Subgroups — C₁₁×#11297 #14588490

Order 2816.

578 conjugacy classes of subgroups.

The subgroup lattice has 284 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	C₁₁×#1742	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1738	C₂	1	2	yes	maximal
4	C₂×C₁₁×#341	C₂	1	2	yes	maximal
5	C₁₁×#1729	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
7	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
8	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
11	C₁₁×#424	—	2	4	no	—
12	C₁₁×#423	—	2	2	no	—
13	C₁₁×#343	C₄	1	4	yes	—
14	C₁₁×#341	—	2	4	no	—
15	C₁₁×#341	—	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	1	no	—
21	C₂×C₁₁×M₁₆	—	2	2	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	—	2	2	no	—
28	C₂×C₁₁×M₁₆	—	2	2	no	—
29	C₂×C₁₁×M₁₆	—	2	2	no	—
30	C₂×C₁₁×M₁₆	—	2	2	no	—
31	C₂×C₁₁×M₁₆	C₂×C₄	1	4	yes	—
32	C₂×C₁₁×M₁₆	D₄	1	4	yes	—
33	C₂×C₁₁×M₁₆	Q₈	1	2	yes	—
34	C₂²×C₈×C₁₁	—	2	1	no	—
35	C₂²×C₈×C₁₁	—	2	1	no	—
36	C₂²×C₈×C₁₁	—	2	2	no	—
37	C₂²×C₈×C₁₁	—	2	2	no	—
38	C₂²×C₈×C₁₁	—	2	1	no	—
39	C₂²×C₈×C₁₁	—	2	2	no	—
40	C₂²×C₈×C₁₁	—	2	2	no	—
41	C₂²×C₈×C₁₁	D₄	1	2	yes	—
42	C₁₁×#117	—	2	2	no	—
43	C₁₁×#117	—	2	2	no	—
44	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
45	C₂×C₁₁×C₂²⋊C₄	Q₈	1	2	yes	—
46	C₂×C₄²×C₁₁	D₄	1	2	yes	—
47	C₁₁×C₄⋊C₈	—	2	8	no	—
48	#11297	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂⁴×C₁₁	C₂×Q₈	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
51	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
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	#41	1	2	yes	—
57	C₂²×C₄×C₁₁	#41	1	2	yes	—
58	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
59	C₂²×C₄×C₁₁	#41	1	2	yes	—
60	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
61	C₁₁×M₁₆	—	2	4	no	—
62	C₁₁×M₁₆	—	2	4	no	—
63	C₁₁×M₁₆	—	2	4	no	—
64	C₁₁×M₁₆	—	2	4	no	—
65	C₁₁×M₁₆	—	2	4	no	—
66	C₁₁×M₁₆	—	4	2	no	—
67	C₁₁×M₁₆	—	4	2	no	—
68	C₁₁×M₁₆	—	4	2	no	—
69	C₁₁×M₁₆	—	4	2	no	—
70	C₁₁×M₁₆	—	4	2	no	—
71	C₂×C₈×C₁₁	—	2	4	no	—
72	C₂×C₈×C₁₁	—	2	4	no	—
73	C₂×C₈×C₁₁	—	2	2	no	—
74	C₂×C₈×C₁₁	—	2	2	no	—
75	C₂×C₈×C₁₁	—	2	4	no	—
76	C₂×C₈×C₁₁	—	4	1	no	—
77	C₂×C₈×C₁₁	—	4	2	no	—
78	C₂×C₈×C₁₁	—	4	2	no	—
79	C₂×C₈×C₁₁	—	4	1	no	—
80	C₂×C₈×C₁₁	—	4	2	no	—
81	C₂×C₈×C₁₁	—	4	1	no	—
82	C₂×C₈×C₁₁	—	4	2	no	—
83	C₂×C₈×C₁₁	—	4	1	no	—
84	C₂×C₈×C₁₁	—	4	2	no	—
85	C₁₁×C₄⋊C₄	—	2	4	no	—
86	C₁₁×C₂²⋊C₄	—	2	4	no	—
87	C₄²×C₁₁	—	2	2	no	—
88	C₄²×C₁₁	—	2	2	no	—
89	#2905	C₂×C₁₁	1	1	yes	characteristic
90	#1742	C₂×C₁₁	1	1	yes	characteristic
91	#1738	C₂×C₁₁	1	2	yes	—
92	C₂×#341	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	C₂²⋊Q₈	1	2	yes	—
97	C₂³×C₁₁	#125	1	2	yes	—
98	C₂³×C₁₁	#125	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	#117	1	2	yes	—
103	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
104	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
105	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
106	C₂×C₄×C₁₁	#120	1	1	yes	characteristic
