Subgroups — #14724452

Order 2816.

560 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13079199	C₂	1	1	yes	maximal, characteristic
2	#13077712	C₂	1	2	yes	maximal
3	#13067523	C₂	1	2	yes	maximal, complemented
4	#13067514	C₂	1	1	yes	maximal, characteristic, complemented
5	#13067432	C₂	1	2	yes	maximal, complemented
6	Q₁₆×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#13067422	C₂	1	1	yes	maximal, characteristic, complemented
8	#13067378	C₂	1	1	yes	maximal, characteristic
9	#13067087	C₂	1	2	yes	maximal
10	#13066898	C₂	1	1	yes	maximal, characteristic
11	C₁₁×#1591	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623109	C₂²	1	2	yes	—
13	C₁₁×#446	C₂²	1	2	yes	—
14	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
15	#10622801	C₄	1	1	yes	characteristic
16	#10622794	C₄	1	1	yes	characteristic
17	C₄×#4326	C₂²	1	2	yes	—
18	Q₈×C₁₁⋊C₈	C₂²	1	2	yes	—
19	#10622500	C₄	1	1	yes	characteristic
20	#10622487	C₄	1	1	yes	characteristic
21	#10622453	—	2	2	no	—
22	#10622448	C₂²	1	2	yes	—
23	#10622444	—	2	2	no	—
24	#10622443	C₂²	1	2	yes	—
25	#10622426	C₄	1	2	yes	—
26	#10622405	C₄	1	2	yes	—
27	#10622322	—	2	2	no	—
28	#10622314	—	2	2	no	—
29	C₄×Dic₄₄	C₂²	1	1	yes	characteristic
30	#10622298	C₂²	1	1	yes	characteristic
31	#10622298	C₂²	1	1	yes	characteristic
32	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
33	#10622292	C₂²	1	2	yes	—
34	C₁₁×#335	C₂²	1	1	yes	characteristic
35	C₁₁×Q₈⋊C₈	C₂²	1	2	yes	—
36	C₈²×C₁₁	C₂²	1	1	yes	characteristic
37	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
38	#10622122	C₂²	1	2	yes	—
39	#10622118	C₂²	1	2	yes	—
40	#10622096	C₂²	1	1	yes	characteristic
41	#10622094	C₂²	1	2	yes	—
42	#10622092	C₂²	1	1	yes	characteristic
43	#10622092	C₂²	1	1	yes	characteristic
44	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
46	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
47	#66999	C₂×C₄	1	2	yes	—
48	#66997	C₂×C₄	1	2	yes	—
49	C₂×#4326	C₂×C₄	1	2	yes	—
50	C₂×Dic₄₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
53	#66950	C₂×C₄	1	2	yes	—
54	#66949	—	2	2	no	—
55	#66942	—	2	2	no	—
56	#66941	C₂×C₄	1	2	yes	—
57	#66925	—	2	2	no	—
58	C₄²×D₁₁	C₂³	1	1	yes	characteristic
59	C₄×Dic₂₂	—	2	2	no	—
60	C₄×Dic₂₂	C₂³	1	2	yes	—
61	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
62	C₁₁×C₄⋊C₈	—	2	2	no	—
63	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
64	C₁₁×#103	C₂×C₄	1	2	yes	—
65	C₁₁×#97	—	2	2	no	—
66	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
68	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
69	#66899	C₂×C₄	1	2	yes	—
70	(C₂×D₁₁)⋊C₈	—	2	2	no	—
71	(C₂×D₁₁)⋊C₈	—	2	1	no	—
72	(C₂×D₁₁)⋊C₈	D₄	1	1	yes	characteristic
73	(C₂×D₁₁)⋊C₈	D₄	1	1	yes	characteristic
74	#66882	C₂×C₄	1	1	yes	characteristic
75	#66880	C₂×C₄	1	2	yes	—
76	#66879	—	2	2	no	—
77	#66879	—	2	2	no	—
78	Dic₁₁⋊C₈	—	2	2	no	—
79	Dic₁₁⋊C₈	—	2	1	no	—
80	Dic₁₁⋊C₈	—	2	2	no	—
81	Dic₁₁⋊C₈	D₄	1	1	yes	characteristic
