Subgroups — C₁₁×#7916 #14585109

Order 2816.

622 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#431	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#383	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1280	C₂	1	4	yes	maximal
5	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
6	C₁₁×#432	—	2	2	no	—
7	C₁₁×#432	C₄	1	4	yes	complemented
8	C₁₁×#431	—	2	2	no	—
9	C₁₁×#431	C₄	1	4	yes	complemented
10	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
11	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
12	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
13	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₁×#97	—	2	1	no	—
15	C₂×C₄×C₈×C₁₁	—	2	1	no	—
16	C₁₁×#383	—	2	1	no	—
17	C₁₁×#383	—	2	1	no	—
18	C₁₁×#383	—	2	1	no	—
19	C₁₁×#383	—	2	1	no	—
20	C₂×C₁₁×#95	C₄	1	2	yes	—
21	C₂×C₁₁×#95	C₄	1	2	yes	—
22	C₂×C₁₁×#95	C₂²	1	2	yes	—
23	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₁	C₂×C₄	1	4	yes	—
25	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
27	C₂²×C₈×C₁₁	—	2	2	no	—
28	C₂²×C₈×C₁₁	—	2	2	no	—
29	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₁₁	D₄	1	2	yes	—
32	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₁	Q₈	1	2	yes	—
37	C₁₁×C₄⋊C₈	—	2	4	no	—
38	C₁₁×C₄⋊C₈	—	2	4	no	—
39	C₁₁×C₂²⋊C₈	—	2	2	no	—
40	C₁₁×C₂²⋊C₈	—	2	2	no	—
41	C₁₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
42	C₁₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
43	C₁₁×#97	—	2	4	no	—
44	C₄×C₈×C₁₁	—	2	4	no	—
45	C₁₁×#95	—	2	2	no	—
46	C₁₁×#95	—	2	2	no	—
47	C₁₁×#95	—	2	2	no	—
48	C₁₁×#95	—	2	2	no	—
49	C₁₁×#95	—	2	2	no	—
50	C₁₁×#95	—	2	2	no	—
51	#7916	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
52	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₁	—	2	4	no	—
54	C₂²×C₄×C₁₁	—	2	4	no	—
55	C₂²×C₄×C₁₁	—	2	8	no	—
56	C₂²×C₄×C₁₁	—	4	2	no	—
57	C₂²×C₄×C₁₁	—	4	2	no	—
58	C₂²×C₄×C₁₁	—	4	4	no	—
59	C₂²×C₄×C₁₁	—	4	4	no	—
60	C₂²×C₄×C₁₁	C₄²	1	2	yes	—
61	C₂²×C₄×C₁₁	C₄²	1	2	yes	—
62	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
67	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
68	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₁	C₂²×C₄	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	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
74	C₂×C₈×C₁₁	—	2	4	no	—
75	C₂×C₈×C₁₁	—	2	4	no	—
76	C₂×C₈×C₁₁	—	4	4	no	—
77	C₂×C₈×C₁₁	—	4	4	no	—
78	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
79	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
80	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
81	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
82	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
83	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
84	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
85	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
86	C₂×#432	C₂×C₁₁	1	1	yes	characteristic
87	C₂×#431	C₂×C₁₁	1	1	yes	characteristic
88	C₂×#383	C₂×C₁₁	1	1	yes	characteristic
89	#1280	C₂×C₁₁	1	4	yes	—
90	C₂³×C₁₁	—	2	2	no	—
91	C₂³×C₁₁	—	2	2	no	—
92	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
93	C₂³×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
95	C₂³×C₁₁	#131	1	4	yes	—
96	C₂×C₄×C₁₁	—	2	4	no	—
