Subgroups — C₁₁×#21518 #14598711

Order 2816.

910 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3035	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#444	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2931	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₁×#131	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1980	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1950	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1929	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1876	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1806	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1770	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1765	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₁×#135	C₂²	1	2	yes	—
13	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×#131	C₂²	1	2	yes	—
15	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
16	C₁₁×#532	C₂²	1	1	yes	characteristic
17	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
18	C₁₁×#464	C₄	1	2	yes	complemented
19	C₁₁×#463	C₄	1	2	yes	complemented
20	C₁₁×#462	C₄	1	1	yes	characteristic, complemented
21	C₁₁×#461	C₄	1	1	yes	characteristic, complemented
22	C₁₁×#460	C₄	1	1	yes	characteristic, complemented
23	C₁₁×#459	C₄	1	1	yes	characteristic, complemented
24	C₁₁×#444	—	2	8	no	—
25	C₁₁×#436	—	2	1	no	—
26	C₁₁×#436	—	2	1	no	—
27	C₈×D₄×C₁₁	—	2	1	no	—
28	C₈×D₄×C₁₁	—	2	1	no	—
29	C₂×C₁₁×#108	C₂²	1	2	yes	—
30	C₁₁×#423	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₁×#104	C₂²	1	2	yes	—
33	C₂×C₁₁×#104	C₂²	1	2	yes	—
34	C₂×C₁₁×#104	C₂²	1	2	yes	—
35	C₁₁×#416	C₂²	1	2	yes	—
36	C₁₁×#408	C₂²	1	2	yes	—
37	C₁₁×#405	—	2	1	no	—
38	C₁₁×#405	—	2	1	no	—
39	C₁₁×#405	C₂²	1	1	yes	characteristic
40	C₁₁×#405	C₂²	1	1	yes	characteristic
41	C₄×C₁₁×M₁₆	—	2	1	no	—
42	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
43	C₂×C₁₁×#97	C₂²	1	2	yes	—
44	C₂×C₄×C₈×C₁₁	—	2	1	no	—
45	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
46	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₁₁×#341	C₂²	1	2	yes	—
48	C₁₁×#339	C₂²	1	2	yes	—
49	C₁₁×#336	C₂²	1	2	yes	—
50	C₂×C₁₁×#41	C₂³	1	2	yes	—
51	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
52	C₁₁×#135	—	2	4	no	—
53	C₁₁×#135	—	2	4	no	—
54	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
55	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
56	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
57	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
58	C₁₁×#131	—	2	2	no	—
59	C₁₁×#131	—	2	2	no	—
60	C₁₁×#131	—	2	2	no	—
61	C₁₁×#131	—	2	4	no	—
62	C₁₁×#131	—	2	4	no	—
63	C₁₁×#131	D₄	1	4	yes	complemented
64	C₂×C₁₁×M₁₆	—	2	1	no	—
65	C₂×C₁₁×M₁₆	—	2	1	no	—
66	C₂×C₁₁×M₁₆	—	2	2	no	—
67	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
68	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
69	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₁	—	2	1	no	—
71	C₂²×C₈×C₁₁	—	2	1	no	—
72	C₂²×C₈×C₁₁	—	2	2	no	—
73	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
74	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
76	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
