Subgroups — #14644176

Order 2816.

522 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077249	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622539	C₂	1	1	yes	maximal, characteristic
3	C₁₁⋊#1308	C₂	1	4	yes	maximal, complemented
4	C₁₁×#2920	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
6	C₁₁×#432	—	2	1	no	—
7	C₁₁×#432	C₂²	1	2	yes	—
8	C₁₁×#431	—	2	1	no	—
9	C₁₁×#431	C₄	1	2	yes	—
10	C₁₁×#423	—	2	1	no	—
11	C₁₁×#407	C₄	1	2	yes	—
12	C₄×C₁₁×M₁₆	—	2	1	no	—
13	#10622820	C₄	1	2	yes	—
14	C₂×C₂²⋊(C₁₁⋊C₈)	C₄	1	2	yes	—
15	#10622539	—	2	1	no	—
16	#10622539	—	2	1	no	—
17	#10622539	—	2	1	no	—
18	#10622539	C₄	1	2	yes	—
19	#10622539	C₂²	1	2	yes	—
20	#10622539	C₂²	1	2	yes	—
21	#10622538	—	2	1	no	—
22	#10622538	C₄	1	2	yes	—
23	#10622537	—	2	1	no	—
24	C₂×C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
25	C₄×#4318	—	2	1	no	—
26	C₂×#66867	—	2	1	no	—
27	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
30	C₂×C₁₁×M₁₆	—	2	2	no	—
31	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
41	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
42	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
43	C₂×#4318	—	2	2	no	—
44	C₂²×C₁₁⋊C₈	—	2	2	no	—
45	C₁₁×C₄⋊C₈	—	2	2	no	—
46	C₁₁×C₄⋊C₈	—	2	2	no	—
47	C₁₁×C₂²⋊C₈	—	2	2	no	—
48	C₁₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
49	C₁₁×#97	—	2	2	no	—
50	C₄×C₈×C₁₁	—	2	2	no	—
51	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
52	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
53	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
54	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
55	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
56	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
57	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
58	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
59	#66867	—	2	2	no	—
60	#66867	—	2	2	no	—
61	#66867	—	2	2	no	—
62	C₄×C₁₁⋊C₈	—	2	2	no	—
63	#8124	—	11	1	no	maximal, Sylow
64	C₂⁴×C₁₁	C₄²	1	1	yes	characteristic
65	C₂²×C₄×C₁₁	—	4	2	no	—
66	C₂²×C₄×C₁₁	—	4	2	no	—
67	C₂²×C₄×C₁₁	—	4	2	no	—
68	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
69	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
86	C₁₁×M₁₆	—	4	4	no	—
87	C₂×C₈×C₁₁	—	2	4	no	—
88	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
89	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
90	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
91	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
92	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
93	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
94	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
95	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
96	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
101	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
104	#4318	—	4	4	no	—
105	C₂×C₁₁⋊C₈	—	2	4	no	—
106	C₂×C₁₁⋊C₈	—	2	4	no	—
107	C₂×C₁₁⋊C₈	—	4	4	no	—
108	#2920	—	11	1	no	—
109	#2920	D₁₁	1	1	yes	characteristic
110	C₂×#432	—	11	1	no	—
111	#1308	—	11	4	no	—
112	C₂³×C₁₁	—	2	2	no	—
113	C₂³×C₁₁	—	4	1	no	—
114	C₂³×C₁₁	—	4	1	no	—
115	C₂³×C₁₁	#95	1	1	yes	characteristic
116	C₂³×C₁₁	#95	1	1	yes	characteristic
117	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
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	2	no	—
124	C₂×C₄×C₁₁	—	2	2	no	—
125	C₂×C₄×C₁₁	—	2	2	no	—
126	C₂×C₄×C₁₁	—	4	1	no	—
127	C₂×C₄×C₁₁	—	4	1	no	—
128	C₂×C₄×C₁₁	—	4	1	no	—
129	C₂×C₄×C₁₁	—	4	1	no	—
130	C₂×C₄×C₁₁	—	4	1	no	—
131	C₂×C₄×C₁₁	—	4	1	no	—
132	C₂×C₄×C₁₁	—	4	1	no	—
133	C₂×C₄×C₁₁	—	4	1	no	—
134	C₂×C₄×C₁₁	—	4	1	no	—
135	C₂×C₄×C₁₁	—	4	1	no	—
136	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
137	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
138	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