107	C₂×C₄×C₁₁	#121	1	2	yes	—
108	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
109	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
110	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
111	C₂×C₄×C₁₁	#123	1	2	yes	—
112	C₂×C₄×C₁₁	#123	1	2	yes	—
113	C₂×C₄×C₁₁	#123	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	#124	1	1	yes	characteristic
117	C₂×C₄×C₁₁	#125	1	2	yes	—
118	C₂×C₄×C₁₁	#126	1	2	yes	—
119	C₂×C₄×C₁₁	#126	1	2	yes	—
120	C₈×C₁₁	—	4	4	no	—
121	C₈×C₁₁	—	4	2	no	—
122	C₈×C₁₁	—	4	4	no	—
123	C₈×C₁₁	—	4	2	no	—
124	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
125	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
126	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
127	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
128	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
129	#424	—	2	4	no	—
130	#423	—	2	2	no	—
131	#343	C₄×C₁₁	1	4	yes	—
132	#341	—	2	4	no	—
133	#341	—	2	4	no	—
134	#336	—	2	2	no	—
135	C₂²×C₁₁	—	2	2	no	—
136	C₂²×C₁₁	—	2	4	no	—
137	C₂²×C₁₁	—	4	2	no	—
138	C₂²×C₁₁	—	4	1	no	—
139	C₂²×C₁₁	—	4	1	no	—
140	C₂²×C₁₁	#382	1	1	yes	characteristic
141	C₂²×C₁₁	#385	1	1	yes	characteristic
142	C₂²×C₁₁	#389	1	1	yes	characteristic
143	C₂²×C₁₁	#398	1	2	yes	—
144	C₂²×C₁₁	#400	1	2	yes	—
145	C₄×C₁₁	—	4	4	no	—
146	C₄×C₁₁	#387	1	2	yes	—
147	C₄×C₁₁	#388	1	2	yes	—
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	#400	1	1	yes	characteristic
152	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
153	C₂×M₁₆	—	2	2	no	—
154	C₂×M₁₆	—	2	2	no	—
155	C₂×M₁₆	—	2	1	no	—
156	C₂×M₁₆	—	2	2	no	—
157	C₂×M₁₆	—	2	2	no	—
158	C₂×M₁₆	—	2	2	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	—	2	2	no	—
165	C₂×M₁₆	—	2	2	no	—
166	C₂×M₁₆	C₂×C₄×C₁₁	1	4	yes	—
167	C₂×M₁₆	D₄×C₁₁	1	4	yes	—
168	C₂×M₁₆	Q₈×C₁₁	1	2	yes	—
169	C₂²×C₈	—	2	1	no	—
170	C₂²×C₈	—	2	1	no	—
171	C₂²×C₈	—	2	2	no	—
172	C₂²×C₈	—	2	2	no	—
173	C₂²×C₈	—	2	1	no	—
174	C₂²×C₈	—	2	2	no	—
175	C₂²×C₈	—	2	2	no	—
176	C₂²×C₈	D₄×C₁₁	1	2	yes	—
177	#117	—	2	2	no	—
178	#117	—	2	2	no	—
179	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
180	C₂×C₂²⋊C₄	Q₈×C₁₁	1	2	yes	—
181	C₂×C₄²	D₄×C₁₁	1	2	yes	—
182	C₄⋊C₈	—	2	8	no	—
183	C₂×C₁₁	—	2	1	no	—
184	C₂×C₁₁	—	2	1	no	—
185	C₂×C₁₁	—	2	2	no	—
186	C₂×C₁₁	—	2	2	no	—
187	C₂×C₁₁	#1442	1	1	yes	characteristic
188	C₂×C₁₁	#1858	1	2	yes	—
189	C₂⁴	C₂×Q₈×C₁₁	1	1	yes	characteristic
190	C₂²×C₄	C₁₁×C₄⋊C₄	1	4	yes	—
191	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
192	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
193	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
194	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
195	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
196	C₂²×C₄	C₁₁×#41	1	2	yes	—
197	C₂²×C₄	C₁₁×#41	1	2	yes	—
198	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
199	C₂²×C₄	C₁₁×#41	1	2	yes	—
200	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
