Subgroups — D₁₁×#2171 #14907003

Order 2816.

654 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₁×#504	C₂	1	2	yes	maximal, complemented
2	D₁₁×#443	C₂	1	1	yes	maximal, characteristic
3	#13070459	C₂	1	1	yes	maximal, characteristic, complemented
4	#13070458	C₂	1	1	yes	maximal, characteristic, complemented
5	#13070457	C₂	1	1	yes	maximal, characteristic, complemented
6	#13070456	C₂	1	2	yes	maximal, complemented
7	#13070455	C₂	1	2	yes	maximal, complemented
8	D₁₁×#364	C₂	1	1	yes	maximal, characteristic, complemented
9	D₁₁×#350	C₂	1	2	yes	maximal, complemented
10	D₁₁×#346	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#2171	C₂	1	1	yes	maximal, characteristic, complemented
12	D₁₁×#135	C₄	1	1	yes	characteristic
13	D₁₁×#131	C₂²	1	2	yes	—
14	C₁₁×#504	C₂²	1	2	yes	complemented
15	C₁₁×#443	C₂²	1	1	yes	characteristic
16	#10622809	C₄	1	1	yes	characteristic
17	#10622757	C₂²	1	2	yes	—
18	#10622753	C₂²	1	2	yes	complemented
19	#10622520	—	2	2	no	—
20	#10622520	C₂²	1	2	yes	complemented
21	D₁₁×M₃₂	—	2	2	no	—
22	D₁₁×M₃₂	C₂²	1	2	yes	—
23	#10622514	—	2	2	no	—
24	#10622514	C₂²	1	2	yes	complemented
25	C₂×C₁₆×D₁₁	—	2	2	no	—
26	C₂×C₁₆×D₁₁	C₂²	1	1	yes	characteristic
27	C₂×C₁₆×D₁₁	C₂²	1	1	yes	characteristic
28	#10622508	C₄	1	1	yes	characteristic
29	D₁₁×#108	C₄	1	1	yes	characteristic
30	#10622437	C₄	1	2	yes	—
31	D₁₁×#104	C₄	1	2	yes	—
32	#10622313	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
34	C₁₁×#364	C₂²	1	1	yes	characteristic, complemented
35	C₁₁×#350	C₂²	1	2	yes	complemented
36	C₁₁×#346	C₂²	1	1	yes	characteristic, complemented
37	#10622199	C₂²	1	2	yes	complemented
38	#10622153	C₂²	1	2	yes	complemented
39	#10622149	C₂²	1	2	yes	complemented
40	#10622146	C₂²	1	2	yes	complemented
41	#10622140	C₂²	1	1	yes	characteristic, complemented
42	#10622140	C₂²	1	1	yes	characteristic, complemented
43	#10622101	C₂²	1	1	yes	characteristic, complemented
44	#10622099	C₂²	1	1	yes	characteristic, complemented
45	#41×D₁₁	C₂×C₄	1	2	yes	—
46	C₁₁×#135	C₂×C₄	1	1	yes	characteristic
47	C₁₁×#131	C₂³	1	2	yes	—
48	#67003	C₂×C₄	1	2	yes	—
49	#67001	C₂×C₄	1	2	yes	—
50	#66972	C₈	1	1	yes	characteristic
51	Q₁₆×D₁₁	C₈	1	1	yes	characteristic
52	#66969	C₈	1	2	yes	—
53	SD₁₆×D₁₁	C₈	1	2	yes	—
54	#66965	C₈	1	1	yes	characteristic
55	D₈×D₁₁	C₈	1	1	yes	characteristic
56	#66960	—	2	2	no	—
57	#66960	C₂×C₄	1	2	yes	—
58	M₁₆×D₁₁	—	2	2	no	—
