Subgroups — D₁₁×#2170 #14906997

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 430 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	#13070454	C₂	1	1	yes	maximal, characteristic, complemented
4	#13070453	C₂	1	1	yes	maximal, characteristic, complemented
5	#13070452	C₂	1	1	yes	maximal, characteristic, complemented
6	#13070451	C₂	1	2	yes	maximal, complemented
7	#13070450	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	C₄×C₁₆×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#2170	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	C₄×C₁₁×C₁₆	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	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
42	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
43	#10622101	C₂²	1	1	yes	characteristic, complemented
44	C₄×C₁₁⋊C₁₆	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	1	yes	characteristic
97	C₁₆×D₁₁	D₄	1	1	yes	characteristic
98	C₁₆×D₁₁	D₄	1	1	yes	characteristic
99	C₁₆×D₁₁	D₄	1	1	yes	characteristic
100	C₂×#2170	—	11	1	no	maximal, Sylow
101	C₁₁×#41	C₂²×C₄	1	2	yes	—
102	#4343	C₂×C₈	1	2	yes	—
103	Q₈×D₁₁	C₂×C₈	1	2	yes	—
104	#4341	—	2	2	no	—
105	#4341	C₂×C₈	1	2	yes	—
106	D₄×D₁₁	—	2	2	no	—
107	D₄×D₁₁	C₂×C₈	1	2	yes	—
108	#4339	—	2	2	no	—
109	#4339	C₂²×C₄	1	2	yes	—
110	C₂×C₄×D₁₁	—	2	2	no	—
111	C₂×C₄×D₁₁	—	2	1	no	—
112	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₁₁×Q₁₆	C₂×C₈	1	1	yes	characteristic
114	C₁₁×SD₁₆	C₂×C₈	1	2	yes	—
115	C₁₁×D₈	C₂×C₈	1	1	yes	characteristic
116	C₁₁×M₁₆	—	2	2	no	—
117	C₁₁×M₁₆	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₁₁	—	2	2	no	—
119	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
121	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
122	#4326	C₂×C₈	1	2	yes	—
123	#4325	C₂×C₈	1	2	yes	—
124	#4324	C₂×C₈	1	2	yes	—
125	#4323	C₂×C₈	1	2	yes	—
126	C₄×Dic₁₁	—	2	1	no	—
127	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
128	#4318	—	2	2	no	—
129	#4318	C₂²×C₄	1	2	yes	—
130	C₂×C₁₁⋊C₈	—	2	2	no	—
131	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
133	Dic₄₄	C₂×C₈	1	1	yes	characteristic
134	D₈₈	C₂×C₈	1	1	yes	characteristic
135	#4314	C₂×C₈	1	2	yes	—
136	#4313	—	2	2	no	—
137	#4313	—	2	2	no	—
138	#4313	—	2	2	no	—
139	C₈×D₁₁	—	2	2	no	—
140	C₈×D₁₁	—	2	2	no	—
141	C₈×D₁₁	—	2	2	no	—
142	C₈×D₁₁	C₂×C₈	1	1	yes	characteristic
143	C₈×D₁₁	C₂×C₈	1	1	yes	characteristic
144	C₈×D₁₁	C₂×C₈	1	1	yes	characteristic
145	C₈×D₁₁	C₂×C₈	1	1	yes	characteristic
146	C₈×D₁₁	C₂×D₄	1	1	yes	characteristic
147	C₈×D₁₁	C₂×D₄	1	1	yes	characteristic
148	C₈×D₁₁	#41	1	1	yes	characteristic
149	C₈×D₁₁	#41	1	1	yes	characteristic
150	C₁₁×C₁₆	—	2	2	no	—
151	C₁₁×C₁₆	—	2	1	no	—
152	C₁₁×C₁₆	C₂×D₄	1	1	yes	characteristic
153	C₁₁×C₁₆	C₂×D₄	1	1	yes	characteristic
154	C₁₁⋊C₁₆	—	2	2	no	—
155	C₁₁⋊C₁₆	—	2	1	no	—
156	C₁₁⋊C₁₆	C₂×D₄	1	1	yes	characteristic
157	C₁₁⋊C₁₆	C₂×D₄	1	1	yes	characteristic
158	C₂×#504	—	11	2	no	—
