Subgroups — D₁₁×#436 #13077299

Order 1408.

552 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×D₁₁	C₂	1	2	yes	maximal, complemented
2	C₄×D₄×D₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
4	#10622741	C₂	1	2	yes	maximal, complemented
5	#10622625	C₂	1	1	yes	maximal, characteristic, complemented
6	#10622451	C₂	1	1	yes	maximal, characteristic, complemented
7	D₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#10622342	C₂	1	2	yes	maximal, complemented
9	D₁₁×C₂²⋊C₈	C₂	1	2	yes	maximal, complemented
10	#10622301	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₈×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₄×D₁₁	C₄	1	1	yes	characteristic
13	C₂²×C₄×D₁₁	C₂²	1	2	yes	—
14	C₂×C₁₁×M₁₆	C₂²	1	2	yes	complemented
15	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
16	D₄×Dic₁₁	C₄	1	1	yes	characteristic
17	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	—
18	C₂×#4318	C₂²	1	2	yes	complemented
19	M₁₆×D₁₁	—	2	8	no	—
20	C₂×#4313	C₂²	1	2	yes	complemented
21	C₂×#4313	C₂²	1	2	yes	complemented
22	C₂×C₈×D₁₁	C₂²	1	2	yes	—
23	C₂×C₈×D₁₁	C₂²	1	1	yes	characteristic
24	C₂×C₈×D₁₁	C₂²	1	1	yes	characteristic
25	#66946	C₄	1	1	yes	characteristic
26	C₄⋊C₄×D₁₁	C₄	1	1	yes	characteristic
27	(C₂²⋊D₁₁)⋊C₄	C₄	1	2	yes	—
28	C₂²⋊C₄×D₁₁	C₄	1	2	yes	—
29	C₄×D₄₄	C₂²	1	1	yes	characteristic
30	C₄²×D₁₁	C₂²	1	1	yes	characteristic
31	C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
32	C₁₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
33	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
34	C₂²⋊(C₁₁⋊C₈)	C₂²	1	2	yes	complemented
35	(C₂×D₁₁)⋊C₈	C₂²	1	2	yes	complemented
36	(C₂×D₁₁)⋊C₈	C₂²	1	2	yes	complemented
37	Dic₁₁⋊C₈	C₂²	1	2	yes	complemented
38	C₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
39	C₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
40	C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
41	C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	C₂³×D₁₁	C₂×C₄	1	2	yes	—
43	C₂×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
45	C₂×C₂²⋊D₁₁	C₂×C₄	1	2	yes	—
46	C₂²×Dic₁₁	C₂×C₄	1	2	yes	—
47	D₄×D₁₁	—	2	4	no	—
48	C₂×D₄₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×D₁₁	—	2	4	no	—
50	C₂×C₄×D₁₁	—	2	4	no	—
51	C₂×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×D₁₁	C₂×C₄	1	2	yes	—
53	C₂×C₄×D₁₁	C₂×C₄	1	2	yes	—
54	C₂×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×D₁₁	C₂³	1	2	yes	—
56	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
57	C₁₁×M₁₆	—	2	4	no	—
58	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
59	C₂×C₈×C₁₁	C₂³	1	2	yes	—
60	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
61	C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₄²×C₁₁	C₂³	1	1	yes	characteristic
