Subgroups — C₁₁×#21527 #14598720

Order 2816.

1014 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#467	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#441	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₁×#97	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₁×C₂²⋊Q₈	C₂	1	2	yes	maximal
5	C₁₁×#1971	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1935	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1892	C₂	1	2	yes	maximal
9	C₁₁×#1807	C₂	1	1	yes	maximal, characteristic
10	C₁₁×#1776	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1763	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
18	C₁₁×#467	C₄	1	8	yes	complemented
19	C₁₁×#441	—	2	4	no	—
20	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×#103	C₂²	1	2	yes	—
24	C₂×C₁₁×#103	C₂²	1	2	yes	—
25	C₂×C₁₁×#103	C₂²	1	2	yes	—
26	C₂×C₁₁×#97	—	2	4	no	—
27	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
28	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
29	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
31	C₁₁×#391	C₂²	1	2	yes	—
32	C₁₁×#389	C₂²	1	2	yes	—
33	C₁₁×#387	—	2	2	no	—
34	C₁₁×#385	—	2	2	no	—
35	C₁₁×#380	C₂²	1	2	yes	—
36	C₄×C₁₁×C₄⋊C₄	—	2	2	no	—
37	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
38	C₄×C₁₁×C₂²⋊C₄	—	2	2	no	—
39	C₁₁×#340	C₂²	1	2	yes	—
40	C₁₁×#340	C₂²	1	2	yes	—
41	C₁₁×#340	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₁	D₄	1	2	yes	—
44	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
45	C₂×C₁₁×Q₁₆	—	2	2	no	—
46	C₂×C₁₁×Q₁₆	—	2	2	no	—
47	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	complemented
48	C₂²×C₈×C₁₁	—	2	2	no	—
49	C₂²×C₈×C₁₁	—	2	2	no	—
50	C₂²×C₈×C₁₁	—	2	2	no	—
51	C₂²×C₈×C₁₁	—	2	2	no	—
52	C₂²×C₈×C₁₁	—	2	2	no	—
53	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
54	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
58	C₁₁×C₂²⋊Q₈	—	2	4	no	—
59	C₁₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
60	C₄×Q₈×C₁₁	—	2	4	no	—
61	C₄×Q₈×C₁₁	—	2	4	no	—
62	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₄²×C₁₁	—	2	2	no	—
71	C₂×C₄²×C₁₁	—	2	2	no	—
72	C₂×C₄²×C₁₁	—	2	2	no	—
73	C₂×C₄²×C₁₁	—	2	2	no	—
74	C₂×C₄²×C₁₁	D₄	1	2	yes	—
75	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
77	C₁₁×#107	C₂×C₄	1	4	yes	complemented
78	C₁₁×#106	—	2	2	no	—
79	C₁₁×#106	—	2	2	no	—
80	C₁₁×#103	—	2	4	no	—
81	C₁₁×#103	—	2	4	no	—
82	C₁₁×#103	C₂×C₄	1	8	yes	complemented
83	C₁₁×#97	—	2	2	no	—
84	C₁₁×#97	—	2	2	no	—
85	C₁₁×#97	—	2	2	no	—
86	C₁₁×#97	D₄	1	4	yes	—
87	C₁₁×#95	—	2	2	no	—
88	C₁₁×#95	—	2	2	no	—
89	C₁₁×#95	—	2	2	no	—
90	C₁₁×#95	—	2	2	no	—
91	C₁₁×#95	—	2	2	no	—
92	#21527	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
94	C₂×Q₈×C₁₁	—	2	2	no	—
95	C₂×Q₈×C₁₁	—	2	2	no	—
96	C₂×Q₈×C₁₁	—	2	2	no	—
97	C₂×Q₈×C₁₁	—	2	2	no	—
98	C₂×Q₈×C₁₁	—	2	2	no	—
99	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₁₁	—	2	1	no	—
101	C₂²×C₄×C₁₁	—	2	1	no	—
102	C₂²×C₄×C₁₁	—	2	1	no	—
103	C₂²×C₄×C₁₁	—	2	1	no	—
104	C₂²×C₄×C₁₁	—	2	4	no	—
105	C₂²×C₄×C₁₁	—	2	2	no	—
106	C₂²×C₄×C₁₁	—	2	2	no	—
107	C₂²×C₄×C₁₁	—	2	4	no	—
108	C₂²×C₄×C₁₁	—	2	2	no	—
109	C₂²×C₄×C₁₁	—	2	2	no	—
