Subgroups — C₁₁×#22256 #14599449

Order 2816.

614 conjugacy classes of subgroups.

The subgroup lattice has 250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3160	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2960	C₂	1	2	yes	maximal
3	C₁₁×#1994	C₂	1	2	yes	maximal
4	C₁₁×#1922	C₂	1	8	yes	maximal
5	C₁₁×#1837	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1744	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#533	C₂²	1	2	yes	—
8	C₁₁×#500	C₄	1	1	yes	characteristic, complemented
9	C₁₁×#500	C₄	1	1	yes	characteristic, complemented
10	C₁₁×#499	C₄	1	4	yes	complemented
11	C₁₁×#498	C₄	1	2	yes	complemented
12	C₁₁×#446	—	2	2	no	—
13	C₁₁×#446	—	2	2	no	—
14	C₈×Q₈×C₁₁	—	2	2	no	—
15	C₈×Q₈×C₁₁	—	2	2	no	—
16	C₁₁×#427	C₂²	1	4	yes	—
17	C₁₁×#424	C₂²	1	4	yes	—
18	C₁₁×#423	C₂²	1	2	yes	—
19	C₁₁×#405	C₂²	1	4	yes	—
20	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
22	C₄³×C₁₁	C₂²	1	1	yes	characteristic
23	C₁₁×#341	C₂²	1	4	yes	—
24	C₁₁×#339	C₂²	1	8	yes	—
25	C₁₁×#336	C₂²	1	4	yes	—
26	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
27	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
28	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
29	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
30	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
31	C₁₁×#125	C₂×C₄	1	4	yes	—
32	C₁₁×C₂²⋊Q₈	—	2	2	no	—
33	C₁₁×C₂²⋊Q₈	—	2	2	no	—
34	C₄×Q₈×C₁₁	—	2	2	no	—
35	C₄×Q₈×C₁₁	—	2	2	no	—
36	C₁₁×#117	C₂³	1	4	yes	—
37	C₂×C₄²×C₁₁	—	2	1	no	—
38	C₂×C₄²×C₁₁	—	2	1	no	—
39	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
40	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
41	C₁₁×#107	C₂×C₄	1	4	yes	—
42	C₁₁×#107	C₂×C₄	1	4	yes	—
43	C₁₁×#106	C₂×C₄	1	8	yes	—
44	C₁₁×C₄⋊C₈	—	2	4	no	—
45	C₁₁×C₄⋊C₈	—	2	4	no	—
46	C₁₁×C₄⋊C₈	—	2	2	no	—
47	C₁₁×C₄⋊C₈	—	2	2	no	—
48	C₁₁×#97	—	2	4	no	—
49	C₄×C₈×C₁₁	—	2	4	no	—
50	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
51	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
52	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
53	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
54	C₄×C₈×C₁₁	D₄	1	2	yes	—
55	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
56	#22256	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₂×Q₈×C₁₁	—	2	2	no	—
58	C₂×Q₈×C₁₁	—	2	2	no	—
59	C₂²×C₄×C₁₁	—	2	2	no	—
60	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
61	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
63	C₁₁×M₁₆	—	2	8	no	—
64	C₂×C₈×C₁₁	—	2	4	no	—
65	C₂×C₈×C₁₁	—	2	4	no	—
66	C₂×C₈×C₁₁	—	2	4	no	—
67	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
68	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
69	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
70	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
71	C₁₁×C₄⋊C₄	—	2	4	no	—
72	C₁₁×C₄⋊C₄	—	2	4	no	—
73	C₁₁×C₄⋊C₄	—	2	2	no	—
74	C₁₁×C₄⋊C₄	—	2	2	no	—
75	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
76	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
77	C₁₁×C₂²⋊C₄	—	2	4	no	—
78	C₄²×C₁₁	—	2	4	no	—
79	C₄²×C₁₁	—	2	4	no	—
80	C₄²×C₁₁	—	2	4	no	—
81	C₄²×C₁₁	—	4	2	no	—
82	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