82	Dic₁₁⋊C₈	D₄	1	1	yes	characteristic
83	C₈×Dic₁₁	—	2	2	no	—
84	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
86	#66874	C₂×C₄	1	2	yes	—
87	#66871	C₂×C₄	1	2	yes	—
88	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
89	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
90	C₄×C₁₁⋊C₈	—	2	2	no	—
91	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
92	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
93	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
94	#17972	—	11	1	no	maximal, Sylow
95	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
96	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×D₁₁	#41	1	1	yes	characteristic
99	C₂×Dic₂₂	—	2	2	no	—
100	C₂×Dic₂₂	C₂²×C₄	1	2	yes	—
101	C₁₁×Q₁₆	—	2	2	no	—
102	C₂×C₈×C₁₁	—	2	2	no	—
103	C₂×C₈×C₁₁	—	2	1	no	—
104	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
108	C₁₁×C₄⋊C₄	—	2	2	no	—
109	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
110	C₄²×C₁₁	—	2	2	no	—
111	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
112	#4326	—	2	4	no	—
113	(C₂×D₁₁)⋊C₄	—	2	2	no	—
114	(C₂×D₁₁)⋊C₄	—	2	2	no	—
115	C₄⋊Dic₁₁	—	2	2	no	—
116	C₄⋊Dic₁₁	C₂²×C₄	1	2	yes	—
117	Dic₁₁⋊C₄	—	2	2	no	—
118	Dic₁₁⋊C₄	—	2	2	no	—
119	Dic₁₁⋊C₄	—	2	2	no	—
120	Dic₁₁⋊C₄	—	2	2	no	—
121	Dic₁₁⋊C₄	—	2	2	no	—
122	C₄×Dic₁₁	—	2	2	no	—
123	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
124	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
125	C₄×Dic₁₁	#41	1	1	yes	characteristic
126	C₂×C₁₁⋊C₈	—	2	2	no	—
127	C₂×C₁₁⋊C₈	—	2	1	no	—
128	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
131	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
132	Dic₄₄	—	2	2	no	—
133	C₈×D₁₁	—	2	2	no	—
134	C₈×D₁₁	—	2	2	no	—
135	#3170	—	11	1	no	—
136	#2985	—	11	2	no	—
137	#1593	—	11	2	no	—
138	#1591	—	11	1	no	—
139	#1591	D₁₁	1	1	yes	characteristic, complemented
140	#1579	—	11	2	no	—
141	C₈×Q₁₆	—	11	1	no	—
142	C₈×Q₁₆	—	11	1	no	—
143	#1568	—	11	1	no	—
144	#1497	—	11	2	no	—
145	#1450	—	11	1	no	—
146	C₂²×D₁₁	C₄×D₄	1	1	yes	characteristic
147	Q₈×C₁₁	—	2	2	no	—
148	Q₈×C₁₁	—	2	2	no	—
149	C₂×C₄×C₁₁	—	2	2	no	—
150	C₂×C₄×C₁₁	—	2	2	no	—
151	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
154	C₂×Dic₁₁	—	2	2	no	—
155	C₂×Dic₁₁	—	2	2	no	—
156	C₂×Dic₁₁	C₄×D₄	1	1	yes	characteristic
157	C₂×Dic₁₁	C₄×D₄	1	1	yes	characteristic
158	C₂×Dic₁₁	C₄×D₄	1	1	yes	characteristic
159	C₄×D₁₁	—	2	1	no	—
160	C₄×D₁₁	—	2	1	no	—
161	C₄×D₁₁	—	2	1	no	—
162	C₄×D₁₁	—	2	1	no	—
163	C₄×D₁₁	—	4	1	no	—
164	Dic₂₂	—	2	2	no	—
165	Dic₂₂	—	2	2	no	—
166	Dic₂₂	—	8	2	no	—
167	C₈×C₁₁	—	2	1	no	—
168	C₈×C₁₁	—	2	1	no	—
169	C₈×C₁₁	—	2	1	no	—
170	C₈×C₁₁	—	4	1	no	—
171	C₈×C₁₁	—	4	2	no	—
172	C₈×C₁₁	#131	1	2	yes	—
173	C₁₁⋊C₈	—	2	1	no	—
174	C₁₁⋊C₈	—	2	1	no	—
175	C₁₁⋊C₈	—	2	1	no	—
176	C₁₁⋊C₈	—	4	1	no	—
177	C₁₁⋊C₈	—	4	2	no	—
178	C₁₁⋊C₈	#131	1	2	yes	—
179	#533	—	11	2	no	—
180	#500	—	11	1	no	—
181	#494	—	11	1	no	—
182	#487	—	11	2	no	—
183	#467	—	11	1	no	—
184	#467	—	11	1	no	—
