Subgroups — D₁₁×#1374 #14668608

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆×D₁₁	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₁₁	C₂	1	1	yes	maximal, characteristic
3	#13066694	C₂	1	1	yes	maximal, characteristic, complemented
4	#13066693	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₁₁	C₄	1	1	yes	characteristic
7	C₂²×C₈×D₁₁	C₂²	1	1	yes	characteristic
8	C₂×C₄²×D₁₁	C₄	1	1	yes	characteristic
9	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₈×Dic₁₁	C₄	1	1	yes	characteristic
12	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
13	C₂²×C₁₁⋊C₁₆	C₂²	1	2	yes	—
14	C₂×C₄×C₁₁⋊C₈	C₄	1	1	yes	characteristic
15	C₂×C₁₆×D₁₁	—	2	4	no	—
16	C₂×C₁₆×D₁₁	—	2	4	no	—
17	C₂×C₁₆×D₁₁	C₄	1	8	yes	complemented
18	C₄×C₈×D₁₁	—	2	4	no	—
19	C₂²×C₄×D₁₁	C₈	1	2	yes	—
20	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
23	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×Dic₁₁	C₈	1	2	yes	—
25	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×D₁₁	—	2	2	no	—
29	C₂×C₈×D₁₁	—	2	2	no	—
30	C₂×C₈×D₁₁	C₈	1	4	yes	—
31	C₂×C₈×D₁₁	C₂×C₄	1	4	yes	—
32	C₂×C₈×D₁₁	D₄	1	2	yes	—
33	C₂×C₈×D₁₁	D₄	1	4	yes	—
34	C₂×C₈×D₁₁	Q₈	1	2	yes	—
35	C₄²×D₁₁	—	2	2	no	—
36	C₄²×D₁₁	—	2	2	no	—
37	C₂×C₁₁×C₁₆	—	2	2	no	—
38	C₂×C₁₁×C₁₆	—	2	2	no	—
39	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	complemented
40	C₄×C₈×C₁₁	—	2	2	no	—
41	C₈×Dic₁₁	—	2	2	no	—
42	C₈×Dic₁₁	—	2	2	no	—
43	C₂×C₁₁⋊C₁₆	—	2	2	no	—
44	C₂×C₁₁⋊C₁₆	—	2	2	no	—
45	C₂×C₁₁⋊C₁₆	C₂×C₄	1	4	yes	complemented
46	C₄×C₁₁⋊C₈	—	2	2	no	—
47	C₁₆×D₁₁	—	2	16	no	—
48	C₂×#1374	—	11	1	no	maximal, Sylow
49	C₂³×D₁₁	C₂×C₈	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
51	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
52	C₂²×Dic₁₁	C₂×C₈	1	2	yes	—
53	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
54	C₂×C₄×D₁₁	—	2	4	no	—
55	C₂×C₄×D₁₁	—	2	4	no	—
56	C₂×C₄×D₁₁	C₁₆	1	8	yes	complemented
57	C₂×C₄×D₁₁	C₄²	1	2	yes	—
58	C₂×C₄×D₁₁	C₂²⋊C₄	1	2	yes	—
59	C₂×C₄×D₁₁	C₄⋊C₄	1	2	yes	—
60	C₂×C₄×D₁₁	C₂×C₈	1	2	yes	—
61	C₂×C₄×D₁₁	M₁₆	1	2	yes	—
62	C₂×C₄×D₁₁	M₁₆	1	2	yes	—
63	C₂×C₈×C₁₁	—	2	1	no	—
64	C₂×C₈×C₁₁	—	2	1	no	—
65	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
66	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
67	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
68	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
69	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
70	C₄²×C₁₁	—	2	1	no	—