59	M₁₆×D₁₁	C₂×C₄	1	2	yes	—
60	#66957	C₂×C₄	1	1	yes	characteristic
61	#66954	—	2	2	no	—
62	#66954	C₂³	1	2	yes	—
63	C₂×C₈×D₁₁	—	2	2	no	—
64	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
66	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
67	C₁₁×M₃₂	—	2	2	no	—
68	C₁₁×M₃₂	C₂³	1	2	yes	—
69	C₂×C₁₁×C₁₆	—	2	2	no	—
70	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
71	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
72	C₁₁×#108	C₂×C₄	1	1	yes	characteristic
73	C₁₁×#104	C₂×C₄	1	2	yes	—
74	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
75	#66901	C₂×C₄	1	2	yes	—
76	#66889	C₂×C₄	1	2	yes	—
77	#66886	C₂×C₄	1	2	yes	—
78	#66883	C₂×C₄	1	1	yes	characteristic
79	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
81	#66876	—	2	2	no	—
82	#66876	C₂³	1	2	yes	—
83	C₂×C₁₁⋊C₁₆	—	2	2	no	—
84	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
85	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
86	#66869	C₂×C₄	1	2	yes	—
87	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
88	#66862	—	2	2	no	—
89	#66862	—	2	2	no	—
90	#66862	—	2	2	no	—
91	C₁₆×D₁₁	—	2	2	no	—
92	C₁₆×D₁₁	—	2	1	no	—
93	C₁₆×D₁₁	—	2	1	no	—
94	C₁₆×D₁₁	—	2	2	no	—
95	C₁₆×D₁₁	—	2	2	no	—
96	C₁₆×D₁₁	D₄	1	2	yes	—
97	C₁₆×D₁₁	D₄	1	2	yes	—
98	C₂×#2171	—	11	1	no	maximal, Sylow
99	C₁₁×#41	C₂²×C₄	1	2	yes	—
100	#4343	C₂×C₈	1	2	yes	—
101	Q₈×D₁₁	C₂×C₈	1	2	yes	—
102	#4341	—	2	2	no	—
103	#4341	C₂×C₈	1	2	yes	—
104	D₄×D₁₁	—	2	2	no	—
105	D₄×D₁₁	C₂×C₈	1	2	yes	—
106	#4339	—	2	2	no	—
107	#4339	C₂²×C₄	1	2	yes	—
108	C₂×C₄×D₁₁	—	2	2	no	—
109	C₂×C₄×D₁₁	—	2	1	no	—
110	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
111	C₁₁×Q₁₆	C₂×C₈	1	1	yes	characteristic
112	C₁₁×SD₁₆	C₂×C₈	1	2	yes	—
113	C₁₁×D₈	C₂×C₈	1	1	yes	characteristic
114	C₁₁×M₁₆	—	2	2	no	—
115	C₁₁×M₁₆	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₁₁	—	2	2	no	—
117	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
119	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
120	#4326	C₂×C₈	1	2	yes	—
121	#4325	C₂×C₈	1	2	yes	—
122	#4324	C₂×C₈	1	2	yes	—
123	#4323	C₂×C₈	1	2	yes	—
124	C₄×Dic₁₁	—	2	1	no	—
125	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
126	#4318	—	2	2	no	—
127	#4318	C₂²×C₄	1	2	yes	—
128	C₂×C₁₁⋊C₈	—	2	2	no	—
129	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
131	Dic₄₄	C₂×C₈	1	1	yes	characteristic
132	D₈₈	C₂×C₈	1	1	yes	characteristic
