Subgroups — C₁₁×#19628 #14596821

Order 2816.

708 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	C₁₁×#3230	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#3226	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#3167	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#3141	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#3139	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1719	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1718	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1711	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1710	C₂	1	2	yes	maximal, complemented
11	C₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#533	C₂²	1	1	yes	characteristic
13	C₁₁×#532	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₁₁×#500	C₂²	1	2	yes	—
17	C₁₁×#500	C₂²	1	2	yes	—
18	C₁₁×#498	C₂²	1	1	yes	characteristic
19	C₁₁×#492	C₂²	1	1	yes	characteristic
20	C₁₁×#491	—	2	2	no	—
21	C₁₁×#489	—	2	2	no	—
22	C₁₁×#487	—	2	2	no	—
23	C₁₁×#487	C₂²	1	1	yes	characteristic
24	C₁₁×#487	C₂²	1	2	yes	—
25	C₁₁×#487	C₂²	1	2	yes	—
26	C₁₁×#487	C₂²	1	2	yes	—
27	C₁₁×#487	C₂²	1	2	yes	—
28	C₁₁×#487	C₂²	1	2	yes	—
29	C₁₁×#487	C₂²	1	2	yes	—
30	C₁₁×#486	C₂²	1	1	yes	characteristic
31	C₁₁×#486	C₂²	1	2	yes	—
32	C₁₁×#486	C₂²	1	2	yes	—
33	C₁₁×#484	—	2	2	no	—
34	C₁₁×#480	—	2	2	no	—
35	C₁₁×#477	—	2	2	no	—
36	C₁₁×#474	—	2	2	no	—
37	C₁₁×#465	—	2	2	no	—
38	C₄×C₁₁×SD₁₆	—	2	2	no	—
39	C₁₁×#431	C₂²	1	1	yes	characteristic
40	C₁₁×#419	—	2	2	no	—
41	C₁₁×#417	—	2	2	no	—
42	C₂×C₁₁×#103	—	2	2	no	—
43	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
45	C₁₁×#322	C₂²	1	2	yes	—
46	C₈²×C₁₁	C₂²	1	2	yes	—
47	C₂×C₁₁×#41	—	2	1	no	—
48	C₂²×Q₈×C₁₁	—	2	1	no	—
49	C₂²×Q₈×C₁₁	—	2	1	no	—
50	C₂×C₁₁×SD₁₆	—	2	2	no	—
51	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
52	C₂²×C₈×C₁₁	D₄	1	2	yes	—
53	C₁₁×C₄⋊Q₈	—	2	1	no	—
54	C₁₁×C₄⋊Q₈	—	2	1	no	—
55	C₁₁×C₄⋊Q₈	—	2	1	no	—
56	C₁₁×C₄⋊Q₈	—	2	1	no	—
57	C₁₁×C₄⋊Q₈	—	2	1	no	—
58	C₁₁×C₄⋊Q₈	—	2	1	no	—
59	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₁₁×#127	C₂³	1	1	yes	characteristic
65	C₁₁×#125	—	2	1	no	—
66	C₁₁×#124	—	2	1	no	—
67	C₁₁×C₂²⋊Q₈	—	2	1	no	—
68	C₁₁×C₂²⋊Q₈	—	2	1	no	—
69	C₁₁×#121	—	2	1	no	—
70	C₁₁×#121	—	2	1	no	—
71	C₄×Q₈×C₁₁	—	2	1	no	—
72	C₄×Q₈×C₁₁	—	2	1	no	—
73	C₄×D₄×C₁₁	—	2	1	no	—
74	C₄×D₄×C₁₁	—	2	1	no	—
75	C₁₁×#117	—	2	1	no	—
76	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
80	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
81	C₁₁×#107	—	2	4	no	—
82	C₁₁×#107	—	2	4	no	—
83	C₁₁×#106	—	2	2	no	—
84	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
85	C₁₁×#103	—	2	4	no	—
86	C₁₁×#103	—	2	4	no	—
87	C₁₁×#103	—	2	4	no	—
88	C₁₁×#103	—	2	4	no	—
89	C₁₁×#103	—	2	4	no	—
90	C₁₁×#103	—	2	2	no	—
91	C₁₁×#103	—	2	4	no	—
92	C₁₁×#102	—	2	4	no	—
93	C₁₁×#102	—	2	2	no	—
94	C₁₁×#102	—	2	4	no	—
95	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
96	C₁₁×#97	D₄	1	2	yes	—
97	C₄×C₈×C₁₁	D₄	1	2	yes	—
98	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₁₁	C₂³	1	2	yes	—
100	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₁₁	C₂³	1	2	yes	—