110	C₂²×C₄×C₁₁	—	4	2	no	—
111	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₁	#41	1	2	yes	—
116	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
117	C₁₁×Q₁₆	—	2	8	no	—
118	C₂×C₈×C₁₁	—	2	8	no	—
119	C₂×C₈×C₁₁	—	2	8	no	—
120	C₂×C₈×C₁₁	—	2	1	no	—
121	C₂×C₈×C₁₁	—	2	1	no	—
122	C₂×C₈×C₁₁	—	2	1	no	—
123	C₂×C₈×C₁₁	—	2	1	no	—
124	C₂×C₈×C₁₁	—	2	1	no	—
125	C₂×C₈×C₁₁	—	2	1	no	—
126	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₁	#41	1	2	yes	—
131	C₂×C₈×C₁₁	#41	1	2	yes	—
132	C₁₁×C₄⋊C₄	—	2	8	no	—
133	C₁₁×C₄⋊C₄	—	2	2	no	—
134	C₁₁×C₄⋊C₄	—	2	2	no	—
135	C₁₁×C₄⋊C₄	—	2	2	no	—
136	C₁₁×C₄⋊C₄	—	2	2	no	—
137	C₁₁×C₄⋊C₄	—	2	2	no	—
138	C₁₁×C₄⋊C₄	—	4	4	no	—
139	C₁₁×C₄⋊C₄	—	4	4	no	—
140	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
141	C₁₁×C₂²⋊C₄	—	2	8	no	—
142	C₁₁×C₂²⋊C₄	—	4	4	no	—
143	C₄²×C₁₁	—	2	4	no	—
144	C₄²×C₁₁	—	2	1	no	—
145	C₄²×C₁₁	—	2	1	no	—
146	C₄²×C₁₁	—	4	4	no	—
147	C₄²×C₁₁	—	4	4	no	—
148	C₄²×C₁₁	C₂×D₄	1	2	yes	—
149	C₄²×C₁₁	#41	1	2	yes	—
150	C₂×#467	C₂×C₁₁	1	1	yes	characteristic
151	C₂×#441	C₂×C₁₁	1	1	yes	characteristic, complemented
152	C₂²×#97	C₂×C₁₁	1	1	yes	characteristic
153	C₄×C₂²⋊Q₈	C₂×C₁₁	1	2	yes	—
154	#1971	C₂×C₁₁	1	1	yes	characteristic, complemented
155	#1943	C₂×C₁₁	1	1	yes	characteristic, complemented
156	#1935	C₂×C₁₁	1	2	yes	complemented
157	#1892	C₂×C₁₁	1	2	yes	—
158	#1807	C₂×C₁₁	1	1	yes	characteristic
159	#1776	C₂×C₁₁	1	1	yes	characteristic, complemented
160	#1763	C₂×C₁₁	1	2	yes	complemented
161	C₂³×C₁₁	—	2	1	no	—
162	C₂³×C₁₁	—	2	1	no	—
163	C₂³×C₁₁	—	2	2	no	—
164	C₂³×C₁₁	C₄×D₄	1	2	yes	—
165	C₂³×C₁₁	#137	1	4	yes	—
166	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₁₁	—	2	4	no	—
168	Q₈×C₁₁	—	2	4	no	—
169	Q₈×C₁₁	—	4	2	no	—
170	Q₈×C₁₁	—	4	2	no	—
171	C₂×C₄×C₁₁	—	2	1	no	—
172	C₂×C₄×C₁₁	—	2	1	no	—
173	C₂×C₄×C₁₁	—	2	2	no	—
174	C₂×C₄×C₁₁	—	2	2	no	—
175	C₂×C₄×C₁₁	—	2	2	no	—
176	C₂×C₄×C₁₁	—	2	2	no	—
177	C₂×C₄×C₁₁	—	2	2	no	—
178	C₂×C₄×C₁₁	—	2	2	no	—
179	C₂×C₄×C₁₁	—	2	4	no	—
180	C₂×C₄×C₁₁	—	2	4	no	—
181	C₂×C₄×C₁₁	—	2	2	no	—
182	C₂×C₄×C₁₁	—	2	2	no	—
183	C₂×C₄×C₁₁	—	2	2	no	—
184	C₂×C₄×C₁₁	—	4	8	no	—
185	C₂×C₄×C₁₁	—	4	2	no	—
186	C₂×C₄×C₁₁	—	4	2	no	—
187	C₂×C₄×C₁₁	—	4	2	no	—
188	C₂×C₄×C₁₁	—	4	2	no	—
189	C₂×C₄×C₁₁	—	4	2	no	—
190	C₂×C₄×C₁₁	—	4	2	no	—
191	C₂×C₄×C₁₁	—	4	2	no	—
192	C₂×C₄×C₁₁	—	4	2	no	—
193	C₂×C₄×C₁₁	—	4	2	no	—
194	C₂×C₄×C₁₁	—	4	2	no	—
195	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
196	C₂×C₄×C₁₁	#121	1	4	yes	—
197	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
203	C₈×C₁₁	—	2	2	no	—
204	C₈×C₁₁	—	2	2	no	—
205	C₈×C₁₁	—	2	2	no	—
206	C₈×C₁₁	C₄×D₄	1	4	yes	—
207	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
208	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
209	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
210	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
211	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
212	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
213	#467	C₄×C₁₁	1	8	yes	complemented
214	#441	—	2	4	no	—
215	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
216	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic
