	#1957	C₂×C₁₁	1	1	yes	characteristic
97	#1845	C₂×C₁₁	1	1	yes	characteristic, complemented
98	#1844	C₂×C₁₁	1	1	yes	characteristic, complemented
99	#1834	C₂×C₁₁	1	1	yes	characteristic, complemented
100	#1273	C₂×C₁₁	1	1	yes	characteristic, complemented
101	C₂³×C₁₁	—	4	2	no	—
102	C₂³×C₁₁	—	8	1	no	—
103	C₂³×C₁₁	—	8	1	no	—
104	C₂³×C₁₁	—	8	1	no	—
105	C₂³×C₁₁	—	8	1	no	—
106	C₂³×C₁₁	—	8	1	no	—
107	C₂³×C₁₁	—	8	1	no	—
108	C₂³×C₁₁	#127	1	1	yes	characteristic
109	D₄×C₁₁	—	4	4	no	—
110	D₄×C₁₁	—	4	4	no	—
111	D₄×C₁₁	—	4	4	no	—
112	D₄×C₁₁	—	8	2	no	—
113	D₄×C₁₁	—	8	2	no	—
114	D₄×C₁₁	—	8	2	no	—
115	C₂×C₄×C₁₁	—	8	1	no	—
116	C₂×C₄×C₁₁	—	8	1	no	—
117	C₂×C₄×C₁₁	—	8	1	no	—
118	C₂×C₄×C₁₁	—	8	1	no	—
119	C₂×C₄×C₁₁	—	8	1	no	—
120	C₂×C₄×C₁₁	—	8	1	no	—
121	C₂×C₄×C₁₁	—	8	1	no	—
122	C₂×C₄×C₁₁	—	8	1	no	—
123	C₂×C₄×C₁₁	—	8	1	no	—
124	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
125	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
126	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
127	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
128	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
129	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
130	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
131	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
132	C₂×C₄×C₁₁	#135	1	2	yes	—
133	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
134	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
135	C₂×C₄×C₁₁	#137	1	2	yes	—
136	C₈×C₁₁	—	2	4	no	—
137	C₈×C₁₁	—	2	4	no	—
138	C₈×C₁₁	—	4	2	no	—
139	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
140	C₂×#107	—	2	2	no	—
141	C₂×#106	—	2	2	no	—
142	C₂×#102	—	2	2	no	—
143	C₂×#102	—	2	2	no	—
144	C₂×#102	—	2	2	no	—
145	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
146	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
147	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
148	#384	C₂²×C₁₁	1	1	yes	characteristic
149	#384	C₂²×C₁₁	1	1	yes	characteristic
150	#384	C₂²×C₁₁	1	1	yes	characteristic
151	#340	—	2	2	no	—
152	C₂²×C₁₁	—	8	2	no	—
153	C₂²×C₁₁	—	8	2	no	—
154	C₂²×C₁₁	—	8	2	no	—
155	C₂²×C₁₁	—	16	1	no	—
156	C₂²×C₁₁	—	16	1	no	—
157	C₂²×C₁₁	—	16	1	no	—
158	C₂²×C₁₁	—	16	1	no	—
159	C₂²×C₁₁	#399	1	1	yes	characteristic
160	C₂²×C₁₁	#492	1	1	yes	characteristic
161	C₂²×C₁₁	#493	1	1	yes	characteristic
162	C₂²×C₁₁	#495	1	1	yes	characteristic
163	C₂²×C₁₁	#496	1	1	yes	characteristic
164	C₂²×C₁₁	#496	1	1	yes	characteristic
165	C₂²×C₁₁	#497	1	1	yes	characteristic
166	C₄×C₁₁	—	16	1	no	—
167	C₄×C₁₁	—	16	1	no	—
