Subgroups — C₁₁×#19632 #14596825

Order 2816.

750 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3230	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×#494	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	C₂²×C₁₁×Q₁₆	—	2	2	no	—
10	C₁₁×#533	C₂²	1	2	yes	—
11	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
12	C₁₁×#501	—	2	4	no	—
13	C₁₁×#500	C₂²	1	4	yes	—
14	C₁₁×#500	C₂²	1	1	yes	characteristic
15	C₁₁×#500	C₂²	1	4	yes	—
16	C₁₁×#498	C₂²	1	4	yes	—
17	C₁₁×#494	—	2	2	no	—
18	C₁₁×#494	C₂²	1	1	yes	characteristic
19	C₁₁×#494	C₂²	1	2	yes	—
20	C₁₁×#494	C₂²	1	2	yes	—
21	C₁₁×#487	C₂²	1	2	yes	—
22	C₁₁×#487	C₂²	1	4	yes	—
23	C₁₁×#484	—	2	4	no	—
24	C₁₁×#477	—	2	4	no	—
25	C₁₁×#467	—	2	2	no	—
26	C₄×C₁₁×Q₁₆	—	2	2	no	—
27	C₁₁×#431	C₂²	1	1	yes	characteristic
28	C₁₁×#428	—	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	4	no	—
35	C₂×C₁₁×Q₁₆	—	2	4	no	—
36	C₂×C₁₁×Q₁₆	—	2	2	no	—
37	C₂×C₁₁×Q₁₆	—	4	8	no	—
38	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
39	C₂²×C₈×C₁₁	D₄	1	2	yes	—
40	C₁₁×C₄⋊Q₈	—	2	2	no	—
41	C₁₁×C₄⋊Q₈	—	2	2	no	—
42	C₁₁×C₄⋊Q₈	—	2	2	no	—
43	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
44	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
45	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
46	C₁₁×#125	—	2	2	no	—
47	C₁₁×C₂²⋊Q₈	—	2	2	no	—
48	C₁₁×C₂²⋊Q₈	—	2	2	no	—
49	C₄×Q₈×C₁₁	—	2	2	no	—
50	C₄×Q₈×C₁₁	—	2	2	no	—
51	C₁₁×#117	—	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	8	no	—
56	C₁₁×#107	—	2	2	no	—
57	C₁₁×#107	—	2	8	no	—
58	C₁₁×#106	—	2	8	no	—
59	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
60	C₁₁×#103	—	2	4	no	—
61	C₁₁×#103	—	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	#19632	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂×Q₈×C₁₁	—	2	2	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	C₂²×C₄×C₁₁	—	4	2	no	—
76	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
79	C₁₁×Q₁₆	—	4	8	no	—
80	C₁₁×Q₁₆	—	4	4	no	—
81	C₁₁×Q₁₆	—	4	8	no	—
82	C₁₁×M₁₆	Q₁₆	1	8	yes	complemented
83	C₂×C₈×C₁₁	—	2	4	no	—
84	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
85	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
86	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
87	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
88	C₁₁×C₄⋊C₄	—	2	4	no	—
89	C₁₁×C₄⋊C₄	—	2	2	no	—
90	C₁₁×C₄⋊C₄	—	2	2	no	—
91	C₁₁×C₄⋊C₄	—	2	4	no	—
92	C₁₁×C₄⋊C₄	—	2	2	no	—
93	C₁₁×C₄⋊C₄	—	2	2	no	—
94	C₁₁×C₄⋊C₄	—	4	2	no	—
95	C₁₁×C₄⋊C₄	—	4	2	no	—
96	C₁₁×C₄⋊C₄	—	4	2	no	—
97	C₁₁×C₄⋊C₄	—	4	2	no	—
98	C₁₁×C₂²⋊C₄	—	4	2	no	—
99	C₄²×C₁₁	—	4	2	no	—
100	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
101	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
104	#3230	C₂×C₁₁	1	2	yes	—
105	#3170	C₂×C₁₁	1	1	yes	characteristic
106	#3165	C₂×C₁₁	1	2	yes	—
107	C₂×#494	C₂×C₁₁	1	1	yes	characteristic
108	#1723	C₂×C₁₁	1	4	yes	complemented
109	#1713	C₂×C₁₁	1	2	yes	complemented
110	#1707	C₂×C₁₁	1	2	yes	complemented
111	C₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic
112	C₂³×C₁₁	#127	1	1	yes	characteristic
113	Q₈×C₁₁	—	4	8	no	—
114	Q₈×C₁₁	—	4	4	no	—
