Subgroups — #14646607

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×D₁₁	C₂	1	1	yes	maximal, characteristic
2	#13068593	C₂	1	2	yes	maximal
3	C₂×#10622118	C₂	1	2	yes	maximal, complemented
4	#13066451	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1277	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₁₁	C₄	1	1	yes	characteristic
7	C₂²×C₈×D₁₁	C₄	1	1	yes	characteristic
8	C₂×C₄²×D₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×(C₂×D₁₁)⋊C₈	—	2	2	no	—
12	C₂×C₈×Dic₁₁	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₁₁	C₄	1	1	yes	characteristic
14	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
15	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
16	C₄×C₈×D₁₁	—	2	4	no	—
17	#10622188	—	2	2	no	—
18	#10622118	—	2	4	no	—
19	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×D₁₁	D₄	1	1	yes	characteristic
21	C₂²×C₄×D₁₁	Q₈	1	1	yes	characteristic
22	C₂²×C₈×C₁₁	—	2	2	no	—
23	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
26	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄×Dic₁₁	D₄	1	1	yes	characteristic
28	C₂×C₄×Dic₁₁	Q₈	1	1	yes	characteristic
29	C₂²×C₁₁⋊C₈	—	2	2	no	—
30	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
32	C₂×C₈×D₁₁	—	2	2	no	—
33	C₂×C₈×D₁₁	—	2	2	no	—
34	C₂×C₈×D₁₁	—	2	2	no	—
35	C₂×C₈×D₁₁	—	2	2	no	—
36	C₂×C₈×D₁₁	—	2	2	no	—
37	C₂×C₈×D₁₁	C₈	1	4	yes	complemented
38	C₄²×D₁₁	—	2	2	no	—
39	C₄²×D₁₁	—	2	2	no	—
40	C₁₁×C₄⋊C₈	—	2	2	no	—
41	C₁₁×C₄⋊C₈	—	2	2	no	—
42	C₄×C₈×C₁₁	—	2	2	no	—
43	(C₂×D₁₁)⋊C₈	—	4	4	no	—
44	C₈×Dic₁₁	—	2	2	no	—
45	C₈×Dic₁₁	—	2	2	no	—
46	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
47	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
48	C₄×C₁₁⋊C₈	D₄	1	4	yes	—
49	#8595	—	11	1	no	maximal, Sylow
50	C₂³×D₁₁	C₄⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
54	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
55	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
56	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
57	C₂×C₄×D₁₁	—	2	2	no	—
58	C₂×C₄×D₁₁	—	2	2	no	—
59	C₂×C₄×D₁₁	—	2	1	no	—
60	C₂×C₄×D₁₁	—	2	1	no	—
61	C₂×C₄×D₁₁	—	2	2	no	—
62	C₂×C₄×D₁₁	—	2	2	no	—
63	C₂×C₄×D₁₁	—	2	1	no	—
64	C₂×C₄×D₁₁	—	2	1	no	—
65	C₂×C₄×D₁₁	—	2	1	no	—
66	C₂×C₄×D₁₁	—	2	1	no	—
67	C₂×C₄×D₁₁	C₂×C₈	1	2	yes	—
68	C₂×C₄×D₁₁	M₁₆	1	2	yes	—
69	C₂×C₄×D₁₁	SD₁₆	1	4	yes	—
70	C₂×C₈×C₁₁	—	2	1	no	—
71	C₂×C₈×C₁₁	—	2	1	no	—
72	C₂×C₈×C₁₁	—	2	1	no	—
73	C₂×C₈×C₁₁	—	2	1	no	—
74	C₂×C₈×C₁₁	—	4	2	no	—
75	C₂×C₈×C₁₁	—	4	2	no	—
76	C₂×C₈×C₁₁	—	4	2	no	—
77	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
78	C₂×C₈×C₁₁	M₁₆	1	2	yes	—
79	C₄²×C₁₁	C₂×D₄	1	2	yes	—
80	C₄²×C₁₁	#41	1	2	yes	—
81	C₄×Dic₁₁	—	2	1	no	—
82	C₄×Dic₁₁	—	2	1	no	—
83	C₄×Dic₁₁	—	2	2	no	—
84	C₄×Dic₁₁	—	2	2	no	—