97	C₂×C₄×C₁₁	—	2	2	no	—
98	C₂×C₄×C₁₁	—	2	2	no	—
99	C₂×C₄×C₁₁	—	2	2	no	—
100	C₂×C₄×C₁₁	—	2	2	no	—
101	C₂×C₄×C₁₁	—	2	2	no	—
102	C₂×C₄×C₁₁	—	2	2	no	—
103	C₂×C₄×C₁₁	—	2	4	no	—
104	C₂×C₄×C₁₁	—	4	2	no	—
105	C₂×C₄×C₁₁	—	4	2	no	—
106	C₂×C₄×C₁₁	—	4	1	no	—
107	C₂×C₄×C₁₁	—	4	1	no	—
108	C₂×C₄×C₁₁	—	4	1	no	—
109	C₂×C₄×C₁₁	—	4	1	no	—
110	C₂×C₄×C₁₁	—	4	4	no	—
111	C₂×C₄×C₁₁	—	4	4	no	—
112	C₂×C₄×C₁₁	—	4	4	no	—
113	C₂×C₄×C₁₁	—	8	8	no	—
114	C₂×C₄×C₁₁	#95	1	2	yes	—
115	C₂×C₄×C₁₁	#95	1	2	yes	—
116	C₂×C₄×C₁₁	#95	1	2	yes	—
117	C₂×C₄×C₁₁	#95	1	2	yes	—
118	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₈×C₁₁	—	4	4	no	—
123	C₈×C₁₁	—	4	4	no	—
124	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
125	#432	—	2	2	no	—
126	#432	C₄×C₁₁	1	4	yes	complemented
127	#431	—	2	2	no	—
128	#431	C₄×C₁₁	1	4	yes	complemented
129	C₂×C₄⋊C₈	—	2	1	no	—
130	C₂×C₄⋊C₈	—	2	1	no	—
131	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
132	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
133	C₂×#97	—	2	1	no	—
134	C₂×C₄×C₈	—	2	1	no	—
135	#383	—	2	1	no	—
136	#383	—	2	1	no	—
137	#383	—	2	1	no	—
138	#383	—	2	1	no	—
139	C₂×#95	C₄×C₁₁	1	2	yes	—
140	C₂×#95	C₄×C₁₁	1	2	yes	—
141	C₂×#95	C₂²×C₁₁	1	2	yes	—
142	C₂²×C₁₁	—	2	8	no	—
143	C₂²×C₁₁	—	2	1	no	—
144	C₂²×C₁₁	—	2	1	no	—
145	C₂²×C₁₁	—	2	1	no	—
146	C₂²×C₁₁	—	2	1	no	—
147	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
148	C₂²×C₁₁	#405	1	2	yes	—
149	C₂²×C₁₁	#408	1	2	yes	—
150	C₂²×C₁₁	#410	1	2	yes	—
151	C₂²×C₁₁	#413	1	2	yes	—
152	C₂²×C₁₁	#424	1	2	yes	—
153	C₄×C₁₁	—	2	2	no	—
154	C₄×C₁₁	—	2	2	no	—
155	C₄×C₁₁	—	2	1	no	—
156	C₄×C₁₁	—	2	1	no	—
157	C₄×C₁₁	—	2	1	no	—
158	C₄×C₁₁	—	2	1	no	—
159	C₄×C₁₁	—	2	2	no	—
160	C₄×C₁₁	—	2	2	no	—
161	C₄×C₁₁	—	8	4	no	—
162	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
163	C₂³×C₄	C₂×C₄×C₁₁	1	4	yes	—
164	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
165	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
166	C₂²×C₈	—	2	2	no	—
167	C₂²×C₈	—	2	2	no	—
168	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
169	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
170	C₂×C₄²	D₄×C₁₁	1	2	yes	—
171	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
172	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
173	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
174	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
175	C₂×C₄²	Q₈×C₁₁	1	2	yes	—
176	C₄⋊C₈	—	2	4	no	—
177	C₄⋊C₈	—	2	4	no	—
178	C₂²⋊C₈	—	2	2	no	—
179	C₂²⋊C₈	—	2	2	no	—
180	C₂²⋊C₈	C₂×C₄×C₁₁	1	4	yes	—
181	C₂²⋊C₈	C₂×C₄×C₁₁	1	4	yes	—
182	#97	—	2	4	no	—
183	C₄×C₈	—	2	4	no	—
184	#95	—	2	2	no	—
185	#95	—	2	2	no	—
186	#95	—	2	2	no	—
187	#95	—	2	2	no	—
188	#95	—	2	2	no	—
189	#95	—	2	2	no	—
190	C₂×C₁₁	—	2	2	no	—
191	C₂×C₁₁	—	2	2	no	—
192	C₂×C₁₁	#1473	1	4	yes	—
193	C₂×C₁₁	#1729	1	1	yes	characteristic
194	C₂×C₁₁	#1740	1	1	yes	characteristic
195	C₂×C₁₁	#1742	1	1	yes	characteristic
196	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
197	C₂²×C₄	—	2	4	no	—
198	C₂²×C₄	—	2	4	no	—
199	C₂²×C₄	—	2	8	no	—
200	C₂²×C₄	—	4	2	no	—
201	C₂²×C₄	—	4	2	no	—
202	C₂²×C₄	—	4	4	no	—
203	C₂²×C₄	—	4	4	no	—
204	C₂²×C₄	C₄²×C₁₁	1	2	yes	—
205	C₂²×C₄	C₄²×C₁₁	1	2	yes	—
