Subgroups — C₁₁×#18073 #14595266

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3169	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2935	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1594	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1586	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1580	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1480	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×#131	—	2	2	no	—
10	C₁₁×#532	C₂²	1	2	yes	—
11	C₁₁×#500	C₄	1	1	yes	characteristic
12	C₁₁×#493	C₄	1	1	yes	characteristic
13	C₁₁×#486	C₄	1	2	yes	—
14	C₁₁×#466	C₄	1	2	yes	—
15	C₁₁×#466	C₄	1	2	yes	—
16	C₄×C₁₁×D₈	C₂²	1	2	yes	—
17	C₄×C₁₁×D₈	C₂²	1	2	yes	—
18	C₁₁×#436	C₂²	1	4	yes	—
19	C₁₁×#435	—	2	4	no	—
20	C₈×D₄×C₁₁	C₂²	1	4	yes	—
21	C₁₁×#431	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
23	C₁₁×#408	—	2	2	no	—
24	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
26	C₁₁×#334	C₂²	1	1	yes	characteristic
27	C₁₁×#334	C₂²	1	2	yes	—
28	C₁₁×#334	C₂²	1	1	yes	characteristic
29	C₁₁×D₄⋊C₈	C₂²	1	4	yes	—
30	C₁₁×D₄⋊C₈	C₂²	1	4	yes	—
31	C₁₁×#322	C₂²	1	2	yes	—
32	C₁₁×#322	C₂²	1	2	yes	—
33	C₂×C₁₁×#41	—	2	2	no	—
34	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
35	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
36	C₁₁×#131	—	4	8	no	—
37	C₂×C₁₁×M₁₆	—	2	4	no	—
38	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
39	C₂²×C₈×C₁₁	—	2	2	no	—
40	C₂²×C₈×C₁₁	—	2	4	no	—
41	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
44	C₁₁×#127	C₂×C₄	1	2	yes	—
45	C₁₁×#124	—	2	2	no	—
46	C₁₁×#121	—	2	2	no	—
47	C₁₁×#121	C₂×C₄	1	4	yes	—
48	C₄×D₄×C₁₁	—	2	2	no	—
49	C₄×D₄×C₁₁	C₂³	1	4	yes	—
50	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
51	C₁₁×#107	C₂×C₄	1	2	yes	—
52	C₁₁×#107	C₂×C₄	1	2	yes	—
53	C₁₁×C₄⋊C₈	—	2	2	no	—
54	C₁₁×C₄⋊C₈	—	2	1	no	—
55	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
56	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
57	C₁₁×#102	C₂×C₄	1	4	yes	—
58	C₁₁×#102	C₂×C₄	1	4	yes	—
59	C₁₁×C₂²⋊C₈	—	2	1	no	—
60	C₁₁×C₂²⋊C₈	—	2	4	no	—
61	C₁₁×C₂²⋊C₈	—	2	4	no	—
62	C₁₁×#97	D₄	1	2	yes	—
63	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
64	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
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	#18073	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₁₁×#41	—	4	4	no	—
71	C₁₁×#41	—	4	4	no	—
72	C₂×Q₈×C₁₁	—	2	2	no	—
73	C₂×D₄×C₁₁	—	2	4	no	—
74	C₂×D₄×C₁₁	—	2	2	no	—
75	C₂×D₄×C₁₁	—	2	2	no	—
76	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
77	C₂²×C₄×C₁₁	—	2	4	no	—
78	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
81	C₁₁×D₈	—	2	4	no	—
82	C₁₁×D₈	—	4	2	no	—
83	C₁₁×M₁₆	—	2	4	no	—
84	C₁₁×M₁₆	—	4	8	no	—
85	C₂×C₈×C₁₁	—	2	2	no	—
86	C₂×C₈×C₁₁	—	2	2	no	—
87	C₂×C₈×C₁₁	—	2	2	no	—
88	C₂×C₈×C₁₁	—	2	2	no	—
89	C₂×C₈×C₁₁	—	4	1	no	—
90	C₂×C₈×C₁₁	—	4	8	no	—
91	C₂×C₈×C₁₁	—	4	4	no	—
92	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
97	C₁₁×C₄⋊C₄	—	2	2	no	—
98	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
99	C₁₁×C₂²⋊C₄	—	2	4	no	—
100	C₁₁×C₂²⋊C₄	—	2	4	no	—
101	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₁₁	#41	1	1	yes	characteristic
104	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
105	#3169	C₂×C₁₁	1	1	yes	characteristic
106	#2935	C₂×C₁₁	1	2	yes	complemented
107	#1594	C₂×C₁₁	1	2	yes	complemented
108	#1586	C₂×C₁₁	1	4	yes	complemented
109	#1580	C₂×C₁₁	1	2	yes	complemented
110	C₂×#334	C₂×C₁₁	1	1	yes	characteristic, complemented
111	#1480	C₂×C₁₁	1	2	yes	complemented
112	#1451	C₂×C₁₁	1	1	yes	characteristic, complemented
113	C₂³×C₁₁	—	2	4	no	—
114	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
115	Q₈×C₁₁	—	4	4	no	—
116	D₄×C₁₁	—	2	4	no	—
