Subgroups — C₁₁×#22990 #14600183

Order 2816.

1064 conjugacy classes of subgroups.

The subgroup lattice has 552 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	2	yes	maximal, complemented
2	C₂×C₁₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₁×#121	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1954	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1923	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1870	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1851	C₂	1	2	yes	maximal, complemented
10	C₈×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₁×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
13	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
14	C₂×C₁₁×#121	C₄	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
18	C₁₁×#436	—	2	4	no	—
19	C₁₁×#436	—	2	8	no	—
20	C₁₁×#423	—	2	4	no	—
21	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₁₁	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×#389	C₄	1	1	yes	characteristic
35	C₁₁×#388	C₄	1	2	yes	—
36	C₁₁×#386	C₄	1	2	yes	—
37	C₁₁×#380	C₄	1	1	yes	characteristic
38	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₁₁×#336	C₂²	1	2	yes	—
41	C₁₁×#336	C₂²	1	2	yes	—
42	C₁₁×#336	C₂²	1	1	yes	characteristic
43	C₁₁×#336	C₂²	1	1	yes	characteristic
44	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
50	C₂×C₁₁×M₁₆	—	2	4	no	—
51	C₂×C₁₁×M₁₆	—	2	4	no	—
52	C₂×C₁₁×M₁₆	—	2	4	no	—
53	C₂×C₁₁×M₁₆	—	2	4	no	—
54	C₂×C₁₁×M₁₆	—	4	2	no	—
55	C₂×C₁₁×M₁₆	—	4	2	no	—
56	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
61	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
62	C₁₁×#121	—	2	4	no	—
63	C₄×D₄×C₁₁	—	2	4	no	—
64	C₄×D₄×C₁₁	—	2	4	no	—
65	C₄×D₄×C₁₁	—	2	2	no	—
66	C₄×D₄×C₁₁	—	2	2	no	—
67	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
73	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
74	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
75	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
76	C₂×C₄²×C₁₁	—	2	2	no	—
77	C₂×C₄²×C₁₁	—	2	2	no	—
78	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
82	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
83	C₁₁×C₄⋊C₈	—	2	4	no	—
84	C₁₁×C₄⋊C₈	—	2	4	no	—
85	C₁₁×C₄⋊C₈	—	2	2	no	—
86	C₁₁×C₄⋊C₈	D₄	1	4	yes	complemented
87	C₁₁×C₂²⋊C₈	—	2	2	no	—
88	C₁₁×C₂²⋊C₈	—	2	4	no	—
89	C₁₁×C₂²⋊C₈	—	2	4	no	—
90	C₁₁×C₂²⋊C₈	—	4	2	no	—
91	C₁₁×C₂²⋊C₈	D₄	1	4	yes	complemented
92	C₄×C₈×C₁₁	—	2	4	no	—
93	C₄×C₈×C₁₁	—	2	2	no	—
94	C₄×C₈×C₁₁	—	2	2	no	—
95	C₁₁×#95	C₂×C₄	1	2	yes	—
96	C₁₁×#95	C₂×C₄	1	2	yes	—
97	C₁₁×#95	C₂×C₄	1	2	yes	—
98	#22990	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
100	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
101	C₂×D₄×C₁₁	—	2	4	no	—
102	C₂×D₄×C₁₁	—	2	2	no	—
103	C₂×D₄×C₁₁	—	2	4	no	—
104	C₂×D₄×C₁₁	—	2	2	no	—
105	C₂×D₄×C₁₁	—	2	2	no	—
106	C₂×D₄×C₁₁	—	4	2	no	—
107	C₂²×C₄×C₁₁	—	2	1	no	—
108	C₂²×C₄×C₁₁	—	2	1	no	—
109	C₂²×C₄×C₁₁	—	2	1	no	—
110	C₂²×C₄×C₁₁	—	2	1	no	—
111	C₂²×C₄×C₁₁	—	2	2	no	—
112	C₂²×C₄×C₁₁	—	2	2	no	—
113	C₂²×C₄×C₁₁	—	2	2	no	—
114	C₂²×C₄×C₁₁	—	2	2	no	—
115	C₂²×C₄×C₁₁	—	2	2	no	—
116	C₂²×C₄×C₁₁	—	2	2	no	—
117	C₂²×C₄×C₁₁	—	2	2	no	—
118	C₂²×C₄×C₁₁	—	2	2	no	—
119	C₂²×C₄×C₁₁	—	2	2	no	—
120	C₂²×C₄×C₁₁	—	2	2	no	—
121	C₂²×C₄×C₁₁	—	2	2	no	—
