Subgroups — C₁₁×#22241 #14599434

Order 2816.

694 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#446	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2399	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1985	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1985	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1917	C₂	1	4	yes	maximal
7	C₁₁×#1916	C₂	1	4	yes	maximal
8	C₁₁×#1832	C₂	1	1	yes	maximal, characteristic
9	C₁₁×#1746	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₁₁×#446	—	2	4	no	—
13	C₈×Q₈×C₁₁	—	2	4	no	—
14	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×#97	C₂²	1	2	yes	—
19	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
22	C₁₁×#398	C₄	1	2	yes	—
23	C₁₁×#398	C₄	1	2	yes	—
24	C₁₁×#395	C₄	1	2	yes	—
25	C₁₁×#395	C₄	1	2	yes	—
26	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
27	C₁₁×#376	C₂²	1	1	yes	characteristic
28	C₁₁×#336	C₂²	1	2	yes	—
29	C₁₁×#336	C₂²	1	4	yes	—
30	C₁₁×#336	C₂²	1	4	yes	—
31	C₁₁×#336	C₂²	1	4	yes	—
32	C₁₁×#336	C₂²	1	2	yes	—
33	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
34	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
36	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
37	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
38	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
40	C₄×Q₈×C₁₁	—	2	2	no	—
41	C₄×Q₈×C₁₁	—	2	2	no	—
42	C₄×Q₈×C₁₁	—	2	2	no	—
43	C₄×Q₈×C₁₁	—	2	2	no	—
44	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
45	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
46	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
47	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
50	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
51	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
52	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
53	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
54	C₁₁×C₄⋊C₈	—	2	4	no	—
55	C₁₁×C₄⋊C₈	—	2	4	no	—
56	C₁₁×C₄⋊C₈	—	2	2	no	—
57	C₁₁×C₄⋊C₈	—	2	2	no	—
58	C₁₁×#97	—	2	4	no	—
59	C₁₁×#97	—	2	2	no	—
60	C₄×C₈×C₁₁	—	2	4	no	—
61	C₄×C₈×C₁₁	D₄	1	4	yes	—
62	C₁₁×#95	C₂×C₄	1	2	yes	—
63	C₁₁×#95	C₂×C₄	1	2	yes	—
64	C₁₁×#95	C₂×C₄	1	4	yes	—
65	C₁₁×#95	C₂×C₄	1	4	yes	—
66	#22241	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
67	C₂×Q₈×C₁₁	—	2	2	no	—
68	C₂×Q₈×C₁₁	—	2	2	no	—
69	C₂×Q₈×C₁₁	—	2	4	no	—
70	C₂×Q₈×C₁₁	—	4	2	no	—
71	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
72	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
73	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
74	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
75	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
79	C₂×C₈×C₁₁	—	2	2	no	—
80	C₂×C₈×C₁₁	—	2	2	no	—
81	C₂×C₈×C₁₁	—	2	2	no	—
82	C₂×C₈×C₁₁	—	2	2	no	—
83	C₂×C₈×C₁₁	—	2	2	no	—
84	C₂×C₈×C₁₁	—	2	4	no	—
85	C₂×C₈×C₁₁	—	2	4	no	—
86	C₂×C₈×C₁₁	—	2	2	no	—
87	C₂×C₈×C₁₁	—	2	2	no	—
88	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
89	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
90	C₁₁×C₄⋊C₄	—	2	4	no	—
91	C₁₁×C₄⋊C₄	—	2	2	no	—
92	C₁₁×C₄⋊C₄	—	2	2	no	—
93	C₁₁×C₄⋊C₄	—	2	4	no	—
94	C₁₁×C₄⋊C₄	—	2	8	no	—
95	C₁₁×C₄⋊C₄	—	4	4	no	—
96	C₄²×C₁₁	—	2	2	no	—
97	C₄²×C₁₁	—	2	2	no	—
98	C₄²×C₁₁	—	2	2	no	—
99	C₄²×C₁₁	—	2	2	no	—
100	C₄²×C₁₁	—	2	2	no	—
101	C₄²×C₁₁	—	2	2	no	—
102	C₄²×C₁₁	C₂×D₄	1	2	yes	—
103	C₄²×C₁₁	#41	1	2	yes	—
104	C₂×#446	C₂×C₁₁	1	1	yes	characteristic
105	C₂×C₈×Q₈	C₂×C₁₁	1	1	yes	characteristic
106	#2399	C₂×C₁₁	1	1	yes	characteristic
107	#1985	C₂×C₁₁	1	1	yes	characteristic
