Subgroups — C₁₁×#22597 #14599790

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2298	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1917	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#1916	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1916	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1916	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1851	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#1850	C₂	1	1	yes	maximal, characteristic
8	C₁₁×#1839	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1832	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1818	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#1753	C₂	1	1	yes	maximal, characteristic
13	C₈×C₁₁×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
14	C₁₁×#1746	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#1729	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×C₄⋊C₈	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×#97	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
29	C₁₁×#388	C₄	1	1	yes	characteristic
30	C₁₁×#388	C₄	1	1	yes	characteristic
31	C₁₁×#388	C₄	1	1	yes	characteristic
32	C₁₁×#388	C₄	1	1	yes	characteristic
33	C₁₁×#387	C₄	1	1	yes	characteristic
34	C₁₁×#387	C₄	1	1	yes	characteristic
35	C₁₁×#387	C₄	1	1	yes	characteristic
36	C₁₁×#387	C₄	1	1	yes	characteristic
37	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₁₁×#376	C₂²	1	1	yes	characteristic
42	C₄³×C₁₁	C₂²	1	1	yes	characteristic
43	C₁₁×#336	C₂²	1	1	yes	characteristic
44	C₁₁×#336	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	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
60	C₂×C₁₁×M₁₆	—	2	2	no	—
61	C₂×C₁₁×M₁₆	—	2	2	no	—
62	C₂×C₁₁×M₁₆	—	4	1	no	—
63	C₂²×C₈×C₁₁	—	2	2	no	—
64	C₂²×C₈×C₁₁	—	2	2	no	—
65	C₂²×C₈×C₁₁	—	4	1	no	—
66	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
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	C₁₁×#117	—	2	2	no	—
75	C₁₁×#117	—	2	2	no	—
76	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
98	C₁₁×C₄⋊C₈	—	2	2	no	—
99	C₁₁×C₄⋊C₈	—	2	2	no	—
100	C₁₁×C₄⋊C₈	—	4	1	no	—
101	C₁₁×C₄⋊C₈	—	4	1	no	—
102	C₁₁×C₂²⋊C₈	—	2	2	no	—
103	C₁₁×C₂²⋊C₈	—	2	2	no	—
104	C₁₁×#97	—	2	2	no	—
105	C₄×C₈×C₁₁	—	2	2	no	—
106	C₄×C₈×C₁₁	—	4	1	no	—
107	C₄×C₈×C₁₁	—	4	1	no	—
108	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
109	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
110	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
111	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
112	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
113	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
114	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
115	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
116	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
117	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
118	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
119	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
120	#22597	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₁	—	2	1	no	—
123	C₂²×C₄×C₁₁	—	2	1	no	—
124	C₂²×C₄×C₁₁	—	2	1	no	—
125	C₂²×C₄×C₁₁	—	2	1	no	—
126	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₁	#41	1	2	yes	—
140	C₂²×C₄×C₁₁	#41	1	2	yes	—
141	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
142	C₁₁×M₁₆	—	4	4	no	—
143	C₂×C₈×C₁₁	—	2	1	no	—
144	C₂×C₈×C₁₁	—	2	1	no	—
145	C₂×C₈×C₁₁	—	2	1	no	—
146	C₂×C₈×C₁₁	—	2	1	no	—
147	C₂×C₈×C₁₁	—	2	1	no	—
148	C₂×C₈×C₁₁	—	2	1	no	—
149	C₂×C₈×C₁₁	—	2	1	no	—
150	C₂×C₈×C₁₁	—	2	1	no	—
151	C₂×C₈×C₁₁	—	2	1	no	—
152	C₂×C₈×C₁₁	—	2	1	no	—
153	C₂×C₈×C₁₁	—	2	1	no	—
154	C₂×C₈×C₁₁	—	2	1	no	—
155	C₂×C₈×C₁₁	—	2	1	no	—
156	C₂×C₈×C₁₁	—	2	1	no	—
157	C₂×C₈×C₁₁	—	2	1	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	—	4	4	no	—
166	C₂×C₈×C₁₁	#41	1	2	yes	—
167	C₂×C₈×C₁₁	#41	1	2	yes	—
168	C₁₁×C₄⋊C₄	—	2	2	no	—
169	C₁₁×C₄⋊C₄	—	2	2	no	—
170	C₁₁×C₄⋊C₄	—	2	2	no	—
171	C₁₁×C₄⋊C₄	—	2	2	no	—
172	C₁₁×C₄⋊C₄	—	2	2	no	—
173	C₁₁×C₄⋊C₄	—	4	1	no	—
