Subgroups — C₁₁×#22790 #14599983

Order 2816.

762 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2293	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1924	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#1924	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1917	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1916	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1870	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#1869	C₂	1	1	yes	maximal, characteristic
8	C₁₁×#1839	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1818	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1798	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1753	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#1752	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₁×#1750	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₁×#1745	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#1729	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
33	C₁₁×#390	C₄	1	1	yes	characteristic
34	C₁₁×#390	C₄	1	1	yes	characteristic
35	C₁₁×#389	C₄	1	1	yes	characteristic
36	C₁₁×#389	C₄	1	1	yes	characteristic
37	C₁₁×#388	C₄	1	1	yes	characteristic
38	C₁₁×#388	C₄	1	1	yes	characteristic
39	C₁₁×#388	C₄	1	1	yes	characteristic
40	C₁₁×#388	C₄	1	1	yes	characteristic
41	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₄³×C₁₁	C₂²	1	1	yes	characteristic
45	C₁₁×#336	C₂²	1	1	yes	characteristic
46	C₁₁×#336	C₂²	1	1	yes	characteristic
47	C₁₁×#336	C₂²	1	1	yes	characteristic
48	C₁₁×#336	C₂²	1	1	yes	characteristic
49	C₁₁×#336	C₂²	1	1	yes	characteristic
50	C₁₁×#336	C₂²	1	1	yes	characteristic
51	C₁₁×#336	C₂²	1	1	yes	characteristic
52	C₁₁×#336	C₂²	1	1	yes	characteristic
53	C₁₁×#336	C₂²	1	1	yes	characteristic
54	C₁₁×#336	C₂²	1	1	yes	characteristic
55	C₁₁×#336	C₂²	1	1	yes	characteristic
56	C₁₁×#336	C₂²	1	1	yes	characteristic
57	C₁₁×#336	C₂²	1	1	yes	characteristic
58	C₁₁×#336	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
62	C₂×C₁₁×M₁₆	—	2	2	no	—
63	C₂×C₁₁×M₁₆	—	2	2	no	—
64	C₂×C₁₁×M₁₆	—	4	1	no	—
65	C₂²×C₈×C₁₁	—	2	2	no	—
66	C₂²×C₈×C₁₁	—	2	2	no	—
67	C₂²×C₈×C₁₁	—	4	1	no	—
68	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
76	C₄×D₄×C₁₁	—	2	2	no	—
77	C₄×D₄×C₁₁	—	2	2	no	—
78	C₁₁×#117	—	4	1	no	—
79	C₁₁×#117	—	4	1	no	—
80	C₁₁×#117	—	4	1	no	—
81	C₁₁×#117	—	4	1	no	—
82	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
108	C₁₁×C₄⋊C₈	—	4	1	no	—
109	C₁₁×C₄⋊C₈	—	4	1	no	—
110	C₁₁×C₂²⋊C₈	—	2	2	no	—
111	C₁₁×C₂²⋊C₈	—	2	2	no	—
112	C₁₁×C₂²⋊C₈	—	2	2	no	—
113	C₁₁×C₂²⋊C₈	—	2	2	no	—
114	C₁₁×C₂²⋊C₈	—	4	1	no	—
115	C₁₁×C₂²⋊C₈	—	4	1	no	—
116	C₁₁×#97	—	2	2	no	—
117	C₁₁×#97	—	2	2	no	—
118	C₁₁×#97	—	4	1	no	—
119	C₄×C₈×C₁₁	—	4	1	no	—
120	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
121	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
122	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
123	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
124	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
125	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
