Subgroups — C₁₁×#19637 #14596830

Order 2816.

750 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#3208	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#3170	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#3139	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#3138	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×#486	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#1720	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1719	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1711	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1708	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×#533	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
16	C₁₁×#500	C₂²	1	1	yes	characteristic, complemented
17	C₁₁×#498	C₂²	1	2	yes	complemented
18	C₁₁×#494	C₂²	1	1	yes	characteristic, complemented
19	C₁₁×#492	C₂²	1	2	yes	—
20	C₁₁×#491	—	2	2	no	—
21	C₁₁×#490	—	2	2	no	—
22	C₁₁×#487	C₂²	1	1	yes	characteristic, complemented
23	C₁₁×#487	C₂²	1	1	yes	characteristic, complemented
24	C₁₁×#487	C₂²	1	2	yes	complemented
25	C₁₁×#487	C₂²	1	2	yes	complemented
26	C₁₁×#487	C₂²	1	2	yes	complemented
27	C₁₁×#486	—	2	2	no	—
28	C₁₁×#486	C₂²	1	2	yes	—
29	C₁₁×#486	C₂²	1	2	yes	—
30	C₁₁×#486	C₂²	1	2	yes	—
31	C₁₁×#486	C₂²	1	2	yes	—
32	C₁₁×#486	C₂²	1	2	yes	—
33	C₁₁×#483	—	2	2	no	—
34	C₁₁×#475	—	2	2	no	—
35	C₁₁×#467	—	2	2	no	—
36	C₁₁×#460	—	2	2	no	—
37	C₁₁×#450	—	2	2	no	—
38	C₄×C₁₁×Q₁₆	—	2	2	no	—
39	C₁₁×#431	C₂²	1	1	yes	characteristic
40	C₁₁×#419	—	2	2	no	—
41	C₁₁×#418	—	2	2	no	—
42	C₂×C₁₁×#102	—	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	complemented
46	C₈²×C₁₁	C₂²	1	2	yes	complemented
47	C₂²×Q₈×C₁₁	—	2	1	no	—
48	C₂²×D₄×C₁₁	—	2	1	no	—
49	C₂²×D₄×C₁₁	—	2	1	no	—
50	C₂²×D₄×C₁₁	—	2	1	no	—
51	C₂×C₁₁×Q₁₆	—	2	2	no	—
52	C₂×C₁₁×SD₁₆	—	2	4	no	—
53	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
54	C₂²×C₈×C₁₁	D₄	1	2	yes	—
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	C₂³	1	1	yes	characteristic
59	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
62	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₁₁×#127	—	2	1	no	—
64	C₁₁×#127	—	2	1	no	—
65	C₁₁×#127	—	2	1	no	—
66	C₁₁×#127	C₂³	1	2	yes	—
67	C₁₁×#125	—	2	1	no	—
68	C₁₁×#125	—	2	1	no	—
69	C₁₁×C₂²⋊Q₈	—	2	1	no	—
70	C₁₁×C₂²⋊Q₈	—	2	1	no	—
71	C₁₁×C₂²⋊Q₈	—	2	1	no	—
72	C₁₁×C₂²⋊Q₈	—	2	1	no	—
73	C₄×Q₈×C₁₁	—	2	1	no	—
74	C₄×Q₈×C₁₁	—	2	1	no	—
75	C₄×Q₈×C₁₁	—	2	1	no	—
76	C₄×Q₈×C₁₁	—	2	1	no	—
77	C₁₁×#117	—	2	1	no	—
78	C₁₁×#117	—	2	1	no	—
79	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
81	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
82	C₁₁×#107	—	2	2	no	—
83	C₁₁×#106	—	2	4	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	2	no	—
88	C₁₁×#103	—	2	2	no	—
89	C₁₁×#103	—	2	4	no	—
90	C₁₁×#102	—	2	4	no	—
91	C₁₁×#102	—	2	4	no	—
92	C₁₁×#102	—	2	4	no	—
93	C₁₁×#102	—	2	4	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	2	yes	—
99	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₁₁	C₂³	1	2	yes	—
102	#19637	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂⁴×C₁₁	—	4	1	no	—
104	C₂×Q₈×C₁₁	—	2	1	no	—
105	C₂×Q₈×C₁₁	—	2	2	no	—
106	C₂×Q₈×C₁₁	—	2	1	no	—
107	C₂×Q₈×C₁₁	—	2	1	no	—
108	C₂×Q₈×C₁₁	—	2	1	no	—
109	C₂×Q₈×C₁₁	—	4	1	no	—
110	C₂×Q₈×C₁₁	—	4	4	no	—
111	C₂×D₄×C₁₁	—	2	2	no	—