115	Q₈×C₁₁	—	4	4	no	—
116	Q₈×C₁₁	—	8	4	no	—
117	C₂×C₄×C₁₁	—	2	2	no	—
118	C₂×C₄×C₁₁	—	2	2	no	—
119	C₂×C₄×C₁₁	—	4	2	no	—
120	C₂×C₄×C₁₁	—	4	2	no	—
121	C₂×C₄×C₁₁	—	4	4	no	—
122	C₂×C₄×C₁₁	—	8	4	no	—
123	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
124	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
125	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
126	C₂×C₄×C₁₁	C₂×Q₁₆	1	4	yes	—
127	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
128	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
129	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
130	C₈×C₁₁	—	2	2	no	—
131	C₈×C₁₁	—	2	4	no	—
132	C₈×C₁₁	C₂×Q₁₆	1	8	yes	complemented
133	C₈×C₁₁	AGL(1,ℤ/8)	1	4	yes	—
134	C₂²×Q₁₆	—	2	2	no	—
135	#533	C₂²×C₁₁	1	2	yes	—
136	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
137	#501	—	2	4	no	—
138	#500	C₂²×C₁₁	1	4	yes	—
139	#500	C₂²×C₁₁	1	1	yes	characteristic
140	#500	C₂²×C₁₁	1	4	yes	—
141	#498	C₂²×C₁₁	1	4	yes	—
142	#494	—	2	2	no	—
143	#494	C₂²×C₁₁	1	2	yes	—
144	#494	C₂²×C₁₁	1	2	yes	—
145	#494	C₂²×C₁₁	1	1	yes	characteristic
146	#487	C₂²×C₁₁	1	2	yes	—
147	#487	C₂²×C₁₁	1	4	yes	—
148	#484	—	2	4	no	—
149	#477	—	2	4	no	—
150	#467	—	2	2	no	—
151	C₄×Q₁₆	—	2	2	no	—
152	#431	C₂²×C₁₁	1	1	yes	characteristic
153	#428	—	2	4	no	—
154	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
155	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
156	#322	C₂²×C₁₁	1	2	yes	—
157	C₈²	C₂²×C₁₁	1	2	yes	—
158	C₂²×C₁₁	—	2	1	no	—
159	C₂²×C₁₁	—	2	1	no	—
160	C₂²×C₁₁	#494	1	2	yes	—
161	C₂²×C₁₁	C₂×#127	1	1	yes	characteristic
162	C₄×C₁₁	—	2	1	no	—
163	C₄×C₁₁	—	2	1	no	—
164	C₄×C₁₁	—	8	4	no	—
165	C₄×C₁₁	—	8	2	no	—
166	C₄×C₁₁	—	8	2	no	—
167	C₄×C₁₁	#494	1	2	yes	—
168	C₄×C₁₁	C₂²×Q₁₆	1	2	yes	—
169	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
170	C₄×C₁₁	#578	1	2	yes	—
171	C₂²×Q₈	—	2	2	no	—
172	C₂×Q₁₆	—	2	4	no	—
173	C₂×Q₁₆	—	2	4	no	—
174	C₂×Q₁₆	—	2	2	no	—
175	C₂×Q₁₆	—	4	8	no	—
176	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
177	C₂²×C₈	D₄×C₁₁	1	2	yes	—
178	C₄⋊Q₈	—	2	2	no	—
179	C₄⋊Q₈	—	2	2	no	—
180	C₄⋊Q₈	—	2	2	no	—
181	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
182	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
183	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
184	#125	—	2	2	no	—
185	C₂²⋊Q₈	—	2	2	no	—
186	C₂²⋊Q₈	—	2	2	no	—
187	C₄×Q₈	—	2	2	no	—
188	C₄×Q₈	—	2	2	no	—
189	#117	—	2	2	no	—
190	C₂×C₄⋊C₄	—	2	2	no	—
191	C₂×C₄⋊C₄	—	2	2	no	—
192	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
193	#107	—	2	8	no	—
194	#107	—	2	2	no	—
195	#107	—	2	8	no	—
196	#106	—	2	8	no	—
197	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
198	#103	—	2	4	no	—
199	#103	—	2	8	no	—
200	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
201	#97	D₄×C₁₁	1	2	yes	—
202	C₄×C₈	D₄×C₁₁	1	2	yes	—
203	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
204	C₄×C₈	C₂³×C₁₁	1	2	yes	—
205	C₄×C₈	C₂³×C₁₁	1	2	yes	—
206	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
207	C₂×C₁₁	—	2	2	no	—
208	C₂×C₁₁	C₂×#494	1	1	yes	characteristic
209	C₂×C₁₁	#3151	1	1	yes	characteristic
210	C₂×C₁₁	#3156	1	1	yes	characteristic
