Subgroups — C₁₁×#22264 #14599457

Order 2816.

1018 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#436	C₂	1	2	yes	maximal, complemented
2	C₄×C₁₁×#127	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1954	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1870	C₂	1	8	yes	maximal, complemented
5	C₁₁×#1831	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1744	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₁×M₁₆	C₂²	1	4	yes	—
8	C₂×C₁₁×#127	C₄	1	1	yes	characteristic
9	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
11	C₁₁×#436	—	2	8	no	—
12	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	—
14	C₂×C₁₁×C₂²⋊C₈	C₂²	1	8	yes	—
15	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
17	C₁₁×#390	C₄	1	2	yes	—
18	C₁₁×#390	C₄	1	4	yes	—
19	C₁₁×#384	C₄	1	1	yes	characteristic
20	C₄³×C₁₁	C₂²	1	1	yes	characteristic
21	C₁₁×#336	C₂²	1	4	yes	—
22	C₁₁×#336	C₂²	1	4	yes	—
23	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
24	C₂²×D₄×C₁₁	C₂×C₄	1	4	yes	—
25	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
26	C₂×C₁₁×M₁₆	—	2	8	no	—
27	C₂×C₁₁×M₁₆	—	4	8	no	—
28	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
29	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
30	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
31	C₁₁×#127	—	2	4	no	—
32	C₄×D₄×C₁₁	—	2	4	no	—
33	C₄×D₄×C₁₁	—	2	4	no	—
34	C₄×D₄×C₁₁	—	4	8	no	—
35	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
36	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
37	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	4	yes	—
38	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	8	yes	—
39	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
41	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
43	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
44	C₁₁×C₄⋊C₈	—	2	4	no	—
45	C₁₁×C₂²⋊C₈	—	2	8	no	—
46	C₁₁×C₂²⋊C₈	—	4	8	no	—
47	C₄×C₈×C₁₁	—	2	2	no	—
48	C₄×C₈×C₁₁	D₄	1	4	yes	complemented
49	#22264	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂⁴×C₁₁	C₂²×C₄	1	4	yes	—
51	C₂×D₄×C₁₁	—	2	4	no	—
52	C₂×D₄×C₁₁	—	2	8	no	—
53	C₂×D₄×C₁₁	—	2	4	no	—
54	C₂×D₄×C₁₁	—	2	4	no	—
55	C₂×D₄×C₁₁	—	4	4	no	—
56	C₂×D₄×C₁₁	—	4	4	no	—
57	C₂²×C₄×C₁₁	—	2	4	no	—
58	C₂²×C₄×C₁₁	—	2	4	no	—
59	C₂²×C₄×C₁₁	—	2	8	no	—
60	C₂²×C₄×C₁₁	—	2	8	no	—
61	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
62	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
63	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
65	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
67	C₁₁×M₁₆	—	4	16	no	—
68	C₂×C₈×C₁₁	—	2	4	no	—
69	C₂×C₈×C₁₁	—	2	2	no	—
70	C₂×C₈×C₁₁	—	2	4	no	—
71	C₂×C₈×C₁₁	—	2	4	no	—
72	C₂×C₈×C₁₁	—	2	8	no	—
73	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
74	C₁₁×C₄⋊C₄	—	2	4	no	—
75	C₁₁×C₄⋊C₄	—	4	4	no	—
76	C₁₁×C₂²⋊C₄	—	2	8	no	—
77	C₁₁×C₂²⋊C₄	—	4	8	no	—
78	C₄²×C₁₁	—	2	2	no	—
79	C₄²×C₁₁	—	2	4	no	—
80	C₄²×C₁₁	—	4	2	no	—
81	C₄²×C₁₁	M₁₆	1	4	yes	complemented
82	C₄²×C₁₁	C₂×D₄	1	2	yes	—
83	C₄²×C₁₁	#41	1	2	yes	—
84	C₂×#436	C₂×C₁₁	1	2	yes	complemented
85	C₄×#127	C₂×C₁₁	1	1	yes	characteristic
86	#1954	C₂×C₁₁	1	2	yes	complemented
87	#1870	C₂×C₁₁	1	8	yes	complemented
88	#1831	C₂×C₁₁	1	1	yes	characteristic, complemented
89	#1744	C₂×C₁₁	1	1	yes	characteristic, complemented
90	C₂³×C₁₁	—	2	4	no	—
91	C₂³×C₁₁	—	2	8	no	—
92	C₂³×C₁₁	—	2	4	no	—
93	C₂³×C₁₁	—	2	4	no	—
94	C₂³×C₁₁	—	2	8	no	—
