Subgroups — C₁₁×#10264 #14587457

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#461	C₂	1	2	yes	maximal
3	C₁₁×#1954	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×#332	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1277	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₁₁×SD₁₆	—	2	2	no	—
7	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
9	C₁₁×#500	—	2	4	no	—
10	C₁₁×#461	—	2	4	no	—
11	C₁₁×#461	—	2	4	no	—
12	C₂×C₁₁×#107	—	2	2	no	—
13	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₁×#103	—	2	2	no	—
16	C₂×C₁₁×C₂²⋊C₈	—	2	2	no	—
17	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₁₁×#332	—	2	4	no	—
19	C₂²×Q₈×C₁₁	—	2	2	no	—
20	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₁	—	2	1	no	—
22	C₂×C₁₁×SD₁₆	—	2	8	no	—
23	C₂×C₁₁×SD₁₆	—	4	4	no	—
24	C₂×C₁₁×SD₁₆	—	4	4	no	—
25	C₂²×C₈×C₁₁	—	2	2	no	—
26	C₂²×C₈×C₁₁	—	2	1	no	—
27	C₂²×C₈×C₁₁	D₄	1	2	yes	—
28	C₁₁×C₄⋊Q₈	—	2	2	no	—
29	C₁₁×C₄⋊Q₈	—	2	2	no	—
30	C₁₁×C₄⋊Q₈	—	2	2	no	—
31	C₁₁×C₄⋊Q₈	D₄	1	4	yes	—
32	C₄×D₄×C₁₁	—	2	2	no	—
33	C₄×D₄×C₁₁	—	2	2	no	—
34	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
35	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
36	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
37	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
38	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
39	C₁₁×#107	—	2	8	no	—
40	C₁₁×C₄⋊C₈	—	2	2	no	—
41	C₁₁×C₄⋊C₈	—	2	2	no	—
42	C₁₁×C₄⋊C₈	D₄	1	4	yes	—
43	C₁₁×#103	—	2	8	no	—
44	C₁₁×C₂²⋊C₈	—	4	4	no	—
45	C₄×C₈×C₁₁	—	2	2	no	—
46	#10264	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂⁴×C₁₁	—	2	1	no	—
48	C₂×Q₈×C₁₁	—	2	4	no	—
49	C₂×Q₈×C₁₁	—	4	2	no	—
50	C₂×Q₈×C₁₁	—	4	2	no	—
51	C₂×Q₈×C₁₁	—	4	2	no	—
52	C₂×Q₈×C₁₁	—	4	2	no	—
53	C₂×Q₈×C₁₁	—	4	2	no	—
54	C₂×D₄×C₁₁	—	2	2	no	—
55	C₂×D₄×C₁₁	—	2	1	no	—
56	C₂×D₄×C₁₁	—	2	2	no	—
57	C₂×D₄×C₁₁	D₈	1	2	yes	—
58	C₂²×C₄×C₁₁	—	2	1	no	—
59	C₂²×C₄×C₁₁	—	4	2	no	—
60	C₂²×C₄×C₁₁	—	4	1	no	—
61	C₂²×C₄×C₁₁	—	4	1	no	—
62	C₂²×C₄×C₁₁	—	4	2	no	—
63	C₂²×C₄×C₁₁	—	4	2	no	—
64	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
67	C₁₁×SD₁₆	—	4	16	no	—
68	C₂×C₈×C₁₁	—	2	2	no	—
69	C₂×C₈×C₁₁	—	2	4	no	—
70	C₂×C₈×C₁₁	—	2	2	no	—
71	C₂×C₈×C₁₁	—	4	1	no	—
72	C₂×C₈×C₁₁	—	4	2	no	—
73	C₂×C₈×C₁₁	—	4	2	no	—
