Subgroups — C₁₁×#19633 #14596826

Order 2816.

710 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	C₁₁×#3209	C₂	1	2	yes	maximal
2	C₁₁×#3170	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#3165	C₂	1	2	yes	maximal
4	C₂×C₁₁×#500	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1723	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1713	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1707	C₂	1	2	yes	maximal, complemented
8	C₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic
9	C₁₁×#533	C₂²	1	2	yes	—
10	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
11	C₁₁×#501	—	2	4	no	—
12	C₁₁×#500	—	2	2	no	—
13	C₁₁×#500	C₂²	1	2	yes	—
14	C₁₁×#500	C₂²	1	2	yes	—
15	C₁₁×#500	C₂²	1	4	yes	—
16	C₁₁×#500	C₂²	1	1	yes	characteristic
17	C₁₁×#498	C₂²	1	4	yes	—
18	C₁₁×#494	C₂²	1	1	yes	characteristic
19	C₁₁×#494	C₂²	1	4	yes	—
20	C₁₁×#487	C₂²	1	2	yes	—
21	C₁₁×#487	C₂²	1	4	yes	—
22	C₁₁×#467	—	2	2	no	—
23	C₁₁×#462	—	2	4	no	—
24	C₁₁×#451	—	2	4	no	—
25	C₄×C₁₁×Q₁₆	—	2	2	no	—
26	C₁₁×#431	C₂²	1	1	yes	characteristic
27	C₁₁×#428	—	2	4	no	—
28	C₂×C₁₁×#107	—	2	2	no	—
29	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
31	C₁₁×#322	C₂²	1	2	yes	—
32	C₈²×C₁₁	C₂²	1	2	yes	—
33	C₂²×Q₈×C₁₁	—	2	2	no	—
34	C₂×C₁₁×Q₁₆	—	2	2	no	—
35	C₂×C₁₁×Q₁₆	—	2	8	no	—
36	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
37	C₂²×C₈×C₁₁	D₄	1	2	yes	—
38	C₁₁×C₄⋊Q₈	—	2	2	no	—
39	C₁₁×C₄⋊Q₈	—	2	2	no	—
40	C₁₁×C₄⋊Q₈	—	2	2	no	—
41	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
42	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
43	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
44	C₁₁×#125	—	2	2	no	—
45	C₁₁×C₂²⋊Q₈	—	2	2	no	—
46	C₁₁×C₂²⋊Q₈	—	2	2	no	—
47	C₄×Q₈×C₁₁	—	2	2	no	—
48	C₄×Q₈×C₁₁	—	2	2	no	—
49	C₁₁×#117	—	2	2	no	—
50	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
51	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
52	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
53	C₁₁×#107	—	2	4	no	—
54	C₁₁×#107	—	2	4	no	—
55	C₁₁×#107	—	2	8	no	—
56	C₁₁×#107	—	2	2	no	—
57	C₁₁×#106	—	2	8	no	—
58	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
59	C₁₁×#103	—	2	4	no	—
60	C₁₁×#103	—	2	8	no	—
61	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
62	C₁₁×#97	D₄	1	2	yes	—
63	C₄×C₈×C₁₁	D₄	1	2	yes	—
64	C₄×C₈×C₁₁	C₂³	1	2	yes	—
65	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
66	C₄×C₈×C₁₁	C₂³	1	2	yes	—
67	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
68	#19633	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₂×Q₈×C₁₁	—	2	2	no	—
70	C₂×Q₈×C₁₁	—	2	4	no	—
71	C₂×Q₈×C₁₁	—	2	2	no	—
72	C₂×Q₈×C₁₁	—	4	2	no	—
73	C₂×Q₈×C₁₁	—	8	4	no	—
74	C₂²×C₄×C₁₁	—	4	2	no	—
75	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₁₁×Q₁₆	—	4	4	no	—
79	C₁₁×Q₁₆	—	8	8	no	—
80	C₁₁×M₁₆	Q₁₆	1	8	yes	complemented
81	C₂×C₈×C₁₁	—	2	4	no	—
82	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
83	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
84	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
85	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
86	C₁₁×C₄⋊C₄	—	2	2	no	—
87	C₁₁×C₄⋊C₄	—	2	2	no	—
88	C₁₁×C₄⋊C₄	—	2	2	no	—
89	C₁₁×C₄⋊C₄	—	2	4	no	—
90	C₁₁×C₄⋊C₄	—	2	4	no	—
91	C₁₁×C₄⋊C₄	—	2	2	no	—
92	C₁₁×C₄⋊C₄	—	4	2	no	—
93	C₁₁×C₄⋊C₄	—	4	2	no	—
94	C₁₁×C₄⋊C₄	—	4	2	no	—
95	C₁₁×C₄⋊C₄	—	4	2	no	—
96	C₁₁×C₂²⋊C₄	—	4	2	no	—
97	C₄²×C₁₁	—	4	2	no	—