77	C₁₁×#127	C₂×C₄	1	1	yes	characteristic
78	C₁₁×#124	C₂×C₄	1	2	yes	—
79	C₁₁×#121	—	2	1	no	—
80	C₁₁×#121	—	2	1	no	—
81	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
82	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
83	C₄×D₄×C₁₁	—	2	1	no	—
84	C₄×D₄×C₁₁	—	2	1	no	—
85	C₄×D₄×C₁₁	—	2	1	no	—
86	C₄×D₄×C₁₁	—	2	1	no	—
87	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
88	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
89	C₁₁×#117	—	2	1	no	—
90	C₁₁×#117	C₂³	1	1	yes	characteristic
91	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
92	C₂×C₄²×C₁₁	—	2	1	no	—
93	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
94	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
95	C₁₁×#108	—	2	4	no	—
96	C₁₁×C₄⋊C₈	—	2	1	no	—
97	C₁₁×C₄⋊C₈	—	2	1	no	—
98	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
100	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
101	C₁₁×#104	—	2	4	no	—
102	C₁₁×#104	—	2	4	no	—
103	C₁₁×#104	—	2	4	no	—
104	C₁₁×#103	C₂×C₄	1	2	yes	—
105	C₁₁×#103	C₂×C₄	1	2	yes	—
106	C₁₁×#102	C₂×C₄	1	2	yes	—
107	C₁₁×#102	C₂×C₄	1	2	yes	—
108	C₁₁×C₂²⋊C₈	—	2	2	no	—
109	C₁₁×C₂²⋊C₈	—	2	2	no	—
110	C₁₁×#97	—	2	4	no	—
111	C₁₁×#97	—	2	1	no	—
112	C₁₁×#97	—	2	1	no	—
113	C₁₁×#97	—	2	1	no	—
114	C₄×C₈×C₁₁	—	2	1	no	—
115	C₄×C₈×C₁₁	—	2	1	no	—
116	C₄×C₈×C₁₁	—	2	1	no	—
117	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
118	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
119	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
120	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
121	C₁₁×#95	—	2	1	no	—
122	#21518	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₁₁×#41	—	2	1	no	—
124	C₁₁×#41	—	2	1	no	—
125	C₁₁×#41	—	2	2	no	—
126	C₁₁×#41	—	2	2	no	—
127	C₁₁×#41	—	2	2	no	—
128	C₁₁×#41	—	2	2	no	—
129	C₁₁×#41	C₂×D₄	1	2	yes	—
130	C₁₁×#41	#41	1	2	yes	—
131	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
132	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
133	C₂×D₄×C₁₁	—	2	1	no	—
134	C₂×D₄×C₁₁	—	2	2	no	—
135	C₂×D₄×C₁₁	—	2	1	no	—
136	C₂×D₄×C₁₁	—	2	1	no	—
137	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
138	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₁	—	2	1	no	—
140	C₂²×C₄×C₁₁	—	2	1	no	—
141	C₂²×C₄×C₁₁	—	2	1	no	—
142	C₂²×C₄×C₁₁	—	2	2	no	—
143	C₂²×C₄×C₁₁	—	2	2	no	—
144	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
145	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
146	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
147	C₁₁×Q₁₆	—	2	4	no	—
148	C₁₁×SD₁₆	—	2	4	no	—
149	C₁₁×SD₁₆	—	2	4	no	—
150	C₁₁×D₈	—	2	4	no	—
151	C₁₁×M₁₆	—	2	4	no	—
152	C₁₁×M₁₆	—	2	4	no	—
153	C₁₁×M₁₆	—	2	2	no	—
154	C₁₁×M₁₆	—	2	1	no	—
155	C₁₁×M₁₆	—	2	1	no	—
156	C₁₁×M₁₆	—	2	2	no	—
157	C₁₁×M₁₆	—	4	4	no	—
158	C₁₁×M₁₆	C₂×D₄	1	2	yes	—
159	C₁₁×M₁₆	#41	1	2	yes	—
160	C₂×C₈×C₁₁	—	2	4	no	—
161	C₂×C₈×C₁₁	—	2	4	no	—
162	C₂×C₈×C₁₁	—	2	2	no	—
163	C₂×C₈×C₁₁	—	2	1	no	—
164	C₂×C₈×C₁₁	—	2	1	no	—
165	C₂×C₈×C₁₁	—	2	2	no	—
166	C₂×C₈×C₁₁	—	2	1	no	—
167	C₂×C₈×C₁₁	—	2	1	no	—
168	C₂×C₈×C₁₁	—	2	2	no	—
169	C₂×C₈×C₁₁	—	4	4	no	—
170	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