71	C₄²×C₁₁	—	2	1	no	—
72	C₄×Dic₁₁	—	2	4	no	—
73	C₄×Dic₁₁	—	2	1	no	—
74	C₄×Dic₁₁	—	2	1	no	—
75	C₂×C₁₁⋊C₈	—	2	1	no	—
76	C₂×C₁₁⋊C₈	—	2	1	no	—
77	C₂×C₁₁⋊C₈	C₄²	1	2	yes	—
78	C₂×C₁₁⋊C₈	C₂²⋊C₄	1	2	yes	—
79	C₂×C₁₁⋊C₈	C₄⋊C₄	1	2	yes	—
80	C₂×C₁₁⋊C₈	C₂×C₈	1	2	yes	—
81	C₈×D₁₁	—	2	8	no	—
82	C₈×D₁₁	C₂²⋊C₄	1	8	yes	—
83	C₈×D₁₁	C₄⋊C₄	1	8	yes	—
84	C₁₁×C₁₆	—	2	4	no	—
85	C₁₁⋊C₁₆	—	2	4	no	—
86	C₂³×C₁₆	—	11	2	no	—
87	C₂²×C₄×C₈	—	11	1	no	—
88	#1374	—	11	2	no	—
89	#1374	—	11	1	no	—
90	#1374	D₁₁	1	1	yes	characteristic, direct product factor
91	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
92	C₂²×D₁₁	C₄×C₈	1	2	yes	—
93	C₂²×D₁₁	C₂²⋊C₈	1	2	yes	—
94	C₂²×D₁₁	C₄⋊C₈	1	2	yes	—
95	C₂²×D₁₁	C₂×C₁₆	1	4	yes	—
96	C₂²×D₁₁	M₃₂	1	4	yes	—
97	C₂×C₄×C₁₁	—	2	2	no	—
98	C₂×C₄×C₁₁	—	2	2	no	—
99	C₂×C₄×C₁₁	C₂×C₁₆	1	4	yes	complemented
100	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
101	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
104	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
105	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
106	C₂×Dic₁₁	—	2	2	no	—
107	C₂×Dic₁₁	—	2	2	no	—
108	C₂×Dic₁₁	C₄×C₈	1	2	yes	—
109	C₂×Dic₁₁	C₂²⋊C₈	1	2	yes	—
110	C₂×Dic₁₁	C₄⋊C₈	1	2	yes	—
111	C₂×Dic₁₁	C₂×C₁₆	1	4	yes	complemented
112	C₄×D₁₁	—	2	16	no	—
113	C₄×D₁₁	#95	1	4	yes	—
114	C₄×D₁₁	#97	1	4	yes	—
115	C₄×D₁₁	C₂²⋊C₈	1	4	yes	—
116	C₄×D₁₁	C₄⋊C₈	1	4	yes	—
117	C₈×C₁₁	—	2	2	no	—
118	C₈×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
119	C₈×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
120	C₁₁⋊C₈	—	2	2	no	—
121	C₁₁⋊C₈	#95	1	4	yes	—
122	C₂³×C₈	—	11	1	no	—
123	C₂³×C₈	—	11	1	no	—
124	C₂²×C₄²	—	11	1	no	—
125	C₂²×C₁₆	—	11	2	no	—
126	C₂²×C₁₆	—	11	8	no	—
127	C₂²×C₁₆	—	22	4	no	—
128	C₂²×C₁₆	—	22	4	no	—
129	C₂²×C₁₆	C₂×D₁₁	1	2	yes	—
130	C₂×C₄×C₈	—	11	1	no	—
131	C₂×C₄×C₈	—	11	1	no	—
132	C₂×C₄×C₈	—	11	1	no	—
133	C₂×C₄×C₈	—	22	4	no	—
134	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
135	C₂²×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
136	C₂²×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
137	C₂²×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
138	C₂²×C₁₁	C₂²×C₁₆	1	2	yes	—
139	C₂²×C₁₁	C₂×M₃₂	1	2	yes	—
140	C₂×D₁₁	#336	1	4	yes	—
141	C₂×D₁₁	C₄×C₁₆	1	4	yes	—
142	C₂×D₁₁	#346	1	4	yes	—
143	C₂×D₁₁	C₂²⋊C₁₆	1	8	yes	—
144	C₂×D₁₁	C₄⋊C₁₆	1	8	yes	—
145	C₄×C₁₁	—	2	4	no	—
146	C₄×C₁₁	C₂×#95	1	1	yes	characteristic
147	C₄×C₁₁	C₂×#97	1	1	yes	characteristic
