Subgroups — C₁₁×#11947 #14589140

Order 2816.

354 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3169	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2162	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#335	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1364	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1361	C₂	1	2	yes	maximal, complemented
6	C₁₁×#532	—	2	1	no	—
7	C₁₁×#500	C₂²	1	1	yes	characteristic
8	C₁₁×#493	C₂²	1	1	yes	characteristic
9	C₁₁×#486	—	2	1	no	—
10	C₁₁×#466	—	2	1	no	—
11	C₁₁×#466	C₄	1	2	yes	—
12	C₄×C₁₁×D₈	—	2	1	no	—
13	C₄×C₁₁×D₈	C₄	1	2	yes	—
14	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
15	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
17	C₁₁×C₂²⋊C₁₆	—	2	1	no	—
18	C₄×C₁₁×C₁₆	—	2	1	no	—
19	C₁₁×#335	—	2	1	no	—
20	C₁₁×#335	C₂²	1	2	yes	—
21	C₂×C₁₁×#41	—	4	1	no	—
22	C₂×C₁₁×D₈	—	2	1	no	—
23	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₁	—	4	1	no	—
25	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
27	C₁₁×C₄⋊Q₈	—	2	1	no	—
28	C₁₁×#127	—	2	1	no	—
29	C₁₁×#124	—	4	1	no	—
30	C₁₁×#121	—	2	2	no	—
31	C₁₁×#121	—	4	1	no	—
32	C₄×D₄×C₁₁	—	2	2	no	—
33	C₄×D₄×C₁₁	—	4	1	no	—
34	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
35	C₂×C₁₁×C₁₆	—	2	2	no	—
36	C₁₁×#107	—	2	1	no	—
37	C₁₁×#107	C₂×C₄	1	2	yes	—
38	C₁₁×C₄⋊C₈	—	2	2	no	—
39	C₁₁×C₄⋊C₈	—	4	1	no	—
40	C₁₁×#102	—	2	2	no	—
41	C₁₁×#102	—	2	2	no	—
42	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
44	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
45	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
46	#11947	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₁₁×#41	—	8	2	no	—
48	C₁₁×#41	—	8	2	no	—
49	C₂×Q₈×C₁₁	—	4	1	no	—
50	C₂×D₄×C₁₁	—	2	2	no	—
51	C₂×D₄×C₁₁	—	4	2	no	—
52	C₂×D₄×C₁₁	—	4	1	no	—
53	C₂×D₄×C₁₁	—	4	1	no	—
54	C₂²×C₄×C₁₁	—	4	2	no	—
55	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
57	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
58	C₁₁×D₈	—	4	2	no	—
59	C₁₁×D₈	—	4	2	no	—
60	C₂×C₈×C₁₁	—	2	2	no	—
61	C₂×C₈×C₁₁	—	4	1	no	—
62	C₂×C₈×C₁₁	—	4	2	no	—
63	C₂×C₈×C₁₁	—	8	2	no	—
64	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
68	C₁₁×C₄⋊C₄	—	2	2	no	—
69	C₁₁×C₄⋊C₄	—	4	1	no	—
70	C₁₁×C₂²⋊C₄	—	4	2	no	—
71	C₁₁×C₂²⋊C₄	—	4	2	no	—
72	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₄²×C₁₁	D₈	1	1	yes	characteristic
74	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
75	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
76	C₁₁×C₁₆	—	4	2	no	—
77	#3169	C₂×C₁₁	1	1	yes	characteristic
78	#2162	C₂×C₁₁	1	1	yes	characteristic, complemented
79	C₂×#335	C₂×C₁₁	1	1	yes	characteristic, complemented
80	#1364	C₂×C₁₁	1	2	yes	complemented
81	#1361	C₂×C₁₁	1	2	yes	complemented
82	C₂³×C₁₁	—	4	2	no	—
83	C₂³×C₁₁	#102	1	1	yes	characteristic
84	Q₈×C₁₁	—	8	1	no	—
85	Q₈×C₁₁	—	8	1	no	—
86	D₄×C₁₁	—	4	2	no	—
87	D₄×C₁₁	—	4	2	no	—