185	#467	—	11	2	no	—
186	#446	—	11	2	no	—
187	#446	—	22	2	no	—
188	#446	—	22	2	no	—
189	#446	C₂×D₁₁	1	2	yes	—
190	C₈×Q₈	—	11	2	no	—
191	C₈×Q₈	—	11	2	no	—
192	C₄×Q₁₆	—	11	2	no	—
193	C₄×Q₁₆	—	11	1	no	—
194	C₄×Q₁₆	C₂×D₁₁	1	1	yes	characteristic
195	#433	—	22	2	no	—
196	#433	—	22	2	no	—
197	#432	—	11	2	no	—
198	#431	—	11	1	no	—
199	#431	—	11	1	no	—
200	C₂×C₄×C₈	—	11	1	no	—
201	#335	—	11	1	no	—
202	#335	C₂×D₁₁	1	1	yes	characteristic
203	#334	—	11	2	no	—
204	Q₈⋊C₈	—	11	2	no	—
205	Q₈⋊C₈	—	11	2	no	—
206	Q₈⋊C₈	—	11	2	no	—
207	Q₈⋊C₈	C₂×D₁₁	1	2	yes	—
208	#322	—	11	1	no	—
209	#322	—	11	1	no	—
210	C₈²	—	11	1	no	—
211	C₈²	C₂×D₁₁	1	1	yes	characteristic
212	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
213	C₂×D₁₁	—	2	1	no	—
214	C₂×D₁₁	—	2	1	no	—
215	C₂×D₁₁	—	2	1	no	—
216	C₄×C₁₁	—	2	1	no	—
217	C₄×C₁₁	—	4	2	no	—
218	C₄×C₁₁	—	4	2	no	—
219	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
220	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
221	C₄×C₁₁	#578	1	1	yes	characteristic
222	C₄×C₁₁	#578	1	1	yes	characteristic
223	Dic₁₁	—	2	1	no	—
224	Dic₁₁	—	2	1	no	—
225	Dic₁₁	—	2	1	no	—
226	Dic₁₁	—	4	2	no	—
227	Dic₁₁	—	4	2	no	—
228	C₂×Q₁₆	—	11	2	no	—
229	C₂×Q₁₆	—	11	1	no	—
230	C₂×Q₁₆	C₄×D₁₁	1	1	yes	characteristic
231	C₂²×C₈	—	11	1	no	—
232	C₂²×C₈	—	11	1	no	—
233	C₄⋊Q₈	—	11	2	no	—
234	C₄⋊Q₈	—	11	2	no	—
235	#125	—	22	2	no	—
236	C₂²⋊Q₈	—	11	2	no	—
237	C₂²⋊Q₈	—	11	2	no	—
238	C₂²⋊Q₈	—	22	2	no	—
239	C₄×Q₈	—	11	2	no	—
240	C₄×Q₈	—	22	2	no	—
241	C₄×Q₈	C₂²×D₁₁	1	2	yes	—
242	#117	—	22	2	no	—
243	C₂×C₄²	—	11	1	no	—
244	#107	—	11	1	no	—
245	#107	—	11	2	no	—
246	#107	C₄×D₁₁	1	1	yes	characteristic
247	C₄⋊C₈	—	2	2	no	—
248	C₄⋊C₈	—	11	1	no	—
249	C₄⋊C₈	—	11	1	no	—
250	C₄⋊C₈	—	11	2	no	—
251	C₄⋊C₈	—	22	2	no	—
252	C₄⋊C₈	—	22	1	no	—
253	C₄⋊C₈	—	22	2	no	—
254	C₄⋊C₈	—	22	2	no	—
255	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
256	#103	—	11	2	no	—
257	#103	—	11	2	no	—
258	#103	—	11	2	no	—
259	#103	C₄×D₁₁	1	2	yes	—
260	C₂²⋊C₈	—	11	1	no	—
261	C₂²⋊C₈	—	11	1	no	—
262	C₂²⋊C₈	—	22	1	no	—
263	C₂²⋊C₈	—	22	2	no	—
264	#97	—	2	2	no	—
265	#97	—	22	2	no	—
266	#97	—	22	2	no	—
267	C₄×C₈	—	11	1	no	—
268	C₄×C₈	—	11	1	no	—
269	C₄×C₈	—	11	1	no	—
270	C₄×C₈	—	11	1	no	—
271	C₄×C₈	—	11	1	no	—
272	C₄×C₈	—	22	2	no	—
273	C₄×C₈	—	22	2	no	—
274	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
275	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
276	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
277	C₂×C₁₁	#2931	1	1	yes	characteristic
278	C₂×C₁₁	#2950	1	1	yes	characteristic
279	C₂×C₁₁	#2957	1	1	yes	characteristic
280	D₁₁	—	4	1	no	—
281	C₂×Q₈	—	11	2	no	—
282	C₂×Q₈	—	22	2	no	—
283	C₂×Q₈	C₂×C₄×D₁₁	1	2	yes	—
284	C₂²×C₄	—	11	1	no	—
285	C₂²×C₄	—	11	1	no	—
286	C₂²×C₄	—	11	1	no	—
287	Q₁₆	—	2	2	no	—
288	Q₁₆	—	22	4	no	—
289	Q₁₆	—	22	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	11	1	no	—
293	C₂×C₈	—	11	1	no	—
294	C₂×C₈	—	11	1	no	—
295	C₂×C₈	—	11	1	no	—
