Subgroups — C₁₁×#21952 #14599145

Order 2816.

826 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#431	C₂	1	2	yes	maximal
2	C₁₁×#2285	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1939	C₂	1	8	yes	maximal, complemented
4	C₁₁×#1798	C₂	1	4	yes	maximal
5	C₂×C₁₁×#117	C₂²	1	2	yes	—
6	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
7	C₁₁×#431	—	2	8	no	—
8	C₂×C₁₁×C₄⋊C₈	C₂²	1	4	yes	—
9	C₂×C₁₁×C₄⋊C₈	C₂²	1	8	yes	—
10	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	—
11	C₂×C₄×C₈×C₁₁	C₂²	1	4	yes	—
12	C₁₁×#384	C₄	1	2	yes	—
13	C₁₁×#382	C₄	1	2	yes	—
14	C₁₁×#380	C₄	1	4	yes	—
15	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
16	C₁₁×#336	C₂²	1	8	yes	—
17	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
18	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
19	C₂²×C₈×C₁₁	C₂³	1	8	yes	—
20	C₁₁×#117	—	4	4	no	—
21	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	8	yes	—
22	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
23	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	4	yes	—
24	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₁	D₄	1	4	yes	—
27	C₂×C₄²×C₁₁	Q₈	1	4	yes	—
28	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
29	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
30	C₁₁×C₄⋊C₈	—	2	8	no	—
31	C₁₁×C₄⋊C₈	—	4	8	no	—
32	C₁₁×C₂²⋊C₈	—	2	8	no	—
33	C₄×C₈×C₁₁	—	2	8	no	—
34	C₁₁×#95	C₂×C₄	1	8	yes	—
35	#21952	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₁	—	2	8	no	—
38	C₂²×C₄×C₁₁	—	2	2	no	—
39	C₂²×C₄×C₁₁	—	2	2	no	—
40	C₂²×C₄×C₁₁	C₄⋊C₄	1	8	yes	—
41	C₂²×C₄×C₁₁	C₂²×C₄	1	8	yes	—
42	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
43	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
45	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
46	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
47	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
48	C₂×C₈×C₁₁	—	2	8	no	—
49	C₂×C₈×C₁₁	—	2	8	no	—
50	C₂×C₈×C₁₁	—	2	8	no	—
51	C₁₁×C₄⋊C₄	—	2	16	no	—
52	C₁₁×C₄⋊C₄	—	4	4	no	—
53	C₁₁×C₂²⋊C₄	—	4	4	no	—
54	C₄²×C₁₁	—	2	8	no	—
55	C₄²×C₁₁	C₄⋊C₄	1	4	yes	—
56	C₄²×C₁₁	C₄⋊C₄	1	4	yes	—
57	C₄²×C₁₁	C₂×D₄	1	4	yes	—
58	C₄²×C₁₁	C₂×Q₈	1	4	yes	—
59	C₂×#431	C₂×C₁₁	1	2	yes	—
60	#2285	C₂×C₁₁	1	1	yes	characteristic
61	#1939	C₂×C₁₁	1	8	yes	complemented
62	#1798	C₂×C₁₁	1	4	yes	—
63	C₂³×C₁₁	—	2	1	no	—
64	C₂³×C₁₁	—	2	1	no	—
65	C₂³×C₁₁	—	2	4	no	—
66	C₂³×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
67	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
68	C₂×C₄×C₁₁	—	2	1	no	—
69	C₂×C₄×C₁₁	—	2	1	no	—
70	C₂×C₄×C₁₁	—	2	4	no	—
71	C₂×C₄×C₁₁	—	2	4	no	—
72	C₂×C₄×C₁₁	—	2	4	no	—
73	C₂×C₄×C₁₁	—	2	16	no	—
74	C₂×C₄×C₁₁	—	2	8	no	—
75	C₂×C₄×C₁₁	—	2	16	no	—
76	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
77	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
78	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
79	C₂×C₄×C₁₁	#131	1	8	yes	—
80	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
82	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
83	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
84	C₈×C₁₁	—	4	8	no	—
85	C₂×#117	C₂²×C₁₁	1	2	yes	—
86	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
87	#431	—	2	8	no	—
88	C₂×C₄⋊C₈	C₂²×C₁₁	1	4	yes	—
89	C₂×C₄⋊C₈	C₂²×C₁₁	1	8	yes	—
90	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	—
91	C₂×C₄×C₈	C₂²×C₁₁	1	4	yes	—
92	#384	C₄×C₁₁	1	2	yes	—
93	#382	C₄×C₁₁	1	2	yes	—
94	#380	C₄×C₁₁	1	4	yes	—
95	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
96	#336	C₂²×C₁₁	1	8	yes	—
97	C₂²×C₁₁	—	2	2	no	—
98	C₂²×C₁₁	—	2	4	no	—
99	C₂²×C₁₁	—	4	2	no	—
100	C₂²×C₁₁	—	4	2	no	—
101	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
102	C₂²×C₁₁	#518	1	1	yes	characteristic