112	C₂×D₄×C₁₁	—	2	2	no	—
113	C₂×D₄×C₁₁	—	2	2	no	—
114	C₂×D₄×C₁₁	—	4	4	no	—
115	C₂×D₄×C₁₁	—	4	1	no	—
116	C₂×D₄×C₁₁	—	4	1	no	—
117	C₂×D₄×C₁₁	—	4	1	no	—
118	C₂×D₄×C₁₁	—	4	4	no	—
119	C₂×D₄×C₁₁	—	8	2	no	—
120	C₂²×C₄×C₁₁	—	4	1	no	—
121	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
124	C₁₁×Q₁₆	—	4	4	no	—
125	C₁₁×SD₁₆	—	8	4	no	—
126	C₁₁×M₁₆	—	2	4	no	—
127	C₂×C₈×C₁₁	—	4	2	no	—
128	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
131	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
132	C₁₁×C₄⋊C₄	—	2	2	no	—
133	C₁₁×C₄⋊C₄	—	2	1	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	1	no	—
138	C₁₁×C₄⋊C₄	—	2	2	no	—
139	C₁₁×C₄⋊C₄	—	2	1	no	—
140	C₁₁×C₄⋊C₄	—	2	1	no	—
141	C₁₁×C₄⋊C₄	—	2	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×C₄⋊C₄	—	4	1	no	—
147	C₁₁×C₄⋊C₄	—	4	1	no	—
148	C₁₁×C₂²⋊C₄	—	4	1	no	—
149	C₁₁×C₂²⋊C₄	—	4	1	no	—
150	C₄²×C₁₁	—	4	1	no	—
151	C₄²×C₁₁	—	4	1	no	—
152	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
156	#3229	C₂×C₁₁	1	1	yes	characteristic, complemented
157	#3208	C₂×C₁₁	1	1	yes	characteristic
158	#3170	C₂×C₁₁	1	1	yes	characteristic, complemented
159	#3139	C₂×C₁₁	1	1	yes	characteristic, complemented
160	#3138	C₂×C₁₁	1	1	yes	characteristic
161	C₂×#486	C₂×C₁₁	1	1	yes	characteristic
162	#1720	C₂×C₁₁	1	2	yes	complemented
163	#1719	C₂×C₁₁	1	2	yes	complemented
164	#1711	C₂×C₁₁	1	2	yes	complemented
165	#1708	C₂×C₁₁	1	2	yes	complemented
166	C₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
167	C₂³×C₁₁	—	4	2	no	—
168	C₂³×C₁₁	—	8	2	no	—
169	C₂³×C₁₁	—	8	2	no	—
170	C₂³×C₁₁	—	8	2	no	—
171	C₂³×C₁₁	#127	1	1	yes	characteristic
172	Q₈×C₁₁	—	4	4	no	—
173	Q₈×C₁₁	—	4	2	no	—
174	Q₈×C₁₁	—	4	2	no	—
175	Q₈×C₁₁	—	4	2	no	—
176	Q₈×C₁₁	—	4	2	no	—
177	Q₈×C₁₁	—	8	2	no	—
178	D₄×C₁₁	—	4	4	no	—
179	D₄×C₁₁	—	4	4	no	—
180	D₄×C₁₁	—	4	4	no	—
181	D₄×C₁₁	—	8	2	no	—
182	D₄×C₁₁	—	8	2	no	—
183	D₄×C₁₁	—	8	2	no	—
184	C₂×C₄×C₁₁	—	2	2	no	—
185	C₂×C₄×C₁₁	—	2	2	no	—
186	C₂×C₄×C₁₁	—	4	1	no	—
187	C₂×C₄×C₁₁	—	4	1	no	—
188	C₂×C₄×C₁₁	—	4	1	no	—
189	C₂×C₄×C₁₁	—	4	1	no	—
190	C₂×C₄×C₁₁	—	4	2	no	—
191	C₂×C₄×C₁₁	—	8	2	no	—
192	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
193	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
194	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
195	C₂×C₄×C₁₁	#135	1	4	yes	—
196	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
199	C₈×C₁₁	—	2	4	no	—
200	C₈×C₁₁	—	2	2	no	—
201	C₈×C₁₁	—	2	2	no	—
202	C₈×C₁₁	—	2	4	no	—
203	#533	C₂²×C₁₁	1	1	yes	characteristic
204	#533	C₂²×C₁₁	1	1	yes	characteristic
205	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
206	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
207	#500	C₂²×C₁₁	1	1	yes	characteristic, complemented
208	#498	C₂²×C₁₁	1	2	yes	complemented
209	#494	C₂²×C₁₁	1	1	yes	characteristic, complemented
210	#492	C₂²×C₁₁	1	2	yes	—
211	#491	—	2	2	no	—
212	#490	—	2	2	no	—
213	#487	C₂²×C₁₁	1	2	yes	complemented
214	#487	C₂²×C₁₁	1	2	yes	complemented
215	#487	C₂²×C₁₁	1	1	yes	characteristic, complemented
216	#487	C₂²×C₁₁	1	1	yes	characteristic, complemented
217	#487	C₂²×C₁₁	1	2	yes	complemented
218	#486	—	2	2	no	—
219	#486	C₂²×C₁₁	1	2	yes	—
220	#486	C₂²×C₁₁	1	2	yes	—
221	#486	C₂²×C₁₁	1	2	yes	—
222	#486	C₂²×C₁₁	1	2	yes	—
223	#486	C₂²×C₁₁	1	2	yes	—
224	#483	—	2	2	no	—