64	C₂²⋊Dic₁₁	C₂×C₄	1	2	yes	—
65	(C₂×D₁₁)⋊C₄	C₂×C₄	1	2	yes	—
66	(C₂×D₁₁)⋊C₄	C₂×C₄	1	2	yes	—
67	C₄⋊Dic₁₁	C₂×C₄	1	1	yes	characteristic
68	Dic₁₁⋊C₄	C₂×C₄	1	2	yes	—
69	C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
70	C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
71	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
72	#4318	—	2	4	no	—
73	C₂×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
74	C₂×C₁₁⋊C₈	C₂³	1	2	yes	—
75	C₂×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
76	#4313	—	2	4	no	—
77	#4313	—	2	4	no	—
78	C₈×D₁₁	—	2	4	no	—
79	C₈×D₁₁	—	2	2	no	—
80	C₈×D₁₁	D₄	1	4	yes	complemented
81	C₂×#436	—	11	1	no	maximal, Sylow
82	C₂³×C₁₁	C₂²×C₄	1	2	yes	—
83	C₂²×D₁₁	—	2	4	no	—
84	C₂²×D₁₁	—	2	4	no	—
85	C₂²×D₁₁	—	2	4	no	—
86	C₂²×D₁₁	C₂²×C₄	1	2	yes	—
87	C₂²×D₁₁	C₂²×C₄	1	1	yes	characteristic
88	D₄×C₁₁	—	2	2	no	—
89	C₂×C₄×C₁₁	—	2	2	no	—
90	C₂×C₄×C₁₁	—	2	2	no	—
91	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₄×C₁₁	C₂²×C₄	1	2	yes	—
93	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
95	C₂²⋊D₁₁	—	2	4	no	—
96	C₂×Dic₁₁	—	2	4	no	—
97	C₂×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
98	C₂×Dic₁₁	C₂²×C₄	1	2	yes	—
99	C₂×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
100	C₂×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
101	D₄₄	—	2	2	no	—
102	C₄×D₁₁	—	2	4	no	—
103	C₄×D₁₁	—	2	2	no	—
104	C₄×D₁₁	—	2	2	no	—
105	C₄×D₁₁	—	2	2	no	—
106	C₄×D₁₁	—	2	4	no	—
107	C₄×D₁₁	M₁₆	1	4	yes	complemented
108	C₄×D₁₁	C₂×D₄	1	2	yes	—
109	C₄×D₁₁	#41	1	2	yes	—
110	C₈×C₁₁	—	2	2	no	—
111	C₈×C₁₁	—	2	1	no	—
112	C₈×C₁₁	C₂×D₄	1	2	yes	complemented
113	C₁₁⋊C₈	—	2	2	no	—
114	C₁₁⋊C₈	—	2	1	no	—
115	C₁₁⋊C₈	C₂×D₄	1	2	yes	complemented
116	C₂²×M₁₆	—	11	2	no	—
117	C₂×C₄×D₄	—	11	1	no	—
118	#436	—	11	2	no	—
119	#436	—	11	1	no	—
120	#436	—	11	1	no	—
121	#436	—	11	2	no	—
122	#436	—	11	1	no	—
123	#436	D₁₁	1	1	yes	characteristic, direct product factor
124	C₂×C₄⋊C₈	—	11	1	no	—
125	C₂×C₂²⋊C₈	—	11	2	no	—
126	C₂×C₄×C₈	—	11	1	no	—
127	C₂²×C₁₁	—	2	2	no	—
128	C₂²×C₁₁	—	2	2	no	—
129	C₂²×C₁₁	—	2	2	no	—
130	C₂²×C₁₁	C₂³×C₄	1	1	yes	characteristic
131	C₂×D₁₁	—	2	2	no	—
132	C₂×D₁₁	—	2	2	no	—
133	C₂×D₁₁	—	2	2	no	—
134	C₂×D₁₁	—	4	8	no	—
135	C₂×D₁₁	C₄×D₄	1	2	yes	—
136	C₂×D₁₁	C₂×M₁₆	1	2	yes	—
137	C₂×D₁₁	#131	1	2	yes	—
138	C₄×C₁₁	—	2	2	no	—
139	C₄×C₁₁	—	2	1	no	—
140	C₄×C₁₁	C₂×M₁₆	1	2	yes	complemented
141	C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
142	C₄×C₁₁	C₂×#41	1	1	yes	characteristic
143	Dic₁₁	—	2	2	no	—
144	Dic₁₁	—	2	1	no	—
145	Dic₁₁	C₄×D₄	1	2	yes	—
146	Dic₁₁	C₂×M₁₆	1	2	yes	complemented
147	C₂²×D₄	—	11	1	no	—
148	C₂³×C₄	—	11	2	no	—
149	C₂×M₁₆	—	11	2	no	—
150	C₂×M₁₆	—	11	2	no	—
151	C₂×M₁₆	—	11	2	no	—
