Subgroups — C₁₁×#22074 #14599267

Order 2816.

816 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#436	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2395	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1924	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1923	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1916	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1916	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1869	C₂	1	1	yes	maximal, characteristic
11	C₁₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₁×#1850	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₁×#1818	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
21	C₁₁×#436	—	2	4	no	—
22	C₁₁×#424	—	2	4	no	—
23	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
38	C₁₁×#400	C₄	1	1	yes	characteristic
39	C₁₁×#399	C₄	1	1	yes	characteristic
40	C₁₁×#398	C₄	1	1	yes	characteristic
41	C₁₁×#397	C₄	1	1	yes	characteristic
42	C₁₁×#397	C₄	1	1	yes	characteristic
43	C₁₁×#397	C₄	1	1	yes	characteristic
44	C₁₁×#394	C₄	1	1	yes	characteristic
45	C₁₁×#394	C₄	1	1	yes	characteristic
46	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₁₁×C₂²⋊C₄	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	C₁₁×#336	C₂²	1	1	yes	characteristic
60	C₁₁×#336	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
64	C₂×C₁₁×M₁₆	—	2	2	no	—
65	C₂×C₁₁×M₁₆	—	4	1	no	—
66	C₂×C₁₁×M₁₆	—	4	1	no	—
67	C₂×C₁₁×M₁₆	—	4	1	no	—
68	C₂×C₁₁×M₁₆	—	4	1	no	—
69	C₂×C₁₁×M₁₆	D₄	1	4	yes	—
70	C₂²×C₈×C₁₁	—	2	2	no	—
71	C₂²×C₈×C₁₁	—	4	1	no	—
72	C₂²×C₈×C₁₁	—	4	1	no	—
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	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
81	C₄×D₄×C₁₁	—	2	2	no	—
82	C₄×D₄×C₁₁	—	2	2	no	—
83	C₁₁×#117	—	2	2	no	—
84	C₁₁×#117	—	2	2	no	—
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×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×C₁₁×C₄⋊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×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄²×C₁₁	C₂³	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	C₁₁×C₄⋊C₈	—	2	2	no	—
108	C₁₁×C₄⋊C₈	—	2	2	no	—
109	C₁₁×C₄⋊C₈	—	2	2	no	—
110	C₁₁×C₄⋊C₈	—	2	2	no	—
111	C₁₁×C₄⋊C₈	—	2	2	no	—
112	C₁₁×C₄⋊C₈	—	4	1	no	—
113	C₁₁×C₄⋊C₈	—	4	1	no	—
114	C₁₁×C₂²⋊C₈	—	2	2	no	—
115	C₁₁×C₂²⋊C₈	—	2	2	no	—
116	C₁₁×C₂²⋊C₈	—	2	2	no	—
117	C₁₁×C₂²⋊C₈	—	4	1	no	—
118	C₁₁×C₂²⋊C₈	—	4	1	no	—
119	C₁₁×#97	—	4	1	no	—
120	C₄×C₈×C₁₁	—	2	2	no	—
121	C₄×C₈×C₁₁	—	4	1	no	—
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	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
127	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
128	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
129	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
130	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
131	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
132	#22074	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
134	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
135	C₂×D₄×C₁₁	—	2	2	no	—
136	C₂×D₄×C₁₁	—	2	2	no	—
137	C₂×D₄×C₁₁	—	4	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	—	2	1	no	—
143	C₂²×C₄×C₁₁	—	2	1	no	—
144	C₂²×C₄×C₁₁	—	2	1	no	—
145	C₂²×C₄×C₁₁	—	2	1	no	—
146	C₂²×C₄×C₁₁	—	2	1	no	—
147	C₂²×C₄×C₁₁	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₁	#41	1	2	yes	—
162	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
163	C₁₁×M₁₆	—	4	4	no	—
164	C₁₁×M₁₆	—	4	4	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	—	2	1	no	—
181	C₂×C₈×C₁₁	—	2	1	no	—
182	C₂×C₈×C₁₁	—	2	1	no	—
183	C₂×C₈×C₁₁	—	2	1	no	—
184	C₂×C₈×C₁₁	—	2	1	no	—
185	C₂×C₈×C₁₁	—	2	1	no	—
186	C₂×C₈×C₁₁	—	2	1	no	—
187	C₂×C₈×C₁₁	—	4	4	no	—
188	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
189	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
190	C₁₁×C₄⋊C₄	—	2	2	no	—
191	C₁₁×C₄⋊C₄	—	2	2	no	—
192	C₁₁×C₄⋊C₄	—	2	2	no	—
193	C₁₁×C₄⋊C₄	—	2	2	no	—
194	C₁₁×C₄⋊C₄	—	2	2	no	—
195	C₁₁×C₄⋊C₄	—	2	2	no	—
196	C₁₁×C₄⋊C₄	—	4	1	no	—
197	C₁₁×C₂²⋊C₄	—	2	2	no	—
198	C₁₁×C₂²⋊C₄	—	2	2	no	—
199	C₁₁×C₂²⋊C₄	—	2	2	no	—
200	C₁₁×C₂²⋊C₄	—	2	2	no	—
201	C₁₁×C₂²⋊C₄	—	2	2	no	—
202	C₁₁×C₂²⋊C₄	—	2	2	no	—