108	#1985	C₂×C₁₁	1	1	yes	characteristic
109	#1917	C₂×C₁₁	1	4	yes	—
110	#1916	C₂×C₁₁	1	4	yes	—
111	#1832	C₂×C₁₁	1	1	yes	characteristic
112	#1746	C₂×C₁₁	1	1	yes	characteristic
113	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
114	Q₈×C₁₁	—	2	8	no	—
115	Q₈×C₁₁	—	4	4	no	—
116	C₂×C₄×C₁₁	—	2	2	no	—
117	C₂×C₄×C₁₁	—	2	2	no	—
118	C₂×C₄×C₁₁	—	2	2	no	—
119	C₂×C₄×C₁₁	—	2	2	no	—
120	C₂×C₄×C₁₁	—	2	2	no	—
121	C₂×C₄×C₁₁	—	2	2	no	—
122	C₂×C₄×C₁₁	—	2	2	no	—
123	C₂×C₄×C₁₁	—	2	4	no	—
124	C₂×C₄×C₁₁	—	2	4	no	—
125	C₂×C₄×C₁₁	—	2	4	no	—
126	C₂×C₄×C₁₁	—	2	2	no	—
127	C₂×C₄×C₁₁	—	2	4	no	—
128	C₂×C₄×C₁₁	—	2	4	no	—
129	C₂×C₄×C₁₁	—	2	2	no	—
130	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
131	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
132	C₂×C₄×C₁₁	#131	1	4	yes	—
133	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
135	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
136	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
137	C₈×C₁₁	—	2	2	no	—
138	C₈×C₁₁	—	2	2	no	—
139	C₈×C₁₁	—	4	2	no	—
140	C₈×C₁₁	—	4	2	no	—
141	C₈×C₁₁	—	4	2	no	—
142	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
143	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
144	#446	—	2	4	no	—
145	C₈×Q₈	—	2	4	no	—
146	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
147	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
148	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
149	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
150	C₂×#97	C₂²×C₁₁	1	2	yes	—
151	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
152	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
153	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
154	#398	C₄×C₁₁	1	2	yes	—
155	#398	C₄×C₁₁	1	2	yes	—
156	#395	C₄×C₁₁	1	2	yes	—
157	#395	C₄×C₁₁	1	2	yes	—
158	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
159	#376	C₂²×C₁₁	1	1	yes	characteristic
160	#336	C₂²×C₁₁	1	4	yes	—
161	#336	C₂²×C₁₁	1	2	yes	—
162	#336	C₂²×C₁₁	1	4	yes	—
163	#336	C₂²×C₁₁	1	4	yes	—
164	#336	C₂²×C₁₁	1	2	yes	—
165	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
166	C₂²×C₁₁	#519	1	2	yes	—
167	C₂²×C₁₁	C₂×#131	1	2	yes	—
168	C₂²×C₁₁	#568	1	2	yes	—
169	C₄×C₁₁	—	2	2	no	—
170	C₄×C₁₁	—	2	4	no	—
171	C₄×C₁₁	—	2	2	no	—
172	C₄×C₁₁	—	4	2	no	—
173	C₄×C₁₁	—	4	2	no	—
174	C₄×C₁₁	—	4	2	no	—
175	C₄×C₁₁	—	4	4	no	—
176	C₄×C₁₁	#536	1	1	yes	characteristic
177	C₄×C₁₁	#536	1	1	yes	characteristic
178	C₄×C₁₁	#541	1	2	yes	—
179	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
180	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
181	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
182	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
183	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
184	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
185	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
186	C₄×Q₈	—	2	2	no	—
187	C₄×Q₈	—	2	2	no	—
188	C₄×Q₈	—	2	2	no	—
189	C₄×Q₈	—	2	2	no	—
190	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
191	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
192	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
193	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
194	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
195	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
196	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
197	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
198	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