152	C₂×M₁₆	—	22	8	no	—
153	C₂×M₁₆	C₂×D₁₁	1	2	yes	complemented
154	C₂²×C₈	—	11	1	no	—
155	C₂²×C₈	—	11	2	no	—
156	C₂²×C₈	—	11	1	no	—
157	C₄×D₄	—	11	1	no	—
158	C₄×D₄	—	11	2	no	—
159	C₄×D₄	—	11	1	no	—
160	C₄×D₄	—	11	2	no	—
161	C₄×D₄	—	11	1	no	—
162	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
163	C₂×C₄⋊C₄	—	11	1	no	—
164	C₂×C₂²⋊C₄	—	11	2	no	—
165	C₂×C₄²	—	11	1	no	—
166	C₄⋊C₈	—	11	2	no	—
167	C₄⋊C₈	—	11	1	no	—
168	C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic, complemented
169	C₂²⋊C₈	—	11	2	no	—
170	C₂²⋊C₈	—	11	2	no	—
171	C₂²⋊C₈	—	11	2	no	—
172	C₂²⋊C₈	C₂×D₁₁	1	2	yes	complemented
173	C₄×C₈	—	11	1	no	—
174	C₄×C₈	—	11	1	no	—
175	C₄×C₈	—	11	1	no	—
176	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic, complemented
177	C₂×C₁₁	—	4	2	no	—
178	C₂×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
179	C₂×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
180	C₂×C₁₁	C₂×#131	1	1	yes	characteristic
181	D₁₁	—	4	2	no	—
182	D₁₁	#436	1	4	yes	direct product factor
183	C₂⁴	—	11	2	no	—
184	C₂×D₄	—	11	2	no	—
185	C₂×D₄	—	11	1	no	—
186	C₂×D₄	—	22	4	no	—
187	C₂×D₄	C₄×D₁₁	1	1	yes	characteristic
188	C₂²×C₄	—	11	1	no	—
189	C₂²×C₄	—	11	1	no	—
190	C₂²×C₄	—	11	2	no	—
191	C₂²×C₄	—	11	1	no	—
192	C₂²×C₄	—	11	2	no	—
193	C₂²×C₄	—	11	2	no	—
194	C₂²×C₄	—	11	2	no	—
195	C₂²×C₄	—	22	4	no	—
196	C₂²×C₄	—	22	4	no	—
197	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
198	M₁₆	—	2	4	no	—
199	M₁₆	—	22	4	no	—
200	M₁₆	—	22	4	no	—
201	M₁₆	—	22	4	no	—
202	C₂×C₈	—	11	1	no	—
203	C₂×C₈	—	11	4	no	—
204	C₂×C₈	—	11	1	no	—
205	C₂×C₈	—	11	2	no	—
206	C₂×C₈	—	22	4	no	—
207	C₂×C₈	—	22	2	no	—
208	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
209	C₂×C₈	C₂²×D₁₁	1	2	yes	—
210	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
211	C₄⋊C₄	—	11	2	no	—
212	C₄⋊C₄	—	11	1	no	—
213	C₄⋊C₄	C₄×D₁₁	1	1	yes	characteristic
214	C₂²⋊C₄	—	11	2	no	—
215	C₂²⋊C₄	—	11	2	no	—
216	C₂²⋊C₄	—	11	2	no	—
217	C₂²⋊C₄	C₄×D₁₁	1	2	yes	—
218	C₄²	—	11	1	no	—
219	C₄²	—	11	1	no	—
220	C₄²	—	11	1	no	—
221	C₄²	C₂²×D₁₁	1	1	yes	characteristic
222	C₁₁	C₂×#436	1	1	yes	characteristic, complemented, Sylow
223	C₂³	—	11	1	no	—
224	C₂³	—	11	2	no	—
225	C₂³	—	22	4	no	—
226	C₂³	—	22	4	no	—
227	C₂³	—	22	4	no	—
228	C₂³	C₂×C₄×D₁₁	1	2	yes	—
229	D₄	—	2	2	no	—
230	D₄	—	22	4	no	—
231	D₄	—	22	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	11	1	no	—
235	C₂×C₄	—	11	1	no	—
236	C₂×C₄	—	11	4	no	—
237	C₂×C₄	—	11	2	no	—
238	C₂×C₄	—	11	2	no	—
239	C₂×C₄	—	11	1	no	—
240	C₂×C₄	—	11	2	no	—
241	C₂×C₄	—	22	4	no	—
242	C₂×C₄	—	22	4	no	—
243	C₂×C₄	—	22	2	no	—
244	C₂×C₄	—	22	4	no	—
245	C₂×C₄	—	22	2	no	—
246	C₂×C₄	—	22	2	no	—
247	C₂×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
