Subgroups — #14719449

Order 2816.

718 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077583	C₂	1	1	yes	maximal, characteristic
2	#13077260	C₂	1	1	yes	maximal, characteristic
3	#13066916	C₂	1	2	yes	maximal, complemented
4	#13066911	C₂	1	2	yes	maximal, complemented
5	#13066909	C₂	1	1	yes	maximal, characteristic, complemented
6	#13066908	C₂	1	2	yes	maximal, complemented
7	#13066906	C₂	1	1	yes	maximal, characteristic, complemented
8	#13066905	C₂	1	2	yes	maximal, complemented
9	C₈×#4318	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10622092	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₁×#41	C₂	1	1	yes	maximal, characteristic
12	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
13	C₈×Q₈×C₁₁	C₄	1	2	yes	—
14	C₈×D₄×C₁₁	C₄	1	2	yes	—
15	C₈×D₄×C₁₁	C₄	1	4	yes	—
16	C₁₁×#431	C₂²	1	1	yes	characteristic
17	C₁₁×#431	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
20	#10622847	C₄	1	2	yes	—
21	#10622637	C₄	1	2	yes	—
22	#10622625	C₄	1	2	yes	—
23	#10622624	C₄	1	4	yes	—
24	#10622613	C₄	1	4	yes	—
25	#10622612	C₄	1	2	yes	—
26	#10622538	C₂²	1	2	yes	—
27	#10622538	C₂²	1	2	yes	—
28	#10622538	C₂²	1	1	yes	characteristic
29	#10622538	C₂²	1	2	yes	—
30	C₄×#4318	C₂²	1	1	yes	characteristic
31	C₄×#4318	C₂²	1	2	yes	—
32	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
34	#10622093	C₂²	1	2	yes	—
35	#10622093	C₂²	1	2	yes	—
36	#10622092	C₂²	1	1	yes	characteristic
37	#10622092	C₂²	1	1	yes	characteristic
38	#10622092	C₂²	1	1	yes	characteristic
39	#10622092	C₂²	1	1	yes	characteristic
40	#10622092	C₂²	1	2	yes	—
41	#10622092	C₂²	1	2	yes	—
42	#10622092	C₂²	1	2	yes	—
43	C₈×C₁₁⋊C₈	C₂²	1	2	yes	—
44	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
46	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
47	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
48	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
49	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
50	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
51	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
52	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
53	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
54	C₁₁×#117	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
57	C₂×#4318	C₂×C₄	1	2	yes	—
58	C₂×#4318	C₂×C₄	1	4	yes	—
59	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
60	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
61	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
62	C₁₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
63	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
64	C₁₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
65	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
66	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
67	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
68	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
69	C₄×C₈×C₁₁	C₂³	1	2	yes	—
70	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
71	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
72	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
73	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
