Subgroups — C₁₁×#19636 #14596829

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3229	C₂	1	2	yes	maximal
2	C₁₁×#3170	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#500	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#3139	C₂	1	2	yes	maximal
5	C₁₁×#1718	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1710	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×#500	—	2	2	no	—
12	C₁₁×#500	C₂²	1	2	yes	—
13	C₁₁×#500	C₂²	1	2	yes	—
14	C₁₁×#500	C₂²	1	1	yes	characteristic
15	C₁₁×#498	C₂²	1	4	yes	—
16	C₁₁×#494	C₂²	1	1	yes	characteristic
17	C₁₁×#491	—	2	4	no	—
18	C₁₁×#487	C₂²	1	2	yes	—
19	C₁₁×#487	C₂²	1	4	yes	—
20	C₁₁×#487	C₂²	1	4	yes	—
21	C₁₁×#487	C₂²	1	4	yes	—
22	C₁₁×#483	—	2	4	no	—
23	C₁₁×#475	—	2	4	no	—
24	C₁₁×#467	—	2	2	no	—
25	C₄×C₁₁×Q₁₆	—	2	2	no	—
26	C₁₁×#431	C₂²	1	1	yes	characteristic
27	C₂×C₁₁×#107	—	2	2	no	—
28	C₁₁×#419	—	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	C₂²×Q₈×C₁₁	—	2	2	no	—
34	C₂×C₁₁×Q₁₆	—	2	2	no	—
35	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
36	C₂²×C₈×C₁₁	D₄	1	2	yes	—
37	C₁₁×C₄⋊Q₈	—	2	2	no	—
38	C₁₁×C₄⋊Q₈	—	2	2	no	—
39	C₁₁×C₄⋊Q₈	—	2	2	no	—
40	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
41	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
42	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
43	C₁₁×#125	—	2	2	no	—
44	C₁₁×C₂²⋊Q₈	—	2	2	no	—
45	C₁₁×C₂²⋊Q₈	—	2	2	no	—
46	C₄×Q₈×C₁₁	—	2	2	no	—
47	C₄×Q₈×C₁₁	—	2	2	no	—
48	C₁₁×#117	—	2	2	no	—
49	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
50	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
51	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
52	C₁₁×#107	—	2	4	no	—
53	C₁₁×#107	—	2	4	no	—
54	C₁₁×#107	—	2	2	no	—
55	C₁₁×#106	—	2	8	no	—
56	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
57	C₁₁×#103	—	2	8	no	—
58	C₁₁×#103	—	2	8	no	—
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	1	yes	characteristic
65	C₄×C₈×C₁₁	C₂³	1	2	yes	—
66	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₄×C₈×C₁₁	C₂³	1	2	yes	—
68	#19636	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	—	4	8	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×M₁₆	—	2	4	no	—
80	C₂×C₈×C₁₁	—	2	4	no	—
81	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
82	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
83	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
84	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
85	C₁₁×C₄⋊C₄	—	2	2	no	—
86	C₁₁×C₄⋊C₄	—	2	2	no	—
87	C₁₁×C₄⋊C₄	—	2	4	no	—
88	C₁₁×C₄⋊C₄	—	2	2	no	—
89	C₁₁×C₄⋊C₄	—	2	2	no	—
90	C₁₁×C₄⋊C₄	—	2	4	no	—
91	C₁₁×C₄⋊C₄	—	4	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×C₂²⋊C₄	—	4	2	no	—
96	C₄²×C₁₁	—	4	2	no	—
97	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
98	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
99	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
100	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
101	#3229	C₂×C₁₁	1	2	yes	—
102	#3170	C₂×C₁₁	1	1	yes	characteristic
103	C₂×#500	C₂×C₁₁	1	1	yes	characteristic
104	#3139	C₂×C₁₁	1	2	yes	—