148	C₄×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
149	C₄×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
150	Dic₁₁	—	2	4	no	—
151	Dic₁₁	#336	1	4	yes	—
152	C₂³×C₄	—	11	1	no	—
153	C₂³×C₄	—	11	2	no	—
154	C₂²×C₈	—	11	1	no	—
155	C₂²×C₈	—	11	4	no	—
156	C₂²×C₈	—	11	4	no	—
157	C₂²×C₈	—	11	2	no	—
158	C₂²×C₈	—	11	2	no	—
159	C₂²×C₈	—	11	1	no	—
160	C₂²×C₈	—	11	4	no	—
161	C₂²×C₈	—	22	2	no	—
162	C₂²×C₈	—	22	2	no	—
163	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
164	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
165	C₂×C₄²	—	11	2	no	—
166	C₂×C₄²	—	11	1	no	—
167	C₂×C₄²	—	22	2	no	—
168	C₂×C₄²	—	22	2	no	—
169	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
170	C₂×C₁₆	—	2	2	no	—
171	C₂×C₁₆	—	2	2	no	—
172	C₂×C₁₆	—	11	4	no	—
173	C₂×C₁₆	—	22	16	no	—
174	C₂×C₁₆	—	22	2	no	—
175	C₂×C₁₆	—	22	2	no	—
176	C₂×C₁₆	C₄×D₁₁	1	4	yes	complemented
177	C₄×C₈	—	2	2	no	—
178	C₄×C₈	—	22	2	no	—
179	C₄×C₈	—	22	2	no	—
180	C₄×C₈	—	22	2	no	—
181	C₂×C₁₁	C₂×#336	1	1	yes	characteristic
182	C₂×C₁₁	C₂×C₄×C₁₆	1	1	yes	characteristic
183	C₂×C₁₁	C₂×#346	1	1	yes	characteristic
184	C₂×C₁₁	C₂×C₂²⋊C₁₆	1	2	yes	—
185	C₂×C₁₁	C₂×C₄⋊C₁₆	1	2	yes	—
186	D₁₁	#1374	1	8	yes	direct product factor
187	C₂⁴	—	11	1	no	—
188	C₂²×C₄	—	11	1	no	—
189	C₂²×C₄	—	11	2	no	—
190	C₂²×C₄	—	11	2	no	—
191	C₂²×C₄	—	11	2	no	—
192	C₂²×C₄	—	11	2	no	—
193	C₂²×C₄	—	11	2	no	—
194	C₂²×C₄	—	11	2	no	—
195	C₂²×C₄	—	11	2	no	—
196	C₂²×C₄	—	11	8	no	—
197	C₂²×C₄	—	22	4	no	—
198	C₂²×C₄	—	22	4	no	—
199	C₂²×C₄	C₈×D₁₁	1	2	yes	—
200	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
201	C₂×C₈	—	2	1	no	—
202	C₂×C₈	—	2	1	no	—
203	C₂×C₈	—	11	2	no	—
204	C₂×C₈	—	11	2	no	—
205	C₂×C₈	—	11	2	no	—
206	C₂×C₈	—	11	8	no	—
207	C₂×C₈	—	11	8	no	—
208	C₂×C₈	—	11	2	no	—
209	C₂×C₈	—	22	8	no	—
210	C₂×C₈	—	22	1	no	—
211	C₂×C₈	—	22	1	no	—
212	C₂×C₈	C₈×D₁₁	1	2	yes	—
213	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
214	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
215	C₂×C₈	D₄×D₁₁	1	2	yes	—
216	C₂×C₈	Q₈×D₁₁	1	1	yes	characteristic
217	C₄²	—	2	1	no	—
218	C₄²	—	2	1	no	—
219	C₄²	—	22	4	no	—
220	C₄²	—	22	1	no	—
221	C₄²	—	22	1	no	—
222	C₁₆	—	2	4	no	—
223	C₁₆	—	22	4	no	—
224	C₁₁	C₂×#1374	1	1	yes	characteristic, complemented, Sylow
225	C₂³	—	11	4	no	—
226	C₂³	—	11	4	no	—
227	C₂³	—	11	2	no	—
228	C₂³	—	11	2	no	—
229	C₂³	—	11	2	no	—
230	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	11	2	no	—
