Subgroups — C₁₁×#23263 #14600456

Order 2816.

692 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×#125	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1916	C₂	1	4	yes	maximal
3	C₁₁×#1916	C₂	1	4	yes	maximal
4	C₈×C₁₁×C₄⋊C₄	C₂	1	4	yes	maximal
5	C₁₁×#1744	C₂	1	2	yes	maximal
6	C₂×C₁₁×#125	C₄	1	1	yes	characteristic
7	C₂×C₁₁×C₄⋊C₈	C₂²	1	4	yes	—
8	C₂×C₄×C₈×C₁₁	C₂²	1	4	yes	—
9	C₂×C₄×C₈×C₁₁	C₂²	1	4	yes	—
10	C₁₁×#389	C₄	1	2	yes	—
11	C₁₁×#387	C₄	1	4	yes	—
12	C₁₁×#382	C₄	1	1	yes	characteristic
13	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
14	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
15	C₄³×C₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×#336	C₂²	1	4	yes	—
17	C₁₁×#336	C₂²	1	4	yes	—
18	C₁₁×#336	C₂²	1	2	yes	—
19	C₁₁×#336	C₂²	1	4	yes	—
20	C₁₁×#336	C₂²	1	2	yes	—
21	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
22	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
23	C₁₁×#125	C₈	1	8	yes	complemented
24	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
25	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
26	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
27	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
33	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
34	C₁₁×C₄⋊C₈	—	2	8	no	—
35	C₄×C₈×C₁₁	—	2	8	no	—
36	C₄×C₈×C₁₁	—	2	8	no	—
37	C₁₁×#95	C₂×C₄	1	4	yes	—
38	C₁₁×#95	C₂×C₄	1	4	yes	—
39	C₁₁×#95	C₂×C₄	1	4	yes	—
40	#23263	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
43	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
44	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
45	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
47	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
48	C₂×C₈×C₁₁	—	2	4	no	—
49	C₂×C₈×C₁₁	—	2	4	no	—
50	C₂×C₈×C₁₁	—	2	4	no	—
51	C₂×C₈×C₁₁	—	2	4	no	—
52	C₂×C₈×C₁₁	—	2	4	no	—
53	C₂×C₈×C₁₁	#41	1	8	yes	—
54	C₁₁×C₄⋊C₄	—	2	8	no	—
55	C₁₁×C₄⋊C₄	—	4	2	no	—
56	C₁₁×C₄⋊C₄	C₂×C₈	1	16	yes	—
57	C₁₁×C₄⋊C₄	C₂×C₈	1	8	yes	—
58	C₄²×C₁₁	—	2	4	no	—
59	C₄²×C₁₁	—	2	4	no	—
60	C₄²×C₁₁	—	2	4	no	—
61	C₄²×C₁₁	—	2	4	no	—
62	C₄²×C₁₁	—	2	2	no	—
63	C₄²×C₁₁	—	4	1	no	—
64	C₄²×C₁₁	C₂×C₈	1	4	yes	—
65	C₄×#125	C₂×C₁₁	1	1	yes	characteristic
66	#1916	C₂×C₁₁	1	4	yes	—
67	#1916	C₂×C₁₁	1	4	yes	—
68	C₈×C₄⋊C₄	C₂×C₁₁	1	4	yes	—
69	#1744	C₂×C₁₁	1	2	yes	—
70	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
71	C₂×C₄×C₁₁	—	2	2	no	—
72	C₂×C₄×C₁₁	—	2	4	no	—
73	C₂×C₄×C₁₁	—	2	2	no	—
74	C₂×C₄×C₁₁	—	2	1	no	—
75	C₂×C₄×C₁₁	—	2	2	no	—
76	C₂×C₄×C₁₁	—	2	4	no	—
77	C₂×C₄×C₁₁	—	2	1	no	—
78	C₂×C₄×C₁₁	—	2	2	no	—
79	C₂×C₄×C₁₁	—	2	4	no	—
80	C₂×C₄×C₁₁	—	2	1	no	—
81	C₂×C₄×C₁₁	—	2	2	no	—
82	C₂×C₄×C₁₁	—	2	4	no	—
83	C₂×C₄×C₁₁	—	2	4	no	—
84	C₂×C₄×C₁₁	C₂²×C₈	1	4	yes	—
85	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
86	C₂×C₄×C₁₁	C₂²×C₈	1	8	yes	—
87	C₂×C₄×C₁₁	#131	1	4	yes	—
88	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
89	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
90	C₈×C₁₁	—	2	8	no	—
91	C₈×C₁₁	—	4	4	no	—
92	C₂×#125	C₄×C₁₁	1	1	yes	characteristic
93	C₂×C₄⋊C₈	C₂²×C₁₁	1	4	yes	—
94	C₂×C₄×C₈	C₂²×C₁₁	1	4	yes	—
95	C₂×C₄×C₈	C₂²×C₁₁	1	4	yes	—
96	#389	C₄×C₁₁	1	2	yes	—
97	#387	C₄×C₁₁	1	4	yes	—
98	#382	C₄×C₁₁	1	1	yes	characteristic
99	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
100	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
101	C₄³	C₂²×C₁₁	1	1	yes	characteristic
102	#336	C₂²×C₁₁	1	4	yes	—
103	#336	C₂²×C₁₁	1	4	yes	—
104	#336	C₂²×C₁₁	1	2	yes	—
105	#336	C₂²×C₁₁	1	4	yes	—
106	#336	C₂²×C₁₁	1	2	yes	—
107	C₂²×C₁₁	C₄×#41	1	2	yes	—
108	C₂²×C₁₁	#519	1	1	yes	characteristic
109	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
