Subgroups — C₁₁×#11971 #14589164

Order 2816.

330 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#500	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2162	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1567	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1364	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₁×C₄⋊Q₈	—	2	1	no	—
6	C₁₁×#500	—	2	1	no	—
7	C₁₁×#500	—	2	1	no	—
8	C₁₁×#500	C₄	1	2	yes	—
9	C₁₁×#500	C₂²	1	2	yes	—
10	C₂×C₁₁×#107	—	2	1	no	—
11	C₂×C₁₁×#107	C₄	1	2	yes	—
12	C₁₁×#423	—	2	1	no	—
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
15	C₁₁×C₂²⋊C₁₆	—	2	1	no	—
16	C₄×C₁₁×C₁₆	—	2	1	no	—
17	C₁₁×#335	—	2	1	no	—
18	C₁₁×#335	C₂²	1	2	yes	—
19	C₂²×Q₈×C₁₁	—	4	1	no	—
20	C₂×C₁₁×M₁₆	—	4	1	no	—
21	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
23	C₁₁×C₄⋊Q₈	—	2	2	no	—
24	C₁₁×C₄⋊Q₈	—	2	2	no	—
25	C₁₁×C₄⋊Q₈	—	4	1	no	—
26	C₁₁×C₄⋊Q₈	—	4	1	no	—
27	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
28	C₂×C₁₁×C₄⋊C₄	—	4	1	no	—
29	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
30	C₂×C₁₁×C₁₆	—	2	2	no	—
31	C₁₁×#107	—	2	2	no	—
32	C₁₁×#107	—	2	2	no	—
33	C₁₁×#107	—	2	2	no	—
34	C₁₁×#107	C₂×C₄	1	4	yes	—
35	C₁₁×C₄⋊C₈	—	2	2	no	—
36	C₁₁×C₄⋊C₈	—	4	1	no	—
37	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
39	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
40	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
41	#11971	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×Q₈×C₁₁	—	4	2	no	—
43	C₂×Q₈×C₁₁	—	4	2	no	—
44	C₂×Q₈×C₁₁	—	8	2	no	—
45	C₂×Q₈×C₁₁	—	8	2	no	—
46	C₂²×C₄×C₁₁	—	4	2	no	—
47	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
50	C₁₁×M₁₆	—	8	2	no	—
51	C₂×C₈×C₁₁	—	2	2	no	—
52	C₂×C₈×C₁₁	—	2	2	no	—
53	C₂×C₈×C₁₁	—	4	2	no	—
54	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
58	C₁₁×C₄⋊C₄	—	2	4	no	—
59	C₁₁×C₄⋊C₄	—	4	2	no	—
60	C₁₁×C₄⋊C₄	—	4	2	no	—
61	C₁₁×C₄⋊C₄	—	4	2	no	—
62	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
63	C₄²×C₁₁	D₈	1	1	yes	characteristic
64	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
65	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
66	C₁₁×C₁₆	—	4	2	no	—
67	C₂×#500	C₂×C₁₁	1	1	yes	characteristic
68	#2162	C₂×C₁₁	1	1	yes	characteristic
69	#1567	C₂×C₁₁	1	1	yes	characteristic
70	#1364	C₂×C₁₁	1	4	yes	complemented
71	C₂³×C₁₁	#102	1	1	yes	characteristic
72	Q₈×C₁₁	—	8	4	no	—
73	Q₈×C₁₁	—	8	2	no	—
74	Q₈×C₁₁	—	8	2	no	—
75	C₂×C₄×C₁₁	—	2	2	no	—
76	C₂×C₄×C₁₁	—	2	1	no	—
77	C₂×C₄×C₁₁	—	2	1	no	—
78	C₂×C₄×C₁₁	—	4	4	no	—
79	C₂×C₄×C₁₁	—	8	4	no	—
80	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
81	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
82	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
83	C₂×C₄×C₁₁	D₁₆	1	2	yes	—
84	C₂×C₄×C₁₁	SD₃₂	1	2	yes	—
85	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
87	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
88	C₈×C₁₁	—	2	1	no	—
89	C₈×C₁₁	—	2	1	no	—
90	C₈×C₁₁	—	8	2	no	—
91	C₈×C₁₁	#101	1	2	yes	—
92	C₈×C₁₁	#137	1	2	yes	—
93	C₂×C₄⋊Q₈	—	2	1	no	—
94	#500	—	2	1	no	—
95	#500	—	2	1	no	—
96	#500	C₄×C₁₁	1	2	yes	—
97	#500	C₂²×C₁₁	1	2	yes	—
98	C₂×#107	—	2	1	no	—
99	C₂×#107	C₄×C₁₁	1	2	yes	—
100	#423	—	2	1	no	—
101	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
102	C₄⋊C₁₆	C₂²×C₁₁	1	2	yes	—
103	C₂²⋊C₁₆	—	2	1	no	—
104	C₄×C₁₆	—	2	1	no	—
105	#335	—	2	1	no	—
106	#335	C₂²×C₁₁	1	2	yes	—
107	C₂²×C₁₁	—	2	1	no	—
108	C₂²×C₁₁	—	2	1	no	—
109	C₂²×C₁₁	#357	1	2	yes	—
110	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
111	C₄×C₁₁	—	2	1	no	—
112	C₄×C₁₁	—	2	1	no	—
113	C₄×C₁₁	—	8	4	no	—
114	C₄×C₁₁	#357	1	2	yes	—
115	C₄×C₁₁	#362	1	2	yes	—
116	C₄×C₁₁	C₂×#101	1	1	yes	characteristic
