Subgroups — C₁₁×#19635 #14596828

Order 2816.

878 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3208	C₂	1	2	yes	maximal, complemented
2	C₁₁×#3170	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#493	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#3138	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1717	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1709	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1706	C₂	1	2	yes	maximal, complemented
8	C₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₁×D₈	—	2	2	no	—
10	C₁₁×#533	C₂²	1	2	yes	—
11	C₂×C₁₁×#127	C₂²	1	2	yes	—
12	C₁₁×#500	C₂²	1	1	yes	characteristic, complemented
13	C₁₁×#494	C₂²	1	1	yes	characteristic, complemented
14	C₁₁×#493	—	2	2	no	—
15	C₁₁×#493	C₂²	1	2	yes	—
16	C₁₁×#493	C₂²	1	2	yes	—
17	C₁₁×#492	C₂²	1	4	yes	complemented
18	C₁₁×#490	—	2	4	no	—
19	C₁₁×#487	C₂²	1	2	yes	complemented
20	C₁₁×#486	C₂²	1	4	yes	complemented
21	C₁₁×#486	C₂²	1	4	yes	complemented
22	C₁₁×#486	C₂²	1	4	yes	complemented
23	C₁₁×#467	—	2	2	no	—
24	C₁₁×#460	—	2	4	no	—
25	C₁₁×#450	—	2	4	no	—
26	C₄×C₁₁×Q₁₆	—	2	2	no	—
27	C₁₁×#431	C₂²	1	1	yes	characteristic
28	C₁₁×#418	—	2	4	no	—
29	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
31	C₁₁×#322	C₂²	1	2	yes	complemented
32	C₈²×C₁₁	C₂²	1	2	yes	complemented
33	C₂²×D₄×C₁₁	—	2	2	no	—
34	C₂²×D₄×C₁₁	—	2	2	no	—
35	C₂²×D₄×C₁₁	—	2	2	no	—
36	C₂×C₁₁×Q₁₆	—	2	2	no	—
37	C₂×C₁₁×SD₁₆	—	2	8	no	—
38	C₂×C₁₁×D₈	—	2	4	no	—
39	C₂×C₁₁×D₈	—	2	4	no	—
40	C₂×C₁₁×D₈	—	4	8	no	—
41	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
42	C₂²×C₈×C₁₁	D₄	1	2	yes	—
43	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
44	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
45	C₁₁×#127	—	2	2	no	—
46	C₁₁×#127	—	2	2	no	—
47	C₁₁×#127	—	2	2	no	—
48	C₁₁×#127	C₂³	1	4	yes	—
49	C₁₁×#125	—	2	2	no	—
50	C₁₁×C₂²⋊Q₈	—	2	2	no	—
51	C₁₁×C₂²⋊Q₈	—	2	2	no	—
52	C₄×Q₈×C₁₁	—	2	2	no	—
53	C₄×Q₈×C₁₁	—	2	2	no	—
54	C₁₁×#117	—	2	2	no	—
55	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
56	C₁₁×#107	—	2	2	no	—
57	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
58	C₁₁×#103	—	2	4	no	—
59	C₁₁×#102	—	2	8	no	—
60	C₁₁×#102	—	2	8	no	—
61	C₁₁×#102	—	2	8	no	—
62	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
63	C₁₁×#97	D₄	1	2	yes	—
64	C₄×C₈×C₁₁	D₄	1	2	yes	—
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	#19635	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂⁴×C₁₁	—	4	2	no	—
71	C₂×Q₈×C₁₁	—	2	2	no	—
72	C₂×Q₈×C₁₁	—	2	2	no	—
73	C₂×D₄×C₁₁	—	2	4	no	—
74	C₂×D₄×C₁₁	—	2	4	no	—
75	C₂×D₄×C₁₁	—	2	4	no	—
76	C₂×D₄×C₁₁	—	4	8	no	—
77	C₂×D₄×C₁₁	—	4	2	no	—
78	C₂×D₄×C₁₁	—	4	2	no	—
79	C₂×D₄×C₁₁	—	4	2	no	—
80	C₂×D₄×C₁₁	—	4	8	no	—
81	C₂×D₄×C₁₁	—	8	4	no	—
82	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
