Subgroups — C₁₁×#22236 #14599429

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3131	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2961	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2932	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1995	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1963	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1929	C₂	1	4	yes	maximal, complemented
7	C₁₁×#1866	C₂	1	4	yes	maximal, complemented
8	C₁₁×#1848	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1746	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#131	C₂²	1	2	yes	—
11	C₁₁×#533	C₂²	1	1	yes	characteristic
12	C₁₁×#532	C₂²	1	1	yes	characteristic
13	C₁₁×#488	C₄	1	4	yes	complemented
14	C₁₁×#487	C₄	1	2	yes	complemented
15	C₁₁×#486	C₄	1	2	yes	complemented
16	C₁₁×#446	—	2	4	no	—
17	C₁₁×#435	—	2	4	no	—
18	C₂×C₁₁×#108	C₂²	1	4	yes	—
19	C₁₁×#424	C₂²	1	2	yes	—
20	C₁₁×#423	C₂²	1	1	yes	characteristic
21	C₁₁×#423	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×#104	C₂²	1	4	yes	—
23	C₁₁×#416	C₂²	1	4	yes	—
24	C₁₁×#408	C₂²	1	2	yes	—
25	C₁₁×#405	C₂²	1	2	yes	—
26	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
28	C₁₁×#376	C₂²	1	1	yes	characteristic
29	C₁₁×#339	C₂²	1	4	yes	—
30	C₁₁×#336	C₂²	1	2	yes	—
31	C₁₁×#336	C₂²	1	2	yes	—
32	C₂×C₁₁×#41	C₂³	1	2	yes	—
33	C₁₁×#131	—	4	4	no	—
34	C₂×C₁₁×M₁₆	—	2	2	no	—
35	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
36	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
37	C₂²×C₈×C₁₁	—	2	2	no	—
38	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
39	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
41	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
42	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
43	C₁₁×#127	C₂×C₄	1	1	yes	characteristic
44	C₁₁×#125	C₂×C₄	1	2	yes	—
45	C₁₁×#124	C₂×C₄	1	2	yes	—
46	C₁₁×C₂²⋊Q₈	—	2	2	no	—
47	C₁₁×#121	—	2	2	no	—
48	C₄×Q₈×C₁₁	—	2	2	no	—
49	C₄×D₄×C₁₁	—	2	2	no	—
50	C₁₁×#117	C₂³	1	2	yes	—
51	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
52	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
53	C₁₁×#108	—	4	4	no	—
54	C₁₁×C₄⋊C₈	—	2	4	no	—
55	C₁₁×C₄⋊C₈	—	2	2	no	—
56	C₁₁×C₄⋊C₈	—	2	2	no	—
57	C₁₁×#104	—	4	4	no	—
58	C₁₁×#103	C₂×C₄	1	8	yes	—
59	C₁₁×#102	C₂×C₄	1	8	yes	—
60	C₁₁×C₂²⋊C₈	—	2	4	no	—
61	C₁₁×#97	—	2	2	no	—
62	C₁₁×#97	D₄	1	4	yes	—
63	C₄×C₈×C₁₁	—	2	2	no	—
64	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
65	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
66	C₁₁×#95	—	2	2	no	—
67	#22236	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₁₁×#41	—	2	4	no	—
69	C₁₁×#41	—	2	4	no	—
70	C₂×Q₈×C₁₁	—	2	2	no	—
71	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
72	C₂×D₄×C₁₁	—	2	2	no	—
73	C₂×D₄×C₁₁	—	2	2	no	—
74	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
75	C₂²×C₄×C₁₁	—	2	2	no	—
76	C₂²×C₄×C₁₁	—	2	2	no	—
77	C₂²×C₄×C₁₁	#41	1	2	yes	—
78	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
79	C₁₁×M₁₆	—	2	4	no	—
80	C₁₁×M₁₆	—	2	4	no	—
81	C₁₁×M₁₆	—	4	4	no	—
82	C₂×C₈×C₁₁	—	2	2	no	—
83	C₂×C₈×C₁₁	—	2	2	no	—
84	C₂×C₈×C₁₁	—	2	2	no	—
85	C₂×C₈×C₁₁	—	2	2	no	—
86	C₂×C₈×C₁₁	—	2	2	no	—
87	C₂×C₈×C₁₁	—	2	2	no	—
88	C₂×C₈×C₁₁	—	4	4	no	—
89	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
90	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
91	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
92	C₁₁×C₄⋊C₄	—	2	2	no	—
93	C₁₁×C₄⋊C₄	—	2	4	no	—
94	C₁₁×C₄⋊C₄	—	2	2	no	—
95	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
96	C₁₁×C₂²⋊C₄	—	2	2	no	—
97	C₁₁×C₂²⋊C₄	—	2	4	no	—
98	C₄²×C₁₁	—	2	2	no	—
99	C₄²×C₁₁	—	2	2	no	—
100	C₄²×C₁₁	—	2	2	no	—
