Subgroups — #13077611

Order 1408.

372 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10623069	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#435	C₂	1	1	yes	maximal, characteristic, complemented
3	#10622740	C₂	1	1	yes	maximal, characteristic, complemented
4	#10622735	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×C₂²⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#66879	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#10622453	C₂	1	1	yes	maximal, characteristic, complemented
9	#10622444	C₂	1	1	yes	maximal, characteristic, complemented
10	#10622343	C₂	1	1	yes	maximal, characteristic, complemented
11	#10622343	C₂	1	1	yes	maximal, characteristic, complemented
12	#10622333	C₂	1	1	yes	maximal, characteristic, complemented
13	#10622331	C₂	1	1	yes	maximal, characteristic, complemented
14	#10622321	C₂	1	1	yes	maximal, characteristic, complemented
15	#10622314	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
19	#66992	C₄	1	1	yes	characteristic
20	#66988	C₄	1	1	yes	characteristic
21	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
22	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
23	#66979	C₂²	1	1	yes	characteristic
24	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic
25	C₂²×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
26	C₂²×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×#4313	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₁₁	C₂²	1	1	yes	characteristic
29	#66951	C₄	1	1	yes	characteristic
30	#66942	C₄	1	1	yes	characteristic
31	#66939	C₄	1	1	yes	characteristic
32	#66938	C₄	1	1	yes	characteristic
33	#66932	C₄	1	1	yes	characteristic
34	#66931	C₄	1	1	yes	characteristic
35	#66925	C₂²	1	1	yes	characteristic
36	C₄×Dic₂₂	C₂²	1	1	yes	characteristic
37	C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₁₁×#97	C₂²	1	1	yes	characteristic
41	C₂²⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
42	C₂²⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
43	(C₂×D₁₁)⋊C₈	C₂²	1	1	yes	characteristic
44	(C₂×D₁₁)⋊C₈	C₂²	1	1	yes	characteristic
45	#66879	C₂²	1	1	yes	characteristic
46	#66879	C₂²	1	1	yes	characteristic
47	#66879	C₂²	1	1	yes	characteristic
48	#66879	C₂²	1	1	yes	characteristic
49	#66879	C₂²	1	1	yes	characteristic
50	Dic₁₁⋊C₈	C₂²	1	1	yes	characteristic
51	Dic₁₁⋊C₈	C₂²	1	1	yes	characteristic
52	Dic₁₁⋊C₈	C₂²	1	1	yes	characteristic
53	Dic₁₁⋊C₈	C₂²	1	1	yes	characteristic
54	C₈×Dic₁₁	C₂²	1	1	yes	characteristic
55	C₈×Dic₁₁	C₂²	1	1	yes	characteristic
56	C₈×Dic₁₁	C₂²	1	1	yes	characteristic
57	C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
58	C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
59	C₂×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
62	C₂×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
63	C₂×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
64	C₂²×Dic₁₁	C₂×C₄	1	1	yes	characteristic
65	C₂²×Dic₁₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
67	C₂×Dic₂₂	C₂×C₄	1	1	yes	characteristic
68	C₁₁×M₁₆	—	2	2	no	—
69	C₂×C₈×C₁₁	—	2	2	no	—
