Subgroups — C₁₁×#11961 #14589154

Order 2816.

498 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#493	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2162	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#1567	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1361	C₂	1	4	yes	maximal, complemented
5	C₂²×C₁₁×D₈	—	2	1	no	—
6	C₂²×C₁₁×D₈	C₄	1	2	yes	—
7	C₂×C₁₁×#127	—	2	1	no	—
8	C₁₁×#493	—	2	1	no	—
9	C₁₁×#493	—	2	1	no	—
10	C₁₁×#493	C₄	1	2	yes	—
11	C₁₁×#493	C₂²	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	complemented
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	complemented
19	C₂²×D₄×C₁₁	—	2	2	no	—
20	C₂²×D₄×C₁₁	—	4	1	no	—
21	C₂²×D₄×C₁₁	—	4	1	no	—
22	C₂×C₁₁×D₈	—	2	2	no	—
23	C₂×C₁₁×D₈	—	2	2	no	—
24	C₂×C₁₁×D₈	—	2	2	no	—
25	C₂×C₁₁×D₈	—	4	4	no	—
26	C₂×C₁₁×D₈	—	4	4	no	—
27	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	—
28	C₂×C₁₁×M₁₆	—	4	1	no	—
29	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
31	C₁₁×#127	—	2	2	no	—
32	C₁₁×#127	—	2	2	no	—
33	C₁₁×#127	—	4	1	no	—
34	C₁₁×#127	—	4	1	no	—
35	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
36	C₂×C₁₁×C₁₆	—	2	2	no	—
37	C₁₁×C₄⋊C₈	—	2	2	no	—
38	C₁₁×C₄⋊C₈	—	4	1	no	—
39	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
42	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
43	#11961	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂⁴×C₁₁	—	4	2	no	—
45	C₂×D₄×C₁₁	—	2	4	no	—
46	C₂×D₄×C₁₁	—	4	4	no	—
47	C₂×D₄×C₁₁	—	4	4	no	—
48	C₂×D₄×C₁₁	—	4	2	no	—
49	C₂×D₄×C₁₁	—	4	2	no	—
50	C₂×D₄×C₁₁	—	4	2	no	—
51	C₂×D₄×C₁₁	—	4	2	no	—
52	C₂×D₄×C₁₁	—	4	2	no	—
53	C₂×D₄×C₁₁	—	8	4	no	—
54	C₂×D₄×C₁₁	—	8	2	no	—
55	C₂×D₄×C₁₁	—	8	2	no	—
56	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
58	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
59	C₁₁×D₈	—	4	4	no	—
60	C₁₁×D₈	—	4	4	no	—
61	C₁₁×D₈	—	4	4	no	—
62	C₁₁×D₈	—	4	4	no	—
63	C₁₁×M₁₆	—	8	2	no	—
64	C₂×C₈×C₁₁	—	2	2	no	—
65	C₂×C₈×C₁₁	—	2	2	no	—
66	C₂×C₈×C₁₁	—	4	2	no	—
67	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
72	C₄²×C₁₁	D₈	1	1	yes	characteristic
73	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
74	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
75	C₁₁×C₁₆	—	4	2	no	—
76	C₂×#493	C₂×C₁₁	1	1	yes	characteristic
77	#2162	C₂×C₁₁	1	1	yes	characteristic, complemented
78	#1567	C₂×C₁₁	1	1	yes	characteristic, complemented
79	#1361	C₂×C₁₁	1	4	yes	complemented
80	C₂³×C₁₁	—	4	4	no	—
81	C₂³×C₁₁	—	8	4	no	—
82	C₂³×C₁₁	—	8	4	no	—
83	C₂³×C₁₁	—	8	4	no	—
84	C₂³×C₁₁	#102	1	1	yes	characteristic
85	D₄×C₁₁	—	4	4	no	—
86	D₄×C₁₁	—	4	4	no	—
87	D₄×C₁₁	—	8	4	no	—
88	D₄×C₁₁	—	8	4	no	—
89	D₄×C₁₁	—	8	4	no	—
90	D₄×C₁₁	—	8	4	no	—
91	D₄×C₁₁	—	8	2	no	—
92	D₄×C₁₁	—	8	2	no	—
93	C₂×C₄×C₁₁	—	2	2	no	—
94	C₂×C₄×C₁₁	—	2	1	no	—
