Subgroups — C₁₁×#13195 #14590388

Order 2816.

438 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#443	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#364	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#350	C₂	1	2	yes	maximal, complemented
4	C₁₁×#2113	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₁×#135	C₄	1	1	yes	characteristic
7	C₂×C₁₁×#131	C₂²	1	2	yes	—
8	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
9	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
11	C₁₁×#443	—	2	2	no	—
12	C₁₁×#443	—	2	2	no	—
13	C₂×C₁₁×#108	C₄	1	1	yes	characteristic
14	C₂×C₁₁×#104	C₄	1	2	yes	—
15	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×#364	—	2	2	no	—
17	C₁₁×#350	—	2	4	no	—
18	C₁₁×C₂²⋊C₁₆	—	2	4	no	—
19	C₄×C₁₁×C₁₆	—	2	2	no	—
20	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
21	C₁₁×#135	—	2	2	no	—
22	C₁₁×#135	—	2	2	no	—
23	C₂×C₁₁×Q₁₆	C₈	1	1	yes	characteristic
24	C₂×C₁₁×SD₁₆	C₈	1	2	yes	—
25	C₂×C₁₁×D₈	C₈	1	1	yes	characteristic
26	C₁₁×#131	—	2	2	no	—
27	C₁₁×#131	—	2	2	no	—
28	C₁₁×#131	—	2	2	no	—
29	C₁₁×#131	—	2	2	no	—
30	C₂×C₁₁×M₁₆	—	2	2	no	—
31	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₁₁	—	2	2	no	—
33	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
35	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
36	C₁₁×M₃₂	—	2	2	no	—
37	C₁₁×M₃₂	—	2	2	no	—
38	C₂×C₁₁×C₁₆	—	2	1	no	—
39	C₂×C₁₁×C₁₆	—	2	1	no	—
40	C₂×C₁₁×C₁₆	—	2	1	no	—
41	C₂×C₁₁×C₁₆	—	2	1	no	—
42	C₂×C₁₁×C₁₆	—	2	2	no	—
43	C₂×C₁₁×C₁₆	D₄	1	2	yes	—
44	C₂×C₁₁×C₁₆	D₄	1	2	yes	—
45	C₁₁×#108	—	2	2	no	—
46	C₁₁×#104	—	2	4	no	—
47	C₄×C₈×C₁₁	D₄	1	2	yes	—
48	C₄×C₈×C₁₁	D₄	1	2	yes	—
49	#13195	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₁₁×#41	—	2	2	no	—
51	C₁₁×#41	—	2	2	no	—
52	C₁₁×#41	—	2	2	no	—
53	C₁₁×#41	—	2	2	no	—
54	C₂×Q₈×C₁₁	C₂×C₈	1	2	yes	—
55	C₂×D₄×C₁₁	—	2	2	no	—
56	C₂×D₄×C₁₁	C₂×C₈	1	2	yes	—
57	C₂²×C₄×C₁₁	—	2	1	no	—
58	C₂²×C₄×C₁₁	—	2	2	no	—
59	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
60	C₁₁×Q₁₆	—	2	2	no	—
61	C₁₁×SD₁₆	—	2	4	no	—
62	C₁₁×D₈	—	2	2	no	—
63	C₁₁×M₁₆	—	2	2	no	—
64	C₁₁×M₁₆	—	2	2	no	—
65	C₁₁×M₁₆	—	4	2	no	—
66	C₁₁×M₁₆	—	4	2	no	—
67	C₂×C₈×C₁₁	—	2	2	no	—
68	C₂×C₈×C₁₁	—	4	2	no	—
69	C₂×C₈×C₁₁	—	4	2	no	—
70	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
71	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
72	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
73	C₂×C₈×C₁₁	M₁₆	1	2	yes	—
74	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
75	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
76	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
77	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
79	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
80	C₄²×C₁₁	—	2	1	no	—
81	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
82	C₁₁×C₁₆	—	2	2	no	—
83	C₁₁×C₁₆	—	2	2	no	—
84	C₁₁×C₁₆	—	4	2	no	—
85	C₂×#443	C₂×C₁₁	1	1	yes	characteristic
86	C₂×#364	C₂×C₁₁	1	1	yes	characteristic, complemented
87	C₂×#350	C₂×C₁₁	1	2	yes	complemented