174	C₁₁×C₂²⋊C₄	—	2	2	no	—
175	C₁₁×C₂²⋊C₄	—	2	2	no	—
176	C₁₁×C₂²⋊C₄	—	2	2	no	—
177	C₁₁×C₂²⋊C₄	—	2	2	no	—
178	C₁₁×C₂²⋊C₄	—	2	2	no	—
179	C₁₁×C₂²⋊C₄	—	4	1	no	—
180	C₄²×C₁₁	—	2	2	no	—
181	C₄²×C₁₁	—	2	2	no	—
182	C₄²×C₁₁	—	2	2	no	—
183	C₄²×C₁₁	—	2	1	no	—
184	C₄²×C₁₁	—	2	1	no	—
185	C₄²×C₁₁	—	2	1	no	—
186	C₄²×C₁₁	—	2	1	no	—
187	C₄²×C₁₁	—	2	1	no	—
188	C₄²×C₁₁	—	2	1	no	—
189	C₄²×C₁₁	—	2	1	no	—
190	C₄²×C₁₁	—	2	1	no	—
191	C₄²×C₁₁	—	2	1	no	—
192	C₄²×C₁₁	—	2	1	no	—
193	C₄²×C₁₁	—	2	1	no	—
194	C₄²×C₁₁	—	2	1	no	—
195	C₄²×C₁₁	—	4	1	no	—
196	#2298	C₂×C₁₁	1	1	yes	characteristic
197	#1917	C₂×C₁₁	1	1	yes	characteristic, complemented
198	#1916	C₂×C₁₁	1	1	yes	characteristic, complemented
199	#1916	C₂×C₁₁	1	1	yes	characteristic, complemented
200	#1916	C₂×C₁₁	1	1	yes	characteristic, complemented
201	#1851	C₂×C₁₁	1	1	yes	characteristic
202	#1850	C₂×C₁₁	1	1	yes	characteristic
203	#1839	C₂×C₁₁	1	1	yes	characteristic, complemented
204	#1832	C₂×C₁₁	1	1	yes	characteristic, complemented
205	#1818	C₂×C₁₁	1	1	yes	characteristic
206	C₄×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
207	#1753	C₂×C₁₁	1	1	yes	characteristic
208	C₈×C₂²⋊C₄	C₂×C₁₁	1	1	yes	characteristic
209	#1746	C₂×C₁₁	1	1	yes	characteristic, complemented
210	#1729	C₂×C₁₁	1	1	yes	characteristic
211	C₂³×C₁₁	—	2	1	no	—
212	C₂³×C₁₁	—	2	1	no	—
213	C₂³×C₁₁	—	2	1	no	—
214	C₂³×C₁₁	—	2	1	no	—
215	C₂³×C₁₁	—	2	1	no	—
216	C₂³×C₁₁	—	2	1	no	—
217	C₂³×C₁₁	#117	1	2	yes	—
218	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₁	—	2	1	no	—
220	C₂×C₄×C₁₁	—	2	1	no	—
221	C₂×C₄×C₁₁	—	2	1	no	—
222	C₂×C₄×C₁₁	—	2	1	no	—
223	C₂×C₄×C₁₁	—	2	1	no	—
224	C₂×C₄×C₁₁	—	2	1	no	—
225	C₂×C₄×C₁₁	—	2	1	no	—
226	C₂×C₄×C₁₁	—	2	1	no	—
227	C₂×C₄×C₁₁	—	2	2	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	1	no	—
234	C₂×C₄×C₁₁	—	2	1	no	—
235	C₂×C₄×C₁₁	—	2	1	no	—
236	C₂×C₄×C₁₁	—	2	1	no	—
237	C₂×C₄×C₁₁	—	2	1	no	—
238	C₂×C₄×C₁₁	—	2	1	no	—
239	C₂×C₄×C₁₁	—	2	1	no	—
240	C₂×C₄×C₁₁	—	2	1	no	—
241	C₂×C₄×C₁₁	—	2	1	no	—
242	C₂×C₄×C₁₁	—	2	1	no	—
243	C₂×C₄×C₁₁	—	2	1	no	—
244	C₂×C₄×C₁₁	—	2	1	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	1	no	—
250	C₂×C₄×C₁₁	—	2	1	no	—
251	C₂×C₄×C₁₁	—	2	1	no	—
252	C₂×C₄×C₁₁	—	2	1	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	#117	1	2	yes	—
259	C₂×C₄×C₁₁	#131	1	2	yes	—
260	C₂×C₄×C₁₁	#131	1	2	yes	—
261	C₂×C₄×C₁₁	#131	1	2	yes	—
262	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
266	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
267	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
268	C₈×C₁₁	—	2	2	no	—
269	C₈×C₁₁	—	2	2	no	—
270	C₈×C₁₁	—	4	1	no	—
271	C₈×C₁₁	—	4	1	no	—
272	C₈×C₁₁	—	4	1	no	—
273	C₈×C₁₁	—	4	1	no	—
274	C₈×C₁₁	—	4	1	no	—
275	C₈×C₁₁	—	4	1	no	—
276	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
277	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
278	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
279	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
282	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
283	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
285	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
286	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
287	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
288	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
289	#388	C₄×C₁₁	1	1	yes	characteristic
290	#388	C₄×C₁₁	1	1	yes	characteristic
291	#388	C₄×C₁₁	1	1	yes	characteristic
292	#388	C₄×C₁₁	1	1	yes	characteristic
293	#387	C₄×C₁₁	1	1	yes	characteristic
294	#387	C₄×C₁₁	1	1	yes	characteristic
295	#387	C₄×C₁₁	1	1	yes	characteristic
296	#387	C₄×C₁₁	1	1	yes	characteristic
297	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
298	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
299	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
300	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
301	#376	C₂²×C₁₁	1	1	yes	characteristic
302	C₄³	C₂²×C₁₁	1	1	yes	characteristic
303	#336	C₂²×C₁₁	1	1	yes	characteristic