83	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
84	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
85	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
86	#3160	C₂×C₁₁	1	1	yes	characteristic
87	#2960	C₂×C₁₁	1	2	yes	—
88	#1994	C₂×C₁₁	1	2	yes	—
89	#1922	C₂×C₁₁	1	8	yes	—
90	#1837	C₂×C₁₁	1	1	yes	characteristic
91	#1744	C₂×C₁₁	1	1	yes	characteristic
92	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
93	Q₈×C₁₁	—	4	4	no	—
94	Q₈×C₁₁	—	4	4	no	—
95	C₂×C₄×C₁₁	—	2	2	no	—
96	C₂×C₄×C₁₁	—	2	2	no	—
97	C₂×C₄×C₁₁	—	2	4	no	—
98	C₂×C₄×C₁₁	—	2	4	no	—
99	C₂×C₄×C₁₁	—	2	4	no	—
100	C₂×C₄×C₁₁	—	4	2	no	—
101	C₂×C₄×C₁₁	—	4	2	no	—
102	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
103	C₂×C₄×C₁₁	C₄×D₄	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	C₂³×C₄	1	1	yes	characteristic
107	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
108	C₂×C₄×C₁₁	2₋¹⁺⁴	1	4	yes	—
109	C₈×C₁₁	—	2	2	no	—
110	C₈×C₁₁	—	2	2	no	—
111	C₈×C₁₁	—	2	2	no	—
112	C₈×C₁₁	—	2	2	no	—
113	C₈×C₁₁	—	4	4	no	—
114	#533	C₂²×C₁₁	1	2	yes	—
115	#500	C₄×C₁₁	1	1	yes	characteristic, complemented
116	#500	C₄×C₁₁	1	1	yes	characteristic, complemented
117	#499	C₄×C₁₁	1	4	yes	complemented
118	#498	C₄×C₁₁	1	2	yes	complemented
119	#446	—	2	2	no	—
120	#446	—	2	2	no	—
121	C₈×Q₈	—	2	2	no	—
122	C₈×Q₈	—	2	2	no	—
123	#427	C₂²×C₁₁	1	4	yes	—
124	#424	C₂²×C₁₁	1	4	yes	—
125	#423	C₂²×C₁₁	1	2	yes	—
126	#405	C₂²×C₁₁	1	4	yes	—
127	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
128	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
129	C₄³	C₂²×C₁₁	1	1	yes	characteristic
130	#341	C₂²×C₁₁	1	4	yes	—
131	#339	C₂²×C₁₁	1	8	yes	—
132	#336	C₂²×C₁₁	1	4	yes	—
133	C₂²×C₁₁	—	2	1	no	—
134	C₂²×C₁₁	—	2	1	no	—
135	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
136	C₂²×C₁₁	#541	1	2	yes	—
137	C₄×C₁₁	—	2	1	no	—
138	C₄×C₁₁	—	2	1	no	—
139	C₄×C₁₁	—	4	4	no	—
140	C₄×C₁₁	—	4	4	no	—
141	C₄×C₁₁	—	4	4	no	—
142	C₄×C₁₁	#443	1	2	yes	—
143	C₄×C₁₁	#444	1	2	yes	—
144	C₄×C₁₁	#519	1	2	yes	—
145	C₄×C₁₁	#536	1	2	yes	—
146	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
147	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
148	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
149	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
150	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
151	#125	C₂×C₄×C₁₁	1	4	yes	—
152	C₂²⋊Q₈	—	2	2	no	—
153	C₂²⋊Q₈	—	2	2	no	—
154	C₄×Q₈	—	2	2	no	—
155	C₄×Q₈	—	2	2	no	—
156	#117	C₂³×C₁₁	1	4	yes	—
157	C₂×C₄²	—	2	1	no	—
158	C₂×C₄²	—	2	1	no	—
159	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
160	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
161	#107	C₂×C₄×C₁₁	1	4	yes	—
162	#107	C₂×C₄×C₁₁	1	4	yes	—
163	#106	C₂×C₄×C₁₁	1	8	yes	—
164	C₄⋊C₈	—	2	4	no	—
165	C₄⋊C₈	—	2	4	no	—
166	C₄⋊C₈	—	2	2	no	—
167	C₄⋊C₈	—	2	2	no	—
168	#97	—	2	4	no	—
169	C₄×C₈	—	2	4	no	—
170	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
171	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
172	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
173	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
174	C₄×C₈	D₄×C₁₁	1	2	yes	—