171	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
172	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
173	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₁₁	#41	1	2	yes	—
178	C₁₁×C₄⋊C₄	—	2	1	no	—
179	C₁₁×C₄⋊C₄	—	2	1	no	—
180	C₁₁×C₄⋊C₄	—	2	1	no	—
181	C₁₁×C₄⋊C₄	—	2	1	no	—
182	C₁₁×C₄⋊C₄	—	4	2	no	—
183	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
184	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
185	C₁₁×C₂²⋊C₄	—	2	1	no	—
186	C₁₁×C₂²⋊C₄	—	2	1	no	—
187	C₁₁×C₂²⋊C₄	—	2	1	no	—
188	C₁₁×C₂²⋊C₄	—	2	2	no	—
189	C₁₁×C₂²⋊C₄	—	2	2	no	—
190	C₄²×C₁₁	—	2	1	no	—
191	C₄²×C₁₁	—	2	1	no	—
192	C₄²×C₁₁	—	2	1	no	—
193	C₄²×C₁₁	—	2	2	no	—
194	C₄²×C₁₁	—	2	2	no	—
195	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
196	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
197	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
199	#3035	C₂×C₁₁	1	1	yes	characteristic
200	C₂×#444	C₂×C₁₁	1	2	yes	complemented
201	#2931	C₂×C₁₁	1	1	yes	characteristic, complemented
202	C₄×#131	C₂×C₁₁	1	1	yes	characteristic, complemented
203	#1980	C₂×C₁₁	1	1	yes	characteristic, complemented
204	#1950	C₂×C₁₁	1	1	yes	characteristic, complemented
205	#1929	C₂×C₁₁	1	2	yes	complemented
206	#1876	C₂×C₁₁	1	2	yes	complemented
207	#1806	C₂×C₁₁	1	1	yes	characteristic, complemented
208	#1770	C₂×C₁₁	1	1	yes	characteristic, complemented
209	#1765	C₂×C₁₁	1	2	yes	complemented
210	C₂³×C₁₁	—	2	1	no	—
211	C₂³×C₁₁	—	2	2	no	—
212	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
213	Q₈×C₁₁	—	2	1	no	—
214	Q₈×C₁₁	—	2	2	no	—
215	Q₈×C₁₁	—	2	2	no	—
216	Q₈×C₁₁	C₄×D₄	1	2	yes	—
217	D₄×C₁₁	—	2	2	no	—
218	D₄×C₁₁	—	2	2	no	—
219	D₄×C₁₁	—	2	2	no	—
220	D₄×C₁₁	—	2	1	no	—
221	D₄×C₁₁	—	2	2	no	—
222	D₄×C₁₁	—	4	2	no	—
223	D₄×C₁₁	—	4	2	no	—
224	D₄×C₁₁	—	4	2	no	—
225	D₄×C₁₁	—	4	2	no	—
226	D₄×C₁₁	C₄×D₄	1	2	yes	—
227	C₂×C₄×C₁₁	—	2	1	no	—
228	C₂×C₄×C₁₁	—	2	2	no	—
229	C₂×C₄×C₁₁	—	2	2	no	—
230	C₂×C₄×C₁₁	—	2	2	no	—
231	C₂×C₄×C₁₁	—	2	1	no	—
232	C₂×C₄×C₁₁	—	2	1	no	—
233	C₂×C₄×C₁₁	—	2	2	no	—
234	C₂×C₄×C₁₁	—	4	1	no	—
235	C₂×C₄×C₁₁	—	4	2	no	—
236	C₂×C₄×C₁₁	—	4	2	no	—
237	C₂×C₄×C₁₁	—	4	2	no	—
238	C₂×C₄×C₁₁	—	4	2	no	—
239	C₂×C₄×C₁₁	—	4	2	no	—
240	C₂×C₄×C₁₁	—	4	2	no	—
241	C₂×C₄×C₁₁	—	4	2	no	—
242	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
247	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
252	C₈×C₁₁	—	2	2	no	—
253	C₈×C₁₁	—	2	2	no	—
254	C₈×C₁₁	—	2	2	no	—
255	C₈×C₁₁	—	2	1	no	—
256	C₈×C₁₁	—	2	2	no	—
257	C₈×C₁₁	—	2	1	no	—
258	C₈×C₁₁	—	4	2	no	—
259	C₈×C₁₁	#121	1	2	yes	—
260	C₈×C₁₁	#121	1	2	yes	—
261	C₂×#135	C₂²×C₁₁	1	2	yes	—
262	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
263	C₂×#131	C₂²×C₁₁	1	2	yes	—
264	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
265	#532	C₂²×C₁₁	1	1	yes	characteristic
266	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
267	#464	C₄×C₁₁	1	2	yes	complemented
268	#463	C₄×C₁₁	1	2	yes	complemented
269	#462	C₄×C₁₁	1	1	yes	characteristic, complemented
270	#461	C₄×C₁₁	1	1	yes	characteristic, complemented
271	#460	C₄×C₁₁	1	1	yes	characteristic, complemented
272	#459	C₄×C₁₁	1	1	yes	characteristic, complemented
273	#444	—	2	8	no	—