117	C₄×C₁₁	#419	1	1	yes	characteristic
118	C₄×C₁₁	C₂×D₁₆	1	1	yes	characteristic
119	C₄×C₁₁	C₂×SD₃₂	1	1	yes	characteristic
120	C₂²×Q₈	—	4	1	no	—
121	C₂×M₁₆	—	4	1	no	—
122	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
123	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
124	C₄⋊Q₈	—	2	2	no	—
125	C₄⋊Q₈	—	2	2	no	—
126	C₄⋊Q₈	—	4	1	no	—
127	C₄⋊Q₈	—	4	1	no	—
128	C₂×C₄⋊C₄	—	2	2	no	—
129	C₂×C₄⋊C₄	—	4	1	no	—
130	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
131	C₂×C₁₆	—	2	2	no	—
132	#107	—	2	2	no	—
133	#107	—	2	2	no	—
134	#107	—	2	2	no	—
135	#107	C₂×C₄×C₁₁	1	4	yes	—
136	C₄⋊C₈	—	2	2	no	—
137	C₄⋊C₈	—	4	1	no	—
138	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
139	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
140	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
141	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
142	C₂×C₁₁	—	2	2	no	—
143	C₂×C₁₁	#1546	1	1	yes	characteristic
144	C₂×C₁₁	C₂×#357	1	1	yes	characteristic
145	C₂×C₁₁	C₂×#362	1	1	yes	characteristic
146	C₂×Q₈	—	4	2	no	—
147	C₂×Q₈	—	4	2	no	—
148	C₂×Q₈	—	8	2	no	—
149	C₂×Q₈	—	8	2	no	—
150	C₂²×C₄	—	4	2	no	—
151	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄	C₁₁×D₈	1	1	yes	characteristic
153	C₂²×C₄	C₁₁×SD₁₆	1	1	yes	characteristic
154	M₁₆	—	8	2	no	—
155	C₂×C₈	—	2	2	no	—
156	C₂×C₈	—	2	2	no	—
157	C₂×C₈	—	4	2	no	—
158	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
161	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
162	C₄⋊C₄	—	2	4	no	—
163	C₄⋊C₄	—	4	2	no	—
164	C₄⋊C₄	—	4	2	no	—
165	C₄⋊C₄	—	4	2	no	—
166	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
167	C₄²	C₁₁×D₈	1	1	yes	characteristic
168	C₄²	C₁₁×SD₁₆	1	1	yes	characteristic
169	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
170	C₁₆	—	4	2	no	—
171	C₁₁	#11971	1	1	yes	characteristic, direct product factor, Sylow
172	C₂³	C₁₁×#102	1	1	yes	characteristic
173	Q₈	—	8	2	no	—
174	Q₈	—	8	2	no	—
175	Q₈	—	8	4	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	1	no	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	4	4	no	—
180	C₂×C₄	—	8	4	no	—
181	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
182	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
183	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
184	C₂×C₄	C₁₁×D₁₆	1	2	yes	—
185	C₂×C₄	C₁₁×SD₃₂	1	2	yes	—
186	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
187	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
188	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
189	C₈	—	2	1	no	—
190	C₈	—	2	1	no	—
191	C₈	—	8	2	no	—
192	C₈	C₁₁×#101	1	2	yes	—
193	C₈	C₁₁×#137	1	2	yes	—
194	C₂²	—	2	1	no	—
195	C₂²	—	2	1	no	—
196	C₂²	C₁₁×#357	1	2	yes	—
197	C₂²	C₂×C₁₁×#102	1	1	yes	characteristic
198	C₄	—	2	1	no	—
199	C₄	—	2	1	no	—
200	C₄	—	8	4	no	—
201	C₄	C₁₁×#357	1	2	yes	—
202	C₄	C₁₁×#362	1	2	yes	—
203	C₄	C₂×C₁₁×#101	1	1	yes	characteristic
204	C₄	C₁₁×#419	1	1	yes	characteristic
205	C₄	C₂×C₁₁×D₁₆	1	1	yes	characteristic
206	C₄	C₂×C₁₁×SD₃₂	1	1	yes	characteristic
207	C₂	—	2	2	no	—
208	C₂	C₁₁×#1546	1	1	yes	characteristic
209	C₂	C₂×C₁₁×#357	1	1	yes	characteristic
210	C₂	C₂×C₁₁×#362	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₂³×C₁₁	#102
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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
4. C₁₁×#1364	C₂	semidirect
41. #11971	C₁₁	direct (N × H)
70. #1364	C₂×C₁₁	semidirect
171. C₁₁	#11971	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×#500	2
C₁₁×#2162	2
C₁₁×#1567	2
C₁₁×#1364	2
#11971	11

Subgroups — C11×#11971 #14589164

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11971 #14589164