74	C₂×C₈×C₁₁	—	4	2	no	—
75	C₂×C₈×C₁₁	SD₁₆	1	4	yes	complemented
76	C₁₁×C₄⋊C₄	—	2	2	no	—
77	C₁₁×C₄⋊C₄	—	2	4	no	—
78	C₁₁×C₄⋊C₄	—	2	4	no	—
79	C₁₁×C₄⋊C₄	—	4	2	no	—
80	C₁₁×C₄⋊C₄	—	4	2	no	—
81	C₁₁×C₂²⋊C₄	—	4	2	no	—
82	C₄²×C₁₁	C₂×D₄	1	2	yes	—
83	C₄²×C₁₁	C₂×D₄	1	2	yes	—
84	C₂×#500	C₂×C₁₁	1	1	yes	characteristic, complemented
85	C₂×#461	C₂×C₁₁	1	2	yes	—
86	#1954	C₂×C₁₁	1	1	yes	characteristic
87	C₂×#332	C₂×C₁₁	1	2	yes	complemented
88	#1277	C₂×C₁₁	1	1	yes	characteristic, complemented
89	C₂³×C₁₁	—	2	2	no	—
90	C₂³×C₁₁	—	4	1	no	—
91	C₂³×C₁₁	—	4	2	no	—
92	C₂³×C₁₁	—	4	1	no	—
93	C₂³×C₁₁	—	4	2	no	—
94	C₂³×C₁₁	#121	1	1	yes	characteristic
95	Q₈×C₁₁	—	4	4	no	—
96	Q₈×C₁₁	—	4	4	no	—
97	Q₈×C₁₁	—	8	2	no	—
98	Q₈×C₁₁	—	8	2	no	—
99	D₄×C₁₁	—	2	4	no	—
100	D₄×C₁₁	—	4	2	no	—
101	C₂×C₄×C₁₁	—	2	2	no	—
102	C₂×C₄×C₁₁	—	4	1	no	—
103	C₂×C₄×C₁₁	—	4	4	no	—
104	C₂×C₄×C₁₁	—	4	2	no	—
105	C₂×C₄×C₁₁	—	8	2	no	—
106	C₂×C₄×C₁₁	—	8	2	no	—
107	C₂×C₄×C₁₁	—	8	2	no	—
108	C₂×C₄×C₁₁	—	8	1	no	—
109	C₂×C₄×C₁₁	—	8	1	no	—
110	C₂×C₄×C₁₁	#120	1	2	yes	—
111	C₂×C₄×C₁₁	#120	1	1	yes	characteristic
112	C₂×C₄×C₁₁	#121	1	2	yes	—
113	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
114	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
115	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
116	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
117	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
118	C₂×C₄×C₁₁	#137	1	2	yes	—
119	C₈×C₁₁	—	2	4	no	—
120	C₈×C₁₁	—	4	4	no	—
121	C₈×C₁₁	—	8	1	no	—
122	C₂²×SD₁₆	—	2	2	no	—
123	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
124	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
125	#500	—	2	4	no	—
126	#461	—	2	4	no	—
127	#461	—	2	4	no	—
128	C₂×#107	—	2	2	no	—
129	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
130	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
131	C₂×#103	—	2	2	no	—
132	C₂×C₂²⋊C₈	—	2	2	no	—
133	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
134	#332	—	2	4	no	—
135	C₂²×C₁₁	—	4	4	no	—
136	C₂²×C₁₁	—	4	2	no	—
137	C₂²×C₁₁	—	8	2	no	—
138	C₂²×C₁₁	—	8	1	no	—
139	C₂²×C₁₁	—	8	1	no	—
140	C₂²×C₁₁	#392	1	1	yes	characteristic
141	C₂²×C₁₁	#461	1	2	yes	—
142	C₂²×C₁₁	#466	1	1	yes	characteristic