103	C₂²×C₁₁	#519	1	1	yes	characteristic
104	C₂²×C₁₁	C₂×#131	1	4	yes	—
105	C₄×C₁₁	—	2	2	no	—
106	C₄×C₁₁	—	2	4	no	—
107	C₄×C₁₁	—	4	8	no	—
108	C₄×C₁₁	#424	1	8	yes	—
109	C₄×C₁₁	#537	1	2	yes	—
110	C₄×C₁₁	#544	1	2	yes	—
111	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
112	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
113	C₂²×C₈	C₂³×C₁₁	1	8	yes	—
114	#117	—	4	4	no	—
115	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	8	yes	—
116	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
117	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
118	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
119	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
120	C₂×C₄²	D₄×C₁₁	1	4	yes	—
121	C₂×C₄²	Q₈×C₁₁	1	4	yes	—
122	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
123	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
124	C₄⋊C₈	—	2	8	no	—
125	C₄⋊C₈	—	4	8	no	—
126	C₂²⋊C₈	—	2	8	no	—
127	C₄×C₈	—	2	8	no	—
128	#95	C₂×C₄×C₁₁	1	8	yes	—
129	C₂×C₁₁	—	4	2	no	—
130	C₂×C₁₁	#2316	1	1	yes	characteristic
131	C₂×C₁₁	C₂×#424	1	2	yes	—
132	C₂×C₁₁	#2979	1	2	yes	—
133	C₂×C₁₁	#2986	1	2	yes	—
134	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
135	C₂²×C₄	—	2	8	no	—
136	C₂²×C₄	—	2	2	no	—
137	C₂²×C₄	—	2	2	no	—
138	C₂²×C₄	C₁₁×C₄⋊C₄	1	8	yes	—
139	C₂²×C₄	C₂²×C₄×C₁₁	1	8	yes	—
140	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
141	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
142	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
143	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
144	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
145	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
146	C₂×C₈	—	2	8	no	—
147	C₂×C₈	—	2	8	no	—
148	C₂×C₈	—	2	8	no	—
149	C₄⋊C₄	—	2	16	no	—
150	C₄⋊C₄	—	4	4	no	—
151	C₂²⋊C₄	—	4	4	no	—
152	C₄²	—	2	8	no	—
153	C₄²	C₁₁×C₄⋊C₄	1	4	yes	—
154	C₄²	C₁₁×C₄⋊C₄	1	4	yes	—
155	C₄²	C₂×D₄×C₁₁	1	4	yes	—
156	C₄²	C₂×Q₈×C₁₁	1	4	yes	—
157	C₁₁	#21952	1	1	yes	characteristic, direct product factor, Sylow
158	C₂³	—	2	1	no	—
159	C₂³	—	2	1	no	—
160	C₂³	—	2	4	no	—
161	C₂³	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
162	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	4	no	—
166	C₂×C₄	—	2	4	no	—
167	C₂×C₄	—	2	4	no	—
168	C₂×C₄	—	2	16	no	—
169	C₂×C₄	—	2	8	no	—
170	C₂×C₄	—	2	16	no	—
171	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
172	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	4	yes	—
173	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	4	yes	—
174	C₂×C₄	C₁₁×#131	1	8	yes	—
175	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
176	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
177	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
178	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
179	C₈	—	4	8	no	—
180	C₂²	—	2	4	no	—
181	C₂²	—	2	2	no	—
182	C₂²	—	4	2	no	—
183	C₂²	—	4	2	no	—
184	C₂²	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
185	C₂²	C₁₁×#518	1	1	yes	characteristic
186	C₂²	C₁₁×#519	1	1	yes	characteristic
187	C₂²	C₂×C₁₁×#131	1	4	yes	—
188	C₄	—	2	4	no	—
189	C₄	—	2	2	no	—
190	C₄	—	4	8	no	—
191	C₄	C₁₁×#424	1	8	yes	—
192	C₄	C₁₁×#537	1	2	yes	—
193	C₄	C₁₁×#544	1	2	yes	—
194	C₂	—	4	2	no	—
195	C₂	C₁₁×#2316	1	1	yes	characteristic
196	C₂	C₂×C₁₁×#424	1	2	yes	—
197	C₂	C₁₁×#2979	1	2	yes	—
198	C₂	C₁₁×#2986	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1939	C₂	semidirect
35. #21952	C₁₁	direct (N × H)
61. #1939	C₂×C₁₁	semidirect
157. C₁₁	#21952	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×#431	2
C₁₁×#2285	2
C₁₁×#1939	2
C₁₁×#1798	2
#21952	11

Subgroups — C11×#21952 #14599145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21952 #14599145