Subgroups — C₁₁×#18091 #14595284

Order 2816.

644 conjugacy classes of subgroups.

The subgroup lattice has 304 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×#2979	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1594	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1581	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1580	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1484	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#532	C₂²	1	2	yes	—
10	C₁₁×#500	C₄	1	1	yes	characteristic
11	C₁₁×#493	C₄	1	1	yes	characteristic
12	C₁₁×#486	C₄	1	2	yes	—
13	C₁₁×#466	C₄	1	2	yes	—
14	C₁₁×#466	C₄	1	2	yes	—
15	C₄×C₁₁×D₈	C₂²	1	2	yes	—
16	C₄×C₁₁×D₈	C₂²	1	2	yes	—
17	C₁₁×#436	—	2	2	no	—
18	C₁₁×#436	C₂²	1	4	yes	—
19	C₈×D₄×C₁₁	—	2	2	no	—
20	C₈×D₄×C₁₁	C₂²	1	4	yes	—
21	C₁₁×#431	C₂²	1	2	yes	—
22	C₁₁×#431	C₂²	1	1	yes	characteristic
23	C₁₁×#408	—	2	4	no	—
24	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
26	C₁₁×#335	C₂²	1	2	yes	—
27	C₁₁×#334	C₂²	1	1	yes	characteristic
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	C₂×C₁₁×M₁₆	—	2	1	no	—
37	C₂×C₁₁×M₁₆	—	2	4	no	—
38	C₂²×C₈×C₁₁	—	2	4	no	—
39	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
41	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
42	C₁₁×#127	C₂×C₄	1	2	yes	—
43	C₁₁×#124	—	2	2	no	—
44	C₁₁×#121	—	2	2	no	—
45	C₁₁×#121	C₂×C₄	1	4	yes	—
46	C₄×D₄×C₁₁	—	2	2	no	—
47	C₄×D₄×C₁₁	C₂³	1	4	yes	—
48	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
49	C₁₁×#107	C₂×C₄	1	2	yes	—
50	C₁₁×#107	C₂×C₄	1	2	yes	—
51	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
52	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
53	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
54	C₁₁×#102	C₂×C₄	1	4	yes	—
55	C₁₁×#102	C₂×C₄	1	4	yes	—
56	C₁₁×C₂²⋊C₈	—	2	2	no	—
57	C₁₁×C₂²⋊C₈	—	2	4	no	—
58	C₁₁×C₂²⋊C₈	—	2	4	no	—
59	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
60	C₁₁×#97	—	2	1	no	—
61	C₄×C₈×C₁₁	—	2	2	no	—
62	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
63	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
64	C₄×C₈×C₁₁	C₂³	1	2	yes	—
65	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
66	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₄×C₈×C₁₁	C₂³	1	2	yes	—
68	#18091	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₁₁×#41	—	8	2	no	—
70	C₁₁×#41	—	8	2	no	—
71	C₂×Q₈×C₁₁	—	2	2	no	—
72	C₂×D₄×C₁₁	—	2	4	no	—
73	C₂×D₄×C₁₁	—	2	2	no	—
74	C₂×D₄×C₁₁	—	2	2	no	—
75	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
76	C₂²×C₄×C₁₁	—	2	4	no	—
77	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
80	C₁₁×D₈	—	2	4	no	—
81	C₁₁×D₈	—	4	2	no	—
82	C₁₁×M₁₆	—	4	2	no	—
83	C₁₁×M₁₆	—	8	4	no	—
84	C₂×C₈×C₁₁	—	2	2	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	—	4	1	no	—
89	C₂×C₈×C₁₁	—	8	4	no	—
90	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
95	C₁₁×C₄⋊C₄	—	2	2	no	—
96	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
97	C₁₁×C₂²⋊C₄	—	2	4	no	—
98	C₁₁×C₂²⋊C₄	—	2	4	no	—
99	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
100	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
101	C₄²×C₁₁	#41	1	1	yes	characteristic
102	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
103	#3169	C₂×C₁₁	1	1	yes	characteristic
104	#2979	C₂×C₁₁	1	2	yes	complemented
105	#1594	C₂×C₁₁	1	2	yes	complemented
106	#1581	C₂×C₁₁	1	4	yes	complemented
107	#1580	C₂×C₁₁	1	2	yes	complemented
108	#1564	C₂×C₁₁	1	1	yes	characteristic, complemented
109	#1484	C₂×C₁₁	1	2	yes	complemented
110	#1451	C₂×C₁₁	1	1	yes	characteristic, complemented