102	#19628	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₁₁×#41	—	4	4	no	—
104	C₂×Q₈×C₁₁	—	2	1	no	—
105	C₂×Q₈×C₁₁	—	2	1	no	—
106	C₂×Q₈×C₁₁	—	2	2	no	—
107	C₂×Q₈×C₁₁	—	2	2	no	—
108	C₂×Q₈×C₁₁	—	2	1	no	—
109	C₂×Q₈×C₁₁	—	4	4	no	—
110	C₂×Q₈×C₁₁	—	4	1	no	—
111	C₂×Q₈×C₁₁	—	4	1	no	—
112	C₂×Q₈×C₁₁	—	4	4	no	—
113	C₂×D₄×C₁₁	—	2	1	no	—
114	C₂×D₄×C₁₁	—	2	1	no	—
115	C₂×D₄×C₁₁	—	2	1	no	—
116	C₂×D₄×C₁₁	—	4	1	no	—
117	C₂²×C₄×C₁₁	—	4	1	no	—
118	C₂²×C₄×C₁₁	—	4	1	no	—
119	C₂²×C₄×C₁₁	—	4	1	no	—
120	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
123	C₁₁×SD₁₆	—	4	4	no	—
124	C₁₁×M₁₆	—	2	4	no	—
125	C₂×C₈×C₁₁	—	4	2	no	—
126	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
129	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
130	C₁₁×C₄⋊C₄	—	2	2	no	—
131	C₁₁×C₄⋊C₄	—	2	1	no	—
132	C₁₁×C₄⋊C₄	—	2	2	no	—
133	C₁₁×C₄⋊C₄	—	2	2	no	—
134	C₁₁×C₄⋊C₄	—	2	1	no	—
135	C₁₁×C₄⋊C₄	—	2	1	no	—
136	C₁₁×C₄⋊C₄	—	2	1	no	—
137	C₁₁×C₄⋊C₄	—	2	2	no	—
138	C₁₁×C₄⋊C₄	—	2	1	no	—
139	C₁₁×C₄⋊C₄	—	2	1	no	—
140	C₁₁×C₄⋊C₄	—	4	1	no	—
141	C₁₁×C₄⋊C₄	—	4	1	no	—
142	C₁₁×C₄⋊C₄	—	4	1	no	—
143	C₁₁×C₄⋊C₄	—	4	1	no	—
144	C₁₁×C₄⋊C₄	—	4	1	no	—
145	C₁₁×C₄⋊C₄	—	4	1	no	—
146	C₁₁×C₂²⋊C₄	—	4	1	no	—
147	C₁₁×C₂²⋊C₄	—	4	1	no	—
148	C₁₁×C₂²⋊C₄	—	4	1	no	—
149	C₄²×C₁₁	—	4	1	no	—
150	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
154	#3230	C₂×C₁₁	1	1	yes	characteristic, complemented
155	#3226	C₂×C₁₁	1	1	yes	characteristic
156	#3167	C₂×C₁₁	1	1	yes	characteristic
157	#3141	C₂×C₁₁	1	1	yes	characteristic
158	#3139	C₂×C₁₁	1	1	yes	characteristic, complemented
159	C₂×#487	C₂×C₁₁	1	1	yes	characteristic, complemented
160	#1719	C₂×C₁₁	1	2	yes	complemented
161	#1718	C₂×C₁₁	1	2	yes	complemented
162	#1711	C₂×C₁₁	1	2	yes	complemented
163	#1710	C₂×C₁₁	1	2	yes	complemented
164	C₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
165	C₂³×C₁₁	—	4	1	no	—
166	C₂³×C₁₁	#127	1	1	yes	characteristic
167	Q₈×C₁₁	—	4	4	no	—
168	Q₈×C₁₁	—	4	2	no	—
169	Q₈×C₁₁	—	4	2	no	—
170	Q₈×C₁₁	—	4	4	no	—
171	Q₈×C₁₁	—	4	2	no	—
172	Q₈×C₁₁	—	8	2	no	—
173	Q₈×C₁₁	—	8	2	no	—
174	D₄×C₁₁	—	4	2	no	—
175	D₄×C₁₁	—	4	2	no	—
176	D₄×C₁₁	—	4	2	no	—
177	D₄×C₁₁	—	8	2	no	—
178	C₂×C₄×C₁₁	—	2	2	no	—
179	C₂×C₄×C₁₁	—	2	2	no	—
180	C₂×C₄×C₁₁	—	4	1	no	—
181	C₂×C₄×C₁₁	—	4	1	no	—
182	C₂×C₄×C₁₁	—	4	1	no	—
183	C₂×C₄×C₁₁	—	4	2	no	—
184	C₂×C₄×C₁₁	—	4	2	no	—
185	C₂×C₄×C₁₁	—	8	2	no	—
186	C₂×C₄×C₁₁	—	8	2	no	—
187	C₂×C₄×C₁₁	—	8	2	no	—
188	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
189	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
190	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
191	C₂×C₄×C₁₁	#135	1	4	yes	—
192	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
195	C₈×C₁₁	—	2	4	no	—
196	C₈×C₁₁	—	2	2	no	—
197	C₈×C₁₁	—	2	2	no	—
198	C₈×C₁₁	—	2	4	no	—
199	#533	C₂²×C₁₁	1	1	yes	characteristic
200	#532	C₂²×C₁₁	1	1	yes	characteristic
201	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
202	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
203	#500	C₂²×C₁₁	1	2	yes	—
204	#500	C₂²×C₁₁	1	2	yes	—