122	C₂²×C₄×C₁₁	—	4	1	no	—
123	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
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	2	yes	—
129	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₁	#41	1	2	yes	—
133	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
134	C₁₁×M₁₆	—	4	8	no	—
135	C₁₁×M₁₆	—	4	8	no	—
136	C₂×C₈×C₁₁	—	2	2	no	—
137	C₂×C₈×C₁₁	—	2	1	no	—
138	C₂×C₈×C₁₁	—	2	1	no	—
139	C₂×C₈×C₁₁	—	2	2	no	—
140	C₂×C₈×C₁₁	—	2	2	no	—
141	C₂×C₈×C₁₁	—	2	1	no	—
142	C₂×C₈×C₁₁	—	2	1	no	—
143	C₂×C₈×C₁₁	—	2	1	no	—
144	C₂×C₈×C₁₁	—	2	1	no	—
145	C₂×C₈×C₁₁	—	2	2	no	—
146	C₂×C₈×C₁₁	—	2	1	no	—
147	C₂×C₈×C₁₁	—	2	1	no	—
148	C₂×C₈×C₁₁	—	2	2	no	—
149	C₂×C₈×C₁₁	—	2	1	no	—
150	C₂×C₈×C₁₁	—	2	1	no	—
151	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
153	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
154	C₁₁×C₄⋊C₄	—	2	4	no	—
155	C₁₁×C₄⋊C₄	—	2	2	no	—
156	C₁₁×C₄⋊C₄	—	2	2	no	—
157	C₁₁×C₄⋊C₄	M₁₆	1	4	yes	complemented
158	C₁₁×C₂²⋊C₄	—	2	4	no	—
159	C₁₁×C₂²⋊C₄	—	2	4	no	—
160	C₁₁×C₂²⋊C₄	—	2	4	no	—
161	C₁₁×C₂²⋊C₄	—	2	4	no	—
162	C₁₁×C₂²⋊C₄	—	2	4	no	—
163	C₄²×C₁₁	—	2	2	no	—
164	C₄²×C₁₁	—	2	2	no	—
165	C₄²×C₁₁	—	2	2	no	—
166	C₄²×C₁₁	—	2	1	no	—
167	C₄²×C₁₁	—	2	1	no	—
168	C₄²×C₁₁	—	2	2	no	—
169	C₄²×C₁₁	C₂×D₄	1	2	yes	—
170	C₄²×C₁₁	#41	1	2	yes	—
171	C₂×#436	C₂×C₁₁	1	2	yes	complemented
172	C₂×#436	C₂×C₁₁	1	1	yes	characteristic, complemented
173	C₂×#423	C₂×C₁₁	1	1	yes	characteristic, complemented
174	C₄×#121	C₂×C₁₁	1	1	yes	characteristic
175	#1954	C₂×C₁₁	1	1	yes	characteristic, complemented
176	#1939	C₂×C₁₁	1	1	yes	characteristic, complemented
177	#1923	C₂×C₁₁	1	2	yes	complemented
178	#1870	C₂×C₁₁	1	2	yes	complemented
179	#1851	C₂×C₁₁	1	2	yes	complemented
180	C₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
181	C₄×C₂²⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
182	C₂³×C₁₁	—	2	1	no	—
183	C₂³×C₁₁	—	2	1	no	—
184	C₂³×C₁₁	—	2	1	no	—
185	C₂³×C₁₁	—	2	1	no	—
186	C₂³×C₁₁	—	2	1	no	—
187	C₂³×C₁₁	—	2	1	no	—
188	C₂³×C₁₁	—	2	2	no	—
189	C₂³×C₁₁	—	2	2	no	—
190	C₂³×C₁₁	—	2	2	no	—
191	C₂³×C₁₁	—	2	2	no	—
192	C₂³×C₁₁	—	2	2	no	—
193	C₂³×C₁₁	—	2	2	no	—
194	C₂³×C₁₁	—	2	2	no	—
195	C₂³×C₁₁	C₄×D₄	1	2	yes	—
196	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
197	D₄×C₁₁	—	4	8	no	—
198	D₄×C₁₁	—	4	4	no	—
199	C₂×C₄×C₁₁	—	2	1	no	—
200	C₂×C₄×C₁₁	—	2	1	no	—
201	C₂×C₄×C₁₁	—	2	2	no	—
202	C₂×C₄×C₁₁	—	2	1	no	—
203	C₂×C₄×C₁₁	—	2	1	no	—
204	C₂×C₄×C₁₁	—	2	1	no	—
205	C₂×C₄×C₁₁	—	2	1	no	—
206	C₂×C₄×C₁₁	—	2	2	no	—
207	C₂×C₄×C₁₁	—	2	2	no	—
208	C₂×C₄×C₁₁	—	2	2	no	—
209	C₂×C₄×C₁₁	—	2	2	no	—
210	C₂×C₄×C₁₁	—	2	2	no	—
211	C₂×C₄×C₁₁	—	2	1	no	—
212	C₂×C₄×C₁₁	—	2	2	no	—
213	C₂×C₄×C₁₁	—	2	2	no	—
214	C₂×C₄×C₁₁	—	2	2	no	—
215	C₂×C₄×C₁₁	—	2	2	no	—
216	C₂×C₄×C₁₁	—	2	1	no	—
217	C₂×C₄×C₁₁	—	2	2	no	—
218	C₂×C₄×C₁₁	—	2	2	no	—
219	C₂×C₄×C₁₁	—	2	1	no	—
220	C₂×C₄×C₁₁	—	4	4	no	—
221	C₂×C₄×C₁₁	—	4	2	no	—
222	C₂×C₄×C₁₁	—	4	2	no	—
223	C₂×C₄×C₁₁	—	4	2	no	—
224	C₂×C₄×C₁₁	—	4	2	no	—
225	C₂×C₄×C₁₁	—	4	4	no	—
226	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
227	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
228	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
229	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