126	#22790	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
129	C₂×D₄×C₁₁	—	2	2	no	—
130	C₂×D₄×C₁₁	—	2	2	no	—
131	C₂×D₄×C₁₁	—	4	1	no	—
132	C₂²×C₄×C₁₁	—	2	1	no	—
133	C₂²×C₄×C₁₁	—	2	1	no	—
134	C₂²×C₄×C₁₁	—	2	1	no	—
135	C₂²×C₄×C₁₁	—	2	1	no	—
136	C₂²×C₄×C₁₁	—	2	1	no	—
137	C₂²×C₄×C₁₁	—	2	1	no	—
138	C₂²×C₄×C₁₁	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₁	#41	1	2	yes	—
155	C₂²×C₄×C₁₁	#41	1	2	yes	—
156	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
157	C₁₁×M₁₆	—	4	4	no	—
158	C₂×C₈×C₁₁	—	2	1	no	—
159	C₂×C₈×C₁₁	—	2	1	no	—
160	C₂×C₈×C₁₁	—	2	1	no	—
161	C₂×C₈×C₁₁	—	2	1	no	—
162	C₂×C₈×C₁₁	—	2	1	no	—
163	C₂×C₈×C₁₁	—	2	1	no	—
164	C₂×C₈×C₁₁	—	2	1	no	—
165	C₂×C₈×C₁₁	—	2	1	no	—
166	C₂×C₈×C₁₁	—	2	1	no	—
167	C₂×C₈×C₁₁	—	2	1	no	—
168	C₂×C₈×C₁₁	—	2	1	no	—
169	C₂×C₈×C₁₁	—	2	1	no	—
170	C₂×C₈×C₁₁	—	2	1	no	—
171	C₂×C₈×C₁₁	—	2	1	no	—
172	C₂×C₈×C₁₁	—	2	1	no	—
173	C₂×C₈×C₁₁	—	2	1	no	—
174	C₂×C₈×C₁₁	—	2	1	no	—
175	C₂×C₈×C₁₁	—	2	1	no	—
176	C₂×C₈×C₁₁	—	2	1	no	—
177	C₂×C₈×C₁₁	—	2	1	no	—
178	C₂×C₈×C₁₁	—	2	1	no	—
179	C₂×C₈×C₁₁	—	2	1	no	—
180	C₂×C₈×C₁₁	—	4	4	no	—
181	C₂×C₈×C₁₁	#41	1	2	yes	—
182	C₂×C₈×C₁₁	#41	1	2	yes	—
183	C₁₁×C₄⋊C₄	—	2	2	no	—
184	C₁₁×C₄⋊C₄	—	2	2	no	—
185	C₁₁×C₄⋊C₄	—	4	1	no	—
186	C₁₁×C₄⋊C₄	—	4	1	no	—
187	C₁₁×C₄⋊C₄	—	4	1	no	—
188	C₁₁×C₄⋊C₄	—	4	1	no	—
189	C₁₁×C₄⋊C₄	—	4	1	no	—
190	C₁₁×C₂²⋊C₄	—	2	2	no	—
191	C₁₁×C₂²⋊C₄	—	2	2	no	—
192	C₁₁×C₂²⋊C₄	—	4	1	no	—
193	C₁₁×C₂²⋊C₄	—	4	1	no	—
194	C₁₁×C₂²⋊C₄	—	4	1	no	—
195	C₁₁×C₂²⋊C₄	—	4	1	no	—
196	C₁₁×C₂²⋊C₄	—	4	1	no	—
197	C₁₁×C₂²⋊C₄	—	4	1	no	—
198	C₁₁×C₂²⋊C₄	—	4	1	no	—
199	C₁₁×C₂²⋊C₄	—	4	1	no	—
200	C₄²×C₁₁	—	2	2	no	—
201	C₄²×C₁₁	—	2	1	no	—
202	C₄²×C₁₁	—	2	1	no	—
203	C₄²×C₁₁	—	2	1	no	—
204	C₄²×C₁₁	—	2	1	no	—
205	C₄²×C₁₁	—	2	1	no	—
206	C₄²×C₁₁	—	2	1	no	—
207	C₄²×C₁₁	—	2	1	no	—
208	C₄²×C₁₁	—	2	1	no	—
209	C₄²×C₁₁	—	2	1	no	—
210	C₄²×C₁₁	—	2	1	no	—
211	C₄²×C₁₁	—	4	1	no	—
212	C₄²×C₁₁	—	4	1	no	—
213	C₄²×C₁₁	—	4	1	no	—
214	#2293	C₂×C₁₁	1	1	yes	characteristic
215	#1924	C₂×C₁₁	1	1	yes	characteristic, complemented
216	#1924	C₂×C₁₁	1	1	yes	characteristic, complemented
217	#1917	C₂×C₁₁	1	1	yes	characteristic, complemented
218	#1916	C₂×C₁₁	1	1	yes	characteristic, complemented
219	#1870	C₂×C₁₁	1	1	yes	characteristic
220	#1869	C₂×C₁₁	1	1	yes	characteristic
221	#1839	C₂×C₁₁	1	1	yes	characteristic, complemented
222	#1818	C₂×C₁₁	1	1	yes	characteristic, complemented
223	#1798	C₂×C₁₁	1	1	yes	characteristic, complemented
224	#1753	C₂×C₁₁	1	1	yes	characteristic, complemented
225	#1752	C₂×C₁₁	1	1	yes	characteristic, complemented
226	#1750	C₂×C₁₁	1	1	yes	characteristic, complemented
227	#1745	C₂×C₁₁	1	1	yes	characteristic, complemented
228	#1729	C₂×C₁₁	1	1	yes	characteristic, complemented
229	C₂³×C₁₁	—	2	1	no	—
230	C₂³×C₁₁	—	2	1	no	—
231	C₂³×C₁₁	—	2	1	no	—
232	C₂³×C₁₁	—	2	1	no	—
233	C₂³×C₁₁	—	2	1	no	—
234	C₂³×C₁₁	—	2	1	no	—
235	C₂³×C₁₁	—	2	1	no	—
236	C₂³×C₁₁	—	2	1	no	—
237	C₂³×C₁₁	—	2	1	no	—
238	C₂³×C₁₁	—	2	1	no	—
239	C₂³×C₁₁	—	2	1	no	—
240	C₂³×C₁₁	—	2	1	no	—
241	C₂³×C₁₁	—	2	1	no	—