110	C₂²×C₁₁	C₂×#131	1	2	yes	—
111	C₂²×C₁₁	#568	1	1	yes	characteristic
112	C₄×C₁₁	—	2	4	no	—
113	C₄×C₁₁	—	2	8	no	—
114	C₄×C₁₁	—	2	4	no	—
115	C₄×C₁₁	—	2	2	no	—
116	C₄×C₁₁	—	4	4	no	—
117	C₄×C₁₁	—	4	1	no	—
118	C₄×C₁₁	#552	1	4	yes	—
119	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
120	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
121	#125	C₈×C₁₁	1	8	yes	complemented
122	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
123	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
124	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
125	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
126	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
127	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
128	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
129	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
130	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
131	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
132	C₄⋊C₈	—	2	8	no	—
133	C₄×C₈	—	2	8	no	—
134	C₄×C₈	—	2	8	no	—
135	#95	C₂×C₄×C₁₁	1	4	yes	—
136	#95	C₂×C₄×C₁₁	1	4	yes	—
137	#95	C₂×C₄×C₁₁	1	4	yes	—
138	C₂×C₁₁	#2371	1	1	yes	characteristic
139	C₂×C₁₁	C₈×#41	1	2	yes	—
140	C₂×C₁₁	#2968	1	2	yes	—
141	C₂×C₁₁	#2982	1	1	yes	characteristic
142	C₂×C₁₁	#2986	1	1	yes	characteristic
143	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
144	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
145	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
146	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
147	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
148	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
149	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
150	C₂×C₈	—	2	4	no	—
151	C₂×C₈	—	2	4	no	—
152	C₂×C₈	—	2	4	no	—
153	C₂×C₈	—	2	4	no	—
154	C₂×C₈	—	2	4	no	—
155	C₂×C₈	C₁₁×#41	1	8	yes	—
156	C₄⋊C₄	—	2	8	no	—
157	C₄⋊C₄	—	4	2	no	—
158	C₄⋊C₄	C₂×C₈×C₁₁	1	16	yes	—
159	C₄⋊C₄	C₂×C₈×C₁₁	1	8	yes	—
160	C₄²	—	2	4	no	—
161	C₄²	—	2	4	no	—
162	C₄²	—	2	4	no	—
163	C₄²	—	2	4	no	—
164	C₄²	—	2	2	no	—
165	C₄²	—	4	1	no	—
166	C₄²	C₂×C₈×C₁₁	1	4	yes	—
167	C₁₁	#23263	1	1	yes	characteristic, direct product factor, Sylow
168	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	1	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	4	no	—
175	C₂×C₄	—	2	1	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	4	no	—
181	C₂×C₄	—	2	4	no	—
182	C₂×C₄	C₂²×C₈×C₁₁	1	4	yes	—
183	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
184	C₂×C₄	C₂²×C₈×C₁₁	1	8	yes	—
185	C₂×C₄	C₁₁×#131	1	4	yes	—
186	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
187	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
188	C₈	—	2	8	no	—
189	C₈	—	4	4	no	—
190	C₂²	C₄×C₁₁×#41	1	2	yes	—
191	C₂²	C₁₁×#519	1	1	yes	characteristic
192	C₂²	C₂³×C₈×C₁₁	1	1	yes	characteristic
193	C₂²	C₂×C₁₁×#131	1	2	yes	—
194	C₂²	C₁₁×#568	1	1	yes	characteristic
195	C₄	—	2	4	no	—
196	C₄	—	2	8	no	—
197	C₄	—	2	4	no	—
198	C₄	—	2	2	no	—
199	C₄	—	4	4	no	—
200	C₄	—	4	1	no	—
201	C₄	C₁₁×#552	1	4	yes	—
202	C₂	C₁₁×#2371	1	1	yes	characteristic
203	C₂	C₈×C₁₁×#41	1	2	yes	—
204	C₂	C₁₁×#2968	1	2	yes	—
205	C₂	C₁₁×#2982	1	1	yes	characteristic
206	C₂	C₁₁×#2986	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle, prime radical	C₂³×C₁₁	C₂³×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
23. C₁₁×#125	C₈	semidirect
40. #23263	C₁₁	direct (N × H)
121. #125	C₈×C₁₁	semidirect
167. C₁₁	#23263	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₁×#125	2
C₁₁×#1916	2
C₈×C₁₁×C₄⋊C₄	2
C₁₁×#1744	2
#23263	11

Subgroups — C11×#23263 #14600456

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23263 #14600456