159	C₂×#443	—	11	1	no	—
160	#2170	—	11	2	no	—
161	#2170	—	11	1	no	—
162	#2170	—	11	1	no	—
163	#2170	—	11	2	no	—
164	#2170	—	11	1	no	—
165	#2170	D₁₁	1	1	yes	characteristic, direct product factor
166	C₂×#364	—	11	1	no	—
167	C₂×#350	—	11	2	no	—
168	C₂×C₄×C₁₆	—	11	1	no	—
169	C₂²×D₁₁	—	2	2	no	—
170	C₂²×D₁₁	#131	1	1	yes	characteristic
171	Q₈×C₁₁	C₂²×C₈	1	2	yes	—
172	D₄×C₁₁	—	2	2	no	—
173	D₄×C₁₁	C₂²×C₈	1	2	yes	—
174	C₂×C₄×C₁₁	—	2	1	no	—
175	C₂×C₄×C₁₁	—	2	2	no	—
176	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
177	C₂²⋊D₁₁	—	2	2	no	—
178	C₂²⋊D₁₁	—	2	2	no	—
179	C₂²⋊D₁₁	—	2	2	no	—
180	C₂×Dic₁₁	—	2	1	no	—
181	C₂×Dic₁₁	—	2	2	no	—
182	C₂×Dic₁₁	#131	1	1	yes	characteristic
183	D₄₄	—	2	2	no	—
184	D₄₄	C₂²×C₈	1	2	yes	—
185	C₄×D₁₁	—	2	4	no	—
186	C₄×D₁₁	—	2	2	no	—
187	C₄×D₁₁	—	2	2	no	—
188	C₄×D₁₁	—	2	2	no	—
189	C₄×D₁₁	C₄×D₄	1	1	yes	characteristic
190	C₄×D₁₁	C₄×D₄	1	1	yes	characteristic
191	C₄×D₁₁	C₂²×C₈	1	1	yes	characteristic
192	C₄×D₁₁	C₂²×C₈	1	1	yes	characteristic
193	Dic₂₂	—	2	2	no	—
194	Dic₂₂	C₂²×C₈	1	2	yes	—
195	C₈×C₁₁	—	2	2	no	—
196	C₈×C₁₁	C₂²×C₈	1	1	yes	characteristic
197	C₈×C₁₁	C₂²×C₈	1	1	yes	characteristic
198	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
199	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
200	C₁₁⋊C₈	—	2	2	no	—
201	C₁₁⋊C₈	C₄×D₄	1	1	yes	characteristic
202	C₁₁⋊C₈	C₄×D₄	1	1	yes	characteristic
203	C₁₁⋊C₈	C₂²×C₈	1	1	yes	characteristic
204	C₁₁⋊C₈	C₂²×C₈	1	1	yes	characteristic
205	C₂×#135	—	11	1	no	—
206	C₂×#131	—	11	2	no	—
207	#504	—	11	2	no	—
208	#504	—	11	2	no	—
209	#504	—	11	2	no	—
210	#504	—	22	2	no	—
211	#504	—	22	2	no	—
212	#504	C₂×D₁₁	1	2	yes	complemented
213	C₂×M₃₂	—	11	2	no	—
214	C₂×M₃₂	—	22	2	no	—
215	C₂²×C₁₆	—	11	1	no	—
216	C₂²×C₁₆	—	11	1	no	—
217	C₂²×C₁₆	—	22	2	no	—
218	#443	—	11	1	no	—
219	#443	—	11	2	no	—
220	#443	—	11	1	no	—
221	#443	—	11	2	no	—
222	#443	—	11	1	no	—
223	#443	C₂×D₁₁	1	1	yes	characteristic
224	C₂×#108	—	11	1	no	—
225	C₂×#104	—	11	2	no	—
226	C₂×C₄×C₈	—	11	1	no	—
227	#364	—	11	2	no	—
228	#364	—	11	1	no	—
229	#364	C₂×D₁₁	1	1	yes	characteristic, complemented
230	#350	—	11	2	no	—
231	#350	—	11	2	no	—
232	#350	—	11	2	no	—
233	#350	C₂×D₁₁	1	2	yes	complemented
234	C₄×C₁₆	—	11	1	no	—
235	C₄×C₁₆	—	11	1	no	—
236	C₄×C₁₆	—	11	1	no	—
237	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic, complemented
238	C₂²×C₁₁	—	2	2	no	—
239	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
240	C₂×D₁₁	—	2	2	no	—
241	C₂×D₁₁	—	2	2	no	—
242	C₂×D₁₁	—	4	4	no	—
243	C₂×D₁₁	C₈×D₄	1	1	yes	characteristic
244	C₂×D₁₁	C₈×D₄	1	1	yes	characteristic
245	C₄×C₁₁	—	2	2	no	—
246	C₄×C₁₁	—	2	2	no	—
247	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
248	C₄×C₁₁	C₂³×C₈	1	1	yes	characteristic
249	Dic₁₁	—	2	2	no	—
250	Dic₁₁	—	2	2	no	—
251	Dic₁₁	C₈×D₄	1	1	yes	characteristic
252	Dic₁₁	C₈×D₄	1	1	yes	characteristic
253	C₂×#41	—	11	2	no	—