230	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
231	C₂×C₄×C₁₁	#131	1	2	yes	—
232	C₂×C₄×C₁₁	#131	1	2	yes	—
233	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
239	C₈×C₁₁	—	2	4	no	—
240	C₈×C₁₁	—	2	2	no	—
241	C₈×C₁₁	—	2	2	no	—
242	C₈×C₁₁	—	4	2	no	—
243	C₈×C₁₁	—	4	1	no	—
244	C₈×C₁₁	—	4	1	no	—
245	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
246	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
247	C₂×#121	C₄×C₁₁	1	1	yes	characteristic
248	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
249	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
250	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
251	#436	—	2	4	no	—
252	#436	—	2	8	no	—
253	#423	—	2	4	no	—
254	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
255	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
256	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
257	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
258	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
259	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
260	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
261	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
262	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
263	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
264	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
265	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
266	#390	C₄×C₁₁	1	1	yes	characteristic
267	#389	C₄×C₁₁	1	1	yes	characteristic
268	#388	C₄×C₁₁	1	2	yes	—
269	#386	C₄×C₁₁	1	2	yes	—
270	#380	C₄×C₁₁	1	1	yes	characteristic
271	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
272	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
273	#336	C₂²×C₁₁	1	1	yes	characteristic
274	#336	C₂²×C₁₁	1	2	yes	—
275	#336	C₂²×C₁₁	1	2	yes	—
276	#336	C₂²×C₁₁	1	1	yes	characteristic
277	C₂²×C₁₁	—	2	2	no	—
278	C₂²×C₁₁	—	2	2	no	—
279	C₂²×C₁₁	—	2	2	no	—
280	C₂²×C₁₁	—	4	1	no	—
281	C₂²×C₁₁	—	4	1	no	—
282	C₂²×C₁₁	—	4	1	no	—
283	C₂²×C₁₁	—	4	1	no	—
284	C₂²×C₁₁	—	4	2	no	—
285	C₂²×C₁₁	—	4	2	no	—
286	C₂²×C₁₁	—	4	2	no	—
287	C₂²×C₁₁	—	4	2	no	—
288	C₂²×C₁₁	—	4	2	no	—
289	C₂²×C₁₁	—	4	2	no	—
290	C₂²×C₁₁	—	4	2	no	—
291	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
292	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
293	C₂²×C₁₁	#520	1	1	yes	characteristic
294	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
295	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
296	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
297	C₂²×C₁₁	#568	1	1	yes	characteristic
298	C₄×C₁₁	—	2	2	no	—
299	C₄×C₁₁	—	2	2	no	—
300	C₄×C₁₁	—	2	2	no	—
301	C₄×C₁₁	—	2	4	no	—
302	C₄×C₁₁	—	4	2	no	—
303	C₄×C₁₁	—	4	1	no	—
304	C₄×C₁₁	—	4	2	no	—
305	C₄×C₁₁	#436	1	4	yes	complemented
306	C₄×C₁₁	D₄²	1	1	yes	characteristic
307	C₄×C₁₁	#547	1	1	yes	characteristic
308	C₄×C₁₁	#548	1	1	yes	characteristic
309	C₄×C₁₁	#553	1	1	yes	characteristic
310	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
311	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
312	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
313	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
314	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