203	C₁₁×C₂²⋊C₄	—	4	1	no	—
204	C₁₁×C₂²⋊C₄	—	4	1	no	—
205	C₁₁×C₂²⋊C₄	—	4	1	no	—
206	C₁₁×C₂²⋊C₄	—	4	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	—	2	1	no	—
212	C₄²×C₁₁	—	2	1	no	—
213	C₄²×C₁₁	—	2	1	no	—
214	C₄²×C₁₁	—	2	1	no	—
215	C₄²×C₁₁	—	2	1	no	—
216	C₄²×C₁₁	—	2	1	no	—
217	C₂×#436	C₂×C₁₁	1	1	yes	characteristic
218	C₂×#424	C₂×C₁₁	1	1	yes	characteristic, complemented
219	#2395	C₂×C₁₁	1	1	yes	characteristic
220	#1940	C₂×C₁₁	1	1	yes	characteristic, complemented
221	#1939	C₂×C₁₁	1	1	yes	characteristic, complemented
222	#1924	C₂×C₁₁	1	1	yes	characteristic, complemented
223	#1923	C₂×C₁₁	1	1	yes	characteristic, complemented
224	#1916	C₂×C₁₁	1	1	yes	characteristic, complemented
225	#1916	C₂×C₁₁	1	1	yes	characteristic, complemented
226	#1869	C₂×C₁₁	1	1	yes	characteristic
227	#1851	C₂×C₁₁	1	1	yes	characteristic, complemented
228	#1851	C₂×C₁₁	1	1	yes	characteristic, complemented
229	#1850	C₂×C₁₁	1	1	yes	characteristic, complemented
230	#1818	C₂×C₁₁	1	1	yes	characteristic, complemented
231	#1753	C₂×C₁₁	1	1	yes	characteristic, complemented
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	—	2	1	no	—
243	C₂³×C₁₁	—	2	1	no	—
244	C₂³×C₁₁	—	2	1	no	—
245	C₂³×C₁₁	C₄×D₄	1	2	yes	—
246	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
247	D₄×C₁₁	—	4	4	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	2	no	—
255	C₂×C₄×C₁₁	—	2	2	no	—
256	C₂×C₄×C₁₁	—	2	2	no	—
257	C₂×C₄×C₁₁	—	2	2	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	—	2	1	no	—
284	C₂×C₄×C₁₁	—	2	1	no	—
285	C₂×C₄×C₁₁	—	4	1	no	—
286	C₂×C₄×C₁₁	—	4	1	no	—
287	C₂×C₄×C₁₁	—	4	1	no	—
288	C₂×C₄×C₁₁	—	4	1	no	—
289	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
290	C₂×C₄×C₁₁	#131	1	2	yes	—
291	C₂×C₄×C₁₁	#131	1	2	yes	—
292	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
295	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
296	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
297	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
298	C₈×C₁₁	—	2	2	no	—
299	C₈×C₁₁	—	2	2	no	—
300	C₈×C₁₁	—	4	1	no	—
301	C₈×C₁₁	—	4	1	no	—
302	C₈×C₁₁	—	4	1	no	—
303	C₈×C₁₁	—	4	1	no	—
304	C₈×C₁₁	—	4	1	no	—
305	C₈×C₁₁	—	4	1	no	—
306	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
307	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
308	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
309	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
310	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
311	#436	—	2	4	no	—
312	#424	—	2	4	no	—
313	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
314	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
315	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
316	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
317	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
318	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
319	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
320	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
321	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
322	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
323	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
324	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
325	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
326	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
327	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
328	#400	C₄×C₁₁	1	1	yes	characteristic
329	#399	C₄×C₁₁	1	1	yes	characteristic
330	#398	C₄×C₁₁	1	1	yes	characteristic
331	#397	C₄×C₁₁	1	1	yes	characteristic
332	#397	C₄×C₁₁	1	1	yes	characteristic
333	#397	C₄×C₁₁	1	1	yes	characteristic
334	#394	C₄×C₁₁	1	1	yes	characteristic
335	#394	C₄×C₁₁	1	1	yes	characteristic
336	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
337	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
338	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
339	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
340	C₄×C₂²⋊C₄	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	#336	C₂²×C₁₁	1	1	yes	characteristic
347	#336	C₂²×C₁₁	1	1	yes	characteristic