274	#436	—	2	1	no	—
275	#436	—	2	1	no	—
276	C₈×D₄	—	2	1	no	—
277	C₈×D₄	—	2	1	no	—
278	C₂×#108	C₂²×C₁₁	1	2	yes	—
279	#423	C₂²×C₁₁	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
281	C₂×#104	C₂²×C₁₁	1	2	yes	—
282	C₂×#104	C₂²×C₁₁	1	2	yes	—
283	C₂×#104	C₂²×C₁₁	1	2	yes	—
284	#416	C₂²×C₁₁	1	2	yes	—
285	#408	C₂²×C₁₁	1	2	yes	—
286	#405	—	2	1	no	—
287	#405	—	2	1	no	—
288	#405	C₂²×C₁₁	1	1	yes	characteristic
289	#405	C₂²×C₁₁	1	1	yes	characteristic
290	C₄×M₁₆	—	2	1	no	—
291	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
292	C₂×#97	C₂²×C₁₁	1	2	yes	—
293	C₂×C₄×C₈	—	2	1	no	—
294	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
295	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
296	#341	C₂²×C₁₁	1	2	yes	—
297	#339	C₂²×C₁₁	1	2	yes	—
298	#336	C₂²×C₁₁	1	2	yes	—
299	C₂²×C₁₁	—	2	1	no	—
300	C₂²×C₁₁	—	2	1	no	—
301	C₂²×C₁₁	—	2	2	no	—
302	C₂²×C₁₁	—	4	1	no	—
303	C₂²×C₁₁	—	4	1	no	—
304	C₂²×C₁₁	—	4	2	no	—
305	C₂²×C₁₁	—	4	2	no	—
306	C₂²×C₁₁	—	4	2	no	—
307	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
308	C₂²×C₁₁	#529	1	1	yes	characteristic
309	C₂²×C₁₁	#532	1	1	yes	characteristic
310	C₄×C₁₁	—	2	1	no	—
311	C₄×C₁₁	—	2	1	no	—
312	C₄×C₁₁	—	2	1	no	—
313	C₄×C₁₁	—	2	2	no	—
314	C₄×C₁₁	—	4	1	no	—
315	C₄×C₁₁	—	4	1	no	—
316	C₄×C₁₁	—	4	2	no	—
317	C₄×C₁₁	—	8	2	no	—
318	C₄×C₁₁	#444	1	2	yes	complemented
319	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
320	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
321	C₄×C₁₁	C₂×#121	1	1	yes	characteristic
322	C₄×C₁₁	#525	1	1	yes	characteristic
323	C₂×#41	C₂³×C₁₁	1	2	yes	—
324	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
325	#135	—	2	4	no	—
326	#135	—	2	4	no	—
327	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
328	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
329	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
330	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
331	#131	—	2	2	no	—
332	#131	—	2	2	no	—
333	#131	—	2	2	no	—
334	#131	—	2	4	no	—
335	#131	—	2	4	no	—
336	#131	D₄×C₁₁	1	4	yes	complemented
337	C₂×M₁₆	—	2	1	no	—
338	C₂×M₁₆	—	2	1	no	—
339	C₂×M₁₆	—	2	2	no	—
340	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
341	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
342	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
343	C₂²×C₈	—	2	1	no	—
344	C₂²×C₈	—	2	1	no	—
345	C₂²×C₈	—	2	2	no	—
346	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
347	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
349	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
350	#127	C₂×C₄×C₁₁	1	1	yes	characteristic
351	#124	C₂×C₄×C₁₁	1	2	yes	—
352	#121	—	2	1	no	—
353	#121	—	2	1	no	—
354	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
355	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
356	C₄×D₄	—	2	1	no	—
357	C₄×D₄	—	2	1	no	—
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	—	2	1	no	—
360	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
361	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
362	#117	—	2	1	no	—
363	#117	C₂³×C₁₁	1	1	yes	characteristic
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄²	—	2	1	no	—
