Subgroups — C₁₁×#11288 #14588481

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2905	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#344	C₂	1	2	yes	maximal
3	C₁₁×#1740	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1729	C₂	1	2	yes	maximal
5	C₁₁×#1729	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
7	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
8	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×#117	C₂²	1	2	yes	—
10	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
11	C₁₁×#424	—	2	4	no	—
12	C₁₁×#423	—	2	2	no	—
13	C₁₁×#344	—	2	4	no	—
14	C₁₁×#342	C₄	1	4	yes	—
15	C₁₁×#336	—	2	4	no	—
16	C₁₁×#336	—	2	2	no	—
17	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
18	C₂×C₁₁×M₁₆	—	2	2	no	—
19	C₂×C₁₁×M₁₆	—	2	2	no	—
20	C₂×C₁₁×M₁₆	—	2	2	no	—
21	C₂×C₁₁×M₁₆	—	2	1	no	—
22	C₂×C₁₁×M₁₆	—	2	2	no	—
23	C₂×C₁₁×M₁₆	—	2	2	no	—
24	C₂×C₁₁×M₁₆	—	2	2	no	—
25	C₂×C₁₁×M₁₆	—	2	2	no	—
26	C₂×C₁₁×M₁₆	—	2	2	no	—
27	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
28	C₂²×C₈×C₁₁	—	2	2	no	—
29	C₂²×C₈×C₁₁	—	2	1	no	—
30	C₂²×C₈×C₁₁	—	2	1	no	—
31	C₂²×C₈×C₁₁	—	2	2	no	—
32	C₂²×C₈×C₁₁	—	2	1	no	—
33	C₂²×C₈×C₁₁	D₄	1	4	yes	—
34	C₂²×C₈×C₁₁	Q₈	1	2	yes	—
35	C₁₁×#117	—	2	2	no	—
36	C₁₁×#117	—	2	2	no	—
37	C₁₁×#117	—	2	2	no	—
38	C₁₁×#117	—	2	2	no	—
39	C₁₁×#117	—	2	2	no	—
40	C₁₁×#117	—	2	2	no	—
41	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
42	C₂×C₁₁×C₄⋊C₄	Q₈	1	2	yes	—
43	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	4	yes	—
44	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₁₁	—	2	2	no	—
46	C₂×C₄²×C₁₁	D₄	1	2	yes	—
47	C₁₁×C₄⋊C₈	—	2	8	no	—
48	#11288	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	—	2	4	no	—
51	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
52	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
53	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
56	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
57	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
58	C₂²×C₄×C₁₁	#41	1	2	yes	—
59	C₂²×C₄×C₁₁	#41	1	2	yes	—
60	C₂²×C₄×C₁₁	#41	1	2	yes	—
61	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
62	C₁₁×M₁₆	—	2	4	no	—
63	C₁₁×M₁₆	—	4	2	no	—
64	C₁₁×M₁₆	—	4	2	no	—
65	C₁₁×M₁₆	—	4	2	no	—
66	C₁₁×M₁₆	—	4	2	no	—
67	C₁₁×M₁₆	—	4	2	no	—
68	C₂×C₈×C₁₁	—	2	4	no	—
69	C₂×C₈×C₁₁	—	2	2	no	—
70	C₂×C₈×C₁₁	—	2	4	no	—
71	C₂×C₈×C₁₁	—	2	4	no	—
72	C₂×C₈×C₁₁	—	2	2	no	—
73	C₂×C₈×C₁₁	—	2	4	no	—
74	C₂×C₈×C₁₁	—	4	1	no	—
75	C₂×C₈×C₁₁	—	4	1	no	—
76	C₂×C₈×C₁₁	—	4	1	no	—
77	C₂×C₈×C₁₁	—	4	2	no	—
78	C₂×C₈×C₁₁	—	4	1	no	—
79	C₁₁×C₄⋊C₄	—	2	4	no	—
80	C₁₁×C₄⋊C₄	—	4	2	no	—
81	C₁₁×C₄⋊C₄	—	4	2	no	—
82	C₁₁×C₂²⋊C₄	—	2	4	no	—
83	C₁₁×C₂²⋊C₄	—	2	4	no	—
84	C₁₁×C₂²⋊C₄	—	2	4	no	—
85	C₄²×C₁₁	—	2	2	no	—
86	C₄²×C₁₁	—	2	2	no	—
87	C₄²×C₁₁	—	4	2	no	—
88	C₄²×C₁₁	—	4	2	no	—
89	#2905	C₂×C₁₁	1	1	yes	characteristic
90	C₂×#344	C₂×C₁₁	1	2	yes	—
91	#1740	C₂×C₁₁	1	1	yes	characteristic
92	#1729	C₂×C₁₁	1	2	yes	—
93	#1729	C₂×C₁₁	1	1	yes	characteristic
94	C₂³×C₁₁	—	4	2	no	—
95	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
96	C₂³×C₁₁	#117	1	2	yes	—
97	C₂³×C₁₁	C₄×D₄	1	2	yes	—
98	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
99	C₂³×C₁₁	C₄×Q₈	1	1	yes	characteristic
100	C₂×C₄×C₁₁	—	2	4	no	—
101	C₂×C₄×C₁₁	—	4	4	no	—