175	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
176	C₂×C₁₁	—	2	2	no	—
177	C₂×C₁₁	#2327	1	1	yes	characteristic
178	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
179	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
180	C₂×Q₈	—	2	2	no	—
181	C₂×Q₈	—	2	2	no	—
182	C₂²×C₄	—	2	2	no	—
183	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
184	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
185	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
186	M₁₆	—	2	8	no	—
187	C₂×C₈	—	2	4	no	—
188	C₂×C₈	—	2	4	no	—
189	C₂×C₈	—	2	4	no	—
190	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
191	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
192	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
193	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
194	C₄⋊C₄	—	2	4	no	—
195	C₄⋊C₄	—	2	4	no	—
196	C₄⋊C₄	—	2	2	no	—
197	C₄⋊C₄	—	2	2	no	—
198	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
199	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
200	C₂²⋊C₄	—	2	4	no	—
201	C₄²	—	2	4	no	—
202	C₄²	—	2	4	no	—
203	C₄²	—	2	4	no	—
204	C₄²	—	4	2	no	—
205	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
206	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
207	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
208	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
209	C₁₁	#22256	1	1	yes	characteristic, direct product factor, Sylow
210	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
211	Q₈	—	4	4	no	—
212	Q₈	—	4	4	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	—	2	4	no	—
217	C₂×C₄	—	2	4	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
221	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
222	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
223	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
224	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
225	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
226	C₂×C₄	C₁₁×2₋¹⁺⁴	1	4	yes	—
227	C₈	—	2	2	no	—
228	C₈	—	2	2	no	—
229	C₈	—	2	2	no	—
230	C₈	—	2	2	no	—
231	C₈	—	4	4	no	—
232	C₂²	—	2	1	no	—
233	C₂²	—	2	1	no	—
234	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
235	C₂²	C₁₁×#541	1	2	yes	—
236	C₄	—	2	1	no	—
237	C₄	—	2	1	no	—
238	C₄	—	4	4	no	—
239	C₄	—	4	4	no	—
240	C₄	—	4	4	no	—
241	C₄	C₁₁×#443	1	2	yes	—
242	C₄	C₁₁×#444	1	2	yes	—
243	C₄	C₁₁×#519	1	2	yes	—
244	C₄	C₁₁×#536	1	2	yes	—
245	C₂	—	2	2	no	—
246	C₂	C₁₁×#2327	1	1	yes	characteristic
247	C₂	C₂×C₁₁×#443	1	1	yes	characteristic
248	C₂	C₂×C₁₁×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂³×C₁₁	C₂×#41
LCS	G ▷ C₂×C₄ ▷ 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
8. C₁₁×#500	C₄	semidirect
9. C₁₁×#500	C₄	semidirect
10. C₁₁×#499	C₄	semidirect
11. C₁₁×#498	C₄	semidirect
56. #22256	C₁₁	direct (N × H)
115. #500	C₄×C₁₁	semidirect
116. #500	C₄×C₁₁	semidirect
117. #499	C₄×C₁₁	semidirect
118. #498	C₄×C₁₁	semidirect
209. C₁₁	#22256	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×#3160	2
C₁₁×#2960	2
C₁₁×#1994	2
C₁₁×#1922	2
C₁₁×#1837	2
C₁₁×#1744	2
#22256	11

Subgroups — C11×#22256 #14599449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22256 #14599449