Subgroups — C₁₁×#11972 #14589165

Order 2816.

330 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	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×#1365	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	#11972	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	4	no	—
45	C₂²×C₄×C₁₁	—	4	2	no	—
46	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
48	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
49	C₁₁×M₁₆	—	8	2	no	—
50	C₂×C₈×C₁₁	—	2	2	no	—
51	C₂×C₈×C₁₁	—	2	2	no	—
52	C₂×C₈×C₁₁	—	4	2	no	—
53	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
54	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
57	C₁₁×C₄⋊C₄	—	2	4	no	—
58	C₁₁×C₄⋊C₄	—	4	2	no	—
59	C₁₁×C₄⋊C₄	—	4	2	no	—
60	C₁₁×C₄⋊C₄	—	4	2	no	—
61	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
62	C₄²×C₁₁	D₈	1	1	yes	characteristic
63	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
64	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
65	C₁₁×C₁₆	—	4	2	no	—
66	C₂×#500	C₂×C₁₁	1	1	yes	characteristic
67	#2162	C₂×C₁₁	1	1	yes	characteristic
68	#1567	C₂×C₁₁	1	1	yes	characteristic
69	#1365	C₂×C₁₁	1	4	yes	complemented
70	C₂³×C₁₁	#102	1	1	yes	characteristic
71	Q₈×C₁₁	—	8	4	no	—
72	Q₈×C₁₁	—	8	4	no	—
73	C₂×C₄×C₁₁	—	2	2	no	—
74	C₂×C₄×C₁₁	—	2	1	no	—
75	C₂×C₄×C₁₁	—	2	1	no	—
76	C₂×C₄×C₁₁	—	4	4	no	—
77	C₂×C₄×C₁₁	—	8	4	no	—
78	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
79	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
80	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
81	C₂×C₄×C₁₁	SD₃₂	1	2	yes	—
82	C₂×C₄×C₁₁	Q₃₂	1	2	yes	—
83	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
85	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
86	C₈×C₁₁	—	2	1	no	—
87	C₈×C₁₁	—	2	1	no	—
88	C₈×C₁₁	—	8	2	no	—
89	C₈×C₁₁	#101	1	2	yes	—
90	C₈×C₁₁	#137	1	2	yes	—
91	C₂×C₄⋊Q₈	—	2	1	no	—
92	#500	—	2	1	no	—
93	#500	—	2	1	no	—
94	#500	C₄×C₁₁	1	2	yes	—
95	#500	C₂²×C₁₁	1	2	yes	—
96	C₂×#107	—	2	1	no	—
97	C₂×#107	C₄×C₁₁	1	2	yes	—
98	#423	—	2	1	no	—
99	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
100	C₄⋊C₁₆	C₂²×C₁₁	1	2	yes	—
101	C₂²⋊C₁₆	—	2	1	no	—
102	C₄×C₁₆	—	2	1	no	—
103	#335	—	2	1	no	—
104	#335	C₂²×C₁₁	1	2	yes	—
105	C₂²×C₁₁	—	2	1	no	—
106	C₂²×C₁₁	—	2	1	no	—
107	C₂²×C₁₁	#358	1	2	yes	—
108	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
109	C₄×C₁₁	—	2	1	no	—
110	C₄×C₁₁	—	2	1	no	—
111	C₄×C₁₁	—	8	4	no	—
112	C₄×C₁₁	#358	1	2	yes	—
113	C₄×C₁₁	#361	1	2	yes	—
114	C₄×C₁₁	C₂×#101	1	1	yes	characteristic
115	C₄×C₁₁	#419	1	1	yes	characteristic
116	C₄×C₁₁	C₂×SD₃₂	1	1	yes	characteristic
117	C₄×C₁₁	C₂×Q₃₂	1	1	yes	characteristic
118	C₂²×Q₈	—	4	1	no	—
119	C₂×M₁₆	—	4	1	no	—
120	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
121	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
122	C₄⋊Q₈	—	2	2	no	—
123	C₄⋊Q₈	—	2	2	no	—
124	C₄⋊Q₈	—	4	1	no	—
125	C₄⋊Q₈	—	4	1	no	—
126	C₂×C₄⋊C₄	—	2	2	no	—
127	C₂×C₄⋊C₄	—	4	1	no	—
