Subgroups — C₁₁×#11966 #14589159

Order 2816.

400 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3147	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2163	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#1567	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1362	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1361	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#135	—	2	1	no	—
7	C₂×C₁₁×#135	C₄	1	2	yes	—
8	C₁₁×#532	—	2	1	no	—
9	C₁₁×#495	—	2	1	no	—
10	C₁₁×#495	C₄	1	2	yes	—
11	C₁₁×#494	C₂²	1	1	yes	characteristic
12	C₁₁×#493	C₂²	1	1	yes	characteristic
13	C₁₁×#492	—	2	1	no	—
14	C₁₁×#423	—	2	1	no	—
15	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
17	C₁₁×C₂²⋊C₁₆	—	2	1	no	—
18	C₁₁×#346	—	2	1	no	—
19	C₁₁×#335	—	2	1	no	—
20	C₁₁×#335	C₂²	1	2	yes	—
21	C₂×C₁₁×#41	—	2	2	no	—
22	C₁₁×#135	—	4	4	no	—
23	C₁₁×#135	—	4	4	no	—
24	C₂×C₁₁×Q₁₆	—	2	1	no	—
25	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
26	C₂×C₁₁×SD₁₆	—	2	2	no	—
27	C₂×C₁₁×SD₁₆	—	2	2	no	—
28	C₂×C₁₁×D₈	—	2	1	no	—
29	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
30	C₂×C₁₁×M₁₆	—	4	1	no	—
31	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
33	C₁₁×C₄⋊Q₈	—	2	1	no	—
34	C₁₁×#127	—	2	1	no	—
35	C₁₁×#124	—	2	2	no	—
36	C₁₁×#121	—	4	1	no	—
37	C₁₁×#121	—	4	1	no	—
38	C₄×D₄×C₁₁	—	4	1	no	—
39	C₄×D₄×C₁₁	—	4	1	no	—
40	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
41	C₂×C₁₁×C₁₆	—	2	2	no	—
42	C₁₁×C₄⋊C₈	—	2	2	no	—
43	C₁₁×C₄⋊C₈	—	4	1	no	—
44	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
46	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
47	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
48	#11966	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₁₁×#41	—	4	4	no	—
50	C₁₁×#41	—	4	4	no	—
51	C₂×Q₈×C₁₁	—	2	2	no	—
52	C₂×D₄×C₁₁	—	2	2	no	—
53	C₂×D₄×C₁₁	—	4	2	no	—
54	C₂×D₄×C₁₁	—	4	1	no	—
55	C₂×D₄×C₁₁	—	4	1	no	—
56	C₂²×C₄×C₁₁	—	4	2	no	—
57	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
59	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
60	C₁₁×Q₁₆	—	4	2	no	—
61	C₁₁×Q₁₆	—	4	2	no	—
62	C₁₁×SD₁₆	—	4	4	no	—
63	C₁₁×SD₁₆	—	4	4	no	—
64	C₁₁×D₈	—	4	2	no	—
65	C₁₁×D₈	—	4	2	no	—
66	C₁₁×M₁₆	—	8	2	no	—
67	C₂×C₈×C₁₁	—	2	2	no	—
68	C₂×C₈×C₁₁	—	2	2	no	—
69	C₂×C₈×C₁₁	—	4	2	no	—
70	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
74	C₁₁×C₄⋊C₄	—	4	1	no	—
75	C₁₁×C₄⋊C₄	—	4	1	no	—
76	C₁₁×C₂²⋊C₄	—	4	2	no	—
77	C₁₁×C₂²⋊C₄	—	4	2	no	—
78	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
79	C₄²×C₁₁	D₈	1	1	yes	characteristic
80	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
81	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
82	C₁₁×C₁₆	—	4	2	no	—
83	#3147	C₂×C₁₁	1	1	yes	characteristic
84	#2163	C₂×C₁₁	1	1	yes	characteristic, complemented
85	#1567	C₂×C₁₁	1	1	yes	characteristic, complemented
86	#1362	C₂×C₁₁	1	2	yes	complemented
87	#1361	C₂×C₁₁	1	2	yes	complemented
88	C₂³×C₁₁	—	4	2	no	—