133	#4314	C₂×C₈	1	2	yes	—
134	#4313	—	2	2	no	—
135	#4313	—	2	2	no	—
136	#4313	—	2	2	no	—
137	C₈×D₁₁	—	2	2	no	—
138	C₈×D₁₁	—	2	2	no	—
139	C₈×D₁₁	—	2	2	no	—
140	C₈×D₁₁	C₂×C₈	1	1	yes	characteristic
141	C₈×D₁₁	C₂×C₈	1	1	yes	characteristic
142	C₈×D₁₁	C₂×C₈	1	1	yes	characteristic
143	C₈×D₁₁	C₂×C₈	1	1	yes	characteristic
144	C₈×D₁₁	C₂×D₄	1	1	yes	characteristic
145	C₈×D₁₁	C₂×D₄	1	1	yes	characteristic
146	C₈×D₁₁	#41	1	1	yes	characteristic
147	C₈×D₁₁	#41	1	1	yes	characteristic
148	C₁₁×C₁₆	—	2	2	no	—
149	C₁₁×C₁₆	—	2	1	no	—
150	C₁₁×C₁₆	C₂×D₄	1	2	yes	—
151	C₁₁⋊C₁₆	—	2	2	no	—
152	C₁₁⋊C₁₆	—	2	1	no	—
153	C₁₁⋊C₁₆	C₂×D₄	1	2	yes	—
154	C₂×#504	—	11	2	no	—
155	C₂×#443	—	11	1	no	—
156	#2171	—	11	2	no	—
157	#2171	—	11	1	no	—
158	#2171	—	11	1	no	—
159	#2171	—	11	2	no	—
160	#2171	—	11	1	no	—
161	#2171	D₁₁	1	1	yes	characteristic, direct product factor
162	C₂×#364	—	11	1	no	—
163	C₂×#350	—	11	2	no	—
164	C₂×#346	—	11	1	no	—
165	C₂²×D₁₁	—	2	2	no	—
166	C₂²×D₁₁	#131	1	1	yes	characteristic
167	Q₈×C₁₁	C₂²×C₈	1	2	yes	—
168	D₄×C₁₁	—	2	2	no	—
169	D₄×C₁₁	C₂²×C₈	1	2	yes	—
170	C₂×C₄×C₁₁	—	2	2	no	—
171	C₂×C₄×C₁₁	—	2	1	no	—
172	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
173	C₂²⋊D₁₁	—	2	2	no	—
174	C₂²⋊D₁₁	—	2	2	no	—
175	C₂²⋊D₁₁	—	2	2	no	—
176	C₂×Dic₁₁	—	2	2	no	—
177	C₂×Dic₁₁	—	2	1	no	—
178	C₂×Dic₁₁	#131	1	1	yes	characteristic
179	D₄₄	—	2	2	no	—
180	D₄₄	C₂²×C₈	1	2	yes	—
181	C₄×D₁₁	—	2	2	no	—
182	C₄×D₁₁	—	2	2	no	—
183	C₄×D₁₁	—	2	2	no	—
184	C₄×D₁₁	—	4	2	no	—
185	C₄×D₁₁	C₄×D₄	1	1	yes	characteristic
186	C₄×D₁₁	C₄×D₄	1	1	yes	characteristic
187	C₄×D₁₁	C₂²×C₈	1	1	yes	characteristic
188	C₄×D₁₁	C₂²×C₈	1	1	yes	characteristic
189	Dic₂₂	—	2	2	no	—
190	Dic₂₂	C₂²×C₈	1	2	yes	—
191	C₈×C₁₁	—	2	2	no	—
192	C₈×C₁₁	C₂²×C₈	1	1	yes	characteristic
193	C₈×C₁₁	C₂²×C₈	1	1	yes	characteristic
194	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
195	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
196	C₁₁⋊C₈	—	2	2	no	—
197	C₁₁⋊C₈	C₄×D₄	1	1	yes	characteristic
198	C₁₁⋊C₈	C₄×D₄	1	1	yes	characteristic
199	C₁₁⋊C₈	C₂²×C₈	1	1	yes	characteristic
200	C₁₁⋊C₈	C₂²×C₈	1	1	yes	characteristic
201	C₂×#135	—	11	1	no	—
202	C₂×#131	—	11	2	no	—
203	#504	—	11	2	no	—
204	#504	—	11	2	no	—
205	#504	—	11	2	no	—
206	#504	—	22	2	no	—
207	#504	—	22	2	no	—
208	#504	C₂×D₁₁	1	2	yes	complemented
209	C₂×M₃₂	—	11	2	no	—
210	C₂×M₃₂	—	22	2	no	—