225	#475	—	2	2	no	—
226	#467	—	2	2	no	—
227	#460	—	2	2	no	—
228	#450	—	2	2	no	—
229	C₄×Q₁₆	—	2	2	no	—
230	#431	C₂²×C₁₁	1	1	yes	characteristic
231	#419	—	2	2	no	—
232	#418	—	2	2	no	—
233	C₂×#102	—	2	2	no	—
234	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
235	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
236	#322	C₂²×C₁₁	1	2	yes	complemented
237	C₈²	C₂²×C₁₁	1	2	yes	complemented
238	C₂²×C₁₁	—	2	1	no	—
239	C₂²×C₁₁	—	2	1	no	—
240	C₂²×C₁₁	—	8	2	no	—
241	C₂²×C₁₁	—	8	2	no	—
242	C₂²×C₁₁	—	8	2	no	—
243	C₂²×C₁₁	—	16	4	no	—
244	C₂²×C₁₁	#495	1	2	yes	—
245	C₂²×C₁₁	C₂×#127	1	1	yes	characteristic
246	C₄×C₁₁	—	2	1	no	—
247	C₄×C₁₁	—	2	1	no	—
248	C₄×C₁₁	—	8	2	no	—
249	C₄×C₁₁	—	8	1	no	—
250	C₄×C₁₁	—	8	1	no	—
251	C₄×C₁₁	—	8	1	no	—
252	C₄×C₁₁	—	8	1	no	—
253	C₄×C₁₁	#495	1	2	yes	—
254	C₄×C₁₁	C₂×#135	1	2	yes	—
255	C₄×C₁₁	#575	1	2	yes	—
256	C₄×C₁₁	#577	1	2	yes	—
257	C₂²×Q₈	—	2	1	no	—
258	C₂²×D₄	—	2	1	no	—
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	—	2	1	no	—
261	C₂×Q₁₆	—	2	2	no	—
262	C₂×SD₁₆	—	2	4	no	—
263	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
264	C₂²×C₈	D₄×C₁₁	1	2	yes	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
269	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
270	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
271	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
272	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
273	#127	—	2	1	no	—
274	#127	—	2	1	no	—
275	#127	—	2	1	no	—
276	#127	C₂³×C₁₁	1	2	yes	—
277	#125	—	2	1	no	—
278	#125	—	2	1	no	—
279	C₂²⋊Q₈	—	2	1	no	—
280	C₂²⋊Q₈	—	2	1	no	—
281	C₂²⋊Q₈	—	2	1	no	—
282	C₂²⋊Q₈	—	2	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×Q₈	—	2	1	no	—
285	C₄×Q₈	—	2	1	no	—
286	C₄×Q₈	—	2	1	no	—
287	#117	—	2	1	no	—
288	#117	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
292	#107	—	2	2	no	—
293	#106	—	2	4	no	—
294	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
295	#103	—	2	4	no	—
296	#103	—	2	4	no	—
297	#103	—	2	2	no	—
298	#103	—	2	2	no	—
299	#103	—	2	4	no	—
300	#102	—	2	4	no	—
301	#102	—	2	4	no	—
302	#102	—	2	4	no	—
303	#102	—	2	4	no	—
304	#102	—	2	4	no	—
305	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
306	#97	D₄×C₁₁	1	2	yes	—
307	C₄×C₈	D₄×C₁₁	1	2	yes	—
308	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
309	C₄×C₈	C₂³×C₁₁	1	2	yes	—
310	C₄×C₈	C₂³×C₁₁	1	2	yes	—
311	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
312	C₂×C₁₁	—	2	2	no	—
313	C₂×C₁₁	—	16	2	no	—
314	C₂×C₁₁	C₂×#495	1	1	yes	characteristic
315	C₂×C₁₁	#3153	1	1	yes	characteristic
316	C₂×C₁₁	#3154	1	1	yes	characteristic
317	C₂⁴	—	4	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	4	1	no	—
324	C₂×Q₈	—	4	4	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	4	4	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	—	4	1	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	4	no	—
333	C₂×D₄	—	8	2	no	—
334	C₂²×C₄	—	4	1	no	—
335	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
338	Q₁₆	—	4	4	no	—
339	SD₁₆	—	8	4	no	—
340	M₁₆	—	2	4	no	—
341	C₂×C₈	—	4	2	no	—
342	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
343	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
344	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
