Subgroups — C₁₁×#19624 #14596817

Order 2816.

772 conjugacy classes of subgroups.

The subgroup lattice has 428 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×#3227	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#3167	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#3165	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#3152	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1716	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1714	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1708	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1707	C₂	1	2	yes	maximal, complemented
11	C₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×#137	—	2	2	no	—
13	C₁₁×#533	C₂²	1	1	yes	characteristic
14	C₁₁×#532	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₁₁×#501	—	2	2	no	—
18	C₁₁×#500	C₂²	1	2	yes	—
19	C₁₁×#498	C₂²	1	2	yes	—
20	C₁₁×#498	C₂²	1	1	yes	characteristic
21	C₁₁×#498	C₂²	1	2	yes	—
22	C₁₁×#498	C₂²	1	2	yes	—
23	C₁₁×#497	—	2	2	no	—
24	C₁₁×#494	C₂²	1	2	yes	—
25	C₁₁×#492	C₂²	1	2	yes	—
26	C₁₁×#492	C₂²	1	1	yes	characteristic
27	C₁₁×#487	—	2	2	no	—
28	C₁₁×#487	C₂²	1	1	yes	characteristic
29	C₁₁×#487	C₂²	1	2	yes	—
30	C₁₁×#487	C₂²	1	2	yes	—
31	C₁₁×#487	C₂²	1	2	yes	—
32	C₁₁×#486	C₂²	1	1	yes	characteristic
33	C₁₁×#486	C₂²	1	2	yes	—
34	C₁₁×#483	—	2	2	no	—
35	C₁₁×#481	—	2	2	no	—
36	C₁₁×#476	—	2	2	no	—
37	C₁₁×#475	—	2	2	no	—
38	C₁₁×#465	—	2	2	no	—
39	C₄×C₁₁×SD₁₆	—	2	2	no	—
40	C₁₁×#431	C₂²	1	1	yes	characteristic
41	C₁₁×#428	—	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	C₁₁×#137	—	4	8	no	—
51	C₂×C₁₁×Q₁₆	—	2	4	no	—
52	C₂×C₁₁×SD₁₆	—	2	4	no	—
53	C₂×C₁₁×SD₁₆	—	2	2	no	—
54	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
55	C₂²×C₈×C₁₁	D₄	1	2	yes	—
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	—	2	1	no	—
60	C₁₁×C₄⋊Q₈	—	2	1	no	—
61	C₁₁×C₄⋊Q₈	—	2	1	no	—
62	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
67	C₁₁×#127	C₂³	1	1	yes	characteristic
68	C₁₁×#125	—	2	1	no	—
69	C₁₁×#124	—	2	1	no	—
70	C₁₁×C₂²⋊Q₈	—	2	1	no	—
71	C₁₁×C₂²⋊Q₈	—	2	1	no	—
72	C₁₁×#121	—	2	1	no	—
73	C₁₁×#121	—	2	1	no	—
74	C₄×Q₈×C₁₁	—	2	1	no	—
75	C₄×Q₈×C₁₁	—	2	1	no	—
76	C₄×D₄×C₁₁	—	2	1	no	—
77	C₄×D₄×C₁₁	—	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×C₁₁×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
83	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
84	C₁₁×#107	—	2	4	no	—
85	C₁₁×#106	—	2	4	no	—
86	C₁₁×#106	—	2	2	no	—
87	C₁₁×#106	—	2	4	no	—
88	C₁₁×#106	—	2	4	no	—
89	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
90	C₁₁×#103	—	2	4	no	—
91	C₁₁×#103	—	2	4	no	—
92	C₁₁×#103	—	2	2	no	—
93	C₁₁×#103	—	2	4	no	—
94	C₁₁×#102	—	2	2	no	—
95	C₁₁×#102	—	2	4	no	—
96	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
97	C₁₁×#97	D₄	1	2	yes	—
98	C₄×C₈×C₁₁	D₄	1	2	yes	—
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	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
103	#19624	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₁₁×#41	—	4	4	no	—