217	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic
218	C₂×#103	C₂²×C₁₁	1	2	yes	—
219	C₂×#103	C₂²×C₁₁	1	2	yes	—
220	C₂×#103	C₂²×C₁₁	1	2	yes	—
221	C₂×#97	—	2	4	no	—
222	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
223	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
224	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
225	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
226	#391	C₂²×C₁₁	1	2	yes	—
227	#389	C₂²×C₁₁	1	2	yes	—
228	#387	—	2	2	no	—
229	#385	—	2	2	no	—
230	#380	C₂²×C₁₁	1	2	yes	—
231	C₄×C₄⋊C₄	—	2	2	no	—
232	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
233	C₄×C₂²⋊C₄	—	2	2	no	—
234	#340	C₂²×C₁₁	1	2	yes	—
235	#340	C₂²×C₁₁	1	2	yes	—
236	#340	C₂²×C₁₁	1	2	yes	—
237	C₂²×C₁₁	—	2	4	no	—
238	C₂²×C₁₁	—	2	2	no	—
239	C₂²×C₁₁	—	2	4	no	—
240	C₂²×C₁₁	—	2	2	no	—
241	C₂²×C₁₁	#441	1	4	yes	complemented
242	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
243	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
244	C₂²×C₁₁	#532	1	1	yes	characteristic
245	C₂²×C₁₁	C₂×#137	1	2	yes	—
246	C₂²×C₁₁	#575	1	2	yes	—
247	C₄×C₁₁	—	2	4	no	—
248	C₄×C₁₁	—	2	2	no	—
249	C₄×C₁₁	—	4	4	no	—
250	C₄×C₁₁	—	4	2	no	—
251	C₄×C₁₁	—	4	4	no	—
252	C₄×C₁₁	—	8	2	no	—
253	C₄×C₁₁	—	8	2	no	—
254	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
255	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
256	C₄×C₁₁	#525	1	1	yes	characteristic
257	C₄×C₁₁	#529	1	1	yes	characteristic
258	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
259	C₂³×C₄	D₄×C₁₁	1	2	yes	—
260	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
261	C₂×Q₁₆	—	2	2	no	—
262	C₂×Q₁₆	—	2	2	no	—
263	C₂×Q₁₆	C₂×C₄×C₁₁	1	4	yes	complemented
264	C₂²×C₈	—	2	2	no	—
265	C₂²×C₈	—	2	2	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	—
270	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
274	C₂²⋊Q₈	—	2	4	no	—
275	C₂²⋊Q₈	C₂×C₄×C₁₁	1	8	yes	—
276	C₄×Q₈	—	2	4	no	—
277	C₄×Q₈	—	2	4	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	D₄×C₁₁	1	2	yes	—
291	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
293	#107	C₂×C₄×C₁₁	1	4	yes	complemented
294	#106	—	2	2	no	—
295	#106	—	2	2	no	—
296	#103	—	2	4	no	—
297	#103	—	2	4	no	—
298	#103	C₂×C₄×C₁₁	1	8	yes	complemented
299	#97	—	2	2	no	—
300	#97	—	2	2	no	—
301	#97	—	2	2	no	—
302	#97	D₄×C₁₁	1	4	yes	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	—	2	2	no	—
308	C₂×C₁₁	—	2	4	no	—
309	C₂×C₁₁	C₄×#121	1	1	yes	characteristic
310	C₂×C₁₁	C₂×#441	1	1	yes	characteristic
311	C₂×C₁₁	#2943	1	1	yes	characteristic
312	C₂×C₁₁	#3056	1	2	yes	—
313	C₂×C₁₁	#3181	1	2	yes	—
314	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
336	C₂²×C₄	C₁₁×#41	1	2	yes	—
337	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
338	Q₁₆	—	2	8	no	—
339	C₂×C₈	—	2	8	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	8	no	—
347	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
348	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
349	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
350	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
351	C₂×C₈	C₁₁×#41	1	2	yes	—
352	C₂×C₈	C₁₁×#41	1	2	yes	—
