Subgroups — C₁₁×#17956 #14595149

Order 2816.

750 conjugacy classes of subgroups.

The subgroup lattice has 290 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	C₁₁×#2931	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1589	C₂	1	4	yes	maximal, complemented
4	C₈×C₁₁×D₈	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1567	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1492	C₂	1	2	yes	maximal, complemented
7	C₂×C₈²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₁×#131	—	2	2	no	—
9	C₁₁×#532	C₂²	1	2	yes	—
10	C₁₁×#500	C₄	1	1	yes	characteristic
11	C₁₁×#493	C₄	1	1	yes	characteristic
12	C₁₁×#486	C₄	1	2	yes	—
13	C₁₁×#466	C₄	1	4	yes	—
14	C₄×C₁₁×D₈	C₂²	1	4	yes	—
15	C₁₁×#436	—	2	2	no	—
16	C₁₁×#436	C₂²	1	4	yes	—
17	C₈×D₄×C₁₁	—	2	2	no	—
18	C₈×D₄×C₁₁	C₂²	1	4	yes	—
19	C₁₁×#423	C₂²	1	2	yes	—
20	C₁₁×#408	—	2	2	no	—
21	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
24	C₁₁×#335	C₂²	1	4	yes	—
25	C₁₁×D₄⋊C₈	C₂²	1	8	yes	—
26	C₈²×C₁₁	C₂²	1	2	yes	—
27	C₈²×C₁₁	C₂²	1	2	yes	—
28	C₂×C₁₁×#41	—	2	2	no	—
29	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	—
30	C₁₁×#131	—	4	8	no	—
31	C₂×C₁₁×M₁₆	—	2	2	no	—
32	C₂×C₁₁×M₁₆	—	2	4	no	—
33	C₂²×C₈×C₁₁	—	2	1	no	—
34	C₂²×C₈×C₁₁	—	2	4	no	—
35	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
38	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
39	C₁₁×#127	C₂×C₄	1	2	yes	—
40	C₁₁×#124	—	2	2	no	—
41	C₁₁×#121	—	2	2	no	—
42	C₁₁×#121	C₂×C₄	1	4	yes	—
43	C₄×D₄×C₁₁	—	2	2	no	—
44	C₄×D₄×C₁₁	C₂³	1	4	yes	—
45	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
46	C₁₁×#107	C₂×C₄	1	4	yes	—
47	C₁₁×C₄⋊C₈	—	2	2	no	—
48	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
49	C₁₁×#102	C₂×C₄	1	8	yes	—
50	C₁₁×C₂²⋊C₈	—	2	4	no	—
51	C₁₁×C₂²⋊C₈	—	2	4	no	—
52	C₄×C₈×C₁₁	—	2	1	no	—
53	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
54	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
55	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
56	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
57	C₄×C₈×C₁₁	C₂³	1	2	yes	—
58	C₄×C₈×C₁₁	C₂³	1	2	yes	—
59	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
60	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
61	#17956	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₁₁×#41	—	4	4	no	—
63	C₁₁×#41	—	4	4	no	—
64	C₂×Q₈×C₁₁	—	2	2	no	—
65	C₂×D₄×C₁₁	—	2	4	no	—
66	C₂×D₄×C₁₁	—	2	2	no	—
67	C₂×D₄×C₁₁	—	2	2	no	—
68	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
69	C₂²×C₄×C₁₁	—	2	4	no	—
70	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
73	C₁₁×D₈	—	2	8	no	—
74	C₁₁×M₁₆	—	4	8	no	—
75	C₁₁×M₁₆	—	4	4	no	—
76	C₂×C₈×C₁₁	—	2	4	no	—
77	C₂×C₈×C₁₁	—	2	4	no	—
78	C₂×C₈×C₁₁	—	2	2	no	—
79	C₂×C₈×C₁₁	—	2	4	no	—
80	C₂×C₈×C₁₁	—	2	2	no	—
81	C₂×C₈×C₁₁	—	4	8	no	—
82	C₂×C₈×C₁₁	D₈	1	4	yes	complemented
83	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
84	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
85	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
86	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
87	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
89	C₁₁×C₄⋊C₄	—	2	2	no	—
90	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
91	C₁₁×C₂²⋊C₄	—	2	4	no	—
92	C₁₁×C₂²⋊C₄	—	2	4	no	—
93	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
94	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
95	C₄²×C₁₁	#41	1	1	yes	characteristic
96	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
97	#3169	C₂×C₁₁	1	1	yes	characteristic
98	#2931	C₂×C₁₁	1	2	yes	complemented
99	#1589	C₂×C₁₁	1	4	yes	complemented
100	C₈×D₈	C₂×C₁₁	1	4	yes	complemented
101	#1567	C₂×C₁₁	1	1	yes	characteristic, complemented
102	#1492	C₂×C₁₁	1	2	yes	complemented