254	#135	—	11	2	no	—
255	#135	—	11	1	no	—
256	#135	—	11	2	no	—
257	#135	—	11	1	no	—
258	#135	—	11	1	no	—
259	#135	C₄×D₁₁	1	1	yes	characteristic
260	C₂×Q₁₆	—	11	1	no	—
261	C₂×SD₁₆	—	11	2	no	—
262	C₂×D₈	—	11	1	no	—
263	#131	—	11	2	no	—
264	#131	—	11	2	no	—
265	#131	—	11	2	no	—
266	#131	—	22	2	no	—
267	#131	—	22	2	no	—
268	#131	C₂²×D₁₁	1	2	yes	—
269	C₂×M₁₆	—	11	2	no	—
270	C₂×M₁₆	—	22	2	no	—
271	C₂²×C₈	—	11	1	no	—
272	C₂²×C₈	—	11	1	no	—
273	C₂²×C₈	—	22	2	no	—
274	C₂×C₄²	—	11	1	no	—
275	M₃₂	—	2	2	no	—
276	M₃₂	—	11	2	no	—
277	M₃₂	—	22	2	no	—
278	M₃₂	—	22	2	no	—
279	M₃₂	—	22	2	no	—
280	M₃₂	—	22	2	no	—
281	M₃₂	C₂²×D₁₁	1	2	yes	—
282	C₂×C₁₆	—	2	2	no	—
283	C₂×C₁₆	—	11	1	no	—
284	C₂×C₁₆	—	11	1	no	—
285	C₂×C₁₆	—	11	1	no	—
286	C₂×C₁₆	—	11	1	no	—
287	C₂×C₁₆	—	11	1	no	—
288	C₂×C₁₆	—	11	1	no	—
289	C₂×C₁₆	—	22	2	no	—
290	C₂×C₁₆	—	22	1	no	—
291	C₂×C₁₆	—	22	1	no	—
292	C₂×C₁₆	—	22	2	no	—
293	C₂×C₁₆	—	22	2	no	—
294	C₂×C₁₆	—	22	2	no	—
295	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
296	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
297	#108	—	11	2	no	—
298	#108	—	11	1	no	—
299	#108	C₄×D₁₁	1	1	yes	characteristic
300	#104	—	11	2	no	—
301	#104	—	11	2	no	—
302	#104	—	11	2	no	—
303	#104	C₄×D₁₁	1	2	yes	—
304	C₄×C₈	—	11	1	no	—
305	C₄×C₈	—	11	1	no	—
306	C₄×C₈	—	11	1	no	—
307	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
308	C₂×C₁₁	—	2	1	no	—
309	C₂×C₁₁	—	4	2	no	—
310	C₂×C₁₁	C₂×C₈×D₄	1	1	yes	characteristic
311	D₁₁	—	2	1	no	—
312	D₁₁	—	4	2	no	—
313	D₁₁	#2170	1	2	yes	direct product factor
314	#41	—	11	2	no	—
315	#41	—	11	2	no	—
316	#41	—	11	2	no	—
317	#41	—	22	2	no	—
318	#41	—	22	2	no	—
319	#41	C₂×C₄×D₁₁	1	2	yes	—
320	C₂×Q₈	—	11	2	no	—
321	C₂×D₄	—	11	2	no	—
322	C₂×D₄	—	22	2	no	—
323	C₂²×C₄	—	11	1	no	—
324	C₂²×C₄	—	22	2	no	—
325	C₂²×C₄	—	22	1	no	—
326	Q₁₆	—	11	2	no	—
327	Q₁₆	—	11	1	no	—
328	Q₁₆	C₈×D₁₁	1	1	yes	characteristic
329	SD₁₆	—	11	2	no	—
330	SD₁₆	—	11	2	no	—
331	SD₁₆	—	11	2	no	—
332	SD₁₆	C₈×D₁₁	1	2	yes	—
333	D₈	—	11	2	no	—
334	D₈	—	11	1	no	—
335	D₈	C₈×D₁₁	1	1	yes	characteristic
336	M₁₆	—	2	2	no	—
337	M₁₆	—	11	2	no	—
338	M₁₆	—	22	2	no	—
339	M₁₆	—	22	2	no	—
340	M₁₆	—	22	2	no	—
341	M₁₆	—	22	2	no	—
342	M₁₆	C₂×C₄×D₁₁	1	2	yes	—
343	C₂×C₈	—	2	2	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	—	11	1	no	—
349	C₂×C₈	—	11	1	no	—
350	C₂×C₈	—	11	1	no	—
351	C₂×C₈	—	11	1	no	—
352	C₂×C₈	—	11	1	no	—
353	C₂×C₈	—	11	1	no	—
354	C₂×C₈	—	22	2	no	—
355	C₂×C₈	—	22	2	no	—
356	C₂×C₈	—	22	2	no	—
357	C₂×C₈	—	22	2	no	—
358	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
359	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
360	C₄²	—	11	1	no	—
361	C₄²	—	22	1	no	—
362	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
363	C₁₆	—	2	2	no	—
364	C₁₆	—	2	1	no	—
365	C₁₆	—	11	1	no	—
366	C₁₆	—	11	1	no	—
367	C₁₆	—	22	2	no	—
368	C₁₆	—	22	1	no	—
369	C₁₆	D₄×D₁₁	1	1	yes	characteristic
