Subgroups — C₁₁×#11981 #14589174

Order 2816.

358 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3169	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#1567	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1364	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1361	C₂	1	2	yes	maximal, complemented
6	C₁₁×#532	—	2	1	no	—
7	C₂²×C₁₁×C₁₆	—	2	1	no	—
8	C₁₁×#500	C₂²	1	1	yes	characteristic
9	C₁₁×#493	C₂²	1	1	yes	characteristic
10	C₁₁×#486	—	2	1	no	—
11	C₁₁×#466	—	2	1	no	—
12	C₁₁×#466	C₄	1	2	yes	—
13	C₄×C₁₁×D₈	—	2	1	no	—
14	C₄×C₁₁×D₈	C₄	1	2	yes	—
15	C₁₁×#423	—	2	1	no	—
16	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
17	C₁₁×C₄⋊C₁₆	—	2	1	no	—
18	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
19	C₁₁×#335	—	2	1	no	—
20	C₁₁×#335	C₂²	1	2	yes	—
21	C₂×C₁₁×#41	—	4	1	no	—
22	C₂×C₁₁×D₈	—	2	1	no	—
23	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
24	C₂×C₁₁×M₁₆	—	4	1	no	—
25	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
27	C₁₁×C₄⋊Q₈	—	2	1	no	—
28	C₁₁×#127	—	2	1	no	—
29	C₁₁×#124	—	4	1	no	—
30	C₁₁×#121	—	2	2	no	—
31	C₁₁×#121	—	4	1	no	—
32	C₄×D₄×C₁₁	—	2	2	no	—
33	C₄×D₄×C₁₁	—	4	1	no	—
34	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
35	C₂×C₁₁×C₁₆	—	2	2	no	—
36	C₂×C₁₁×C₁₆	—	4	2	no	—
37	C₁₁×#107	—	2	1	no	—
38	C₁₁×#107	C₂×C₄	1	2	yes	—
39	C₁₁×C₄⋊C₈	—	2	2	no	—
40	C₁₁×C₄⋊C₈	—	4	1	no	—
41	C₁₁×#102	—	2	2	no	—
42	C₁₁×#102	—	2	2	no	—
43	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
45	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
46	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
47	#11981	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₁₁×#41	—	8	2	no	—
49	C₁₁×#41	—	8	2	no	—
50	C₂×Q₈×C₁₁	—	4	1	no	—
51	C₂×D₄×C₁₁	—	2	2	no	—
52	C₂×D₄×C₁₁	—	4	2	no	—
53	C₂×D₄×C₁₁	—	4	1	no	—
54	C₂×D₄×C₁₁	—	4	1	no	—
55	C₂²×C₄×C₁₁	—	4	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	1	no	—
60	C₁₁×D₈	—	4	1	no	—
61	C₁₁×D₈	—	4	2	no	—
62	C₁₁×M₁₆	—	8	2	no	—
63	C₂×C₈×C₁₁	—	2	1	no	—
64	C₂×C₈×C₁₁	—	2	1	no	—
65	C₂×C₈×C₁₁	—	4	1	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	C₁₁×C₄⋊C₄	—	2	2	no	—
72	C₁₁×C₄⋊C₄	—	4	1	no	—
73	C₁₁×C₂²⋊C₄	—	4	2	no	—
74	C₁₁×C₂²⋊C₄	—	4	2	no	—
75	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₄²×C₁₁	D₈	1	1	yes	characteristic
77	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
78	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
79	C₁₁×C₁₆	—	4	2	no	—
80	#3169	C₂×C₁₁	1	1	yes	characteristic
81	C₂×C₄⋊C₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
82	#1567	C₂×C₁₁	1	1	yes	characteristic, complemented
83	#1364	C₂×C₁₁	1	2	yes	complemented
84	#1361	C₂×C₁₁	1	2	yes	complemented
85	C₂³×C₁₁	—	4	2	no	—
86	C₂³×C₁₁	#102	1	1	yes	characteristic
87	Q₈×C₁₁	—	8	1	no	—
88	Q₈×C₁₁	—	8	1	no	—
89	D₄×C₁₁	—	4	2	no	—
90	D₄×C₁₁	—	4	2	no	—