205	#498	C₂²×C₁₁	1	1	yes	characteristic
206	#492	C₂²×C₁₁	1	1	yes	characteristic
207	#491	—	2	2	no	—
208	#489	—	2	2	no	—
209	#487	—	2	2	no	—
210	#487	C₂²×C₁₁	1	2	yes	—
211	#487	C₂²×C₁₁	1	2	yes	—
212	#487	C₂²×C₁₁	1	2	yes	—
213	#487	C₂²×C₁₁	1	2	yes	—
214	#487	C₂²×C₁₁	1	2	yes	—
215	#487	C₂²×C₁₁	1	1	yes	characteristic
216	#487	C₂²×C₁₁	1	2	yes	—
217	#486	C₂²×C₁₁	1	2	yes	—
218	#486	C₂²×C₁₁	1	1	yes	characteristic
219	#486	C₂²×C₁₁	1	2	yes	—
220	#484	—	2	2	no	—
221	#480	—	2	2	no	—
222	#477	—	2	2	no	—
223	#474	—	2	2	no	—
224	#465	—	2	2	no	—
225	C₄×SD₁₆	—	2	2	no	—
226	#431	C₂²×C₁₁	1	1	yes	characteristic
227	#419	—	2	2	no	—
228	#417	—	2	2	no	—
229	C₂×#103	—	2	2	no	—
230	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
231	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
232	#322	C₂²×C₁₁	1	2	yes	—
233	C₈²	C₂²×C₁₁	1	2	yes	—
234	C₂²×C₁₁	—	2	1	no	—
235	C₂²×C₁₁	—	2	1	no	—
236	C₂²×C₁₁	—	8	1	no	—
237	C₂²×C₁₁	—	8	1	no	—
238	C₂²×C₁₁	—	8	1	no	—
239	C₂²×C₁₁	#495	1	2	yes	—
240	C₂²×C₁₁	C₂×#127	1	1	yes	characteristic
241	C₄×C₁₁	—	2	1	no	—
242	C₄×C₁₁	—	2	1	no	—
243	C₄×C₁₁	—	8	1	no	—
244	C₄×C₁₁	—	8	2	no	—
245	C₄×C₁₁	—	8	2	no	—
246	C₄×C₁₁	—	8	1	no	—
247	C₄×C₁₁	—	8	1	no	—
248	C₄×C₁₁	#495	1	2	yes	—
249	C₄×C₁₁	C₂×#135	1	2	yes	—
250	C₄×C₁₁	#575	1	2	yes	—
251	C₄×C₁₁	#578	1	2	yes	—
252	C₂×#41	—	2	1	no	—
253	C₂²×Q₈	—	2	1	no	—
254	C₂²×Q₈	—	2	1	no	—
255	C₂×SD₁₆	—	2	2	no	—
256	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
257	C₂²×C₈	D₄×C₁₁	1	2	yes	—
258	C₄⋊Q₈	—	2	1	no	—
259	C₄⋊Q₈	—	2	1	no	—
260	C₄⋊Q₈	—	2	1	no	—
261	C₄⋊Q₈	—	2	1	no	—
262	C₄⋊Q₈	—	2	1	no	—
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
265	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
266	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
267	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
268	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
269	#127	C₂³×C₁₁	1	1	yes	characteristic
270	#125	—	2	1	no	—
271	#124	—	2	1	no	—
272	C₂²⋊Q₈	—	2	1	no	—
273	C₂²⋊Q₈	—	2	1	no	—
274	#121	—	2	1	no	—
275	#121	—	2	1	no	—
276	C₄×Q₈	—	2	1	no	—
277	C₄×Q₈	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	#117	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
286	#107	—	2	4	no	—
287	#107	—	2	4	no	—
288	#106	—	2	2	no	—
289	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
290	#103	—	2	4	no	—
291	#103	—	2	4	no	—
292	#103	—	2	4	no	—
293	#103	—	2	4	no	—
294	#103	—	2	4	no	—
295	#103	—	2	2	no	—
296	#103	—	2	4	no	—
297	#102	—	2	4	no	—
298	#102	—	2	2	no	—
299	#102	—	2	4	no	—
300	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
301	#97	D₄×C₁₁	1	2	yes	—
302	C₄×C₈	D₄×C₁₁	1	2	yes	—
303	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
304	C₄×C₈	C₂³×C₁₁	1	2	yes	—
305	C₄×C₈	C₂³×C₁₁	1	2	yes	—
306	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
307	C₂×C₁₁	—	2	2	no	—
308	C₂×C₁₁	—	16	1	no	—
309	C₂×C₁₁	C₂×#495	1	1	yes	characteristic
310	C₂×C₁₁	#3153	1	1	yes	characteristic
311	C₂×C₁₁	#3156	1	1	yes	characteristic
312	#41	—	4	4	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	4	4	no	—