95	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
96	D₄×C₁₁	—	4	16	no	—
97	D₄×C₁₁	—	4	8	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	4	no	—
102	C₂×C₄×C₁₁	—	2	2	no	—
103	C₂×C₄×C₁₁	—	2	8	no	—
104	C₂×C₄×C₁₁	—	2	2	no	—
105	C₂×C₄×C₁₁	—	2	2	no	—
106	C₂×C₄×C₁₁	—	4	4	no	—
107	C₂×C₄×C₁₁	—	4	4	no	—
108	C₂×C₄×C₁₁	—	4	8	no	—
109	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
110	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
111	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
112	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
113	C₂×C₄×C₁₁	#131	1	2	yes	—
114	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
115	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
116	C₂×C₄×C₁₁	H(5,𝔽₂)	1	4	yes	—
117	C₈×C₁₁	—	2	4	no	—
118	C₈×C₁₁	—	4	4	no	—
119	C₈×C₁₁	—	4	2	no	—
120	C₂²×M₁₆	C₂²×C₁₁	1	4	yes	—
121	C₂×#127	C₄×C₁₁	1	1	yes	characteristic
122	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
123	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
124	#436	—	2	8	no	—
125	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
126	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	—
127	C₂×C₂²⋊C₈	C₂²×C₁₁	1	8	yes	—
128	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
129	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
130	#390	C₄×C₁₁	1	2	yes	—
131	#390	C₄×C₁₁	1	4	yes	—
132	#384	C₄×C₁₁	1	1	yes	characteristic
133	C₄³	C₂²×C₁₁	1	1	yes	characteristic
134	#336	C₂²×C₁₁	1	4	yes	—
135	#336	C₂²×C₁₁	1	4	yes	—
136	C₂²×C₁₁	—	4	4	no	—
137	C₂²×C₁₁	—	4	4	no	—
138	C₂²×C₁₁	—	4	4	no	—
139	C₂²×C₁₁	—	4	8	no	—
140	C₂²×C₁₁	—	4	8	no	—
141	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
142	C₂²×C₁₁	#518	1	2	yes	—
143	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
144	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
145	C₂²×C₁₁	#568	1	2	yes	—
146	C₄×C₁₁	—	2	2	no	—
147	C₄×C₁₁	—	2	4	no	—
148	C₄×C₁₁	—	4	4	no	—
149	C₄×C₁₁	—	4	2	no	—
150	C₄×C₁₁	#436	1	4	yes	—
151	C₄×C₁₁	#535	1	2	yes	—
152	C₄×C₁₁	#540	1	2	yes	—
153	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
154	C₂²×D₄	C₂×C₄×C₁₁	1	4	yes	—
155	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
156	C₂×M₁₆	—	2	8	no	—
157	C₂×M₁₆	—	4	8	no	—
158	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
159	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
160	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
161	#127	—	2	4	no	—
162	C₄×D₄	—	2	4	no	—
163	C₄×D₄	—	2	4	no	—
164	C₄×D₄	—	4	8	no	—
165	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
166	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
167	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
168	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	8	yes	—
169	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
170	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
171	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
172	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
173	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
174	C₄⋊C₈	—	2	4	no	—
175	C₂²⋊C₈	—	2	8	no	—
176	C₂²⋊C₈	—	4	8	no	—
177	C₄×C₈	—	2	2	no	—
178	C₄×C₈	D₄×C₁₁	1	4	yes	complemented
179	C₂×C₁₁	—	8	4	no	—
180	C₂×C₁₁	#2328	1	1	yes	characteristic
181	C₂×C₁₁	C₂×#436	1	1	yes	characteristic
182	C₂×C₁₁	#2932	1	1	yes	characteristic
183	C₂×C₁₁	#2975	1	2	yes	—
184	C₂×C₁₁	#2981	1	2	yes	—
185	C₂⁴	C₂²×C₄×C₁₁	1	4	yes	—
186	C₂×D₄	—	2	4	no	—
187	C₂×D₄	—	2	8	no	—