242	C₂³×C₁₁	#117	1	2	yes	—
243	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
244	D₄×C₁₁	—	4	4	no	—
245	C₂×C₄×C₁₁	—	2	1	no	—
246	C₂×C₄×C₁₁	—	2	1	no	—
247	C₂×C₄×C₁₁	—	2	1	no	—
248	C₂×C₄×C₁₁	—	2	1	no	—
249	C₂×C₄×C₁₁	—	2	2	no	—
250	C₂×C₄×C₁₁	—	2	2	no	—
251	C₂×C₄×C₁₁	—	2	2	no	—
252	C₂×C₄×C₁₁	—	2	2	no	—
253	C₂×C₄×C₁₁	—	2	1	no	—
254	C₂×C₄×C₁₁	—	2	1	no	—
255	C₂×C₄×C₁₁	—	2	1	no	—
256	C₂×C₄×C₁₁	—	2	1	no	—
257	C₂×C₄×C₁₁	—	2	1	no	—
258	C₂×C₄×C₁₁	—	2	1	no	—
259	C₂×C₄×C₁₁	—	2	1	no	—
260	C₂×C₄×C₁₁	—	2	1	no	—
261	C₂×C₄×C₁₁	—	2	1	no	—
262	C₂×C₄×C₁₁	—	2	1	no	—
263	C₂×C₄×C₁₁	—	2	1	no	—
264	C₂×C₄×C₁₁	—	2	1	no	—
265	C₂×C₄×C₁₁	—	2	1	no	—
266	C₂×C₄×C₁₁	—	2	1	no	—
267	C₂×C₄×C₁₁	—	2	1	no	—
268	C₂×C₄×C₁₁	—	2	1	no	—
269	C₂×C₄×C₁₁	—	2	1	no	—
270	C₂×C₄×C₁₁	—	2	1	no	—
271	C₂×C₄×C₁₁	—	2	1	no	—
272	C₂×C₄×C₁₁	—	2	1	no	—
273	C₂×C₄×C₁₁	—	2	1	no	—
274	C₂×C₄×C₁₁	—	2	1	no	—
275	C₂×C₄×C₁₁	—	2	1	no	—
276	C₂×C₄×C₁₁	—	2	1	no	—
277	C₂×C₄×C₁₁	—	2	1	no	—
278	C₂×C₄×C₁₁	—	2	1	no	—
279	C₂×C₄×C₁₁	—	2	1	no	—
280	C₂×C₄×C₁₁	—	2	1	no	—
281	C₂×C₄×C₁₁	—	2	1	no	—
282	C₂×C₄×C₁₁	—	2	1	no	—
283	C₂×C₄×C₁₁	—	4	1	no	—
284	C₂×C₄×C₁₁	—	4	1	no	—
285	C₂×C₄×C₁₁	—	4	1	no	—
286	C₂×C₄×C₁₁	—	4	1	no	—
287	C₂×C₄×C₁₁	#117	1	2	yes	—
288	C₂×C₄×C₁₁	#131	1	2	yes	—
289	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
292	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
294	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
295	C₈×C₁₁	—	2	2	no	—
296	C₈×C₁₁	—	2	2	no	—
297	C₈×C₁₁	—	4	1	no	—
298	C₈×C₁₁	—	4	1	no	—
299	C₈×C₁₁	—	4	1	no	—
300	C₈×C₁₁	—	4	1	no	—
301	C₈×C₁₁	—	4	1	no	—
302	C₈×C₁₁	—	4	1	no	—
303	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
304	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
305	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
306	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
307	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
308	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
309	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
310	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
311	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
312	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
313	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
314	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
315	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
316	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
317	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
318	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
319	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
320	#390	C₄×C₁₁	1	1	yes	characteristic
321	#390	C₄×C₁₁	1	1	yes	characteristic
322	#389	C₄×C₁₁	1	1	yes	characteristic
323	#389	C₄×C₁₁	1	1	yes	characteristic
324	#388	C₄×C₁₁	1	1	yes	characteristic
325	#388	C₄×C₁₁	1	1	yes	characteristic
326	#388	C₄×C₁₁	1	1	yes	characteristic
327	#388	C₄×C₁₁	1	1	yes	characteristic
328	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
329	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