103	C₂×C₈²	C₂×C₁₁	1	1	yes	characteristic, complemented
104	C₂³×C₁₁	—	2	4	no	—
105	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
106	Q₈×C₁₁	—	4	4	no	—
107	D₄×C₁₁	—	2	8	no	—
108	D₄×C₁₁	—	4	8	no	—
109	D₄×C₁₁	—	4	4	no	—
110	D₄×C₁₁	—	4	4	no	—
111	C₂×C₄×C₁₁	—	2	2	no	—
112	C₂×C₄×C₁₁	—	2	2	no	—
113	C₂×C₄×C₁₁	—	2	4	no	—
114	C₂×C₄×C₁₁	—	4	4	no	—
115	C₂×C₄×C₁₁	—	4	4	no	—
116	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
117	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
118	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
119	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
120	C₂×C₄×C₁₁	#135	1	2	yes	—
121	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
123	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
124	C₈×C₁₁	—	2	4	no	—
125	C₈×C₁₁	—	2	2	no	—
126	C₈×C₁₁	—	2	1	no	—
127	C₈×C₁₁	—	2	1	no	—
128	C₈×C₁₁	—	4	4	no	—
129	C₈×C₁₁	#131	1	4	yes	complemented
130	C₈×C₁₁	C₂×D₈	1	2	yes	—
131	C₈×C₁₁	C₂×D₈	1	2	yes	—
132	C₂×#131	—	2	2	no	—
133	#532	C₂²×C₁₁	1	2	yes	—
134	#500	C₄×C₁₁	1	1	yes	characteristic
135	#493	C₄×C₁₁	1	1	yes	characteristic
136	#486	C₄×C₁₁	1	2	yes	—
137	#466	C₄×C₁₁	1	4	yes	—
138	C₄×D₈	C₂²×C₁₁	1	4	yes	—
139	#436	—	2	2	no	—
140	#436	C₂²×C₁₁	1	4	yes	—
141	C₈×D₄	—	2	2	no	—
142	C₈×D₄	C₂²×C₁₁	1	4	yes	—
143	#423	C₂²×C₁₁	1	2	yes	—
144	#408	—	2	2	no	—
145	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
146	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
147	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
148	#335	C₂²×C₁₁	1	4	yes	—
149	D₄⋊C₈	C₂²×C₁₁	1	8	yes	—
150	C₈²	C₂²×C₁₁	1	2	yes	—
151	C₈²	C₂²×C₁₁	1	2	yes	—
152	C₂²×C₁₁	—	2	1	no	—
153	C₂²×C₁₁	—	2	1	no	—
154	C₂²×C₁₁	—	4	4	no	—
155	C₂²×C₁₁	—	4	4	no	—
156	C₂²×C₁₁	—	4	4	no	—
157	C₂²×C₁₁	C₄×D₈	1	2	yes	—
158	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
159	C₄×C₁₁	—	2	1	no	—
160	C₄×C₁₁	—	2	1	no	—
161	C₄×C₁₁	—	4	4	no	—
162	C₄×C₁₁	C₄×D₈	1	2	yes	—
163	C₄×C₁₁	#443	1	2	yes	—
164	C₄×C₁₁	C₂×#131	1	2	yes	—
165	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
166	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
167	C₂×#41	—	2	2	no	—
168	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	—
169	#131	—	4	8	no	—
170	C₂×M₁₆	—	2	2	no	—
171	C₂×M₁₆	—	2	4	no	—
172	C₂²×C₈	—	2	1	no	—
173	C₂²×C₈	—	2	4	no	—
174	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
175	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
176	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
177	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
178	#127	C₂×C₄×C₁₁	1	2	yes	—
179	#124	—	2	2	no	—
180	#121	—	2	2	no	—
181	#121	C₂×C₄×C₁₁	1	4	yes	—
182	C₄×D₄	—	2	2	no	—
183	C₄×D₄	C₂³×C₁₁	1	4	yes	—
184	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
185	#107	C₂×C₄×C₁₁	1	4	yes	—
186	C₄⋊C₈	—	2	2	no	—
187	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
188	#102	C₂×C₄×C₁₁	1	8	yes	—
189	C₂²⋊C₈	—	2	4	no	—
190	C₂²⋊C₈	—	2	4	no	—
191	C₄×C₈	—	2	1	no	—
192	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
193	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
194	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
195	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
196	C₄×C₈	C₂³×C₁₁	1	2	yes	—
197	C₄×C₈	C₂³×C₁₁	1	2	yes	—
198	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
199	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
200	C₂×C₁₁	—	2	2	no	—
201	C₂×C₁₁	—	8	4	no	—
202	C₂×C₁₁	#2931	1	1	yes	characteristic
203	C₂×C₁₁	C₂×C₄×D₈	1	1	yes	characteristic
204	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
205	#41	—	4	4	no	—
206	#41	—	4	4	no	—
207	C₂×Q₈	—	2	2	no	—
208	C₂×D₄	—	2	4	no	—
209	C₂×D₄	—	2	2	no	—