85	C₂×C₁₁⋊C₈	—	2	1	no	—
86	C₂×C₁₁⋊C₈	—	2	1	no	—
87	C₂×C₁₁⋊C₈	—	4	2	no	—
88	C₂×C₁₁⋊C₈	—	4	2	no	—
89	C₂×C₁₁⋊C₈	—	4	2	no	—
90	C₂×C₁₁⋊C₈	C₂²⋊C₄	1	2	yes	—
91	C₂×C₁₁⋊C₈	C₂²⋊C₄	1	2	yes	—
92	C₂×C₁₁⋊C₈	C₂×C₈	1	2	yes	—
93	C₂×C₁₁⋊C₈	M₁₆	1	2	yes	—
94	C₈×D₁₁	—	2	8	no	—
95	C₈×D₁₁	—	2	8	no	—
96	C₂²×C₄×C₈	—	11	1	no	—
97	#1797	—	11	2	no	—
98	C₂×#334	—	11	2	no	—
99	#1277	—	11	1	no	—
100	#1277	D₁₁	1	1	yes	characteristic, complemented
101	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
102	C₂²×D₁₁	—	2	1	no	—
103	C₂²×D₁₁	—	2	1	no	—
104	C₂²×D₁₁	—	2	1	no	—
105	C₂²×D₁₁	—	2	1	no	—
106	C₂²×D₁₁	C₄⋊C₈	1	2	yes	—
107	C₂²×D₁₁	#106	1	2	yes	—
108	C₂²×D₁₁	#108	1	2	yes	—
109	C₂×C₄×C₁₁	—	2	1	no	—
110	C₂×C₄×C₁₁	—	2	1	no	—
111	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
113	C₂×C₄×C₁₁	#121	1	2	yes	—
114	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
115	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
116	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
117	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
118	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
119	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
120	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
121	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
122	C₂×Dic₁₁	—	2	1	no	—
123	C₂×Dic₁₁	—	2	1	no	—
124	C₂×Dic₁₁	—	2	1	no	—
125	C₂×Dic₁₁	—	2	1	no	—
126	C₂×Dic₁₁	—	2	1	no	—
127	C₂×Dic₁₁	—	2	1	no	—
128	C₂×Dic₁₁	C₄⋊C₈	1	2	yes	—
129	C₂×Dic₁₁	#106	1	2	yes	—
130	C₂×Dic₁₁	#108	1	2	yes	—
131	C₄×D₁₁	—	2	8	no	—
132	C₄×D₁₁	—	2	2	no	—
133	C₄×D₁₁	—	2	2	no	—
134	C₄×D₁₁	—	2	2	no	—
135	C₄×D₁₁	—	2	2	no	—
136	C₄×D₁₁	—	2	4	no	—
137	C₄×D₁₁	—	2	4	no	—
138	C₈×C₁₁	—	2	2	no	—
139	C₈×C₁₁	—	2	2	no	—
140	C₈×C₁₁	—	8	2	no	—
141	C₁₁⋊C₈	—	2	2	no	—
142	C₁₁⋊C₈	—	8	2	no	—
143	C₁₁⋊C₈	C₂²⋊C₈	1	4	yes	complemented
144	C₂³×C₈	—	11	1	no	—
145	C₂³×C₈	—	11	1	no	—
146	C₂²×C₄²	—	11	1	no	—
147	C₂×C₄⋊C₈	—	11	2	no	—
148	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
149	C₂×C₂²⋊C₈	—	22	2	no	—
150	C₂×C₄×C₈	—	11	1	no	—
151	C₂×C₄×C₈	—	11	1	no	—
152	C₂×C₄×C₈	—	11	1	no	—
153	C₂×C₄×C₈	—	22	4	no	—
154	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
155	#336	—	22	2	no	—
156	#334	—	22	4	no	—
157	C₂²×C₁₁	#380	1	1	yes	characteristic
158	C₂²×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
159	C₂²×C₁₁	#423	1	1	yes	characteristic
160	C₂²×C₁₁	C₂×#106	1	1	yes	characteristic
161	C₂²×C₁₁	#427	1	1	yes	characteristic
162	C₂²×C₁₁	C₂×#108	1	1	yes	characteristic
163	C₂²×C₁₁	C₂×#108	1	1	yes	characteristic
164	C₂×D₁₁	—	2	2	no	—
165	C₂×D₁₁	—	2	2	no	—
166	C₂×D₁₁	—	2	2	no	—
167	C₂×D₁₁	—	2	2	no	—
168	C₂×D₁₁	—	2	2	no	—
169	C₂×D₁₁	—	2	2	no	—
170	C₂×D₁₁	#334	1	4	yes	complemented
171	C₄×C₁₁	—	2	2	no	—