105	C₂×Q₈×C₁₁	—	2	1	no	—
106	C₂×Q₈×C₁₁	—	2	2	no	—
107	C₂×Q₈×C₁₁	—	2	1	no	—
108	C₂×Q₈×C₁₁	—	2	1	no	—
109	C₂×Q₈×C₁₁	—	2	2	no	—
110	C₂×Q₈×C₁₁	—	4	4	no	—
111	C₂×Q₈×C₁₁	—	4	1	no	—
112	C₂×Q₈×C₁₁	—	4	1	no	—
113	C₂×Q₈×C₁₁	—	4	4	no	—
114	C₂×D₄×C₁₁	—	2	1	no	—
115	C₂×D₄×C₁₁	—	2	1	no	—
116	C₂×D₄×C₁₁	—	2	1	no	—
117	C₂×D₄×C₁₁	—	4	1	no	—
118	C₂²×C₄×C₁₁	—	4	1	no	—
119	C₂²×C₄×C₁₁	—	4	1	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	8	no	—
125	C₁₁×SD₁₆	—	4	4	no	—
126	C₁₁×SD₁₆	—	4	8	no	—
127	C₁₁×M₁₆	SD₁₆	1	8	yes	complemented
128	C₂×C₈×C₁₁	—	4	2	no	—
129	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
132	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
133	C₁₁×C₄⋊C₄	—	2	2	no	—
134	C₁₁×C₄⋊C₄	—	2	1	no	—
135	C₁₁×C₄⋊C₄	—	2	2	no	—
136	C₁₁×C₄⋊C₄	—	2	2	no	—
137	C₁₁×C₄⋊C₄	—	2	1	no	—
138	C₁₁×C₄⋊C₄	—	2	1	no	—
139	C₁₁×C₄⋊C₄	—	2	1	no	—
140	C₁₁×C₄⋊C₄	—	2	1	no	—
141	C₁₁×C₄⋊C₄	—	2	2	no	—
142	C₁₁×C₄⋊C₄	—	2	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×C₄⋊C₄	—	4	1	no	—
149	C₁₁×C₂²⋊C₄	—	4	1	no	—
150	C₁₁×C₂²⋊C₄	—	4	1	no	—
151	C₁₁×C₂²⋊C₄	—	4	1	no	—
152	C₄²×C₁₁	—	4	1	no	—
153	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
157	#3229	C₂×C₁₁	1	1	yes	characteristic, complemented
158	#3227	C₂×C₁₁	1	1	yes	characteristic
159	#3167	C₂×C₁₁	1	1	yes	characteristic
160	#3165	C₂×C₁₁	1	1	yes	characteristic, complemented
161	#3152	C₂×C₁₁	1	1	yes	characteristic
162	C₂×#487	C₂×C₁₁	1	1	yes	characteristic, complemented
163	#1716	C₂×C₁₁	1	2	yes	complemented
164	#1714	C₂×C₁₁	1	2	yes	complemented
165	#1708	C₂×C₁₁	1	2	yes	complemented
166	#1707	C₂×C₁₁	1	2	yes	complemented
167	C₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
168	C₂³×C₁₁	—	4	1	no	—
169	C₂³×C₁₁	#127	1	1	yes	characteristic
170	Q₈×C₁₁	—	4	4	no	—
171	Q₈×C₁₁	—	4	2	no	—
172	Q₈×C₁₁	—	4	2	no	—
173	Q₈×C₁₁	—	4	4	no	—
174	Q₈×C₁₁	—	4	2	no	—
175	Q₈×C₁₁	—	8	2	no	—
176	Q₈×C₁₁	—	8	2	no	—
177	D₄×C₁₁	—	4	2	no	—
178	D₄×C₁₁	—	4	2	no	—
179	D₄×C₁₁	—	4	2	no	—
180	D₄×C₁₁	—	8	2	no	—
181	C₂×C₄×C₁₁	—	2	2	no	—
182	C₂×C₄×C₁₁	—	2	2	no	—
183	C₂×C₄×C₁₁	—	4	1	no	—
184	C₂×C₄×C₁₁	—	4	1	no	—
185	C₂×C₄×C₁₁	—	4	1	no	—
186	C₂×C₄×C₁₁	—	4	2	no	—
187	C₂×C₄×C₁₁	—	4	2	no	—
188	C₂×C₄×C₁₁	—	8	2	no	—
189	C₂×C₄×C₁₁	—	8	2	no	—
190	C₂×C₄×C₁₁	—	8	2	no	—
191	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
192	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
193	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
194	C₂×C₄×C₁₁	C₂×SD₁₆	1	4	yes	—
195	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
198	C₈×C₁₁	—	2	2	no	—
199	C₈×C₁₁	—	2	2	no	—
200	C₈×C₁₁	—	2	4	no	—
201	C₈×C₁₁	C₂×SD₁₆	1	8	yes	—
202	C₂×#137	—	2	2	no	—
203	#533	C₂²×C₁₁	1	1	yes	characteristic
204	#532	C₂²×C₁₁	1	1	yes	characteristic
205	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
206	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
207	#501	—	2	2	no	—
208	#500	C₂²×C₁₁	1	2	yes	—
209	#498	C₂²×C₁₁	1	2	yes	—
210	#498	C₂²×C₁₁	1	1	yes	characteristic
211	#498	C₂²×C₁₁	1	2	yes	—
