Subgroups — C₁₁×#21431 #14598624

Order 2816.

810 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×#117	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1924	C₂	1	4	yes	maximal
3	C₁₁×#1917	C₂	1	4	yes	maximal, complemented
4	C₄×C₁₁×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₁×C₂²⋊C₈	C₂	1	2	yes	maximal
6	C₁₁×#1744	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₁₁×#97	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₁×#117	C₄	1	1	yes	characteristic
9	C₂×C₁₁×#117	C₄	1	1	yes	characteristic
10	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×C₄⋊C₈	C₂²	1	4	yes	—
12	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	—
13	C₂×C₁₁×#97	C₂²	1	4	yes	—
14	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
16	C₄×C₁₁×C₄⋊C₄	C₄	1	2	yes	—
17	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
18	C₄×C₁₁×C₂²⋊C₄	C₄	1	2	yes	—
19	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₁₁×#376	C₄	1	1	yes	characteristic
21	C₁₁×#376	C₄	1	1	yes	characteristic
22	C₄³×C₁₁	C₂²	1	1	yes	characteristic
23	C₄³×C₁₁	C₂²	1	1	yes	characteristic
24	C₁₁×#336	C₂²	1	4	yes	—
25	C₁₁×#336	C₂²	1	4	yes	—
26	C₁₁×#336	C₂²	1	4	yes	—
27	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
30	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
31	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
32	C₁₁×#117	—	2	4	no	—
33	C₁₁×#117	—	2	4	no	—
34	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
35	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
36	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
37	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₁₁	—	2	4	no	—
39	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
48	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
49	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
50	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
51	C₁₁×C₄⋊C₈	—	2	8	no	—
52	C₁₁×C₂²⋊C₈	—	2	8	no	—
53	C₁₁×#97	—	2	8	no	—
54	C₄×C₈×C₁₁	—	2	4	no	—
55	C₄×C₈×C₁₁	—	2	4	no	—
56	C₁₁×#95	C₂×C₄	1	2	yes	—
57	C₁₁×#95	C₂×C₄	1	2	yes	—
58	C₁₁×#95	C₂×C₄	1	2	yes	—
59	C₁₁×#95	C₂×C₄	1	2	yes	—
60	#21431	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	—	2	2	no	—
63	C₂²×C₄×C₁₁	—	2	2	no	—
64	C₂²×C₄×C₁₁	—	2	2	no	—
65	C₂²×C₄×C₁₁	—	2	4	no	—
66	C₂²×C₄×C₁₁	—	2	4	no	—
67	C₂²×C₄×C₁₁	—	2	2	no	—
68	C₂²×C₄×C₁₁	M₁₆	1	4	yes	—
69	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₁	C₂²×C₄	1	2	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	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
79	C₂×C₈×C₁₁	—	2	4	no	—
80	C₂×C₈×C₁₁	—	2	4	no	—
81	C₂×C₈×C₁₁	—	2	4	no	—
82	C₂×C₈×C₁₁	—	2	4	no	—
83	C₂×C₈×C₁₁	—	2	4	no	—
84	C₂×C₈×C₁₁	#41	1	8	yes	—
85	C₁₁×C₄⋊C₄	—	2	4	no	—
86	C₁₁×C₄⋊C₄	—	2	4	no	—
87	C₁₁×C₂²⋊C₄	—	2	4	no	—
88	C₁₁×C₂²⋊C₄	—	2	4	no	—
89	C₄²×C₁₁	—	2	2	no	—
90	C₄²×C₁₁	—	2	2	no	—
91	C₄²×C₁₁	—	2	2	no	—
92	C₄²×C₁₁	—	2	2	no	—
93	C₄²×C₁₁	—	2	2	no	—
94	C₄²×C₁₁	—	2	4	no	—
95	C₄²×C₁₁	—	2	4	no	—
96	C₄²×C₁₁	—	2	4	no	—
97	C₄²×C₁₁	—	2	4	no	—
98	C₄²×C₁₁	—	2	2	no	—
99	C₄²×C₁₁	M₁₆	1	4	yes	—
100	C₄²×C₁₁	#41	1	4	yes	—
101	C₄×#117	C₂×C₁₁	1	1	yes	characteristic
102	#1924	C₂×C₁₁	1	4	yes	—
103	#1917	C₂×C₁₁	1	4	yes	complemented
104	C₄×C₄⋊C₈	C₂×C₁₁	1	2	yes	complemented
105	C₄×C₂²⋊C₈	C₂×C₁₁	1	2	yes	—
106	#1744	C₂×C₁₁	1	1	yes	characteristic, complemented
107	C₄×#97	C₂×C₁₁	1	1	yes	characteristic, complemented
108	C₂³×C₁₁	—	2	1	no	—
109	C₂³×C₁₁	—	2	2	no	—
110	C₂³×C₁₁	—	2	1	no	—
111	C₂³×C₁₁	—	2	2	no	—
112	C₂³×C₁₁	C₂×M₁₆	1	2	yes	—
113	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
114	C₂×C₄×C₁₁	—	2	1	no	—
115	C₂×C₄×C₁₁	—	2	2	no	—
116	C₂×C₄×C₁₁	—	2	1	no	—
117	C₂×C₄×C₁₁	—	2	2	no	—
118	C₂×C₄×C₁₁	—	2	8	no	—
119	C₂×C₄×C₁₁	—	2	1	no	—
120	C₂×C₄×C₁₁	—	2	1	no	—
121	C₂×C₄×C₁₁	—	2	2	no	—