315	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
316	C₂×M₁₆	—	2	4	no	—
317	C₂×M₁₆	—	2	4	no	—
318	C₂×M₁₆	—	2	4	no	—
319	C₂×M₁₆	—	2	4	no	—
320	C₂×M₁₆	—	4	2	no	—
321	C₂×M₁₆	—	4	2	no	—
322	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
323	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
325	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
326	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
328	#121	—	2	4	no	—
329	C₄×D₄	—	2	4	no	—
330	C₄×D₄	—	2	4	no	—
331	C₄×D₄	—	2	2	no	—
332	C₄×D₄	—	2	2	no	—
333	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
335	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
338	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
339	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
340	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
341	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	—	2	2	no	—
344	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
345	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
346	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
347	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
348	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
349	C₄⋊C₈	—	2	4	no	—
350	C₄⋊C₈	—	2	4	no	—
351	C₄⋊C₈	—	2	2	no	—
352	C₄⋊C₈	D₄×C₁₁	1	4	yes	complemented
353	C₂²⋊C₈	—	2	2	no	—
354	C₂²⋊C₈	—	2	4	no	—
355	C₂²⋊C₈	—	2	4	no	—
356	C₂²⋊C₈	—	4	2	no	—
357	C₂²⋊C₈	D₄×C₁₁	1	4	yes	complemented
358	C₄×C₈	—	2	4	no	—
359	C₄×C₈	—	2	2	no	—
360	C₄×C₈	—	2	2	no	—
361	#95	C₂×C₄×C₁₁	1	2	yes	—
362	#95	C₂×C₄×C₁₁	1	2	yes	—
363	#95	C₂×C₄×C₁₁	1	2	yes	—
364	C₂×C₁₁	—	4	2	no	—
365	C₂×C₁₁	—	8	2	no	—
366	C₂×C₁₁	#2361	1	1	yes	characteristic
367	C₂×C₁₁	C₂×#436	1	1	yes	characteristic
368	C₂×C₁₁	#2931	1	1	yes	characteristic
369	C₂×C₁₁	#2933	1	1	yes	characteristic
370	C₂×C₁₁	D₄×M₁₆	1	1	yes	characteristic
371	C₂×C₁₁	#2991	1	1	yes	characteristic
372	C₂×C₁₁	#2993	1	1	yes	characteristic
373	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
374	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	4	1	no	—
397	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
398	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
399	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
400	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
401	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
402	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
403	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
404	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
406	C₂²×C₄	C₁₁×#41	1	2	yes	—
407	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
408	M₁₆	—	4	8	no	—
409	M₁₆	—	4	8	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
426	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
427	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	C₁₁×M₁₆	1	4	yes	complemented
432	C₂²⋊C₄	—	2	4	no	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	2	4	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	2	no	—
443	C₄²	C₂×D₄×C₁₁	1	2	yes	—
444	C₄²	C₁₁×#41	1	2	yes	—
445	C₁₁	#22990	1	1	yes	characteristic, direct product factor, Sylow
446	C₂³	—	2	1	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	C₄×D₄×C₁₁	1	2	yes	—
