Subgroups — C₁₁×#11968 #14589161

Order 2816.

296 conjugacy classes of subgroups.

The subgroup lattice has 218 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×#2162	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1566	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1363	C₂	1	4	yes	maximal, complemented
5	C₁₁×#533	—	2	1	no	—
6	C₁₁×#500	C₄	1	1	yes	characteristic
7	C₁₁×#500	C₄	1	1	yes	characteristic
8	C₁₁×#499	—	2	1	no	—
9	C₁₁×#499	C₂²	1	2	yes	—
10	C₁₁×#498	—	2	1	no	—
11	C₁₁×#427	—	2	1	no	—
12	C₁₁×#427	C₄	1	2	yes	—
13	C₁₁×#423	—	2	1	no	—
14	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
16	C₁₁×C₂²⋊C₁₆	—	2	1	no	—
17	C₄×C₁₁×C₁₆	—	2	1	no	—
18	C₁₁×#334	—	2	1	no	—
19	C₁₁×#334	C₂²	1	2	yes	—
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	1	no	—
24	C₁₁×C₄⋊Q₈	—	2	1	no	—
25	C₁₁×#125	—	2	2	no	—
26	C₁₁×C₂²⋊Q₈	—	4	1	no	—
27	C₁₁×C₂²⋊Q₈	—	4	1	no	—
28	C₄×Q₈×C₁₁	—	4	1	no	—
29	C₄×Q₈×C₁₁	—	4	1	no	—
30	C₁₁×#117	—	2	2	no	—
31	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
32	C₂×C₁₁×C₁₆	—	2	2	no	—
33	C₁₁×#107	—	2	1	no	—
34	C₁₁×#107	—	2	1	no	—
35	C₁₁×#107	C₂×C₄	1	2	yes	—
36	C₁₁×#107	C₂×C₄	1	2	yes	—
37	C₁₁×#106	—	2	2	no	—
38	C₁₁×#106	—	2	2	no	—
39	C₁₁×C₄⋊C₈	—	2	2	no	—
40	C₁₁×C₄⋊C₈	—	4	1	no	—
41	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
43	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
44	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
45	#11968	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×Q₈×C₁₁	—	4	1	no	—
47	C₂×Q₈×C₁₁	—	4	1	no	—
48	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
51	C₁₁×M₁₆	—	8	2	no	—
52	C₂×C₈×C₁₁	—	2	2	no	—
53	C₂×C₈×C₁₁	—	2	2	no	—
54	C₂×C₈×C₁₁	—	4	2	no	—
55	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
57	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
59	C₁₁×C₄⋊C₄	—	2	2	no	—
60	C₁₁×C₄⋊C₄	—	2	2	no	—
61	C₁₁×C₄⋊C₄	—	4	1	no	—
62	C₁₁×C₄⋊C₄	—	4	1	no	—
63	C₁₁×C₄⋊C₄	—	4	2	no	—
64	C₁₁×C₄⋊C₄	—	4	2	no	—
65	C₁₁×C₂²⋊C₄	—	4	2	no	—
66	C₄²×C₁₁	—	4	2	no	—
67	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
68	C₄²×C₁₁	D₈	1	1	yes	characteristic
69	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
70	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
71	C₁₁×C₁₆	—	4	2	no	—
72	#3160	C₂×C₁₁	1	1	yes	characteristic
73	#2162	C₂×C₁₁	1	1	yes	characteristic
74	#1566	C₂×C₁₁	1	1	yes	characteristic
75	#1363	C₂×C₁₁	1	4	yes	complemented
76	C₂³×C₁₁	#102	1	1	yes	characteristic
77	Q₈×C₁₁	—	8	2	no	—
78	Q₈×C₁₁	—	8	2	no	—
79	C₂×C₄×C₁₁	—	2	2	no	—
80	C₂×C₄×C₁₁	—	2	2	no	—
81	C₂×C₄×C₁₁	—	2	1	no	—
82	C₂×C₄×C₁₁	—	2	1	no	—
83	C₂×C₄×C₁₁	—	4	2	no	—
84	C₂×C₄×C₁₁	—	4	2	no	—
85	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
86	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
87	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
88	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
90	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
91	C₈×C₁₁	—	2	1	no	—
92	C₈×C₁₁	—	2	1	no	—
93	C₈×C₁₁	—	8	2	no	—
94	C₈×C₁₁	#101	1	2	yes	—
95	C₈×C₁₁	#137	1	2	yes	—
96	#533	—	2	1	no	—
97	#500	C₄×C₁₁	1	1	yes	characteristic
98	#500	C₄×C₁₁	1	1	yes	characteristic
99	#499	—	2	1	no	—
100	#499	C₂²×C₁₁	1	2	yes	—
101	#498	—	2	1	no	—
102	#427	—	2	1	no	—
103	#427	C₄×C₁₁	1	2	yes	—
104	#423	—	2	1	no	—
105	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
106	C₄⋊C₁₆	C₂²×C₁₁	1	2	yes	—
107	C₂²⋊C₁₆	—	2	1	no	—
108	C₄×C₁₆	—	2	1	no	—
109	#334	—	2	1	no	—
110	#334	C₂²×C₁₁	1	2	yes	—
111	C₂²×C₁₁	—	2	1	no	—
112	C₂²×C₁₁	—	2	1	no	—
113	C₂²×C₁₁	—	2	1	no	—
