Subgroups — #14907415

Order 2816.

486 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Q₈×D₁₁	C₂	1	1	yes	maximal, characteristic
2	#13070525	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070524	C₂	1	1	yes	maximal, characteristic, complemented
4	#13070523	C₂	1	2	yes	maximal, complemented
5	#13070522	C₂	1	2	yes	maximal, complemented
6	#13070521	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070418	C₂	1	2	yes	maximal
8	#13070417	C₂	1	2	yes	maximal
9	#13070414	C₂	1	1	yes	maximal, characteristic
10	#13070413	C₂	1	1	yes	maximal, characteristic
11	C₁₁×#2183	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×Q₈×D₁₁	C₄	1	1	yes	characteristic
13	C₈×Q₈×C₁₁	C₂²	1	1	yes	characteristic
14	Q₈×C₁₁⋊C₈	C₄	1	1	yes	characteristic
15	D₁₁×C₄⋊C₈	C₄	1	1	yes	characteristic
16	D₁₁×C₄⋊C₈	C₄	1	2	yes	—
17	#10622443	C₄	1	1	yes	characteristic
18	#10622443	C₄	1	2	yes	—
19	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
20	C₄×C₈×D₁₁	C₂²	1	2	yes	—
21	C₈×Dic₂₂	C₂²	1	1	yes	characteristic
22	C₈×Dic₂₂	C₂²	1	2	yes	—
23	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
24	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
25	C₁₁×#346	C₂²	1	2	yes	—
26	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
27	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
28	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
29	(C₂×D₁₁)⋊C₁₆	C₂²	1	2	yes	—
30	#10622140	C₂²	1	2	yes	—
31	#10622140	C₂²	1	2	yes	—
32	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
33	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
34	Dic₁₁⋊C₁₆	C₂²	1	2	yes	—
35	Dic₁₁⋊C₁₆	C₂²	1	2	yes	—
36	C₁₆×Dic₁₁	C₂²	1	2	yes	—
37	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
38	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	—
39	#10622099	C₂²	1	2	yes	—
40	C₄×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
41	C₂×Q₈×D₁₁	C₈	1	1	yes	characteristic
42	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
43	Q₈×Dic₁₁	C₈	1	1	yes	characteristic
44	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
46	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
47	C₄⋊C₄×D₁₁	C₈	1	2	yes	—
48	C₄⋊C₄×D₁₁	C₈	1	1	yes	characteristic
49	#66940	C₈	1	1	yes	characteristic
50	#66940	C₈	1	2	yes	—
51	C₄²×D₁₁	C₂×C₄	1	2	yes	—
52	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
53	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
54	C₄×Dic₂₂	C₂×C₄	1	2	yes	—
55	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
56	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
57	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
58	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
59	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
60	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
61	C₄×C₈×C₁₁	C₂³	1	2	yes	—
62	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
63	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
64	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