319	C₂×Q₈	—	4	1	no	—
320	C₂×Q₈	—	4	1	no	—
321	C₂×Q₈	—	4	4	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
332	SD₁₆	—	4	4	no	—
333	M₁₆	—	2	4	no	—
334	C₂×C₈	—	4	2	no	—
335	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
336	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
337	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
338	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₂²⋊C₄	—	4	1	no	—
356	C₂²⋊C₄	—	4	1	no	—
357	C₂²⋊C₄	—	4	1	no	—
358	C₄²	—	4	1	no	—
359	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
360	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
361	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
362	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
363	C₁₁	#19628	1	1	yes	characteristic, direct product factor, Sylow
364	C₂³	—	4	1	no	—
365	C₂³	C₁₁×#127	1	1	yes	characteristic
366	Q₈	—	4	4	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	4	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	8	2	no	—
372	Q₈	—	8	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	8	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	8	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	8	2	no	—
387	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
388	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
389	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
390	C₂×C₄	C₁₁×#135	1	4	yes	—
391	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
392	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
394	C₈	—	2	4	no	—
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	2	4	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	C₁₁×#495	1	2	yes	—
404	C₂²	C₂×C₁₁×#127	1	1	yes	characteristic
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	8	1	no	—
408	C₄	—	8	2	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	1	no	—
411	C₄	—	8	1	no	—
412	C₄	C₁₁×#495	1	2	yes	—
413	C₄	C₂×C₁₁×#135	1	2	yes	—
414	C₄	C₁₁×#575	1	2	yes	—
415	C₄	C₁₁×#578	1	2	yes	—
416	C₂	—	2	2	no	—
417	C₂	—	16	1	no	—
418	C₂	C₂×C₁₁×#495	1	1	yes	characteristic
419	C₂	C₁₁×#3153	1	1	yes	characteristic
420	C₂	C₁₁×#3156	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₁₁×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#3230	C₂	semidirect
5. C₁₁×#3139	C₂	semidirect
6. C₂×C₁₁×#487	C₂	semidirect
7. C₁₁×#1719	C₂	semidirect
8. C₁₁×#1718	C₂	semidirect
9. C₁₁×#1711	C₂	semidirect
10. C₁₁×#1710	C₂	semidirect
11. C₈×C₁₁×M₁₆	C₂	semidirect
102. #19628	C₁₁	direct (N × H)
154. #3230	C₂×C₁₁	semidirect
158. #3139	C₂×C₁₁	semidirect
159. C₂×#487	C₂×C₁₁	semidirect
160. #1719	C₂×C₁₁	semidirect
161. #1718	C₂×C₁₁	semidirect
162. #1711	C₂×C₁₁	semidirect
163. #1710	C₂×C₁₁	semidirect
164. C₈×M₁₆	C₂×C₁₁	semidirect
363. C₁₁	#19628	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#3230	2
C₁₁×#3226	2
C₁₁×#3167	2
C₁₁×#3141	2
C₁₁×#3139	2
C₂×C₁₁×#487	2
C₁₁×#1719	2
C₁₁×#1718	2
C₁₁×#1711	2
C₁₁×#1710	2
C₈×C₁₁×M₁₆	2
#19628	11

Subgroups — C11×#19628 #14596821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19628 #14596821