102	C₂×C₄×C₁₁	—	4	8	no	—
103	C₂×C₄×C₁₁	—	4	4	no	—
104	C₂×C₄×C₁₁	#120	1	1	yes	characteristic
105	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
106	C₂×C₄×C₁₁	#121	1	2	yes	—
107	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
108	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
109	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
110	C₂×C₄×C₁₁	#123	1	2	yes	—
111	C₂×C₄×C₁₁	#123	1	2	yes	—
112	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
113	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
114	C₂×C₄×C₁₁	#124	1	2	yes	—
115	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
116	C₂×C₄×C₁₁	#125	1	2	yes	—
117	C₂×C₄×C₁₁	#125	1	2	yes	—
118	C₂×C₄×C₁₁	#125	1	1	yes	characteristic
119	C₂×C₄×C₁₁	#126	1	2	yes	—
120	C₂×C₄×C₁₁	#126	1	2	yes	—
121	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
122	C₈×C₁₁	—	4	2	no	—
123	C₈×C₁₁	—	4	4	no	—
124	C₈×C₁₁	—	4	2	no	—
125	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
126	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
127	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
128	C₂×#117	C₂²×C₁₁	1	2	yes	—
129	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
130	#424	—	2	4	no	—
131	#423	—	2	2	no	—
132	#344	—	2	4	no	—
133	#342	C₄×C₁₁	1	4	yes	—
134	#336	—	2	4	no	—
135	#336	—	2	2	no	—
136	C₂²×C₁₁	—	2	2	no	—
137	C₂²×C₁₁	—	2	4	no	—
138	C₂²×C₁₁	—	4	2	no	—
139	C₂²×C₁₁	—	4	1	no	—
140	C₂²×C₁₁	—	4	1	no	—
141	C₂²×C₁₁	#382	1	1	yes	characteristic
142	C₂²×C₁₁	#385	1	1	yes	characteristic
143	C₂²×C₁₁	#387	1	2	yes	—
144	C₂²×C₁₁	#388	1	2	yes	—
145	C₂²×C₁₁	#389	1	1	yes	characteristic
146	C₄×C₁₁	—	4	4	no	—
147	C₄×C₁₁	—	8	4	no	—
148	C₄×C₁₁	#393	1	1	yes	characteristic
149	C₄×C₁₁	#394	1	1	yes	characteristic
150	C₄×C₁₁	#397	1	1	yes	characteristic
151	C₄×C₁₁	#398	1	2	yes	—
152	C₄×C₁₁	#400	1	1	yes	characteristic
153	C₄×C₁₁	#400	1	2	yes	—
154	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
155	C₂×M₁₆	—	2	2	no	—
156	C₂×M₁₆	—	2	2	no	—
157	C₂×M₁₆	—	2	2	no	—
158	C₂×M₁₆	—	2	1	no	—
159	C₂×M₁₆	—	2	2	no	—
160	C₂×M₁₆	—	2	2	no	—
161	C₂×M₁₆	—	2	2	no	—
162	C₂×M₁₆	—	2	2	no	—
163	C₂×M₁₆	—	2	2	no	—
164	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
165	C₂²×C₈	—	2	2	no	—
166	C₂²×C₈	—	2	1	no	—
167	C₂²×C₈	—	2	1	no	—
168	C₂²×C₈	—	2	2	no	—
169	C₂²×C₈	—	2	1	no	—
170	C₂²×C₈	D₄×C₁₁	1	4	yes	—
171	C₂²×C₈	Q₈×C₁₁	1	2	yes	—
172	#117	—	2	2	no	—
173	#117	—	2	2	no	—
174	#117	—	2	2	no	—
175	#117	—	2	2	no	—
176	#117	—	2	2	no	—
177	#117	—	2	2	no	—
178	C₂×C₄⋊C₄	—	2	2	no	—
179	C₂×C₄⋊C₄	Q₈×C₁₁	1	2	yes	—
180	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
181	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
182	C₂×C₄²	—	2	2	no	—
183	C₂×C₄²	D₄×C₁₁	1	2	yes	—
184	C₄⋊C₈	—	2	8	no	—
185	C₂×C₁₁	—	2	2	no	—
186	C₂×C₁₁	—	2	1	no	—
187	C₂×C₁₁	—	2	2	no	—
188	C₂×C₁₁	—	2	1	no	—
189	C₂×C₁₁	#1442	1	1	yes	characteristic
190	C₂×C₁₁	#1868	1	2	yes	—
191	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
192	C₂²×C₄	—	2	4	no	—
193	C₂²×C₄	C₁₁×C₄⋊C₄	1	4	yes	—
194	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
195	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
196	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
197	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