98	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
99	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
100	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
101	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
102	#3209	C₂×C₁₁	1	2	yes	—
103	#3170	C₂×C₁₁	1	1	yes	characteristic
104	#3165	C₂×C₁₁	1	2	yes	—
105	C₂×#500	C₂×C₁₁	1	1	yes	characteristic
106	#1723	C₂×C₁₁	1	4	yes	complemented
107	#1713	C₂×C₁₁	1	2	yes	complemented
108	#1707	C₂×C₁₁	1	2	yes	complemented
109	C₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic
110	C₂³×C₁₁	#127	1	1	yes	characteristic
111	Q₈×C₁₁	—	4	4	no	—
112	Q₈×C₁₁	—	4	4	no	—
113	Q₈×C₁₁	—	4	8	no	—
114	Q₈×C₁₁	—	8	4	no	—
115	C₂×C₄×C₁₁	—	2	2	no	—
116	C₂×C₄×C₁₁	—	2	2	no	—
117	C₂×C₄×C₁₁	—	4	2	no	—
118	C₂×C₄×C₁₁	—	4	2	no	—
119	C₂×C₄×C₁₁	—	4	4	no	—
120	C₂×C₄×C₁₁	—	8	4	no	—
121	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
122	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
123	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
124	C₂×C₄×C₁₁	C₂×Q₁₆	1	4	yes	—
125	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
126	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
127	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
128	C₈×C₁₁	—	2	2	no	—
129	C₈×C₁₁	—	2	4	no	—
130	C₈×C₁₁	C₂×Q₁₆	1	8	yes	—
131	C₈×C₁₁	#137	1	4	yes	—
132	#533	C₂²×C₁₁	1	2	yes	—
133	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
134	#501	—	2	4	no	—
135	#500	—	2	2	no	—
136	#500	C₂²×C₁₁	1	2	yes	—
137	#500	C₂²×C₁₁	1	2	yes	—
138	#500	C₂²×C₁₁	1	4	yes	—
139	#500	C₂²×C₁₁	1	1	yes	characteristic
140	#498	C₂²×C₁₁	1	4	yes	—
141	#494	C₂²×C₁₁	1	1	yes	characteristic
142	#494	C₂²×C₁₁	1	4	yes	—
143	#487	C₂²×C₁₁	1	2	yes	—
144	#487	C₂²×C₁₁	1	4	yes	—
145	#467	—	2	2	no	—
146	#462	—	2	4	no	—
147	#451	—	2	4	no	—
148	C₄×Q₁₆	—	2	2	no	—
149	#431	C₂²×C₁₁	1	1	yes	characteristic
150	#428	—	2	4	no	—
151	C₂×#107	—	2	2	no	—
152	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
153	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
154	#322	C₂²×C₁₁	1	2	yes	—
155	C₈²	C₂²×C₁₁	1	2	yes	—
156	C₂²×C₁₁	—	2	1	no	—
157	C₂²×C₁₁	—	2	1	no	—
158	C₂²×C₁₁	#494	1	2	yes	—
159	C₂²×C₁₁	C₂×#127	1	1	yes	characteristic
160	C₄×C₁₁	—	2	1	no	—
161	C₄×C₁₁	—	2	1	no	—
162	C₄×C₁₁	—	8	2	no	—
163	C₄×C₁₁	—	8	4	no	—
164	C₄×C₁₁	—	8	2	no	—
165	C₄×C₁₁	#494	1	2	yes	—
166	C₄×C₁₁	C₂²×Q₁₆	1	2	yes	—
167	C₄×C₁₁	C₂×#137	1	2	yes	—
168	C₄×C₁₁	#576	1	2	yes	—
169	C₂²×Q₈	—	2	2	no	—
170	C₂×Q₁₆	—	2	2	no	—
171	C₂×Q₁₆	—	2	8	no	—
172	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
173	C₂²×C₈	D₄×C₁₁	1	2	yes	—
174	C₄⋊Q₈	—	2	2	no	—
175	C₄⋊Q₈	—	2	2	no	—
176	C₄⋊Q₈	—	2	2	no	—
177	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
178	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
179	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
180	#125	—	2	2	no	—
181	C₂²⋊Q₈	—	2	2	no	—
182	C₂²⋊Q₈	—	2	2	no	—
183	C₄×Q₈	—	2	2	no	—
184	C₄×Q₈	—	2	2	no	—
185	#117	—	2	2	no	—
186	C₂×C₄⋊C₄	—	2	2	no	—
187	C₂×C₄⋊C₄	—	2	2	no	—
188	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
189	#107	—	2	4	no	—
190	#107	—	2	4	no	—
191	#107	—	2	8	no	—
192	#107	—	2	2	no	—
193	#106	—	2	8	no	—
194	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
195	#103	—	2	4	no	—
196	#103	—	2	8	no	—
197	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
198	#97	D₄×C₁₁	1	2	yes	—
199	C₄×C₈	D₄×C₁₁	1	2	yes	—