65	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
66	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
67	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
68	C₈×Dic₁₁	C₂³	1	2	yes	—
69	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
70	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
71	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
72	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
73	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
74	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
76	#33497	—	11	1	no	maximal, Sylow
77	C₂×Q₈×C₁₁	C₂×C₈	1	1	yes	characteristic
78	Q₈×D₁₁	—	2	4	no	—
79	C₂×C₄×D₁₁	C₂×C₈	1	2	yes	—
80	C₂×C₄×D₁₁	C₂×C₈	1	2	yes	—
81	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
82	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
83	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
84	C₂×Dic₂₂	C₂×C₈	1	2	yes	—
85	C₂×Dic₂₂	C₂×C₈	1	1	yes	characteristic
86	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
88	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
89	C₁₁×C₄⋊C₄	C₂×C₈	1	2	yes	—
90	C₁₁×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
91	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
92	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
93	C₄⋊Dic₁₁	C₂×C₈	1	2	yes	—
94	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
95	Dic₁₁⋊C₄	C₂×C₈	1	2	yes	—
96	Dic₁₁⋊C₄	C₂×C₈	1	2	yes	—
97	Dic₁₁⋊C₄	C₂×C₈	1	2	yes	—
98	C₄×Dic₁₁	C₂×C₈	1	2	yes	—
99	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
100	C₄×Dic₁₁	C₂×C₈	1	2	yes	—
101	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
102	C₄×Dic₁₁	C₂²×C₄	1	2	yes	—
103	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
107	C₈×D₁₁	—	2	1	no	—
108	C₈×D₁₁	—	2	1	no	—
109	C₈×D₁₁	—	4	1	no	—
110	C₈×D₁₁	—	4	2	no	—
111	C₁₁×C₁₆	—	2	1	no	—
112	C₁₁×C₁₆	—	2	1	no	—
113	C₁₁×C₁₆	—	2	2	no	—
114	C₁₁⋊C₁₆	—	2	1	no	—
115	C₁₁⋊C₁₆	—	2	2	no	—
116	C₁₁⋊C₁₆	—	2	1	no	—
117	C₂×C₈×Q₈	—	11	1	no	—
118	#2183	—	11	1	no	—
119	#2183	—	11	1	no	—
120	#2183	—	11	2	no	—
121	#2183	—	11	2	no	—
122	#2183	—	11	1	no	—
123	#2183	D₁₁	1	1	yes	characteristic, complemented
124	#2163	—	11	2	no	—
125	#2163	—	11	2	no	—
126	#2162	—	11	1	no	—
127	#2162	—	11	1	no	—
128	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
129	Q₈×C₁₁	—	2	2	no	—
130	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
131	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
132	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
133	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
134	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
135	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
136	C₂×Dic₁₁	C₂²×C₈	1	2	yes	—
137	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
138	C₂×Dic₁₁	C₂²×C₈	1	2	yes	—
139	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
140	C₄×D₁₁	—	2	4	no	—
141	C₄×D₁₁	—	2	1	no	—
142	C₄×D₁₁	—	2	1	no	—
143	C₄×D₁₁	—	4	2	no	—