234	C₂×C₄	—	11	2	no	—
235	C₂×C₄	—	11	2	no	—
236	C₂×C₄	—	11	4	no	—
237	C₂×C₄	—	11	4	no	—
238	C₂×C₄	—	11	4	no	—
239	C₂×C₄	—	11	4	no	—
240	C₂×C₄	—	11	4	no	—
241	C₂×C₄	—	22	16	no	—
242	C₂×C₄	—	22	2	no	—
243	C₂×C₄	—	22	2	no	—
244	C₂×C₄	C₁₆×D₁₁	1	4	yes	complemented
245	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
246	C₂×C₄	C₂²⋊C₄×D₁₁	1	1	yes	characteristic
247	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
248	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
249	C₂×C₄	M₁₆×D₁₁	1	1	yes	characteristic
250	C₂×C₄	M₁₆×D₁₁	1	1	yes	characteristic
251	C₈	—	2	2	no	—
252	C₈	—	11	4	no	—
253	C₈	—	22	2	no	—
254	C₈	C₂²⋊C₄×D₁₁	1	2	yes	—
255	C₈	C₄⋊C₄×D₁₁	1	2	yes	—
256	C₂²	—	11	4	no	—
257	C₂²	—	11	8	no	—
258	C₂²	—	11	4	no	—
259	C₂²	—	11	4	no	—
260	C₂²	—	11	8	no	—
261	C₂²	C₄×C₈×D₁₁	1	1	yes	characteristic
262	C₂²	D₁₁×C₂²⋊C₈	1	1	yes	characteristic
263	C₂²	D₁₁×C₄⋊C₈	1	1	yes	characteristic
264	C₂²	C₂×C₁₆×D₁₁	1	2	yes	—
265	C₂²	D₁₁×M₃₂	1	2	yes	—
266	C₄	—	2	4	no	—
267	C₄	—	11	4	no	—
268	C₄	—	22	4	no	—
269	C₄	D₁₁×#95	1	1	yes	characteristic
270	C₄	D₁₁×#97	1	1	yes	characteristic
271	C₄	D₁₁×C₂²⋊C₈	1	1	yes	characteristic
272	C₄	D₁₁×C₄⋊C₈	1	1	yes	characteristic
273	C₂	—	11	8	no	—
274	C₂	D₁₁×#336	1	1	yes	characteristic
275	C₂	C₄×C₁₆×D₁₁	1	1	yes	characteristic
276	C₂	D₁₁×#346	1	1	yes	characteristic
277	C₂	D₁₁×C₂²⋊C₁₆	1	2	yes	—
278	C₂	D₁₁×C₄⋊C₁₆	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₁₁
commutator	C₂×C₁₁	C₂×C₄×C₁₆
Fitting	C₁₁×#1374	C₂
socle	C₂³×C₁₁	C₂²×C₈
prime radical	C₂³×D₁₁	C₂×C₈
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#1374	D₁₁
hypocenter	C₁₁	C₂×#1374
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₈ ◁ #1374

Complements

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

N	H ≅ G/N	type
3. #13066694	C₂	semidirect
4. #13066693	C₂	semidirect
5. C₁₁×#1374	C₂	semidirect
17. C₂×C₁₆×D₁₁	C₄	semidirect
39. C₂×C₁₁×C₁₆	C₂×C₄	semidirect
45. C₂×C₁₁⋊C₁₆	C₂×C₄	semidirect
56. C₂×C₄×D₁₁	C₁₆	semidirect
90. #1374	D₁₁	direct (N × H)
99. C₂×C₄×C₁₁	C₂×C₁₆	semidirect
111. C₂×Dic₁₁	C₂×C₁₆	semidirect
176. C₂×C₁₆	C₄×D₁₁	semidirect
186. D₁₁	#1374	direct (N × H)
224. C₁₁	C₂×#1374	semidirect
244. C₂×C₄	C₁₆×D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₆×D₁₁	2
C₂×C₄×C₈×D₁₁	2
#13066694	2
#13066693	2
C₁₁×#1374	2
C₂×#1374	11

Subgroups — D11×#1374 #14668608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×#1374 #14668608