Subgroups — C₁₁×#19639 #14596832

Order 2816.

794 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3227	C₂	1	2	yes	maximal, complemented
2	C₁₁×#3169	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#494	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#3141	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1720	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1709	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, complemented
9	C₂²×C₁₁×Q₁₆	—	2	2	no	—
10	C₁₁×#532	C₂²	1	2	yes	—
11	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
12	C₁₁×#500	C₂²	1	1	yes	characteristic
13	C₁₁×#498	C₂²	1	4	yes	—
14	C₁₁×#494	—	2	2	no	—
15	C₁₁×#494	C₂²	1	2	yes	—
16	C₁₁×#494	C₂²	1	2	yes	—
17	C₁₁×#493	C₂²	1	1	yes	characteristic
18	C₁₁×#489	—	2	4	no	—
19	C₁₁×#487	C₂²	1	4	yes	—
20	C₁₁×#486	C₂²	1	2	yes	—
21	C₁₁×#486	C₂²	1	4	yes	—
22	C₁₁×#486	C₂²	1	4	yes	—
23	C₁₁×#481	—	2	4	no	—
24	C₁₁×#476	—	2	4	no	—
25	C₁₁×#466	—	2	2	no	—
26	C₄×C₁₁×D₈	—	2	2	no	—
27	C₁₁×#431	C₂²	1	1	yes	characteristic
28	C₁₁×#417	—	2	4	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	C₂×C₁₁×#41	—	2	2	no	—
34	C₂²×Q₈×C₁₁	—	2	2	no	—
35	C₂×C₁₁×Q₁₆	—	2	4	no	—
36	C₂×C₁₁×Q₁₆	—	2	4	no	—
37	C₂×C₁₁×Q₁₆	—	4	8	no	—
38	C₂×C₁₁×D₈	—	2	2	no	—
39	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
40	C₂²×C₈×C₁₁	D₄	1	2	yes	—
41	C₁₁×C₄⋊Q₈	—	2	2	no	—
42	C₁₁×C₄⋊Q₈	—	2	2	no	—
43	C₁₁×C₄⋊Q₈	—	2	2	no	—
44	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
45	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
46	C₁₁×#127	C₂³	1	2	yes	—
47	C₁₁×#124	—	2	2	no	—
48	C₁₁×#121	—	2	2	no	—
49	C₁₁×#121	—	2	2	no	—
50	C₄×D₄×C₁₁	—	2	2	no	—
51	C₄×D₄×C₁₁	—	2	2	no	—
52	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
53	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
54	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
55	C₁₁×#107	—	2	2	no	—
56	C₁₁×#106	—	2	8	no	—
57	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
58	C₁₁×#103	—	2	8	no	—
59	C₁₁×#102	—	2	8	no	—
60	C₁₁×#102	—	2	4	no	—
61	C₁₁×#102	—	2	8	no	—
62	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
63	C₁₁×#97	D₄	1	2	yes	—
64	C₄×C₈×C₁₁	D₄	1	2	yes	—
65	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
66	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₄×C₈×C₁₁	C₂³	1	2	yes	—
68	C₄×C₈×C₁₁	C₂³	1	2	yes	—
69	#19639	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₁₁×#41	—	4	8	no	—
71	C₂×Q₈×C₁₁	—	2	2	no	—
72	C₂×Q₈×C₁₁	—	2	4	no	—
73	C₂×Q₈×C₁₁	—	4	8	no	—
74	C₂×Q₈×C₁₁	—	4	2	no	—
75	C₂×D₄×C₁₁	—	2	2	no	—
76	C₂×D₄×C₁₁	—	2	2	no	—
77	C₂×D₄×C₁₁	—	2	2	no	—
78	C₂×D₄×C₁₁	—	4	2	no	—
79	C₂²×C₄×C₁₁	—	4	2	no	—
80	C₂²×C₄×C₁₁	—	4	2	no	—
81	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
84	C₁₁×Q₁₆	—	4	8	no	—
85	C₁₁×Q₁₆	—	4	8	no	—
86	C₁₁×D₈	—	4	4	no	—
87	C₁₁×M₁₆	—	2	4	no	—
88	C₂×C₈×C₁₁	—	2	4	no	—
89	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
90	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
91	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
92	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
93	C₁₁×C₄⋊C₄	—	2	4	no	—
94	C₁₁×C₄⋊C₄	—	2	4	no	—
95	C₁₁×C₄⋊C₄	—	2	2	no	—
96	C₁₁×C₄⋊C₄	—	2	2	no	—
97	C₁₁×C₄⋊C₄	—	4	2	no	—
98	C₁₁×C₄⋊C₄	—	4	2	no	—
99	C₁₁×C₂²⋊C₄	—	4	2	no	—
100	C₁₁×C₂²⋊C₄	—	4	2	no	—
101	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
105	#3227	C₂×C₁₁	1	2	yes	complemented
106	#3169	C₂×C₁₁	1	1	yes	characteristic
107	C₂×#494	C₂×C₁₁	1	1	yes	characteristic, complemented
