Subgroups — D₁₁×#1567 #14722772

Order 2816.

854 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₁×#423	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₁₁	C₂	1	1	yes	maximal, characteristic
3	#13067375	C₂	1	1	yes	maximal, characteristic, complemented
4	#13067374	C₂	1	2	yes	maximal, complemented
5	#13067373	C₂	1	4	yes	maximal, complemented
6	D₁₁×#335	C₂	1	4	yes	maximal, complemented
7	C₁₁×#1567	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₁₁	—	2	2	no	—
9	C₂²×C₈×D₁₁	C₄	1	2	yes	—
10	C₂×C₄²×D₁₁	C₂²	1	1	yes	characteristic
11	C₁₁×#423	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	#10622731	—	2	2	no	—
14	C₂×C₈×Dic₁₁	C₄	1	2	yes	—
15	#10622537	C₂²	1	2	yes	—
16	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
17	#10622450	—	2	2	no	—
18	#10622450	C₂²	1	4	yes	—
19	D₁₁×C₄⋊C₈	—	2	2	no	—
20	D₁₁×C₄⋊C₈	C₂²	1	4	yes	—
21	C₄×C₈×D₁₁	C₄	1	1	yes	characteristic
22	C₄×C₈×D₁₁	C₄	1	1	yes	characteristic
23	C₄×C₈×D₁₁	C₄	1	1	yes	characteristic
24	C₄×C₈×D₁₁	C₄	1	1	yes	characteristic
25	C₄×C₈×D₁₁	C₂²	1	2	yes	—
26	C₄×C₈×D₁₁	C₂²	1	2	yes	—
27	C₁₁×#335	C₂²	1	4	yes	complemented
28	#10622117	C₂²	1	8	yes	complemented
29	#10622096	C₂²	1	4	yes	complemented
30	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×D₁₁	D₄	1	1	yes	characteristic
32	C₂²×C₄×D₁₁	Q₈	1	1	yes	characteristic
33	C₂×C₁₁×M₁₆	—	2	2	no	—
34	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
35	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
36	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×Dic₁₁	D₄	1	1	yes	characteristic
38	C₂×C₄×Dic₁₁	Q₈	1	1	yes	characteristic
39	C₂×#4318	—	2	2	no	—
40	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
41	M₁₆×D₁₁	—	4	8	no	—
42	C₂×#4313	—	2	4	no	—
43	C₂×C₈×D₁₁	—	2	8	no	—
44	C₂×C₈×D₁₁	—	2	4	no	—
45	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
46	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
47	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
48	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
49	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
51	C₄²×D₁₁	D₄	1	1	yes	characteristic
52	C₄²×D₁₁	D₄	1	1	yes	characteristic
53	C₄²×D₁₁	Q₈	1	1	yes	characteristic
54	C₄²×D₁₁	Q₈	1	1	yes	characteristic
55	C₄²×D₁₁	C₂³	1	1	yes	characteristic
56	C₄²×D₁₁	C₂³	1	1	yes	characteristic
57	C₁₁×C₄⋊C₈	—	2	2	no	—
58	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
59	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
60	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
61	C₄×C₈×C₁₁	C₂³	1	2	yes	—
62	Dic₁₁⋊C₈	—	2	4	no	—
63	Dic₁₁⋊C₈	—	2	4	no	—
64	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
65	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
66	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
67	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
68	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
69	C₄⋊(C₁₁⋊C₈)	C₂³	1	4	yes	—
70	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
71	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
72	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
73	C₂×#1567	—	11	1	no	maximal, Sylow
74	C₂³×D₁₁	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
78	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂×C₄×D₁₁	—	2	4	no	—
82	C₂×C₄×D₁₁	—	2	4	no	—
83	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