89	C₂³×C₁₁	#102	1	1	yes	characteristic
90	Q₈×C₁₁	—	4	2	no	—
91	Q₈×C₁₁	—	4	2	no	—
92	D₄×C₁₁	—	4	2	no	—
93	D₄×C₁₁	—	4	2	no	—
94	D₄×C₁₁	—	8	2	no	—
95	D₄×C₁₁	—	8	4	no	—
96	D₄×C₁₁	—	8	1	no	—
97	D₄×C₁₁	—	8	1	no	—
98	C₂×C₄×C₁₁	—	2	1	no	—
99	C₂×C₄×C₁₁	—	2	1	no	—
100	C₂×C₄×C₁₁	—	2	1	no	—
101	C₂×C₄×C₁₁	—	2	1	no	—
102	C₂×C₄×C₁₁	—	4	1	no	—
103	C₂×C₄×C₁₁	—	4	2	no	—
104	C₂×C₄×C₁₁	—	8	4	no	—
105	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
106	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
107	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
108	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
110	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
111	C₈×C₁₁	—	2	1	no	—
112	C₈×C₁₁	—	2	1	no	—
113	C₈×C₁₁	—	8	2	no	—
114	C₈×C₁₁	#100	1	2	yes	—
115	C₈×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
116	C₂×#135	—	2	1	no	—
117	C₂×#135	C₄×C₁₁	1	2	yes	—
118	#532	—	2	1	no	—
119	#495	—	2	1	no	—
120	#495	C₄×C₁₁	1	2	yes	—
121	#494	C₂²×C₁₁	1	1	yes	characteristic
122	#493	C₂²×C₁₁	1	1	yes	characteristic
123	#492	—	2	1	no	—
124	#423	—	2	1	no	—
125	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
126	C₄⋊C₁₆	C₂²×C₁₁	1	2	yes	—
127	C₂²⋊C₁₆	—	2	1	no	—
128	#346	—	2	1	no	—
129	#335	—	2	1	no	—
130	#335	C₂²×C₁₁	1	2	yes	—
131	C₂²×C₁₁	—	2	1	no	—
132	C₂²×C₁₁	—	2	1	no	—
133	C₂²×C₁₁	—	2	1	no	—
134	C₂²×C₁₁	—	8	2	no	—
135	C₂²×C₁₁	—	8	2	no	—
136	C₂²×C₁₁	—	8	2	no	—
137	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
138	C₄×C₁₁	—	2	1	no	—
139	C₄×C₁₁	—	2	1	no	—
140	C₄×C₁₁	—	2	1	no	—
141	C₄×C₁₁	—	2	1	no	—
142	C₄×C₁₁	—	8	2	no	—
143	C₄×C₁₁	C₂×#100	1	1	yes	characteristic
144	C₄×C₁₁	#418	1	1	yes	characteristic
145	C₄×C₁₁	#509	1	1	yes	characteristic
146	C₄×C₁₁	#510	1	1	yes	characteristic
147	C₂×#41	—	2	2	no	—
148	#135	—	4	4	no	—
149	#135	—	4	4	no	—
150	C₂×Q₁₆	—	2	1	no	—
151	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
152	C₂×SD₁₆	—	2	2	no	—
153	C₂×SD₁₆	—	2	2	no	—
154	C₂×D₈	—	2	1	no	—
155	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
156	C₂×M₁₆	—	4	1	no	—
157	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
158	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
159	C₄⋊Q₈	—	2	1	no	—
160	#127	—	2	1	no	—
161	#124	—	2	2	no	—
162	#121	—	4	1	no	—
163	#121	—	4	1	no	—
164	C₄×D₄	—	4	1	no	—
165	C₄×D₄	—	4	1	no	—
166	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
167	C₂×C₁₆	—	2	2	no	—
168	C₄⋊C₈	—	2	2	no	—
169	C₄⋊C₈	—	4	1	no	—
170	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
171	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
172	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
173	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
174	C₂×C₁₁	—	4	1	no	—
175	C₂×C₁₁	—	16	2	no	—
176	C₂×C₁₁	#1545	1	1	yes	characteristic
177	C₂×C₁₁	#2139	1	1	yes	characteristic
178	C₂×C₁₁	#2148	1	1	yes	characteristic
179	#41	—	4	4	no	—
180	#41	—	4	4	no	—
181	C₂×Q₈	—	2	2	no	—