304	#336	C₂²×C₁₁	1	1	yes	characteristic
305	#336	C₂²×C₁₁	1	1	yes	characteristic
306	#336	C₂²×C₁₁	1	1	yes	characteristic
307	#336	C₂²×C₁₁	1	1	yes	characteristic
308	#336	C₂²×C₁₁	1	1	yes	characteristic
309	#336	C₂²×C₁₁	1	1	yes	characteristic
310	#336	C₂²×C₁₁	1	1	yes	characteristic
311	#336	C₂²×C₁₁	1	1	yes	characteristic
312	#336	C₂²×C₁₁	1	1	yes	characteristic
313	#336	C₂²×C₁₁	1	1	yes	characteristic
314	#336	C₂²×C₁₁	1	1	yes	characteristic
315	#336	C₂²×C₁₁	1	1	yes	characteristic
316	#336	C₂²×C₁₁	1	1	yes	characteristic
317	#336	C₂²×C₁₁	1	1	yes	characteristic
318	#336	C₂²×C₁₁	1	1	yes	characteristic
319	C₂²×C₁₁	—	2	2	no	—
320	C₂²×C₁₁	—	2	2	no	—
321	C₂²×C₁₁	—	2	2	no	—
322	C₂²×C₁₁	—	4	1	no	—
323	C₂²×C₁₁	—	4	1	no	—
324	C₂²×C₁₁	—	4	1	no	—
325	C₂²×C₁₁	—	4	1	no	—
326	C₂²×C₁₁	C₂×#117	1	1	yes	characteristic
327	C₂²×C₁₁	C₄×#41	1	1	yes	characteristic
328	C₂²×C₁₁	#520	1	1	yes	characteristic
329	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
330	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
331	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
332	C₂²×C₁₁	#568	1	1	yes	characteristic
333	C₄×C₁₁	—	2	2	no	—
334	C₄×C₁₁	—	2	2	no	—
335	C₄×C₁₁	—	2	2	no	—
336	C₄×C₁₁	—	2	2	no	—
337	C₄×C₁₁	—	4	1	no	—
338	C₄×C₁₁	—	4	1	no	—
339	C₄×C₁₁	—	4	1	no	—
340	C₄×C₁₁	—	4	1	no	—
341	C₄×C₁₁	—	4	1	no	—
342	C₄×C₁₁	—	4	1	no	—
343	C₄×C₁₁	—	4	1	no	—
344	C₄×C₁₁	—	4	1	no	—
345	C₄×C₁₁	—	4	1	no	—
346	C₄×C₁₁	#551	1	1	yes	characteristic
347	C₄×C₁₁	#551	1	1	yes	characteristic
348	C₄×C₁₁	#552	1	1	yes	characteristic
349	C₄×C₁₁	#552	1	1	yes	characteristic
350	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
351	C₂×M₁₆	—	2	2	no	—
352	C₂×M₁₆	—	2	2	no	—
353	C₂×M₁₆	—	4	1	no	—
354	C₂²×C₈	—	2	2	no	—
355	C₂²×C₈	—	2	2	no	—
356	C₂²×C₈	—	4	1	no	—
357	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
358	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
359	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
360	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
361	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
362	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
365	#117	—	2	2	no	—
366	#117	—	2	2	no	—
367	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
373	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
374	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
375	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
377	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
378	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
379	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
380	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
381	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
382	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
384	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
385	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
388	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
389	C₄⋊C₈	—	2	2	no	—
390	C₄⋊C₈	—	2	2	no	—
391	C₄⋊C₈	—	4	1	no	—
392	C₄⋊C₈	—	4	1	no	—
393	C₂²⋊C₈	—	2	2	no	—
394	C₂²⋊C₈	—	2	2	no	—
395	#97	—	2	2	no	—
396	C₄×C₈	—	2	2	no	—
397	C₄×C₈	—	4	1	no	—
398	C₄×C₈	—	4	1	no	—
399	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
400	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
401	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
402	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
403	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
404	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
405	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
406	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
407	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
408	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
409	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
410	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
411	C₂×C₁₁	—	4	2	no	—
412	C₂×C₁₁	#2343	1	1	yes	characteristic
413	C₂×C₁₁	#2922	1	1	yes	characteristic
414	C₂×C₁₁	#2925	1	1	yes	characteristic