348	#336	C₂²×C₁₁	1	1	yes	characteristic
349	#336	C₂²×C₁₁	1	1	yes	characteristic
350	#336	C₂²×C₁₁	1	1	yes	characteristic
351	C₂²×C₁₁	—	2	2	no	—
352	C₂²×C₁₁	—	2	2	no	—
353	C₂²×C₁₁	—	2	2	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	—	4	1	no	—
361	C₂²×C₁₁	—	4	1	no	—
362	C₂²×C₁₁	—	4	1	no	—
363	C₂²×C₁₁	—	4	1	no	—
364	C₂²×C₁₁	—	4	1	no	—
365	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
366	C₂²×C₁₁	#520	1	1	yes	characteristic
367	C₂²×C₁₁	#520	1	1	yes	characteristic
368	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
369	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
370	C₂²×C₁₁	#568	1	1	yes	characteristic
371	C₂²×C₁₁	#568	1	1	yes	characteristic
372	C₄×C₁₁	—	2	2	no	—
373	C₄×C₁₁	—	2	2	no	—
374	C₄×C₁₁	—	2	2	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	—	4	1	no	—
380	C₄×C₁₁	—	4	1	no	—
381	C₄×C₁₁	—	4	1	no	—
382	C₄×C₁₁	—	4	1	no	—
383	C₄×C₁₁	—	4	1	no	—
384	C₄×C₁₁	#534	1	1	yes	characteristic
385	C₄×C₁₁	#536	1	1	yes	characteristic
386	C₄×C₁₁	#539	1	1	yes	characteristic
387	C₄×C₁₁	#539	1	1	yes	characteristic
388	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
389	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
391	C₂×M₁₆	—	2	2	no	—
392	C₂×M₁₆	—	4	1	no	—
393	C₂×M₁₆	—	4	1	no	—
394	C₂×M₁₆	—	4	1	no	—
395	C₂×M₁₆	—	4	1	no	—
396	C₂×M₁₆	D₄×C₁₁	1	4	yes	—
397	C₂²×C₈	—	2	2	no	—
398	C₂²×C₈	—	4	1	no	—
399	C₂²×C₈	—	4	1	no	—
400	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
401	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
402	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
403	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
404	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
405	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
406	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
407	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	2	no	—
410	#117	—	2	2	no	—
411	#117	—	2	2	no	—
412	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
418	C₂×C₄⋊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×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
427	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
428	C₂×C₂²⋊C₄	C₂×C₄×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	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
434	C₄⋊C₈	—	2	2	no	—
435	C₄⋊C₈	—	2	2	no	—
436	C₄⋊C₈	—	2	2	no	—
437	C₄⋊C₈	—	2	2	no	—
438	C₄⋊C₈	—	2	2	no	—
439	C₄⋊C₈	—	4	1	no	—
440	C₄⋊C₈	—	4	1	no	—
441	C₂²⋊C₈	—	2	2	no	—
442	C₂²⋊C₈	—	2	2	no	—
443	C₂²⋊C₈	—	2	2	no	—
444	C₂²⋊C₈	—	4	1	no	—
445	C₂²⋊C₈	—	4	1	no	—
446	#97	—	4	1	no	—
447	C₄×C₈	—	2	2	no	—
448	C₄×C₈	—	4	1	no	—
449	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
450	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
451	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
452	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
453	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
454	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
455	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
456	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
457	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
458	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
459	C₂×C₁₁	—	4	2	no	—
460	C₂×C₁₁	—	8	1	no	—
461	C₂×C₁₁	#2322	1	1	yes	characteristic
462	C₂×C₁₁	#2933	1	1	yes	characteristic
463	C₂×C₁₁	#2935	1	1	yes	characteristic
464	C₂×C₁₁	#2993	1	1	yes	characteristic
465	C₂×C₁₁	#2993	1	1	yes	characteristic
466	C₂×C₁₁	#2994	1	1	yes	characteristic
467	C₂×C₁₁	#2995	1	1	yes	characteristic
468	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
469	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	4	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
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	C₂²×C₄×C₁₁	1	1	yes	characteristic
487	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
488	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
489	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
490	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
491	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