172	C₄×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
173	C₄×C₁₁	#407	1	1	yes	characteristic
174	C₄×C₁₁	#431	1	1	yes	characteristic
175	C₄×C₁₁	#432	1	1	yes	characteristic
176	C₄×C₁₁	#465	1	2	yes	—
177	C₄×C₁₁	#465	1	2	yes	—
178	Dic₁₁	—	2	2	no	—
179	Dic₁₁	—	2	2	no	—
180	Dic₁₁	—	2	2	no	—
181	C₂³×C₄	—	11	1	no	—
182	C₂³×C₄	—	11	1	no	—
183	C₂³×C₄	—	11	1	no	—
184	C₂²×C₈	—	2	2	no	—
185	C₂²×C₈	—	11	1	no	—
186	C₂²×C₈	—	11	1	no	—
187	C₂²×C₈	—	11	4	no	—
188	C₂²×C₈	—	22	2	no	—
189	C₂²×C₈	—	22	2	no	—
190	C₂²×C₈	—	22	2	no	—
191	C₂²×C₈	—	22	2	no	—
192	C₂²×C₈	—	22	2	no	—
193	C₂²×C₈	—	22	2	no	—
194	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
195	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
196	C₂×C₄²	—	11	1	no	—
197	C₂×C₄²	—	11	1	no	—
198	C₂×C₄²	—	11	1	no	—
199	C₂×C₄²	—	22	2	no	—
200	C₂×C₄²	—	22	2	no	—
201	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
202	C₄⋊C₈	—	2	2	no	—
203	C₄⋊C₈	—	2	2	no	—
204	C₄⋊C₈	—	22	2	no	—
205	C₄⋊C₈	—	22	2	no	—
206	C₂²⋊C₈	—	44	4	no	—
207	C₄×C₈	—	2	2	no	—
208	C₄×C₈	—	11	4	no	—
209	C₄×C₈	—	22	2	no	—
210	C₄×C₈	—	22	2	no	—
211	C₂×C₁₁	C₂×#334	1	1	yes	characteristic
212	C₂×C₁₁	#1564	1	1	yes	characteristic
213	C₂×C₁₁	#1566	1	1	yes	characteristic
214	C₂×C₁₁	#1568	1	1	yes	characteristic
215	C₂×C₁₁	#1797	1	1	yes	characteristic
216	C₂×C₁₁	#1807	1	1	yes	characteristic
217	C₂×C₁₁	#1810	1	1	yes	characteristic
218	D₁₁	—	2	4	no	—
219	C₂⁴	—	11	1	no	—
220	C₂²×C₄	—	11	1	no	—
221	C₂²×C₄	—	11	1	no	—
222	C₂²×C₄	—	11	1	no	—
223	C₂²×C₄	—	11	2	no	—
224	C₂²×C₄	—	11	2	no	—
225	C₂²×C₄	—	11	4	no	—
226	C₂²×C₄	—	22	2	no	—
227	C₂²×C₄	—	22	2	no	—
228	C₂²×C₄	—	22	1	no	—
229	C₂²×C₄	—	22	1	no	—
230	C₂²×C₄	—	22	2	no	—
231	C₂²×C₄	—	22	2	no	—
232	C₂²×C₄	—	22	1	no	—
233	C₂²×C₄	—	22	1	no	—
234	C₂²×C₄	—	22	1	no	—
235	C₂²×C₄	—	22	1	no	—
236	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
237	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
238	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
239	C₂×C₈	—	2	1	no	—
240	C₂×C₈	—	2	1	no	—
241	C₂×C₈	—	2	1	no	—
242	C₂×C₈	—	2	1	no	—
243	C₂×C₈	—	4	2	no	—
244	C₂×C₈	—	4	2	no	—
245	C₂×C₈	—	4	2	no	—
246	C₂×C₈	—	11	2	no	—
247	C₂×C₈	—	11	2	no	—
248	C₂×C₈	—	11	2	no	—
249	C₂×C₈	—	11	2	no	—
250	C₂×C₈	—	22	8	no	—
251	C₂×C₈	—	22	8	no	—
252	C₂×C₈	—	22	1	no	—
253	C₂×C₈	—	22	1	no	—
254	C₂×C₈	—	44	2	no	—
255	C₂×C₈	—	44	2	no	—
256	C₂×C₈	—	44	2	no	—
257	C₂×C₈	C₈×D₁₁	1	2	yes	—
258	C₂×C₈	#4313	1	2	yes	—
259	C₄²	—	22	1	no	—
260	C₄²	—	22	1	no	—
261	C₄²	—	22	2	no	—
262	C₄²	—	22	2	no	—
263	C₄²	#4339	1	2	yes	—
264	C₄²	D₄×D₁₁	1	2	yes	—
265	C₁₁	#8595	1	1	yes	characteristic, complemented, Sylow
266	C₂³	—	11	2	no	—
267	C₂³	—	11	2	no	—
268	C₂³	—	11	2	no	—
269	C₂³	—	22	1	no	—
270	C₂³	—	22	1	no	—
271	C₂³	—	22	1	no	—