144	C₄×D₁₁	—	4	1	no	—
145	C₄×D₁₁	M₃₂	1	4	yes	—
146	Dic₂₂	—	2	2	no	—
147	Dic₂₂	—	2	4	no	—
148	C₈×C₁₁	—	2	1	no	—
149	C₈×C₁₁	—	2	2	no	—
150	C₈×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
151	C₈×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
152	C₁₁⋊C₈	—	2	1	no	—
153	C₁₁⋊C₈	—	2	1	no	—
154	C₁₁⋊C₈	—	2	2	no	—
155	C₂×C₄×Q₈	—	11	1	no	—
156	C₈×Q₈	—	11	1	no	—
157	C₈×Q₈	—	11	2	no	—
158	C₈×Q₈	—	11	1	no	—
159	C₈×Q₈	—	11	2	no	—
160	C₈×Q₈	—	11	1	no	—
161	C₈×Q₈	C₂×D₁₁	1	1	yes	characteristic
162	C₂×C₄⋊C₈	—	11	1	no	—
163	C₂×C₄⋊C₈	—	11	2	no	—
164	C₂×C₄×C₈	—	11	1	no	—
165	C₂×C₄×C₈	—	11	2	no	—
166	C₄⋊C₁₆	—	11	1	no	—
167	C₄⋊C₁₆	—	11	1	no	—
168	C₄⋊C₁₆	—	11	2	no	—
169	C₄⋊C₁₆	—	11	2	no	—
170	C₄⋊C₁₆	—	11	1	no	—
171	C₄⋊C₁₆	—	11	2	no	—
172	C₄⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
173	C₄⋊C₁₆	C₂×D₁₁	1	2	yes	—
174	C₂²⋊C₁₆	—	11	2	no	—
175	C₂²⋊C₁₆	—	11	1	no	—
176	C₂²⋊C₁₆	—	11	1	no	—
177	#346	—	11	2	no	—
178	#346	—	11	2	no	—
179	#346	—	11	2	no	—
180	#346	C₂×D₁₁	1	2	yes	—
181	C₄×C₁₆	—	11	2	no	—
182	C₄×C₁₆	—	11	1	no	—
183	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
184	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
185	C₂×D₁₁	—	2	1	no	—
186	C₂×D₁₁	—	2	1	no	—
187	C₂×D₁₁	C₂×M₃₂	1	2	yes	—
188	C₄×C₁₁	—	2	2	no	—
189	C₄×C₁₁	—	2	2	no	—
190	C₄×C₁₁	—	2	1	no	—
191	C₄×C₁₁	C₂×M₃₂	1	2	yes	—
192	C₄×C₁₁	#519	1	1	yes	characteristic
193	C₄×C₁₁	#568	1	1	yes	characteristic
194	Dic₁₁	—	2	2	no	—
195	Dic₁₁	—	2	2	no	—
196	Dic₁₁	—	2	1	no	—
197	Dic₁₁	—	2	1	no	—
198	Dic₁₁	C₂×M₃₂	1	2	yes	—
199	C₂²×Q₈	—	11	1	no	—
200	C₂²×C₈	—	11	1	no	—
201	C₂²×C₈	—	11	1	no	—
202	C₂²×C₈	—	11	2	no	—
203	C₄×Q₈	—	11	1	no	—
204	C₄×Q₈	—	11	2	no	—
205	C₄×Q₈	—	11	1	no	—
206	C₄×Q₈	—	11	2	no	—
207	C₄×Q₈	—	11	1	no	—
208	C₄×Q₈	C₄×D₁₁	1	1	yes	characteristic
209	C₂×C₄⋊C₄	—	11	1	no	—
210	C₂×C₄⋊C₄	—	11	2	no	—
211	C₂×C₄²	—	11	1	no	—
212	C₂×C₄²	—	11	2	no	—
213	C₂×C₁₆	—	11	1	no	—
214	C₂×C₁₆	—	11	2	no	—
215	C₂×C₁₆	—	11	1	no	—
216	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
217	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
218	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
219	C₄⋊C₈	—	11	2	no	—
220	C₄⋊C₈	—	11	2	no	—
221	C₄⋊C₈	—	11	2	no	—
222	C₄⋊C₈	—	11	2	no	—
223	C₄⋊C₈	—	11	1	no	—
224	C₄⋊C₈	C₄×D₁₁	1	2	yes	—
225	C₄⋊C₈	C₄×D₁₁	1	1	yes	characteristic
226	C₄×C₈	—	11	1	no	—
227	C₄×C₈	—	11	2	no	—
228	C₄×C₈	—	11	1	no	—
229	C₄×C₈	—	11	2	no	—
230	C₄×C₈	—	11	1	no	—
231	C₄×C₈	—	11	2	no	—
232	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
233	C₄×C₈	C₂²×D₁₁	1	2	yes	—
234	C₂×C₁₁	#2982	1	1	yes	characteristic
235	C₂×C₁₁	C₂²×M₃₂	1	1	yes	characteristic
236	C₂×C₁₁	#3407	1	1	yes	characteristic
237	D₁₁	—	2	2	no	—
238	C₂×Q₈	—	11	2	no	—
239	C₂×Q₈	—	11	1	no	—
240	C₂×Q₈	—	22	4	no	—
241	C₂×Q₈	C₈×D₁₁	1	1	yes	characteristic
242	C₂²×C₄	—	11	1	no	—
243	C₂²×C₄	—	11	2	no	—
244	C₂²×C₄	—	11	1	no	—
245	C₂²×C₄	—	11	1	no	—
246	C₂²×C₄	—	11	2	no	—
247	C₂×C₈	—	11	1	no	—
248	C₂×C₈	—	11	1	no	—
