Subgroups — C₁₁×#13194 #14590387

Order 2816.

466 conjugacy classes of subgroups.

The subgroup lattice has 268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#436	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2150	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#349	C₂	1	4	yes	maximal, complemented
4	C₄×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
6	C₂×C₄×D₄×C₁₁	C₄	1	1	yes	characteristic
7	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
8	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
9	C₁₁×#436	—	2	1	no	—
10	C₁₁×#436	—	2	1	no	—
11	C₁₁×#436	—	2	1	no	—
12	C₁₁×#436	—	2	1	no	—
13	C₂×C₁₁×C₄⋊C₈	C₄	1	1	yes	characteristic
14	C₂×C₁₁×C₂²⋊C₈	C₄	1	2	yes	—
15	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×C₄⋊C₁₆	—	2	1	no	—
17	C₁₁×C₄⋊C₁₆	—	2	1	no	—
18	C₁₁×#349	—	2	8	no	—
19	C₁₁×#346	—	2	1	no	—
20	C₄×C₁₁×C₁₆	—	2	1	no	—
21	C₂²×D₄×C₁₁	C₈	1	1	yes	characteristic
22	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
23	C₂×C₁₁×M₁₆	—	2	4	no	—
24	C₂×C₁₁×M₁₆	—	2	2	no	—
25	C₂×C₁₁×M₁₆	—	2	2	no	—
26	C₂×C₁₁×M₁₆	—	2	4	no	—
27	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
28	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
30	C₄×D₄×C₁₁	—	2	1	no	—
31	C₄×D₄×C₁₁	—	2	1	no	—
32	C₄×D₄×C₁₁	—	2	1	no	—
33	C₄×D₄×C₁₁	—	2	1	no	—
34	C₂×C₁₁×C₄⋊C₄	C₈	1	1	yes	characteristic
35	C₂×C₁₁×C₂²⋊C₄	C₈	1	2	yes	—
36	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
37	C₁₁×M₃₂	—	2	2	no	—
38	C₁₁×M₃₂	—	2	4	no	—
39	C₁₁×M₃₂	D₄	1	4	yes	complemented
40	C₂×C₁₁×C₁₆	—	2	2	no	—
41	C₂×C₁₁×C₁₆	—	2	2	no	—
42	C₁₁×C₄⋊C₈	—	2	1	no	—
43	C₁₁×C₄⋊C₈	—	2	1	no	—
44	C₁₁×C₂²⋊C₈	—	2	2	no	—
45	C₁₁×C₂²⋊C₈	—	2	2	no	—
46	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
47	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
48	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
49	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
50	#13194	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂⁴×C₁₁	C₂×C₈	1	2	yes	—
52	C₂×D₄×C₁₁	—	2	1	no	—
53	C₂×D₄×C₁₁	—	2	1	no	—
54	C₂×D₄×C₁₁	—	4	2	no	—
55	C₂²×C₄×C₁₁	—	2	2	no	—
56	C₂²×C₄×C₁₁	—	2	4	no	—
57	C₂²×C₄×C₁₁	—	2	2	no	—
58	C₂²×C₄×C₁₁	—	2	4	no	—
59	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
60	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
61	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
63	C₁₁×M₁₆	—	4	4	no	—
64	C₁₁×M₁₆	—	4	2	no	—
65	C₁₁×M₁₆	—	4	2	no	—
66	C₂×C₈×C₁₁	—	2	2	no	—
67	C₂×C₈×C₁₁	—	2	4	no	—
68	C₂×C₈×C₁₁	—	2	2	no	—
69	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
74	C₂×C₈×C₁₁	#41	1	2	yes	—
75	C₁₁×C₄⋊C₄	—	2	1	no	—
76	C₁₁×C₄⋊C₄	—	2	1	no	—
77	C₁₁×C₂²⋊C₄	—	2	2	no	—
78	C₁₁×C₂²⋊C₄	—	2	2	no	—
79	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
80	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
81	C₄²×C₁₁	M₁₆	1	1	yes	characteristic
82	C₄²×C₁₁	M₁₆	1	1	yes	characteristic
83	C₁₁×C₁₆	—	2	4	no	—
84	C₁₁×C₁₆	—	4	2	no	—
85	C₂×#436	C₂×C₁₁	1	1	yes	characteristic
86	#2150	C₂×C₁₁	1	1	yes	characteristic, complemented
87	C₂×#349	C₂×C₁₁	1	4	yes	complemented
88	C₄×M₃₂	C₂×C₁₁	1	1	yes	characteristic, complemented
89	C₂³×C₁₁	—	2	2	no	—
90	C₂³×C₁₁	—	2	4	no	—
91	C₂³×C₁₁	—	4	2	no	—