272	C₂³	—	22	1	no	—
273	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
274	C₂×C₄	—	2	1	no	—
275	C₂×C₄	—	2	1	no	—
276	C₂×C₄	—	11	2	no	—
277	C₂×C₄	—	11	2	no	—
278	C₂×C₄	—	11	2	no	—
279	C₂×C₄	—	22	8	no	—
280	C₂×C₄	—	22	1	no	—
281	C₂×C₄	—	22	1	no	—
282	C₂×C₄	—	22	1	no	—
283	C₂×C₄	—	22	1	no	—
284	C₂×C₄	—	22	1	no	—
285	C₂×C₄	—	22	1	no	—
286	C₂×C₄	—	22	2	no	—
287	C₂×C₄	—	22	2	no	—
288	C₂×C₄	—	22	2	no	—
289	C₂×C₄	—	22	2	no	—
290	C₂×C₄	—	22	4	no	—
291	C₂×C₄	—	22	4	no	—
292	C₂×C₄	#66925	1	1	yes	characteristic
293	C₂×C₄	C₂²⋊C₄×D₁₁	1	1	yes	characteristic
294	C₂×C₄	#66937	1	2	yes	—
295	C₂×C₄	#66949	1	2	yes	—
296	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
297	C₂×C₄	C₂×#4313	1	1	yes	characteristic
298	C₂×C₄	M₁₆×D₁₁	1	1	yes	characteristic
299	C₂×C₄	M₁₆×D₁₁	1	1	yes	characteristic
300	C₂×C₄	#66965	1	1	yes	characteristic
301	C₂×C₄	SD₁₆×D₁₁	1	2	yes	—
302	C₂×C₄	#66972	1	1	yes	characteristic
303	C₈	—	2	2	no	—
304	C₈	—	2	2	no	—
305	C₈	—	8	2	no	—
306	C₈	—	11	4	no	—
307	C₈	—	22	2	no	—
308	C₈	—	88	2	no	—
309	C₂²	—	11	4	no	—
310	C₂²	—	22	2	no	—
311	C₂²	—	22	2	no	—
312	C₂²	—	22	2	no	—
313	C₂²	—	22	2	no	—
314	C₂²	—	22	2	no	—
315	C₂²	—	22	2	no	—
316	C₂²	#10622280	1	1	yes	characteristic
317	C₂²	D₁₁×C₄⋊C₈	1	1	yes	characteristic
318	C₂²	#10622450	1	1	yes	characteristic
319	C₂²	D₁₁×#106	1	1	yes	characteristic
320	C₂²	#10622493	1	1	yes	characteristic
321	C₂²	D₁₁×#108	1	1	yes	characteristic
322	C₂²	D₁₁×#108	1	1	yes	characteristic
323	C₄	—	2	2	no	—
324	C₄	—	22	2	no	—
325	C₄	—	22	2	no	—
326	C₄	—	22	2	no	—
327	C₄	#10622298	1	1	yes	characteristic
328	C₄	#10622318	1	1	yes	characteristic
329	C₄	D₁₁×C₂²⋊C₈	1	1	yes	characteristic
330	C₄	#10622339	1	1	yes	characteristic
331	C₄	#10622391	1	2	yes	—
332	C₄	#10622420	1	2	yes	—
333	C₂	—	22	4	no	—
334	C₂	D₁₁×#334	1	1	yes	characteristic
335	C₂	#13067363	1	1	yes	characteristic
336	C₂	#13067370	1	1	yes	characteristic
337	C₂	#13067378	1	1	yes	characteristic
338	C₂	#13068595	1	1	yes	characteristic
339	C₂	#13068640	1	1	yes	characteristic
340	C₂	#13068653	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1277	C₂
socle	C₂³×C₁₁	C₂×C₄⋊C₄
prime radical	C₂³×D₁₁	C₄⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1277	D₁₁
hypocenter	C₁₁	#8595
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

Complements

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

N	H ≅ G/N	type
3. C₂×#10622118	C₂	semidirect
4. #13066451	C₂	semidirect
5. C₁₁×#1277	C₂	semidirect
37. C₂×C₈×D₁₁	C₈	semidirect
100. #1277	D₁₁	semidirect
143. C₁₁⋊C₈	C₂²⋊C₈	semidirect
170. C₂×D₁₁	#334	semidirect
265. C₁₁	#8595	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₈×D₁₁	2
#13068593	2
C₂×#10622118	2
#13066451	2
C₁₁×#1277	2
#8595	11