101	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₁₁	C₂×D₄	1	2	yes	—
104	#3131	C₂×C₁₁	1	1	yes	characteristic
105	#2961	C₂×C₁₁	1	1	yes	characteristic, complemented
106	#2932	C₂×C₁₁	1	1	yes	characteristic
107	#1995	C₂×C₁₁	1	1	yes	characteristic, complemented
108	#1963	C₂×C₁₁	1	1	yes	characteristic
109	#1929	C₂×C₁₁	1	4	yes	complemented
110	#1866	C₂×C₁₁	1	4	yes	complemented
111	#1848	C₂×C₁₁	1	1	yes	characteristic, complemented
112	#1746	C₂×C₁₁	1	1	yes	characteristic, complemented
113	C₂³×C₁₁	—	2	2	no	—
114	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
115	Q₈×C₁₁	—	2	4	no	—
116	Q₈×C₁₁	—	8	2	no	—
117	D₄×C₁₁	—	2	4	no	—
118	D₄×C₁₁	—	4	4	no	—
119	D₄×C₁₁	—	8	2	no	—
120	C₂×C₄×C₁₁	—	2	4	no	—
121	C₂×C₄×C₁₁	—	2	2	no	—
122	C₂×C₄×C₁₁	—	4	2	no	—
123	C₂×C₄×C₁₁	—	4	2	no	—
124	C₂×C₄×C₁₁	—	4	2	no	—
125	C₂×C₄×C₁₁	—	4	4	no	—
126	C₂×C₄×C₁₁	—	4	2	no	—
127	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
128	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
129	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
131	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
132	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
133	C₈×C₁₁	—	2	4	no	—
134	C₈×C₁₁	—	2	2	no	—
135	C₈×C₁₁	—	2	2	no	—
136	C₈×C₁₁	—	4	2	no	—
137	C₈×C₁₁	—	4	2	no	—
138	C₂×#131	C₂²×C₁₁	1	2	yes	—
139	#533	C₂²×C₁₁	1	1	yes	characteristic
140	#532	C₂²×C₁₁	1	1	yes	characteristic
141	#488	C₄×C₁₁	1	4	yes	complemented
142	#487	C₄×C₁₁	1	2	yes	complemented
143	#486	C₄×C₁₁	1	2	yes	complemented
144	#446	—	2	4	no	—
145	#435	—	2	4	no	—
146	C₂×#108	C₂²×C₁₁	1	4	yes	—
147	#424	C₂²×C₁₁	1	2	yes	—
148	#423	C₂²×C₁₁	1	1	yes	characteristic
149	#423	C₂²×C₁₁	1	1	yes	characteristic
150	C₂×#104	C₂²×C₁₁	1	4	yes	—
151	#416	C₂²×C₁₁	1	4	yes	—
152	#408	C₂²×C₁₁	1	2	yes	—
153	#405	C₂²×C₁₁	1	2	yes	—
154	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
155	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
156	#376	C₂²×C₁₁	1	1	yes	characteristic
157	#339	C₂²×C₁₁	1	4	yes	—
158	#336	C₂²×C₁₁	1	2	yes	—
159	#336	C₂²×C₁₁	1	2	yes	—
160	C₂²×C₁₁	—	2	2	no	—
161	C₂²×C₁₁	—	4	2	no	—
162	C₂²×C₁₁	—	4	4	no	—
163	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
164	C₂²×C₁₁	#542	1	2	yes	—
165	C₄×C₁₁	—	2	2	no	—
166	C₄×C₁₁	—	2	2	no	—
167	C₄×C₁₁	—	4	2	no	—
168	C₄×C₁₁	—	4	4	no	—
169	C₄×C₁₁	—	8	2	no	—
170	C₄×C₁₁	#520	1	2	yes	—
171	C₄×C₁₁	#535	1	1	yes	characteristic
172	C₄×C₁₁	#536	1	1	yes	characteristic
173	C₂×#41	C₂³×C₁₁	1	2	yes	—
174	#131	—	4	4	no	—
175	C₂×M₁₆	—	2	2	no	—
176	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
177	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
178	C₂²×C₈	—	2	2	no	—
179	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
180	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
181	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
182	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
183	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
184	#127	C₂×C₄×C₁₁	1	1	yes	characteristic
185	#125	C₂×C₄×C₁₁	1	2	yes	—
186	#124	C₂×C₄×C₁₁	1	2	yes	—
187	C₂²⋊Q₈	—	2	2	no	—
188	#121	—	2	2	no	—
189	C₄×Q₈	—	2	2	no	—
190	C₄×D₄	—	2	2	no	—
191	#117	C₂³×C₁₁	1	2	yes	—
192	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
193	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
194	#108	—	4	4	no	—
195	C₄⋊C₈	—	2	4	no	—
196	C₄⋊C₈	—	2	2	no	—
197	C₄⋊C₈	—	2	2	no	—
198	#104	—	4	4	no	—
199	#103	C₂×C₄×C₁₁	1	8	yes	—
200	#102	C₂×C₄×C₁₁	1	8	yes	—
201	C₂²⋊C₈	—	2	4	no	—
202	#97	—	2	2	no	—
203	#97	D₄×C₁₁	1	4	yes	—
204	C₄×C₈	—	2	2	no	—
205	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