92	C₂³×C₁₁	—	4	2	no	—
93	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
94	D₄×C₁₁	—	4	2	no	—
95	D₄×C₁₁	—	4	2	no	—
96	C₂×C₄×C₁₁	—	2	2	no	—
97	C₂×C₄×C₁₁	—	2	2	no	—
98	C₂×C₄×C₁₁	—	2	4	no	—
99	C₂×C₄×C₁₁	—	4	1	no	—
100	C₂×C₄×C₁₁	—	4	2	no	—
101	C₂×C₄×C₁₁	—	4	2	no	—
102	C₂×C₄×C₁₁	—	4	4	no	—
103	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
104	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
105	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
106	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
107	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
109	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
110	C₂×C₄×C₁₁	#131	1	2	yes	—
111	C₈×C₁₁	—	2	1	no	—
112	C₈×C₁₁	—	2	1	no	—
113	C₈×C₁₁	—	4	2	no	—
114	C₈×C₁₁	#121	1	2	yes	—
115	C₈×C₁₁	#124	1	1	yes	characteristic
116	C₈×C₁₁	#127	1	1	yes	characteristic
117	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
118	C₂×C₄×D₄	C₄×C₁₁	1	1	yes	characteristic
119	C₂×M₃₂	C₂²×C₁₁	1	2	yes	—
120	C₂×M₃₂	C₂²×C₁₁	1	2	yes	—
121	#436	—	2	1	no	—
122	#436	—	2	1	no	—
123	#436	—	2	1	no	—
124	#436	—	2	1	no	—
125	C₂×C₄⋊C₈	C₄×C₁₁	1	1	yes	characteristic
126	C₂×C₂²⋊C₈	C₄×C₁₁	1	2	yes	—
127	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
128	C₄⋊C₁₆	—	2	1	no	—
129	C₄⋊C₁₆	—	2	1	no	—
130	#349	—	2	8	no	—
131	#346	—	2	1	no	—
132	C₄×C₁₆	—	2	1	no	—
133	C₂²×C₁₁	—	2	1	no	—
134	C₂²×C₁₁	—	2	1	no	—
135	C₂²×C₁₁	—	4	2	no	—
136	C₂²×C₁₁	—	4	2	no	—
137	C₂²×C₁₁	—	4	2	no	—
138	C₂²×C₁₁	—	8	4	no	—
139	C₂²×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
140	C₂²×C₁₁	C₈×D₄	1	2	yes	—
141	C₄×C₁₁	—	2	1	no	—
142	C₄×C₁₁	—	2	1	no	—
143	C₄×C₁₁	—	2	1	no	—
144	C₄×C₁₁	—	4	2	no	—
145	C₄×C₁₁	#349	1	2	yes	complemented
146	C₄×C₁₁	#390	1	1	yes	characteristic
147	C₄×C₁₁	#408	1	1	yes	characteristic
148	C₄×C₁₁	#436	1	2	yes	—
149	C₂²×D₄	C₈×C₁₁	1	1	yes	characteristic
150	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
151	C₂×M₁₆	—	2	4	no	—
152	C₂×M₁₆	—	2	2	no	—
153	C₂×M₁₆	—	2	2	no	—
154	C₂×M₁₆	—	2	4	no	—
155	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
156	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
157	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
158	C₄×D₄	—	2	1	no	—
159	C₄×D₄	—	2	1	no	—
160	C₄×D₄	—	2	1	no	—
161	C₄×D₄	—	2	1	no	—
162	C₂×C₄⋊C₄	C₈×C₁₁	1	1	yes	characteristic
163	C₂×C₂²⋊C₄	C₈×C₁₁	1	2	yes	—
164	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
165	M₃₂	—	2	2	no	—
166	M₃₂	—	2	4	no	—
167	M₃₂	D₄×C₁₁	1	4	yes	complemented
168	C₂×C₁₆	—	2	2	no	—
169	C₂×C₁₆	—	2	2	no	—
170	C₄⋊C₈	—	2	1	no	—
171	C₄⋊C₈	—	2	1	no	—
172	C₂²⋊C₈	—	2	2	no	—
173	C₂²⋊C₈	—	2	2	no	—
174	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
175	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
176	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
177	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
178	C₂×C₁₁	—	2	2	no	—
179	C₂×C₁₁	—	8	2	no	—
180	C₂×C₁₁	#1954	1	1	yes	characteristic
181	C₂×C₁₁	C₂×#349	1	1	yes	characteristic
182	C₂×C₁₁	#2115	1	1	yes	characteristic
183	C₂⁴	C₂×C₈×C₁₁	1	2	yes	—
184	C₂×D₄	—	2	1	no	—
185	C₂×D₄	—	2	1	no	—
186	C₂×D₄	—	4	2	no	—
187	C₂²×C₄	—	2	2	no	—
188	C₂²×C₄	—	2	4	no	—