143	C₂²×C₁₁	#469	1	1	yes	characteristic
144	C₂²×C₁₁	#473	1	2	yes	—
145	C₄×C₁₁	—	2	2	no	—
146	C₄×C₁₁	—	8	4	no	—
147	C₄×C₁₁	—	8	1	no	—
148	C₄×C₁₁	#447	1	2	yes	—
149	C₄×C₁₁	#448	1	2	yes	—
150	C₄×C₁₁	#449	1	2	yes	—
151	C₄×C₁₁	#492	1	1	yes	characteristic
152	C₄×C₁₁	#497	1	1	yes	characteristic
153	C₂²×Q₈	—	2	2	no	—
154	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
155	C₂³×C₄	—	2	1	no	—
156	C₂×SD₁₆	—	2	8	no	—
157	C₂×SD₁₆	—	4	4	no	—
158	C₂×SD₁₆	—	4	4	no	—
159	C₂²×C₈	—	2	2	no	—
160	C₂²×C₈	—	2	1	no	—
161	C₂²×C₈	D₄×C₁₁	1	2	yes	—
162	C₄⋊Q₈	—	2	2	no	—
163	C₄⋊Q₈	—	2	2	no	—
164	C₄⋊Q₈	—	2	2	no	—
165	C₄⋊Q₈	D₄×C₁₁	1	4	yes	—
166	C₄×D₄	—	2	2	no	—
167	C₄×D₄	—	2	2	no	—
168	C₂×C₄⋊C₄	—	2	2	no	—
169	C₂×C₄⋊C₄	—	2	2	no	—
170	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
171	C₂×C₂²⋊C₄	—	2	1	no	—
172	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
173	#107	—	2	8	no	—
174	C₄⋊C₈	—	2	2	no	—
175	C₄⋊C₈	—	2	2	no	—
176	C₄⋊C₈	D₄×C₁₁	1	4	yes	—
177	#103	—	2	8	no	—
178	C₂²⋊C₈	—	4	4	no	—
179	C₄×C₈	—	2	2	no	—
180	C₂×C₁₁	—	8	2	no	—
181	C₂×C₁₁	#1673	1	2	yes	—
182	C₂×C₁₁	#1693	1	2	yes	—
183	C₂×C₁₁	#1999	1	1	yes	characteristic
184	C₂×C₁₁	#2013	1	1	yes	characteristic
185	C₂×C₁₁	#2020	1	1	yes	characteristic
186	C₂⁴	—	2	1	no	—
187	C₂×Q₈	—	2	4	no	—
188	C₂×Q₈	—	4	2	no	—
189	C₂×Q₈	—	4	2	no	—
190	C₂×Q₈	—	4	2	no	—
191	C₂×Q₈	—	4	2	no	—
192	C₂×Q₈	—	4	2	no	—
193	C₂×D₄	—	2	2	no	—
194	C₂×D₄	—	2	1	no	—
195	C₂×D₄	—	2	2	no	—
196	C₂×D₄	C₁₁×D₈	1	2	yes	—
197	C₂²×C₄	—	2	1	no	—
198	C₂²×C₄	—	4	2	no	—
199	C₂²×C₄	—	4	1	no	—
200	C₂²×C₄	—	4	1	no	—
201	C₂²×C₄	—	4	2	no	—
202	C₂²×C₄	—	4	2	no	—
203	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
204	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
205	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
206	SD₁₆	—	4	16	no	—
207	C₂×C₈	—	2	2	no	—
208	C₂×C₈	—	2	2	no	—
209	C₂×C₈	—	2	4	no	—
210	C₂×C₈	—	4	2	no	—
211	C₂×C₈	—	4	2	no	—
212	C₂×C₈	—	4	1	no	—
213	C₂×C₈	—	4	2	no	—
214	C₂×C₈	C₁₁×SD₁₆	1	4	yes	complemented
215	C₄⋊C₄	—	2	2	no	—
216	C₄⋊C₄	—	2	4	no	—
217	C₄⋊C₄	—	2	4	no	—
218	C₄⋊C₄	—	4	2	no	—
219	C₄⋊C₄	—	4	2	no	—
220	C₂²⋊C₄	—	4	2	no	—
221	C₄²	C₂×D₄×C₁₁	1	2	yes	—
222	C₄²	C₂×D₄×C₁₁	1	2	yes	—
223	C₁₁	#10264	1	1	yes	characteristic, direct product factor, Sylow