85	C₁₁×Q₁₆	—	4	4	no	—
86	C₁₁×SD₁₆	—	8	8	no	—
87	C₁₁×D₈	—	4	8	no	—
88	C₁₁×D₈	—	4	8	no	—
89	C₁₁×M₁₆	—	2	4	no	—
90	C₂×C₈×C₁₁	—	2	4	no	—
91	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
92	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
93	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
94	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
95	C₁₁×C₄⋊C₄	—	2	2	no	—
96	C₁₁×C₄⋊C₄	—	2	2	no	—
97	C₁₁×C₄⋊C₄	—	2	2	no	—
98	C₁₁×C₄⋊C₄	—	2	2	no	—
99	C₁₁×C₄⋊C₄	—	4	2	no	—
100	C₁₁×C₄⋊C₄	—	4	2	no	—
101	C₁₁×C₂²⋊C₄	—	4	2	no	—
102	C₄²×C₁₁	—	4	2	no	—
103	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
107	#3208	C₂×C₁₁	1	2	yes	complemented
108	#3170	C₂×C₁₁	1	1	yes	characteristic, complemented
109	C₂×#493	C₂×C₁₁	1	1	yes	characteristic
110	#3138	C₂×C₁₁	1	2	yes	complemented
111	#1717	C₂×C₁₁	1	4	yes	complemented
112	#1709	C₂×C₁₁	1	2	yes	complemented
113	#1706	C₂×C₁₁	1	2	yes	complemented
114	C₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
115	C₂³×C₁₁	—	4	4	no	—
116	C₂³×C₁₁	—	8	4	no	—
117	C₂³×C₁₁	—	8	4	no	—
118	C₂³×C₁₁	—	8	4	no	—
119	C₂³×C₁₁	#127	1	1	yes	characteristic
120	Q₈×C₁₁	—	4	4	no	—
121	Q₈×C₁₁	—	4	4	no	—
122	D₄×C₁₁	—	4	8	no	—
123	D₄×C₁₁	—	4	8	no	—
124	D₄×C₁₁	—	4	8	no	—
125	D₄×C₁₁	—	8	4	no	—
126	D₄×C₁₁	—	8	4	no	—
127	D₄×C₁₁	—	8	4	no	—
128	C₂×C₄×C₁₁	—	2	2	no	—
129	C₂×C₄×C₁₁	—	2	2	no	—
130	C₂×C₄×C₁₁	—	4	2	no	—
131	C₂×C₄×C₁₁	—	4	2	no	—
132	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
133	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
134	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
135	C₂×C₄×C₁₁	#135	1	4	yes	—
136	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
139	C₈×C₁₁	—	2	4	no	—
140	C₈×C₁₁	—	2	2	no	—
141	C₈×C₁₁	—	2	4	no	—
142	C₈×C₁₁	AGL(1,ℤ/8)	1	4	yes	—
143	C₂²×D₈	—	2	2	no	—
144	#533	C₂²×C₁₁	1	2	yes	—
145	C₂×#127	C₂²×C₁₁	1	2	yes	—
146	#500	C₂²×C₁₁	1	1	yes	characteristic, complemented
147	#494	C₂²×C₁₁	1	1	yes	characteristic, complemented
148	#493	—	2	2	no	—
149	#493	C₂²×C₁₁	1	2	yes	—
150	#493	C₂²×C₁₁	1	2	yes	—
151	#492	C₂²×C₁₁	1	4	yes	complemented
152	#490	—	2	4	no	—
153	#487	C₂²×C₁₁	1	2	yes	complemented
154	#486	C₂²×C₁₁	1	4	yes	complemented
155	#486	C₂²×C₁₁	1	4	yes	complemented
156	#486	C₂²×C₁₁	1	4	yes	complemented
157	#467	—	2	2	no	—
158	#460	—	2	4	no	—
159	#450	—	2	4	no	—
160	C₄×Q₁₆	—	2	2	no	—
161	#431	C₂²×C₁₁	1	1	yes	characteristic
162	#418	—	2	4	no	—
163	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
164	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
165	#322	C₂²×C₁₁	1	2	yes	complemented
166	C₈²	C₂²×C₁₁	1	2	yes	complemented
167	C₂²×C₁₁	—	2	1	no	—
168	C₂²×C₁₁	—	2	1	no	—
169	C₂²×C₁₁	—	8	4	no	—
170	C₂²×C₁₁	—	8	4	no	—
171	C₂²×C₁₁	—	8	4	no	—
172	C₂²×C₁₁	—	16	8	no	—
173	C₂²×C₁₁	#495	1	2	yes	—