108	#3141	C₂×C₁₁	1	2	yes	complemented
109	#1720	C₂×C₁₁	1	4	yes	complemented
110	#1709	C₂×C₁₁	1	2	yes	complemented
111	#1707	C₂×C₁₁	1	2	yes	complemented
112	C₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
113	C₂³×C₁₁	—	4	2	no	—
114	C₂³×C₁₁	#127	1	1	yes	characteristic
115	Q₈×C₁₁	—	4	4	no	—
116	Q₈×C₁₁	—	4	8	no	—
117	Q₈×C₁₁	—	8	4	no	—
118	D₄×C₁₁	—	4	4	no	—
119	D₄×C₁₁	—	4	4	no	—
120	D₄×C₁₁	—	4	4	no	—
121	D₄×C₁₁	—	8	4	no	—
122	C₂×C₄×C₁₁	—	2	2	no	—
123	C₂×C₄×C₁₁	—	2	2	no	—
124	C₂×C₄×C₁₁	—	4	2	no	—
125	C₂×C₄×C₁₁	—	4	4	no	—
126	C₂×C₄×C₁₁	—	8	4	no	—
127	C₂×C₄×C₁₁	—	8	4	no	—
128	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
129	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
130	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
131	C₂×C₄×C₁₁	#135	1	4	yes	—
132	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
133	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
135	C₈×C₁₁	—	2	4	no	—
136	C₈×C₁₁	—	2	2	no	—
137	C₈×C₁₁	—	2	4	no	—
138	C₈×C₁₁	AGL(1,ℤ/8)	1	4	yes	—
139	C₂²×Q₁₆	—	2	2	no	—
140	#532	C₂²×C₁₁	1	2	yes	—
141	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
142	#500	C₂²×C₁₁	1	1	yes	characteristic
143	#498	C₂²×C₁₁	1	4	yes	—
144	#494	—	2	2	no	—
145	#494	C₂²×C₁₁	1	2	yes	—
146	#494	C₂²×C₁₁	1	2	yes	—
147	#493	C₂²×C₁₁	1	1	yes	characteristic
148	#489	—	2	4	no	—
149	#487	C₂²×C₁₁	1	4	yes	—
150	#486	C₂²×C₁₁	1	4	yes	—
151	#486	C₂²×C₁₁	1	2	yes	—
152	#486	C₂²×C₁₁	1	4	yes	—
153	#481	—	2	4	no	—
154	#476	—	2	4	no	—
155	#466	—	2	2	no	—
156	C₄×D₈	—	2	2	no	—
157	#431	C₂²×C₁₁	1	1	yes	characteristic
158	#417	—	2	4	no	—
159	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
160	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
161	#322	C₂²×C₁₁	1	2	yes	—
162	C₈²	C₂²×C₁₁	1	2	yes	—
163	C₂²×C₁₁	—	2	1	no	—
164	C₂²×C₁₁	—	2	1	no	—
165	C₂²×C₁₁	—	8	2	no	—
166	C₂²×C₁₁	—	8	2	no	—
167	C₂²×C₁₁	—	8	2	no	—
168	C₂²×C₁₁	#495	1	2	yes	—
169	C₂²×C₁₁	C₂×#127	1	1	yes	characteristic
170	C₄×C₁₁	—	2	1	no	—
171	C₄×C₁₁	—	2	1	no	—
172	C₄×C₁₁	—	8	2	no	—
173	C₄×C₁₁	—	8	4	no	—
174	C₄×C₁₁	#495	1	2	yes	—
175	C₄×C₁₁	C₂×#135	1	2	yes	—
176	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
177	C₄×C₁₁	#578	1	2	yes	—
178	C₂×#41	—	2	2	no	—
179	C₂²×Q₈	—	2	2	no	—
180	C₂×Q₁₆	—	2	4	no	—
181	C₂×Q₁₆	—	2	4	no	—
182	C₂×Q₁₆	—	4	8	no	—
183	C₂×D₈	—	2	2	no	—
184	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
185	C₂²×C₈	D₄×C₁₁	1	2	yes	—
186	C₄⋊Q₈	—	2	2	no	—
187	C₄⋊Q₈	—	2	2	no	—
188	C₄⋊Q₈	—	2	2	no	—
189	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
190	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
191	#127	C₂³×C₁₁	1	2	yes	—
192	#124	—	2	2	no	—
193	#121	—	2	2	no	—
194	#121	—	2	2	no	—
195	C₄×D₄	—	2	2	no	—
196	C₄×D₄	—	2	2	no	—
197	C₂×C₄⋊C₄	—	2	2	no	—
198	C₂×C₄⋊C₄	—	2	2	no	—
199	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
200	#107	—	2	2	no	—
201	#106	—	2	8	no	—
202	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
203	#103	—	2	8	no	—
204	#102	—	2	8	no	—
205	#102	—	2	4	no	—
206	#102	—	2	8	no	—
207	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
208	#97	D₄×C₁₁	1	2	yes	—
209	C₄×C₈	D₄×C₁₁	1	2	yes	—
210	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
211	C₄×C₈	C₂³×C₁₁	1	2	yes	—
212	C₄×C₈	C₂³×C₁₁	1	2	yes	—
213	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
214	C₂×C₁₁	—	2	2	no	—
215	C₂×C₁₁	—	16	2	no	—
216	C₂×C₁₁	C₂×#495	1	1	yes	characteristic
217	C₂×C₁₁	#3151	1	1	yes	characteristic