492	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
493	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
494	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
496	C₂²×C₄	C₁₁×#41	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
498	M₁₆	—	4	4	no	—
499	M₁₆	—	4	4	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	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	4	4	no	—
523	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
524	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	4	1	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	2	no	—
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	4	1	no	—
539	C₂²⋊C₄	—	4	1	no	—
540	C₂²⋊C₄	—	4	1	no	—
541	C₂²⋊C₄	—	4	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₁₁	#22074	1	1	yes	characteristic, direct product factor, Sylow
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	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	C₄×D₄×C₁₁	1	2	yes	—
567	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
568	D₄	—	4	4	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	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	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	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	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
611	C₂×C₄	C₁₁×#131	1	2	yes	—
612	C₂×C₄	C₁₁×#131	1	2	yes	—
613	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
614	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
615	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
616	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
617	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
618	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
619	C₈	—	2	2	no	—
620	C₈	—	2	2	no	—
621	C₈	—	4	1	no	—
622	C₈	—	4	1	no	—
623	C₈	—	4	1	no	—
624	C₈	—	4	1	no	—
625	C₈	—	4	1	no	—
626	C₈	—	4	1	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	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	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	1	no	—
641	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
642	C₂²	C₁₁×#520	1	1	yes	characteristic
643	C₂²	C₁₁×#520	1	1	yes	characteristic
644	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
645	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
646	C₂²	C₁₁×#568	1	1	yes	characteristic
647	C₂²	C₁₁×#568	1	1	yes	characteristic
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	4	1	no	—
655	C₄	—	4	1	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	1	no	—
659	C₄	—	4	1	no	—
660	C₄	C₁₁×#534	1	1	yes	characteristic
661	C₄	C₁₁×#536	1	1	yes	characteristic
662	C₄	C₁₁×#539	1	1	yes	characteristic
663	C₄	C₁₁×#539	1	1	yes	characteristic
664	C₂	—	4	2	no	—
665	C₂	—	8	1	no	—
666	C₂	C₁₁×#2322	1	1	yes	characteristic
667	C₂	C₁₁×#2933	1	1	yes	characteristic
668	C₂	C₁₁×#2935	1	1	yes	characteristic
669	C₂	C₁₁×#2993	1	1	yes	characteristic
670	C₂	C₁₁×#2993	1	1	yes	characteristic
671	C₂	C₁₁×#2994	1	1	yes	characteristic
672	C₂	C₁₁×#2995	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. C₂×C₁₁×#424	C₂	semidirect
4. C₁₁×#1940	C₂	semidirect
5. C₁₁×#1939	C₂	semidirect
6. C₁₁×#1924	C₂	semidirect
7. C₁₁×#1923	C₂	semidirect
8. C₁₁×#1916	C₂	semidirect
9. C₁₁×#1916	C₂	semidirect
11. C₁₁×#1851	C₂	semidirect
12. C₁₁×#1851	C₂	semidirect
13. C₁₁×#1850	C₂	semidirect
14. C₁₁×#1818	C₂	semidirect
15. C₁₁×#1753	C₂	semidirect
132. #22074	C₁₁	direct (N × H)
218. C₂×#424	C₂×C₁₁	semidirect
220. #1940	C₂×C₁₁	semidirect
221. #1939	C₂×C₁₁	semidirect
222. #1924	C₂×C₁₁	semidirect
223. #1923	C₂×C₁₁	semidirect
224. #1916	C₂×C₁₁	semidirect
225. #1916	C₂×C₁₁	semidirect
227. #1851	C₂×C₁₁	semidirect
228. #1851	C₂×C₁₁	semidirect
229. #1850	C₂×C₁₁	semidirect
230. #1818	C₂×C₁₁	semidirect
231. #1753	C₂×C₁₁	semidirect
552. C₁₁	#22074	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#436	2
C₂×C₁₁×#424	2
C₁₁×#2395	2
C₁₁×#1940	2
C₁₁×#1939	2
C₁₁×#1924	2
C₁₁×#1923	2
C₁₁×#1916	2
C₁₁×#1869	2
C₁₁×#1851	2
C₁₁×#1850	2
C₁₁×#1818	2
C₁₁×#1753	2
#22074	11

Subgroups — C11×#22074 #14599267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22074 #14599267