211	C₂²×C₁₆	—	11	1	no	—
212	C₂²×C₁₆	—	11	1	no	—
213	C₂²×C₁₆	—	22	2	no	—
214	#443	—	11	1	no	—
215	#443	—	11	2	no	—
216	#443	—	11	1	no	—
217	#443	—	11	2	no	—
218	#443	—	11	1	no	—
219	#443	C₂×D₁₁	1	1	yes	characteristic
220	C₂×#108	—	11	1	no	—
221	C₂×#104	—	11	2	no	—
222	C₂×C₄×C₈	—	11	1	no	—
223	#364	—	11	2	no	—
224	#364	—	11	1	no	—
225	#364	C₂×D₁₁	1	1	yes	characteristic, complemented
226	#350	—	11	2	no	—
227	#350	—	11	2	no	—
228	#350	—	11	2	no	—
229	#350	C₂×D₁₁	1	2	yes	complemented
230	#346	—	11	1	no	—
231	#346	—	11	1	no	—
232	#346	—	11	1	no	—
233	#346	C₂×D₁₁	1	1	yes	characteristic, complemented
234	C₂²×C₁₁	—	2	2	no	—
235	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
236	C₂×D₁₁	—	2	2	no	—
237	C₂×D₁₁	—	2	2	no	—
238	C₂×D₁₁	—	4	4	no	—
239	C₂×D₁₁	C₈×D₄	1	1	yes	characteristic
240	C₂×D₁₁	C₈×D₄	1	1	yes	characteristic
241	C₄×C₁₁	—	2	2	no	—
242	C₄×C₁₁	—	4	1	no	—
243	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
244	C₄×C₁₁	C₂³×C₈	1	1	yes	characteristic
245	Dic₁₁	—	2	2	no	—
246	Dic₁₁	—	4	1	no	—
247	Dic₁₁	C₈×D₄	1	1	yes	characteristic
248	Dic₁₁	C₈×D₄	1	1	yes	characteristic
249	C₂×#41	—	11	2	no	—
250	#135	—	11	2	no	—
251	#135	—	11	1	no	—
252	#135	—	11	2	no	—
253	#135	—	11	1	no	—
254	#135	—	11	1	no	—
255	#135	C₄×D₁₁	1	1	yes	characteristic
256	C₂×Q₁₆	—	11	1	no	—
257	C₂×SD₁₆	—	11	2	no	—
258	C₂×D₈	—	11	1	no	—
259	#131	—	11	2	no	—
260	#131	—	11	2	no	—
261	#131	—	11	2	no	—
262	#131	—	22	2	no	—
263	#131	—	22	2	no	—
264	#131	C₂²×D₁₁	1	2	yes	—
265	C₂×M₁₆	—	11	2	no	—
266	C₂×M₁₆	—	22	2	no	—
267	C₂²×C₈	—	11	1	no	—
268	C₂²×C₈	—	11	1	no	—
269	C₂²×C₈	—	22	2	no	—
270	C₂×C₄²	—	11	1	no	—
271	M₃₂	—	2	2	no	—
272	M₃₂	—	11	2	no	—
273	M₃₂	—	22	2	no	—
274	M₃₂	—	22	2	no	—
275	M₃₂	—	22	2	no	—
276	M₃₂	—	22	2	no	—
277	M₃₂	C₂²×D₁₁	1	2	yes	—
278	C₂×C₁₆	—	2	2	no	—
279	C₂×C₁₆	—	11	1	no	—
280	C₂×C₁₆	—	11	2	no	—
281	C₂×C₁₆	—	11	2	no	—
282	C₂×C₁₆	—	11	1	no	—
283	C₂×C₁₆	—	22	2	no	—
284	C₂×C₁₆	—	22	1	no	—
285	C₂×C₁₆	—	22	1	no	—
286	C₂×C₁₆	—	22	2	no	—
287	C₂×C₁₆	—	22	2	no	—
288	C₂×C₁₆	—	22	2	no	—
289	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
290	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
291	#108	—	11	2	no	—
292	#108	—	11	1	no	—
293	#108	C₄×D₁₁	1	1	yes	characteristic
294	#104	—	11	2	no	—
295	#104	—	11	2	no	—
296	#104	—	11	2	no	—
297	#104	C₄×D₁₁	1	2	yes	—
298	C₄×C₈	—	11	1	no	—