224	C₂³	—	2	2	no	—
225	C₂³	—	4	1	no	—
226	C₂³	—	4	2	no	—
227	C₂³	—	4	1	no	—
228	C₂³	—	4	2	no	—
229	C₂³	C₁₁×#121	1	1	yes	characteristic
230	Q₈	—	4	4	no	—
231	Q₈	—	4	4	no	—
232	Q₈	—	8	2	no	—
233	Q₈	—	8	2	no	—
234	D₄	—	2	4	no	—
235	D₄	—	4	2	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	—	4	1	no	—
238	C₂×C₄	—	4	4	no	—
239	C₂×C₄	—	4	2	no	—
240	C₂×C₄	—	8	2	no	—
241	C₂×C₄	—	8	2	no	—
242	C₂×C₄	—	8	1	no	—
243	C₂×C₄	—	8	1	no	—
244	C₂×C₄	—	8	2	no	—
245	C₂×C₄	C₁₁×#120	1	2	yes	—
246	C₂×C₄	C₁₁×#120	1	1	yes	characteristic
247	C₂×C₄	C₁₁×#121	1	2	yes	—
248	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
249	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
250	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
251	C₂×C₄	C₁₁×#135	1	1	yes	characteristic
252	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
253	C₂×C₄	C₁₁×#137	1	2	yes	—
254	C₈	—	2	4	no	—
255	C₈	—	4	4	no	—
256	C₈	—	8	1	no	—
257	C₂²	—	4	4	no	—
258	C₂²	—	4	2	no	—
259	C₂²	—	8	2	no	—
260	C₂²	—	8	1	no	—
261	C₂²	—	8	1	no	—
262	C₂²	C₁₁×#392	1	1	yes	characteristic
263	C₂²	C₁₁×#461	1	2	yes	—
264	C₂²	C₁₁×#466	1	1	yes	characteristic
265	C₂²	C₁₁×#469	1	1	yes	characteristic
266	C₂²	C₁₁×#473	1	2	yes	—
267	C₄	—	2	2	no	—
268	C₄	—	8	4	no	—
269	C₄	—	8	1	no	—
270	C₄	C₁₁×#447	1	2	yes	—
271	C₄	C₁₁×#448	1	2	yes	—
272	C₄	C₁₁×#449	1	2	yes	—
273	C₄	C₁₁×#492	1	1	yes	characteristic
274	C₄	C₁₁×#497	1	1	yes	characteristic
275	C₂	—	8	2	no	—
276	C₂	C₁₁×#1673	1	2	yes	—
277	C₂	C₁₁×#1693	1	2	yes	—
278	C₂	C₁₁×#1999	1	1	yes	characteristic
279	C₂	C₁₁×#2013	1	1	yes	characteristic
280	C₂	C₁₁×#2020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂²×D₄×C₁₁	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#500	C₂	semidirect
4. C₂×C₁₁×#332	C₂	semidirect
5. C₁₁×#1277	C₂	semidirect
46. #10264	C₁₁	direct (N × H)
75. C₂×C₈×C₁₁	SD₁₆	semidirect
84. C₂×#500	C₂×C₁₁	semidirect
87. C₂×#332	C₂×C₁₁	semidirect
88. #1277	C₂×C₁₁	semidirect
214. C₂×C₈	C₁₁×SD₁₆	semidirect
223. C₁₁	#10264	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×#500	2
C₂×C₁₁×#461	2
C₁₁×#1954	2
C₂×C₁₁×#332	2
C₁₁×#1277	2
#10264	11

Subgroups — C11×#10264 #14587457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#10264 #14587457