105	#1718	C₂×C₁₁	1	4	yes	complemented
106	#1710	C₂×C₁₁	1	2	yes	complemented
107	#1707	C₂×C₁₁	1	2	yes	complemented
108	C₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic
109	C₂³×C₁₁	#127	1	1	yes	characteristic
110	Q₈×C₁₁	—	4	8	no	—
111	Q₈×C₁₁	—	4	4	no	—
112	Q₈×C₁₁	—	4	4	no	—
113	Q₈×C₁₁	—	8	4	no	—
114	C₂×C₄×C₁₁	—	2	2	no	—
115	C₂×C₄×C₁₁	—	2	2	no	—
116	C₂×C₄×C₁₁	—	4	2	no	—
117	C₂×C₄×C₁₁	—	4	2	no	—
118	C₂×C₄×C₁₁	—	4	4	no	—
119	C₂×C₄×C₁₁	—	8	4	no	—
120	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
121	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
122	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
123	C₂×C₄×C₁₁	#135	1	4	yes	—
124	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
125	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
126	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
127	C₈×C₁₁	—	2	4	no	—
128	C₈×C₁₁	—	2	2	no	—
129	C₈×C₁₁	—	2	4	no	—
130	C₈×C₁₁	#137	1	4	yes	—
131	#533	C₂²×C₁₁	1	2	yes	—
132	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
133	#500	—	2	2	no	—
134	#500	C₂²×C₁₁	1	2	yes	—
135	#500	C₂²×C₁₁	1	2	yes	—
136	#500	C₂²×C₁₁	1	1	yes	characteristic
137	#498	C₂²×C₁₁	1	4	yes	—
138	#494	C₂²×C₁₁	1	1	yes	characteristic
139	#491	—	2	4	no	—
140	#487	C₂²×C₁₁	1	4	yes	—
141	#487	C₂²×C₁₁	1	4	yes	—
142	#487	C₂²×C₁₁	1	2	yes	—
143	#487	C₂²×C₁₁	1	4	yes	—
144	#483	—	2	4	no	—
145	#475	—	2	4	no	—
146	#467	—	2	2	no	—
147	C₄×Q₁₆	—	2	2	no	—
148	#431	C₂²×C₁₁	1	1	yes	characteristic
149	C₂×#107	—	2	2	no	—
150	#419	—	2	4	no	—
151	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
152	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
153	#322	C₂²×C₁₁	1	2	yes	—
154	C₈²	C₂²×C₁₁	1	2	yes	—
155	C₂²×C₁₁	—	2	1	no	—
156	C₂²×C₁₁	—	2	1	no	—
157	C₂²×C₁₁	#495	1	2	yes	—
158	C₂²×C₁₁	C₂×#127	1	1	yes	characteristic
159	C₄×C₁₁	—	2	1	no	—
160	C₄×C₁₁	—	2	1	no	—
161	C₄×C₁₁	—	8	4	no	—
162	C₄×C₁₁	—	8	2	no	—
163	C₄×C₁₁	—	8	2	no	—
164	C₄×C₁₁	#495	1	2	yes	—
165	C₄×C₁₁	C₂×#135	1	2	yes	—
166	C₄×C₁₁	C₂×#137	1	2	yes	—
167	C₄×C₁₁	#578	1	2	yes	—
168	C₂²×Q₈	—	2	2	no	—
169	C₂×Q₁₆	—	2	2	no	—
170	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
171	C₂²×C₈	D₄×C₁₁	1	2	yes	—
172	C₄⋊Q₈	—	2	2	no	—
173	C₄⋊Q₈	—	2	2	no	—
174	C₄⋊Q₈	—	2	2	no	—
175	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
176	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
177	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
178	#125	—	2	2	no	—
179	C₂²⋊Q₈	—	2	2	no	—
180	C₂²⋊Q₈	—	2	2	no	—
181	C₄×Q₈	—	2	2	no	—
182	C₄×Q₈	—	2	2	no	—
183	#117	—	2	2	no	—
184	C₂×C₄⋊C₄	—	2	2	no	—
185	C₂×C₄⋊C₄	—	2	2	no	—
186	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
187	#107	—	2	4	no	—
188	#107	—	2	4	no	—
189	#107	—	2	2	no	—
190	#106	—	2	8	no	—
191	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
192	#103	—	2	8	no	—
193	#103	—	2	8	no	—
194	#103	—	2	4	no	—
195	#103	—	2	8	no	—
196	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
197	#97	D₄×C₁₁	1	2	yes	—
198	C₄×C₈	D₄×C₁₁	1	2	yes	—
199	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
200	C₄×C₈	C₂³×C₁₁	1	2	yes	—
201	C₄×C₈	C₂³×C₁₁	1	2	yes	—