299	C₄×C₈	—	11	1	no	—
300	C₄×C₈	—	11	1	no	—
301	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
302	C₂×C₁₁	—	2	1	no	—
303	C₂×C₁₁	—	4	2	no	—
304	C₂×C₁₁	C₂×C₈×D₄	1	1	yes	characteristic
305	D₁₁	—	2	1	no	—
306	D₁₁	—	4	2	no	—
307	D₁₁	#2171	1	2	yes	direct product factor
308	#41	—	11	2	no	—
309	#41	—	11	2	no	—
310	#41	—	11	2	no	—
311	#41	—	22	2	no	—
312	#41	—	22	2	no	—
313	#41	C₂×C₄×D₁₁	1	2	yes	—
314	C₂×Q₈	—	11	2	no	—
315	C₂×D₄	—	11	2	no	—
316	C₂×D₄	—	22	2	no	—
317	C₂²×C₄	—	11	1	no	—
318	C₂²×C₄	—	22	2	no	—
319	C₂²×C₄	—	22	1	no	—
320	Q₁₆	—	11	2	no	—
321	Q₁₆	—	11	1	no	—
322	Q₁₆	C₈×D₁₁	1	1	yes	characteristic
323	SD₁₆	—	11	2	no	—
324	SD₁₆	—	11	2	no	—
325	SD₁₆	—	11	2	no	—
326	SD₁₆	C₈×D₁₁	1	2	yes	—
327	D₈	—	11	2	no	—
328	D₈	—	11	1	no	—
329	D₈	C₈×D₁₁	1	1	yes	characteristic
330	M₁₆	—	2	2	no	—
331	M₁₆	—	11	2	no	—
332	M₁₆	—	22	2	no	—
333	M₁₆	—	22	2	no	—
334	M₁₆	—	22	2	no	—
335	M₁₆	—	22	2	no	—
336	M₁₆	C₂×C₄×D₁₁	1	2	yes	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	11	1	no	—
339	C₂×C₈	—	11	1	no	—
340	C₂×C₈	—	11	1	no	—
341	C₂×C₈	—	11	1	no	—
342	C₂×C₈	—	11	1	no	—
343	C₂×C₈	—	11	1	no	—
344	C₂×C₈	—	11	1	no	—
345	C₂×C₈	—	11	1	no	—
346	C₂×C₈	—	11	1	no	—
347	C₂×C₈	—	11	1	no	—
348	C₂×C₈	—	22	2	no	—
349	C₂×C₈	—	22	2	no	—
350	C₂×C₈	—	22	2	no	—
351	C₂×C₈	—	22	2	no	—
352	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
353	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
354	C₄²	—	11	1	no	—
355	C₄²	—	22	1	no	—
356	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
357	C₁₆	—	2	2	no	—
358	C₁₆	—	2	1	no	—
359	C₁₆	—	11	2	no	—
360	C₁₆	—	22	2	no	—
361	C₁₆	—	22	1	no	—
362	C₁₆	D₄×D₁₁	1	2	yes	—
363	C₁₁	C₂×#2171	1	1	yes	characteristic, complemented, Sylow
364	C₂³	—	11	1	no	—
365	C₂³	—	22	2	no	—
366	Q₈	—	11	2	no	—
367	Q₈	—	22	2	no	—
368	Q₈	C₂×C₈×D₁₁	1	2	yes	—
369	D₄	—	2	2	no	—
370	D₄	—	11	2	no	—
371	D₄	—	22	2	no	—
372	D₄	—	22	2	no	—
373	D₄	—	22	2	no	—
374	D₄	—	22	2	no	—
375	D₄	C₂×C₈×D₁₁	1	2	yes	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	11	1	no	—
379	C₂×C₄	—	11	1	no	—
380	C₂×C₄	—	11	1	no	—
381	C₂×C₄	—	11	1	no	—
382	C₂×C₄	—	11	1	no	—
383	C₂×C₄	—	22	2	no	—
384	C₂×C₄	—	22	2	no	—
385	C₂×C₄	—	22	2	no	—
386	C₂×C₄	—	22	2	no	—
387	C₂×C₄	—	22	1	no	—
388	C₂×C₄	—	44	2	no	—
389	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
390	C₈	—	2	2	no	—
391	C₈	—	11	1	no	—
392	C₈	—	11	1	no	—
393	C₈	—	11	1	no	—
