Subgroups — C₁₁×#11963 #14589156

Order 2816.

396 conjugacy classes of subgroups.

The subgroup lattice has 256 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×#2162	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#1568	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×#432	—	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	C₄×C₁₁×C₁₆	—	2	1	no	—
19	C₁₁×#335	C₂²	1	2	yes	—
20	C₁₁×#334	—	2	1	no	—
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	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
32	C₁₁×C₄⋊Q₈	—	2	1	no	—
33	C₁₁×#127	—	2	1	no	—
34	C₁₁×#124	—	2	2	no	—
35	C₁₁×#121	—	4	1	no	—
36	C₁₁×#121	—	4	1	no	—
37	C₄×D₄×C₁₁	—	4	1	no	—
38	C₄×D₄×C₁₁	—	4	1	no	—
39	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
40	C₂×C₁₁×C₁₆	—	2	2	no	—
41	C₁₁×C₄⋊C₈	—	2	2	no	—
42	C₁₁×C₂²⋊C₈	—	4	1	no	—
43	C₁₁×#97	—	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	#11963	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	C₂×C₈×C₁₁	—	2	2	no	—
67	C₂×C₈×C₁₁	—	2	2	no	—
68	C₂×C₈×C₁₁	—	4	2	no	—
69	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
73	C₁₁×C₄⋊C₄	—	4	1	no	—
74	C₁₁×C₄⋊C₄	—	4	1	no	—
75	C₁₁×C₂²⋊C₄	—	4	2	no	—
76	C₁₁×C₂²⋊C₄	—	4	2	no	—
77	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
78	C₄²×C₁₁	D₈	1	1	yes	characteristic
79	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
80	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
81	C₁₁×C₁₆	—	4	2	no	—
82	#3147	C₂×C₁₁	1	1	yes	characteristic
83	#2162	C₂×C₁₁	1	1	yes	characteristic, complemented
84	#1568	C₂×C₁₁	1	1	yes	characteristic, complemented
85	#1362	C₂×C₁₁	1	2	yes	complemented
86	#1361	C₂×C₁₁	1	2	yes	complemented
87	C₂³×C₁₁	—	4	2	no	—
88	C₂³×C₁₁	#102	1	1	yes	characteristic
89	Q₈×C₁₁	—	4	2	no	—
90	Q₈×C₁₁	—	4	2	no	—
91	D₄×C₁₁	—	4	2	no	—
92	D₄×C₁₁	—	4	2	no	—
93	D₄×C₁₁	—	8	2	no	—
94	D₄×C₁₁	—	8	4	no	—
95	D₄×C₁₁	—	8	2	no	—
96	C₂×C₄×C₁₁	—	2	1	no	—
97	C₂×C₄×C₁₁	—	2	1	no	—
98	C₂×C₄×C₁₁	—	2	2	no	—
99	C₂×C₄×C₁₁	—	4	1	no	—
100	C₂×C₄×C₁₁	—	4	2	no	—
101	C₂×C₄×C₁₁	—	8	4	no	—
102	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
103	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
104	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
105	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
107	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
108	C₈×C₁₁	—	2	1	no	—
109	C₈×C₁₁	—	2	1	no	—
110	C₈×C₁₁	—	8	2	no	—
111	C₈×C₁₁	#100	1	2	yes	—
112	C₈×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
113	C₂×#135	—	2	1	no	—
114	C₂×#135	C₄×C₁₁	1	2	yes	—
115	#532	—	2	1	no	—
116	#495	—	2	1	no	—
117	#495	C₄×C₁₁	1	2	yes	—
118	#494	C₂²×C₁₁	1	1	yes	characteristic
119	#493	C₂²×C₁₁	1	1	yes	characteristic
120	#492	—	2	1	no	—
121	#432	—	2	1	no	—
122	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
123	C₄⋊C₁₆	C₂²×C₁₁	1	2	yes	—
124	C₂²⋊C₁₆	—	2	1	no	—
125	C₄×C₁₆	—	2	1	no	—
126	#335	C₂²×C₁₁	1	2	yes	—
127	#334	—	2	1	no	—
128	C₂²×C₁₁	—	2	1	no	—
129	C₂²×C₁₁	—	2	1	no	—
130	C₂²×C₁₁	—	2	1	no	—
131	C₂²×C₁₁	—	8	2	no	—
132	C₂²×C₁₁	—	8	2	no	—
133	C₂²×C₁₁	—	8	2	no	—
134	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
135	C₄×C₁₁	—	2	1	no	—
136	C₄×C₁₁	—	2	1	no	—
137	C₄×C₁₁	—	2	1	no	—
138	C₄×C₁₁	—	2	1	no	—
139	C₄×C₁₁	—	8	2	no	—
140	C₄×C₁₁	C₂×#100	1	1	yes	characteristic
141	C₄×C₁₁	#418	1	1	yes	characteristic
142	C₄×C₁₁	#508	1	2	yes	—
143	C₂×#41	—	2	2	no	—
144	#135	—	4	4	no	—
145	#135	—	4	4	no	—
146	C₂×Q₁₆	—	2	1	no	—
147	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
148	C₂×SD₁₆	—	2	2	no	—
149	C₂×SD₁₆	—	2	2	no	—
150	C₂×D₈	—	2	1	no	—
151	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