174	C₂²×C₁₁	C₂×#127	1	1	yes	characteristic
175	C₄×C₁₁	—	2	1	no	—
176	C₄×C₁₁	—	2	1	no	—
177	C₄×C₁₁	—	8	2	no	—
178	C₄×C₁₁	—	8	2	no	—
179	C₄×C₁₁	#495	1	2	yes	—
180	C₄×C₁₁	C₂×#135	1	2	yes	—
181	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
182	C₄×C₁₁	#576	1	2	yes	—
183	C₂²×D₄	—	2	2	no	—
184	C₂²×D₄	—	2	2	no	—
185	C₂²×D₄	—	2	2	no	—
186	C₂×Q₁₆	—	2	2	no	—
187	C₂×SD₁₆	—	2	8	no	—
188	C₂×D₈	—	2	4	no	—
189	C₂×D₈	—	2	4	no	—
190	C₂×D₈	—	4	8	no	—
191	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
192	C₂²×C₈	D₄×C₁₁	1	2	yes	—
193	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
194	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
195	#127	—	2	2	no	—
196	#127	—	2	2	no	—
197	#127	—	2	2	no	—
198	#127	C₂³×C₁₁	1	4	yes	—
199	#125	—	2	2	no	—
200	C₂²⋊Q₈	—	2	2	no	—
201	C₂²⋊Q₈	—	2	2	no	—
202	C₄×Q₈	—	2	2	no	—
203	C₄×Q₈	—	2	2	no	—
204	#117	—	2	2	no	—
205	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
206	#107	—	2	2	no	—
207	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
208	#103	—	2	4	no	—
209	#102	—	2	8	no	—
210	#102	—	2	8	no	—
211	#102	—	2	8	no	—
212	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
213	#97	D₄×C₁₁	1	2	yes	—
214	C₄×C₈	D₄×C₁₁	1	2	yes	—
215	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
216	C₄×C₈	C₂³×C₁₁	1	2	yes	—
217	C₄×C₈	C₂³×C₁₁	1	2	yes	—
218	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
219	C₂×C₁₁	—	2	2	no	—
220	C₂×C₁₁	—	16	4	no	—
221	C₂×C₁₁	C₂×#495	1	1	yes	characteristic
222	C₂×C₁₁	#3151	1	1	yes	characteristic
223	C₂×C₁₁	#3155	1	1	yes	characteristic
224	C₂⁴	—	4	2	no	—
225	C₂×Q₈	—	2	2	no	—
226	C₂×Q₈	—	2	2	no	—
227	C₂×D₄	—	2	4	no	—
228	C₂×D₄	—	2	4	no	—
229	C₂×D₄	—	2	4	no	—
230	C₂×D₄	—	4	8	no	—
231	C₂×D₄	—	4	2	no	—
232	C₂×D₄	—	4	2	no	—
233	C₂×D₄	—	4	2	no	—
234	C₂×D₄	—	4	8	no	—
235	C₂×D₄	—	8	4	no	—
236	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
237	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
238	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
239	Q₁₆	—	4	4	no	—
240	SD₁₆	—	8	8	no	—
241	D₈	—	4	8	no	—
242	D₈	—	4	8	no	—
243	M₁₆	—	2	4	no	—
244	C₂×C₈	—	2	4	no	—
245	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
246	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
247	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
248	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
249	C₄⋊C₄	—	2	2	no	—
250	C₄⋊C₄	—	2	2	no	—
251	C₄⋊C₄	—	2	2	no	—
252	C₄⋊C₄	—	2	2	no	—
253	C₄⋊C₄	—	4	2	no	—
254	C₄⋊C₄	—	4	2	no	—
255	C₂²⋊C₄	—	4	2	no	—
256	C₄²	—	4	2	no	—
257	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
258	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
259	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
260	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
