Subgroups — C₁₁×#21954 #14599147

Order 2816.

798 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#431	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2285	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1940	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1939	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1798	C₂	1	4	yes	maximal
7	C₂×C₁₁×#117	C₂²	1	2	yes	—
8	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
9	C₁₁×#432	—	2	4	no	—
10	C₁₁×#431	—	2	4	no	—
11	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
12	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₁₁×C₄⋊C₈	C₂²	1	8	yes	—
14	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₁×#97	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
18	C₁₁×#384	C₄	1	2	yes	—
19	C₁₁×#382	C₄	1	2	yes	—
20	C₁₁×#380	C₄	1	2	yes	—
21	C₁₁×#380	C₄	1	2	yes	—
22	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
23	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
24	C₁₁×#336	C₂²	1	8	yes	—
25	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
28	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
29	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
30	C₁₁×#117	—	4	4	no	—
31	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
32	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
33	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
34	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	4	yes	—
35	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₁	D₄	1	4	yes	—
38	C₂×C₄²×C₁₁	Q₈	1	4	yes	—
39	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
40	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
41	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
42	C₁₁×C₄⋊C₈	—	2	4	no	—
43	C₁₁×C₄⋊C₈	—	2	4	no	—
44	C₁₁×C₄⋊C₈	—	4	8	no	—
45	C₁₁×C₂²⋊C₈	—	2	4	no	—
46	C₁₁×C₂²⋊C₈	—	2	4	no	—
47	C₁₁×#97	—	2	4	no	—
48	C₄×C₈×C₁₁	—	2	4	no	—
49	C₁₁×#95	C₂×C₄	1	4	yes	—
50	C₁₁×#95	C₂×C₄	1	4	yes	—
51	#21954	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
52	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₁	—	2	4	no	—
54	C₂²×C₄×C₁₁	—	2	2	no	—
55	C₂²×C₄×C₁₁	—	2	2	no	—
56	C₂²×C₄×C₁₁	—	4	2	no	—
57	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
58	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
59	C₂²×C₄×C₁₁	C₂²×C₄	1	8	yes	—
60	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
66	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
67	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
68	C₂×C₈×C₁₁	—	2	4	no	—
69	C₂×C₈×C₁₁	—	2	4	no	—
70	C₂×C₈×C₁₁	—	2	4	no	—
71	C₂×C₈×C₁₁	—	2	4	no	—
72	C₂×C₈×C₁₁	—	2	4	no	—
73	C₂×C₈×C₁₁	—	2	4	no	—
74	C₁₁×C₄⋊C₄	—	2	8	no	—
75	C₁₁×C₄⋊C₄	—	4	4	no	—
76	C₁₁×C₄⋊C₄	—	4	4	no	—
77	C₁₁×C₂²⋊C₄	—	4	4	no	—
78	C₄²×C₁₁	—	2	8	no	—
79	C₄²×C₁₁	C₄⋊C₄	1	4	yes	—
80	C₄²×C₁₁	C₄⋊C₄	1	4	yes	—
81	C₄²×C₁₁	C₂×D₄	1	2	yes	—
82	C₄²×C₁₁	C₂×D₄	1	2	yes	—
83	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
84	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
85	C₂×#432	C₂×C₁₁	1	1	yes	characteristic
86	C₂×#431	C₂×C₁₁	1	1	yes	characteristic
87	#2285	C₂×C₁₁	1	1	yes	characteristic
88	#1940	C₂×C₁₁	1	4	yes	complemented
89	#1939	C₂×C₁₁	1	4	yes	complemented
90	#1798	C₂×C₁₁	1	4	yes	—
91	C₂³×C₁₁	—	2	1	no	—
92	C₂³×C₁₁	—	2	1	no	—
93	C₂³×C₁₁	—	2	2	no	—
94	C₂³×C₁₁	—	2	2	no	—
95	C₂³×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
96	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
97	C₂×C₄×C₁₁	—	2	1	no	—
98	C₂×C₄×C₁₁	—	2	1	no	—