210	C₂×D₄	—	2	2	no	—
211	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
212	C₂²×C₄	—	2	4	no	—
213	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
214	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
215	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
216	D₈	—	2	8	no	—
217	M₁₆	—	4	4	no	—
218	M₁₆	—	4	8	no	—
219	C₂×C₈	—	2	4	no	—
220	C₂×C₈	—	2	2	no	—
221	C₂×C₈	—	2	2	no	—
222	C₂×C₈	—	2	4	no	—
223	C₂×C₈	—	2	4	no	—
224	C₂×C₈	—	4	8	no	—
225	C₂×C₈	C₁₁×D₈	1	4	yes	complemented
226	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
227	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
228	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
229	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
230	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
231	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
232	C₄⋊C₄	—	2	2	no	—
233	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
234	C₂²⋊C₄	—	2	4	no	—
235	C₂²⋊C₄	—	2	4	no	—
236	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
237	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
238	C₄²	C₁₁×#41	1	1	yes	characteristic
239	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
240	C₁₁	#17956	1	1	yes	characteristic, direct product factor, Sylow
241	C₂³	—	2	4	no	—
242	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
243	Q₈	—	4	4	no	—
244	D₄	—	2	8	no	—
245	D₄	—	4	8	no	—
246	D₄	—	4	4	no	—
247	D₄	—	4	4	no	—
248	C₂×C₄	—	2	2	no	—
249	C₂×C₄	—	2	2	no	—
250	C₂×C₄	—	2	4	no	—
251	C₂×C₄	—	4	4	no	—
252	C₂×C₄	—	4	4	no	—
253	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
254	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
255	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
256	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
257	C₂×C₄	C₁₁×#135	1	2	yes	—
258	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
259	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
260	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
261	C₈	—	2	4	no	—
262	C₈	—	2	2	no	—
263	C₈	—	2	1	no	—
264	C₈	—	2	1	no	—
265	C₈	—	4	4	no	—
266	C₈	C₁₁×#131	1	4	yes	complemented
267	C₈	C₂×C₁₁×D₈	1	2	yes	—
268	C₈	C₂×C₁₁×D₈	1	2	yes	—
269	C₂²	—	2	1	no	—
270	C₂²	—	2	1	no	—
271	C₂²	—	4	4	no	—
272	C₂²	—	4	4	no	—
273	C₂²	—	4	4	no	—
274	C₂²	C₄×C₁₁×D₈	1	2	yes	—
275	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
276	C₄	—	2	1	no	—
277	C₄	—	2	1	no	—
278	C₄	—	4	4	no	—
279	C₄	C₄×C₁₁×D₈	1	2	yes	—
280	C₄	C₁₁×#443	1	2	yes	—
281	C₄	C₂×C₁₁×#131	1	2	yes	—
282	C₄	C₂²×C₁₁×D₈	1	1	yes	characteristic
283	C₄	C₂×C₁₁×#135	1	1	yes	characteristic
284	C₂	—	2	2	no	—
285	C₂	—	8	4	no	—
286	C₂	C₁₁×#2931	1	1	yes	characteristic
287	C₂	C₂×C₄×C₁₁×D₈	1	1	yes	characteristic
288	C₂	C₂×C₁₁×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₄²	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₁₁×#3169	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₁×#2931	C₂	semidirect
3. C₁₁×#1589	C₂	semidirect
4. C₈×C₁₁×D₈	C₂	semidirect
5. C₁₁×#1567	C₂	semidirect
6. C₁₁×#1492	C₂	semidirect
7. C₂×C₈²×C₁₁	C₂	semidirect
61. #17956	C₁₁	direct (N × H)
82. C₂×C₈×C₁₁	D₈	semidirect
98. #2931	C₂×C₁₁	semidirect
99. #1589	C₂×C₁₁	semidirect
100. C₈×D₈	C₂×C₁₁	semidirect
101. #1567	C₂×C₁₁	semidirect
102. #1492	C₂×C₁₁	semidirect
103. C₂×C₈²	C₂×C₁₁	semidirect
129. C₈×C₁₁	#131	semidirect
225. C₂×C₈	C₁₁×D₈	semidirect
240. C₁₁	#17956	direct (N × H)
266. C₈	C₁₁×#131	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₁×#3169	2
C₁₁×#2931	2
C₁₁×#1589	2
C₈×C₁₁×D₈	2
C₁₁×#1567	2
C₁₁×#1492	2
C₂×C₈²×C₁₁	2
#17956	11

Subgroups — C11×#17956 #14595149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#17956 #14595149