366	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
367	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
368	#108	—	2	4	no	—
369	C₄⋊C₈	—	2	1	no	—
370	C₄⋊C₈	—	2	1	no	—
371	C₄⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
372	C₄⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
373	C₄⋊C₈	C₂×C₄×C₁₁	1	2	yes	—
374	#104	—	2	4	no	—
375	#104	—	2	4	no	—
376	#104	—	2	4	no	—
377	#103	C₂×C₄×C₁₁	1	2	yes	—
378	#103	C₂×C₄×C₁₁	1	2	yes	—
379	#102	C₂×C₄×C₁₁	1	2	yes	—
380	#102	C₂×C₄×C₁₁	1	2	yes	—
381	C₂²⋊C₈	—	2	2	no	—
382	C₂²⋊C₈	—	2	2	no	—
383	#97	—	2	4	no	—
384	#97	—	2	1	no	—
385	#97	—	2	1	no	—
386	#97	—	2	1	no	—
387	C₄×C₈	—	2	1	no	—
388	C₄×C₈	—	2	1	no	—
389	C₄×C₈	—	2	1	no	—
390	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
391	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
392	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
393	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
394	#95	—	2	1	no	—
395	C₂×C₁₁	—	2	1	no	—
396	C₂×C₁₁	—	2	1	no	—
397	C₂×C₁₁	—	4	2	no	—
398	C₂×C₁₁	—	8	2	no	—
399	C₂×C₁₁	C₄×#121	1	1	yes	characteristic
400	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
401	C₂×C₁₁	#2955	1	1	yes	characteristic
402	#41	—	2	1	no	—
403	#41	—	2	1	no	—
404	#41	—	2	2	no	—
405	#41	—	2	2	no	—
406	#41	—	2	2	no	—
407	#41	—	2	2	no	—
408	#41	C₂×D₄×C₁₁	1	2	yes	—
409	#41	C₁₁×#41	1	2	yes	—
410	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
411	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
417	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
424	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
425	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
426	Q₁₆	—	2	4	no	—
427	SD₁₆	—	2	4	no	—
428	SD₁₆	—	2	4	no	—
429	D₈	—	2	4	no	—
430	M₁₆	—	2	4	no	—
431	M₁₆	—	2	1	no	—
432	M₁₆	—	2	1	no	—
433	M₁₆	—	2	4	no	—
434	M₁₆	—	2	2	no	—
435	M₁₆	—	2	2	no	—
436	M₁₆	—	4	4	no	—
437	M₁₆	C₂×D₄×C₁₁	1	2	yes	—
438	M₁₆	C₁₁×#41	1	2	yes	—
439	C₂×C₈	—	2	4	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	2	4	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	4	4	no	—
449	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
450	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
451	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
452	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
453	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
454	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
455	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
456	C₂×C₈	C₁₁×#41	1	2	yes	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	4	2	no	—
462	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
463	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	2	no	—
473	C₄²	—	2	2	no	—
474	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
475	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
476	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
477	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
478	C₁₁	#21518	1	1	yes	characteristic, direct product factor, Sylow
479	C₂³	—	2	1	no	—
480	C₂³	—	2	2	no	—
481	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