88	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
89	C₂×C₄×D₁₁	D₈	1	4	yes	—
90	C₂×C₄×D₁₁	Q₁₆	1	4	yes	—
91	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
94	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
95	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
96	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
97	C₁₁×M₁₆	—	4	4	no	—
98	C₂×C₈×C₁₁	—	2	4	no	—
99	C₂×C₈×C₁₁	—	2	4	no	—
100	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
102	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
105	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
106	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
107	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
108	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
109	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
110	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
111	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
112	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
114	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
115	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
116	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
117	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
118	#4318	—	4	4	no	—
119	C₂×C₁₁⋊C₈	—	2	4	no	—
120	C₂×C₁₁⋊C₈	—	2	4	no	—
121	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
122	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
123	#4313	—	4	8	no	—
124	C₈×D₁₁	—	2	4	no	—
125	C₈×D₁₁	—	2	4	no	—
126	C₈×D₁₁	—	2	4	no	—
127	C₈×D₁₁	—	4	8	no	—
128	C₈×D₁₁	M₁₆	1	8	yes	complemented
129	C₂×#423	—	11	2	no	—
130	C₂²×C₄×C₈	—	11	1	no	—
131	#1567	—	11	2	no	—
132	#1567	—	11	1	no	—
133	#1567	—	11	4	no	—
134	#1567	D₁₁	1	1	yes	characteristic, direct product factor
135	C₂×#335	—	11	4	no	—
136	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂²×D₁₁	—	2	2	no	—
138	C₂²×D₁₁	—	2	2	no	—
139	C₂²×D₁₁	#107	1	4	yes	—
140	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₁	—	2	2	no	—
143	C₂×C₄×C₁₁	—	2	2	no	—
144	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
148	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
149	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
152	C₂×Dic₁₁	—	2	2	no	—
153	C₂×Dic₁₁	—	2	2	no	—
154	C₂×Dic₁₁	#107	1	4	yes	—
155	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₄×D₁₁	—	2	2	no	—
162	C₄×D₁₁	—	2	2	no	—
163	C₄×D₁₁	—	2	2	no	—
164	C₄×D₁₁	—	2	2	no	—
165	C₄×D₁₁	—	2	2	no	—
166	C₄×D₁₁	—	2	2	no	—
167	C₄×D₁₁	#107	1	4	yes	—
168	C₄×D₁₁	#107	1	4	yes	—
169	C₄×D₁₁	#108	1	4	yes	—
170	C₄×D₁₁	C₂×M₁₆	1	4	yes	—
171	C₄×D₁₁	C₂×D₈	1	2	yes	—
172	C₄×D₁₁	C₂×D₈	1	2	yes	—
173	C₄×D₁₁	C₂×Q₁₆	1	2	yes	—
174	C₄×D₁₁	C₂×Q₁₆	1	2	yes	—
175	C₈×C₁₁	—	2	2	no	—
176	C₈×C₁₁	—	4	4	no	—
177	C₈×C₁₁	C₂×M₁₆	1	4	yes	complemented
178	C₁₁⋊C₈	—	2	2	no	—
179	C₁₁⋊C₈	—	4	4	no	—
180	C₁₁⋊C₈	C₂×M₁₆	1	4	yes	complemented
181	C₂²×M₁₆	—	22	2	no	—
182	C₂³×C₈	—	11	2	no	—
183	C₂²×C₄²	—	11	1	no	—
184	#423	—	11	2	no	—
185	#423	—	11	4	no	—
186	#423	—	22	2	no	—
187	#423	—	22	2	no	—
188	#423	C₂×D₁₁	1	2	yes	—
189	C₂×C₄⋊C₈	—	11	4	no	—
190	C₂×C₄⋊C₈	—	22	2	no	—
191	C₂×C₄×C₈	—	11	2	no	—
192	C₂×C₄×C₈	—	11	1	no	—
193	C₂×C₄×C₈	—	11	2	no	—
194	C₂×C₄×C₈	—	11	2	no	—
195	C₂×C₄×C₈	—	11	1	no	—
196	C₂×C₄×C₈	—	11	1	no	—
197	C₂×C₄×C₈	—	11	1	no	—
198	C₂×C₄×C₈	—	11	1	no	—
199	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
200	#335	—	11	8	no	—