128	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
129	C₂×C₁₆	—	2	2	no	—
130	#107	—	2	2	no	—
131	#107	—	2	2	no	—
132	#107	—	2	2	no	—
133	#107	C₂×C₄×C₁₁	1	4	yes	—
134	C₄⋊C₈	—	2	2	no	—
135	C₄⋊C₈	—	4	1	no	—
136	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
137	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
138	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
139	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
140	C₂×C₁₁	—	2	2	no	—
141	C₂×C₁₁	#1546	1	1	yes	characteristic
142	C₂×C₁₁	C₂×#358	1	1	yes	characteristic
143	C₂×C₁₁	C₂×#361	1	1	yes	characteristic
144	C₂×Q₈	—	4	2	no	—
145	C₂×Q₈	—	4	2	no	—
146	C₂×Q₈	—	8	4	no	—
147	C₂²×C₄	—	4	2	no	—
148	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×C₄	C₁₁×D₈	1	1	yes	characteristic
150	C₂²×C₄	C₁₁×SD₁₆	1	1	yes	characteristic
151	M₁₆	—	8	2	no	—
152	C₂×C₈	—	2	2	no	—
153	C₂×C₈	—	2	2	no	—
154	C₂×C₈	—	4	2	no	—
155	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
158	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
159	C₄⋊C₄	—	2	4	no	—
160	C₄⋊C₄	—	4	2	no	—
161	C₄⋊C₄	—	4	2	no	—
162	C₄⋊C₄	—	4	2	no	—
163	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
164	C₄²	C₁₁×D₈	1	1	yes	characteristic
165	C₄²	C₁₁×SD₁₆	1	1	yes	characteristic
166	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
167	C₁₆	—	4	2	no	—
168	C₁₁	#11972	1	1	yes	characteristic, direct product factor, Sylow
169	C₂³	C₁₁×#102	1	1	yes	characteristic
170	Q₈	—	8	4	no	—
171	Q₈	—	8	4	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	1	no	—
174	C₂×C₄	—	2	1	no	—
175	C₂×C₄	—	4	4	no	—
176	C₂×C₄	—	8	4	no	—
177	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
178	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
179	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
180	C₂×C₄	C₁₁×SD₃₂	1	2	yes	—
181	C₂×C₄	C₁₁×Q₃₂	1	2	yes	—
182	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
184	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
185	C₈	—	2	1	no	—
186	C₈	—	2	1	no	—
187	C₈	—	8	2	no	—
188	C₈	C₁₁×#101	1	2	yes	—
189	C₈	C₁₁×#137	1	2	yes	—
190	C₂²	—	2	1	no	—
191	C₂²	—	2	1	no	—
192	C₂²	C₁₁×#358	1	2	yes	—
193	C₂²	C₂×C₁₁×#102	1	1	yes	characteristic
194	C₄	—	2	1	no	—
195	C₄	—	2	1	no	—
196	C₄	—	8	4	no	—
197	C₄	C₁₁×#358	1	2	yes	—
198	C₄	C₁₁×#361	1	2	yes	—
199	C₄	C₂×C₁₁×#101	1	1	yes	characteristic
200	C₄	C₁₁×#419	1	1	yes	characteristic
201	C₄	C₂×C₁₁×SD₃₂	1	1	yes	characteristic
202	C₄	C₂×C₁₁×Q₃₂	1	1	yes	characteristic
203	C₂	—	2	2	no	—
204	C₂	C₁₁×#1546	1	1	yes	characteristic
205	C₂	C₂×C₁₁×#358	1	1	yes	characteristic
206	C₂	C₂×C₁₁×#361	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×#1365	C₂	semidirect
41. #11972	C₁₁	direct (N × H)
69. #1365	C₂×C₁₁	semidirect
168. C₁₁	#11972	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×#1365	2
#11972	11

Subgroups — C11×#11972 #14589165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11972 #14589165