200	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
201	C₄×C₈	C₂³×C₁₁	1	2	yes	—
202	C₄×C₈	C₂³×C₁₁	1	2	yes	—
203	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
204	C₂×C₁₁	—	2	2	no	—
205	C₂×C₁₁	C₂×#494	1	1	yes	characteristic
206	C₂×C₁₁	#3152	1	1	yes	characteristic
207	C₂×C₁₁	#3155	1	1	yes	characteristic
208	C₂×Q₈	—	2	2	no	—
209	C₂×Q₈	—	2	4	no	—
210	C₂×Q₈	—	2	2	no	—
211	C₂×Q₈	—	4	2	no	—
212	C₂×Q₈	—	8	4	no	—
213	C₂²×C₄	—	4	2	no	—
214	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
215	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
216	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
217	Q₁₆	—	4	4	no	—
218	Q₁₆	—	8	8	no	—
219	M₁₆	C₁₁×Q₁₆	1	8	yes	complemented
220	C₂×C₈	—	2	4	no	—
221	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
222	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
223	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
224	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
225	C₄⋊C₄	—	2	2	no	—
226	C₄⋊C₄	—	2	2	no	—
227	C₄⋊C₄	—	2	2	no	—
228	C₄⋊C₄	—	2	4	no	—
229	C₄⋊C₄	—	2	4	no	—
230	C₄⋊C₄	—	2	2	no	—
231	C₄⋊C₄	—	4	2	no	—
232	C₄⋊C₄	—	4	2	no	—
233	C₄⋊C₄	—	4	2	no	—
234	C₄⋊C₄	—	4	2	no	—
235	C₂²⋊C₄	—	4	2	no	—
236	C₄²	—	4	2	no	—
237	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
238	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
239	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
240	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
241	C₁₁	#19633	1	1	yes	characteristic, direct product factor, Sylow
242	C₂³	C₁₁×#127	1	1	yes	characteristic
243	Q₈	—	4	4	no	—
244	Q₈	—	4	4	no	—
245	Q₈	—	4	8	no	—
246	Q₈	—	8	4	no	—
247	C₂×C₄	—	2	2	no	—
248	C₂×C₄	—	2	2	no	—
249	C₂×C₄	—	4	2	no	—
250	C₂×C₄	—	4	2	no	—
251	C₂×C₄	—	4	4	no	—
252	C₂×C₄	—	8	4	no	—
253	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
254	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
255	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
256	C₂×C₄	C₂×C₁₁×Q₁₆	1	4	yes	—
257	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
258	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
259	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
260	C₈	—	2	2	no	—
261	C₈	—	2	4	no	—
262	C₈	C₂×C₁₁×Q₁₆	1	8	yes	—
263	C₈	C₁₁×#137	1	4	yes	—
264	C₂²	—	2	1	no	—
265	C₂²	—	2	1	no	—
266	C₂²	C₁₁×#494	1	2	yes	—
267	C₂²	C₂×C₁₁×#127	1	1	yes	characteristic
268	C₄	—	2	1	no	—
269	C₄	—	2	1	no	—
270	C₄	—	8	2	no	—
271	C₄	—	8	4	no	—
272	C₄	—	8	2	no	—
273	C₄	C₁₁×#494	1	2	yes	—
274	C₄	C₂²×C₁₁×Q₁₆	1	2	yes	—
275	C₄	C₂×C₁₁×#137	1	2	yes	—
276	C₄	C₁₁×#576	1	2	yes	—
277	C₂	—	2	2	no	—
278	C₂	C₂×C₁₁×#494	1	1	yes	characteristic
279	C₂	C₁₁×#3152	1	1	yes	characteristic
280	C₂	C₁₁×#3155	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₂³×C₁₁	#127
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₁×#1723	C₂	semidirect
6. C₁₁×#1713	C₂	semidirect
7. C₁₁×#1707	C₂	semidirect
68. #19633	C₁₁	direct (N × H)
80. C₁₁×M₁₆	Q₁₆	semidirect
106. #1723	C₂×C₁₁	semidirect
107. #1713	C₂×C₁₁	semidirect
108. #1707	C₂×C₁₁	semidirect
219. M₁₆	C₁₁×Q₁₆	semidirect
241. C₁₁	#19633	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×#3209	2
C₁₁×#3170	2
C₁₁×#3165	2
C₂×C₁₁×#500	2
C₁₁×#1723	2
C₁₁×#1713	2
C₁₁×#1707	2
C₈×C₁₁×M₁₆	2
#19633	11

Subgroups — C11×#19633 #14596826

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19633 #14596826