122	C₂×C₄×C₁₁	—	2	2	no	—
123	C₂×C₄×C₁₁	—	2	2	no	—
124	C₂×C₄×C₁₁	—	2	2	no	—
125	C₂×C₄×C₁₁	—	2	2	no	—
126	C₂×C₄×C₁₁	—	2	2	no	—
127	C₂×C₄×C₁₁	—	2	2	no	—
128	C₂×C₄×C₁₁	—	2	2	no	—
129	C₂×C₄×C₁₁	—	2	2	no	—
130	C₂×C₄×C₁₁	—	2	2	no	—
131	C₂×C₄×C₁₁	—	2	2	no	—
132	C₂×C₄×C₁₁	—	4	4	no	—
133	C₂×C₄×C₁₁	—	4	4	no	—
134	C₂×C₄×C₁₁	#117	1	2	yes	—
135	C₂×C₄×C₁₁	#117	1	2	yes	—
136	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
137	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
138	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
139	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
140	C₂×C₄×C₁₁	#131	1	4	yes	—
141	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
142	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
143	C₈×C₁₁	—	2	8	no	—
144	C₈×C₁₁	—	4	4	no	—
145	C₂×#117	C₄×C₁₁	1	1	yes	characteristic
146	C₂×#117	C₄×C₁₁	1	1	yes	characteristic
147	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
148	C₂×C₄⋊C₈	C₂²×C₁₁	1	4	yes	—
149	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	—
150	C₂×#97	C₂²×C₁₁	1	4	yes	—
151	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
152	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
153	C₄×C₄⋊C₄	C₄×C₁₁	1	2	yes	—
154	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
155	C₄×C₂²⋊C₄	C₄×C₁₁	1	2	yes	—
156	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
157	#376	C₄×C₁₁	1	1	yes	characteristic
158	#376	C₄×C₁₁	1	1	yes	characteristic
159	C₄³	C₂²×C₁₁	1	1	yes	characteristic
160	C₄³	C₂²×C₁₁	1	1	yes	characteristic
161	#336	C₂²×C₁₁	1	4	yes	—
162	#336	C₂²×C₁₁	1	4	yes	—
163	#336	C₂²×C₁₁	1	4	yes	—
164	C₂²×C₁₁	—	2	2	no	—
165	C₂²×C₁₁	—	2	4	no	—
166	C₂²×C₁₁	—	4	1	no	—
167	C₂²×C₁₁	—	4	2	no	—
168	C₂²×C₁₁	—	4	1	no	—
169	C₂²×C₁₁	C₂×#117	1	1	yes	characteristic
170	C₂²×C₁₁	C₄×#41	1	2	yes	—
171	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
172	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
173	C₂²×C₁₁	C₂×#131	1	2	yes	—
174	C₄×C₁₁	—	2	2	no	—
175	C₄×C₁₁	—	2	4	no	—
176	C₄×C₁₁	—	4	1	no	—
177	C₄×C₁₁	—	4	2	no	—
178	C₄×C₁₁	—	4	2	no	—
179	C₄×C₁₁	—	4	2	no	—
180	C₄×C₁₁	—	4	1	no	—
181	C₄×C₁₁	#432	1	4	yes	—
182	C₄×C₁₁	#433	1	4	yes	—
183	C₄×C₁₁	#529	1	4	yes	—
184	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
185	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
186	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
187	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
188	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
189	#117	—	2	4	no	—
190	#117	—	2	4	no	—
191	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
192	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
193	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
194	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
195	C₂×C₄²	—	2	4	no	—
196	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
197	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
198	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
199	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
200	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
201	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
202	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
203	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
204	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
205	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
206	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
207	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
208	C₄⋊C₈	—	2	8	no	—
209	C₂²⋊C₈	—	2	8	no	—
210	#97	—	2	8	no	—
211	C₄×C₈	—	2	4	no	—
212	C₄×C₈	—	2	4	no	—
213	#95	C₂×C₄×C₁₁	1	2	yes	—
214	#95	C₂×C₄×C₁₁	1	2	yes	—
215	#95	C₂×C₄×C₁₁	1	2	yes	—
216	#95	C₂×C₄×C₁₁	1	2	yes	—
217	C₂×C₁₁	—	4	2	no	—