189	C₂²×C₄	—	2	2	no	—
190	C₂²×C₄	—	2	4	no	—
191	C₂²×C₄	C₂×C₈×C₁₁	1	2	yes	—
192	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
193	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
194	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
195	M₁₆	—	4	4	no	—
196	M₁₆	—	4	2	no	—
197	M₁₆	—	4	2	no	—
198	C₂×C₈	—	2	2	no	—
199	C₂×C₈	—	2	2	no	—
200	C₂×C₈	—	2	4	no	—
201	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
202	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
204	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
205	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
206	C₂×C₈	C₁₁×#41	1	2	yes	—
207	C₄⋊C₄	—	2	1	no	—
208	C₄⋊C₄	—	2	1	no	—
209	C₂²⋊C₄	—	2	2	no	—
210	C₂²⋊C₄	—	2	2	no	—
211	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
212	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
213	C₄²	C₁₁×M₁₆	1	1	yes	characteristic
214	C₄²	C₁₁×M₁₆	1	1	yes	characteristic
215	C₁₆	—	2	4	no	—
216	C₁₆	—	4	2	no	—
217	C₁₁	#13194	1	1	yes	characteristic, direct product factor, Sylow
218	C₂³	—	2	2	no	—
219	C₂³	—	2	4	no	—
220	C₂³	—	4	2	no	—
221	C₂³	—	4	2	no	—
222	C₂³	C₂²×C₈×C₁₁	1	1	yes	characteristic
223	D₄	—	4	2	no	—
224	D₄	—	4	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	4	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	4	no	—
232	C₂×C₄	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
233	C₂×C₄	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
234	C₂×C₄	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
235	C₂×C₄	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
236	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
238	C₂×C₄	C₂×C₁₁×M₁₆	1	1	yes	characteristic
239	C₂×C₄	C₁₁×#131	1	2	yes	—
240	C₈	—	2	1	no	—
241	C₈	—	2	1	no	—
242	C₈	—	4	2	no	—
243	C₈	C₁₁×#121	1	2	yes	—
244	C₈	C₁₁×#124	1	1	yes	characteristic
245	C₈	C₁₁×#127	1	1	yes	characteristic
246	C₂²	—	2	1	no	—
247	C₂²	—	2	1	no	—
248	C₂²	—	4	2	no	—
249	C₂²	—	4	2	no	—
250	C₂²	—	4	2	no	—
251	C₂²	—	8	4	no	—
252	C₂²	C₂×C₁₁×C₂²⋊C₈	1	1	yes	characteristic
253	C₂²	C₈×D₄×C₁₁	1	2	yes	—
254	C₄	—	2	1	no	—
255	C₄	—	2	1	no	—
256	C₄	—	2	1	no	—
257	C₄	—	4	2	no	—
258	C₄	C₁₁×#349	1	2	yes	complemented
259	C₄	C₁₁×#390	1	1	yes	characteristic
260	C₄	C₁₁×#408	1	1	yes	characteristic
261	C₄	C₁₁×#436	1	2	yes	—
262	C₂	—	2	2	no	—
263	C₂	—	8	2	no	—
264	C₂	C₁₁×#1954	1	1	yes	characteristic
265	C₂	C₂×C₁₁×#349	1	1	yes	characteristic
266	C₂	C₁₁×#2115	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₈×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
socle	C₂²×C₁₁	C₂×C₂²⋊C₈
prime radical	C₂²×D₄×C₁₁	C₈
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2150	C₂	semidirect
3. C₂×C₁₁×#349	C₂	semidirect
4. C₄×C₁₁×M₃₂	C₂	semidirect
39. C₁₁×M₃₂	D₄	semidirect
50. #13194	C₁₁	direct (N × H)
86. #2150	C₂×C₁₁	semidirect
87. C₂×#349	C₂×C₁₁	semidirect
88. C₄×M₃₂	C₂×C₁₁	semidirect
145. C₄×C₁₁	#349	semidirect
167. M₃₂	D₄×C₁₁	semidirect
217. C₁₁	#13194	direct (N × H)
258. C₄	C₁₁×#349	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#436	2
C₁₁×#2150	2
C₂×C₁₁×#349	2
C₄×C₁₁×M₃₂	2
#13194	11

Subgroups — C11×#13194 #14590387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#13194 #14590387