70	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
71	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
72	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
73	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
74	C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₄²×C₁₁	C₂³	1	1	yes	characteristic
78	C₂²⋊Dic₁₁	C₂×C₄	1	1	yes	characteristic
79	C₂²⋊Dic₁₁	C₂×C₄	1	1	yes	characteristic
80	C₂²⋊Dic₁₁	C₂×C₄	1	1	yes	characteristic
81	C₂²⋊Dic₁₁	C₂×C₄	1	1	yes	characteristic
82	(C₂×D₁₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
83	(C₂×D₁₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
84	(C₂×D₁₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
85	(C₂×D₁₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₄⋊Dic₁₁	C₂×C₄	1	1	yes	characteristic
87	C₄⋊Dic₁₁	C₂×C₄	1	1	yes	characteristic
88	C₄⋊Dic₁₁	C₂×C₄	1	1	yes	characteristic
89	Dic₁₁⋊C₄	C₂×C₄	1	1	yes	characteristic
90	Dic₁₁⋊C₄	C₂×C₄	1	1	yes	characteristic
91	Dic₁₁⋊C₄	C₂×C₄	1	1	yes	characteristic
92	Dic₁₁⋊C₄	C₂×C₄	1	1	yes	characteristic
93	Dic₁₁⋊C₄	C₂×C₄	1	1	yes	characteristic
94	Dic₁₁⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
96	C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
97	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
98	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
99	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
100	C₂×C₁₁⋊C₈	—	2	2	no	—
101	C₂×C₁₁⋊C₈	—	2	2	no	—
102	C₂×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
103	C₂×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
104	C₂×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
105	C₂×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
106	#4313	—	2	2	no	—
107	C₈×D₁₁	—	2	2	no	—
108	#2968	—	11	1	no	maximal, Sylow
109	C₂³×C₁₁	C₂²×C₄	1	1	yes	characteristic
110	C₂³×C₁₁	C₂²×C₄	1	1	yes	characteristic
111	C₂²×D₁₁	C₂²×C₄	1	1	yes	characteristic
112	D₄×C₁₁	—	2	2	no	—
113	C₂×C₄×C₁₁	—	2	1	no	—
114	C₂×C₄×C₁₁	—	2	1	no	—
115	C₂×C₄×C₁₁	—	2	1	no	—
116	C₂×C₄×C₁₁	—	2	1	no	—
117	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
122	C₂²⋊D₁₁	—	2	2	no	—
123	C₂²⋊D₁₁	—	4	1	no	—
124	C₂×Dic₁₁	—	2	2	no	—
125	C₂×Dic₁₁	—	4	1	no	—
126	C₂×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
127	C₂×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₂×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
129	C₂×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₂×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₂×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
132	C₂×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
133	C₄×D₁₁	—	2	1	no	—
134	C₄×D₁₁	—	2	1	no	—
135	Dic₂₂	—	4	1	no	—
136	C₈×C₁₁	—	2	1	no	—
137	C₈×C₁₁	—	2	1	no	—
138	C₈×C₁₁	—	2	1	no	—
139	C₈×C₁₁	#41	1	2	yes	—
140	C₁₁⋊C₈	—	2	1	no	—
141	C₁₁⋊C₈	—	2	1	no	—
142	C₁₁⋊C₈	—	2	1	no	—
143	C₁₁⋊C₈	#41	1	2	yes	—
144	#529	—	11	1	no	—
145	#446	—	11	1	no	—
146	#446	—	11	1	no	—
147	#435	—	11	1	no	—
148	#435	—	11	1	no	—
149	#435	—	11	1	no	—
150	#435	D₁₁	1	1	yes	characteristic, complemented