74	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
75	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
76	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
77	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
78	#66867	C₂×C₄	1	2	yes	—
79	#66867	C₂×C₄	1	4	yes	—
80	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
81	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
82	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
83	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
84	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
85	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
86	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
87	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
88	#17329	—	11	1	no	maximal, Sylow
89	C₁₁×#41	—	2	4	no	—
90	C₂×Q₈×C₁₁	C₄²	1	1	yes	characteristic
91	C₂×D₄×C₁₁	C₄²	1	2	yes	—
92	C₂×D₄×C₁₁	C₄²	1	1	yes	characteristic
93	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₁₁	—	4	2	no	—
100	C₂×C₈×C₁₁	—	4	4	no	—
101	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
104	C₁₁×C₄⋊C₄	C₄²	1	2	yes	—
105	C₁₁×C₄⋊C₄	C₄²	1	2	yes	—
106	C₁₁×C₄⋊C₄	C₄²	1	1	yes	characteristic
107	C₁₁×C₄⋊C₄	C₄²	1	1	yes	characteristic
108	C₁₁×C₂²⋊C₄	C₄²	1	2	yes	—
109	C₁₁×C₂²⋊C₄	C₄²	1	2	yes	—
110	C₁₁×C₂²⋊C₄	C₄²	1	2	yes	—
111	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
114	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
115	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
116	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
118	#4318	—	2	4	no	—
119	#4318	—	4	4	no	—
120	C₂×C₁₁⋊C₈	—	2	4	no	—
121	C₂×C₁₁⋊C₈	—	4	2	no	—
122	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
123	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
124	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
125	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
126	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
127	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
128	#2965	—	11	1	no	—
129	C₈×#41	D₁₁	1	1	yes	characteristic
130	#2922	—	11	1	no	—
131	#1454	—	11	2	no	—
132	#1453	—	11	2	no	—
133	#1452	—	11	1	no	—
134	#1452	—	11	2	no	—
135	#1451	—	11	1	no	—
136	#1451	—	11	2	no	—
137	C₈×M₁₆	—	11	1	no	—
138	C₂×#322	—	11	1	no	—
139	C₂³×C₁₁	C₂×C₄²	1	2	yes	—
140	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
141	Q₈×C₁₁	—	2	2	no	—
142	D₄×C₁₁	—	2	4	no	—
143	D₄×C₁₁	—	2	2	no	—
144	C₂×C₄×C₁₁	—	2	4	no	—
145	C₂×C₄×C₁₁	—	2	2	no	—
146	C₂×C₄×C₁₁	—	2	4	no	—
147	C₂×C₄×C₁₁	—	2	2	no	—
148	C₂×C₄×C₁₁	—	2	4	no	—
149	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₁₁	C₂×C₄²	1	2	yes	—
151	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
152	C₂×C₄×C₁₁	C₂×C₄²	1	2	yes	—
153	C₂×C₄×C₁₁	C₂×C₄²	1	2	yes	—
154	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₁₁	#131	1	4	yes	—
156	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
159	C₈×C₁₁	—	2	2	no	—
160	C₈×C₁₁	—	2	2	no	—
161	C₈×C₁₁	—	2	4	no	—
162	C₁₁⋊C₈	—	2	2	no	—
163	C₁₁⋊C₈	—	2	2	no	—
164	C₁₁⋊C₈	—	2	4	no	—
165	C₁₁⋊C₈	—	2	2	no	—
166	C₁₁⋊C₈	—	2	2	no	—
167	C₁₁⋊C₈	—	2	4	no	—
168	C₄×#41	C₂×D₁₁	1	1	yes	characteristic
169	#446	—	11	2	no	—