201	#335	—	11	4	no	—
202	#335	C₂×D₁₁	1	4	yes	complemented
203	C₂²×C₁₁	—	2	1	no	—
204	C₂²×C₁₁	—	2	1	no	—
205	C₂²×C₁₁	C₂×#107	1	2	yes	—
206	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
207	C₂×D₁₁	—	2	1	no	—
208	C₂×D₁₁	—	2	1	no	—
209	C₂×D₁₁	—	2	8	no	—
210	C₂×D₁₁	#423	1	2	yes	—
211	C₂×D₁₁	C₂×#107	1	2	yes	—
212	C₂×D₁₁	C₂×#107	1	2	yes	—
213	C₂×D₁₁	C₂×#108	1	2	yes	—
214	C₄×C₁₁	—	2	1	no	—
215	C₄×C₁₁	—	2	1	no	—
216	C₄×C₁₁	C₂×#107	1	2	yes	—
217	C₄×C₁₁	C₂×#108	1	2	yes	—
218	C₄×C₁₁	C₂²×M₁₆	1	2	yes	—
219	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
220	C₄×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
221	Dic₁₁	—	2	1	no	—
222	Dic₁₁	—	2	1	no	—
223	Dic₁₁	#423	1	2	yes	—
224	Dic₁₁	C₂×#107	1	2	yes	—
225	Dic₁₁	C₂×#107	1	2	yes	—
226	Dic₁₁	C₂×#108	1	2	yes	—
227	C₂³×C₄	—	11	1	no	—
228	C₂³×C₄	—	11	1	no	—
229	C₂³×C₄	—	11	1	no	—
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	—	22	4	no	—
232	C₂×M₁₆	—	22	2	no	—
233	C₂×M₁₆	—	44	8	no	—
234	C₂²×C₈	—	11	2	no	—
235	C₂²×C₈	—	11	2	no	—
236	C₂²×C₈	—	11	2	no	—
237	C₂²×C₈	—	11	2	no	—
238	C₂²×C₈	—	11	2	no	—
239	C₂²×C₈	—	22	8	no	—
240	C₂²×C₈	—	22	4	no	—
241	C₂²×C₈	C₄×D₁₁	1	2	yes	—
242	C₂×C₄²	—	11	1	no	—
243	C₂×C₄²	—	11	1	no	—
244	C₂×C₄²	—	11	1	no	—
245	C₂×C₄²	—	11	1	no	—
246	C₂×C₄²	—	11	1	no	—
247	C₂×C₄²	—	11	1	no	—
248	C₂×C₄²	—	11	1	no	—
249	C₂×C₄²	—	11	1	no	—
250	C₂×C₄²	—	11	1	no	—
251	C₂×C₄²	—	11	1	no	—
252	C₂×C₄²	—	11	1	no	—
253	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	11	4	no	—
256	C₄⋊C₈	—	22	4	no	—
257	C₄⋊C₈	—	22	4	no	—
258	C₄⋊C₈	—	22	2	no	—
259	C₄⋊C₈	C₂²×D₁₁	1	4	yes	—
260	C₄×C₈	—	11	2	no	—
261	C₄×C₈	—	11	2	no	—
262	C₄×C₈	—	11	2	no	—
263	C₄×C₈	—	11	2	no	—
264	C₄×C₈	—	11	1	no	—
265	C₄×C₈	—	11	1	no	—
266	C₄×C₈	—	11	2	no	—
267	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
268	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
269	C₄×C₈	C₂²×D₁₁	1	2	yes	—
270	C₂×C₁₁	—	2	2	no	—
271	C₂×C₁₁	C₂×#423	1	1	yes	characteristic
272	C₂×C₁₁	C₂²×#107	1	1	yes	characteristic
273	C₂×C₁₁	C₂²×#108	1	1	yes	characteristic
274	D₁₁	—	2	2	no	—
275	D₁₁	#1567	1	4	yes	direct product factor
276	C₂⁴	—	11	1	no	—
277	C₂²×C₄	—	11	1	no	—
278	C₂²×C₄	—	11	1	no	—
279	C₂²×C₄	—	11	1	no	—
280	C₂²×C₄	—	11	1	no	—
281	C₂²×C₄	—	11	4	no	—
282	C₂²×C₄	—	11	4	no	—
283	C₂²×C₄	—	11	1	no	—
284	C₂²×C₄	—	11	1	no	—
285	C₂²×C₄	—	11	1	no	—
286	C₂²×C₄	—	11	1	no	—
287	C₂²×C₄	—	11	1	no	—
288	C₂²×C₄	—	11	1	no	—
289	C₂²×C₄	—	11	1	no	—
290	C₂²×C₄	—	11	1	no	—
291	C₂²×C₄	—	11	1	no	—
292	C₂²×C₄	—	11	1	no	—
293	C₂²×C₄	—	11	1	no	—
294	C₂²×C₄	—	22	4	no	—
295	C₂²×C₄	—	22	4	no	—
296	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
297	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
298	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
299	M₁₆	—	4	4	no	—
300	M₁₆	—	44	8	no	—
301	M₁₆	—	44	4	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	11	2	no	—
305	C₂×C₈	—	11	8	no	—
306	C₂×C₈	—	11	2	no	—
307	C₂×C₈	—	22	4	no	—
308	C₂×C₈	—	22	4	no	—
309	C₂×C₈	—	22	4	no	—
310	C₂×C₈	—	22	4	no	—
311	C₂×C₈	—	22	4	no	—
312	C₂×C₈	—	44	8	no	—
313	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
314	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
315	C₄²	—	11	1	no	—
316	C₄²	—	11	1	no	—
317	C₄²	—	11	1	no	—
318	C₄²	—	11	1	no	—
319	C₄²	—	11	1	no	—
320	C₄²	—	11	1	no	—
321	C₄²	—	11	1	no	—
322	C₄²	—	11	1	no	—
323	C₄²	—	11	1	no	—