99	C₂×C₄×C₁₁	—	2	2	no	—
100	C₂×C₄×C₁₁	—	2	2	no	—
101	C₂×C₄×C₁₁	—	2	2	no	—
102	C₂×C₄×C₁₁	—	2	4	no	—
103	C₂×C₄×C₁₁	—	2	4	no	—
104	C₂×C₄×C₁₁	—	2	8	no	—
105	C₂×C₄×C₁₁	—	2	8	no	—
106	C₂×C₄×C₁₁	—	2	8	no	—
107	C₂×C₄×C₁₁	—	2	8	no	—
108	C₂×C₄×C₁₁	—	4	4	no	—
109	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
110	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
111	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
112	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
113	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
114	C₂×C₄×C₁₁	#131	1	4	yes	—
115	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
116	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
117	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
118	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
119	C₈×C₁₁	—	4	4	no	—
120	C₈×C₁₁	—	4	4	no	—
121	C₂×#117	C₂²×C₁₁	1	2	yes	—
122	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
123	#432	—	2	4	no	—
124	#431	—	2	4	no	—
125	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
126	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
127	C₂×C₄⋊C₈	C₂²×C₁₁	1	8	yes	—
128	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
129	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
130	C₂×#97	C₂²×C₁₁	1	2	yes	—
131	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
132	#384	C₄×C₁₁	1	2	yes	—
133	#382	C₄×C₁₁	1	2	yes	—
134	#380	C₄×C₁₁	1	2	yes	—
135	#380	C₄×C₁₁	1	2	yes	—
136	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
137	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
138	#336	C₂²×C₁₁	1	8	yes	—
139	C₂²×C₁₁	—	2	2	no	—
140	C₂²×C₁₁	—	2	2	no	—
141	C₂²×C₁₁	—	2	2	no	—
142	C₂²×C₁₁	—	4	2	no	—
143	C₂²×C₁₁	—	4	2	no	—
144	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
145	C₂²×C₁₁	#518	1	1	yes	characteristic
146	C₂²×C₁₁	#519	1	1	yes	characteristic
147	C₂²×C₁₁	C₂×#131	1	2	yes	—
148	C₂²×C₁₁	#568	1	2	yes	—
149	C₄×C₁₁	—	2	2	no	—
150	C₄×C₁₁	—	2	2	no	—
151	C₄×C₁₁	—	2	2	no	—
152	C₄×C₁₁	—	2	2	no	—
153	C₄×C₁₁	—	4	8	no	—
154	C₄×C₁₁	#424	1	4	yes	—
155	C₄×C₁₁	#537	1	2	yes	—
156	C₄×C₁₁	#544	1	2	yes	—
157	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
158	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
159	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
160	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
161	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
162	#117	—	4	4	no	—
163	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
164	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
165	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
166	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
167	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
168	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
169	C₂×C₄²	D₄×C₁₁	1	4	yes	—
170	C₂×C₄²	Q₈×C₁₁	1	4	yes	—
171	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
172	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
173	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
174	C₄⋊C₈	—	2	4	no	—
175	C₄⋊C₈	—	2	4	no	—
176	C₄⋊C₈	—	4	8	no	—
177	C₂²⋊C₈	—	2	4	no	—
178	C₂²⋊C₈	—	2	4	no	—
179	#97	—	2	4	no	—
180	C₄×C₈	—	2	4	no	—
181	#95	C₂×C₄×C₁₁	1	4	yes	—
182	#95	C₂×C₄×C₁₁	1	4	yes	—
183	C₂×C₁₁	—	4	2	no	—
184	C₂×C₁₁	#2316	1	1	yes	characteristic
185	C₂×C₁₁	C₂×#424	1	1	yes	characteristic
186	C₂×C₁₁	#2905	1	1	yes	characteristic
187	C₂×C₁₁	#2981	1	2	yes	—
188	C₂×C₁₁	#2985	1	2	yes	—