117	D₄×C₁₁	—	2	4	no	—
118	D₄×C₁₁	—	4	8	no	—
119	D₄×C₁₁	—	4	4	no	—
120	D₄×C₁₁	—	8	2	no	—
121	C₂×C₄×C₁₁	—	2	1	no	—
122	C₂×C₄×C₁₁	—	2	1	no	—
123	C₂×C₄×C₁₁	—	2	4	no	—
124	C₂×C₄×C₁₁	—	4	1	no	—
125	C₂×C₄×C₁₁	—	4	4	no	—
126	C₂×C₄×C₁₁	—	4	4	no	—
127	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
128	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
129	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
130	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	4	yes	—
131	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
133	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
134	C₈×C₁₁	—	2	1	no	—
135	C₈×C₁₁	—	2	1	no	—
136	C₈×C₁₁	—	2	1	no	—
137	C₈×C₁₁	—	2	4	no	—
138	C₈×C₁₁	—	4	2	no	—
139	C₈×C₁₁	—	4	2	no	—
140	C₈×C₁₁	—	4	2	no	—
141	C₈×C₁₁	#131	1	2	yes	complemented
142	C₂×#131	—	2	2	no	—
143	#532	C₂²×C₁₁	1	2	yes	—
144	#500	C₄×C₁₁	1	1	yes	characteristic
145	#493	C₄×C₁₁	1	1	yes	characteristic
146	#486	C₄×C₁₁	1	2	yes	—
147	#466	C₄×C₁₁	1	2	yes	—
148	#466	C₄×C₁₁	1	2	yes	—
149	C₄×D₈	C₂²×C₁₁	1	2	yes	—
150	C₄×D₈	C₂²×C₁₁	1	2	yes	—
151	#436	C₂²×C₁₁	1	4	yes	—
152	#435	—	2	4	no	—
153	C₈×D₄	C₂²×C₁₁	1	4	yes	—
154	#431	C₂²×C₁₁	1	1	yes	characteristic
155	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
156	#408	—	2	2	no	—
157	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
158	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
159	#334	C₂²×C₁₁	1	1	yes	characteristic
160	#334	C₂²×C₁₁	1	2	yes	—
161	#334	C₂²×C₁₁	1	1	yes	characteristic
162	D₄⋊C₈	C₂²×C₁₁	1	4	yes	—
163	D₄⋊C₈	C₂²×C₁₁	1	4	yes	—
164	#322	C₂²×C₁₁	1	2	yes	—
165	#322	C₂²×C₁₁	1	2	yes	—
166	C₂²×C₁₁	—	2	1	no	—
167	C₂²×C₁₁	—	2	1	no	—
168	C₂²×C₁₁	—	4	4	no	—
169	C₂²×C₁₁	—	4	4	no	—
170	C₂²×C₁₁	—	4	4	no	—
171	C₂²×C₁₁	#442	1	2	yes	—
172	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
173	C₄×C₁₁	—	2	1	no	—
174	C₄×C₁₁	—	2	1	no	—
175	C₄×C₁₁	—	2	1	no	—
176	C₄×C₁₁	—	4	4	no	—
177	C₄×C₁₁	#442	1	2	yes	—
178	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
179	C₄×C₁₁	#568	1	1	yes	characteristic
180	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
181	C₂×#41	—	2	2	no	—
182	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
183	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
184	#131	—	4	8	no	—
185	C₂×M₁₆	—	2	4	no	—
186	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
187	C₂²×C₈	—	2	2	no	—
188	C₂²×C₈	—	2	4	no	—
189	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
190	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
191	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
192	#127	C₂×C₄×C₁₁	1	2	yes	—
193	#124	—	2	2	no	—
194	#121	—	2	2	no	—
195	#121	C₂×C₄×C₁₁	1	4	yes	—
196	C₄×D₄	—	2	2	no	—
197	C₄×D₄	C₂³×C₁₁	1	4	yes	—
198	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
199	#107	C₂×C₄×C₁₁	1	2	yes	—
200	#107	C₂×C₄×C₁₁	1	2	yes	—
201	C₄⋊C₈	—	2	2	no	—
202	C₄⋊C₈	—	2	1	no	—
203	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
204	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
205	#102	C₂×C₄×C₁₁	1	4	yes	—
206	#102	C₂×C₄×C₁₁	1	4	yes	—
207	C₂²⋊C₈	—	2	1	no	—
208	C₂²⋊C₈	—	2	4	no	—
209	C₂²⋊C₈	—	2	4	no	—
210	#97	D₄×C₁₁	1	2	yes	—
211	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
212	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
213	C₄×C₈	C₂³×C₁₁	1	2	yes	—
214	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
215	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
216	C₄×C₈	C₂³×C₁₁	1	2	yes	—
217	C₂×C₁₁	—	2	2	no	—
218	C₂×C₁₁	—	8	4	no	—
219	C₂×C₁₁	#2935	1	1	yes	characteristic
220	C₂×C₁₁	C₂×#442	1	1	yes	characteristic
221	C₂×C₁₁	#2957	1	1	yes	characteristic
222	#41	—	4	4	no	—
223	#41	—	4	4	no	—
224	C₂×Q₈	—	2	2	no	—
225	C₂×D₄	—	2	4	no	—