168	C₄×C₁₁	—	16	1	no	—
169	C₄×C₁₁	#474	1	2	yes	—
170	C₄×C₁₁	#476	1	2	yes	—
171	C₄×C₁₁	#478	1	2	yes	—
172	C₄×C₁₁	#480	1	2	yes	—
173	C₄×C₁₁	#481	1	2	yes	—
174	C₄×C₁₁	#482	1	2	yes	—
175	C₂²×D₄	—	2	1	no	—
176	C₂²×D₄	—	2	1	no	—
177	C₂²×D₄	—	2	1	no	—
178	C₂²×C₈	D₄×C₁₁	1	2	yes	—
179	C₂²×C₈	D₄×C₁₁	1	2	yes	—
180	C₂²×C₈	D₄×C₁₁	1	2	yes	—
181	#127	—	2	1	no	—
182	#127	—	2	1	no	—
183	#127	—	2	1	no	—
184	#127	Q₈×C₁₁	1	2	yes	—
185	C₂×C₄⋊C₄	—	2	1	no	—
186	C₂×C₄⋊C₄	—	2	1	no	—
187	C₂×C₄⋊C₄	—	2	1	no	—
188	C₂×C₄⋊C₄	—	2	1	no	—
189	C₂×C₄⋊C₄	—	2	1	no	—
190	C₂×C₄⋊C₄	—	2	1	no	—
191	C₂×C₄⋊C₄	—	2	1	no	—
192	C₂×C₄⋊C₄	—	2	1	no	—
193	C₂×C₄⋊C₄	—	2	1	no	—
194	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
195	#107	—	4	4	no	—
196	#106	—	4	4	no	—
197	#102	—	4	4	no	—
198	#102	—	4	4	no	—
199	#102	—	4	4	no	—
200	C₄×C₈	—	2	1	no	—
201	C₄×C₈	—	2	1	no	—
202	C₄×C₈	—	2	1	no	—
203	C₄×C₈	—	2	1	no	—
204	C₄×C₈	—	2	1	no	—
205	C₄×C₈	—	2	1	no	—
206	C₂×C₁₁	—	16	2	no	—
207	C₂×C₁₁	#1706	1	1	yes	characteristic
208	C₂×C₁₁	#1714	1	1	yes	characteristic
209	C₂×C₁₁	#1720	1	1	yes	characteristic
210	C₂×C₁₁	#1721	1	1	yes	characteristic
211	C₂×C₁₁	#2092	1	1	yes	characteristic
212	C₂×C₁₁	#2093	1	1	yes	characteristic
213	C₂×C₁₁	#2094	1	1	yes	characteristic
214	C₂⁴	—	4	1	no	—
215	C₂×D₄	—	2	2	no	—
216	C₂×D₄	—	2	2	no	—
217	C₂×D₄	—	2	2	no	—
218	C₂×D₄	—	4	1	no	—
219	C₂×D₄	—	4	1	no	—
220	C₂×D₄	—	4	1	no	—
221	C₂×D₄	—	4	2	no	—
222	C₂×D₄	—	4	2	no	—
223	C₂×D₄	—	4	2	no	—
224	C₂×D₄	—	4	2	no	—
225	C₂×D₄	—	4	2	no	—
226	C₂×D₄	—	4	2	no	—
227	C₂²×C₄	—	4	1	no	—
228	C₂²×C₄	—	4	1	no	—
229	C₂²×C₄	—	4	1	no	—
230	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
231	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
232	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
233	C₂×C₈	—	2	2	no	—
234	C₂×C₈	—	2	2	no	—
235	C₂×C₈	—	2	2	no	—
236	C₂×C₈	—	2	2	no	—
237	C₂×C₈	—	2	2	no	—
238	C₂×C₈	—	2	2	no	—
239	C₂×C₈	—	2	2	no	—
240	C₂×C₈	C₁₁×D₈	1	4	yes	—
241	C₂×C₈	C₁₁×SD₁₆	1	4	yes	—
242	C₄⋊C₄	—	4	2	no	—
243	C₄⋊C₄	—	4	2	no	—
244	C₄⋊C₄	—	4	2	no	—
245	C₄⋊C₄	—	4	2	no	—
246	C₄⋊C₄	—	4	2	no	—
247	C₄⋊C₄	—	4	2	no	—
248	C₄⋊C₄	—	4	2	no	—
249	C₄⋊C₄	—	4	2	no	—
250	C₄⋊C₄	—	4	2	no	—
251	C₄²	C₂×Q₈×C₁₁	1	1	yes	characteristic
252	C₄²	C₁₁×#41	1	1	yes	characteristic
253	C₄²	C₁₁×#41	1	1	yes	characteristic
254	C₄²	C₁₁×#41	1	1	yes	characteristic
255	C₁₁	#10672	1	1	yes	characteristic, direct product factor, Sylow
256	C₂³	—	4	2	no	—
257	C₂³	—	8	1	no	—
258	C₂³	—	8	1	no	—
259	C₂³	—	8	1	no	—
260	C₂³	—	8	1	no	—
261	C₂³	—	8	1	no	—
262	C₂³	—	8	1	no	—