188	C₂×D₄	—	2	4	no	—
189	C₂×D₄	—	2	4	no	—
190	C₂×D₄	—	4	4	no	—
191	C₂×D₄	—	4	4	no	—
192	C₂²×C₄	—	2	4	no	—
193	C₂²×C₄	—	2	4	no	—
194	C₂²×C₄	—	2	8	no	—
195	C₂²×C₄	—	2	8	no	—
196	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
197	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
198	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
199	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
200	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
201	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
202	M₁₆	—	4	16	no	—
203	C₂×C₈	—	2	4	no	—
204	C₂×C₈	—	2	4	no	—
205	C₂×C₈	—	2	2	no	—
206	C₂×C₈	—	2	4	no	—
207	C₂×C₈	—	2	8	no	—
208	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
209	C₄⋊C₄	—	2	4	no	—
210	C₄⋊C₄	—	4	4	no	—
211	C₂²⋊C₄	—	2	8	no	—
212	C₂²⋊C₄	—	4	8	no	—
213	C₄²	—	2	2	no	—
214	C₄²	—	2	4	no	—
215	C₄²	—	4	2	no	—
216	C₄²	C₁₁×M₁₆	1	4	yes	complemented
217	C₄²	C₂×D₄×C₁₁	1	2	yes	—
218	C₄²	C₁₁×#41	1	2	yes	—
219	C₁₁	#22264	1	1	yes	characteristic, direct product factor, Sylow
220	C₂³	—	2	4	no	—
221	C₂³	—	2	8	no	—
222	C₂³	—	2	4	no	—
223	C₂³	—	2	4	no	—
224	C₂³	—	2	8	no	—
225	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
226	D₄	—	4	16	no	—
227	D₄	—	4	8	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	4	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	8	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	4	4	no	—
237	C₂×C₄	—	4	4	no	—
238	C₂×C₄	—	4	8	no	—
239	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
240	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
241	C₂×C₄	C₂×C₁₁×M₁₆	1	4	yes	—
242	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
243	C₂×C₄	C₁₁×#131	1	2	yes	—
244	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
245	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
246	C₂×C₄	C₁₁×H(5,𝔽₂)	1	4	yes	—
247	C₈	—	2	4	no	—
248	C₈	—	4	4	no	—
249	C₈	—	4	2	no	—
250	C₂²	—	4	4	no	—
251	C₂²	—	4	4	no	—
252	C₂²	—	4	8	no	—
253	C₂²	—	4	8	no	—
254	C₂²	—	4	4	no	—
255	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
256	C₂²	C₁₁×#518	1	2	yes	—
257	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
258	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
259	C₂²	C₁₁×#568	1	2	yes	—
260	C₄	—	2	2	no	—
261	C₄	—	2	4	no	—
262	C₄	—	4	2	no	—
263	C₄	—	4	4	no	—
264	C₄	C₁₁×#436	1	4	yes	—
265	C₄	C₁₁×#535	1	2	yes	—
266	C₄	C₁₁×#540	1	2	yes	—
267	C₂	—	8	4	no	—
268	C₂	C₁₁×#2328	1	1	yes	characteristic
269	C₂	C₂×C₁₁×#436	1	1	yes	characteristic
270	C₂	C₁₁×#2932	1	1	yes	characteristic
271	C₂	C₁₁×#2975	1	2	yes	—
272	C₂	C₁₁×#2981	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂³×C₁₁	C₂³×C₄
prime radical	C₂×C₁₁×#127	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#436	C₂	semidirect
3. C₁₁×#1954	C₂	semidirect
4. C₁₁×#1870	C₂	semidirect
5. C₁₁×#1831	C₂	semidirect
6. C₁₁×#1744	C₂	semidirect
48. C₄×C₈×C₁₁	D₄	semidirect
49. #22264	C₁₁	direct (N × H)
81. C₄²×C₁₁	M₁₆	semidirect
84. C₂×#436	C₂×C₁₁	semidirect
86. #1954	C₂×C₁₁	semidirect
87. #1870	C₂×C₁₁	semidirect
88. #1831	C₂×C₁₁	semidirect
89. #1744	C₂×C₁₁	semidirect
178. C₄×C₈	D₄×C₁₁	semidirect
216. C₄²	C₁₁×M₁₆	semidirect
219. C₁₁	#22264	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×#436	2
C₄×C₁₁×#127	2
C₁₁×#1954	2
C₁₁×#1870	2
C₁₁×#1831	2
C₁₁×#1744	2
#22264	11

Subgroups — C11×#22264 #14599457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22264 #14599457