88	D₄×C₁₁	—	8	2	no	—
89	D₄×C₁₁	—	8	4	no	—
90	D₄×C₁₁	—	8	1	no	—
91	D₄×C₁₁	—	8	1	no	—
92	C₂×C₄×C₁₁	—	2	1	no	—
93	C₂×C₄×C₁₁	—	2	1	no	—
94	C₂×C₄×C₁₁	—	4	1	no	—
95	C₂×C₄×C₁₁	—	4	2	no	—
96	C₂×C₄×C₁₁	—	8	4	no	—
97	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
98	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
99	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
100	C₂×C₄×C₁₁	D₁₆	1	2	yes	—
101	C₂×C₄×C₁₁	SD₃₂	1	2	yes	—
102	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
104	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
105	C₈×C₁₁	—	2	1	no	—
106	C₈×C₁₁	—	2	1	no	—
107	C₈×C₁₁	—	2	1	no	—
108	C₈×C₁₁	—	8	2	no	—
109	C₈×C₁₁	#135	1	2	yes	—
110	#532	—	2	1	no	—
111	#500	C₂²×C₁₁	1	1	yes	characteristic
112	#493	C₂²×C₁₁	1	1	yes	characteristic
113	#486	—	2	1	no	—
114	#466	—	2	1	no	—
115	#466	C₄×C₁₁	1	2	yes	—
116	C₄×D₈	—	2	1	no	—
117	C₄×D₈	C₄×C₁₁	1	2	yes	—
118	C₂×C₄⋊C₈	—	2	1	no	—
119	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
120	C₄⋊C₁₆	C₂²×C₁₁	1	2	yes	—
121	C₂²⋊C₁₆	—	2	1	no	—
122	C₄×C₁₆	—	2	1	no	—
123	#335	—	2	1	no	—
124	#335	C₂²×C₁₁	1	2	yes	—
125	C₂²×C₁₁	—	2	1	no	—
126	C₂²×C₁₁	—	2	1	no	—
127	C₂²×C₁₁	—	8	2	no	—
128	C₂²×C₁₁	—	8	2	no	—
129	C₂²×C₁₁	—	8	2	no	—
130	C₂²×C₁₁	#357	1	2	yes	—
131	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
132	C₄×C₁₁	—	2	1	no	—
133	C₄×C₁₁	—	2	1	no	—
134	C₄×C₁₁	—	2	1	no	—
135	C₄×C₁₁	—	8	2	no	—
136	C₄×C₁₁	#357	1	2	yes	—
137	C₄×C₁₁	#413	1	1	yes	characteristic
138	C₄×C₁₁	#416	1	1	yes	characteristic
139	C₄×C₁₁	C₂×D₁₆	1	1	yes	characteristic
140	C₄×C₁₁	C₂×SD₃₂	1	1	yes	characteristic
141	C₂×#41	—	4	1	no	—
142	C₂×D₈	—	2	1	no	—
143	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
144	C₂²×C₈	—	4	1	no	—
145	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
146	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
147	C₄⋊Q₈	—	2	1	no	—
148	#127	—	2	1	no	—
149	#124	—	4	1	no	—
150	#121	—	2	2	no	—
151	#121	—	4	1	no	—
152	C₄×D₄	—	2	2	no	—
153	C₄×D₄	—	4	1	no	—
154	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
155	C₂×C₁₆	—	2	2	no	—
156	#107	—	2	1	no	—
157	#107	C₂×C₄×C₁₁	1	2	yes	—
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	4	1	no	—
160	#102	—	2	2	no	—
161	#102	—	2	2	no	—
162	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
163	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
164	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
165	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
166	C₂×C₁₁	—	2	2	no	—
167	C₂×C₁₁	—	16	2	no	—
168	C₂×C₁₁	#1540	1	1	yes	characteristic
169	C₂×C₁₁	C₂×#357	1	1	yes	characteristic
170	C₂×C₁₁	#2148	1	1	yes	characteristic
171	#41	—	8	2	no	—
172	#41	—	8	2	no	—
173	C₂×Q₈	—	4	1	no	—
174	C₂×D₄	—	2	2	no	—
175	C₂×D₄	—	4	2	no	—
176	C₂×D₄	—	4	1	no	—
177	C₂×D₄	—	4	1	no	—
178	C₂²×C₄	—	4	2	no	—
179	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