249	C₂×C₈	—	11	2	no	—
250	C₂×C₈	—	22	1	no	—
251	C₂×C₈	—	22	1	no	—
252	C₂×C₈	—	44	1	no	—
253	C₂×C₈	—	44	2	no	—
254	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
255	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
256	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
257	C₄⋊C₄	—	11	2	no	—
258	C₄⋊C₄	—	11	2	no	—
259	C₄⋊C₄	—	11	2	no	—
260	C₄⋊C₄	—	11	2	no	—
261	C₄⋊C₄	—	11	1	no	—
262	C₄⋊C₄	C₈×D₁₁	1	2	yes	—
263	C₄⋊C₄	C₈×D₁₁	1	1	yes	characteristic
264	C₄²	—	11	1	no	—
265	C₄²	—	11	2	no	—
266	C₄²	—	11	1	no	—
267	C₄²	—	11	2	no	—
268	C₄²	—	11	1	no	—
269	C₄²	—	11	2	no	—
270	C₄²	C₂×C₄×D₁₁	1	2	yes	—
271	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
272	C₁₆	—	2	1	no	—
273	C₁₆	—	2	2	no	—
274	C₁₆	—	2	1	no	—
275	C₁₆	—	22	1	no	—
276	C₁₆	—	22	2	no	—
277	C₁₆	—	22	1	no	—
278	C₁₁	#33497	1	1	yes	characteristic, complemented, Sylow
279	C₂³	—	11	1	no	—
280	Q₈	—	2	2	no	—
281	Q₈	—	22	4	no	—
282	Q₈	—	22	2	no	—
283	C₂×C₄	—	11	1	no	—
284	C₂×C₄	—	11	4	no	—
285	C₂×C₄	—	11	1	no	—
286	C₂×C₄	—	11	2	no	—
287	C₂×C₄	—	11	1	no	—
288	C₂×C₄	—	11	2	no	—
289	C₂×C₄	—	22	4	no	—
290	C₂×C₄	—	22	1	no	—
291	C₂×C₄	—	22	1	no	—
292	C₂×C₄	—	44	1	no	—
293	C₂×C₄	—	44	2	no	—
294	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
295	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
296	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
297	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
298	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
299	C₈	—	2	1	no	—
300	C₈	—	2	2	no	—
301	C₈	—	22	1	no	—
302	C₈	—	22	2	no	—
303	C₈	—	22	1	no	—
304	C₈	#67040	1	1	yes	characteristic
305	C₈	#67043	1	1	yes	characteristic
306	C₂²	—	11	2	no	—
307	C₂²	—	22	1	no	—
308	C₂²	—	22	1	no	—
309	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
310	C₄	—	2	2	no	—
311	C₄	—	2	1	no	—
312	C₄	—	2	2	no	—
313	C₄	—	11	2	no	—
314	C₄	—	22	2	no	—
315	C₄	—	22	2	no	—
316	C₄	—	22	1	no	—
317	C₄	—	22	1	no	—
318	C₄	D₁₁×M₃₂	1	2	yes	—
319	C₄	#10623103	1	1	yes	characteristic
320	C₄	#10623281	1	1	yes	characteristic
321	C₂	—	22	2	no	—
322	C₂	#13077695	1	1	yes	characteristic
323	C₂	C₂×D₁₁×M₃₂	1	1	yes	characteristic
324	C₂	#13081717	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₁₁×#2183	C₂
prime radical	C₂²×D₁₁	C₂²×C₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2183	D₁₁
hypocenter	C₁₁	#33497
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ #2183

Complements

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

N	H ≅ G/N	type
2. #13070525	C₂	semidirect
3. #13070524	C₂	semidirect
4. #13070523	C₂	semidirect
5. #13070522	C₂	semidirect
6. #13070521	C₂	semidirect
11. C₁₁×#2183	C₂	semidirect
123. #2183	D₁₁	semidirect
278. C₁₁	#33497	semidirect

Maximal subgroups

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

subgroup	index
C₈×Q₈×D₁₁	2
#13070525	2
#13070524	2
#13070523	2
#13070522	2
#13070521	2
#13070418	2
#13070417	2
#13070414	2
#13070413	2
C₁₁×#2183	2
#33497	11