201	M₁₆	—	2	4	no	—
202	M₁₆	—	2	4	no	—
203	M₁₆	—	2	4	no	—
204	M₁₆	—	2	4	no	—
205	M₁₆	—	2	4	no	—
206	M₁₆	—	4	2	no	—
207	M₁₆	—	4	2	no	—
208	M₁₆	—	4	2	no	—
209	M₁₆	—	4	2	no	—
210	M₁₆	—	4	2	no	—
211	C₂×C₈	—	2	4	no	—
212	C₂×C₈	—	2	4	no	—
213	C₂×C₈	—	2	2	no	—
214	C₂×C₈	—	2	2	no	—
215	C₂×C₈	—	2	4	no	—
216	C₂×C₈	—	4	1	no	—
217	C₂×C₈	—	4	2	no	—
218	C₂×C₈	—	4	2	no	—
219	C₂×C₈	—	4	1	no	—
220	C₂×C₈	—	4	2	no	—
221	C₂×C₈	—	4	1	no	—
222	C₂×C₈	—	4	2	no	—
223	C₂×C₈	—	4	1	no	—
224	C₂×C₈	—	4	2	no	—
225	C₄⋊C₄	—	2	4	no	—
226	C₂²⋊C₄	—	2	4	no	—
227	C₄²	—	2	2	no	—
228	C₄²	—	2	2	no	—
229	C₁₁	#11297	1	1	yes	characteristic, direct product factor, Sylow
230	C₂³	—	4	2	no	—
231	C₂³	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
232	C₂³	C₁₁×C₂²⋊Q₈	1	2	yes	—
233	C₂³	C₁₁×#125	1	2	yes	—
234	C₂³	C₁₁×#125	1	1	yes	characteristic
235	C₂³	C₁₁×C₄⋊Q₈	1	1	yes	characteristic
236	C₂×C₄	—	2	4	no	—
237	C₂×C₄	—	4	4	no	—
238	C₂×C₄	C₁₁×#117	1	2	yes	—
239	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
240	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
241	C₂×C₄	C₄×Q₈×C₁₁	1	1	yes	characteristic
242	C₂×C₄	C₁₁×#120	1	1	yes	characteristic
243	C₂×C₄	C₁₁×#121	1	2	yes	—
244	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
245	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
246	C₂×C₄	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
247	C₂×C₄	C₁₁×#123	1	2	yes	—
248	C₂×C₄	C₁₁×#123	1	2	yes	—
249	C₂×C₄	C₁₁×#123	1	1	yes	characteristic
250	C₂×C₄	C₁₁×#124	1	2	yes	—
251	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
252	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
253	C₂×C₄	C₁₁×#125	1	2	yes	—
254	C₂×C₄	C₁₁×#126	1	2	yes	—
255	C₂×C₄	C₁₁×#126	1	2	yes	—
256	C₈	—	4	4	no	—
257	C₈	—	4	2	no	—
258	C₈	—	4	4	no	—
259	C₈	—	4	2	no	—
260	C₂²	—	2	2	no	—
261	C₂²	—	2	4	no	—
262	C₂²	—	4	2	no	—
263	C₂²	—	4	1	no	—
264	C₂²	—	4	1	no	—
265	C₂²	C₁₁×#382	1	1	yes	characteristic
266	C₂²	C₁₁×#385	1	1	yes	characteristic
267	C₂²	C₁₁×#389	1	1	yes	characteristic
268	C₂²	C₁₁×#398	1	2	yes	—
269	C₂²	C₁₁×#400	1	2	yes	—
270	C₄	—	4	4	no	—
271	C₄	C₁₁×#387	1	2	yes	—
272	C₄	C₁₁×#388	1	2	yes	—
273	C₄	C₁₁×#393	1	1	yes	characteristic
274	C₄	C₁₁×#394	1	1	yes	characteristic
275	C₄	C₁₁×#397	1	1	yes	characteristic
276	C₄	C₁₁×#400	1	1	yes	characteristic
277	C₂	—	2	1	no	—
278	C₂	—	2	1	no	—
279	C₂	—	2	2	no	—
280	C₂	—	2	2	no	—
281	C₂	C₁₁×#1442	1	1	yes	characteristic
282	C₂	C₁₁×#1858	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	#120
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
socle	C₂²×C₁₁	#385
prime radical	C₂⁴×C₁₁	C₂×Q₈
LCS	G ▷ C₂²×C₄ ▷ 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. #11297	C₁₁	direct (N × H)
229. C₁₁	#11297	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
C₁₁×#1742	2
C₁₁×#1738	2
C₂×C₁₁×#341	2
C₁₁×#1729	2
#11297	11

Subgroups — C11×#11297 #14588490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11297 #14588490