263	C₂³	C₁₁×#127	1	1	yes	characteristic
264	D₄	—	4	4	no	—
265	D₄	—	4	4	no	—
266	D₄	—	4	4	no	—
267	D₄	—	8	2	no	—
268	D₄	—	8	2	no	—
269	D₄	—	8	2	no	—
270	C₂×C₄	—	8	1	no	—
271	C₂×C₄	—	8	1	no	—
272	C₂×C₄	—	8	1	no	—
273	C₂×C₄	—	8	1	no	—
274	C₂×C₄	—	8	1	no	—
275	C₂×C₄	—	8	1	no	—
276	C₂×C₄	—	8	1	no	—
277	C₂×C₄	—	8	1	no	—
278	C₂×C₄	—	8	1	no	—
279	C₂×C₄	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
280	C₂×C₄	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
281	C₂×C₄	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
282	C₂×C₄	C₁₁×#123	1	1	yes	characteristic
283	C₂×C₄	C₁₁×#123	1	1	yes	characteristic
284	C₂×C₄	C₁₁×#123	1	1	yes	characteristic
285	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
286	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
287	C₂×C₄	C₁₁×#135	1	2	yes	—
288	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
289	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
290	C₂×C₄	C₁₁×#137	1	2	yes	—
291	C₈	—	2	4	no	—
292	C₈	—	2	4	no	—
293	C₈	—	4	2	no	—
294	C₂²	—	8	2	no	—
295	C₂²	—	8	2	no	—
296	C₂²	—	8	2	no	—
297	C₂²	—	16	1	no	—
298	C₂²	—	16	1	no	—
299	C₂²	—	16	1	no	—
300	C₂²	—	16	1	no	—
301	C₂²	C₁₁×#399	1	1	yes	characteristic
302	C₂²	C₁₁×#492	1	1	yes	characteristic
303	C₂²	C₁₁×#493	1	1	yes	characteristic
304	C₂²	C₁₁×#495	1	1	yes	characteristic
305	C₂²	C₁₁×#496	1	1	yes	characteristic
306	C₂²	C₁₁×#496	1	1	yes	characteristic
307	C₂²	C₁₁×#497	1	1	yes	characteristic
308	C₄	—	16	1	no	—
309	C₄	—	16	1	no	—
310	C₄	—	16	1	no	—
311	C₄	C₁₁×#474	1	2	yes	—
312	C₄	C₁₁×#476	1	2	yes	—
313	C₄	C₁₁×#478	1	2	yes	—
314	C₄	C₁₁×#480	1	2	yes	—
315	C₄	C₁₁×#481	1	2	yes	—
316	C₄	C₁₁×#482	1	2	yes	—
317	C₂	—	16	2	no	—
318	C₂	C₁₁×#1706	1	1	yes	characteristic
319	C₂	C₁₁×#1714	1	1	yes	characteristic
320	C₂	C₁₁×#1720	1	1	yes	characteristic
321	C₂	C₁₁×#1721	1	1	yes	characteristic
322	C₂	C₁₁×#2092	1	1	yes	characteristic
323	C₂	C₁₁×#2093	1	1	yes	characteristic
324	C₂	C₁₁×#2094	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂×C₁₁×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₁×#1845	C₂	semidirect
5. C₁₁×#1844	C₂	semidirect
6. C₁₁×#1834	C₂	semidirect
7. C₁₁×#1273	C₂	semidirect
52. #10672	C₁₁	direct (N × H)
97. #1845	C₂×C₁₁	semidirect
98. #1844	C₂×C₁₁	semidirect
99. #1834	C₂×C₁₁	semidirect
100. #1273	C₂×C₁₁	semidirect
255. C₁₁	#10672	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×#1957	2
C₁₁×#1845	2
C₁₁×#1844	2
C₁₁×#1834	2
C₁₁×#1273	2
#10672	11

Subgroups — C11×#10672 #14587865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#10672 #14587865