415	C₂×C₁₁	#2966	1	1	yes	characteristic
416	C₂×C₁₁	#2969	1	1	yes	characteristic
417	C₂×C₁₁	#2992	1	1	yes	characteristic
418	C₂×C₁₁	#2994	1	1	yes	characteristic
419	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
425	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
426	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
427	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
428	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
429	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
430	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
431	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
432	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
433	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
434	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
435	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
436	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
437	C₂²×C₄	C₁₁×#41	1	2	yes	—
438	C₂²×C₄	C₁₁×#41	1	2	yes	—
439	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
440	M₁₆	—	4	4	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	4	4	no	—
464	C₂×C₈	C₁₁×#41	1	2	yes	—
465	C₂×C₈	C₁₁×#41	1	2	yes	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	2	2	no	—
476	C₂²⋊C₄	—	2	2	no	—
477	C₂²⋊C₄	—	4	1	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	4	1	no	—
494	C₁₁	#22597	1	1	yes	characteristic, direct product factor, Sylow
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	C₁₁×#117	1	2	yes	—
502	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	C₁₁×#117	1	2	yes	—
543	C₂×C₄	C₁₁×#131	1	2	yes	—
544	C₂×C₄	C₁₁×#131	1	2	yes	—
545	C₂×C₄	C₁₁×#131	1	2	yes	—
546	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
547	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
548	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
549	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
550	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
551	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
552	C₈	—	2	2	no	—
553	C₈	—	2	2	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	1	no	—
556	C₈	—	4	1	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	C₂×C₁₁×#117	1	1	yes	characteristic
568	C₂²	C₄×C₁₁×#41	1	1	yes	characteristic
569	C₂²	C₁₁×#520	1	1	yes	characteristic
570	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
571	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
572	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
573	C₂²	C₁₁×#568	1	1	yes	characteristic
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	C₁₁×#551	1	1	yes	characteristic
588	C₄	C₁₁×#551	1	1	yes	characteristic
589	C₄	C₁₁×#552	1	1	yes	characteristic
590	C₄	C₁₁×#552	1	1	yes	characteristic
591	C₂	—	4	2	no	—
592	C₂	C₁₁×#2343	1	1	yes	characteristic
593	C₂	C₁₁×#2922	1	1	yes	characteristic
594	C₂	C₁₁×#2925	1	1	yes	characteristic
595	C₂	C₁₁×#2966	1	1	yes	characteristic
596	C₂	C₁₁×#2969	1	1	yes	characteristic
597	C₂	C₁₁×#2992	1	1	yes	characteristic
598	C₂	C₁₁×#2994	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	C₂⁴×C₁₁	C₂²×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×#1917	C₂	semidirect
3. C₁₁×#1916	C₂	semidirect
4. C₁₁×#1916	C₂	semidirect
5. C₁₁×#1916	C₂	semidirect
8. C₁₁×#1839	C₂	semidirect
9. C₁₁×#1832	C₂	semidirect
11. C₄×C₁₁×C₄⋊C₈	C₂	semidirect
14. C₁₁×#1746	C₂	semidirect
120. #22597	C₁₁	direct (N × H)
197. #1917	C₂×C₁₁	semidirect
198. #1916	C₂×C₁₁	semidirect
199. #1916	C₂×C₁₁	semidirect
200. #1916	C₂×C₁₁	semidirect
203. #1839	C₂×C₁₁	semidirect
204. #1832	C₂×C₁₁	semidirect
206. C₄×C₄⋊C₈	C₂×C₁₁	semidirect
209. #1746	C₂×C₁₁	semidirect
494. C₁₁	#22597	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×#2298	2
C₁₁×#1917	2
C₁₁×#1916	2
C₁₁×#1851	2
C₁₁×#1850	2
C₁₁×#1839	2
C₁₁×#1832	2
C₁₁×#1818	2
C₄×C₁₁×C₄⋊C₈	2
C₁₁×#1753	2
C₈×C₁₁×C₂²⋊C₄	2
C₁₁×#1746	2
C₁₁×#1729	2
#22597	11

Subgroups — C11×#22597 #14599790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22597 #14599790