189	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
190	C₂²×C₄	—	2	4	no	—
191	C₂²×C₄	—	2	2	no	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	4	2	no	—
194	C₂²×C₄	C₁₁×C₄⋊C₄	1	4	yes	—
195	C₂²×C₄	C₁₁×C₄⋊C₄	1	4	yes	—
196	C₂²×C₄	C₂²×C₄×C₁₁	1	8	yes	—
197	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
198	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
199	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
200	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
201	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
202	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
203	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
204	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
205	C₂×C₈	—	2	4	no	—
206	C₂×C₈	—	2	4	no	—
207	C₂×C₈	—	2	4	no	—
208	C₂×C₈	—	2	4	no	—
209	C₂×C₈	—	2	4	no	—
210	C₂×C₈	—	2	4	no	—
211	C₄⋊C₄	—	2	8	no	—
212	C₄⋊C₄	—	4	4	no	—
213	C₄⋊C₄	—	4	4	no	—
214	C₂²⋊C₄	—	4	4	no	—
215	C₄²	—	2	8	no	—
216	C₄²	C₁₁×C₄⋊C₄	1	4	yes	—
217	C₄²	C₁₁×C₄⋊C₄	1	4	yes	—
218	C₄²	C₂×D₄×C₁₁	1	2	yes	—
219	C₄²	C₂×D₄×C₁₁	1	2	yes	—
220	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
221	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
222	C₁₁	#21954	1	1	yes	characteristic, direct product factor, Sylow
223	C₂³	—	2	1	no	—
224	C₂³	—	2	1	no	—
225	C₂³	—	2	2	no	—
226	C₂³	—	2	2	no	—
227	C₂³	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
228	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
229	C₂×C₄	—	2	1	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	2	4	no	—
235	C₂×C₄	—	2	4	no	—
236	C₂×C₄	—	2	8	no	—
237	C₂×C₄	—	2	8	no	—
238	C₂×C₄	—	2	8	no	—
239	C₂×C₄	—	2	8	no	—
240	C₂×C₄	—	4	4	no	—
241	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
242	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
243	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
244	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
245	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
246	C₂×C₄	C₁₁×#131	1	4	yes	—
247	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
248	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
249	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
250	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
251	C₈	—	4	4	no	—
252	C₈	—	4	4	no	—
253	C₂²	—	2	2	no	—
254	C₂²	—	2	2	no	—
255	C₂²	—	2	2	no	—
256	C₂²	—	4	2	no	—
257	C₂²	—	4	2	no	—
258	C₂²	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
259	C₂²	C₁₁×#518	1	1	yes	characteristic
260	C₂²	C₁₁×#519	1	1	yes	characteristic
261	C₂²	C₂×C₁₁×#131	1	2	yes	—
262	C₂²	C₁₁×#568	1	2	yes	—
263	C₄	—	2	2	no	—
264	C₄	—	2	2	no	—
265	C₄	—	2	2	no	—
266	C₄	—	2	2	no	—
267	C₄	—	4	8	no	—
268	C₄	C₁₁×#424	1	4	yes	—
269	C₄	C₁₁×#537	1	2	yes	—
270	C₄	C₁₁×#544	1	2	yes	—
271	C₂	—	4	2	no	—
272	C₂	C₁₁×#2316	1	1	yes	characteristic
273	C₂	C₂×C₁₁×#424	1	1	yes	characteristic
274	C₂	C₁₁×#2905	1	1	yes	characteristic
275	C₂	C₁₁×#2981	1	2	yes	—
276	C₂	C₁₁×#2985	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	C₂⁴×C₁₁	C₂²×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
4. C₁₁×#1940	C₂	semidirect
5. C₁₁×#1939	C₂	semidirect
51. #21954	C₁₁	direct (N × H)
88. #1940	C₂×C₁₁	semidirect
89. #1939	C₂×C₁₁	semidirect
222. C₁₁	#21954	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×#432	2
C₂×C₁₁×#431	2
C₁₁×#2285	2
C₁₁×#1940	2
C₁₁×#1939	2
C₁₁×#1798	2
#21954	11

Subgroups — C11×#21954 #14599147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21954 #14599147