261	C₁₁	#19635	1	1	yes	characteristic, direct product factor, Sylow
262	C₂³	—	4	4	no	—
263	C₂³	—	8	4	no	—
264	C₂³	—	8	4	no	—
265	C₂³	—	8	4	no	—
266	C₂³	C₁₁×#127	1	1	yes	characteristic
267	Q₈	—	4	4	no	—
268	Q₈	—	4	4	no	—
269	D₄	—	4	8	no	—
270	D₄	—	4	8	no	—
271	D₄	—	4	8	no	—
272	D₄	—	8	4	no	—
273	D₄	—	8	4	no	—
274	D₄	—	8	4	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	4	2	no	—
278	C₂×C₄	—	4	2	no	—
279	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
280	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
281	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
282	C₂×C₄	C₁₁×#135	1	4	yes	—
283	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
284	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
285	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
286	C₈	—	2	4	no	—
287	C₈	—	2	2	no	—
288	C₈	—	2	4	no	—
289	C₈	C₁₁×AGL(1,ℤ/8)	1	4	yes	—
290	C₂²	—	2	1	no	—
291	C₂²	—	2	1	no	—
292	C₂²	—	8	4	no	—
293	C₂²	—	8	4	no	—
294	C₂²	—	8	4	no	—
295	C₂²	—	16	8	no	—
296	C₂²	C₁₁×#495	1	2	yes	—
297	C₂²	C₂×C₁₁×#127	1	1	yes	characteristic
298	C₄	—	2	1	no	—
299	C₄	—	2	1	no	—
300	C₄	—	8	2	no	—
301	C₄	—	8	2	no	—
302	C₄	C₁₁×#495	1	2	yes	—
303	C₄	C₂×C₁₁×#135	1	2	yes	—
304	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	2	yes	—
305	C₄	C₁₁×#576	1	2	yes	—
306	C₂	—	2	2	no	—
307	C₂	—	16	4	no	—
308	C₂	C₂×C₁₁×#495	1	1	yes	characteristic
309	C₂	C₁₁×#3151	1	1	yes	characteristic
310	C₂	C₁₁×#3155	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#493	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#3208	C₂	semidirect
2. C₁₁×#3170	C₂	semidirect
4. C₁₁×#3138	C₂	semidirect
5. C₁₁×#1717	C₂	semidirect
6. C₁₁×#1709	C₂	semidirect
7. C₁₁×#1706	C₂	semidirect
8. C₈×C₁₁×M₁₆	C₂	semidirect
12. C₁₁×#500	C₂²	semidirect
13. C₁₁×#494	C₂²	semidirect
17. C₁₁×#492	C₂²	semidirect
19. C₁₁×#487	C₂²	semidirect
20. C₁₁×#486	C₂²	semidirect
21. C₁₁×#486	C₂²	semidirect
22. C₁₁×#486	C₂²	semidirect
31. C₁₁×#322	C₂²	semidirect
32. C₈²×C₁₁	C₂²	semidirect
69. #19635	C₁₁	direct (N × H)
107. #3208	C₂×C₁₁	semidirect
108. #3170	C₂×C₁₁	semidirect
110. #3138	C₂×C₁₁	semidirect
111. #1717	C₂×C₁₁	semidirect
112. #1709	C₂×C₁₁	semidirect
113. #1706	C₂×C₁₁	semidirect
114. C₈×M₁₆	C₂×C₁₁	semidirect
146. #500	C₂²×C₁₁	semidirect
147. #494	C₂²×C₁₁	semidirect
151. #492	C₂²×C₁₁	semidirect
153. #487	C₂²×C₁₁	semidirect
154. #486	C₂²×C₁₁	semidirect
155. #486	C₂²×C₁₁	semidirect
156. #486	C₂²×C₁₁	semidirect
165. #322	C₂²×C₁₁	semidirect
166. C₈²	C₂²×C₁₁	semidirect
261. C₁₁	#19635	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×#3208	2
C₁₁×#3170	2
C₂×C₁₁×#493	2
C₁₁×#3138	2
C₁₁×#1717	2
C₁₁×#1709	2
C₁₁×#1706	2
C₈×C₁₁×M₁₆	2
#19635	11

Subgroups — C11×#19635 #14596828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19635 #14596828