394	C₈	—	11	1	no	—
395	C₈	—	22	2	no	—
396	C₈	C₂×C₈×D₁₁	1	1	yes	characteristic
397	C₈	C₂×C₈×D₁₁	1	1	yes	characteristic
398	C₈	C₂×D₄×D₁₁	1	1	yes	characteristic
399	C₈	#41×D₁₁	1	1	yes	characteristic
400	C₂²	—	2	2	no	—
401	C₂²	—	11	1	no	—
402	C₂²	—	11	1	no	—
403	C₂²	—	22	2	no	—
404	C₂²	—	22	2	no	—
405	C₂²	—	44	4	no	—
406	C₂²	D₁₁×#131	1	1	yes	characteristic
407	C₄	—	2	2	no	—
408	C₄	—	4	1	no	—
409	C₄	—	11	1	no	—
410	C₄	—	11	1	no	—
411	C₄	—	22	2	no	—
412	C₄	—	44	1	no	—
413	C₄	C₄×D₄×D₁₁	1	1	yes	characteristic
414	C₄	C₂²×C₈×D₁₁	1	1	yes	characteristic
415	C₂	—	2	1	no	—
416	C₂	—	4	2	no	—
417	C₂	—	11	2	no	—
418	C₂	—	22	1	no	—
419	C₂	—	44	2	no	—
420	C₂	C₈×D₄×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₄×D₁₁
commutator	C₄×C₁₁	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₁₁×#2171	C₂
socle	C₂×C₁₁	C₂×C₈×D₄
prime radical	D₁₁×#135	C₄
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2171	D₁₁
hypocenter	C₁₁	C₂×#2171
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ #2171

Complements

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

N	H ≅ G/N	type
1. D₁₁×#504	C₂	semidirect
3. #13070459	C₂	semidirect
4. #13070458	C₂	semidirect
5. #13070457	C₂	semidirect
6. #13070456	C₂	semidirect
7. #13070455	C₂	semidirect
8. D₁₁×#364	C₂	semidirect
9. D₁₁×#350	C₂	semidirect
10. D₁₁×#346	C₂	semidirect
11. C₁₁×#2171	C₂	semidirect
14. C₁₁×#504	C₂²	semidirect
18. #10622753	C₂²	semidirect
20. #10622520	C₂²	semidirect
24. #10622514	C₂²	semidirect
34. C₁₁×#364	C₂²	semidirect
35. C₁₁×#350	C₂²	semidirect
36. C₁₁×#346	C₂²	semidirect
37. #10622199	C₂²	semidirect
38. #10622153	C₂²	semidirect
39. #10622149	C₂²	semidirect
40. #10622146	C₂²	semidirect
41. #10622140	C₂²	semidirect
42. #10622140	C₂²	semidirect
43. #10622101	C₂²	semidirect
44. #10622099	C₂²	semidirect
161. #2171	D₁₁	direct (N × H)
208. #504	C₂×D₁₁	semidirect
225. #364	C₂×D₁₁	semidirect
229. #350	C₂×D₁₁	semidirect
233. #346	C₂×D₁₁	semidirect
307. D₁₁	#2171	direct (N × H)
363. C₁₁	C₂×#2171	semidirect

Maximal subgroups

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

subgroup	index
D₁₁×#504	2
D₁₁×#443	2
#13070459	2
#13070458	2
#13070457	2
#13070456	2
#13070455	2
D₁₁×#364	2
D₁₁×#350	2
D₁₁×#346	2
C₁₁×#2171	2
C₂×#2171	11

Subgroups — D11×#2171 #14907003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×#2171 #14907003