212	#498	C₂²×C₁₁	1	2	yes	—
213	#497	—	2	2	no	—
214	#494	C₂²×C₁₁	1	2	yes	—
215	#492	C₂²×C₁₁	1	2	yes	—
216	#492	C₂²×C₁₁	1	1	yes	characteristic
217	#487	—	2	2	no	—
218	#487	C₂²×C₁₁	1	2	yes	—
219	#487	C₂²×C₁₁	1	2	yes	—
220	#487	C₂²×C₁₁	1	1	yes	characteristic
221	#487	C₂²×C₁₁	1	2	yes	—
222	#486	C₂²×C₁₁	1	1	yes	characteristic
223	#486	C₂²×C₁₁	1	2	yes	—
224	#483	—	2	2	no	—
225	#481	—	2	2	no	—
226	#476	—	2	2	no	—
227	#475	—	2	2	no	—
228	#465	—	2	2	no	—
229	C₄×SD₁₆	—	2	2	no	—
230	#431	C₂²×C₁₁	1	1	yes	characteristic
231	#428	—	2	2	no	—
232	C₂×#103	—	2	2	no	—
233	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
234	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
235	#322	C₂²×C₁₁	1	2	yes	—
236	C₈²	C₂²×C₁₁	1	2	yes	—
237	C₂²×C₁₁	—	2	1	no	—
238	C₂²×C₁₁	—	2	1	no	—
239	C₂²×C₁₁	—	8	1	no	—
240	C₂²×C₁₁	—	8	1	no	—
241	C₂²×C₁₁	—	8	1	no	—
242	C₂²×C₁₁	#492	1	2	yes	—
243	C₂²×C₁₁	C₂×#127	1	1	yes	characteristic
244	C₄×C₁₁	—	2	1	no	—
245	C₄×C₁₁	—	2	1	no	—
246	C₄×C₁₁	—	8	1	no	—
247	C₄×C₁₁	—	8	2	no	—
248	C₄×C₁₁	—	8	2	no	—
249	C₄×C₁₁	—	8	1	no	—
250	C₄×C₁₁	—	8	1	no	—
251	C₄×C₁₁	#492	1	2	yes	—
252	C₄×C₁₁	C₂²×SD₁₆	1	2	yes	—
253	C₄×C₁₁	#575	1	2	yes	—
254	C₄×C₁₁	#578	1	2	yes	—
255	C₂×#41	—	2	1	no	—
256	C₂²×Q₈	—	2	1	no	—
257	C₂²×Q₈	—	2	1	no	—
258	#137	—	4	8	no	—
259	C₂×Q₁₆	—	2	4	no	—
260	C₂×SD₁₆	—	2	4	no	—
261	C₂×SD₁₆	—	2	2	no	—
262	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
263	C₂²×C₈	D₄×C₁₁	1	2	yes	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	—	2	1	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
271	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
272	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
273	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
274	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
275	#127	C₂³×C₁₁	1	1	yes	characteristic
276	#125	—	2	1	no	—
277	#124	—	2	1	no	—
278	C₂²⋊Q₈	—	2	1	no	—
279	C₂²⋊Q₈	—	2	1	no	—
280	#121	—	2	1	no	—
281	#121	—	2	1	no	—
282	C₄×Q₈	—	2	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	2	1	no	—
286	#117	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	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	4	no	—
293	#106	—	2	4	no	—
294	#106	—	2	2	no	—
295	#106	—	2	4	no	—
296	#106	—	2	4	no	—
297	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
298	#103	—	2	4	no	—
299	#103	—	2	4	no	—
300	#103	—	2	2	no	—
301	#103	—	2	4	no	—
302	#102	—	2	2	no	—
303	#102	—	2	4	no	—
304	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
305	#97	D₄×C₁₁	1	2	yes	—
306	C₄×C₈	D₄×C₁₁	1	2	yes	—
307	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
308	C₄×C₈	C₂³×C₁₁	1	2	yes	—
309	C₄×C₈	C₂³×C₁₁	1	2	yes	—
310	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
311	C₂×C₁₁	—	2	2	no	—
312	C₂×C₁₁	—	16	1	no	—
313	C₂×C₁₁	C₂×#492	1	1	yes	characteristic
314	C₂×C₁₁	#3153	1	1	yes	characteristic
315	C₂×C₁₁	#3156	1	1	yes	characteristic
316	#41	—	4	4	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	4	4	no	—
323	C₂×Q₈	—	4	1	no	—