330	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
331	C₄³	C₂²×C₁₁	1	1	yes	characteristic
332	#336	C₂²×C₁₁	1	1	yes	characteristic
333	#336	C₂²×C₁₁	1	1	yes	characteristic
334	#336	C₂²×C₁₁	1	1	yes	characteristic
335	#336	C₂²×C₁₁	1	1	yes	characteristic
336	#336	C₂²×C₁₁	1	1	yes	characteristic
337	#336	C₂²×C₁₁	1	1	yes	characteristic
338	#336	C₂²×C₁₁	1	1	yes	characteristic
339	#336	C₂²×C₁₁	1	1	yes	characteristic
340	#336	C₂²×C₁₁	1	1	yes	characteristic
341	#336	C₂²×C₁₁	1	1	yes	characteristic
342	#336	C₂²×C₁₁	1	1	yes	characteristic
343	#336	C₂²×C₁₁	1	1	yes	characteristic
344	#336	C₂²×C₁₁	1	1	yes	characteristic
345	#336	C₂²×C₁₁	1	1	yes	characteristic
346	C₂²×C₁₁	—	2	2	no	—
347	C₂²×C₁₁	—	2	2	no	—
348	C₂²×C₁₁	—	2	2	no	—
349	C₂²×C₁₁	—	4	1	no	—
350	C₂²×C₁₁	—	4	1	no	—
351	C₂²×C₁₁	—	4	1	no	—
352	C₂²×C₁₁	—	4	1	no	—
353	C₂²×C₁₁	—	4	1	no	—
354	C₂²×C₁₁	—	4	1	no	—
355	C₂²×C₁₁	—	4	1	no	—
356	C₂²×C₁₁	—	4	1	no	—
357	C₂²×C₁₁	—	4	1	no	—
358	C₂²×C₁₁	—	4	1	no	—
359	C₂²×C₁₁	—	4	1	no	—
360	C₂²×C₁₁	C₂×#117	1	1	yes	characteristic
361	C₂²×C₁₁	C₄×#41	1	1	yes	characteristic
362	C₂²×C₁₁	#518	1	1	yes	characteristic
363	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
364	C₂²×C₁₁	#568	1	1	yes	characteristic
365	C₂²×C₁₁	#568	1	1	yes	characteristic
366	C₂²×C₁₁	#568	1	1	yes	characteristic
367	C₄×C₁₁	—	2	2	no	—
368	C₄×C₁₁	—	2	2	no	—
369	C₄×C₁₁	—	4	1	no	—
370	C₄×C₁₁	—	4	1	no	—
371	C₄×C₁₁	—	4	1	no	—
372	C₄×C₁₁	—	4	1	no	—
373	C₄×C₁₁	—	4	1	no	—
374	C₄×C₁₁	—	4	1	no	—
375	C₄×C₁₁	—	4	1	no	—
376	C₄×C₁₁	—	4	1	no	—
377	C₄×C₁₁	—	4	1	no	—
378	C₄×C₁₁	—	4	1	no	—
379	C₄×C₁₁	#551	1	1	yes	characteristic
380	C₄×C₁₁	#551	1	1	yes	characteristic
381	C₄×C₁₁	#553	1	1	yes	characteristic
382	C₄×C₁₁	#553	1	1	yes	characteristic
383	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
384	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
385	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
386	C₂×M₁₆	—	2	2	no	—
387	C₂×M₁₆	—	2	2	no	—
388	C₂×M₁₆	—	4	1	no	—
389	C₂²×C₈	—	2	2	no	—
390	C₂²×C₈	—	2	2	no	—
391	C₂²×C₈	—	4	1	no	—
392	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
394	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
395	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
396	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
398	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
399	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	—	2	2	no	—
402	#117	—	4	1	no	—
403	#117	—	4	1	no	—
404	#117	—	4	1	no	—
405	#117	—	4	1	no	—
406	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
413	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
414	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
415	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
417	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
418	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
419	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
421	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
423	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