114	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
115	C₄×C₁₁	—	2	1	no	—
116	C₄×C₁₁	—	2	1	no	—
117	C₄×C₁₁	—	2	1	no	—
118	C₄×C₁₁	—	8	2	no	—
119	C₄×C₁₁	—	8	2	no	—
120	C₄×C₁₁	#359	1	2	yes	—
121	C₄×C₁₁	#360	1	2	yes	—
122	C₄×C₁₁	C₂×#101	1	1	yes	characteristic
123	C₄×C₁₁	#419	1	1	yes	characteristic
124	C₂×M₁₆	—	4	1	no	—
125	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
126	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
127	C₄⋊Q₈	—	2	1	no	—
128	C₄⋊Q₈	—	2	1	no	—
129	#125	—	2	2	no	—
130	C₂²⋊Q₈	—	4	1	no	—
131	C₂²⋊Q₈	—	4	1	no	—
132	C₄×Q₈	—	4	1	no	—
133	C₄×Q₈	—	4	1	no	—
134	#117	—	2	2	no	—
135	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
136	C₂×C₁₆	—	2	2	no	—
137	#107	—	2	1	no	—
138	#107	—	2	1	no	—
139	#107	C₂×C₄×C₁₁	1	2	yes	—
140	#107	C₂×C₄×C₁₁	1	2	yes	—
141	#106	—	2	2	no	—
142	#106	—	2	2	no	—
143	C₄⋊C₈	—	2	2	no	—
144	C₄⋊C₈	—	4	1	no	—
145	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
146	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
147	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
148	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
149	C₂×C₁₁	—	4	1	no	—
150	C₂×C₁₁	#1546	1	1	yes	characteristic
151	C₂×C₁₁	C₂×#359	1	1	yes	characteristic
152	C₂×C₁₁	C₂×#360	1	1	yes	characteristic
153	C₂×Q₈	—	4	1	no	—
154	C₂×Q₈	—	4	1	no	—
155	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄	C₁₁×D₈	1	1	yes	characteristic
157	C₂²×C₄	C₁₁×SD₁₆	1	1	yes	characteristic
158	M₁₆	—	8	2	no	—
159	C₂×C₈	—	2	2	no	—
160	C₂×C₈	—	2	2	no	—
161	C₂×C₈	—	4	2	no	—
162	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
165	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
166	C₄⋊C₄	—	2	2	no	—
167	C₄⋊C₄	—	2	2	no	—
168	C₄⋊C₄	—	4	1	no	—
169	C₄⋊C₄	—	4	1	no	—
170	C₄⋊C₄	—	4	2	no	—
171	C₄⋊C₄	—	4	2	no	—
172	C₂²⋊C₄	—	4	2	no	—
173	C₄²	—	4	2	no	—
174	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
175	C₄²	C₁₁×D₈	1	1	yes	characteristic
176	C₄²	C₁₁×SD₁₆	1	1	yes	characteristic
177	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
178	C₁₆	—	4	2	no	—
179	C₁₁	#11968	1	1	yes	characteristic, direct product factor, Sylow
180	C₂³	C₁₁×#102	1	1	yes	characteristic
181	Q₈	—	8	2	no	—
182	Q₈	—	8	2	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	4	2	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
190	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
191	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
192	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
193	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
194	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
195	C₈	—	2	1	no	—
196	C₈	—	2	1	no	—
197	C₈	—	8	2	no	—
198	C₈	C₁₁×#101	1	2	yes	—
199	C₈	C₁₁×#137	1	2	yes	—
200	C₂²	—	2	1	no	—
201	C₂²	—	2	1	no	—
202	C₂²	—	2	1	no	—
203	C₂²	C₂×C₁₁×#102	1	1	yes	characteristic
204	C₄	—	2	1	no	—
205	C₄	—	2	1	no	—
206	C₄	—	2	1	no	—
207	C₄	—	8	2	no	—
208	C₄	—	8	2	no	—
209	C₄	C₁₁×#359	1	2	yes	—
210	C₄	C₁₁×#360	1	2	yes	—
211	C₄	C₂×C₁₁×#101	1	1	yes	characteristic
212	C₄	C₁₁×#419	1	1	yes	characteristic
213	C₂	—	4	1	no	—
214	C₂	C₁₁×#1546	1	1	yes	characteristic
215	C₂	C₂×C₁₁×#359	1	1	yes	characteristic
216	C₂	C₂×C₁₁×#360	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×#1363	C₂	semidirect
45. #11968	C₁₁	direct (N × H)
75. #1363	C₂×C₁₁	semidirect
179. C₁₁	#11968	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×#2162	2
C₁₁×#1566	2
C₁₁×#1363	2
#11968	11

Subgroups — C11×#11968 #14589161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11968 #14589161