460	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
461	D₄	—	4	8	no	—
462	D₄	—	4	4	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
491	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
492	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
493	C₂×C₄	C₂×C₁₁×M₁₆	1	4	yes	—
494	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
495	C₂×C₄	C₁₁×#131	1	2	yes	—
496	C₂×C₄	C₁₁×#131	1	2	yes	—
497	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
499	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
500	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
501	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
502	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
503	C₈	—	2	4	no	—
504	C₈	—	2	2	no	—
505	C₈	—	2	2	no	—
506	C₈	—	4	2	no	—
507	C₈	—	4	1	no	—
508	C₈	—	4	1	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	4	1	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	1	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
524	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
525	C₂²	C₁₁×#520	1	1	yes	characteristic
526	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
527	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
528	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
529	C₂²	C₁₁×#568	1	1	yes	characteristic
530	C₄	—	2	2	no	—
531	C₄	—	2	2	no	—
532	C₄	—	2	4	no	—
533	C₄	—	2	2	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	2	no	—
537	C₄	C₁₁×#436	1	4	yes	complemented
538	C₄	D₄²×C₁₁	1	1	yes	characteristic
539	C₄	C₁₁×#547	1	1	yes	characteristic
540	C₄	C₁₁×#548	1	1	yes	characteristic
541	C₄	C₁₁×#553	1	1	yes	characteristic
542	C₂	—	4	2	no	—
543	C₂	—	8	2	no	—
544	C₂	C₁₁×#2361	1	1	yes	characteristic
545	C₂	C₂×C₁₁×#436	1	1	yes	characteristic
546	C₂	C₁₁×#2931	1	1	yes	characteristic
547	C₂	C₁₁×#2933	1	1	yes	characteristic
548	C₂	D₄×C₁₁×M₁₆	1	1	yes	characteristic
549	C₂	C₁₁×#2991	1	1	yes	characteristic
550	C₂	C₁₁×#2993	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	C₂×C₁₁×#121	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
1. C₂×C₁₁×#436	C₂	semidirect
2. C₂×C₁₁×#436	C₂	semidirect
3. C₂×C₁₁×#423	C₂	semidirect
5. C₁₁×#1954	C₂	semidirect
6. C₁₁×#1939	C₂	semidirect
7. C₁₁×#1923	C₂	semidirect
8. C₁₁×#1870	C₂	semidirect
9. C₁₁×#1851	C₂	semidirect
10. C₈×C₁₁×C₄⋊C₄	C₂	semidirect
11. C₄×C₁₁×C₂²⋊C₈	C₂	semidirect
86. C₁₁×C₄⋊C₈	D₄	semidirect
91. C₁₁×C₂²⋊C₈	D₄	semidirect
98. #22990	C₁₁	direct (N × H)
157. C₁₁×C₄⋊C₄	M₁₆	semidirect
171. C₂×#436	C₂×C₁₁	semidirect
172. C₂×#436	C₂×C₁₁	semidirect
173. C₂×#423	C₂×C₁₁	semidirect
175. #1954	C₂×C₁₁	semidirect
176. #1939	C₂×C₁₁	semidirect
177. #1923	C₂×C₁₁	semidirect
178. #1870	C₂×C₁₁	semidirect
179. #1851	C₂×C₁₁	semidirect
180. C₈×C₄⋊C₄	C₂×C₁₁	semidirect
181. C₄×C₂²⋊C₈	C₂×C₁₁	semidirect
305. C₄×C₁₁	#436	semidirect
352. C₄⋊C₈	D₄×C₁₁	semidirect
357. C₂²⋊C₈	D₄×C₁₁	semidirect
431. C₄⋊C₄	C₁₁×M₁₆	semidirect
445. C₁₁	#22990	direct (N × H)
537. C₄	C₁₁×#436	semidirect

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×#423	2
C₄×C₁₁×#121	2
C₁₁×#1954	2
C₁₁×#1939	2
C₁₁×#1923	2
C₁₁×#1870	2
C₁₁×#1851	2
C₈×C₁₁×C₄⋊C₄	2
C₄×C₁₁×C₂²⋊C₈	2
#22990	11

Subgroups — C11×#22990 #14600183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22990 #14600183