88	#2113	C₂×C₁₁	1	2	yes	complemented
89	C₂×C₄×C₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
90	C₂³×C₁₁	—	2	2	no	—
91	C₂³×C₁₁	#131	1	1	yes	characteristic
92	Q₈×C₁₁	—	2	2	no	—
93	Q₈×C₁₁	—	2	2	no	—
94	D₄×C₁₁	—	2	2	no	—
95	D₄×C₁₁	—	2	2	no	—
96	D₄×C₁₁	—	4	2	no	—
97	D₄×C₁₁	—	4	2	no	—
98	C₂×C₄×C₁₁	—	2	4	no	—
99	C₂×C₄×C₁₁	—	2	2	no	—
100	C₂×C₄×C₁₁	—	2	2	no	—
101	C₂×C₄×C₁₁	—	4	2	no	—
102	C₂×C₄×C₁₁	—	4	2	no	—
103	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
105	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
106	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
107	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
108	C₂×C₄×C₁₁	#131	1	1	yes	characteristic
109	C₈×C₁₁	—	4	2	no	—
110	C₈×C₁₁	C₂²⋊C₈	1	2	yes	—
111	C₈×C₁₁	C₂²⋊C₈	1	2	yes	—
112	C₈×C₁₁	#121	1	1	yes	characteristic
113	C₈×C₁₁	#121	1	1	yes	characteristic
114	C₈×C₁₁	#124	1	1	yes	characteristic
115	C₈×C₁₁	#127	1	1	yes	characteristic
116	C₂×#135	C₄×C₁₁	1	1	yes	characteristic
117	C₂×#131	C₂²×C₁₁	1	2	yes	—
118	C₂×M₃₂	C₂²×C₁₁	1	2	yes	—
119	C₂²×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
120	C₂²×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
121	#443	—	2	2	no	—
122	#443	—	2	2	no	—
123	C₂×#108	C₄×C₁₁	1	1	yes	characteristic
124	C₂×#104	C₄×C₁₁	1	2	yes	—
125	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
126	#364	—	2	2	no	—
127	#350	—	2	4	no	—
128	C₂²⋊C₁₆	—	2	4	no	—
129	C₄×C₁₆	—	2	2	no	—
130	C₂²×C₁₁	—	2	2	no	—
131	C₂²×C₁₁	—	4	4	no	—
132	C₂²×C₁₁	—	4	2	no	—
133	C₂²×C₁₁	#408	1	1	yes	characteristic
134	C₂²×C₁₁	C₈×D₄	1	1	yes	characteristic
135	C₂²×C₁₁	#436	1	1	yes	characteristic
136	C₄×C₁₁	—	2	4	no	—
137	C₄×C₁₁	—	4	2	no	—
138	C₄×C₁₁	#390	1	1	yes	characteristic
139	C₄×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
140	C₄×C₁₁	C₈×D₄	1	1	yes	characteristic
141	C₄×C₁₁	#436	1	1	yes	characteristic
142	C₂×#41	C₂×C₄×C₁₁	1	2	yes	—
143	#135	—	2	2	no	—
144	#135	—	2	2	no	—
145	C₂×Q₁₆	C₈×C₁₁	1	1	yes	characteristic
146	C₂×SD₁₆	C₈×C₁₁	1	2	yes	—
147	C₂×D₈	C₈×C₁₁	1	1	yes	characteristic
148	#131	—	2	2	no	—
149	#131	—	2	2	no	—
150	#131	—	2	2	no	—
151	#131	—	2	2	no	—
152	C₂×M₁₆	—	2	2	no	—
153	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
154	C₂²×C₈	—	2	2	no	—
155	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
156	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
157	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
158	M₃₂	—	2	2	no	—
159	M₃₂	—	2	2	no	—
160	C₂×C₁₆	—	2	1	no	—
161	C₂×C₁₆	—	2	1	no	—
162	C₂×C₁₆	—	2	1	no	—
163	C₂×C₁₆	—	2	1	no	—
164	C₂×C₁₆	—	2	2	no	—
165	C₂×C₁₆	D₄×C₁₁	1	2	yes	—
166	C₂×C₁₆	D₄×C₁₁	1	2	yes	—
167	#108	—	2	2	no	—
168	#104	—	2	4	no	—
169	C₄×C₈	D₄×C₁₁	1	2	yes	—
170	C₄×C₈	D₄×C₁₁	1	2	yes	—
171	C₂×C₁₁	—	2	1	no	—
172	C₂×C₁₁	—	2	1	no	—
173	C₂×C₁₁	—	8	2	no	—
174	C₂×C₁₁	#1954	1	1	yes	characteristic
175	C₂×C₁₁	#2170	1	2	yes	—
176	#41	—	2	2	no	—
177	#41	—	2	2	no	—
178	#41	—	2	2	no	—
179	#41	—	2	2	no	—
180	C₂×Q₈	C₂×C₈×C₁₁	1	2	yes	—
181	C₂×D₄	—	2	2	no	—