324	C₂×Q₈	—	4	1	no	—
325	C₂×Q₈	—	4	4	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
336	Q₁₆	—	4	8	no	—
337	SD₁₆	—	4	4	no	—
338	SD₁₆	—	4	8	no	—
339	M₁₆	C₁₁×SD₁₆	1	8	yes	complemented
340	C₂×C₈	—	4	2	no	—
341	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
342	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
343	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
344	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	4	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	C₂²⋊C₄	—	4	1	no	—
362	C₂²⋊C₄	—	4	1	no	—
363	C₂²⋊C₄	—	4	1	no	—
364	C₄²	—	4	1	no	—
365	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
366	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
367	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
368	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
369	C₁₁	#19624	1	1	yes	characteristic, direct product factor, Sylow
370	C₂³	—	4	1	no	—
371	C₂³	C₁₁×#127	1	1	yes	characteristic
372	Q₈	—	4	4	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	4	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	8	2	no	—
378	Q₈	—	8	2	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	8	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	8	2	no	—
391	C₂×C₄	—	8	2	no	—
392	C₂×C₄	—	8	2	no	—
393	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
394	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
395	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
396	C₂×C₄	C₂×C₁₁×SD₁₆	1	4	yes	—
397	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	—	2	2	no	—
402	C₈	—	2	4	no	—
403	C₈	C₂×C₁₁×SD₁₆	1	8	yes	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	C₁₁×#492	1	2	yes	—
410	C₂²	C₂×C₁₁×#127	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	8	2	no	—
414	C₄	—	8	1	no	—
415	C₄	—	8	1	no	—
416	C₄	—	8	1	no	—
417	C₄	—	8	2	no	—
418	C₄	C₁₁×#492	1	2	yes	—
419	C₄	C₂²×C₁₁×SD₁₆	1	2	yes	—
420	C₄	C₁₁×#575	1	2	yes	—
421	C₄	C₁₁×#578	1	2	yes	—
422	C₂	—	2	2	no	—
423	C₂	—	16	1	no	—
424	C₂	C₂×C₁₁×#492	1	1	yes	characteristic
425	C₂	C₁₁×#3153	1	1	yes	characteristic
426	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×#3229	C₂	semidirect
4. C₁₁×#3165	C₂	semidirect
6. C₂×C₁₁×#487	C₂	semidirect
7. C₁₁×#1716	C₂	semidirect
8. C₁₁×#1714	C₂	semidirect
9. C₁₁×#1708	C₂	semidirect
10. C₁₁×#1707	C₂	semidirect
11. C₈×C₁₁×M₁₆	C₂	semidirect
103. #19624	C₁₁	direct (N × H)
127. C₁₁×M₁₆	SD₁₆	semidirect
157. #3229	C₂×C₁₁	semidirect
160. #3165	C₂×C₁₁	semidirect
162. C₂×#487	C₂×C₁₁	semidirect
163. #1716	C₂×C₁₁	semidirect
164. #1714	C₂×C₁₁	semidirect
165. #1708	C₂×C₁₁	semidirect
166. #1707	C₂×C₁₁	semidirect
167. C₈×M₁₆	C₂×C₁₁	semidirect
339. M₁₆	C₁₁×SD₁₆	semidirect
369. C₁₁	#19624	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×#3227	2
C₁₁×#3167	2
C₁₁×#3165	2
C₁₁×#3152	2
C₂×C₁₁×#487	2
C₁₁×#1716	2
C₁₁×#1714	2
C₁₁×#1708	2
C₁₁×#1707	2
C₈×C₁₁×M₁₆	2
#19624	11

Subgroups — C11×#19624 #14596817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19624 #14596817