424	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
425	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
426	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
429	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
430	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
432	C₄⋊C₈	—	4	1	no	—
433	C₄⋊C₈	—	4	1	no	—
434	C₂²⋊C₈	—	2	2	no	—
435	C₂²⋊C₈	—	2	2	no	—
436	C₂²⋊C₈	—	2	2	no	—
437	C₂²⋊C₈	—	2	2	no	—
438	C₂²⋊C₈	—	4	1	no	—
439	C₂²⋊C₈	—	4	1	no	—
440	#97	—	2	2	no	—
441	#97	—	2	2	no	—
442	#97	—	4	1	no	—
443	C₄×C₈	—	4	1	no	—
444	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
445	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
446	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
447	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
448	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
449	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
450	C₂×C₁₁	—	4	2	no	—
451	C₂×C₁₁	—	8	1	no	—
452	C₂×C₁₁	#2353	1	1	yes	characteristic
453	C₂×C₁₁	#2923	1	1	yes	characteristic
454	C₂×C₁₁	#2924	1	1	yes	characteristic
455	C₂×C₁₁	#2967	1	1	yes	characteristic
456	C₂×C₁₁	#2969	1	1	yes	characteristic
457	C₂×C₁₁	#2980	1	1	yes	characteristic
458	C₂×C₁₁	#2981	1	1	yes	characteristic
459	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
460	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	4	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
475	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
476	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
477	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
478	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
479	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
480	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
481	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
482	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
483	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
484	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
485	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
486	C₂²×C₄	C₁₁×#41	1	2	yes	—
487	C₂²×C₄	C₁₁×#41	1	2	yes	—
488	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
489	M₁₆	—	4	4	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	4	4	no	—
513	C₂×C₈	C₁₁×#41	1	2	yes	—
514	C₂×C₈	C₁₁×#41	1	2	yes	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	4	1	no	—
518	C₄⋊C₄	—	4	1	no	—
519	C₄⋊C₄	—	4	1	no	—
520	C₄⋊C₄	—	4	1	no	—
521	C₄⋊C₄	—	4	1	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	4	1	no	—
525	C₂²⋊C₄	—	4	1	no	—
526	C₂²⋊C₄	—	4	1	no	—
527	C₂²⋊C₄	—	4	1	no	—
528	C₂²⋊C₄	—	4	1	no	—
529	C₂²⋊C₄	—	4	1	no	—
530	C₂²⋊C₄	—	4	1	no	—
531	C₂²⋊C₄	—	4	1	no	—
532	C₄²	—	2	2	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	4	1	no	—
544	C₄²	—	4	1	no	—
545	C₄²	—	4	1	no	—
546	C₁₁	#22790	1	1	yes	characteristic, direct product factor, Sylow
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	2	1	no	—
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	C₁₁×#117	1	2	yes	—