206	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
207	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
208	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
209	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
210	C₂²×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
211	C₂²×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
212	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
213	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
214	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
215	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
216	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
217	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
218	C₂×C₈	—	2	4	no	—
219	C₂×C₈	—	2	4	no	—
220	C₂×C₈	—	4	4	no	—
221	C₂×C₈	—	4	4	no	—
222	C₄²	C₁₁×C₂²⋊C₄	1	2	yes	—
223	C₄²	C₁₁×C₂²⋊C₄	1	2	yes	—
224	C₄²	C₁₁×C₂²⋊C₄	1	2	yes	—
225	C₄²	C₁₁×C₂²⋊C₄	1	2	yes	—
226	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
227	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
228	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
229	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
230	C₁₁	#7916	1	1	yes	characteristic, direct product factor, Sylow
231	C₂³	—	2	2	no	—
232	C₂³	—	2	2	no	—
233	C₂³	C₂×C₄²×C₁₁	1	1	yes	characteristic
234	C₂³	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
235	C₂³	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
236	C₂³	C₁₁×#131	1	4	yes	—
237	C₂×C₄	—	2	4	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	2	4	no	—
245	C₂×C₄	—	4	2	no	—
246	C₂×C₄	—	4	2	no	—
247	C₂×C₄	—	4	1	no	—
248	C₂×C₄	—	4	1	no	—
249	C₂×C₄	—	4	1	no	—
250	C₂×C₄	—	4	1	no	—
251	C₂×C₄	—	4	4	no	—
252	C₂×C₄	—	4	4	no	—
253	C₂×C₄	—	4	4	no	—
254	C₂×C₄	—	8	8	no	—
255	C₂×C₄	C₁₁×#95	1	2	yes	—
256	C₂×C₄	C₁₁×#95	1	2	yes	—
257	C₂×C₄	C₁₁×#95	1	2	yes	—
258	C₂×C₄	C₁₁×#95	1	2	yes	—
259	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
262	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
263	C₈	—	4	4	no	—
264	C₈	—	4	4	no	—
265	C₂²	—	2	8	no	—
266	C₂²	—	2	1	no	—
267	C₂²	—	2	1	no	—
268	C₂²	—	2	1	no	—
269	C₂²	—	2	1	no	—
270	C₂²	C₂×C₁₁×#95	1	1	yes	characteristic
271	C₂²	C₁₁×#405	1	2	yes	—
272	C₂²	C₁₁×#408	1	2	yes	—
273	C₂²	C₁₁×#410	1	2	yes	—
274	C₂²	C₁₁×#413	1	2	yes	—
275	C₂²	C₁₁×#424	1	2	yes	—
276	C₄	—	2	2	no	—
277	C₄	—	2	2	no	—
278	C₄	—	2	1	no	—
279	C₄	—	2	1	no	—
280	C₄	—	2	1	no	—
281	C₄	—	2	1	no	—
282	C₄	—	2	2	no	—
283	C₄	—	2	2	no	—
284	C₄	—	8	4	no	—
285	C₂	—	2	2	no	—
286	C₂	—	2	2	no	—
287	C₂	C₁₁×#1473	1	4	yes	—
288	C₂	C₁₁×#1729	1	1	yes	characteristic
289	C₂	C₁₁×#1740	1	1	yes	characteristic
290	C₂	C₁₁×#1742	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂×C₂²⋊C₄
commutator	C₂³	C₂×C₄²×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₂⁴×C₁₁	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₁₁×#432	C₄	semidirect
9. C₁₁×#431	C₄	semidirect
51. #7916	C₁₁	direct (N × H)
126. #432	C₄×C₁₁	semidirect
128. #431	C₄×C₁₁	semidirect
230. C₁₁	#7916	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#432	2
C₂×C₁₁×#431	2
C₂×C₁₁×#383	2
C₁₁×#1280	2
#7916	11

Subgroups — C11×#7916 #14585109

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#7916 #14585109