95	C₂×C₄×C₁₁	—	2	1	no	—
96	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
97	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
98	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
99	C₂×C₄×C₁₁	D₁₆	1	2	yes	—
100	C₂×C₄×C₁₁	SD₃₂	1	2	yes	—
101	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
103	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
104	C₈×C₁₁	—	2	1	no	—
105	C₈×C₁₁	—	2	1	no	—
106	C₈×C₁₁	—	8	2	no	—
107	C₈×C₁₁	#100	1	2	yes	—
108	C₈×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
109	C₂²×D₈	—	2	1	no	—
110	C₂²×D₈	C₄×C₁₁	1	2	yes	—
111	C₂×#127	—	2	1	no	—
112	#493	—	2	1	no	—
113	#493	—	2	1	no	—
114	#493	C₄×C₁₁	1	2	yes	—
115	#493	C₂²×C₁₁	1	2	yes	—
116	#423	—	2	1	no	—
117	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
118	C₄⋊C₁₆	C₂²×C₁₁	1	2	yes	complemented
119	C₂²⋊C₁₆	—	2	1	no	—
120	C₄×C₁₆	—	2	1	no	—
121	#335	—	2	1	no	—
122	#335	C₂²×C₁₁	1	2	yes	complemented
123	C₂²×C₁₁	—	2	1	no	—
124	C₂²×C₁₁	—	2	1	no	—
125	C₂²×C₁₁	—	8	4	no	—
126	C₂²×C₁₁	—	8	4	no	—
127	C₂²×C₁₁	—	8	4	no	—
128	C₂²×C₁₁	—	16	8	no	—
129	C₂²×C₁₁	#357	1	2	yes	—
130	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
131	C₄×C₁₁	—	2	1	no	—
132	C₄×C₁₁	—	2	1	no	—
133	C₄×C₁₁	#357	1	2	yes	—
134	C₄×C₁₁	#361	1	2	yes	—
135	C₄×C₁₁	C₂×#100	1	1	yes	characteristic
136	C₄×C₁₁	#418	1	1	yes	characteristic
137	C₄×C₁₁	C₂×D₁₆	1	1	yes	characteristic
138	C₄×C₁₁	C₂×SD₃₂	1	1	yes	characteristic
139	C₂²×D₄	—	2	2	no	—
140	C₂²×D₄	—	4	1	no	—
141	C₂²×D₄	—	4	1	no	—
142	C₂×D₈	—	2	2	no	—
143	C₂×D₈	—	2	2	no	—
144	C₂×D₈	—	2	2	no	—
145	C₂×D₈	—	4	4	no	—
146	C₂×D₈	—	4	4	no	—
147	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	—
148	C₂×M₁₆	—	4	1	no	—
149	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
150	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
151	#127	—	2	2	no	—
152	#127	—	2	2	no	—
153	#127	—	4	1	no	—
154	#127	—	4	1	no	—
155	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
156	C₂×C₁₆	—	2	2	no	—
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	4	1	no	—
159	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
160	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
161	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
162	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
163	C₂×C₁₁	—	2	2	no	—
164	C₂×C₁₁	—	16	4	no	—
165	C₂×C₁₁	#1545	1	1	yes	characteristic
166	C₂×C₁₁	C₂×#357	1	1	yes	characteristic
167	C₂×C₁₁	C₂×#361	1	1	yes	characteristic
168	C₂⁴	—	4	2	no	—
169	C₂×D₄	—	2	4	no	—
170	C₂×D₄	—	4	4	no	—
171	C₂×D₄	—	4	4	no	—
172	C₂×D₄	—	4	2	no	—
173	C₂×D₄	—	4	2	no	—
174	C₂×D₄	—	4	2	no	—
175	C₂×D₄	—	4	2	no	—
176	C₂×D₄	—	4	2	no	—
177	C₂×D₄	—	8	4	no	—
178	C₂×D₄	—	8	2	no	—
179	C₂×D₄	—	8	2	no	—
180	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