111	C₂³×C₁₁	—	2	4	no	—
112	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
113	Q₈×C₁₁	—	8	2	no	—
114	D₄×C₁₁	—	2	4	no	—
115	D₄×C₁₁	—	2	4	no	—
116	D₄×C₁₁	—	4	4	no	—
117	D₄×C₁₁	—	8	2	no	—
118	D₄×C₁₁	—	8	4	no	—
119	C₂×C₄×C₁₁	—	2	1	no	—
120	C₂×C₄×C₁₁	—	2	1	no	—
121	C₂×C₄×C₁₁	—	2	2	no	—
122	C₂×C₄×C₁₁	—	2	2	no	—
123	C₂×C₄×C₁₁	—	2	4	no	—
124	C₂×C₄×C₁₁	—	4	4	no	—
125	C₂×C₄×C₁₁	—	4	4	no	—
126	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
127	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
128	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
129	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
131	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
132	C₈×C₁₁	—	2	1	no	—
133	C₈×C₁₁	—	2	1	no	—
134	C₈×C₁₁	—	2	1	no	—
135	C₈×C₁₁	—	2	4	no	—
136	C₈×C₁₁	—	4	2	no	—
137	C₈×C₁₁	—	4	2	no	—
138	C₈×C₁₁	—	4	2	no	—
139	C₈×C₁₁	#131	1	2	yes	—
140	#532	C₂²×C₁₁	1	2	yes	—
141	#500	C₄×C₁₁	1	1	yes	characteristic
142	#493	C₄×C₁₁	1	1	yes	characteristic
143	#486	C₄×C₁₁	1	2	yes	—
144	#466	C₄×C₁₁	1	2	yes	—
145	#466	C₄×C₁₁	1	2	yes	—
146	C₄×D₈	C₂²×C₁₁	1	2	yes	—
147	C₄×D₈	C₂²×C₁₁	1	2	yes	—
148	#436	—	2	2	no	—
149	#436	C₂²×C₁₁	1	4	yes	—
150	C₈×D₄	—	2	2	no	—
151	C₈×D₄	C₂²×C₁₁	1	4	yes	—
152	#431	C₂²×C₁₁	1	2	yes	—
153	#431	C₂²×C₁₁	1	1	yes	characteristic
154	#408	—	2	4	no	—
155	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
156	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
157	#335	C₂²×C₁₁	1	2	yes	—
158	#334	C₂²×C₁₁	1	1	yes	characteristic
159	#334	C₂²×C₁₁	1	1	yes	characteristic
160	D₄⋊C₈	C₂²×C₁₁	1	4	yes	—
161	D₄⋊C₈	C₂²×C₁₁	1	4	yes	—
162	#322	C₂²×C₁₁	1	2	yes	—
163	#322	C₂²×C₁₁	1	2	yes	—
164	C₂²×C₁₁	—	2	1	no	—
165	C₂²×C₁₁	—	2	1	no	—
166	C₂²×C₁₁	—	2	1	no	—
167	C₂²×C₁₁	—	4	4	no	—
168	C₂²×C₁₁	—	4	4	no	—
169	C₂²×C₁₁	—	4	4	no	—
170	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
171	C₄×C₁₁	—	2	1	no	—
172	C₄×C₁₁	—	2	1	no	—
173	C₄×C₁₁	—	2	1	no	—
174	C₄×C₁₁	—	4	4	no	—
175	C₄×C₁₁	#444	1	2	yes	—
176	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
177	C₄×C₁₁	#568	1	1	yes	characteristic
178	C₄×C₁₁	#576	1	2	yes	—
179	C₂×#41	—	2	2	no	—
180	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
181	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
182	C₂×M₁₆	—	2	1	no	—
183	C₂×M₁₆	—	2	4	no	—
184	C₂²×C₈	—	2	4	no	—
185	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
186	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
187	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
188	#127	C₂×C₄×C₁₁	1	2	yes	—
189	#124	—	2	2	no	—
190	#121	—	2	2	no	—
191	#121	C₂×C₄×C₁₁	1	4	yes	—
192	C₄×D₄	—	2	2	no	—
193	C₄×D₄	C₂³×C₁₁	1	4	yes	—
194	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
195	#107	C₂×C₄×C₁₁	1	2	yes	—
196	#107	C₂×C₄×C₁₁	1	2	yes	—
197	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
198	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
199	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
200	#102	C₂×C₄×C₁₁	1	4	yes	—
201	#102	C₂×C₄×C₁₁	1	4	yes	—
202	C₂²⋊C₈	—	2	2	no	—
203	C₂²⋊C₈	—	2	4	no	—
204	C₂²⋊C₈	—	2	4	no	—
205	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
206	#97	—	2	1	no	—
207	C₄×C₈	—	2	2	no	—
208	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
209	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
210	C₄×C₈	C₂³×C₁₁	1	2	yes	—
211	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
212	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
213	C₄×C₈	C₂³×C₁₁	1	2	yes	—
214	C₂×C₁₁	—	4	1	no	—
215	C₂×C₁₁	—	8	4	no	—
216	C₂×C₁₁	#2935	1	1	yes	characteristic