151	C₈×D₄	—	11	1	no	—
152	C₈×D₄	—	11	1	no	—
153	#433	—	11	1	no	—
154	#433	—	11	1	no	—
155	#431	—	11	1	no	—
156	#405	—	11	1	no	—
157	#405	—	11	1	no	—
158	C₂×#97	—	11	1	no	—
159	C₂²×C₁₁	—	2	1	no	—
160	C₂²×C₁₁	—	2	1	no	—
161	C₂²×C₁₁	—	2	1	no	—
162	C₂²×C₁₁	—	2	1	no	—
163	C₂²×C₁₁	—	2	1	no	—
164	C₂²×C₁₁	#131	1	2	yes	—
165	C₂²×C₁₁	C₂³×C₄	1	1	yes	characteristic
166	C₂×D₁₁	—	2	1	no	—
167	C₂×D₁₁	—	2	1	no	—
168	C₂×D₁₁	—	2	1	no	—
169	C₄×C₁₁	—	2	1	no	—
170	C₄×C₁₁	—	2	1	no	—
171	C₄×C₁₁	—	2	1	no	—
172	C₄×C₁₁	—	2	1	no	—
173	C₄×C₁₁	C₂×#41	1	1	yes	characteristic
174	C₄×C₁₁	C₂×#41	1	1	yes	characteristic
175	Dic₁₁	—	2	1	no	—
176	Dic₁₁	—	2	1	no	—
177	Dic₁₁	—	2	1	no	—
178	Dic₁₁	—	2	1	no	—
179	Dic₁₁	—	2	1	no	—
180	Dic₁₁	—	2	1	no	—
181	Dic₁₁	—	2	1	no	—
182	C₂×M₁₆	—	11	1	no	—
183	C₂×M₁₆	C₂×D₁₁	1	1	yes	characteristic
184	C₂²×C₈	—	11	1	no	—
185	C₂²×C₈	—	11	1	no	—
186	C₂²×C₈	—	11	1	no	—
187	C₂²×C₈	C₂×D₁₁	1	1	yes	characteristic
188	#126	—	11	1	no	—
189	#126	—	11	1	no	—
190	#125	—	11	1	no	—
191	#124	—	11	1	no	—
192	#123	—	11	1	no	—
193	#123	—	11	1	no	—
194	C₂²⋊Q₈	—	11	1	no	—
195	#121	—	11	1	no	—
196	C₄×Q₈	—	11	1	no	—
197	C₄×D₄	—	11	1	no	—
198	C₄×D₄	—	11	1	no	—
199	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
200	#117	—	11	1	no	—
201	#117	—	11	1	no	—
202	C₂×C₄²	—	11	1	no	—
203	C₄⋊C₈	—	11	1	no	—
204	C₄⋊C₈	—	11	1	no	—
205	C₄⋊C₈	—	11	1	no	—
206	C₄⋊C₈	—	11	1	no	—
207	C₄⋊C₈	—	11	1	no	—
208	C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
209	C₂²⋊C₈	—	11	1	no	—
210	C₂²⋊C₈	—	11	1	no	—
211	C₂²⋊C₈	—	11	1	no	—
212	C₂²⋊C₈	—	11	1	no	—
213	C₂²⋊C₈	C₂×D₁₁	1	1	yes	characteristic
214	C₂²⋊C₈	C₂×D₁₁	1	1	yes	characteristic
215	#97	—	11	1	no	—
216	#97	—	11	1	no	—
217	#97	—	11	1	no	—
218	#97	—	11	1	no	—
219	#97	—	11	1	no	—
220	#97	C₂×D₁₁	1	1	yes	characteristic
221	C₄×C₈	—	11	1	no	—
222	C₄×C₈	—	11	1	no	—
223	C₄×C₈	—	11	1	no	—
224	C₄×C₈	—	11	1	no	—
225	C₂×C₁₁	—	2	2	no	—
226	C₂×C₁₁	—	4	1	no	—
227	C₂×C₁₁	C₄×#41	1	1	yes	characteristic
228	C₂×C₁₁	C₂×#131	1	1	yes	characteristic
229	C₂×C₁₁	#568	1	1	yes	characteristic
230	D₁₁	—	4	1	no	—
231	C₂×Q₈	—	11	1	no	—
232	C₂×D₄	—	11	1	no	—
233	C₂×D₄	—	11	1	no	—
234	C₂×D₄	C₄×D₁₁	1	1	yes	characteristic
235	C₂²×C₄	—	11	1	no	—
236	C₂²×C₄	—	11	1	no	—
237	C₂²×C₄	—	11	1	no	—
238	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
239	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
240	M₁₆	—	2	2	no	—
241	M₁₆	—	22	2	no	—
242	C₂×C₈	—	2	2	no	—
243	C₂×C₈	—	11	1	no	—
244	C₂×C₈	—	11	1	no	—
245	C₂×C₈	—	11	1	no	—
246	C₂×C₈	—	11	1	no	—
247	C₂×C₈	—	22	2	no	—
248	C₂×C₈	—	22	2	no	—
249	C₂×C₈	—	22	2	no	—
250	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
251	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
252	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
253	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
254	C₄⋊C₄	—	11	1	no	—
255	C₄⋊C₄	—	11	1	no	—
256	C₄⋊C₄	—	11	1	no	—
257	C₄⋊C₄	—	11	1	no	—
258	C₄⋊C₄	—	11	1	no	—
259	C₄⋊C₄	—	11	1	no	—
260	C₄⋊C₄	—	11	1	no	—
261	C₄⋊C₄	—	11	1	no	—
262	C₄⋊C₄	—	11	1	no	—