170	C₈×Q₈	Dic₁₁	1	2	yes	—
171	#436	—	11	2	no	—
172	#435	—	11	4	no	—
173	C₈×D₄	Dic₁₁	1	2	yes	—
174	C₈×D₄	Dic₁₁	1	4	yes	—
175	#433	—	11	4	no	—
176	#431	—	11	2	no	—
177	#431	—	11	2	no	—
178	#431	—	11	1	no	—
179	#431	—	11	2	no	—
180	#431	C₂×D₁₁	1	1	yes	characteristic
181	#431	C₂×D₁₁	1	2	yes	—
182	#424	—	11	2	no	—
183	#408	—	11	2	no	—
184	C₄×M₁₆	—	11	1	no	—
185	C₄×M₁₆	—	11	2	no	—
186	C₂×C₄×C₈	—	11	1	no	—
187	C₂×C₄×C₈	—	11	1	no	—
188	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
189	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
190	#322	—	11	1	no	—
191	#322	—	11	1	no	—
192	#322	—	11	1	no	—
193	#322	—	11	1	no	—
194	#322	—	11	2	no	—
195	#322	—	11	2	no	—
196	#322	—	11	2	no	—
197	#322	—	11	2	no	—
198	#322	—	11	2	no	—
199	C₈²	—	11	2	no	—
200	C₂²×C₁₁	—	2	1	no	—
201	C₂²×C₁₁	—	2	1	no	—
202	C₂²×C₁₁	—	2	2	no	—
203	C₂²×C₁₁	—	2	2	no	—
204	C₂²×C₁₁	—	2	2	no	—
205	C₂²×C₁₁	#405	1	2	yes	—
206	C₂²×C₁₁	C₂²×C₄²	1	1	yes	characteristic
207	C₄×C₁₁	—	2	2	no	—
208	C₄×C₁₁	—	2	1	no	—
209	C₄×C₁₁	—	2	2	no	—
210	C₄×C₁₁	—	2	1	no	—
211	C₄×C₁₁	—	2	2	no	—
212	C₄×C₁₁	#405	1	2	yes	—
213	C₄×C₁₁	C₂×#131	1	2	yes	—
214	C₄×C₁₁	#568	1	2	yes	—
215	C₄×C₁₁	#568	1	2	yes	—
216	C₂×#41	C₄×D₁₁	1	1	yes	characteristic
217	C₂×M₁₆	—	11	2	no	—
218	C₂×M₁₆	—	11	4	no	—
219	C₂²×C₈	—	11	2	no	—
220	C₂²×C₈	—	11	2	no	—
221	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
222	C₂²×C₈	C₂×Dic₁₁	1	4	yes	—
223	C₄×Q₈	C₄×D₁₁	1	1	yes	characteristic
224	C₄×Q₈	C₂×Dic₁₁	1	1	yes	characteristic
225	C₄×D₄	C₄×D₁₁	1	2	yes	—
226	C₄×D₄	C₄×D₁₁	1	1	yes	characteristic
227	C₄×D₄	C₂×Dic₁₁	1	2	yes	—
228	C₄×D₄	C₂×Dic₁₁	1	1	yes	characteristic
229	#117	C₄×D₁₁	1	1	yes	characteristic
230	#117	C₄×D₁₁	1	2	yes	—
231	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
232	C₂×C₄²	C₂²×D₁₁	1	2	yes	—
233	C₄⋊C₈	—	11	4	no	—
234	C₄⋊C₈	—	11	4	no	—
235	C₄⋊C₈	—	11	4	no	—
236	C₄⋊C₈	—	11	2	no	—
237	C₄⋊C₈	C₂×Dic₁₁	1	2	yes	—
238	C₄⋊C₈	C₂×Dic₁₁	1	4	yes	—
239	C₂²⋊C₈	—	11	4	no	—
240	C₂²⋊C₈	—	11	4	no	—
241	C₂²⋊C₈	—	11	2	no	—
242	C₂²⋊C₈	—	11	4	no	—
243	C₂²⋊C₈	C₂×Dic₁₁	1	2	yes	—
244	C₂²⋊C₈	C₂×Dic₁₁	1	4	yes	—
245	#97	—	11	2	no	—
246	#97	—	11	4	no	—
247	C₄×C₈	—	11	2	no	—
248	C₄×C₈	—	11	2	no	—
249	C₄×C₈	—	11	2	no	—
250	C₄×C₈	—	11	2	no	—
251	C₄×C₈	—	11	1	no	—
252	C₄×C₈	—	11	1	no	—
253	C₄×C₈	—	11	1	no	—
254	C₄×C₈	—	11	1	no	—
255	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
256	C₄×C₈	C₂×Dic₁₁	1	4	yes	—
257	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
258	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
259	C₄×C₈	C₂²×D₁₁	1	2	yes	—
260	C₂×C₁₁	—	2	2	no	—
261	C₂×C₁₁	—	4	2	no	—
262	C₂×C₁₁	C₂×#405	1	1	yes	characteristic
263	C₂×C₁₁	#2875	1	1	yes	characteristic
264	C₂×C₁₁	#2875	1	1	yes	characteristic
265	#41	—	2	4	no	—
266	C₂×Q₈	C₄×Dic₁₁	1	1	yes	characteristic
267	C₂×D₄	C₄×Dic₁₁	1	2	yes	—
268	C₂×D₄	C₄×Dic₁₁	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₄×D₁₁	1	2	yes	—
270	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₄×D₁₁	1	2	yes	—
272	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
273	C₂²×C₄	C₂²×Dic₁₁	1	2	yes	—
274	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
275	M₁₆	—	22	4	no	—