324	C₄²	—	11	1	no	—
325	C₄²	—	11	1	no	—
326	C₄²	—	11	1	no	—
327	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
328	C₄²	D₄×D₁₁	1	1	yes	characteristic
329	C₄²	Q₈×D₁₁	1	1	yes	characteristic
330	C₄²	C₂³×D₁₁	1	1	yes	characteristic
331	C₁₁	C₂×#1567	1	1	yes	characteristic, complemented, Sylow
332	C₂³	—	11	1	no	—
333	C₂³	—	11	4	no	—
334	C₂³	—	11	1	no	—
335	C₂³	—	22	2	no	—
336	C₂³	—	22	2	no	—
337	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	11	4	no	—
341	C₂×C₄	—	11	1	no	—
342	C₂×C₄	—	11	1	no	—
343	C₂×C₄	—	11	1	no	—
344	C₂×C₄	—	11	1	no	—
345	C₂×C₄	—	11	4	no	—
346	C₂×C₄	—	11	4	no	—
347	C₂×C₄	—	11	4	no	—
348	C₂×C₄	—	11	4	no	—
349	C₂×C₄	—	11	2	no	—
350	C₂×C₄	—	11	2	no	—
351	C₂×C₄	—	11	2	no	—
352	C₂×C₄	—	11	2	no	—
353	C₂×C₄	—	11	1	no	—
354	C₂×C₄	—	11	1	no	—
355	C₂×C₄	—	22	2	no	—
356	C₂×C₄	—	22	2	no	—
357	C₂×C₄	—	22	2	no	—
358	C₂×C₄	—	22	2	no	—
359	C₂×C₄	—	22	2	no	—
360	C₂×C₄	—	22	2	no	—
361	C₂×C₄	—	22	2	no	—
362	C₂×C₄	—	22	2	no	—
363	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
364	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
365	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
366	C₂×C₄	D₈×D₁₁	1	2	yes	—
367	C₂×C₄	Q₁₆×D₁₁	1	2	yes	—
368	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
369	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
370	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
371	C₈	—	2	2	no	—
372	C₈	—	4	4	no	—
373	C₈	—	11	4	no	—
374	C₈	—	22	2	no	—
375	C₈	—	44	4	no	—
376	C₈	M₁₆×D₁₁	1	4	yes	complemented
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	11	2	no	—
380	C₂²	—	11	2	no	—
381	C₂²	—	11	2	no	—
382	C₂²	—	11	2	no	—
383	C₂²	—	22	8	no	—
384	C₂²	—	22	1	no	—
385	C₂²	—	22	1	no	—
386	C₂²	D₁₁×#107	1	2	yes	—
387	C₂²	C₂×C₄⋊C₄×D₁₁	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	11	2	no	—
391	C₄	—	11	2	no	—
392	C₄	—	11	2	no	—
393	C₄	—	11	2	no	—
394	C₄	—	22	1	no	—
395	C₄	—	22	1	no	—
396	C₄	D₁₁×#107	1	2	yes	—
397	C₄	D₁₁×#108	1	2	yes	—
398	C₄	C₂×M₁₆×D₁₁	1	2	yes	—
399	C₄	C₂×D₈×D₁₁	1	1	yes	characteristic
400	C₄	C₂×Q₁₆×D₁₁	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	11	4	no	—
403	C₂	—	22	2	no	—
404	C₂	D₁₁×#423	1	1	yes	characteristic
405	C₂	C₂×D₁₁×#107	1	1	yes	characteristic
406	C₂	C₂×D₁₁×#108	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×#1567	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₁	C₄⋊C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1567	D₁₁
hypocenter	C₁₁	C₂×#1567
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

Complements

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

N	H ≅ G/N	type
3. #13067375	C₂	semidirect
4. #13067374	C₂	semidirect
5. #13067373	C₂	semidirect
6. D₁₁×#335	C₂	semidirect
7. C₁₁×#1567	C₂	semidirect
27. C₁₁×#335	C₂²	semidirect
28. #10622117	C₂²	semidirect
29. #10622096	C₂²	semidirect
128. C₈×D₁₁	M₁₆	semidirect
134. #1567	D₁₁	direct (N × H)
177. C₈×C₁₁	C₂×M₁₆	semidirect
180. C₁₁⋊C₈	C₂×M₁₆	semidirect
202. #335	C₂×D₁₁	semidirect
275. D₁₁	#1567	direct (N × H)
331. C₁₁	C₂×#1567	semidirect
376. C₈	M₁₆×D₁₁	semidirect

Maximal subgroups

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

subgroup	index
D₁₁×#423	2
C₂×C₄×C₈×D₁₁	2
#13067375	2
#13067374	2
#13067373	2
D₁₁×#335	2
C₁₁×#1567	2
C₂×#1567	11

Subgroups — D11×#1567 #14722772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×#1567 #14722772