226	C₂×D₄	—	2	2	no	—
227	C₂×D₄	—	2	2	no	—
228	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
229	C₂²×C₄	—	2	4	no	—
230	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
231	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
232	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
233	D₈	—	2	4	no	—
234	D₈	—	4	2	no	—
235	M₁₆	—	2	4	no	—
236	M₁₆	—	4	8	no	—
237	C₂×C₈	—	2	2	no	—
238	C₂×C₈	—	2	2	no	—
239	C₂×C₈	—	2	2	no	—
240	C₂×C₈	—	2	2	no	—
241	C₂×C₈	—	4	1	no	—
242	C₂×C₈	—	4	8	no	—
243	C₂×C₈	—	4	4	no	—
244	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
245	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
246	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
247	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
248	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
249	C₄⋊C₄	—	2	2	no	—
250	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
251	C₂²⋊C₄	—	2	4	no	—
252	C₂²⋊C₄	—	2	4	no	—
253	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
254	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
255	C₄²	C₁₁×#41	1	1	yes	characteristic
256	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
257	C₁₁	#18073	1	1	yes	characteristic, direct product factor, Sylow
258	C₂³	—	2	4	no	—
259	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
260	Q₈	—	4	4	no	—
261	D₄	—	2	4	no	—
262	D₄	—	2	4	no	—
263	D₄	—	4	8	no	—
264	D₄	—	4	4	no	—
265	D₄	—	8	2	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	1	no	—
268	C₂×C₄	—	2	4	no	—
269	C₂×C₄	—	4	1	no	—
270	C₂×C₄	—	4	4	no	—
271	C₂×C₄	—	4	4	no	—
272	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
273	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
274	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
275	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	4	yes	—
276	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
277	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
278	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
279	C₈	—	2	1	no	—
280	C₈	—	2	1	no	—
281	C₈	—	2	1	no	—
282	C₈	—	2	4	no	—
283	C₈	—	4	2	no	—
284	C₈	—	4	2	no	—
285	C₈	—	4	2	no	—
286	C₈	C₁₁×#131	1	2	yes	complemented
287	C₂²	—	2	1	no	—
288	C₂²	—	2	1	no	—
289	C₂²	—	4	4	no	—
290	C₂²	—	4	4	no	—
291	C₂²	—	4	4	no	—
292	C₂²	C₁₁×#442	1	2	yes	—
293	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
294	C₄	—	2	1	no	—
295	C₄	—	2	1	no	—
296	C₄	—	2	1	no	—
297	C₄	—	4	4	no	—
298	C₄	C₁₁×#442	1	2	yes	—
299	C₄	C₂×C₁₁×#131	1	1	yes	characteristic
300	C₄	C₁₁×#568	1	1	yes	characteristic
301	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	2	yes	—
302	C₂	—	2	2	no	—
303	C₂	—	8	4	no	—
304	C₂	C₁₁×#2935	1	1	yes	characteristic
305	C₂	C₂×C₁₁×#442	1	1	yes	characteristic
306	C₂	C₁₁×#2957	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	C₁₁×#3169	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₄×C₁₁×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2935	C₂	semidirect
3. C₁₁×#1594	C₂	semidirect
4. C₁₁×#1586	C₂	semidirect
5. C₁₁×#1580	C₂	semidirect
6. C₂×C₁₁×#334	C₂	semidirect
7. C₁₁×#1480	C₂	semidirect
8. C₁₁×#1451	C₂	semidirect
69. #18073	C₁₁	direct (N × H)
106. #2935	C₂×C₁₁	semidirect
107. #1594	C₂×C₁₁	semidirect
108. #1586	C₂×C₁₁	semidirect
109. #1580	C₂×C₁₁	semidirect
110. C₂×#334	C₂×C₁₁	semidirect
111. #1480	C₂×C₁₁	semidirect
112. #1451	C₂×C₁₁	semidirect
141. C₈×C₁₁	#131	semidirect
257. C₁₁	#18073	direct (N × H)
286. C₈	C₁₁×#131	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#3169	2
C₁₁×#2935	2
C₁₁×#1594	2
C₁₁×#1586	2
C₁₁×#1580	2
C₂×C₁₁×#334	2
C₁₁×#1480	2
C₁₁×#1451	2
#18073	11

Subgroups — C11×#18073 #14595266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#18073 #14595266