182	C₂×D₄	—	2	2	no	—
183	C₂×D₄	—	4	2	no	—
184	C₂×D₄	—	4	1	no	—
185	C₂×D₄	—	4	1	no	—
186	C₂²×C₄	—	4	2	no	—
187	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
188	C₂²×C₄	C₁₁×D₈	1	1	yes	characteristic
189	C₂²×C₄	C₁₁×SD₁₆	1	1	yes	characteristic
190	Q₁₆	—	4	2	no	—
191	Q₁₆	—	4	2	no	—
192	SD₁₆	—	4	4	no	—
193	SD₁₆	—	4	4	no	—
194	D₈	—	4	2	no	—
195	D₈	—	4	2	no	—
196	M₁₆	—	8	2	no	—
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	2	2	no	—
199	C₂×C₈	—	4	2	no	—
200	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
202	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
203	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
204	C₄⋊C₄	—	4	1	no	—
205	C₄⋊C₄	—	4	1	no	—
206	C₂²⋊C₄	—	4	2	no	—
207	C₂²⋊C₄	—	4	2	no	—
208	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
209	C₄²	C₁₁×D₈	1	1	yes	characteristic
210	C₄²	C₁₁×SD₁₆	1	1	yes	characteristic
211	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
212	C₁₆	—	4	2	no	—
213	C₁₁	#11966	1	1	yes	characteristic, direct product factor, Sylow
214	C₂³	—	4	2	no	—
215	C₂³	C₁₁×#102	1	1	yes	characteristic
216	Q₈	—	4	2	no	—
217	Q₈	—	4	2	no	—
218	D₄	—	4	2	no	—
219	D₄	—	4	2	no	—
220	D₄	—	8	2	no	—
221	D₄	—	8	4	no	—
222	D₄	—	8	1	no	—
223	D₄	—	8	1	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	8	4	no	—
231	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
232	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
233	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
234	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
236	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
237	C₈	—	2	1	no	—
238	C₈	—	2	1	no	—
239	C₈	—	8	2	no	—
240	C₈	C₁₁×#100	1	2	yes	—
241	C₈	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
242	C₂²	—	2	1	no	—
243	C₂²	—	2	1	no	—
244	C₂²	—	2	1	no	—
245	C₂²	—	8	2	no	—
246	C₂²	—	8	2	no	—
247	C₂²	—	8	2	no	—
248	C₂²	C₂×C₁₁×#102	1	1	yes	characteristic
249	C₄	—	2	1	no	—
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	2	1	no	—
253	C₄	—	8	2	no	—
254	C₄	C₂×C₁₁×#100	1	1	yes	characteristic
255	C₄	C₁₁×#418	1	1	yes	characteristic
256	C₄	C₁₁×#509	1	1	yes	characteristic
257	C₄	C₁₁×#510	1	1	yes	characteristic
258	C₂	—	4	1	no	—
259	C₂	—	16	2	no	—
260	C₂	C₁₁×#1545	1	1	yes	characteristic
261	C₂	C₁₁×#2139	1	1	yes	characteristic
262	C₂	C₁₁×#2148	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₁₁×#3147	C₂
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2163	C₂	semidirect
3. C₁₁×#1567	C₂	semidirect
4. C₁₁×#1362	C₂	semidirect
5. C₁₁×#1361	C₂	semidirect
48. #11966	C₁₁	direct (N × H)
84. #2163	C₂×C₁₁	semidirect
85. #1567	C₂×C₁₁	semidirect
86. #1362	C₂×C₁₁	semidirect
87. #1361	C₂×C₁₁	semidirect
213. C₁₁	#11966	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×#3147	2
C₁₁×#2163	2
C₁₁×#1567	2
C₁₁×#1362	2
C₁₁×#1361	2
#11966	11

Subgroups — C11×#11966 #14589159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11966 #14589159