139	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
140	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
141	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
142	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₈×C₁₁	—	4	4	no	—
149	C₁₁⋊C₈	—	4	4	no	—
150	C₁₁⋊C₈	—	4	4	no	—
151	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
152	#432	—	2	1	no	—
153	#432	—	11	2	no	—
154	#432	—	11	2	no	—
155	#432	—	11	2	no	—
156	#432	—	22	1	no	—
157	#432	—	22	1	no	—
158	#432	—	22	1	no	—
159	#432	C₂×D₁₁	1	2	yes	—
160	#431	—	2	1	no	—
161	#431	—	11	2	no	—
162	#431	—	22	1	no	—
163	#431	Dic₁₁	1	2	yes	—
164	#423	—	2	1	no	—
165	#423	—	22	1	no	—
166	C₂×C₄⋊C₈	—	22	1	no	—
167	#407	—	11	2	no	—
168	#407	Dic₁₁	1	2	yes	—
169	C₂×C₂²⋊C₈	—	11	2	no	—
170	C₄×M₁₆	—	2	1	no	—
171	C₄×M₁₆	—	22	1	no	—
172	C₂×#97	—	22	1	no	—
173	C₂²×C₁₁	—	2	1	no	—
174	C₂²×C₁₁	—	2	1	no	—
175	C₂²×C₁₁	—	2	1	no	—
176	C₂²×C₁₁	—	2	1	no	—
177	C₂²×C₁₁	—	2	1	no	—
178	C₂²×C₁₁	—	2	1	no	—
179	C₂²×C₁₁	—	2	1	no	—
180	C₂²×C₁₁	—	2	1	no	—
181	C₂²×C₁₁	—	4	4	no	—
182	C₂²×C₁₁	#344	1	2	yes	—
183	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
184	C₄×C₁₁	—	2	1	no	—
185	C₄×C₁₁	—	2	1	no	—
186	C₄×C₁₁	—	2	1	no	—
187	C₄×C₁₁	—	2	1	no	—
188	C₄×C₁₁	—	2	1	no	—
189	C₄×C₁₁	—	2	1	no	—
190	C₄×C₁₁	—	2	1	no	—
191	C₄×C₁₁	—	2	1	no	—
192	C₄×C₁₁	—	2	1	no	—
193	C₄×C₁₁	—	2	1	no	—
194	C₄×C₁₁	#344	1	2	yes	—
195	C₄×C₁₁	#344	1	2	yes	—
196	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
197	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
198	C₂³×C₄	C₂×Dic₁₁	1	1	yes	characteristic
199	C₂×M₁₆	—	2	2	no	—
200	C₂×M₁₆	—	22	2	no	—
201	C₂²×C₈	—	22	2	no	—
202	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
203	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
204	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
205	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
206	C₂×C₄²	D₄₄	1	1	yes	characteristic
207	C₂×C₄²	D₄₄	1	1	yes	characteristic
208	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
209	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
210	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
211	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
212	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
213	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
214	C₄⋊C₈	—	2	2	no	—
215	C₄⋊C₈	—	2	2	no	—
216	C₄⋊C₈	—	22	2	no	—
217	C₄⋊C₈	—	22	2	no	—
218	C₄⋊C₈	—	22	2	no	—
219	C₄⋊C₈	—	22	2	no	—
220	C₂²⋊C₈	—	2	2	no	—
221	C₂²⋊C₈	—	11	4	no	—
222	C₂²⋊C₈	—	11	4	no	—
223	C₂²⋊C₈	—	22	2	no	—
224	C₂²⋊C₈	—	22	2	no	—
225	C₂²⋊C₈	C₂×Dic₁₁	1	4	yes	—
226	#97	—	2	2	no	—
227	#97	—	22	2	no	—
228	#97	—	22	2	no	—
229	#97	—	22	2	no	—
230	C₄×C₈	—	2	2	no	—
231	C₄×C₈	—	22	2	no	—
232	C₂×C₁₁	—	2	2	no	—
233	C₂×C₁₁	—	4	1	no	—
234	C₂×C₁₁	—	4	1	no	—
235	C₂×C₁₁	C₂×#344	1	1	yes	characteristic
236	C₂×C₁₁	C₂×#344	1	1	yes	characteristic
237	C₂×C₁₁	C₂×#344	1	1	yes	characteristic
238	C₂⁴	C₄×Dic₁₁	1	1	yes	characteristic
239	C₂²×C₄	—	4	2	no	—
240	C₂²×C₄	—	4	2	no	—
241	C₂²×C₄	—	4	2	no	—
242	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
243	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
244	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
245	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
246	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
247	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
248	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
249	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
250	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
251	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
252	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
253	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
254	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
255	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