248	C₂×C₄	C₂×C₄×D₁₁	1	2	yes	—
249	C₂×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
250	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
251	C₈	—	2	2	no	—
252	C₈	—	2	1	no	—
253	C₈	—	11	2	no	—
254	C₈	—	22	2	no	—
255	C₈	—	22	1	no	—
256	C₈	D₄×D₁₁	1	2	yes	complemented
257	C₂²	—	2	2	no	—
258	C₂²	—	2	2	no	—
259	C₂²	—	2	2	no	—
260	C₂²	—	11	2	no	—
261	C₂²	—	11	2	no	—
262	C₂²	—	11	2	no	—
263	C₂²	—	22	2	no	—
264	C₂²	—	22	2	no	—
265	C₂²	—	22	2	no	—
266	C₂²	—	44	8	no	—
267	C₂²	C₂²×C₄×D₁₁	1	1	yes	characteristic
268	C₄	—	2	1	no	—
269	C₄	—	2	2	no	—
270	C₄	—	11	2	no	—
271	C₄	—	11	2	no	—
272	C₄	—	22	1	no	—
273	C₄	—	22	2	no	—
274	C₄	M₁₆×D₁₁	1	2	yes	complemented
275	C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
276	C₄	#41×D₁₁	1	1	yes	characteristic
277	C₂	—	4	2	no	—
278	C₂	—	11	4	no	—
279	C₂	—	44	2	no	—
280	C₂	C₄×D₄×D₁₁	1	1	yes	characteristic
281	C₂	C₂×M₁₆×D₁₁	1	1	yes	characteristic
282	C₂	D₁₁×#131	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₄
Fitting	C₁₁×#436	C₂
prime radical	C₂×D₄×D₁₁	C₄
cosocle	C₂×C₄×C₁₁	C₂⁴
hypercenter	#436	D₁₁
hypocenter	C₁₁	C₂×#436
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ #436

Complements

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

N	H ≅ G/N	type
1. C₂×M₁₆×D₁₁	C₂	semidirect
3. C₁₁×#436	C₂	semidirect
4. #10622741	C₂	semidirect
5. #10622625	C₂	semidirect
6. #10622451	C₂	semidirect
7. D₁₁×C₄⋊C₈	C₂	semidirect
8. #10622342	C₂	semidirect
9. D₁₁×C₂²⋊C₈	C₂	semidirect
10. #10622301	C₂	semidirect
11. C₄×C₈×D₁₁	C₂	semidirect
14. C₂×C₁₁×M₁₆	C₂²	semidirect
18. C₂×#4318	C₂²	semidirect
20. C₂×#4313	C₂²	semidirect
21. C₂×#4313	C₂²	semidirect
31. C₁₁×C₄⋊C₈	C₂²	semidirect
32. C₁₁×C₂²⋊C₈	C₂²	semidirect
33. C₄×C₈×C₁₁	C₂²	semidirect
34. C₂²⋊(C₁₁⋊C₈)	C₂²	semidirect
35. (C₂×D₁₁)⋊C₈	C₂²	semidirect
36. (C₂×D₁₁)⋊C₈	C₂²	semidirect
37. Dic₁₁⋊C₈	C₂²	semidirect
38. C₈×Dic₁₁	C₂²	semidirect
39. C₈×Dic₁₁	C₂²	semidirect
40. C₄⋊(C₁₁⋊C₈)	C₂²	semidirect
41. C₄×C₁₁⋊C₈	C₂²	semidirect
80. C₈×D₁₁	D₄	semidirect
107. C₄×D₁₁	M₁₆	semidirect
112. C₈×C₁₁	C₂×D₄	semidirect
115. C₁₁⋊C₈	C₂×D₄	semidirect
123. #436	D₁₁	direct (N × H)
140. C₄×C₁₁	C₂×M₁₆	semidirect
146. Dic₁₁	C₂×M₁₆	semidirect
153. C₂×M₁₆	C₂×D₁₁	semidirect
168. C₄⋊C₈	C₂×D₁₁	semidirect
172. C₂²⋊C₈	C₂×D₁₁	semidirect
176. C₄×C₈	C₂×D₁₁	semidirect
182. D₁₁	#436	direct (N × H)
222. C₁₁	C₂×#436	semidirect
256. C₈	D₄×D₁₁	semidirect
274. C₄	M₁₆×D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×D₁₁	2
C₄×D₄×D₁₁	2
C₁₁×#436	2
#10622741	2
#10622625	2
#10622451	2
D₁₁×C₄⋊C₈	2
#10622342	2
D₁₁×C₂²⋊C₈	2
#10622301	2
C₄×C₈×D₁₁	2
C₂×#436	11

Subgroups — D11×#436 #13077299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×#436 #13077299