206	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
207	#95	—	2	2	no	—
208	C₂×C₁₁	—	2	2	no	—
209	C₂×C₁₁	—	8	2	no	—
210	C₂×C₁₁	#2326	1	1	yes	characteristic
211	C₂×C₁₁	#2957	1	2	yes	—
212	#41	—	2	4	no	—
213	#41	—	2	4	no	—
214	C₂×Q₈	—	2	2	no	—
215	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
216	C₂×D₄	—	2	2	no	—
217	C₂×D₄	—	2	2	no	—
218	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
219	C₂²×C₄	—	2	2	no	—
220	C₂²×C₄	—	2	2	no	—
221	C₂²×C₄	C₁₁×#41	1	2	yes	—
222	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
223	M₁₆	—	2	4	no	—
224	M₁₆	—	2	4	no	—
225	M₁₆	—	4	4	no	—
226	C₂×C₈	—	2	2	no	—
227	C₂×C₈	—	2	2	no	—
228	C₂×C₈	—	2	2	no	—
229	C₂×C₈	—	2	2	no	—
230	C₂×C₈	—	2	2	no	—
231	C₂×C₈	—	2	2	no	—
232	C₂×C₈	—	4	4	no	—
233	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
234	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
235	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
236	C₄⋊C₄	—	2	2	no	—
237	C₄⋊C₄	—	2	4	no	—
238	C₄⋊C₄	—	2	2	no	—
239	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
240	C₂²⋊C₄	—	2	2	no	—
241	C₂²⋊C₄	—	2	4	no	—
242	C₄²	—	2	2	no	—
243	C₄²	—	2	2	no	—
244	C₄²	—	2	2	no	—
245	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
246	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
247	C₄²	C₂×D₄×C₁₁	1	2	yes	—
248	C₁₁	#22236	1	1	yes	characteristic, direct product factor, Sylow
249	C₂³	—	2	2	no	—
250	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
251	Q₈	—	2	4	no	—
252	Q₈	—	8	2	no	—
253	D₄	—	2	4	no	—
254	D₄	—	4	4	no	—
255	D₄	—	8	2	no	—
256	C₂×C₄	—	2	4	no	—
257	C₂×C₄	—	2	2	no	—
258	C₂×C₄	—	4	2	no	—
259	C₂×C₄	—	4	2	no	—
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	—	4	4	no	—
262	C₂×C₄	—	4	2	no	—
263	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
264	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
265	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
266	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
267	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
268	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
269	C₈	—	2	4	no	—
270	C₈	—	2	2	no	—
271	C₈	—	2	2	no	—
272	C₈	—	4	2	no	—
273	C₈	—	4	2	no	—
274	C₂²	—	2	2	no	—
275	C₂²	—	4	4	no	—
276	C₂²	—	4	2	no	—
277	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
278	C₂²	C₁₁×#542	1	2	yes	—
279	C₄	—	2	2	no	—
280	C₄	—	2	2	no	—
281	C₄	—	4	4	no	—
282	C₄	—	4	2	no	—
283	C₄	—	8	2	no	—
284	C₄	C₁₁×#520	1	2	yes	—
285	C₄	C₁₁×#535	1	1	yes	characteristic
286	C₄	C₁₁×#536	1	1	yes	characteristic
287	C₂	—	2	2	no	—
288	C₂	—	8	2	no	—
289	C₂	C₁₁×#2326	1	1	yes	characteristic
290	C₂	C₁₁×#2957	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₁₁×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×#97 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2961	C₂	semidirect
4. C₁₁×#1995	C₂	semidirect
6. C₁₁×#1929	C₂	semidirect
7. C₁₁×#1866	C₂	semidirect
8. C₁₁×#1848	C₂	semidirect
9. C₁₁×#1746	C₂	semidirect
13. C₁₁×#488	C₄	semidirect
14. C₁₁×#487	C₄	semidirect
15. C₁₁×#486	C₄	semidirect
67. #22236	C₁₁	direct (N × H)
105. #2961	C₂×C₁₁	semidirect
107. #1995	C₂×C₁₁	semidirect
109. #1929	C₂×C₁₁	semidirect
110. #1866	C₂×C₁₁	semidirect
111. #1848	C₂×C₁₁	semidirect
112. #1746	C₂×C₁₁	semidirect
141. #488	C₄×C₁₁	semidirect
142. #487	C₄×C₁₁	semidirect
143. #486	C₄×C₁₁	semidirect
248. C₁₁	#22236	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×#3131	2
C₁₁×#2961	2
C₁₁×#2932	2
C₁₁×#1995	2
C₁₁×#1963	2
C₁₁×#1929	2
C₁₁×#1866	2
C₁₁×#1848	2
C₁₁×#1746	2
#22236	11

Subgroups — C11×#22236 #14599429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22236 #14599429