561	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
562	D₄	—	4	4	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	C₁₁×#117	1	2	yes	—
606	C₂×C₄	C₁₁×#131	1	2	yes	—
607	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
608	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
609	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
610	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
611	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
612	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
613	C₈	—	2	2	no	—
614	C₈	—	2	2	no	—
615	C₈	—	4	1	no	—
616	C₈	—	4	1	no	—
617	C₈	—	4	1	no	—
618	C₈	—	4	1	no	—
619	C₈	—	4	1	no	—
620	C₈	—	4	1	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	4	1	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	4	1	no	—
627	C₂²	—	4	1	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	1	no	—
630	C₂²	—	4	1	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	C₂×C₁₁×#117	1	1	yes	characteristic
636	C₂²	C₄×C₁₁×#41	1	1	yes	characteristic
637	C₂²	C₁₁×#518	1	1	yes	characteristic
638	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
639	C₂²	C₁₁×#568	1	1	yes	characteristic
640	C₂²	C₁₁×#568	1	1	yes	characteristic
641	C₂²	C₁₁×#568	1	1	yes	characteristic
642	C₄	—	2	2	no	—
643	C₄	—	2	2	no	—
644	C₄	—	4	1	no	—
645	C₄	—	4	1	no	—
646	C₄	—	4	1	no	—
647	C₄	—	4	1	no	—
648	C₄	—	4	1	no	—
649	C₄	—	4	1	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	C₁₁×#551	1	1	yes	characteristic
655	C₄	C₁₁×#551	1	1	yes	characteristic
656	C₄	C₁₁×#553	1	1	yes	characteristic
657	C₄	C₁₁×#553	1	1	yes	characteristic
658	C₂	—	4	2	no	—
659	C₂	—	8	1	no	—
660	C₂	C₁₁×#2353	1	1	yes	characteristic
661	C₂	C₁₁×#2923	1	1	yes	characteristic
662	C₂	C₁₁×#2924	1	1	yes	characteristic
663	C₂	C₁₁×#2967	1	1	yes	characteristic
664	C₂	C₁₁×#2969	1	1	yes	characteristic
665	C₂	C₁₁×#2980	1	1	yes	characteristic
666	C₂	C₁₁×#2981	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₁×#1924	C₂	semidirect
3. C₁₁×#1924	C₂	semidirect
4. C₁₁×#1917	C₂	semidirect
5. C₁₁×#1916	C₂	semidirect
8. C₁₁×#1839	C₂	semidirect
9. C₁₁×#1818	C₂	semidirect
10. C₁₁×#1798	C₂	semidirect
11. C₁₁×#1753	C₂	semidirect
12. C₁₁×#1752	C₂	semidirect
13. C₁₁×#1750	C₂	semidirect
14. C₁₁×#1745	C₂	semidirect
15. C₁₁×#1729	C₂	semidirect
126. #22790	C₁₁	direct (N × H)
215. #1924	C₂×C₁₁	semidirect
216. #1924	C₂×C₁₁	semidirect
217. #1917	C₂×C₁₁	semidirect
218. #1916	C₂×C₁₁	semidirect
221. #1839	C₂×C₁₁	semidirect
222. #1818	C₂×C₁₁	semidirect
223. #1798	C₂×C₁₁	semidirect
224. #1753	C₂×C₁₁	semidirect
225. #1752	C₂×C₁₁	semidirect
226. #1750	C₂×C₁₁	semidirect
227. #1745	C₂×C₁₁	semidirect
228. #1729	C₂×C₁₁	semidirect
546. C₁₁	#22790	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×#2293	2
C₁₁×#1924	2
C₁₁×#1917	2
C₁₁×#1916	2
C₁₁×#1870	2
C₁₁×#1869	2
C₁₁×#1839	2
C₁₁×#1818	2
C₁₁×#1798	2
C₁₁×#1753	2
C₁₁×#1752	2
C₁₁×#1750	2
C₁₁×#1745	2
C₁₁×#1729	2
#22790	11

Subgroups — C11×#22790 #14599983

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22790 #14599983