217	C₂×C₁₁	#2948	1	1	yes	characteristic
218	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
219	#41	—	8	2	no	—
220	#41	—	8	2	no	—
221	C₂×Q₈	—	2	2	no	—
222	C₂×D₄	—	2	4	no	—
223	C₂×D₄	—	2	2	no	—
224	C₂×D₄	—	2	2	no	—
225	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
226	C₂²×C₄	—	2	4	no	—
227	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
228	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
229	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
230	D₈	—	2	4	no	—
231	D₈	—	4	2	no	—
232	M₁₆	—	4	2	no	—
233	M₁₆	—	8	4	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	—	4	1	no	—
239	C₂×C₈	—	8	4	no	—
240	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
241	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
242	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
243	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
244	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
245	C₄⋊C₄	—	2	2	no	—
246	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
247	C₂²⋊C₄	—	2	4	no	—
248	C₂²⋊C₄	—	2	4	no	—
249	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
250	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
251	C₄²	C₁₁×#41	1	1	yes	characteristic
252	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
253	C₁₁	#18091	1	1	yes	characteristic, direct product factor, Sylow
254	C₂³	—	2	4	no	—
255	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
256	Q₈	—	8	2	no	—
257	D₄	—	2	4	no	—
258	D₄	—	2	4	no	—
259	D₄	—	4	4	no	—
260	D₄	—	8	2	no	—
261	D₄	—	8	4	no	—
262	C₂×C₄	—	2	1	no	—
263	C₂×C₄	—	2	1	no	—
264	C₂×C₄	—	2	2	no	—
265	C₂×C₄	—	2	2	no	—
266	C₂×C₄	—	2	4	no	—
267	C₂×C₄	—	4	4	no	—
268	C₂×C₄	—	4	4	no	—
269	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
270	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
271	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
272	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
273	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
274	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
275	C₈	—	2	1	no	—
276	C₈	—	2	1	no	—
277	C₈	—	2	1	no	—
278	C₈	—	2	4	no	—
279	C₈	—	4	2	no	—
280	C₈	—	4	2	no	—
281	C₈	—	4	2	no	—
282	C₈	C₁₁×#131	1	2	yes	—
283	C₂²	—	2	1	no	—
284	C₂²	—	2	1	no	—
285	C₂²	—	2	1	no	—
286	C₂²	—	4	4	no	—
287	C₂²	—	4	4	no	—
288	C₂²	—	4	4	no	—
289	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
290	C₄	—	2	1	no	—
291	C₄	—	2	1	no	—
292	C₄	—	2	1	no	—
293	C₄	—	4	4	no	—
294	C₄	C₁₁×#444	1	2	yes	—
295	C₄	C₂×C₁₁×#131	1	1	yes	characteristic
296	C₄	C₁₁×#568	1	1	yes	characteristic
297	C₄	C₁₁×#576	1	2	yes	—
298	C₂	—	4	1	no	—
299	C₂	—	8	4	no	—
300	C₂	C₁₁×#2935	1	1	yes	characteristic
301	C₂	C₁₁×#2948	1	1	yes	characteristic
302	C₂	C₂×C₁₁×#444	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 ◁ C₁₁×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2979	C₂	semidirect
3. C₁₁×#1594	C₂	semidirect
4. C₁₁×#1581	C₂	semidirect
5. C₁₁×#1580	C₂	semidirect
6. C₁₁×#1564	C₂	semidirect
7. C₁₁×#1484	C₂	semidirect
8. C₁₁×#1451	C₂	semidirect
68. #18091	C₁₁	direct (N × H)
104. #2979	C₂×C₁₁	semidirect
105. #1594	C₂×C₁₁	semidirect
106. #1581	C₂×C₁₁	semidirect
107. #1580	C₂×C₁₁	semidirect
108. #1564	C₂×C₁₁	semidirect
109. #1484	C₂×C₁₁	semidirect
110. #1451	C₂×C₁₁	semidirect
253. C₁₁	#18091	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×#3169	2
C₁₁×#2979	2
C₁₁×#1594	2
C₁₁×#1581	2
C₁₁×#1580	2
C₁₁×#1564	2
C₁₁×#1484	2
C₁₁×#1451	2
#18091	11

Subgroups — C11×#18091 #14595284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#18091 #14595284