211	C₂×Q₈	—	2	2	no	—
212	C₂×Q₈	—	2	2	no	—
213	C₂×Q₈	—	2	4	no	—
214	C₂×Q₈	—	4	8	no	—
215	C₂×Q₈	—	4	2	no	—
216	C₂²×C₄	—	4	2	no	—
217	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
218	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
219	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
220	Q₁₆	—	4	8	no	—
221	Q₁₆	—	4	8	no	—
222	Q₁₆	—	4	4	no	—
223	M₁₆	C₁₁×Q₁₆	1	8	yes	complemented
224	C₂×C₈	—	2	4	no	—
225	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
226	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
227	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
228	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
229	C₄⋊C₄	—	2	4	no	—
230	C₄⋊C₄	—	2	2	no	—
231	C₄⋊C₄	—	2	2	no	—
232	C₄⋊C₄	—	2	4	no	—
233	C₄⋊C₄	—	2	2	no	—
234	C₄⋊C₄	—	2	2	no	—
235	C₄⋊C₄	—	4	2	no	—
236	C₄⋊C₄	—	4	2	no	—
237	C₄⋊C₄	—	4	2	no	—
238	C₄⋊C₄	—	4	2	no	—
239	C₂²⋊C₄	—	4	2	no	—
240	C₄²	—	4	2	no	—
241	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
242	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
243	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
244	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
245	C₁₁	#19632	1	1	yes	characteristic, direct product factor, Sylow
246	C₂³	C₁₁×#127	1	1	yes	characteristic
247	Q₈	—	4	8	no	—
248	Q₈	—	4	4	no	—
249	Q₈	—	4	4	no	—
250	Q₈	—	8	4	no	—
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	4	2	no	—
254	C₂×C₄	—	4	2	no	—
255	C₂×C₄	—	4	4	no	—
256	C₂×C₄	—	8	4	no	—
257	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
258	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
259	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
260	C₂×C₄	C₂×C₁₁×Q₁₆	1	4	yes	—
261	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
262	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
263	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
264	C₈	—	2	2	no	—
265	C₈	—	2	4	no	—
266	C₈	C₂×C₁₁×Q₁₆	1	8	yes	complemented
267	C₈	C₁₁×AGL(1,ℤ/8)	1	4	yes	—
268	C₂²	—	2	1	no	—
269	C₂²	—	2	1	no	—
270	C₂²	C₁₁×#494	1	2	yes	—
271	C₂²	C₂×C₁₁×#127	1	1	yes	characteristic
272	C₄	—	2	1	no	—
273	C₄	—	2	1	no	—
274	C₄	—	8	4	no	—
275	C₄	—	8	2	no	—
276	C₄	—	8	2	no	—
277	C₄	C₁₁×#494	1	2	yes	—
278	C₄	C₂²×C₁₁×Q₁₆	1	2	yes	—
279	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	2	yes	—
280	C₄	C₁₁×#578	1	2	yes	—
281	C₂	—	2	2	no	—
282	C₂	C₂×C₁₁×#494	1	1	yes	characteristic
283	C₂	C₁₁×#3151	1	1	yes	characteristic
284	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×#1723	C₂	semidirect
6. C₁₁×#1713	C₂	semidirect
7. C₁₁×#1707	C₂	semidirect
69. #19632	C₁₁	direct (N × H)
82. C₁₁×M₁₆	Q₁₆	semidirect
108. #1723	C₂×C₁₁	semidirect
109. #1713	C₂×C₁₁	semidirect
110. #1707	C₂×C₁₁	semidirect
132. C₈×C₁₁	C₂×Q₁₆	semidirect
223. M₁₆	C₁₁×Q₁₆	semidirect
245. C₁₁	#19632	direct (N × H)
266. C₈	C₂×C₁₁×Q₁₆	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₁×#3230	2
C₁₁×#3170	2
C₁₁×#3165	2
C₂×C₁₁×#494	2
C₁₁×#1723	2
C₁₁×#1713	2
C₁₁×#1707	2
C₈×C₁₁×M₁₆	2
#19632	11

Subgroups — C11×#19632 #14596825

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19632 #14596825