482	Q₈	—	2	1	no	—
483	Q₈	—	2	2	no	—
484	Q₈	—	2	2	no	—
485	Q₈	C₄×D₄×C₁₁	1	2	yes	—
486	D₄	—	2	2	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	2	no	—
489	D₄	—	2	1	no	—
490	D₄	—	2	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	2	no	—
494	D₄	—	4	2	no	—
495	D₄	C₄×D₄×C₁₁	1	2	yes	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
512	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
513	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
514	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
515	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
518	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
519	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
520	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
521	C₈	—	2	2	no	—
522	C₈	—	2	2	no	—
523	C₈	—	2	2	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	2	no	—
526	C₈	—	2	1	no	—
527	C₈	—	4	2	no	—
528	C₈	C₁₁×#121	1	2	yes	—
529	C₈	C₁₁×#121	1	2	yes	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
539	C₂²	C₁₁×#529	1	1	yes	characteristic
540	C₂²	C₁₁×#532	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	2	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	2	no	—
548	C₄	—	8	2	no	—
549	C₄	C₁₁×#444	1	2	yes	complemented
550	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
551	C₄	C₄×C₁₁×#41	1	1	yes	characteristic
552	C₄	C₂×C₁₁×#121	1	1	yes	characteristic
553	C₄	C₁₁×#525	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	4	2	no	—
557	C₂	—	8	2	no	—
558	C₂	C₄×C₁₁×#121	1	1	yes	characteristic
559	C₂	C₂×C₁₁×#444	1	1	yes	characteristic
560	C₂	C₁₁×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₁₁×#3035	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#444	C₂	semidirect
3. C₁₁×#2931	C₂	semidirect
4. C₄×C₁₁×#131	C₂	semidirect
5. C₁₁×#1980	C₂	semidirect
6. C₁₁×#1950	C₂	semidirect
7. C₁₁×#1929	C₂	semidirect
8. C₁₁×#1876	C₂	semidirect
9. C₁₁×#1806	C₂	semidirect
10. C₁₁×#1770	C₂	semidirect
11. C₁₁×#1765	C₂	semidirect
18. C₁₁×#464	C₄	semidirect
19. C₁₁×#463	C₄	semidirect
20. C₁₁×#462	C₄	semidirect
21. C₁₁×#461	C₄	semidirect
22. C₁₁×#460	C₄	semidirect
23. C₁₁×#459	C₄	semidirect
63. C₁₁×#131	D₄	semidirect
122. #21518	C₁₁	direct (N × H)
200. C₂×#444	C₂×C₁₁	semidirect
201. #2931	C₂×C₁₁	semidirect
202. C₄×#131	C₂×C₁₁	semidirect
203. #1980	C₂×C₁₁	semidirect
204. #1950	C₂×C₁₁	semidirect
205. #1929	C₂×C₁₁	semidirect
206. #1876	C₂×C₁₁	semidirect
207. #1806	C₂×C₁₁	semidirect
208. #1770	C₂×C₁₁	semidirect
209. #1765	C₂×C₁₁	semidirect
267. #464	C₄×C₁₁	semidirect
268. #463	C₄×C₁₁	semidirect
269. #462	C₄×C₁₁	semidirect
270. #461	C₄×C₁₁	semidirect
271. #460	C₄×C₁₁	semidirect
272. #459	C₄×C₁₁	semidirect
318. C₄×C₁₁	#444	semidirect
336. #131	D₄×C₁₁	semidirect
478. C₁₁	#21518	direct (N × H)
549. C₄	C₁₁×#444	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#3035	2
C₂×C₁₁×#444	2
C₁₁×#2931	2
C₄×C₁₁×#131	2
C₁₁×#1980	2
C₁₁×#1950	2
C₁₁×#1929	2
C₁₁×#1876	2
C₁₁×#1806	2
C₁₁×#1770	2
C₁₁×#1765	2
#21518	11

Subgroups — C11×#21518 #14598711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21518 #14598711