202	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
203	C₂×C₁₁	—	2	2	no	—
204	C₂×C₁₁	C₂×#495	1	1	yes	characteristic
205	C₂×C₁₁	#3152	1	1	yes	characteristic
206	C₂×C₁₁	#3156	1	1	yes	characteristic
207	C₂×Q₈	—	2	2	no	—
208	C₂×Q₈	—	2	4	no	—
209	C₂×Q₈	—	2	2	no	—
210	C₂×Q₈	—	4	2	no	—
211	C₂×Q₈	—	4	8	no	—
212	C₂²×C₄	—	4	2	no	—
213	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
214	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
215	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
216	Q₁₆	—	4	4	no	—
217	M₁₆	—	2	4	no	—
218	C₂×C₈	—	2	4	no	—
219	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
220	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
221	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
222	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
223	C₄⋊C₄	—	2	2	no	—
224	C₄⋊C₄	—	2	2	no	—
225	C₄⋊C₄	—	2	4	no	—
226	C₄⋊C₄	—	2	2	no	—
227	C₄⋊C₄	—	2	2	no	—
228	C₄⋊C₄	—	2	4	no	—
229	C₄⋊C₄	—	4	2	no	—
230	C₄⋊C₄	—	4	2	no	—
231	C₄⋊C₄	—	4	2	no	—
232	C₄⋊C₄	—	4	2	no	—
233	C₂²⋊C₄	—	4	2	no	—
234	C₄²	—	4	2	no	—
235	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
236	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
237	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
238	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
239	C₁₁	#19636	1	1	yes	characteristic, direct product factor, Sylow
240	C₂³	C₁₁×#127	1	1	yes	characteristic
241	Q₈	—	4	8	no	—
242	Q₈	—	4	4	no	—
243	Q₈	—	4	4	no	—
244	Q₈	—	8	4	no	—
245	C₂×C₄	—	2	2	no	—
246	C₂×C₄	—	2	2	no	—
247	C₂×C₄	—	4	2	no	—
248	C₂×C₄	—	4	2	no	—
249	C₂×C₄	—	4	4	no	—
250	C₂×C₄	—	8	4	no	—
251	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
252	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
253	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
254	C₂×C₄	C₁₁×#135	1	4	yes	—
255	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
256	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
257	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
258	C₈	—	2	4	no	—
259	C₈	—	2	2	no	—
260	C₈	—	2	4	no	—
261	C₈	C₁₁×#137	1	4	yes	—
262	C₂²	—	2	1	no	—
263	C₂²	—	2	1	no	—
264	C₂²	C₁₁×#495	1	2	yes	—
265	C₂²	C₂×C₁₁×#127	1	1	yes	characteristic
266	C₄	—	2	1	no	—
267	C₄	—	2	1	no	—
268	C₄	—	8	4	no	—
269	C₄	—	8	2	no	—
270	C₄	—	8	2	no	—
271	C₄	C₁₁×#495	1	2	yes	—
272	C₄	C₂×C₁₁×#135	1	2	yes	—
273	C₄	C₂×C₁₁×#137	1	2	yes	—
274	C₄	C₁₁×#578	1	2	yes	—
275	C₂	—	2	2	no	—
276	C₂	C₂×C₁₁×#495	1	1	yes	characteristic
277	C₂	C₁₁×#3152	1	1	yes	characteristic
278	C₂	C₁₁×#3156	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×#1718	C₂	semidirect
6. C₁₁×#1710	C₂	semidirect
7. C₁₁×#1707	C₂	semidirect
68. #19636	C₁₁	direct (N × H)
105. #1718	C₂×C₁₁	semidirect
106. #1710	C₂×C₁₁	semidirect
107. #1707	C₂×C₁₁	semidirect
239. C₁₁	#19636	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×#3229	2
C₁₁×#3170	2
C₂×C₁₁×#500	2
C₁₁×#3139	2
C₁₁×#1718	2
C₁₁×#1710	2
C₁₁×#1707	2
C₈×C₁₁×M₁₆	2
#19636	11

Subgroups — C11×#19636 #14596829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19636 #14596829