256	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
257	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
258	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
259	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
260	M₁₆	—	4	4	no	—
261	M₁₆	—	44	4	no	—
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	—	22	4	no	—
264	C₂×C₈	—	22	4	no	—
265	C₂×C₈	—	44	4	no	—
266	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
267	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
268	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
269	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
270	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
271	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
272	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
273	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
274	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
275	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
276	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
277	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
278	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
279	C₄²	C₂×D₄₄	1	1	yes	characteristic
280	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
281	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
282	C₁₁	#8124	1	1	yes	characteristic, complemented, Sylow
283	C₂³	—	2	2	no	—
284	C₂³	—	4	1	no	—
285	C₂³	—	4	1	no	—
286	C₂³	C₁₁⋊#95	1	1	yes	characteristic
287	C₂³	C₁₁⋊#95	1	1	yes	characteristic
288	C₂³	C₂×C₄×Dic₁₁	1	1	yes	characteristic
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	4	1	no	—
298	C₂×C₄	—	4	1	no	—
299	C₂×C₄	—	4	1	no	—
300	C₂×C₄	—	4	1	no	—
301	C₂×C₄	—	4	1	no	—
302	C₂×C₄	—	4	1	no	—
303	C₂×C₄	—	4	1	no	—
304	C₂×C₄	—	4	1	no	—
305	C₂×C₄	—	4	1	no	—
306	C₂×C₄	—	4	1	no	—
307	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
308	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
309	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
310	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
311	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
312	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
313	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
314	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
315	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
316	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
317	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
318	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
319	C₈	—	4	4	no	—
320	C₈	—	44	4	no	—
321	C₈	—	44	4	no	—
322	C₂²	—	2	1	no	—
323	C₂²	—	2	1	no	—
324	C₂²	—	2	1	no	—
325	C₂²	—	2	1	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	2	1	no	—
328	C₂²	—	2	1	no	—
329	C₂²	—	2	1	no	—
330	C₂²	—	4	4	no	—
331	C₂²	#10622197	1	2	yes	—
332	C₂²	C₂×C₁₁⋊#95	1	1	yes	characteristic
333	C₄	—	2	1	no	—
334	C₄	—	2	1	no	—
335	C₄	—	2	1	no	—
336	C₄	—	2	1	no	—
337	C₄	—	2	1	no	—
338	C₄	—	2	1	no	—
339	C₄	—	2	1	no	—
340	C₄	—	2	1	no	—
341	C₄	—	2	1	no	—
342	C₄	—	2	1	no	—
343	C₄	#10622171	1	2	yes	—
344	C₄	#10622194	1	2	yes	—
345	C₂	—	2	2	no	—
346	C₂	—	4	1	no	—
347	C₂	—	4	1	no	—
348	C₂	C₂×#10622171	1	1	yes	characteristic
349	C₂	C₂×#10622194	1	1	yes	characteristic
350	C₂	C₂×#10622197	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₁₁⋊#95
commutator	C₂³×C₁₁	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#2920	C₂
socle	C₂²×C₁₁	C₂×#95
prime radical	C₂⁴×C₁₁	C₄²
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#2920	D₁₁
hypocenter	C₁₁	#8124
LCS	G ▷ C₂³×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. C₁₁⋊#1308	C₂	semidirect
282. C₁₁	#8124	semidirect

Maximal subgroups

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

subgroup	index
#13077249	2
C₂×#10622539	2
C₁₁⋊#1308	2
C₁₁×#2920	2
#8124	11