180	C₂²×C₄	C₁₁×D₈	1	1	yes	characteristic
181	C₂²×C₄	C₁₁×SD₁₆	1	1	yes	characteristic
182	D₈	—	4	2	no	—
183	D₈	—	4	2	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	4	1	no	—
186	C₂×C₈	—	4	2	no	—
187	C₂×C₈	—	8	2	no	—
188	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
189	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
191	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
192	C₄⋊C₄	—	2	2	no	—
193	C₄⋊C₄	—	4	1	no	—
194	C₂²⋊C₄	—	4	2	no	—
195	C₂²⋊C₄	—	4	2	no	—
196	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
197	C₄²	C₁₁×D₈	1	1	yes	characteristic
198	C₄²	C₁₁×SD₁₆	1	1	yes	characteristic
199	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
200	C₁₆	—	4	2	no	—
201	C₁₁	#11947	1	1	yes	characteristic, direct product factor, Sylow
202	C₂³	—	4	2	no	—
203	C₂³	C₁₁×#102	1	1	yes	characteristic
204	Q₈	—	8	1	no	—
205	Q₈	—	8	1	no	—
206	D₄	—	4	2	no	—
207	D₄	—	4	2	no	—
208	D₄	—	8	2	no	—
209	D₄	—	8	4	no	—
210	D₄	—	8	1	no	—
211	D₄	—	8	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	4	1	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	8	4	no	—
217	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
218	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
219	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
220	C₂×C₄	C₁₁×D₁₆	1	2	yes	—
221	C₂×C₄	C₁₁×SD₃₂	1	2	yes	—
222	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
224	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
225	C₈	—	2	1	no	—
226	C₈	—	2	1	no	—
227	C₈	—	2	1	no	—
228	C₈	—	8	2	no	—
229	C₈	C₁₁×#135	1	2	yes	—
230	C₂²	—	2	1	no	—
231	C₂²	—	2	1	no	—
232	C₂²	—	8	2	no	—
233	C₂²	—	8	2	no	—
234	C₂²	—	8	2	no	—
235	C₂²	C₁₁×#357	1	2	yes	—
236	C₂²	C₂×C₁₁×#102	1	1	yes	characteristic
237	C₄	—	2	1	no	—
238	C₄	—	2	1	no	—
239	C₄	—	2	1	no	—
240	C₄	—	8	2	no	—
241	C₄	C₁₁×#357	1	2	yes	—
242	C₄	C₁₁×#413	1	1	yes	characteristic
243	C₄	C₁₁×#416	1	1	yes	characteristic
244	C₄	C₂×C₁₁×D₁₆	1	1	yes	characteristic
245	C₄	C₂×C₁₁×SD₃₂	1	1	yes	characteristic
246	C₂	—	2	2	no	—
247	C₂	—	16	2	no	—
248	C₂	C₁₁×#1540	1	1	yes	characteristic
249	C₂	C₂×C₁₁×#357	1	1	yes	characteristic
250	C₂	C₁₁×#2148	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	#102
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
socle	C₂²×C₁₁	C₂×#102
prime radical	C₁₁×#3169	C₂
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2162	C₂	semidirect
3. C₂×C₁₁×#335	C₂	semidirect
4. C₁₁×#1364	C₂	semidirect
5. C₁₁×#1361	C₂	semidirect
46. #11947	C₁₁	direct (N × H)
78. #2162	C₂×C₁₁	semidirect
79. C₂×#335	C₂×C₁₁	semidirect
80. #1364	C₂×C₁₁	semidirect
81. #1361	C₂×C₁₁	semidirect
201. C₁₁	#11947	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×#3169	2
C₁₁×#2162	2
C₂×C₁₁×#335	2
C₁₁×#1364	2
C₁₁×#1361	2
#11947	11

Subgroups — C11×#11947 #14589140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11947 #14589140