181	C₂²×C₄	C₁₁×D₈	1	1	yes	characteristic
182	C₂²×C₄	C₁₁×SD₁₆	1	1	yes	characteristic
183	D₈	—	4	4	no	—
184	D₈	—	4	4	no	—
185	D₈	—	4	4	no	—
186	D₈	—	4	4	no	—
187	M₁₆	—	8	2	no	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	—	4	2	no	—
191	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
193	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
194	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
195	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
196	C₄²	C₁₁×D₈	1	1	yes	characteristic
197	C₄²	C₁₁×SD₁₆	1	1	yes	characteristic
198	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
199	C₁₆	—	4	2	no	—
200	C₁₁	#11961	1	1	yes	characteristic, direct product factor, Sylow
201	C₂³	—	4	4	no	—
202	C₂³	—	8	4	no	—
203	C₂³	—	8	4	no	—
204	C₂³	—	8	4	no	—
205	C₂³	C₁₁×#102	1	1	yes	characteristic
206	D₄	—	4	4	no	—
207	D₄	—	4	4	no	—
208	D₄	—	8	4	no	—
209	D₄	—	8	4	no	—
210	D₄	—	8	2	no	—
211	D₄	—	8	2	no	—
212	D₄	—	8	4	no	—
213	D₄	—	8	4	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
218	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
219	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
220	C₂×C₄	C₁₁×D₁₆	1	2	yes	—
221	C₂×C₄	C₁₁×SD₃₂	1	2	yes	—
222	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
224	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
225	C₈	—	2	1	no	—
226	C₈	—	2	1	no	—
227	C₈	—	8	2	no	—
228	C₈	C₁₁×#100	1	2	yes	—
229	C₈	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
230	C₂²	—	2	1	no	—
231	C₂²	—	2	1	no	—
232	C₂²	—	8	4	no	—
233	C₂²	—	8	4	no	—
234	C₂²	—	8	4	no	—
235	C₂²	—	16	8	no	—
236	C₂²	C₁₁×#357	1	2	yes	—
237	C₂²	C₂×C₁₁×#102	1	1	yes	characteristic
238	C₄	—	2	1	no	—
239	C₄	—	2	1	no	—
240	C₄	C₁₁×#357	1	2	yes	—
241	C₄	C₁₁×#361	1	2	yes	—
242	C₄	C₂×C₁₁×#100	1	1	yes	characteristic
243	C₄	C₁₁×#418	1	1	yes	characteristic
244	C₄	C₂×C₁₁×D₁₆	1	1	yes	characteristic
245	C₄	C₂×C₁₁×SD₃₂	1	1	yes	characteristic
246	C₂	—	2	2	no	—
247	C₂	—	16	4	no	—
248	C₂	C₁₁×#1545	1	1	yes	characteristic
249	C₂	C₂×C₁₁×#357	1	1	yes	characteristic
250	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	C₂×C₁₁×#493	C₂
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
2. C₁₁×#2162	C₂	semidirect
3. C₁₁×#1567	C₂	semidirect
4. C₁₁×#1361	C₂	semidirect
14. C₁₁×C₄⋊C₁₆	C₂²	semidirect
18. C₁₁×#335	C₂²	semidirect
43. #11961	C₁₁	direct (N × H)
77. #2162	C₂×C₁₁	semidirect
78. #1567	C₂×C₁₁	semidirect
79. #1361	C₂×C₁₁	semidirect
118. C₄⋊C₁₆	C₂²×C₁₁	semidirect
122. #335	C₂²×C₁₁	semidirect
200. C₁₁	#11961	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×#493	2
C₁₁×#2162	2
C₁₁×#1567	2
C₁₁×#1361	2
#11961	11

Subgroups — C11×#11961 #14589154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11961 #14589154