152	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
153	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
154	C₄⋊Q₈	—	2	1	no	—
155	#127	—	2	1	no	—
156	#124	—	2	2	no	—
157	#121	—	4	1	no	—
158	#121	—	4	1	no	—
159	C₄×D₄	—	4	1	no	—
160	C₄×D₄	—	4	1	no	—
161	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
162	C₂×C₁₆	—	2	2	no	—
163	C₄⋊C₈	—	2	2	no	—
164	C₂²⋊C₈	—	4	1	no	—
165	#97	—	4	1	no	—
166	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
167	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
168	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
169	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
170	C₂×C₁₁	—	4	1	no	—
171	C₂×C₁₁	—	16	2	no	—
172	C₂×C₁₁	#1545	1	1	yes	characteristic
173	C₂×C₁₁	#2138	1	1	yes	characteristic
174	C₂×C₁₁	#2148	1	1	yes	characteristic
175	#41	—	4	4	no	—
176	#41	—	4	4	no	—
177	C₂×Q₈	—	2	2	no	—
178	C₂×D₄	—	2	2	no	—
179	C₂×D₄	—	4	2	no	—
180	C₂×D₄	—	4	1	no	—
181	C₂×D₄	—	4	1	no	—
182	C₂²×C₄	—	4	2	no	—
183	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
184	C₂²×C₄	C₁₁×D₈	1	1	yes	characteristic
185	C₂²×C₄	C₁₁×SD₁₆	1	1	yes	characteristic
186	Q₁₆	—	4	2	no	—
187	Q₁₆	—	4	2	no	—
188	SD₁₆	—	4	4	no	—
189	SD₁₆	—	4	4	no	—
190	D₈	—	4	2	no	—
191	D₈	—	4	2	no	—
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	2	2	no	—
194	C₂×C₈	—	4	2	no	—
195	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
198	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
199	C₄⋊C₄	—	4	1	no	—
200	C₄⋊C₄	—	4	1	no	—
201	C₂²⋊C₄	—	4	2	no	—
202	C₂²⋊C₄	—	4	2	no	—
203	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
204	C₄²	C₁₁×D₈	1	1	yes	characteristic
205	C₄²	C₁₁×SD₁₆	1	1	yes	characteristic
206	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
207	C₁₆	—	4	2	no	—
208	C₁₁	#11963	1	1	yes	characteristic, direct product factor, Sylow
209	C₂³	—	4	2	no	—
210	C₂³	C₁₁×#102	1	1	yes	characteristic
211	Q₈	—	4	2	no	—
212	Q₈	—	4	2	no	—
213	D₄	—	4	2	no	—
214	D₄	—	4	2	no	—
215	D₄	—	8	2	no	—
216	D₄	—	8	4	no	—
217	D₄	—	8	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	4	1	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	8	4	no	—
224	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
225	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
226	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
227	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
229	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
230	C₈	—	2	1	no	—
231	C₈	—	2	1	no	—
232	C₈	—	8	2	no	—
233	C₈	C₁₁×#100	1	2	yes	—
234	C₈	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
235	C₂²	—	2	1	no	—
236	C₂²	—	2	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	8	2	no	—
239	C₂²	—	8	2	no	—
240	C₂²	—	8	2	no	—
241	C₂²	C₂×C₁₁×#102	1	1	yes	characteristic
242	C₄	—	2	1	no	—
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	2	1	no	—
246	C₄	—	8	2	no	—
247	C₄	C₂×C₁₁×#100	1	1	yes	characteristic
248	C₄	C₁₁×#418	1	1	yes	characteristic
249	C₄	C₁₁×#508	1	2	yes	—
250	C₂	—	4	1	no	—
251	C₂	—	16	2	no	—
252	C₂	C₁₁×#1545	1	1	yes	characteristic
253	C₂	C₁₁×#2138	1	1	yes	characteristic
254	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×#2162	C₂	semidirect
3. C₁₁×#1568	C₂	semidirect
4. C₁₁×#1362	C₂	semidirect
5. C₁₁×#1361	C₂	semidirect
48. #11963	C₁₁	direct (N × H)
83. #2162	C₂×C₁₁	semidirect
84. #1568	C₂×C₁₁	semidirect
85. #1362	C₂×C₁₁	semidirect
86. #1361	C₂×C₁₁	semidirect
208. C₁₁	#11963	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×#2162	2
C₁₁×#1568	2
C₁₁×#1362	2
C₁₁×#1361	2
#11963	11

Subgroups — C11×#11963 #14589156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11963 #14589156