370	C₁₆	D₄×D₁₁	1	1	yes	characteristic
371	C₁₁	C₂×#2170	1	1	yes	characteristic, complemented, Sylow
372	C₂³	—	11	1	no	—
373	C₂³	—	22	2	no	—
374	Q₈	—	11	2	no	—
375	Q₈	—	22	2	no	—
376	Q₈	C₂×C₈×D₁₁	1	2	yes	—
377	D₄	—	2	2	no	—
378	D₄	—	11	2	no	—
379	D₄	—	22	2	no	—
380	D₄	—	22	2	no	—
381	D₄	—	22	2	no	—
382	D₄	—	22	2	no	—
383	D₄	C₂×C₈×D₁₁	1	2	yes	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	11	1	no	—
387	C₂×C₄	—	11	1	no	—
388	C₂×C₄	—	11	1	no	—
389	C₂×C₄	—	11	1	no	—
390	C₂×C₄	—	11	1	no	—
391	C₂×C₄	—	22	2	no	—
392	C₂×C₄	—	22	2	no	—
393	C₂×C₄	—	22	4	no	—
394	C₂×C₄	—	22	2	no	—
395	C₂×C₄	—	22	1	no	—
396	C₂×C₄	—	22	2	no	—
397	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	11	1	no	—
400	C₈	—	11	1	no	—
401	C₈	—	11	1	no	—
402	C₈	—	11	1	no	—
403	C₈	—	22	2	no	—
404	C₈	C₂×C₈×D₁₁	1	1	yes	characteristic
405	C₈	C₂×C₈×D₁₁	1	1	yes	characteristic
406	C₈	C₂×D₄×D₁₁	1	1	yes	characteristic
407	C₈	#41×D₁₁	1	1	yes	characteristic
408	C₂²	—	2	2	no	—
409	C₂²	—	11	1	no	—
410	C₂²	—	11	1	no	—
411	C₂²	—	22	2	no	—
412	C₂²	—	22	2	no	—
413	C₂²	—	44	4	no	—
414	C₂²	D₁₁×#131	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	11	1	no	—
418	C₄	—	11	1	no	—
419	C₄	—	22	2	no	—
420	C₄	—	22	2	no	—
421	C₄	C₄×D₄×D₁₁	1	1	yes	characteristic
422	C₄	C₂²×C₈×D₁₁	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	4	2	no	—
425	C₂	—	11	2	no	—
426	C₂	—	22	1	no	—
427	C₂	—	44	2	no	—
428	C₂	C₈×D₄×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₄×D₁₁
commutator	C₄×C₁₁	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₁₁×#2170	C₂
socle	C₂×C₁₁	C₂×C₈×D₄
prime radical	D₁₁×#135	C₄
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2170	D₁₁
hypocenter	C₁₁	C₂×#2170
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ #2170

Complements

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

N	H ≅ G/N	type
1. D₁₁×#504	C₂	semidirect
3. #13070454	C₂	semidirect
4. #13070453	C₂	semidirect
5. #13070452	C₂	semidirect
6. #13070451	C₂	semidirect
7. #13070450	C₂	semidirect
8. D₁₁×#364	C₂	semidirect
9. D₁₁×#350	C₂	semidirect
10. C₄×C₁₆×D₁₁	C₂	semidirect
11. C₁₁×#2170	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. C₄×C₁₁×C₁₆	C₂²	semidirect
37. #10622199	C₂²	semidirect
38. #10622153	C₂²	semidirect
39. #10622149	C₂²	semidirect
40. #10622146	C₂²	semidirect
41. C₁₆×Dic₁₁	C₂²	semidirect
42. C₁₆×Dic₁₁	C₂²	semidirect
43. #10622101	C₂²	semidirect
44. C₄×C₁₁⋊C₁₆	C₂²	semidirect
165. #2170	D₁₁	direct (N × H)
212. #504	C₂×D₁₁	semidirect
229. #364	C₂×D₁₁	semidirect
233. #350	C₂×D₁₁	semidirect
237. C₄×C₁₆	C₂×D₁₁	semidirect
313. D₁₁	#2170	direct (N × H)
371. C₁₁	C₂×#2170	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
#13070454	2
#13070453	2
#13070452	2
#13070451	2
#13070450	2
D₁₁×#364	2
D₁₁×#350	2
C₄×C₁₆×D₁₁	2
C₁₁×#2170	2
C₂×#2170	11

Subgroups — D11×#2170 #14906997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×#2170 #14906997