218	C₂×C₁₁	#2298	1	1	yes	characteristic
219	C₂×C₁₁	C₂×#432	1	1	yes	characteristic
220	C₂×C₁₁	C₂×#433	1	1	yes	characteristic
221	C₂×C₁₁	#2965	1	2	yes	—
222	C₂×C₁₁	#2965	1	2	yes	—
223	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
224	C₂²×C₄	—	2	2	no	—
225	C₂²×C₄	—	2	2	no	—
226	C₂²×C₄	—	2	2	no	—
227	C₂²×C₄	—	2	4	no	—
228	C₂²×C₄	—	2	4	no	—
229	C₂²×C₄	—	2	2	no	—
230	C₂²×C₄	C₁₁×M₁₆	1	4	yes	—
231	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
232	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
233	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
234	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
235	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
236	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
237	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
238	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
239	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
240	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
241	C₂×C₈	—	2	4	no	—
242	C₂×C₈	—	2	4	no	—
243	C₂×C₈	—	2	4	no	—
244	C₂×C₈	—	2	4	no	—
245	C₂×C₈	—	2	4	no	—
246	C₂×C₈	C₁₁×#41	1	8	yes	—
247	C₄⋊C₄	—	2	4	no	—
248	C₄⋊C₄	—	2	4	no	—
249	C₂²⋊C₄	—	2	4	no	—
250	C₂²⋊C₄	—	2	4	no	—
251	C₄²	—	2	2	no	—
252	C₄²	—	2	2	no	—
253	C₄²	—	2	2	no	—
254	C₄²	—	2	2	no	—
255	C₄²	—	2	2	no	—
256	C₄²	—	2	4	no	—
257	C₄²	—	2	4	no	—
258	C₄²	—	2	4	no	—
259	C₄²	—	2	4	no	—
260	C₄²	—	2	2	no	—
261	C₄²	C₁₁×M₁₆	1	4	yes	—
262	C₄²	C₁₁×#41	1	4	yes	—
263	C₁₁	#21431	1	1	yes	characteristic, direct product factor, Sylow
264	C₂³	—	2	1	no	—
265	C₂³	—	2	2	no	—
266	C₂³	—	2	1	no	—
267	C₂³	—	2	2	no	—
268	C₂³	C₂×C₁₁×M₁₆	1	2	yes	—
269	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
270	C₂×C₄	—	2	1	no	—
271	C₂×C₄	—	2	2	no	—
272	C₂×C₄	—	2	1	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	8	no	—
275	C₂×C₄	—	2	1	no	—
276	C₂×C₄	—	2	1	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	4	4	no	—
289	C₂×C₄	—	4	4	no	—
290	C₂×C₄	C₁₁×#117	1	2	yes	—
291	C₂×C₄	C₁₁×#117	1	2	yes	—
292	C₂×C₄	C₂×C₁₁×M₁₆	1	4	yes	—
293	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
294	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
295	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
296	C₂×C₄	C₁₁×#131	1	4	yes	—
297	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
298	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
299	C₈	—	2	8	no	—
300	C₈	—	4	4	no	—
301	C₂²	—	2	2	no	—
302	C₂²	—	2	4	no	—
303	C₂²	—	4	1	no	—
304	C₂²	—	4	2	no	—
305	C₂²	—	4	1	no	—
306	C₂²	C₂×C₁₁×#117	1	1	yes	characteristic
307	C₂²	C₄×C₁₁×#41	1	2	yes	—
308	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
309	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
310	C₂²	C₂×C₁₁×#131	1	2	yes	—
311	C₄	—	2	2	no	—
312	C₄	—	2	4	no	—
313	C₄	—	4	1	no	—
314	C₄	—	4	2	no	—
315	C₄	—	4	2	no	—
316	C₄	—	4	2	no	—
317	C₄	—	4	1	no	—
318	C₄	C₁₁×#432	1	4	yes	—
319	C₄	C₁₁×#433	1	4	yes	—
320	C₄	C₁₁×#529	1	4	yes	—
321	C₂	—	4	2	no	—
322	C₂	C₁₁×#2298	1	1	yes	characteristic
323	C₂	C₂×C₁₁×#432	1	1	yes	characteristic
324	C₂	C₂×C₁₁×#433	1	1	yes	characteristic
325	C₂	C₁₁×#2965	1	2	yes	—
326	C₂	C₁₁×#2965	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1917	C₂	semidirect
4. C₄×C₁₁×C₄⋊C₈	C₂	semidirect
6. C₁₁×#1744	C₂	semidirect
7. C₄×C₁₁×#97	C₂	semidirect
60. #21431	C₁₁	direct (N × H)
103. #1917	C₂×C₁₁	semidirect
104. C₄×C₄⋊C₈	C₂×C₁₁	semidirect
106. #1744	C₂×C₁₁	semidirect
107. C₄×#97	C₂×C₁₁	semidirect
263. C₁₁	#21431	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₁×#117	2
C₁₁×#1924	2
C₁₁×#1917	2
C₄×C₁₁×C₄⋊C₈	2
C₄×C₁₁×C₂²⋊C₈	2
C₁₁×#1744	2
C₄×C₁₁×#97	2
#21431	11

Subgroups — C11×#21431 #14598624

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21431 #14598624