263	C₄⋊C₄	C₄×D₁₁	1	1	yes	characteristic
264	C₂²⋊C₄	—	11	1	no	—
265	C₂²⋊C₄	—	11	1	no	—
266	C₂²⋊C₄	—	11	1	no	—
267	C₂²⋊C₄	—	11	1	no	—
268	C₂²⋊C₄	—	11	1	no	—
269	C₂²⋊C₄	—	11	1	no	—
270	C₂²⋊C₄	—	11	1	no	—
271	C₂²⋊C₄	—	11	1	no	—
272	C₂²⋊C₄	C₄×D₁₁	1	1	yes	characteristic
273	C₂²⋊C₄	C₄×D₁₁	1	1	yes	characteristic
274	C₄²	—	11	1	no	—
275	C₄²	—	11	1	no	—
276	C₄²	—	11	1	no	—
277	C₄²	—	11	1	no	—
278	C₄²	—	11	1	no	—
279	C₄²	C₂²×D₁₁	1	1	yes	characteristic
280	C₁₁	#2968	1	1	yes	characteristic, complemented, Sylow
281	C₂³	—	11	1	no	—
282	C₂³	C₂×C₄×D₁₁	1	1	yes	characteristic
283	C₂³	C₂×C₄×D₁₁	1	1	yes	characteristic
284	Q₈	—	44	1	no	—
285	D₄	—	2	2	no	—
286	D₄	—	22	2	no	—
287	D₄	—	44	1	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	11	1	no	—
293	C₂×C₄	—	11	1	no	—
294	C₂×C₄	—	11	1	no	—
295	C₂×C₄	—	11	1	no	—
296	C₂×C₄	—	11	1	no	—
297	C₂×C₄	—	11	1	no	—
298	C₂×C₄	—	11	1	no	—
299	C₂×C₄	—	22	2	no	—
300	C₂×C₄	—	22	1	no	—
301	C₂×C₄	—	22	1	no	—
302	C₂×C₄	—	44	1	no	—
303	C₂×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
304	C₂×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
305	C₂×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
306	C₂×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
307	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
308	C₈	—	2	1	no	—
309	C₈	—	2	1	no	—
310	C₈	—	2	1	no	—
311	C₈	—	11	2	no	—
312	C₈	—	22	1	no	—
313	C₈	—	22	1	no	—
314	C₈	—	22	1	no	—
315	C₈	#4341	1	2	yes	—
316	C₂²	—	2	1	no	—
317	C₂²	—	2	1	no	—
318	C₂²	—	2	1	no	—
319	C₂²	—	2	1	no	—
320	C₂²	—	2	1	no	—
321	C₂²	—	22	1	no	—
322	C₂²	—	22	1	no	—
323	C₂²	—	22	1	no	—
324	C₂²	#66960	1	2	yes	—
325	C₂²	C₂²×C₄×D₁₁	1	1	yes	characteristic
326	C₄	—	2	1	no	—
327	C₄	—	2	1	no	—
328	C₄	—	2	1	no	—
329	C₄	—	2	1	no	—
330	C₄	—	22	1	no	—
331	C₄	—	22	1	no	—
332	C₄	—	22	1	no	—
333	C₄	—	22	1	no	—
334	C₄	—	22	1	no	—
335	C₄	—	22	1	no	—
336	C₄	—	22	1	no	—
337	C₄	C₂×#4341	1	1	yes	characteristic
338	C₄	#41×D₁₁	1	1	yes	characteristic
339	C₂	—	2	2	no	—
340	C₂	—	4	1	no	—
341	C₂	—	44	1	no	—
342	C₂	C₄×#4341	1	1	yes	characteristic
343	C₂	C₂×#66960	1	1	yes	characteristic
344	C₂	#10623281	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₄
Fitting	C₁₁×#435	C₂
prime radical	#66992	C₄
cosocle	C₂×C₄×C₁₁	C₂⁴
hypercenter	#435	D₁₁
hypocenter	C₁₁	#2968
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
2. C₁₁×#435	C₂	semidirect
3. #10622740	C₂	semidirect
4. #10622735	C₂	semidirect
5. C₈×C₂²⋊D₁₁	C₂	semidirect
6. C₂×#66879	C₂	semidirect
7. D₄×C₁₁⋊C₈	C₂	semidirect
8. #10622453	C₂	semidirect
9. #10622444	C₂	semidirect
10. #10622343	C₂	semidirect
11. #10622343	C₂	semidirect
12. #10622333	C₂	semidirect
13. #10622331	C₂	semidirect
14. #10622321	C₂	semidirect
15. #10622314	C₂	semidirect
150. #435	D₁₁	semidirect
280. C₁₁	#2968	semidirect

Maximal subgroups

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

subgroup	index
#10623069	2
C₁₁×#435	2
#10622740	2
#10622735	2
C₈×C₂²⋊D₁₁	2
C₂×#66879	2
D₄×C₁₁⋊C₈	2
#10622453	2
#10622444	2
#10622343	2
#10622333	2
#10622331	2
#10622321	2
#10622314	2
#2968	11