91	D₄×C₁₁	—	8	2	no	—
92	D₄×C₁₁	—	8	4	no	—
93	D₄×C₁₁	—	8	1	no	—
94	D₄×C₁₁	—	8	1	no	—
95	C₂×C₄×C₁₁	—	2	1	no	—
96	C₂×C₄×C₁₁	—	2	1	no	—
97	C₂×C₄×C₁₁	—	4	1	no	—
98	C₂×C₄×C₁₁	—	4	2	no	—
99	C₂×C₄×C₁₁	—	8	4	no	—
100	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
101	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
102	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
103	C₂×C₄×C₁₁	D₁₆	1	2	yes	—
104	C₂×C₄×C₁₁	SD₃₂	1	2	yes	—
105	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
107	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
108	C₈×C₁₁	—	2	1	no	—
109	C₈×C₁₁	—	2	1	no	—
110	C₈×C₁₁	—	2	1	no	—
111	C₈×C₁₁	—	8	2	no	—
112	C₈×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
113	C₈×C₁₁	#137	1	1	yes	characteristic
114	#532	—	2	1	no	—
115	C₂²×C₁₆	—	2	1	no	—
116	#500	C₂²×C₁₁	1	1	yes	characteristic
117	#493	C₂²×C₁₁	1	1	yes	characteristic
118	#486	—	2	1	no	—
119	#466	—	2	1	no	—
120	#466	C₄×C₁₁	1	2	yes	—
121	C₄×D₈	—	2	1	no	—
122	C₄×D₈	C₄×C₁₁	1	2	yes	—
123	#423	—	2	1	no	—
124	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
125	C₄⋊C₁₆	—	2	1	no	—
126	C₄⋊C₁₆	C₂²×C₁₁	1	2	yes	—
127	#335	—	2	1	no	—
128	#335	C₂²×C₁₁	1	2	yes	—
129	C₂²×C₁₁	—	2	1	no	—
130	C₂²×C₁₁	—	2	1	no	—
131	C₂²×C₁₁	—	8	2	no	—
132	C₂²×C₁₁	—	8	2	no	—
133	C₂²×C₁₁	—	8	2	no	—
134	C₂²×C₁₁	#357	1	2	yes	—
135	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
136	C₄×C₁₁	—	2	1	no	—
137	C₄×C₁₁	—	2	1	no	—
138	C₄×C₁₁	—	2	1	no	—
139	C₄×C₁₁	—	8	2	no	—
140	C₄×C₁₁	#357	1	2	yes	—
141	C₄×C₁₁	#413	1	1	yes	characteristic
142	C₄×C₁₁	#417	1	1	yes	characteristic
143	C₄×C₁₁	C₂×D₁₆	1	1	yes	characteristic
144	C₄×C₁₁	C₂×SD₃₂	1	1	yes	characteristic
145	C₂×#41	—	4	1	no	—
146	C₂×D₈	—	2	1	no	—
147	C₂×D₈	C₂×C₄×C₁₁	1	2	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	C₄⋊Q₈	—	2	1	no	—
152	#127	—	2	1	no	—
153	#124	—	4	1	no	—
154	#121	—	2	2	no	—
155	#121	—	4	1	no	—
156	C₄×D₄	—	2	2	no	—
157	C₄×D₄	—	4	1	no	—
158	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
159	C₂×C₁₆	—	2	2	no	—
160	C₂×C₁₆	—	4	2	no	—
161	#107	—	2	1	no	—
162	#107	C₂×C₄×C₁₁	1	2	yes	—
163	C₄⋊C₈	—	2	2	no	—
164	C₄⋊C₈	—	4	1	no	—
165	#102	—	2	2	no	—
166	#102	—	2	2	no	—
167	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
168	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
169	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
170	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
171	C₂×C₁₁	—	2	2	no	—
172	C₂×C₁₁	—	16	2	no	—
173	C₂×C₁₁	#1547	1	1	yes	characteristic
174	C₂×C₁₁	C₂×#357	1	1	yes	characteristic
175	C₂×C₁₁	#2148	1	1	yes	characteristic
176	#41	—	8	2	no	—
177	#41	—	8	2	no	—
178	C₂×Q₈	—	4	1	no	—
179	C₂×D₄	—	2	2	no	—
180	C₂×D₄	—	4	2	no	—
181	C₂×D₄	—	4	1	no	—
182	C₂×D₄	—	4	1	no	—
183	C₂²×C₄	—	4	2	no	—
184	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