182	C₂×D₄	C₂×C₈×C₁₁	1	2	yes	—
183	C₂²×C₄	—	2	1	no	—
184	C₂²×C₄	—	2	2	no	—
185	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
186	Q₁₆	—	2	2	no	—
187	SD₁₆	—	2	4	no	—
188	D₈	—	2	2	no	—
189	M₁₆	—	2	2	no	—
190	M₁₆	—	2	2	no	—
191	M₁₆	—	4	2	no	—
192	M₁₆	—	4	2	no	—
193	C₂×C₈	—	2	2	no	—
194	C₂×C₈	—	4	2	no	—
195	C₂×C₈	—	4	2	no	—
196	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
197	C₂×C₈	C₂×C₈×C₁₁	1	1	yes	characteristic
198	C₂×C₈	C₂×C₈×C₁₁	1	1	yes	characteristic
199	C₂×C₈	C₁₁×M₁₆	1	2	yes	—
200	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
201	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
202	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
203	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
204	C₂×C₈	C₁₁×#41	1	1	yes	characteristic
205	C₂×C₈	C₁₁×#41	1	1	yes	characteristic
206	C₄²	—	2	1	no	—
207	C₄²	C₁₁×C₂²⋊C₄	1	2	yes	—
208	C₁₆	—	2	2	no	—
209	C₁₆	—	2	2	no	—
210	C₁₆	—	4	2	no	—
211	C₁₁	#13195	1	1	yes	characteristic, direct product factor, Sylow
212	C₂³	—	2	2	no	—
213	C₂³	C₁₁×#131	1	1	yes	characteristic
214	Q₈	—	2	2	no	—
215	Q₈	—	2	2	no	—
216	D₄	—	2	2	no	—
217	D₄	—	2	2	no	—
218	D₄	—	4	2	no	—
219	D₄	—	4	2	no	—
220	C₂×C₄	—	2	4	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
227	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
228	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
229	C₂×C₄	C₂×C₁₁×M₁₆	1	1	yes	characteristic
230	C₂×C₄	C₁₁×#131	1	1	yes	characteristic
231	C₈	—	4	2	no	—
232	C₈	C₁₁×C₂²⋊C₈	1	2	yes	—
233	C₈	C₁₁×C₂²⋊C₈	1	2	yes	—
234	C₈	C₁₁×#121	1	1	yes	characteristic
235	C₈	C₁₁×#121	1	1	yes	characteristic
236	C₈	C₁₁×#124	1	1	yes	characteristic
237	C₈	C₁₁×#127	1	1	yes	characteristic
238	C₂²	—	2	2	no	—
239	C₂²	—	4	4	no	—
240	C₂²	—	4	2	no	—
241	C₂²	C₁₁×#408	1	1	yes	characteristic
242	C₂²	C₈×D₄×C₁₁	1	1	yes	characteristic
243	C₂²	C₁₁×#436	1	1	yes	characteristic
244	C₄	—	2	4	no	—
245	C₄	—	4	2	no	—
246	C₄	C₁₁×#390	1	1	yes	characteristic
247	C₄	C₂×C₁₁×C₂²⋊C₈	1	1	yes	characteristic
248	C₄	C₈×D₄×C₁₁	1	1	yes	characteristic
249	C₄	C₁₁×#436	1	1	yes	characteristic
250	C₂	—	2	1	no	—
251	C₂	—	2	1	no	—
252	C₂	—	8	2	no	—
253	C₂	C₁₁×#1954	1	1	yes	characteristic
254	C₂	C₁₁×#2170	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₁₁	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
socle	C₂²×C₁₁	C₈×D₄
prime radical	C₂×C₁₁×#135	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₁ ◁ C₂²×C₁₁×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#364	C₂	semidirect
3. C₂×C₁₁×#350	C₂	semidirect
4. C₁₁×#2113	C₂	semidirect
5. C₂×C₄×C₁₁×C₁₆	C₂	semidirect
49. #13195	C₁₁	direct (N × H)
86. C₂×#364	C₂×C₁₁	semidirect
87. C₂×#350	C₂×C₁₁	semidirect
88. #2113	C₂×C₁₁	semidirect
89. C₂×C₄×C₁₆	C₂×C₁₁	semidirect
211. C₁₁	#13195	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#443	2
C₂×C₁₁×#364	2
C₂×C₁₁×#350	2
C₁₁×#2113	2
C₂×C₄×C₁₁×C₁₆	2
#13195	11

Subgroups — C11×#13195 #14590388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#13195 #14590388