218	C₂×C₁₁	#3156	1	1	yes	characteristic
219	#41	—	4	8	no	—
220	C₂×Q₈	—	2	2	no	—
221	C₂×Q₈	—	2	4	no	—
222	C₂×Q₈	—	4	8	no	—
223	C₂×Q₈	—	4	2	no	—
224	C₂×D₄	—	2	2	no	—
225	C₂×D₄	—	2	2	no	—
226	C₂×D₄	—	2	2	no	—
227	C₂×D₄	—	4	2	no	—
228	C₂²×C₄	—	4	2	no	—
229	C₂²×C₄	—	4	2	no	—
230	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
231	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
232	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
233	Q₁₆	—	4	8	no	—
234	Q₁₆	—	4	8	no	—
235	D₈	—	4	4	no	—
236	M₁₆	—	2	4	no	—
237	C₂×C₈	—	2	4	no	—
238	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
239	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
240	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
241	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
242	C₄⋊C₄	—	2	4	no	—
243	C₄⋊C₄	—	2	4	no	—
244	C₄⋊C₄	—	2	2	no	—
245	C₄⋊C₄	—	2	2	no	—
246	C₄⋊C₄	—	4	2	no	—
247	C₄⋊C₄	—	4	2	no	—
248	C₂²⋊C₄	—	4	2	no	—
249	C₂²⋊C₄	—	4	2	no	—
250	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
251	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
252	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
253	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
254	C₁₁	#19639	1	1	yes	characteristic, direct product factor, Sylow
255	C₂³	—	4	2	no	—
256	C₂³	C₁₁×#127	1	1	yes	characteristic
257	Q₈	—	4	4	no	—
258	Q₈	—	4	8	no	—
259	Q₈	—	8	4	no	—
260	D₄	—	4	4	no	—
261	D₄	—	4	4	no	—
262	D₄	—	4	4	no	—
263	D₄	—	8	4	no	—
264	C₂×C₄	—	2	2	no	—
265	C₂×C₄	—	2	2	no	—
266	C₂×C₄	—	4	2	no	—
267	C₂×C₄	—	4	4	no	—
268	C₂×C₄	—	8	4	no	—
269	C₂×C₄	—	8	4	no	—
270	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
271	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
272	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
273	C₂×C₄	C₁₁×#135	1	4	yes	—
274	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
275	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
276	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
277	C₈	—	2	4	no	—
278	C₈	—	2	2	no	—
279	C₈	—	2	4	no	—
280	C₈	C₁₁×AGL(1,ℤ/8)	1	4	yes	—
281	C₂²	—	2	1	no	—
282	C₂²	—	2	1	no	—
283	C₂²	—	8	2	no	—
284	C₂²	—	8	2	no	—
285	C₂²	—	8	2	no	—
286	C₂²	C₁₁×#495	1	2	yes	—
287	C₂²	C₂×C₁₁×#127	1	1	yes	characteristic
288	C₄	—	2	1	no	—
289	C₄	—	2	1	no	—
290	C₄	—	8	2	no	—
291	C₄	—	8	4	no	—
292	C₄	C₁₁×#495	1	2	yes	—
293	C₄	C₂×C₁₁×#135	1	2	yes	—
294	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	2	yes	—
295	C₄	C₁₁×#578	1	2	yes	—
296	C₂	—	2	2	no	—
297	C₂	—	16	2	no	—
298	C₂	C₂×C₁₁×#495	1	1	yes	characteristic
299	C₂	C₁₁×#3151	1	1	yes	characteristic
300	C₂	C₁₁×#3156	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₁₁×#3169	C₂
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
1. C₁₁×#3227	C₂	semidirect
3. C₂×C₁₁×#494	C₂	semidirect
4. C₁₁×#3141	C₂	semidirect
5. C₁₁×#1720	C₂	semidirect
6. C₁₁×#1709	C₂	semidirect
7. C₁₁×#1707	C₂	semidirect
8. C₈×C₁₁×M₁₆	C₂	semidirect
69. #19639	C₁₁	direct (N × H)
105. #3227	C₂×C₁₁	semidirect
107. C₂×#494	C₂×C₁₁	semidirect
108. #3141	C₂×C₁₁	semidirect
109. #1720	C₂×C₁₁	semidirect
110. #1709	C₂×C₁₁	semidirect
111. #1707	C₂×C₁₁	semidirect
112. C₈×M₁₆	C₂×C₁₁	semidirect
254. C₁₁	#19639	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×#3227	2
C₁₁×#3169	2
C₂×C₁₁×#494	2
C₁₁×#3141	2
C₁₁×#1720	2
C₁₁×#1709	2
C₁₁×#1707	2
C₈×C₁₁×M₁₆	2
#19639	11

Subgroups — C11×#19639 #14596832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19639 #14596832