276	M₁₆	—	44	4	no	—
277	C₂×C₈	—	4	2	no	—
278	C₂×C₈	—	4	4	no	—
279	C₂×C₈	—	11	2	no	—
280	C₂×C₈	—	11	2	no	—
281	C₂×C₈	—	11	2	no	—
282	C₂×C₈	—	11	2	no	—
283	C₂×C₈	—	11	4	no	—
284	C₂×C₈	—	11	4	no	—
285	C₂×C₈	—	22	4	no	—
286	C₂×C₈	—	44	2	no	—
287	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
288	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
289	C₂×C₈	C₂²×Dic₁₁	1	4	yes	—
290	C₄⋊C₄	C₄×Dic₁₁	1	2	yes	—
291	C₄⋊C₄	C₄×Dic₁₁	1	1	yes	characteristic
292	C₄⋊C₄	C₄×Dic₁₁	1	2	yes	—
293	C₄⋊C₄	C₄×Dic₁₁	1	1	yes	characteristic
294	C₂²⋊C₄	C₄×Dic₁₁	1	2	yes	—
295	C₂²⋊C₄	C₄×Dic₁₁	1	2	yes	—
296	C₂²⋊C₄	C₄×Dic₁₁	1	2	yes	—
297	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
298	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
299	C₄²	C₂×C₄×D₁₁	1	2	yes	—
300	C₄²	C₂×C₄×D₁₁	1	2	yes	—
301	C₄²	C₂²×Dic₁₁	1	2	yes	—
302	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
303	C₄²	C₂³×D₁₁	1	1	yes	characteristic
304	C₁₁	#17329	1	1	yes	characteristic, complemented, Sylow
305	C₂³	C₂×C₄×Dic₁₁	1	2	yes	—
306	C₂³	C₂×C₄×Dic₁₁	1	1	yes	characteristic
307	Q₈	—	2	2	no	—
308	D₄	—	2	4	no	—
309	D₄	—	2	2	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	#66954	1	4	yes	—
316	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
317	C₂×C₄	C₂×C₄×Dic₁₁	1	2	yes	—
318	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
319	C₂×C₄	C₂×C₄×Dic₁₁	1	2	yes	—
320	C₂×C₄	C₂×C₄×Dic₁₁	1	2	yes	—
321	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
322	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
323	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
324	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
325	C₈	—	2	2	no	—
326	C₈	—	2	2	no	—
327	C₈	—	2	4	no	—
328	C₈	—	22	2	no	—
329	C₈	—	22	2	no	—
330	C₈	—	22	4	no	—
331	C₈	—	22	2	no	—
332	C₈	—	22	2	no	—
333	C₈	—	22	4	no	—
334	C₂²	—	2	1	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	2	2	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	2	no	—
339	C₂²	#10622714	1	2	yes	—
340	C₂²	C₂²×C₄×Dic₁₁	1	1	yes	characteristic
341	C₄	—	2	2	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	2	no	—
344	C₄	—	2	1	no	—
345	C₄	—	2	2	no	—
346	C₄	#10622714	1	2	yes	—
347	C₄	C₂×#66954	1	2	yes	—
348	C₄	#10623281	1	2	yes	—
349	C₄	#10623350	1	2	yes	—
350	C₂	—	2	2	no	—
351	C₂	—	4	2	no	—
352	C₂	C₂×#10622714	1	1	yes	characteristic
353	C₂	#13077042	1	1	yes	characteristic
354	C₂	#13077044	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂²×C₄²
Fitting	C₈×C₁₁×#41	C₂
prime radical	C₂×C₁₁×#41	C₂×C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₈×#41	D₁₁
hypocenter	C₁₁	#17329
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
3. #13066916	C₂	semidirect
4. #13066911	C₂	semidirect
5. #13066909	C₂	semidirect
6. #13066908	C₂	semidirect
7. #13066906	C₂	semidirect
8. #13066905	C₂	semidirect
9. C₈×#4318	C₂	semidirect
10. C₂×#10622092	C₂	semidirect
304. C₁₁	#17329	semidirect

Maximal subgroups

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

subgroup	index
#13077583	2
#13077260	2
#13066916	2
#13066911	2
#13066909	2
#13066908	2
#13066906	2
#13066905	2
C₈×#4318	2
C₂×#10622092	2
C₈×C₁₁×#41	2
#17329	11