296	C₂×C₈	—	22	2	no	—
297	C₂×C₈	—	22	2	no	—
298	C₂×C₈	—	22	2	no	—
299	C₂×C₈	—	22	1	no	—
300	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
301	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
302	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
303	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	11	2	no	—
306	C₄⋊C₄	—	22	2	no	—
307	C₄⋊C₄	—	22	2	no	—
308	C₄⋊C₄	—	22	2	no	—
309	C₄⋊C₄	—	22	2	no	—
310	C₄⋊C₄	—	22	2	no	—
311	C₄⋊C₄	—	22	2	no	—
312	C₄⋊C₄	C₂×C₄×D₁₁	1	2	yes	—
313	C₂²⋊C₄	—	22	2	no	—
314	C₂²⋊C₄	—	22	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	11	1	no	—
317	C₄²	—	11	1	no	—
318	C₄²	—	11	1	no	—
319	C₄²	—	22	2	no	—
320	C₄²	C₂³×D₁₁	1	1	yes	characteristic
321	C₁₁	#17972	1	1	yes	characteristic, complemented, Sylow
322	C₂³	—	11	1	no	—
323	Q₈	—	2	2	no	—
324	Q₈	—	2	2	no	—
325	Q₈	—	22	2	no	—
326	Q₈	—	22	2	no	—
327	Q₈	—	88	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	11	1	no	—
331	C₂×C₄	—	11	1	no	—
332	C₂×C₄	—	11	1	no	—
333	C₂×C₄	—	22	1	no	—
334	C₂×C₄	—	22	1	no	—
335	C₂×C₄	—	22	1	no	—
336	C₂×C₄	—	22	1	no	—
337	C₂×C₄	—	22	2	no	—
338	C₂×C₄	—	22	2	no	—
339	C₂×C₄	—	44	1	no	—
340	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
341	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
342	C₂×C₄	#41×D₁₁	1	1	yes	characteristic
343	C₈	—	2	1	no	—
344	C₈	—	2	1	no	—
345	C₈	—	2	1	no	—
346	C₈	—	4	1	no	—
347	C₈	—	4	2	no	—
348	C₈	—	11	2	no	—
349	C₈	—	22	1	no	—
350	C₈	—	22	1	no	—
351	C₈	—	22	1	no	—
352	C₈	—	44	1	no	—
353	C₈	—	44	2	no	—
354	C₈	#66960	1	2	yes	—
355	C₂²	—	22	1	no	—
356	C₂²	—	22	1	no	—
357	C₂²	—	22	1	no	—
358	C₂²	C₄×D₄×D₁₁	1	1	yes	characteristic
359	C₄	—	2	1	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	2	no	—
362	C₄	—	22	1	no	—
363	C₄	—	22	1	no	—
364	C₄	—	22	1	no	—
365	C₄	—	44	2	no	—
366	C₄	—	44	2	no	—
367	C₄	C₂×#66960	1	1	yes	characteristic
368	C₄	D₁₁×#131	1	1	yes	characteristic
369	C₄	#10623297	1	1	yes	characteristic
370	C₄	#10623302	1	1	yes	characteristic
371	C₂	—	44	1	no	—
372	C₂	#13077325	1	1	yes	characteristic
373	C₂	#13077479	1	1	yes	characteristic
374	C₂	#13077528	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#1591	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂²×D₁₁	C₄×D₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1591	D₁₁
hypocenter	C₁₁	#17972
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1591

Complements

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

N	H ≅ G/N	type
3. #13067523	C₂	semidirect
4. #13067514	C₂	semidirect
5. #13067432	C₂	semidirect
6. Q₁₆×C₁₁⋊C₈	C₂	semidirect
7. #13067422	C₂	semidirect
11. C₁₁×#1591	C₂	semidirect
139. #1591	D₁₁	semidirect
321. C₁₁	#17972	semidirect

Maximal subgroups

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

subgroup	index
#13079199	2
#13077712	2
#13067523	2
#13067514	2
#13067432	2
Q₁₆×C₁₁⋊C₈	2
#13067422	2
#13067378	2
#13067087	2
#13066898	2
C₁₁×#1591	2
#17972	11