353	C₄⋊C₄	—	2	8	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	4	4	no	—
360	C₄⋊C₄	—	4	4	no	—
361	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	4	4	no	—
364	C₄²	—	2	4	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	4	4	no	—
368	C₄²	—	4	4	no	—
369	C₄²	C₂×D₄×C₁₁	1	2	yes	—
370	C₄²	C₁₁×#41	1	2	yes	—
371	C₁₁	#21527	1	1	yes	characteristic, direct product factor, Sylow
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	2	no	—
375	C₂³	C₄×D₄×C₁₁	1	2	yes	—
376	C₂³	C₁₁×#137	1	4	yes	—
377	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
378	Q₈	—	2	4	no	—
379	Q₈	—	2	4	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	4	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	8	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
407	C₂×C₄	C₁₁×#121	1	4	yes	—
408	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
410	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
411	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
412	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
413	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	C₄×D₄×C₁₁	1	4	yes	—
418	C₂²	—	2	4	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	2	2	no	—
422	C₂²	C₁₁×#441	1	4	yes	complemented
423	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
424	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
425	C₂²	C₁₁×#532	1	1	yes	characteristic
426	C₂²	C₂×C₁₁×#137	1	2	yes	—
427	C₂²	C₁₁×#575	1	2	yes	—
428	C₄	—	2	4	no	—
429	C₄	—	2	2	no	—
430	C₄	—	4	4	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	4	no	—
433	C₄	—	8	2	no	—
434	C₄	—	8	2	no	—
435	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
436	C₄	C₄×C₁₁×#41	1	1	yes	characteristic
437	C₄	C₁₁×#525	1	1	yes	characteristic
438	C₄	C₁₁×#529	1	1	yes	characteristic
439	C₂	—	2	4	no	—
440	C₂	C₄×C₁₁×#121	1	1	yes	characteristic
441	C₂	C₂×C₁₁×#441	1	1	yes	characteristic
442	C₂	C₁₁×#2943	1	1	yes	characteristic
443	C₂	C₁₁×#3056	1	2	yes	—
444	C₂	C₁₁×#3181	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂⁴×C₁₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#441	C₂	semidirect
5. C₁₁×#1971	C₂	semidirect
6. C₁₁×#1943	C₂	semidirect
7. C₁₁×#1935	C₂	semidirect
10. C₁₁×#1776	C₂	semidirect
11. C₁₁×#1763	C₂	semidirect
18. C₁₁×#467	C₄	semidirect
47. C₂×C₁₁×Q₁₆	C₂×C₄	semidirect
77. C₁₁×#107	C₂×C₄	semidirect
82. C₁₁×#103	C₂×C₄	semidirect
92. #21527	C₁₁	direct (N × H)
151. C₂×#441	C₂×C₁₁	semidirect
154. #1971	C₂×C₁₁	semidirect
155. #1943	C₂×C₁₁	semidirect
156. #1935	C₂×C₁₁	semidirect
159. #1776	C₂×C₁₁	semidirect
160. #1763	C₂×C₁₁	semidirect
213. #467	C₄×C₁₁	semidirect
241. C₂²×C₁₁	#441	semidirect
263. C₂×Q₁₆	C₂×C₄×C₁₁	semidirect
293. #107	C₂×C₄×C₁₁	semidirect
298. #103	C₂×C₄×C₁₁	semidirect
371. C₁₁	#21527	direct (N × H)
422. C₂²	C₁₁×#441	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#467	2
C₂×C₁₁×#441	2
C₂²×C₁₁×#97	2
C₄×C₁₁×C₂²⋊Q₈	2
C₁₁×#1971	2
C₁₁×#1943	2
C₁₁×#1935	2
C₁₁×#1892	2
C₁₁×#1807	2
C₁₁×#1776	2
C₁₁×#1763	2
#21527	11

Subgroups — C11×#21527 #14598720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21527 #14598720