345	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₄⋊C₄	—	4	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₂²⋊C₄	—	4	1	no	—
363	C₂²⋊C₄	—	4	1	no	—
364	C₄²	—	4	1	no	—
365	C₄²	—	4	1	no	—
366	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
367	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
368	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
369	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
370	C₁₁	#19637	1	1	yes	characteristic, direct product factor, Sylow
371	C₂³	—	4	2	no	—
372	C₂³	—	8	2	no	—
373	C₂³	—	8	2	no	—
374	C₂³	—	8	2	no	—
375	C₂³	C₁₁×#127	1	1	yes	characteristic
376	Q₈	—	4	4	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	8	2	no	—
382	D₄	—	4	4	no	—
383	D₄	—	4	4	no	—
384	D₄	—	4	4	no	—
385	D₄	—	8	2	no	—
386	D₄	—	8	2	no	—
387	D₄	—	8	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	8	2	no	—
396	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
397	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
398	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
399	C₂×C₄	C₁₁×#135	1	4	yes	—
400	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
402	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
403	C₈	—	2	4	no	—
404	C₈	—	2	2	no	—
405	C₈	—	2	2	no	—
406	C₈	—	2	4	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	16	4	no	—
413	C₂²	C₁₁×#495	1	2	yes	—
414	C₂²	C₂×C₁₁×#127	1	1	yes	characteristic
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	8	2	no	—
418	C₄	—	8	1	no	—
419	C₄	—	8	1	no	—
420	C₄	—	8	1	no	—
421	C₄	—	8	1	no	—
422	C₄	C₁₁×#495	1	2	yes	—
423	C₄	C₂×C₁₁×#135	1	2	yes	—
424	C₄	C₁₁×#575	1	2	yes	—
425	C₄	C₁₁×#577	1	2	yes	—
426	C₂	—	2	2	no	—
427	C₂	—	16	2	no	—
428	C₂	C₂×C₁₁×#495	1	1	yes	characteristic
429	C₂	C₁₁×#3153	1	1	yes	characteristic
430	C₂	C₁₁×#3154	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#127	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×#3229	C₂	semidirect
3. C₁₁×#3170	C₂	semidirect
4. C₁₁×#3139	C₂	semidirect
7. C₁₁×#1720	C₂	semidirect
8. C₁₁×#1719	C₂	semidirect
9. C₁₁×#1711	C₂	semidirect
10. C₁₁×#1708	C₂	semidirect
11. C₈×C₁₁×M₁₆	C₂	semidirect
16. C₁₁×#500	C₂²	semidirect
17. C₁₁×#498	C₂²	semidirect
18. C₁₁×#494	C₂²	semidirect
22. C₁₁×#487	C₂²	semidirect
23. C₁₁×#487	C₂²	semidirect
24. C₁₁×#487	C₂²	semidirect
25. C₁₁×#487	C₂²	semidirect
26. C₁₁×#487	C₂²	semidirect
45. C₁₁×#322	C₂²	semidirect
46. C₈²×C₁₁	C₂²	semidirect
102. #19637	C₁₁	direct (N × H)
156. #3229	C₂×C₁₁	semidirect
158. #3170	C₂×C₁₁	semidirect
159. #3139	C₂×C₁₁	semidirect
162. #1720	C₂×C₁₁	semidirect
163. #1719	C₂×C₁₁	semidirect
164. #1711	C₂×C₁₁	semidirect
165. #1708	C₂×C₁₁	semidirect
166. C₈×M₁₆	C₂×C₁₁	semidirect
207. #500	C₂²×C₁₁	semidirect
208. #498	C₂²×C₁₁	semidirect
209. #494	C₂²×C₁₁	semidirect
213. #487	C₂²×C₁₁	semidirect
214. #487	C₂²×C₁₁	semidirect
215. #487	C₂²×C₁₁	semidirect
216. #487	C₂²×C₁₁	semidirect
217. #487	C₂²×C₁₁	semidirect
236. #322	C₂²×C₁₁	semidirect
237. C₈²	C₂²×C₁₁	semidirect
370. C₁₁	#19637	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×#3229	2
C₁₁×#3208	2
C₁₁×#3170	2
C₁₁×#3139	2
C₁₁×#3138	2
C₂×C₁₁×#486	2
C₁₁×#1720	2
C₁₁×#1719	2
C₁₁×#1711	2
C₁₁×#1708	2
C₈×C₁₁×M₁₆	2
#19637	11

Subgroups — C11×#19637 #14596830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19637 #14596830