199	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
200	C₄⋊C₈	—	2	4	no	—
201	C₄⋊C₈	—	2	4	no	—
202	C₄⋊C₈	—	2	2	no	—
203	C₄⋊C₈	—	2	2	no	—
204	#97	—	2	4	no	—
205	#97	—	2	2	no	—
206	C₄×C₈	—	2	4	no	—
207	C₄×C₈	D₄×C₁₁	1	4	yes	—
208	#95	C₂×C₄×C₁₁	1	2	yes	—
209	#95	C₂×C₄×C₁₁	1	2	yes	—
210	#95	C₂×C₄×C₁₁	1	4	yes	—
211	#95	C₂×C₄×C₁₁	1	4	yes	—
212	C₂×C₁₁	#2327	1	1	yes	characteristic
213	C₂×C₁₁	#2929	1	1	yes	characteristic
214	C₂×C₁₁	#2930	1	1	yes	characteristic
215	C₂×C₁₁	#2985	1	4	yes	—
216	C₂×Q₈	—	2	2	no	—
217	C₂×Q₈	—	2	2	no	—
218	C₂×Q₈	—	2	4	no	—
219	C₂×Q₈	—	4	2	no	—
220	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
221	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
222	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
223	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
224	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
225	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
226	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
227	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
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	—	2	2	no	—
233	C₂×C₈	—	2	4	no	—
234	C₂×C₈	—	2	4	no	—
235	C₂×C₈	—	2	2	no	—
236	C₂×C₈	—	2	2	no	—
237	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
238	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
239	C₄⋊C₄	—	2	4	no	—
240	C₄⋊C₄	—	2	2	no	—
241	C₄⋊C₄	—	2	2	no	—
242	C₄⋊C₄	—	2	4	no	—
243	C₄⋊C₄	—	2	8	no	—
244	C₄⋊C₄	—	4	4	no	—
245	C₄²	—	2	2	no	—
246	C₄²	—	2	2	no	—
247	C₄²	—	2	2	no	—
248	C₄²	—	2	2	no	—
249	C₄²	—	2	2	no	—
250	C₄²	—	2	2	no	—
251	C₄²	C₂×D₄×C₁₁	1	2	yes	—
252	C₄²	C₁₁×#41	1	2	yes	—
253	C₁₁	#22241	1	1	yes	characteristic, direct product factor, Sylow
254	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
255	Q₈	—	2	8	no	—
256	Q₈	—	4	4	no	—
257	C₂×C₄	—	2	2	no	—
258	C₂×C₄	—	2	2	no	—
259	C₂×C₄	—	2	2	no	—
260	C₂×C₄	—	2	2	no	—
261	C₂×C₄	—	2	2	no	—
262	C₂×C₄	—	2	2	no	—
263	C₂×C₄	—	2	2	no	—
264	C₂×C₄	—	2	4	no	—
265	C₂×C₄	—	2	4	no	—
266	C₂×C₄	—	2	4	no	—
267	C₂×C₄	—	2	2	no	—
268	C₂×C₄	—	2	4	no	—
269	C₂×C₄	—	2	4	no	—
270	C₂×C₄	—	2	2	no	—
271	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
272	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
273	C₂×C₄	C₁₁×#131	1	4	yes	—
274	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
275	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
276	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
277	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
278	C₈	—	2	2	no	—
279	C₈	—	2	2	no	—
280	C₈	—	4	2	no	—
281	C₈	—	4	2	no	—
282	C₈	—	4	2	no	—
283	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
284	C₂²	C₁₁×#519	1	2	yes	—
285	C₂²	C₂×C₁₁×#131	1	2	yes	—
286	C₂²	C₁₁×#568	1	2	yes	—
287	C₄	—	2	2	no	—
288	C₄	—	2	4	no	—
289	C₄	—	2	2	no	—
290	C₄	—	4	2	no	—
291	C₄	—	4	2	no	—
292	C₄	—	4	2	no	—
293	C₄	—	4	4	no	—
294	C₄	C₁₁×#536	1	1	yes	characteristic
295	C₄	C₁₁×#536	1	1	yes	characteristic
296	C₄	C₁₁×#541	1	2	yes	—
297	C₂	C₁₁×#2327	1	1	yes	characteristic
298	C₂	C₁₁×#2929	1	1	yes	characteristic
299	C₂	C₁₁×#2930	1	1	yes	characteristic
300	C₂	C₁₁×#2985	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
66. #22241	C₁₁	direct (N × H)
253. C₁₁	#22241	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×#446	2
C₂×C₈×Q₈×C₁₁	2
C₁₁×#2399	2
C₁₁×#1985	2
C₁₁×#1917	2
C₁₁×#1916	2
C₁₁×#1832	2
C₁₁×#1746	2
#22241	11

Subgroups — C11×#22241 #14599434

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22241 #14599434