185	C₂²×C₄	C₁₁×D₈	1	1	yes	characteristic
186	C₂²×C₄	C₁₁×SD₁₆	1	1	yes	characteristic
187	D₈	—	4	2	no	—
188	D₈	—	4	1	no	—
189	D₈	—	4	1	no	—
190	M₁₆	—	8	2	no	—
191	C₂×C₈	—	2	1	no	—
192	C₂×C₈	—	2	1	no	—
193	C₂×C₈	—	4	1	no	—
194	C₂×C₈	—	4	2	no	—
195	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
198	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
199	C₄⋊C₄	—	2	2	no	—
200	C₄⋊C₄	—	4	1	no	—
201	C₂²⋊C₄	—	4	2	no	—
202	C₂²⋊C₄	—	4	2	no	—
203	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
204	C₄²	C₁₁×D₈	1	1	yes	characteristic
205	C₄²	C₁₁×SD₁₆	1	1	yes	characteristic
206	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
207	C₁₆	—	4	2	no	—
208	C₁₁	#11981	1	1	yes	characteristic, direct product factor, Sylow
209	C₂³	—	4	2	no	—
210	C₂³	C₁₁×#102	1	1	yes	characteristic
211	Q₈	—	8	1	no	—
212	Q₈	—	8	1	no	—
213	D₄	—	4	2	no	—
214	D₄	—	4	2	no	—
215	D₄	—	8	2	no	—
216	D₄	—	8	4	no	—
217	D₄	—	8	1	no	—
218	D₄	—	8	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	4	1	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	8	4	no	—
224	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
225	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
226	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
227	C₂×C₄	C₁₁×D₁₆	1	2	yes	—
228	C₂×C₄	C₁₁×SD₃₂	1	2	yes	—
229	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
231	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
232	C₈	—	2	1	no	—
233	C₈	—	2	1	no	—
234	C₈	—	2	1	no	—
235	C₈	—	8	2	no	—
236	C₈	C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
237	C₈	C₁₁×#137	1	1	yes	characteristic
238	C₂²	—	2	1	no	—
239	C₂²	—	2	1	no	—
240	C₂²	—	8	2	no	—
241	C₂²	—	8	2	no	—
242	C₂²	—	8	2	no	—
243	C₂²	C₁₁×#357	1	2	yes	—
244	C₂²	C₂×C₁₁×#102	1	1	yes	characteristic
245	C₄	—	2	1	no	—
246	C₄	—	2	1	no	—
247	C₄	—	2	1	no	—
248	C₄	—	8	2	no	—
249	C₄	C₁₁×#357	1	2	yes	—
250	C₄	C₁₁×#413	1	1	yes	characteristic
251	C₄	C₁₁×#417	1	1	yes	characteristic
252	C₄	C₂×C₁₁×D₁₆	1	1	yes	characteristic
253	C₄	C₂×C₁₁×SD₃₂	1	1	yes	characteristic
254	C₂	—	2	2	no	—
255	C₂	—	16	2	no	—
256	C₂	C₁₁×#1547	1	1	yes	characteristic
257	C₂	C₂×C₁₁×#357	1	1	yes	characteristic
258	C₂	C₁₁×#2148	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	C₁₁×#3169	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. C₂×C₁₁×C₄⋊C₁₆	C₂	semidirect
3. C₁₁×#1567	C₂	semidirect
4. C₁₁×#1364	C₂	semidirect
5. C₁₁×#1361	C₂	semidirect
47. #11981	C₁₁	direct (N × H)
81. C₂×C₄⋊C₁₆	C₂×C₁₁	semidirect
82. #1567	C₂×C₁₁	semidirect
83. #1364	C₂×C₁₁	semidirect
84. #1361	C₂×C₁₁	semidirect
208. C₁₁	#11981	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×#3169	2
C₂×C₁₁×C₄⋊C₁₆	2
C₁₁×#1567	2
C₁₁×#1364	2
C₁₁×#1361	2
#11981	11

Subgroups — C11×#11981 #14589174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11981 #14589174