198	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
199	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
200	C₂²×C₄	C₁₁×#41	1	2	yes	—
201	C₂²×C₄	C₁₁×#41	1	2	yes	—
202	C₂²×C₄	C₁₁×#41	1	2	yes	—
203	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
204	M₁₆	—	2	4	no	—
205	M₁₆	—	4	2	no	—
206	M₁₆	—	4	2	no	—
207	M₁₆	—	4	2	no	—
208	M₁₆	—	4	2	no	—
209	M₁₆	—	4	2	no	—
210	C₂×C₈	—	2	4	no	—
211	C₂×C₈	—	2	2	no	—
212	C₂×C₈	—	2	4	no	—
213	C₂×C₈	—	2	4	no	—
214	C₂×C₈	—	2	2	no	—
215	C₂×C₈	—	2	4	no	—
216	C₂×C₈	—	4	1	no	—
217	C₂×C₈	—	4	1	no	—
218	C₂×C₈	—	4	1	no	—
219	C₂×C₈	—	4	2	no	—
220	C₂×C₈	—	4	1	no	—
221	C₄⋊C₄	—	2	4	no	—
222	C₄⋊C₄	—	4	2	no	—
223	C₄⋊C₄	—	4	2	no	—
224	C₂²⋊C₄	—	2	4	no	—
225	C₂²⋊C₄	—	2	4	no	—
226	C₂²⋊C₄	—	2	4	no	—
227	C₄²	—	2	2	no	—
228	C₄²	—	2	2	no	—
229	C₄²	—	4	2	no	—
230	C₄²	—	4	2	no	—
231	C₁₁	#11288	1	1	yes	characteristic, direct product factor, Sylow
232	C₂³	—	4	2	no	—
233	C₂³	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
234	C₂³	C₁₁×#117	1	2	yes	—
235	C₂³	C₄×D₄×C₁₁	1	2	yes	—
236	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
237	C₂³	C₄×Q₈×C₁₁	1	1	yes	characteristic
238	C₂×C₄	—	2	4	no	—
239	C₂×C₄	—	4	4	no	—
240	C₂×C₄	—	4	8	no	—
241	C₂×C₄	—	4	4	no	—
242	C₂×C₄	C₁₁×#120	1	1	yes	characteristic
243	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
244	C₂×C₄	C₁₁×#121	1	2	yes	—
245	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
246	C₂×C₄	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
247	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
248	C₂×C₄	C₁₁×#123	1	2	yes	—
249	C₂×C₄	C₁₁×#123	1	2	yes	—
250	C₂×C₄	C₁₁×#123	1	1	yes	characteristic
251	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
252	C₂×C₄	C₁₁×#124	1	2	yes	—
253	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
254	C₂×C₄	C₁₁×#125	1	2	yes	—
255	C₂×C₄	C₁₁×#125	1	2	yes	—
256	C₂×C₄	C₁₁×#125	1	1	yes	characteristic
257	C₂×C₄	C₁₁×#126	1	2	yes	—
258	C₂×C₄	C₁₁×#126	1	2	yes	—
259	C₂×C₄	C₁₁×C₄⋊Q₈	1	1	yes	characteristic
260	C₈	—	4	2	no	—
261	C₈	—	4	4	no	—
262	C₈	—	4	2	no	—
263	C₂²	—	2	2	no	—
264	C₂²	—	2	4	no	—
265	C₂²	—	4	2	no	—
266	C₂²	—	4	1	no	—
267	C₂²	—	4	1	no	—
268	C₂²	C₁₁×#382	1	1	yes	characteristic
269	C₂²	C₁₁×#385	1	1	yes	characteristic
270	C₂²	C₁₁×#387	1	2	yes	—
271	C₂²	C₁₁×#388	1	2	yes	—
272	C₂²	C₁₁×#389	1	1	yes	characteristic
273	C₄	—	4	4	no	—
274	C₄	—	8	4	no	—
275	C₄	C₁₁×#393	1	1	yes	characteristic
276	C₄	C₁₁×#394	1	1	yes	characteristic
277	C₄	C₁₁×#397	1	1	yes	characteristic
278	C₄	C₁₁×#398	1	2	yes	—
279	C₄	C₁₁×#400	1	1	yes	characteristic
280	C₄	C₁₁×#400	1	2	yes	—
281	C₂	—	2	2	no	—
282	C₂	—	2	1	no	—
283	C₂	—	2	2	no	—
284	C₂	—	2	1	no	—
285	C₂	C₁₁×#1442	1	1	yes	characteristic
286	C₂	C₁₁×#1868	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	#120
commutator	C₂⁴	C₂²×C₄×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
socle	C₂²×C₁₁	#385
prime radical	C₂⁴×C₁₁	C₂²×C₄
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
48. #11288	C₁₁	direct (N × H)
231. C₁₁	#11288	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×#2905	2
C₂×C₁₁×#344	2
C₁₁×#1740	2
C₁₁×#1729	2
#11288	11

Subgroups — C11×#11288 #14588481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11288 #14588481